Answers
The hint about this being a linear function is a critical piece of information.
A linear function has a fixed slope, so you can use the slope formula to find that slope using the two given points, (-3,-5) and (-1,-1).
[tex]m=\dfrac{y_2-y_1}{x_2-x_1} = \dfrac{-1-(-5)}{-1-(-3)} = \dfrac{4}{2}=2[/tex]
Now you can use that slope and a point to find the equation of the function.
g(x) = mx + b, but m=2, so g(x) = 2x + b
If we plug in one of the points, we can calculate b:
-5 = 2(-3) + b
-5 = -6 + b
1 = b
Now you have your function: g(x) = 2x + 1
You can use it to calculate the missing values in the table.
Related Questions
For circular motion on a circle of radius r, linear speed equals angular speed divided by r. (T/F)
Answers
For circular motion on a circle of radius r, linear speed equals angular speed divided by r. This statement is false.
What is angular speed?
The definition of angular speed is the rate at which angular displacement changes, and it is written as follows -
ω = θ/t
where θ is the angular displacement, t is the time and ω is the angular speed.
The statement says that for circular motion on a circle of radius r, linear speed equals angular speed divided by r.
Consider that an object moves around a circle of radius r at a constant speed v.
If s is the distance travelled in time t around the circle then linear speed v is defined as v = s/t.
Also if θ is the angle swept out by this object in time t then the angular speed is defined as ω = θ/t.
Thus, there is some relationship between linear speed and angular speed -
Linear speed = v = s/t
= rθ/t = r(θ/t) = rω
where is ω measured in radians per unit time and for a circle of radius r, a central angle of radians subtends an arc whose length s is s = rθ.
Hence, notice that linear speed is equal angular speed multiplied, not divided, by r.
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suppose that f(x) has a domain of [6,17] and a range of [6,13] . what are the domain and range of:
Answers
A) f(x) +5
Domain: x ∈ (5, 15)
Range: f(x) ∈ (12, 22)
B) f(x + 5)
Domain: x ∈ (0, 10)
Range: f(x) ∈ (7, 17)
C) f(5x)
Domain: x ∈ (1, 3)
Range: f(x) ∈ (7, 17)
D) 5f(x)
Domain: x ∈ (5, 15)
Range: f(x) ∈ (35, 85)
Now, According to the question:
Domain:
Consider a function y = t(x), where y is the dependent variable and x is the independent variable. Domain value represents the value(s) of the independent variable at which the given function is defined. On the other hand, the corresponding values of y represents the range of that function.
f(x) has a domain of (5, 15) and a range of (7, 17)
A) f(x) + 5
The domain will be the same as the domain of f(x) but the range will be (7 + 5 , 17 + 5) i.e., (12, 22)
Domain: x ∈ (5, 15)
Range: f(x) ∈ (12, 22)
B) f(x + 5)
The domain will be (5 -5, 15-5) i.e., (0, 10) but the range will be the same.
Domain: x ∈ (0, 10)
Range: f(x) ∈ (7, 17)
C) f(5x)
The domain will be [tex](\frac{5}{5},\frac{15}{5} )[/tex] i.e., (1, 3) but the range will be the same.
Domain: x ∈ (1, 3)
Range: f(x) ∈ (7, 17)
D) The domain will be the same as the domain of f(x) but the same will be (5× 7, 17× 5) i.e., (35, 85)
Domain: x ∈ (5, 15)
Range: f(x) ∈ (35, 85)
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The given question is incomplete,
So, This question like that the given question:
Suppose that f(x) has a domain of (5, 15) and a range of (7,17).
What are the domains and the ranges of the following?
A) f(x) +5
B) f(x + 5)
C) f(5x)
D) 5f(x)
What is the slope below?
Answers
Answer: slope = 7
Step-by-step explanation:
find the 14th term of the sequence 4,7,10,13
Answers
Answer: 43
Step-by-step explanation: Each of the numbers is being added by 3.
