Answer:
y = -110x + 1,600
Step-by-step explanation:
Zachary purchased a computer for $1,600 on a payment plan. Four months after he purchased the computer, his balance was $1,160. Five months after he purchased the computer, his balance was $1,050. What is an equation that models the balance y after x months?
1,160 - 1,050 = $110 change from month 5 to 4
Double check if the rate of decrease is steady over time:
1,600 - ($110 * 4 months) = 1,160
1,600 - ($110 * 5 months) = 1,050
This means, Zachary is paying $110 per month for his computer.
SO:
remaining payment plan balance = initial balance - 110 per month
This can be modeled by the algebraic equation:
y = 1,600 - 110x
rearrange right side:
y = -110x + 1,600
Answer:
[tex]y=-110x+1600[/tex]
Step-by-step explanation:
Given information:
Purchase price = $1,600Balance = $1,160 after 4 months.Balance = $1,050 after 5 months.Define the variables:
Let x be the number of months.Let y be the balance of the payment plan (in dollars).Therefore:
x = 0, y = 1600x = 4, y = 1160x = 5, y = 1050[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]
Determine if the equation is linear by calculating the slope between each pair of (x, y) points:
[tex]\implies \text{Slope}\;(m)=\dfrac{1050-1160}{5-4}=-110[/tex]
[tex]\implies \text{Slope}\;(m)=\dfrac{1160-1600}{4-0}=-110[/tex]
As the slope is the same, the equation is linear.
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
As the initial purchase price of the computer was $1,600, the y-intercept is 1600. We have already calculated the slope. Therefore, substitute the found slope and y-intercept into the slope-intercept formula to create an equation that models the balance y after x months:
[tex]y=-110x+1600[/tex]If f(1) = 4 and f(n) = 4f(n-1) + 5
The value of the function F(0) will be -1 / 4.
What is a function?The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x.
In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are indicated by letters like f, g, and h.
Given that the function is f(n) = 4f(n-1) + 5 and the value of f(1) is 4.
The value of f(0) will be calculated as:-
f(n) = 4f(n-1) + 5
f(1) = 4f(1 - 1 ) + 5
f(1) = 4f(0) + 5
4 = 4f(0) + 5
f(0) = -1 / 4
Therefore, the value of the function F(0) will be -1 / 4.
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The difference between compound and simple interest is:
Simple interest is calculated on the original amount (the
principal) only.
Compound interest is calculated and added in during the
length of the time period, and hence has the effect of
accumulating interest on interest.
A) True
B) False
A) True. Both the given statement about simple interest and compound interest is True.
Simple interest is computed on a loan's principal, or initial loan amount.
Compound interest is often referred to as "interest on interest" since it is calculated using both the principal and the accrued interest from prior periods.
Formula for simple interest - S.I. = (P × T × R) ⁄ 100
Formula for compound interest - C.I. = P(1+R⁄100)t − P
If interest is computed on a compound basis rather than a simple basis, the amount of interest that must be paid on a loan can vary significantly. Positively, the power of compounding can work in your favor when it comes to investments and can be a significant contributor to wealth accumulation.
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Which of the following fits this equation? x<10+1
A.) 11
B.) 19
C.) 10
D.) 40
Answer:
C.] 10
Step-by-step explanation:
We can substitute x for 10. 10 is less than 11 so this makes the statement true.
Please help! I’m stuck
solve & show your work please
The sum is x/(x+5) + (x+10)/(x+1).
The difference is x/(x+5) - (x+10)/(x+1).
What is simplification?
To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
Here, we have
Given: x/(x+5) + (x²+20x+100)/(x²+11x+10)
Sum:
= x/(x+5) + (x²+20x+100)/(x²+11x+10)
= x/(x+5) + (x+10)²/(x+1)(x+10)
= x/(x+5) + (x+10)/(x+1)
Hence, the sum is x/(x+5) + (x+10)/(x+1).
Now, the difference:
= x/(x+5) - (x²+20x+100)/(x²+11x+10)
= x/(x+5) - (x+10)²/(x+1)(x+10)
= x/(x+5) - (x+10)/(x+1)
Hence, the difference is x/(x+5) - (x+10)/(x+1).
