Triangle T was dilated to form triangle T'. Which ratio is the correct scale factor?
Please answer fast and correctly

a) The monthly payment increases by approximately $6.60 for a $1000 increase in the principal. b) The monthly payment increases by approximately $39.25 for an increase in the interest rate from 0.075 to 0.08. c) The monthly payment increases by approximately $32.81 for a decrease in the loan term from 26 years to 24 years.

To solve these problems, we'll use the partial derivatives of the monthly payment function with respect to the principal P, interest rate r, and the length of the loan in months N.

Given values:

- Principal P = 450,000

- Interest rate r = 0.075

- Loan term N = 312 (26 years)

- Monthly payment [tex]\( f(450000, 0.075, 312) = 1962 \)[/tex]

Partial derivatives:

- [tex]\(\frac{\partial f}{\partial P} = 0.0066 \)[/tex]

- [tex]\(\frac{\partial f}{\partial r} = 7849 \)[/tex]

- [tex]\(\frac{\partial f}{\partial N} = -1.3672 \)[/tex]

a) The change in monthly payment per 1000 increase in loan principal

The partial derivative [tex]\(\frac{\partial f}{\partial P}\)[/tex] tells us the rate of change of the monthly payment with respect to the principal. To find the change in the monthly payment for a $1000 increase in the principal:

[tex]\[\Delta f \approx \frac{\partial f}{\partial P} \cdot \Delta P\][/tex]

Here, [tex]\(\Delta P = 1000\):[/tex]

[tex]\[\Delta f \approx 0.0066 \cdot 1000 = 6.6\][/tex]

So, the monthly payment increases by approximately $6.60 for a $1000 increase in the principal.

b) The change in monthly payment if the interest rate changes from [tex]\( r = 0.075 \) to \( r = 0.08 \)[/tex]

The partial derivative [tex]\(\frac{\partial f}{\partial r}\)[/tex] tells us the rate of change of the monthly payment with respect to the interest rate. To find the change in the monthly payment for a change in the interest rate from 0.075 to 0.08, we calculate the difference in the rates:

[tex]\[\Delta r = 0.08 - 0.075 = 0.005\][/tex]

Then, using the partial derivative:

[tex]\[\Delta f \approx \frac{\partial f}{\partial r} \cdot \Delta r\][/tex]

[tex]\[\Delta f \approx 7849 \cdot 0.005 = 39.245\][/tex]

So, the monthly payment increases by approximately $39.25 for an increase in the interest rate from 0.075 to 0.08.

c) The change in monthly payment if the length of the loan changes from 26 to 24 years

The partial derivative [tex]\(\frac{\partial f}{\partial N}\)[/tex] tells us the rate of change of the monthly payment with respect to the length of the loan in months. To find the change in the monthly payment for a change in the loan term from 26 years (312 months) to 24 years (288 months), we calculate the difference in months:

[tex]\[\Delta N = 288 - 312 = -24\][/tex]

Then, using the partial derivative:

[tex]\[\Delta f \approx \frac{\partial f}{\partial N} \cdot \Delta N\][/tex]

[tex]\[\Delta f \approx -1.3672 \cdot (-24) = 32.8128\][/tex]

So, the monthly payment increases by approximately $32.81 for a decrease in the loan term from 26 years to 24 years.

The complete question is

The monthly payment for a home loan is given by a function f(P, r, N) where P is the principal (the initial size of the loan), r the interest rate, and N is the length of the loan in months. Interest rates are expressed as a decimal: A% interest rate is denoted by r = 0.075. If P = 450000, r = 0.075 and N = 312 (a 26-year loan), then the monthly payment is f(450000, 0.075, 312) = 1962. Furthermore, with these values we have

[tex]\frac{\partial f}{\partial P}=0.0066, \quad \frac{\partial f}{\partial r}=7849, \quad \frac{\partial f}{\partial N}=-1.3672[/tex]

Estimate

a) The change in monthly payment per 1000 increase in loan principal.

b) The change in monthly payment if the interest rate changes from r = 0.075 to r = 0.08

c) The change in monthly payment if the length of the loan changes from 26 to 24 years.

