An equation of the line that passes through the point (1, -3) and has a slope of -3 in slope-intercept form is y = 2x + 3.
How to determine an equation of this line?Mathematically, the standard form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the intercept.Next, we would determine the slope of this straight line by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (15 - 3)/(2 - (-4))
Slope (m) = 12/6
Slope (m) = 2.
Therefore, the equation in slope-intercept form is given by:
y = mx + c
y = 2x + 3
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what is 4z−(−3z) in combining like terms
Answer:
7z because 4z-(-3)=4z+3z
Answer:
The answer would be 7z
Step-by-step explanation:
a negative and a negative make a positive so therefore you would just add 4 and 3 together
A basketball team had a 60% decrease in the number of victories it had this season compared to last season. If the team had 48 fewer victories, how many victories did they have this season?
66
32
80
28
please help ASAP
The number of victories that the team had this season is given as follows:
32.
How to obtain the number of victories?The number of victories is obtained applying the proportions in the context of this problem.
A decrease of 48 represents a decrease of 60% of the amount, that is, 60% of the total amount is of 48, hence the amount x is obtained as follows:
0.6x = 48
x = 48/0.6
x = 80.
The amount x represents the number of victories in the previous season, hence the number of victories in the current season is given as follows:
80 - 48 = 32.
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A road descends a vertical distance of 2000 feet over a distance of 3.5 miles as shown in the diagram.
Find the approximate measure of , the angle shown in the diagram. Give your answer to the nearest thousandth of a degree. Show or explain how you found your answer. (Use 1 mile = 5280 feet.)
The value of θ from the triangle ABC is θ = 6.213°
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ABC
Now , the opposite side of the triangle AB = 2,000 feet
The hypotenuse of the triangle AC = 3.5 miles
The hypotenuse of the triangle AC = 3.5 x 5,280
The hypotenuse of the triangle AC = 18,480 feet
Now , from the trigonometric relations ,
sin θ = opposite / hypotenuse
Substituting the values in the equation , we get
sin θ = 2000 / 18480
On simplifying the equation , we get
sin θ = 0.108225
Taking inverse on both sides of the equation , we get
θ = sin⁻¹ ( 0.108225 )
θ = 6.213°
Hence , the value of θ is 6.213°
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What is the slope of a line that is parallel to the line y = 3/4x+2?
O -4/3
O -3/4
O 3/4
O 4/3
As a result, the given line, y = 3/4x+2, and any line having a slope of 3/4 are parallel.
what is slope ?The slope of a line establishes its steepness. "Texture overflow" is the name of a gradient-related math problem (the change in y divided by the change in x). The sloping is the ratio of either the longitudinal (rise) to the horizontal (run) change in elevation between any two places. The gradient form of an equation is used to represent a linear relationship when its expression is expressed as y = mx + b. The y-intercept is situated where the slope of the line is m, b is c, and (0, b). For instance, either y-intercept and curve of something like the calculation y = 3x - 7 (0, 7). The line has a slope of m, a b value at the y-intercept, and (0, b). As
given
Given line equation, y = 3/4x + 2.
The slope of a line parallel to the supplied line must be determined.
Since every line parallel to the provided line will have the same slope as the supplied line since y = 3/4x+2,
Where, y = mx + c is the general equation of the line. m denotes the line's slope, and c the y-intercept.
Therefore, for the given line equation, y = 3/4x+2 Slope is m= 3/4 when we compare and.
As a result, the given line, y = 3/4x+2, and any line having a slope of 3/4 are parallel.
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ed buys a vase for £24 and adds 25% onto the price before putting it into his shop window
What price does the price-tag say in the window
What the a round the the nearest thousand 802957 what is the answer right now please
Answer:
803,000
Step-by-step explanation:
when looking to round find the spot your supposed to go to and if its five or more round up, four or less stays the same
Is this no solution?
Answer: 0=0
Step-by-step explanation:
4(2x-15) = 2(4x-30)
Simplify
8x-60=8x-60
Add 60 to both sides
8x=8x
Answer: 0=0
So the answer is infinite. Theres an infinite about of answers for x.
Answer:
The result of your question would equal: 0 = 0
Step-by-step explanation:
First lets distribute them!