4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52..
For the subspace below, (a) find a basis for the subspace, and (b) state the dimension. P-2q 9p +2r -2q +4r -6p 12r p, q, rin R
Answers
a) basis is [ p , q , r . r ]
b) the dimension. P-2q 9p +2r -2q +4r -6p 12r p, q, rin R is 3 for subspace
since the two given equation are in three variable and constants
2q -r= p -----(1)
r= q -s -----(2)
p= q +2r -----(3)
From (2):
r +s= q (+s on both sides)
s= q -r -----(4) (-r on both sides)
Substitute. (3) into (1):
2q -r= q +2r
2q -q= 2r +r
q= 3r -----(5)
Substitute (5) into (4):
s= 3r -r
s= 2r (proved)
hence subspace is [ p , q , r . r ]
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You own Company X. When you started the company, you Initially Invested $12,000. You also borrowed $12,000 through a five-year (long-term) loan, of which you have paid back $2,018. You have retained $1,291 In earnings to be reinvested in the company, and you decided to put $1,000 of it aside for a long-term Investment. The company owns land and a building worth $8,878 and equipment worth $4,230. As of today, the company has $8,250 in cash, $1,225 In Inventory, and is due to receive accounts worth $675. However, the company owes its suppliers $485 and has a $500 loan to pay off in the next six months
Answers
The preparation of Company X's balance sheet as the current date is as follows:
Company X
Balance SheetAs of current date
Current Assets:Cash $8,250
Inventory 1,225
Accounts Receivable 675 $10,150
Long-term Assets:Long-term investment $1,000
Land and building 8,878
Equipment 4,230 $14,108
Total Assets $24,258
Current Liabilities:Accounts Payable $485
Short-term loan 500 $985
Long-term Liabilities:Long-term loan $9,982
Total liabilities $10,967
Equity:Initial capital $12,000
Retained earnings 1,291 $13,291
Total liabilities and equity $24,258
What is the balance sheet?The balance sheet is a financial statement that shows the assets, liabilities, and equity balances of an entity at a point in time.
Assets describe the things owned by the entity while liabilities refer to its debts. The difference between assets and liabilities is the equity (or the portion of assets belonging to the owners).
Analysis:Initial investment = $12,000
Retained Earnings = $1,291
Long-term loan = $9,982 ($12,000 - $2,018)
Land and building = $8,878
Equipment = $4,230
Cash $8,250
Inventory = $1,225
Accounts Receivable = $675
Accounts Payable = $485
Short-term loan = $500
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Question Completion:Prepare Company X's balance sheet.
function statements are contained within the function ____.
Answers
A function statement is contained within the function block. A function block is a set of instructions within a program that defines what the function should do when it is called.
It is generally surrounded by curly braces and contains one or more lines of code.
A function statement usually contains a formula and calculation. The formula is an expression that specifies the calculation that should be performed when the function is called. The calculation is the result of the formula, which is the value that will be returned when the function is called.
For example, if we have a function that calculates the area of a circle, the formula might be A = πr^2 and the calculation would be A = 3.14 * r^2. The formula describes how the area of a circle is calculated and the calculation is the result of that formula. When the function is called, the calculation will be performed and the result will be returned.
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A watch which was bought for R250, was sold for R375. What profit made on the sale? atima has 56 roses, 48 irises and 16 freesias. She wants to cre ouquets using all the flowers. Calculate the highest number ouquets she can make without having any flowers left over Fatima paid R240 for her flowers and sold the bouquets for
Answers
Solving the provided question, we can say that the highest number bouquets she can make without having any flowers left is calculated by Highest Common Factor so, HCF of 56, 48 and 16 is 8
What is Highest Common Factor?In mathematics, the highest positive integer that divides the corresponding integers is known as the greatest common divisor of two or more non-zero integers. The greatest common factor (HCF) of two or more numbers is the sum of those two or more numbers. As a result, it is frequently referred to as the largest common divisor (GCF). Take the prime factors of the two (or more) integers and determine the shared prime factors to determine the greatest common divisor. Following that, the sum of common prime factors is the greatest common divisor. A specified number divided by the biggest integer results in the greatest common divisor.