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Nolan buys a $12,000, 13-week treasury bill at 5%. What’s his effective rate? Round your answer to the nearest hundredth of a percent
As a result, the actual interest rate is 5.06% since Nolan purchases a $12,000 13-week treasury bill at 5%.
What is interest ?To calculate simple interest, divide the original by the loan rates, the length of time, and other variables. The marketing equation is simple gain = principal + interested + hours. It is easier to compute interest with this system. The method that is most frequently used to calculate this is as a percentage of the principle amount. If someone borrows $100 from a buddy and promises to return him with 5% interest, he may only pay his portion of the 100% interest. $100 (0.05) = $5. You must pay interest on any further borrowings as well as any loans you put out. Interest is frequently calculated as a measure of the entire amount of the loan. This percentage represents the loan's interest rate.
given that,
Simple interest = $12,000 × 0.05 × 13/52 = $150
Simple discount note = ($12,000 - $150) × 13/52 = $2962.5
Effective rate of interest = $150 / $2962.5
Effective rate of interest = 0.0506 or 5.06%
As a result, the actual interest rate is 5.06% since Nolan purchases a $12,000 13-week treasury bill at 5%.
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A strand of straight hair would be most accurately classified as a ______________.
ray
line
line segment
none of the above
The strand of straight hair would be most accurately classified as a ray.
What is a ray?The definition of ray in math is that it is a part of a line that has a fixed starting point but no endpoint.
Given is the strand of straight hair.
Considering the strand of hair to be straight. We can call it as a ray as ray originates from one point and extends away from that point towards infinity.
Therefore, the strand of straight hair would be most accurately classified as a ray.
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if you could help, I'll give brainliest
Type the correct answer in each box. Use numerals instead of words. Consider the systems of equations below. System A has System B, and System C has real solutions. real solutions. System A real solutions. x² + y² y = -1/2x Determine the number of real solutions for each system of equations. System B 17 y = x² 7x + y = - 6x + 5 - 10 System C y = 2x² + 9 8y-17
As a result, the answers are 2, 1, 1 for Systems A, B, and C, respectively.
What is equation?An equation, in its most basic form, is a mathematical statement that states that two mathematical expressions are equal. For example, 3x + 5 = 14 is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.
Here,
The number of real solutions for each system of equations can be determined by counting the number of points where the lines or curves intersect.
System A:
The equation x² + y² = 17 defines a circle with center at the origin and radius √17. The equation y = -1/2x defines a line. Since the circle and line intersect at two points, the system of equations has two real solutions.
Number of real solutions for System A: 2
System B:
The equation y = x² defines a parabola. The equation 7x + y = -6x + 5 defines a line. Since the parabola and line intersect at exactly one point, the system of equations has one real solution.
Number of real solutions for System B: 1
System C:
The equation y = 2x² + 9 defines a parabola. The equation 8y - 17 = 0 defines a line. Since the parabola and line intersect at exactly one point, the system of equations has one real solution.
Number of real solutions for System C: 1
So the answer is 2, 1, 1 for System A, B, C respectively.
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The breadth of a rectangle is 4 m less than its length. If the perimeter of the rectangle is 40 m, find the length and breadth of the rectangle.
Step-by-step explanation:
let the length of rectangle be x
let the breadth of rectangle be x - 4m
the perimeter of rectangle=40m
solution,
perimeter of rectangle=40m
2(l+b)=40m
2(x+x-4)=40m
2(2x-4)=40m
4x-8=40m
4x=40+8
or,4x=48
or,x=48/4
•°•, x=12
so,
length of rectangle=x=12
breadth of rectangle=x-4
= 12-4
=8
Horace wants to estimate the percentage of people who own a tablet computer. He surveys 400 individuals and finds that 195 own a tablet computer. What is the sample proportion for successes?
The sample proportion for successes that estimates the percentage of people who own a tablet computer from Horace's survey of 400 individuals is 48.75%.