4(2x - 15) = 2(4x - 30)
8x - 60 = 2(4x - 30)
8x - 60 = 2(4x - 30)
8x - 60 = 8x - 60. :
4(2x - 15 = (4x - 30)
8x - 60 = 8x - 60.
Add:
8x - 60 = 8x - 60
8x - 60 + 60 = 8x - 60 + 60
Simplifying:
8x - 60 + 60 = 8x - 60 + 60
8x = 8x - 60 + 60
Again:
8x = 8x - 60 + 60
8x = 8x =
8x - 60 + 60 = 8x - 60 + 60
8x = 86
Subtracting:
8x = 8x
8x - 8x = 8x - 8x
Simplifying again...
Combining like terms
8x - 8x = 8x - 8x
0 = 8x - 8x
0 = 8x - 8x
0 = 0
The answer equals:
0 = 0
You have been answered by one of many helper robots.
Rewrite in simplest terms: 0.8 ( − 5 � − 0.8 ) − 0.3 ( 0.5 � − 1 ) 0.8(−5w−0.8)−0.3(0.5w−1)
The expression 0.8(−5w − 0.8) − 0.3(0.5w − 1) in the simplified form will be −4.15w + 0.36.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ 0.8(−5w − 0.8) − 0.3(0.5w − 1)
Simplify the equation, then we have
⇒ 0.8(−5w − 0.8) − 0.3(0.5w − 1)
⇒ −4w − 0.64 − 0.15w + 0.30
⇒ −4.15w + 0.36
The expression 0.8(−5w − 0.8) − 0.3(0.5w − 1) in the simplified form will be −4.15w + 0.36.
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a
[Ω]
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Score on last try: 0 of 1 pts. See Details for more.
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You want to buy a $237,000 home. You plan to pay 20% as a down payment, and take out a 30 year
loan for the rest.
a) How much is the loan amount going to be?
b) What will your monthly payments be if the interest rate is 6%?
c) What will your monthly payments be if the interest rate is 7%?
Enter an integer or decimal number [more]
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The values will be Loan amount=$186900, When simple interest is 6% then monthly payment=$1453.66 per month, When simple interest is 7% monthly payment=$1609.4 per month
What is simple interest?Simple Interest is an easy method of calculating the interest for a loan/principal amount. Simple interest is a concept that is used in many sectors such as banking, finance, automobile, and so on. When you make a payment for a loan, first it goes to the monthly interest and the remaining goes towards the principal amount.
Simple interest formula is given as:
SI=P*R*T/100
Where SI = simple interest
P = principal
R = interest rate (in percentage)
T = time duration (in years)
In order to calculate the total amount, the following formula is used:
Amount (A) = Principal (P) + Simple Interest (SI)
Now,
Initial amount=$237000
Down-payment=20%=20/100*237000=$47400
Amount left=237000-47400=$186900
So, Loan amount=$186900
For interest rate=6%
Total amount=186900+186900*6*30/100
=186900+336420
Total amount=$523320
Therefore, monthly payment=523320/360
monthly payment=$1453.66 per month
For interest rate=7%
Total amount=186900+186900*7*30/100
=186900+392490
Total amount=$579390
Therefore, monthly payment=579390/360
monthly payment=$1609.4 per month
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if u help me for this its basically free brainliest
The required 3/4 is 11/3 and 26/3 times in fractions 11/4 and 6 1/2 respectively.
What is the Ratio?The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
Given ration 3/4
(1)
Fraction 3/4 in 11/4
= 11/4 / 3/4
= 11/3
Although, 3/4 is 11/3 times in the value 11/4
Similarly
(2)
Fraction 3/4 in 6 1/2
= 13 / 2 / [3/4]
= 26/3
Although, 3/4 is 26/3 times the value of 6 1/2.
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A dinner was held to raise money for a children's museum. A ticket for one person cost $200 and a ticket for a couple (two people) cost $350. A total of 130 people attended the dinner, and the ticket sales total was $24,000. What is the total number of tickets that were sold?
Using simultaneous equations, during the dinner to raise money for a children's museum, 90 tickets were sold.
What are simultaneous equations?Simultaneous equations are two or more equations solved concurrently or at the same time.
Simultaneous equations are also called a system of equations.