the highest number bouquets she can make without having any flowers left is calculated by Highest Common Factor so, HCF of 56, 48 and 16 is 8
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Simplify the expression
(Please show the work)
Answers
Answer: 14 - [tex]5x^{2}[/tex]
Step-by-step explanation:
So what I would do is remove those parentheses so you would have
8 + [tex]6x^{2}[/tex] + 6 - [tex]x^{2}[/tex]
Then you are going to combine like terms that would look like
14 - [tex]5x^{2}[/tex]
Hope that is correct
suppose you ask a friend to randomly choose an integer between 1 and 10, inclusive. what is the probability that the number will be more than 7 or odd? (enter your probability as a fraction.)
Answers
The probability that the number will be more than 7 or odd is 7/10.
The number more than 7 or odd is 1, 3, 5, 7, 8, 9, 10
So probability of 7 number is,
P(A) = number of favorable outcomes of an event / total number of events occurring in a sample
P(A) = 7/10
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject because it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.
The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organized in ascending order, the Median is the median value of the given data. While the number in the list that is repeated a maximum of times is the mode.
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flight 202's arrival time is normally distributed with a mean arrival time of 4:30 p.m. and a standard deviation of 15 minutes. find the probability that a randomly chosen arrival time is within the given time period
Answers
The required probability is 0.953.
We know that the mean μ is:
μ = 4:30 p.m.
The standard deviation is:
σ = 0:15 minutes
The Z-score is: Z = (x-μ)/σ
We seek to find probability P(4:00 p.m. < x < 5:00 p.m.)
The Z-score is:
Z = (x-μ)/σ = 4:00 - 4:30/0:15 = -2
The score of Z =-2 means that 4:00 p.m. is -2 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the condition of 2 deviations from the mean has percentage of 2.35% and
Z = (x-μ)/σ = 5:00 - 4:30/0:15 = 2
The score of Z =2 means that 11:00 p.m. is 2 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the condition of 2 deviations from the mean has percentage of 2.35%.
∴ P(4:00 p.m. < x < 5:00 p.m.) = 100% - 2.35% - 2.35%
= 95.3% = 0.953
Thus, the required probability is 0.953.
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The required probability is 0.953.
We know that the mean μ is:
μ = 4:30 p.m.
The standard deviation is:
σ = 0:15 minutes
The Z-score is: Z = (x-μ)/σ
We seek to find probability P(4:00 p.m. < x < 5:00 p.m.)
The Z-score is:
Z = (x-μ)/σ = 4:00 - 4:30/0:15 = -2
The score of Z =-2 means that 4:00 p.m. is -2 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the condition of 2 deviations from the mean has percentage of 2.35% and
Z = (x-μ)/σ = 5:00 - 4:30/0:15 = 2
The score of Z =2 means that 11:00 p.m. is 2 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the condition of 2 deviations from the mean has percentage of 2.35%.
∴ P(4:00 p.m. < x < 5:00 p.m.) = 100% - 2.35% - 2.35%
= 95.3% = 0.953
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Unit 6 Final Test
Would appreciate some help as soon as its available (Has 3 parts) (ASAP)
1. The population of a town was 88 in 2016. The population quadruples every year. (a) Use the exponential growth model to write an equation that estimates the population t years after 2016. (b) Estimate the population of the town in 2023. Show your work. Answer:
2. Convert the following into a single log statement from the many log statements to 1. 7 Log x + 2log y – log 23 – 3 log z NOTE: You must show this in at least two steps. 1st line should be to convert the 2 the 3 and the 7 only. 2nd line can be the final answer. Answer:
3. A savings account is started with an initial deposit of $500. The account earns 7% interest compounded annually. (a) Write an equation to represent the amount of money in the account as a function of time in years. (b) Find the amount of time it takes for the account balance to reach 1 million. Show your work. Note: 1 million is a 1 with 6 zeros. Note2: you must use log functions to solve. Answer:
Answers
1. (a) An equation that estimates the population t years after 2016 is
P = [tex]88({4t)[/tex].
b. The population of the town in 2023 is 2564.