Answer:

C. Both functions have a y-intercept of -2

Step-by-step explanation:

A. Function F in decreasing then increasing, therefore it's incorrect

B. Function F is symmetrical about the y-axis, but Function G is not

C. Both functions intercept the y-axis at (0,-2) so it's correct

D. Only function G shows a linear relationship.

To look at a picture of what Function G looks like. Press y= on your Ti-84 calculator (top left) put the function in, and then press graph (top right)

This is 100% correct. I took algebra 1 last year.

Final answer:

The value of sin A cannot be determined without knowing the value of angle A.

Explanation:

The question is asking for the value of sin A. In mathematics, sin A represents the sine of angle A. The sine function is a mathematical function that relates the ratio of the length of the side opposite the angle to the length of the hypotenuse of a right triangle.

The correct answer to the question is 3/5. To find this value, you need to know the value of angle A. Without that information, we cannot determine the exact value of sin A.

Final answer:

The correct value of SIN A from the given options cannot be determined without additional context. SIN A refers to the ratio of the side opposite to angle 'A' to the hypotenuse in a right triangle or the y-coordinate on the unit circle at angle 'A'. Possible values are within the range of -1 to 1.

Explanation:

The question 'What is SIN A?' is seeking the trigonometric value of the sine function at a particular angle denoted by 'A'. When presented with options like 3/4, 4/3, 3/5, and 4/5, we need additional information regarding angle 'A' or the context of a right triangle or unit circle to determine the correct value. Without this information, we cannot definitively answer which option is correct.

Generally, in a right triangle, SIN A would represent the ratio of the length of the side opposite to angle 'A' to the length of the hypotenuse. Therefore, it is a value between -1 and 1. The options 3/4 and 3/5 could potentially be correct since they are within this range, but 4/3 cannot be because it exceeds this range. In a unit circle context, sin A would represent the y-coordinate of a point on the circle's circumference at an angle 'A' from the x-axis.

Answer:

6

Step-by-step explanation:

260=20+40n

subtract 20

240=40n

divide by 40

n=6

x^-2 matches 1/36

x^-1 matches -1/6

x^0 matches 1

x^1 matches -6

x^2 matches 36

When evaluating expressions with exponents for a specific value, we simply substitute that value for x and follow the order of operations (PEMDAS). Here's the breakdown for each expression:

x^-2: (-6)^-2 = 1/(-6)^2 = 1/36

x^-1: (-6)^-1 = 1/(-6) = -1/6

x^0: (-6)^0 = 1 (any non-zero number raised to the power 0 equals 1)

x^1: (-6)^1 = -6 (any non-zero number raised to the power 1 equals itself)

x^2: (-6)^2 = (-6) * (-6) = 36

Therefore, the matches are as listed above.

Answer:

34.54 in

Step-by-step explanation:

c = 2π r

c = 2 (3.14)(5.5)

c = 34.54 in

Answer:

Area Δ = 102.3 units² ⇒ The answer is (d)

Step-by-step explanation:

* Use the formula of the area:

∵ Area of the triangle = 1/2 (a)(b) sin(C)

∵ We have the length of the 3 sides

∴ Use cos Rule to find the angle C

∵ cos(C) = (a² + b² - c²)/2ab

∵ a = 25 , b = 13 , c = 17

∴ cos(C) = (25² + 13² - 17²)/2(25)(13) = 625 + 169 - 289/650 = 505/650

∴ m∠C = 39°

∴ Area Δ = (1/2)(25)(13)sin(39) = 102.3 units²

∴ The answer is (d)

Answer:

Area Δ = 102.3 units² ⇒ The answer is (d)

Step-by-step explanation:

Use the formula of the area:

∵ Area of the triangle = 1/2 (a)(b) sin(C)

∵ We have the length of the 3 sides

∴ Use cos Rule to find the angle C

∵ cos(C) = (a² + b² - c²)/2ab

∵ a = 25 , b = 13 , c = 17

∴ cos(C) = (25² + 13² - 17²)/2(25)(13) = 625 + 169 - 289/650 = 505/650

∴ m∠C = 39°

∴ Area Δ = (1/2)(25)(13)sin(39) = 102.3 units²

∴ The answer is (d)

Answer:

  v = 0, or v = 8

Step-by-step explanation:

The quadratic can be factored, then the zero product rule applied.

  v^2 -8v = 0

  v(v -8) = 0

A product will be zero when any of the factors is zero. So, the solutions are values of v that make the factors be zero.

  v = 0

  v -8 = 0 . . . ⇒ . . . v = 8

Answer: 43 more times

2580÷60=43.