What is the sample proportion?The sample proportion shows the percentage or proportion of successes or expected outcomes in a sample.
The sample proportion is given as the quotient resulting from the division operation between the successes (numerator) and sample size (denominator), and multiplied by 100.
The Sample Size = 400
The number of tablet computer owners in the sample = 195
The sample proportion = Number of Success/Sample Size x 100
= 195/400 x 100
= 48.75%
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Expand and simplify f(x)= 4(x+6)(x-2)
The expression f(x) = 4(x + 6)(x - 2) can be expanded as follows:
What is a mathematical expression?
A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. The following is the structure of an expression: Expression: (Number/Variable, Math Operator, Math Operator)
f(x) = 4(x^2 - 2x + 6x - 12)
Expanding the inner parentheses,
f(x) = 4(x^2 + 4x - 12)
So, the expanded and simplified form of f(x) = 4(x + 6)(x - 2) is
f(x) = 4x^2 + 16x - 48
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Pleaseanswer to this?
Substitute a = 3, u = 5, t = 7 into the formula v=u+at
To work out v.
How do I do this
Step-by-step explanation:
a=3, u= 5, t=7 (given)
v=u+at
v = 5+ 3×7 = 5+21= 26
v=26
The substitute a = 3, u = 5, t = 7 into the formula v=u+at. The value of V would be 26.
Given, a = 3, u = 5, t = 7
To find, v=u+at or v = u + (a × t)
= 5 + (3 × 7)
= 5 + 21
= 26
Thus, v = 26.
By substituting a = 3, u = 5, t = 7 into the formula v=u+at the value of V would be 26.
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Kyle puts ribbon around his rectangular bulletin board and covers it in paper board measure 4 3/4 feet by 6 1/2
Hi ow much ribbon did he use
How much paper will he need for bulleitin board?
The amount of paper, he will need for the bulletin board is 30.875 square feet.
The required amount of ribbon is 22.5 feet.
What is a rectangular perimeter?The whole distance that a rectangle's borders, or its sides, the cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the total of its four sides.
Given:
Kyle puts ribbon around his rectangular bulletin board and covers it in a paper board measuring 4[tex]\frac{3}{4}[/tex] feet by 6[tex]\frac{1}{2}[/tex].
That means,
the perimeter of the paper board = the perimeter of the rectangular bulletin board
The perimeter of the rectangular bulletin board = 2(4[tex]\frac{3}{4}[/tex] + 6[tex]\frac{1}{2}[/tex])
The perimeter of the rectangular bulletin board = 45/2 feet
The perimeter of the rectangular bulletin board = 22.5 feet.
The amount of paper = (4[tex]\frac{3}{4}[/tex] x 6[tex]\frac{1}{2}[/tex]) = 30.875 square feet.
Therefore, the required amount of ribbon is 22.5 feet.
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Suppose that a series an has positive terms and its partial sums sn satisfy the inequality sn 3 1000 for all n. Explain why an must be convergent.
The series must converge to a finite value.
The proof is given below.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
The partial sums of the series satisfy the inequality s(n) ≥ 1000 for all n.
This means,
The sum of the series is bounded from below by 1000.
Now,
All terms of the series are positive, the sum of the series must either converge to a finite value or diverge to infinity.
For the sake of contradiction,
The series diverges to infinity.
Then for any M > 0, there exists an integer N such that,
a(N) + a{N+1} + a{N+2} + ... > M
This means,
The partial sums of the series start at index N.
i.e
s(N), s{N+1}, s(N+2), ... also diverge to infinity.
This contradicts the fact that they are all bounded from below by 1000.
Thus,
The series must converge to a finite value.
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why is this not a parallelogram
Answer: it’s not because of the angles
Step-by-step explanation:
Answer:
the angles are wrong for it to be a parallelogram
so sorry if I'm wrong
Sally’s budget for food is 1/8 of her yearly salary. Sally’s total food bill for the year is $12,5000. What’s Sally’s yearly salary?