The cost of one-person ticket = $200
The cost of two-people ticket = $350
The total number of attendees at the dinner = 130
The total ticket sales = $24,000
Let number of one-person ticket = x
Let number of two-people ticket = 2y
Equations:x + 2y = 130... Equation 1
200x + 250y = 24000... Equation 2
Multiply Equation 1 by 200:
200x + 400y = 26000... Equation 3
Subtract Equation 2 from Equation 3:
200x + 400y = 26000
-
200x + 350y = 24000
50y = 2000
y = 40
x = 130 - 2y
= 130 - 80
= 50
Thus, the number of tickets sold at the dinner was 90.
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The student used the gift card to spend the same amount of money at the coffee shop every day until the remaining value of the card was $0. This function represents f(n), the value, in dollars, of the gift card after n days.f(n) = −2.5n + 75A. Based on the function, what was the original value, in dollars, of the giftcard? Show or explain how you got your answer.B. Based on the function, how much money, in dollars, did the student spend each day at the coffee shop? Show or explain how you got your answer.C. What was the remaining value, in dollars, of the gift card after 20 days? Show or explain how you got your answer.D. How many days in total did it take until the remaining value of the gift
Answer:
A. The original value of the gift card is 75 dollars, which is the y-intercept of the function.
B. The student spent 2.5 dollars each day at the coffee shop, which is the coefficient of n in the function.
C. After 20 days, the remaining value of the gift card is -2.5 * 20 + 75 = 25 dollars.
D. To find the total number of days until the gift card was used up, we need to find when f(n) = 0. Setting the function equal to 0 and solving for n, we get: 0 = -2.5n + 75, so n = (75)/(-2.5) = 30 days.
2 2/3 +2 1/6 as a fraction
Answer:
You can either write it as a whole number: 4 5/6
Or as 29/6
Step-by-step explanation:
Step-by-step explanation:
first step : convert both terms into real fractions (not mixed numbers).
second step : bring both fractions to the same denominator (bottom part).
third step : perform the addition.
1.
2 2/3 = (2×3 + 2)/3 = 8/3
2 1/6 = (2×6 + 1)/6 = 13/6
2.
we bring both fractions to .../6.
remember, we need to do the same multiplication for the numerator and the denominator to keep the overall value of the fraction unchanged.
to get from 3 to 6 we need to multiply by 2.
so,
8/3 = 8/3 × 2/2 = 16/6
3.
16/6 + 13/6 = 29/6
if you want to convert this to mixed numbers, this would be
29/6 = (4×6 + 5)/6 = 4 5/6
Which inequality does the graph represent? The graph with X-coordinate marks -2, 0, and 2; Y-coordinate marks -2, 0, and 2. There is a line which passes through the points (3, 3), and (2, 3.5). There is shaded region which is above the line. A. y > (–13 )x + 4 B. y ≥ (–13 )x + 4 C. y < (–13 )x + 4 D. y ≤ (–13 )x + 4
The values of {x} are given above upto 2³.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that the graph with x - coordinate marks (-2, 0, and 2) and y -coordinate marks (-2, 0, and 2). There is a line which passes through the points (3, 3) and (2, 3.5).
The inequality line representing the shaded region as -
y ≥ - 13x + 4
Therefore, the inequality line representing the shaded region is y ≥ - 13x + 4.
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3x - 4y= 22
-3x + 2y = -2
X =
y =
answer
y = -10
x = 10
eplanation
Explain why the statement "It will always rain on my birthday" uses inductive reasoning.
Create your own quadratic function ,f(x), and then evaluate the function at f(x-3). Find the domain of your function.
Domain of the function is all real numbers
What is a function?A relation is a function if it has only One y-value for each x-value.
Let us consider a function f(x)= x² + 2x - 3
Now let us find the value of f(x-3)
Plug in the value x as x-3
f(x-3)= (x-3)² + 2(x-3) - 3
= x² +9-6x+ 2x-6 - 3
= x² -4x
The domain of this function is all real numbers. This means that any real value can be plugged into the function and produce a real output.