Step-by-step explanation: 43×60 =2580

This proves that 43 times is correct.

Answer:

c 43

Step-by-step explanation:

Answer:

There are 470 students at the school.

Step-by-step explanation:

141 / x = 3 / 10 since 3/10 is equal to 30% you're looking for a denominator that corresponds equally to 141 and when simplified, 141 / x equals 3 / 10.

Use algebra to solve: 141 * 10 = 3x → 1410 = 3x → 470 = x.

Final answer:

There are 470 students at the school.

Explanation:

In the given question, we are dealing with a basic percentage problem. We are told that 141 students, which is 30% of all students at the school, are playing at least one sport. To find the total number of students in the school, we need to solve for the whole when a part and its percentage are known.

Let x represent the total number of students at the school. According to the question:

30% of x = 141 students

We can set up the equation:

0.30 * x = 141

To find x, we'll divide both sides of the equation by 0.30:

x = 141 / 0.30

Performing the division gives us:

x = 470

Therefore, there are 470 students at the school.

1. You do 180-88 because supplementary angles add up to 180°.

2. 180-88=92°. Angle 4 is 92°

Answer:

92 degrees

Step-by-step explanation:

YOUR WELCOME

PLEASE MARK ME BRAINLIEST

Answer:

Your answer would be 1/4

Step-by-step explanation:

The probability that a randomly selected carton of yoghurt will be raspberry is 1/4. The correct option is b.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

Given that a grocery store has 12 cartons of yoghurt for sale, of which 3 are raspberry.

The probability that a randomly selected carton of yogurt will be,

Probability = Number of favourable outcomes / Number of sample

Probability = 3 / 12

Probability = 1 / 4

Therefore, the probability that a randomly selected carton of yoghurt will be raspberry is 1/4. The correct option is b.

To know more about probability follow

https://brainly.com/question/24756209

#SPJ2

logb(x) = y is equivalent to b^y =x

y = 2

b = 5

x = 25

Substitute the values to get 5^2 = 25

The answer is 12 questions per minute as you divide 36 by 3

Answer=12 questions per minute

Answer:

12

Step-by-step explanation:

Answer:

[tex]d=0.75m[/tex]

Step-by-step explanation:

Let

d------> the distance in miles

m----> the time in minutes

we know that

The speed is equal to divide the distance by the time

so

[tex]speed=d/m[/tex]

we have

[tex]d=2\frac{5}{8}\ miles=\frac{2*8+5}{8}=\frac{21}{8}\ miles[/tex]

[tex]m=3\frac{1}{2}\ minutes=\frac{3*2+1}{2}=\frac{7}{2}\ minutes[/tex]

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

so

In this problem the speed is the constant of proportionality

[tex]d=km[/tex]

Find the value of k

[tex]k=\frac{(21/8)}{(7/2)} =0.75\frac{miles}{minute}[/tex]

[tex]d=0.75m[/tex] ----> linear equation that represent the distance, d, that the car travels in m minutes

There should be 4.5 oz of vinegar and 22.5 oz of oil

-5x+y=0

x+y=27

-6x=-27

1 mile =1760 yd so 5 miles to the library=8800 yd yards hope this helps

Which is the most appropriate to describe a quantity decreasing at a steady rate?

With a linear equation.

1 cm : 25000 cm

On a map with a scale of 1:25,000, 9 cm represents 225,000 km on the ground.

To find how many kilometers on the ground is represented by 9 cm on the map, we can use the scale given. The scale is 1:25,000, which means that 1 cm on the map represents 25,000 cm on the ground. Since we want to find the number of kilometers, we need to convert the units. 1 km is equal to 100,000 cm. So we can set up the proportion: 1 cm (on the map) / 25,000 cm (on the ground) = 9 cm (on the map) / x km (on the ground). Cross multiplying, we get 1 * x km = 25,000 * 9 cm. Solving for x, we find that x = 225,000 km.

https://brainly.com/question/28822423

#SPJ3

Answer:

30 add-on sales to make the goal

Step-by-step explanation:

multiply 35*85% (or 0.85)