2. log x + 2log y - log 23 - 3 log z is equal to log (x + y²)/log (23 + z³).
3. (a) An equation to represent the amount of money in the account as a function of time in years is A = 500(1 + 7/100)ⁿ.
(b) The amount of time it takes for the account balance to reach 1 million
is 112.5 years approximately.
What is the formula for exponential growth and exponential decaying function?The formula for exponential growth is [tex]y = y_0e^{(kt)}.[/tex]
The formula for exponential decay is [tex]y = y_0e^{(-kt)}.[/tex]
1. Given, The population of a town was 88 in 2016. The population quadruples every year.
Therefore, The exponential model of this situation is P = [tex]88({4t)[/tex].
Now, From 2016 to 2023 it is 7 years.
Therefore, P = [tex]88({4\times7})[/tex].
P = 2564.
2. Given, log x + 2log y - log 23 - 3 log z.
= log x + log y² - log 23 - log z³.
= log x + log y² - (log 23 + log z³).
= log (x + y²) - log (23 + z³).
= log (x + y²)/log (23 + z³).
3. Given, A savings account is started with an initial deposit of $500. The account earns 7% interest compounded annually.
We know the formula for compound interest is, A = P(1 + r/100)ⁿ.
a. A = 500(1 + 7/100)ⁿ.
b. 1000000 = 500(1 + 7/100)ⁿ.
2000 = (1 + 7/100)ⁿ.
2000 = 1.07ⁿ.
log_1.07 2000 = n.
n = 112.5 years approximately.
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Rylan earns $200 for working 16 hours this week.
How much does he earn per hour?
Answers
Answer:
Rylan earns $12.50 per hour
Step-by-step explanation:
1. First start by writing the given its always easier when you're able to see the problem.
$200 = 16 hrs
$ x = 1 hr
2. Next divide
[tex]\frac{200}{16}[/tex] = 12.50
Two sides of the triangle abc has side ab = 22 cm and side ac = 8 cm. Compute the probable perimeter of the triangle.
Answers
The perimeter of the triangle is (30+x) cm
What is perimeter of a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.
Perimeter is the distance around the edge of a shape.
To find the perimeter of a triangle , we add all the sides together.
Two sides are 22 cm and 8cm
Represent the other sides of the triangle by x
therefore the perimeter will be calculated as:
22+8+x
P = (30+x)cm
therefore the perimeter of the triangle is( 30+x)cm for any value of x
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miss collier bought a block of cheddar cheese the block weighed 2/3 of a pound she cut the block up into 4 equal slices what was the weight of each slice of cheese
Answers
Answer: 1/6 of a pound
Step-by-step explanation: Hello!
You know that Miss Collier bought a block of cheddar cheese that weighs 2/3 of a pound and she split it into four equal pieces. This can be represented by the equation below:
2/3 divided by 4 = weight of a single slice of cheese
2/3 divided by 4/1 = weight of a single slice of cheese
Take the reciprocal of 4/1. 4/1 turns into 1/4. Then multiply the two fractions.
2/3 x 1/4 = weight of a single slice of cheese.
Multiply the numerators and denominators. 2 x 1 = 2, 3 x 4 = 12.
2/12 = weight of a single slice of cheese.
You can simplify this by dividing the numerator and denominator by 2. 2/2 = 1, 12/2 = 6.
The final answer is: 1/6 of a pound.
the marked price of an article is 2080. After allowing d% discount and levying (d-2)% VAT, the cost of the article becomes Rs. 1997.84. Find the discount amount and VAT amount
Answers
The vat rate is 13%
What is vat rate?
Vat rate is a consumption tax assessed on the value added in each production stage of a good or service.
Given:
MP = 2080
Discount = d%
VAT = (d-2)%
Cost = 1997.84
Apply discount:
2080 - d% = 2080*(1 - 0.01d)Add VAT:
2080*(1 - 0.01d) + (d - 2)%2080*(1 - 0.01d) * (1 + (d -2)/100)2080*(1 - 0.01d) * (0.98 + 0.01d) = 1997.84(1 - 0.01d)(0.98 + 0.01d) = 1997.84/20800.98 + 0.01d - 0.0098d - 0.0001d² = 0.9605- 0.0001d² + 0.0002d + 0.98- 0.9605 = 00.0001d²- 0.0002d - 0.0195 = 0d² - 2d + 195 = 0
Solving the quadratic equation we get:
d = 15
Then
VAT rate = 15 - 2 = 13%
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1. What is the minimum number of divisions made by Euclid's algorithm among all inputs 1 Sab S 10? Give your answer as a number. 2. What is the maximum number of divisions made by Euclia's algorithm among all inputs 1 € ab 10? (to answer this question, check the algorithm's performance on all pairs 1 Sa, bs 10). Give your answer as a number.
Answers
The minimum amount of number of divisions made by Euclid's algorithm among all inputs 1 to 10 is 0, as the greatest common divisor of any two numbers between 1 and 10 must be 1. The maximum number of divisions made by Euclid's algorithm among all inputs 1 to 10 is 19, as the greatest common divisor of 8 and 10 requires 19 divisions.
Euclid's algorithm is an efficient method for finding the greatest common divisor (GCD) of two integers. It works by repeatedly dividing larger numbers by smaller numbers until the remainder is 0. The GCD of two integers is then equal to the smaller number. The minimum number of divisions made by Euclid's algorithm among all inputs 1 to 10 is 0, as the GCD of any two numbers between 1 and 10 must be 1. This is because any two numbers between 1 and 10 have only 1 as their common divisor. On the other hand, the maximum number of divisions made by Euclid's algorithm among all inputs 1 to 10 is 19, as the GCD of 8 and 10 requires 19 divisions. This is due to the fact that 8 and 10 have no common divisors except for 1, so the algorithm must divide 8 by 10 repeatedly until the remainder is 0. Thus, the maximum number of divisions made by Euclid's algorithm among all inputs 1 to 10 is 19.
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Find the mean of tese numbers 2,9,10,6,8
Answers
Answer:324234
Step-by-step explanation:
Answer:
The mean of the data set is 7.
2 + 9 + 10 + 6 + 8
= 35
35 ÷ 5
= 7
Step-by-step explanation:
You're welcome
The angle measures of a triangle are shown in the diagram.
What is the value of x?
The angle measures of a triangle are shown in the diagram.
What is the value of x?
Answers
The value of x is 44.
What do you mean by triangle?The most basic type of triangle is an equilateral triangle, which has three sides of equal length and three equal angles. Another common type of triangle is the right triangle, which has one right angle (90 degrees) and two other angles that add up to 90 degrees. Scalene triangles have no sides or angles of equal length, while isosceles triangles have at least two sides of equal length.
Triangles have many interesting and useful properties that can be used in geometry and other areas of mathematics. For example, the Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side. This theorem can be used to find the length of a missing side in a right triangle.
Triangles also have an important relationship with circles. The circumcenter of a triangle is the center of the circle that passes through all three vertices of the triangle, while the incenter of a triangle is the center of the circle that is tangent to each of the triangle's sides.