Hence, domain of this function is all real numbers
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Given the following table of values for f(x), find f(7)
Find p and q , if X1 = 17, n1 = 25, X2 = 28, and n2 = 80
The solutions are given below:-
Part (a),
X₁ + X₂ have distribution Bi(n₁+n₂, p)
Part (b),
P(X ₁+ X₂ = 1 | X₂ = 0) = np(1-p)ⁿ¹⁻¹
P(X₁+X₂ = 1| X₂ = 1) = (1-p)ⁿ¹
P(X₁ + X₂ = 1) = (1-p)ⁿ¹ * np(1-p)ⁿ²⁻¹+ (1-p)ⁿ²*np(1-p)ⁿ¹-¹
What is binomial distribution?Since both variables are independent but they have the same probability parameter, you can interpret that as if the experiment that models each try in both variables is the same.
When you sum both random variables together, what you obtain as a result is the total amount of success in n₁+n₂ tries of the same experiment, thus X₁+X₂have distribution Bi(n₁ + n₂, p).
b)
Note that, if X₂ = k, then X₁ +X₂ = 1 is equivalent to X₁ = 1-k. Since X1 and X₂ are independent, then P(X₁ +X₂ = 1| X₂ = K) = P(X1=1-k|X₂=k) = P(X₁ = 1-k).
If k = 0, then this probability is equal to P(X₁ = 1) = np(1-p)ⁿ¹⁻¹
If k = 1, then it is equal to P(X₁ = 0) = (1-p)ⁿ¹
Thus,
P(X₁+X₂ = 1) = P(X₁+X₂ = 1| X₂ = 1) * P(X₂=1) + P(X₁+X₂ = 1| X₂ = 0) * P(X₂ = 0) = (1-p)ⁿ¹ * np(1-p)ⁿ²⁻¹+ (1-p)ⁿ²*np(1-p)ⁿ¹-¹.
The complete question is given below.
Let X1 and X2 be two random variables following Binomial distribution Bin(n1,p) and Bin(n2,p), respectively. Assume that X1 and X2 are independent.
(a) The mgf of binomial distribution Bin(n, p) is (1 − p + pet)n. Use this fact to obtain the distribution of X1 + X2.
(b) Find the probability P(X1 + X2 = 1|X2 = k) for k = 0 and 1. Then use the law of total probability to find P (X1 + X2 = 1)
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If the purchase price for a house is $210,600, what is the monthly payment if you put 20% down for a 30-year loan with a fixed rate of 5%?
The monthly payment for a 30-year loan with a fixed rate of 5% is $702.
How is the monthly payment for a 30-year loan determined?Divide the number of payments you make annually by 30, the length of the loan. For instance, 30 x 12 equals 360. Over the course of the loan, you will make 360 payments.
The following equation is used to determine the down payment: down payment = down payment percentage times purchase price. For the sake of this calculation, the down payment percentage must be converted to a decimal.
Purchase price for a house is $210,600
Down payment is 20%.
remaining payment 80% of total price = $210,600*80/100= $168480.
$168480 payment for a 30-year loan with a fixed rate of 5%
then interest will be
interest = 168480 *5*30/100= $84240
total amount to be paid 30 yr= 168480+ 84240= $252720
amount to be paid per month= $252720/(30*12) = $702.
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What is the area of the parallelogram
Answer:
40 units^2
Step-by-step explanation:
The parallelogram shown is basically made of two triangles divided by the x-axis. The bases go from 3 to 13 on the axis, so they have a length of 10. The height of one triangle is from a 0 to 4, which is a height of 4.
The area of a triangle is [tex]\frac{bh}{2}[/tex], so plugging those numbers in gets:
[tex]\frac{4*10}{2}[/tex] = 20
Since there are two triangles it would be double the area: 40 units^2
Write an expression equivalent to 2(x+5).
Answer: 2x+10
same expression, just simplified
Mr.Ramirez 24 cookies. 3 fourths were oatmeal. How many oatmeal cookies did Mr.Ramirez bake
The amount of oatmeal cookies with Mr. Ramirez is 18
How to find the amount to oatmeal cookiesThe problem is dealing with multiplication of fractions
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split.
In the problem saying that 3 fourths were oatmeal means that 3/4 of the cookies where oatmeal hence
number of cookies = 3/4 * 24
number of cookies = 18
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Resolva as expressões a seguir e registre os resultados na forma fracionária e na forma decimal
What is the difference between the area of Figure A and the
area of Figure B? Each grid square represents 1 square foot
The difference between the area of Figure A and the areas of Figure B is 2 ft².