  35*0.85 = 29.75

Since you can't make 0.75 of a goal, round up to the next highest number = 30

Answer:

√50

√65

√145

105 °

Step-by-step explanation:

Given the coordinates

A(-3, 6)

B(2, 1)

C(9, 5)

To find the length of AB ,AC and BC, we will use distance formula

AB:

√(2+3)² + (1-6)²

√5²+5²

√50

BC:

√(9-2)² + (5-1)²

√7² + 4²

√49+16

√65

AC:

√(9+3)² + (5-6)²

√12²+1²

√145

To find ∠ABC

cos(B) =  c² + a² − b² / 2ca

          =  65 + 50 - 145 / 2(√65)(√50)

cosB   = -0.26311

B         = cos^-1(-0.26311)

          = 105 °

Answer:

√50

√65

√145

105 °

Step-by-step explanation:

Answer:

27 meters

Step-by-step explanation:

Think of it like a right triangle. One leg is 50m long (the distance you are from the balloon) and the goal is to find the other leg of the triangle. From the place you're standing, the angle is 28°. In relation to that angle, you're given the adjacent side (50m) and need to find the opposite side. Recall SOH-CAH-TOA. You have to use tangent to get the length. Tan = opposite/adjacent. The tan of 28 = x / 50. Use algebra to solve: tan28 (50) = x; aproximately 26.6m = x. So, the height of the hot air balloon is roughly 26.6m or 27m depending on how you round.

Answer: [tex]x=10.2[/tex]

Step-by-step explanation:

The triangle shown in the image attached is a right triangle.

Therefore, you can calculate the value of x as you can see below:

[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]

In this case, you have that:

adjacent=x

hypotenuse=11

[tex]\alpha=22\°[/tex]

Therefore, when you substitute values and solve for x, you obtain the following result:

[tex]cos(22\°)=\frac{x}{11}\\\\x=11*cos(22\°)\\x=10.2[/tex]

Answer:

The value of x = 10.2

Step-by-step explanation:

From the figure we can see a right angled triangle. One side and one angle are given.We have to find one side of triangle.

Points to remember

Cos θ = Adjacent side/Hypotenuse

To find the value of x

Here  θ = 22°, Hypotenuse = 11, Adjacent side =?

Cos 22 = Adjacent side/Hypotenuse = x/11

x = 11 * Cos 22 = 11 * 0.9271 = 10.2 units

Answer:

The temperature was -26.1° f at 2:30 am.

Step-by-step explanation:

* In this type of problems, we must think about

- What is the meaning of wards;

 above and below or

 raised and dropped or

 increased and decreased

- For above , raised , increase

 we will add the value of them to the initial value

- For below , dropped , decreased

 we will subtract the value of them from the initial value

* In our problem:

- The reading of thermometer is -17° f at 1:00 am.

- The temperature has dropped 9.1° f when the time was 2:30 am.

* Lets use the explanation above

- We will subtract 9.1 from -17

∴ -17 - 9.1 = -26.1° f

* The temperature was -26.1° f at 2:30 am.

Final answer:

To find the temperature at 2:30 am, you subtract the temperature drop of 9.1°F from the initial temperature of -17°F, resulting in a new temperature of -26.1°F.

Explanation:

If a thermometer read -17°F at 1:00 am and by 2:30 am the temperature has dropped by 9.1 degrees Fahrenheit, we calculate the new temperature by simply subtracting the temperature drop from the initial temperature. Subtracting a negative change from the current temperature results in an even lower temperature because you are going further down the scale.

Here's the calculation:

Initial temperature at 1:00 am: -17°F

Temperature drop by 2:30 am: 9.1°F

New temperature at 2:30 am: -17°F - 9.1°F = -26.1°F

Answer:

1.) 0.9265

2.) 63%

3.) 1683

4.) 5.9

I hope this helped and give me brainiest please

Answer:

Step-by-step explanation:

1) From standard distribution table we find that

P(Z<1.45) = 0.5+0.4265

=0.9265 Option d

2) Given that X, The scores on a standardized test is N(500,60)

percent of students who scored below Jake

[tex]=100*P(X<520)\\=100*P(Z<\frac{20}{60} )\\=100(0.5+0.1293)\\=62.93%\\=63%[/tex]

3) X, lengths of new born girls is N(49.2, 1.8)

n = 2000

P(X<51) = P(Z<1) =0.84

No of girls =2000(0.84) =1683

4) P(Z<2.72) is the answer

5)X, ages of cars driven is N(8,3.2)

75% correspond to z=0.675

X = 8+0.675(3.2) =10.16=10.2

Answer:

The length of the arc is [tex]8\pi\ ft[/tex]  

Step-by-step explanation:

we know that

The measure of the arc shown in brown is equal to

[tex]180\°-60\°=120\°[/tex] -----> by central angle

Remember that

The length of the arc of the complete circle (360 degrees) is equal to the circumference

[tex]C=\pi D[/tex]

we have

[tex]D=24\ ft[/tex]

substitute

[tex]C=\pi (24)=24 \pi\ ft[/tex]

so

by proportion

Find the length of the arc for a measure of [tex]120\°[/tex]

[tex]\frac{24\pi }{360} \frac{ft}{degrees} =\frac{x }{120} \frac{ft}{degrees}\\ \\x=120*(24\pi )/360\\ \\ x= 8\pi\ ft[/tex]

Answer:

AAA (Angle Angle Angle) Proving that the angles are the same (Or of the same ratio if diluted), if this is true, the two figures are similar.

SSS (Side Side Side) Proving all the sides are the same size (Or again of the same ratio) also proves similarity.

SAS (Side Angle Side) If two sides and the angle in between are the same, then the triangles are similar.

Step-by-step explanation:

EX)

Triangle A has sides 10, 5, and 12

Triangle B has sides 20, 10, and 24

The relationship is the same between both triangles, just that the sides are multiplied by 2. This is SSS

If Triangle A has two sides 5 and 10 with an angle of 25 degrees, then Triangle B must have that same angle alongside those two sides, or at least a consistent ratio if diluted. Proof SAS

If Triangle A and B have the same angles, they are similar.

Answer: 13

Step-by-step explanation:

[tex]5^{2} + 12^{2} = c^{2} \\25 +144= c^{2} \\\sqrt169= \sqrt c^{2} \\13=c[/tex]

Answer:

Step-by-step explanation:

The angle where the chords cross is the average of the two intercepted arcs:

  ∠AEB = (∠AOB +∠COD)/2 = (76° +80°)/2 = 78°

___

Chord AD connects points A and D.

Answer:

It is B.

Step-by-step explanation:

f(x) = 2(3^x) + 4

As x approaches negative  infinity  2(3^x) approaches zero and f(x) approaches 4.

Answer:

B.[tex]f(x)=2(3^x)+4[/tex]

Step-by-step explanation:

We have to find that which graph has horizontal asymptote at 4

We know that to find the horizontal asymptote , we simply evaluate the limit of the function as it approaches to infinity or it approaches to negative infinity.

A.[tex]f(x)=2x-4[/tex]

[tex]\lim_{x\rightarrow \infty}(2x-4)=\infty[/tex]

[tex]\lim_{x\rightarrow -\infty}(2x-4)=-\infty[/tex]

Limit of function does not exits, so function have not horizontal asymptote.

B.[tex]f(x)=2(3^x)+4[/tex]

[tex]\lim_{x\rightarrow \infty}(2(3^x)+4)=\infty[/tex]

[tex]3^{\infty}=\infty [/tex]

[tex]\lim_{x\rightarrow -\infty}(2(3^x)+4)=4[/tex]

Because [tex]3^{-\infty}=0[/tex]

Hence, function have horizontal asymptote at 4.

C.[tex]f(x)=-3x+4[/tex]

[tex]\lim_{x\rightarrow \infty}(-3x+4)=\infty[/tex]

[tex]\lim_{x\rightarrow -\infty}(-3x+4)=-\infty[/tex]

Hence, function have not horizontal asymptote.

D.[tex]f(x)=3(2^x)-4[/tex]

[tex]\lim_{x\rightarrow \infty}(3(2^x)-4)=\infty[/tex]

Because [tex]2^{\infty}=\infty[/tex]

[tex]\lim_{x\rightarrow -\infty}(3(2^x)-4)=-4[/tex]

[tex]2^{-\infty}=0[/tex]

Hence, function have horizontal asymptote at -4.

Therefore, option B is true.