From the triangle angle sum theorem, we know that the sum of all angles in a triangle is 180 degrees. So for triangle ABC, we have:
angle ABC + angle BCA + angle CAD = 180
50 + (3x - 10) + 2x = 180
Combining like terms and solving for x, we get:
5x = 220
Therefore, x = 44.
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find the solution of the initial value problem y'' 2y' 5y = 12e^-t cos(2t), y(0) = 10, y'(0) = 0
Answers
The solution to the initial value problem is:y(t) = (10 - (12/7))e^(t) cos(2t) + (12/7)e^(-t) cos(2t).
The characteristic equation of this linear second order ordinary differential equation is:
m^2 - 2m + 5 = 0
The roots of this characteristic equation are m = 1 ± 2i, which means the general solution to the homogeneous equation is:
y(t) = c1e^(t) cos(2t) + c2e^(t) sin(2t)
To find the particular solution, we can use the method of undetermined coefficients and guess that yp(t) = Ae^(-t) cos(2t) + Be^(-t) sin(2t).
Substituting this into the differential equation, we get:
2Ae^(-t) cos(2t) - 2Ae^(-t) sin(2t) + 5Ae^(-t) cos(2t) - 5Be^(-t) sin(2t) = 12e^(-t) cos(2t)
Comparing coefficients, we have:
2A - 2A + 5A = 12
7A = 12
A = 12/7
-5B = 0
B = 0
So the particular solution is:
yp(t) = (12/7)e^(-t) cos(2t)
The general solution to the non-homogeneous equation is then:
y(t) = c1e^(t) cos(2t) + c2e^(t) sin(2t) + (12/7)e^(-t) cos(2t)
Using the initial conditions, we can find the values of c1 and c2:
y(0) = 10 = c1 + (12/7)
c1 = 10 - (12/7)
y'(0) = 0 = c2e^(0) sin(0)
c2 = 0
Therefore, the solution to the initial value problem is: y(t) = (10 - (12/7))e^(t) cos(2t) + (12/7)e^(-t) cos(2t)
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How do you find a formula for the general term an of the sequence?
Answers
A sequence is characterised as one that adheres to a predetermined pattern. The following term is created by increasing or decreasing the previous word by a certain amount.
On occasion, an expression is followed by every term in the series. The general formula for an AP is T n = a + (n - 1) d.
What does the sequence's general word mean?Understanding the underlying pattern or rule that creates the sequence is necessary for formulating the general term an of the sequence. Finding a formula for the overall term of a series can be done in a number of ways, including:
1) Finding a pattern: In some cases, a pattern can be found by examining the terms of the sequence and looking for a common ratio or difference. For instance, the formula for the general term can be written as a = a1 + (n - 1)d, where a1 is the first term and d is the common difference, assuming the terms of a sequence are rising by a constant amount.
2) Recurrence relations are used to characterise some sequences. These relations define the nth term in terms of the phrases that came before it. If the recurrence relation, for instance, is a = an-1 + an-2, then the general term's formula can be discovered by resolving the recurrence relation.
3) Making use of generating functions: Sequences can be represented mathematically using generating functions. A formula for the general term of a sequence can be discovered by fiddling with the generating function.
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If the vertex angle of an isosceles triangle measures 86 Degrees, what is the angle measure of one of the base angles
Answers
47 degrees is the the angle measure of one of the base angles.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
We know that an isosceles triangle is composed of a vertex angle and two base angles.
The base angles are congruent to each other.
We also know that the sum of a triangle's angles is 180 degrees.
86+2x=180
Subtract 86 from both sides
2x=180-86
2x=94
Divide both sides by 2
x=47
Hence, 47 degrees is the the angle measure of one of the base angles.