What is the difference between the area of the two figures, Figure A and Figure B?The difference between the area of the two figures, Figure A and Figure B is determined by finding the area of the two figures.
The area of Figure A is found as follows:
The triangle on the right of figure A is cut out and moved to the left in order to form a rectangle.The area of figure A is then calculated.The area of A = 3 × 4
The area of A = 12 ft²
The area of B = ½ × 4 × 3 + ½ × 4 × 2
The area of B = 10 ft²
Difference between the area of A and B = 12 - 10 ft²
Difference between the area of A and B = 2 ft²
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Integrate 1/(1+x2) for limit [0,1].
Answer:
Step-by-step explanation:
A garbage incinerator charges $30, plus $15 per ton, to incinerate a truckload of garbage. The average cost per ton (in dollars) for incinerating n tons of garbage is
given by A(n) =
15n+30
n
a. Use the accompanying graph to determine whether the average cost per ton is increasing or decreasing as the size of the load increases.
b. A company uses trucks with capacities of 9, 16, and 18 tons. What is the average cost per ton for each truck?
erage costq
a. The average cost per ton is increasing as the size of the load increases.
b. For a 9-ton truck, the average cost per ton is $45. For a 16-ton truck, the average cost per ton is $60. For an 18-ton truck, the average cost per ton is $65.
Determine the average cost.This question uses the concept of linear functions.
The equation A(n) = 15n+30 is an example of a linear function, as it is a function of the form f(x) = mx + b, where m is the slope and b is the y-intercept.
The graph of this equation is a straight line, which shows that the average cost per ton is increasing as the size of the load increases.
a. To determine whether the average cost per ton is increasing or decreasing as the size of the load increases, we can look at the graph provided.
The graph shows that as the size of the load increases, the average cost per ton increases.
Therefore, the average cost per ton is increasing as the size of the load increases.
b. To calculate the average cost per ton for each truck, we can use the equation A(n) = 15n+30. For a 9-ton truck, we plug in n = 9 and calculate A(9) = 15(9) + 30 = 135 + 30 = 165. Therefore, the average cost per ton for a 9-ton truck is $45.
For a 16-ton truck, we plug in n = 16 to calculate A(16) = 15(16) + 30 = 240 + 30 = 270.
Therefore, the average cost per ton for a 16-ton truck is $60.
For an 18-ton truck, we plug in n = 18 to calculate A(18) = 15(18) + 30 = 270 + 30 = 300.
Therefore, the average cost per ton for an 18-ton truck is $65.
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Priya says the sum of 1 2/5 and 4/5 is 1 6/5. Kiran says the sum is 11/5. Elena says it is 1 6/10. Tyler says it is 2 1/5. Do you agree with any of them? Use this space to solve the addition problem. Then Justify whether each person's answer is right or wrong using full sentences. You may use drawings if it helps.
The sum of the numbers 1 ²/₅ and ⁴/₅ in different form will be 1 + ⁶/₅, 11 / 5, and 2 ¹/₅. So, Priya, Kiran, and Tyler are correct.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The sum of the numbers 1 ²/₅ and ⁴/₅ is given as,
⇒ 1 ²/₅ + ⁴/₅
⇒ 1 + ²/₅ + ⁴/₅
⇒ 1 + ⁶/₅
⇒ 11 / 5
⇒ 2 ¹/₅
The sum of the numbers 1 ²/₅ and ⁴/₅ in different form will be 1 + ⁶/₅, 11 / 5, and 2 ¹/₅. So, Priya, Kiran, and Tyler are correct.
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Does each relation represent a function
(1,3), (2,5), (2,7), (4,9)
(1,3), (2,5), (3,7), (4,9)
(1,3), (1,5), (1,7), (1,9)
(1,3), (2,3), (3.3), (4.3)
the first one yes
the 2nd one yes
the 3rd one no 4th also no
Step-by-step explanation:
m∠3=82 Find m∠4 I-Ready
The angle 4 is equal to 98degree.
What are supplementary angles?Two angels whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
Given;
m∠3=82
Now
m∠3+m∠4=180 (since the angles are supplementary)
82+m∠4=180
m∠4=180-82
m∠4=98degree
Therefore, the angle 4 will be 98degrees.
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Answer:
98 degrees
Step-by-step explanation: