MATHEMATICS COLLEGE

If EN=16 and BN=20 what is the scale factor of the dilation?

Answers

Answer 1
Answer:

The scale factor of the dilation is approximately 1.25.

To find the scale factor of the dilation, we need to compare the corresponding side lengths of the original figure and the dilated figure.

Let's consider the two corresponding side lengths:

Original side: EN = 16 units

Dilated side: BN = 20 units

The scale factor (k) of the dilation is the ratio of the corresponding side lengths in the dilated figure to the original figure. It can be calculated using the formula:

Scale factor (k) = Dilated side length / Original side length

Substituting the given values:

k = 20 / 16 ≈ 1.25

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The numbers of words defined on randomly selected pages from a dictionary are shown below. Find the mean, median, mode of the listed numbers. 30 31 64 59 57 33 54 77 56 41 What is the mean? Select the correct choice below and ,if necessary ,fill in the answer box within your choice.(around to one decimal place as needed)

Answers

Answer:

30 31 64 59 58 33 54 77 56 41 (arrange it)

30 31 33 41 54 56 58 59 64 77 (done!)

Mean: Find the number in the middle (54+56)/2= 110/2 = 55

Mode: None

Mean: (30+31+33+41+54+56+58+59+64+77)/10=503/10= 50,3

Zachary is buying 4 tires for his car. The table shows the prices and the advertised sales for the same type of tire at 4 tire stores.Based on the advertised sales, at which store will Zachary get the lowest price on 4 tires?​

Answers

Answer:

Zachary is buying 4 tires for his car. The table shows the prices and the advertised sales for the same type of tire at 4 tire stores.

Step-by-step explanation:

At store R, we get the fourth tire for free, if we buy three tires.

Each tire costs $150, so the cost of 3 tires is .

So at store R, we get 4 tires for $450.

At store S, if we buy 4 tires, we pay $70 off for each tire.

Each tire costs $200, so the cost of 4 tires is

If we get $70 off for each tire, we get  for 4 tires.

So at store S, we get 4 tires for

So at store S, we get 4 tires for $520.

Step 2:

At store T, if we buy 4 tires, we pay $200 off the total price.

Each tire costs $175, so the cost of 4 tires is

If we get $200 off the total price, we get  for 4 tires.

So at store T, we get 4 tires for $500.

At store V, if we buy 4 tires, we get 10% of the total price.

Each tire costs $130, so the cost of 4 tires is

If we get 10% off the total price, we get  for 4 tires.

So at store V, we get 4 tires for $468.

Step 3:

So we get 4 tires at store R for $450, we get 4 tires at store S for $520. We get 4 tires at store T for $500 and we get 4 tires at store V for $468.

So Isaiah will get the lowest price on 4 tires at store R.

At store R, we get the fourth tire for free, if we buy three tires.

Each tire costs $150, so the cost of 3 tires is .

So at store R, we get 4 tires for $450.

At store S, if we buy 4 tires, we pay $70 off for each tire.

Each tire costs $200, so the cost of 4 tires is

If we get $70 off for each tire, we get  for 4 tires.

So at store S, we get 4 tires for

So at store S, we get 4 tires for $520.

Step 2:

At store T, if we buy 4 tires, we pay $200 off the total price.

Each tire costs $175, so the cost of 4 tires is

If we get $200 off the total price, we get  for 4 tires.

So at store T, we get 4 tires for $500.

At store V, if we buy 4 tires, we get 10% of the total price.

Each tire costs $130, so the cost of 4 tires is

If we get 10% off the total price, we get  for 4 tires.

So at store V, we get 4 tires for $468.

Step 3:

So we get 4 tires at store R for $450, we get 4 tires at store S for $520. We get 4 tires at store T for $500 and we get 4 tires at store V for $468.

So Isaiah will get the lowest price on 4 tires at store R.

On a map, 2.5 inches represents 300 miles. How many miles are represented by 6 inches?А .05 miles
00
.40 miles
С
600 miles
D
720 miles

Answers

A map of 720 miles represented by 6 inches.

It is given that 2.5 inches represent 300 miles.

It is required to find the miles represented by 6 inches.

How many miles are represented by 6 inches?

First we have to find how many miles we get in one inch. Then we find in how many miles does 6 inches have.

In  2.5 inches, the map represents 300 miles.

In 1 inch, a map represents 300/2.5miles which are equal to 120 miles.

So, in 6 inches, a map represents (120×6) miles which are equal to 720 miles.

Thus in 6 inches, a map represents (120×6)miles which are equal to 720 miles.