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Write the equation of the line in slope-intercept form (y=mx+b):
Answers
a = ( 0 , - 4 )
b = ( - 2 , - 2 )
[tex]m = - \frac{y(a) - y(b)}{x(a) - x(b)} \\ [/tex]
[tex]m \: = \frac{ - 4 - ( - 2)}{0 - ( - 2)} \\ [/tex]
[tex]m = \frac{ - 4 + 2}{2} \\ [/tex]
[tex]m = \frac{ - 2}{2} \\ [/tex]
[tex]m = - 1[/tex]
WILL GIVE BRAINLIEST AND 50 POINTS PLS DO MY HW BY FEBRUARY 2ND
Answers
Answer: dunno, maybe try using your brain?
Step-by-step explanation:
Depreciation is the decrease or loss in value of an item due to age, wear, or market conditions. We usually consider
depreciation on expensive items like cars. Businesses use depreciation as a loss when calculating their income and taxes.
One company buys a new bulldozer for $78750. The company depreciates the bulldozer linearly over its useful life of
16 years. Its salvage value at the end of 16 years is $12350.
A) Express the value of the bulldozer, vas a function of how many years old it is, t. Make sure to use function
notation
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B) The value of the bulldozer after 12 years is $
Answers
The value of the bulldozer after 12 years is 28,950.
Since it is given that the company depreciates the bulldozer linearly over its useful life,
The value of the bulldozer, as a function of time, should be in the form; y=m(t)+c.
where,
y= value of bulldozer
m and c = are some constants
And the boundary conditions are given as,
when t=0, y=78,750
= m(0)+c=78,750
= c = 78,750
and also given,
when t=16, y=12,350
=m(16 )+78,750=12,350
=m=12,350-78,750/16
=m=-4,150
so, the equation comes as,
y=78,750 - 4,150(t)
Value of bulldozer after 12 years would be,
y=78,750 - 4,150(12)
y=28,950
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illustrate the net force f1 f2 as the geometric addition of the two force vectors. (b) compute the net force, the vector sum of the force vectors.
Answers
The magnitude of the net force is 149.33 N.
a) To illustrate the net force F1 + F2 as a geometric addition of the two force vectors, we can use the tail-to-tip method to add the vectors head-to-tail and then connect the tail of the first vector to the tip of the second vector to form the net force vector.
b) To compute the net force as the vector sum of the two force vectors, we can use the components of the two vectors to find the components of the net force. Using the trigonometric relationship between the angle and the components of a force vector, the x and y components of the force vectors can be calculated as follows:
F1x = F1 * cos(30) = 86.6025 N
F1y = F1 * sin(30) = 50 N
F2x = F2 * cos(45) = 35.3553 N
F2y = F2 * sin(45) = 35.3553 N
The x and y components of the net force are found by adding the corresponding components of the individual force vectors:
Fnetx = F1x + F2x = 86.6025 N + 35.3553 N = 122 N
Fnety = F1y + F2y = 50 N + 35.3553 N = 85.3553 N
c) To compute the magnitude of the net force, we use the Pythagorean theorem to find the magnitude from the components:
Fnet = √(Fnetx² + Fnety²) = √(122² + 85.3553²) = 149.33 N
So, the magnitude of the net force is 149.33 N.
Complete Question
Two forces are applied to an object, with magnitudes and directions shown in the image below:
(a) Illustrate the net form F1 + F2 as the geometric addition of the two force vectors.
(b) Compute the net force, the vector sum of the force vectors.
(c) Compute the magnitude of the net force. Include N (newton) for units of force.
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(5) i need help with my math HW I'm stuck with this problem show all ur steps for y & x
Answers
A graph of this system of equations on a coordinate plane is shown in the image attached below.
How to graph the solution to this system of inequalities?In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
y = 2x/5 + 4 ......equation 1.
-2x + 5y = -30 ......equation 2.
Making y the subject of formula in equation 2, we have the following:
5y = 2x - 30
Dividing both sides of the equation by 5, we have:
y = 2x/5 - 30
Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is non existent because the lines are parallel.
In conclusion, the given system of equations has no solution.
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if you add the digits that make my age this year, you'll get a number three times bigger than next year. how old am i?