Answer:
To find Sally's yearly salary, we can use the information that her budget for food is 1/8 of her yearly salary and her total food bill for the year is $12,500. Let's call Sally's yearly salary "S".
Since 1/8 of Sally's yearly salary is dedicated to food, we can write:
S * 1/8 = $12,500
To solve for S, we can divide both sides of the equation by 1/8:
S = $12,500 * 8 = $100,000
So, Sally's yearly salary is $100,000.
Step-by-step explanation:
sec(3x - 15) = csc(14x + 3)
The solution of x in the equation is (-5.855, 2.435)
How to determine the solution of xFrom the question, we have the following parameters that can be used in our computation:
sec(3x - 15) = csc(14x + 3)
Next, we split the equation as follows
y = sec(3x - 15)
y = csc(14x + 3)
Next, we solve the equation graphically
When the graph is plotted, we have one of the points of intersection to be:
(x, y) = (-5.855, 2.435)
Hence, the solution is (-5.855, 2.435)
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What are the x -intercepts of the quadratic function given by the equationf(x)=-x^2-2x+3
Evaluate : cosec2 45° + tan2 45° – 3sin2 90°
Answer:
arcsin (1°/245°) + 4.963586
Step-by-step explanation:
Rewrite the angle as a sum or difference with its reference angle
simplify the expression using the general reduction formula
Remove the parentheses
Simplify using exponent rule with same exponent (ab)n
Simplify using exponent rule with same exponent
Calculate the approximate value
Calculate
Calculate the sum or difference
Irene performed an operation with 83.904 and a number. She ended up moving the decimal point in 83.904 four places to the right Irene ? 10 raised to the power of ?
Irene multiplied 10 raised to the power of 4.
What precisely is a expression?Math requires the use of arithmetic, algebra, and divisions. They result in the following when combined: An equation, some statistics, and a mathematical function Values, factors, and mathematical processes like adding, addition and subtraction, complex numbers, and division can all be found in a statement of fact. Different words and terms can be analysed and evaluated.
Here,
She ended up moving the decimal point in 83.904 four places to the right
i.e.
839040
Irene performed the operation
= 83.9040 / 83.904
= 10000
= 10⁴
Therefore, the solution of the given problem of expression comes out to be Irene performed the operation 83.904 × 10.⁴
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If 0 = 17/4, then find the exact values for the following: sec(0) =_________ csc(0) = _________ tan(0) = _________ cot(0) = _________
The exact values for the following:
Sec(0) = -2.2417
Csc(0) = -1.1173317211
Tan(0) = 2.00630902786
Cot(0) = 0.4984
What are the trigonometric identities?Equations using trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.
Given:
0 = 17/4.
Then the exact values for the following:
Sec(0) = 1 / cos(17/4) = -2.2417
Csc(0) = 1/ sin(17/4) = -1.1173317211
Tan(0) = tan(17/4) = 2.00630902786
Cot(0) = 1/ tan(17/4) = 0.4984
Therefore, the exact values are given above.
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Find AB. Round to nearest tenth
In 2017 the Islamic month of fasting, Ramadan, began on Friday, 26 May. What fraction of the year was this?
Answer:
The Islamic month of Ramadan in 2017 began on Friday, 26 May, which was the 146th day of the year. There are 365 days in a year, so this was approximately 0.4 of the year.
Step-by-step explanation:
Solve the inequalities below. Write the solution set in interval notation and graph the solution.
−
3
2
x
>
−
14
-
3
2
x
>
-
14
Solution:
Interval notation for the solution:
Step-by-step explanation:
(∞,-14/3/2] ∪ [14/3/2, ∞)
The graph of the solution would be the set of all real numbers except for the number -14/3/2. It would be a number line with two open dots on either side of -14/3/2.
True or False? Let P(X, Y) Be The Propositional Function X > Y. The Domain Of Discourse Is Z+ X Zł. Determine The Truth Value Of Vx=YP(X,Y)
For the Propositional Function each proposition ∀x∀y P(x,y) is false.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
It is given that Propositional function -
P(x,y) : x ≥ y
Universal quantifier x Universal quantifier y Propositional function
∀x∀y P(x,y)
For every positive integer = every positive integer ≥ every positive integer
But this is false.