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Answer:

D. 720 miles

Step-by-step explanation:

First, we know that 2.5 inches represents 300 miles. This means that we have to find out how much 1 inch represents in miles. So, we take 300/2.5. This results in 120. So, 1 inch represents 120 miles. Then, we take 6*120 which gets us 720 miles.

Are ray AB and ray BA same? why
​

Answers

Answer:

A length of a ray cannot be measured therefore it's refferd to as infinite. same

Suppose f(x,y)=xy, P=(−4,−4) and v=2i+3j. A. Find the gradient of f. ∇f= i+ j Note: Your answers should be expressions of x and y; e.g. "3x - 4y" B. Find the gradient of f at the point P. (∇f)(P)= i+ j Note: Your answers should be numbers C. Find the directional derivative of f at P in the direction of v. Duf= Note: Your answer should be a number D. Find the maximum rate of change of f at P. Note: Your answer should be a number E. Find the (unit) direction vector in which the maximum rate of change occurs at P. u= i+ j Note: Your answers should be numbers

Answers

Answers:

  • Gradient of f:    \nabla f = y\hat{i} + x\hat{j}
  • Gradient of f at point p: \nabla f = -4\hat{i} -4\hat{j}
  • Directional derivative of f and P in direction of v: \nabla f(P)v = -20\n
  • The maximum rate of change of f at P:  | \nabla f(P)| = 4√(2)
  • The (unit) direction vector in which the maximum rate of change occurs at P is:  v = -(1)/(√(2))\hat{i}-(1)/(√(2))\hat{j}

Step by step solutions:

Given that:

  • f(x,y) = xy
  • P = (-4,4)\n
  • v = 2i + 3j

A: Gradient of f

\nabla f = ((\partial f)/(\partial x), (\partial f)/(\partial y)) = (y,x) = y\hat{i} + x\hat{j}

B: Gradient of f at point P:

Just put the coordinates of p in above formula:

\nabla f = -4\hat{i} -4\hat{j}

C: The directional derivative of f and P in direction of v:

The directional derivative is found by dot product of \nabla f(P) \: \rm and \: \rm v:

\nabla f(P)v = [-4,4][2,3]^T = -20\n

D: The maximum rate of change of f at P is calculated by evaluating the magnitude of gradient vector at P:

| \nabla f(P)| = √((-4)^2 + (-4)^2) = 4√(2)

E: The (unit) direction vector in which the maximum rate of change occurs at P is:

v = ((-4)/(4√(2)), (-4)/(4√(2))) = -(1)/(√(2))\hat{i}-(1)/(√(2))\hat{j}

That vector v is the needed unit vector in this case.

we divided by 4√(2) to make that vector as of unit length.

Learn more about vectors here:

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Answer:

a) The gradient of a function is the vector of partial derivatives. Then

\nabla f=((\partial f)/(\partial x), (\partial f)/(\partial y))=(y,x)=y\hat{i} + x\hat{j}

b) It's enough evaluate P in the gradient.

\nabla f(P)=(-4,-4)=-4\hat{i} - 4 \hat{j}

c) The directional derivative of f at P in direction of V is the dot produtc of \nabla f(P) and v.

\nabla f(P) v=(-4,-4)\left[\begin{array}{ccc}2\n3\end{array}\right] =(-4)2+(-4)3=-20

d) The maximum rate of change of f at P is the magnitude of the gradient vector at P.

||\nabla f(P)||=√((-4)^2+(-4)^2)=√(32)=4√(2)

e) The maximum rate of change occurs in the direction of the gradient. Then

v=(1)/(4√(2))(-4,-4)=((-1)/(√(2)),(-1)/(√(2)))= (-1)/(√(2))\hat{i}-(1)/(√(2))\hat{j}

is the direction vector in which the maximum rate of change occurs at P.

3+ 6 x{( 15 +9)=3-2}. Rajah got 49 while Obet got 39. Whose answer was correct? Prove your answer.asap i need it pls i need solution​

Answers

Answer:

  • 39, Obet is right

Step-by-step explanation:

  • I guess the = should be ÷ or else it doesn't make sense.

Simplify in steps considering the hierarchy of operations:

  • 3 + 6 × {(15 + 9) ÷ 3 - 2} =                  Parenthesis
  • 3 + 6 × {24 ÷ 3 - 2} =                         Parenthesis, division
  • 3 + 6 × {8 - 2} =                                 Parenthesis, subtraction
  • 3 + 6 × 6 =                                         Multiplication
  • 3 + 36 =                                             Addition
  • 39
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