Answers
You are 18 years old this year.
Let's call your age this year "x". Next year, your age will be "x + 1".
We know that the sum of the digits of "x" is three times bigger than the sum of the digits of "x + 1". Let's call the sum of the digits of "x" "s1", and the sum of the digits of "x + 1" "s2".
So we have the equation:
s1 = 3 * s2
If we add the digits of "x + 1", we get "s2 = a + b", where "a" and "b" are the digits of "x + 1".
Expanding the equation and substituting "s2":
s1 = 3 * (a + b)
Expanding the left side of the equation:
s1 = 3a + 3b
So the sum of the digits of "x" is three times the sum of the digits of "x + 1".
Now we need to find the values of "x" for which "s1" is three times bigger than "s2".
One possible solution is "x = 18", because:
"s1" = 1 + 8 = 9"s2" = 1 + 9 = 109 = 3 * 10So the answer is that you are 18 years old this year.
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You are 18 years old this year.
Let's call your age this year "x". Next year, your age will be "x + 1".
We know that the sum of the digits of "x" is three times bigger than the sum of the digits of "x + 1". Let's call the sum of the digits of "x" "s1", and the sum of the digits of "x + 1" "s2".
So we have the equation:
s1 = 3 * s2
If we add the digits of "x + 1", we get "s2 = a + b", where "a" and "b" are the digits of "x + 1".
Expanding the equation and substituting "s2":
s1 = 3 * (a + b)
Expanding the left side of the equation:
s1 = 3a + 3b
So the sum of the digits of "x" is three times the sum of the digits of "x + 1".
Now we need to find the values of "x" for which "s1" is three times bigger than "s2".
One possible solution is "x = 18", because:
"s1" = 1 + 8 = 9
"s2" = 1 + 9 = 10
9 = 3 * 10
So the answer is that you are 18 years old this year.
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a baker uses 4.5 pounds of flour daily
how many ounces of flour will he use in two weeks, use words, numbers, or pictures to explain your thinking
the bakers recipe for a loaf of bread calls for 12 ounces of flour. if he uses all of his flour to make loaves of bread, how many full loaves can he make?
Answers
Answer: 4.5 pounds of flour equals to 72 ounces of flour. There are 14 days in 2 weeks, so 14 times 72 equals 1008 ounces of flour. If the baker uses all their 72 ounces of flour in one day to make loaves of bread, they will make 6 loaves of bread. That is also 84 loaves of bread if they make loaves of bread for 2 weeks straight.
Step-by-step explanation:
Answer:
Step-by-step explanation: Well, one lbs (pound) is equal to 16 oz (ounces)
So take the 4.5 lbs and multiply it by the 16 oz. That'll give you 224 oz
Then take the 224 oz and multiply that by 14, which is the number of days from two weeks. 224 multiplied by 14 is 3,136
To find the loaves of bread, take the 3,136 and divide it by 12, which gives you 261.3, or 261 1/3
How do you find the slope of the tangent line to the graph of f(x)=−x2+4x at x = 4?
Answers
The slope of the tangent line to the graph of f(x) = −x² + 4x at x = 4 is 0, and the equation of the tangent line is y = 0.
The slope of a tangent line to a graph of a function is a measure of how steeply the function is increasing or decreasing at a certain point. A tangent line is a line that just touches the graph at a single point and has the same slope as the graph at that point.
Here we need to find the slope of the tangent line to the graph of
=> f(x) = −x² + 4x at x = 4,
we first need to determine the derivative of the function. The derivative of the function gives us the rate of change of the function, which is the slope of the tangent line.
Here The derivative of f(x) = −x² + 4x is given by
=> f'(x) = −2x + 4.
Now we have to find the slope of the tangent line at x = 4, we evaluate the derivative at x = 4:
=> f'(4) = −2 * 4 + 4 = 0.
So, the slope of the tangent line at x = 4 is 0.
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