Example - x = 1 and x = 2
x < y
Therefore, the given statement is false.
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Let P(x,y) be the propositional function x≥y. The domain of discourse is Z+×Z+. Tell whether each proposition is true or false.
∀x∀yP(x,y)
a car that is traveling 35 miles per hour starts 26 miles away from its destination, which is a parking garage. which function below models the location of the car if it is d miles from the garage h hours after starting towards the garage?
a. d=26-35h
b. d=26h-35
c. d=26-35
d. d=26+35h
The function below that models the location of the car if it is d miles from the garage h hours after starting towards the garage is option a d = 26 - 35h.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).
The distance travelled by the car is given as:
26 miles away from its destination. Let d be the destination the we have the distance in miles as:
26 - d
The formula of the speed is:
Speed = distance / time
35 = (26 - d) / h
Rearranging the equation, we have:
d = 26 - 35h
Hence, the function below that models the location of the car if it is d miles from the garage h hours after starting towards the garage is option a d = 26 - 35h.
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A blueprint with a scale of 1/4 inch equals 1 foot shows a room with dimensions of 3 inches by 3 1/2 inches. What are the actual dimensions of the room 
A 80-kg base runner begins his slide into second base when he is moving at a speed of 4.7 m/s. The coefficient of friction between his clothes and Earth is 0.70. He slides so that his speed is zero just as he reaches the base.A) How much mechanical energy is lost due to friction acting on the runner?B) How far does he slide?
The runner slides a distance of approximately 0.255 meters or 25.5 centimeters, and the mechanical energy lost due to friction is 140.29 J.
What is the coefficient?
A coefficient is a number multiplied by a variable. Examples of coefficients: In the term 14 c 14c 14c, the coefficient is 14. In the term g, the coefficient is 1.
A) The mechanical energy lost due to friction can be calculated as follows:
Initial kinetic energy of the runner: KE = 0.5 * m * v² = 0.5 * 80 kg * (4.7 m/s)² = 140.29 J
The force of friction acting on the runner is given by:
[tex]friction_{force} = friction_{coefficient} * normal_{force}[/tex]
where,
[tex]friction_{coefficient} = 0.70[/tex]
[tex]and normal_{force} = m * g (g = 9.8 m/s^{2} )[/tex]
The normal force is given by:
[tex]normal_{force} = m * g = 80 kg * 9.8 m/s^{2} = 784 N[/tex]
Therefore, the force of friction acting on the runner is: [tex]friction_{force} = 0.70 * 784 N = 548.8 N[/tex]
The work done by friction is given by:
[tex]W = friction_{force} * distance[/tex]
Since the speed of the runner is reduced to zero, the work done by friction is equal to the change in kinetic energy:
[tex]W = KE_{final} - KE_{initial}[/tex]
= 0 - 140.29 J = -140.29 J
So, the mechanical energy lost due to friction is 140.29 J.
B) The distance the runner slides can be calculated using the work-energy theorem, which states that the work done on an object is equal to its change in kinetic energy.
The work done by friction is given by: W = friction_force * distance
Since the friction force is constant, the work done by friction is equal to the change in kinetic energy:
[tex]W = KE_{final} - KE_{initial}[/tex]
= 0 - 140.29 J = -140.29 J
Rearranging this equation and substituting in the known values, we get:
[tex]distance = -W / friction_{force}[/tex]
= -140.29 J / 548.8 N = 0.255 m or 25.5 cm
Hence, the runner slides a distance of approximately 0.255 meters or 25.5 centimeters, and the mechanical energy lost due to friction is 140.29 J.
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a pet store has both dogs and cats. the sum of the numbers of dogs and cats is 39. The difference of the numbers of dogs and cats is 13. there are more dogs than cats. how many cats and dogs are in the pet store
Answer:
see below
Step-by-step explanation:
dogs = x
cats = y
x+y =39
x- y = 13
so add the 2 equations together you get 2x = 52 so x = 26
y = 13