Describe the transformations that would map the graph
of f(x) = x^2 + 1 to the graph of g(x) = (x − 3)^2 − 2.

if triangle ABC is translated 5 units down, the image's coordinates are A′(1, 7), B′(9, 7), and C′(5, 3).

The x and y coordinates of each of a triangle's vertices must be added to or subtracted from to translate the triangle on a coordinate plane.

Triangle ABC must be translated five units lower in this situation. Thus, we must deduct 5 from the y coordinates of each of its vertices.

A(1, -2) changes to A' (1, -7) B(9, -2) changes to B' (9, -7) C(5, 2) changes to C' (5, -3)

As a result, if triangle ABC is translated 5 units down, the image's coordinates are A′(1, 7), B′(9, 7), and C′(5, 3).

learn more about coordinates

https://brainly.com/question/16634867

#SPJ1

Answer:

it should be B but I could be wrong

Step-by-step explanation:

B

Answer:

[tex]f(x)=-3x^2+5[/tex]

[tex]f(2) = -7[/tex]

Step-by-step explanation:

Given equation:

[tex]y+3x^2=5[/tex]

To solve the equation for y in terms of x, simply subtract 3x² from both sides of the equation:

[tex]\implies y+3x^2-3x^2=5-3x^2[/tex]

[tex]\implies y=-3x^2+5[/tex]

Replace y with the function notation f(x):

[tex]f(x)=-3x^2+5[/tex]

Finally, to find the value of f(2), substitute x = 2 into the function:

[tex]\begin{aligned}\implies f(2)&=-3(2)^2+5\\&=-3(4)+5\\&=-12+5\\&=-7\end{aligned}[/tex]

Answer:

Step-by-step explanation:

To find:-

Answer:-

We are here a given a equation, with some steps to follow, in order to find out the value of [tex]f(2)[/tex].

Step 1 :- Solve the equation in terms of y ,

The given equation to us is,

[tex]\longrightarrow y + 3x^2 = 5\\[/tex]

To solve for y , we need to transpose 3x² from LHS to RHS , by doing this , the sign changes from positive to neagative .

[tex]\longrightarrow y = 5 - 3x^2 \\[/tex]

Step 2 :- Replace y with function notation [tex]f(x)[/tex]

Just simply replace y here with f(x) as ,

[tex]\longrightarrow f(x) = 5 - 3x^2\\[/tex]

Step 3 :- Find f(2) .

To calculate the value of f(2) , we need to put x = 2 , in the above equation as ,

[tex]\longrightarrow f(2) = 5 - 3(2)^2\\[/tex]

Simplify,

[tex]\longrightarrow f(2) = 5 - 3(4)\\[/tex]

[tex]\longrightarrow f(2) = 5 - 12\\[/tex]

[tex]\longrightarrow \boxed{ \boldsymbol{f(2) = -7 }} \\[/tex]

Hence the required answer is -7 .

Answer: 98 cm²

Step-by-step explanation:

When a cartographer enlarges a map with a scale factor, both the length and the width are multiplied by the scale factor. In this case, the scale factor is 3.5.

Original dimensions of Colorado on the map:

Length: 4 cm

Width: 2 cm

Enlarged dimensions using the scale factor of 3.5:

Length: 4 cm × 3.5 = 14 cm

Width: 2 cm × 3.5 = 7 cm

To find the area of the enlarged map, multiply the enlarged length and width:

Area = Length × Width

Area = 14 cm × 7 cm

Area = 98 cm²

The area of the enlarged map is 98 cm².

Answer: a = -2

Step-by-step explanation:

8a = -12 + 2a

8a - 2a = -12
6a = -12
a = -12/6

a = -2

The BMI​ of a person whose weight is 176 lb and whose height is 77 inches is 21.

First, let's use the given information to find the constant of proportionality in the BMI formula:

BMI = k × (weight in pounds) / (height in inches)²

When the 6-foot-tall person weighing 177 lb has a BMI of 24, we can plug in the values and solve for k:

24 = k ₓ 177 / (72²)

k = 24 ₓ (72²) / 177

k ≈ 9.94

Now we can use this value of k to find the BMI of the person whose weight is 176 lb and whose height is 77 in:

BMI ≈ 21

BMI = 9.94 ₓ 176 / (77²)

Therefore, the BMI (to the nearest whole number) of the person is 21, which falls within the healthy weight range of 19 to 25.

To know more about BMI visit:

https://brainly.com/question/18697844?

#SPJ1

Answer: (6,-5)

Step-by-step explanation:

The equations that can be used to solve for y in the given situation are:
(A) y(y + 5) = 750

(B) y² – 5y = 750

(D) y(y – 5) + 750 = 0

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°).

A rectangle has equal and parallel opposite sides.

A rectangle has two dimensions—length and width—because it is a two-dimensional form.

The rectangle's longer side is its length, while its shorter side is its breadth.

So, the area formula of the rectangle:

750 = l * w

750 = x * (x-5)

750 = x² - 5x

x² - 5x - 750 = 0

Equations in the options that are similar:

(A) y(y + 5) = 750

(B) y² – 5y = 750

(D) y(y – 5) + 750 = 0

Therefore, the equations that can be used to solve for y in the given situation are:
(A) y(y + 5) = 750

(B) y² – 5y = 750

(D) y(y – 5) + 750 = 0

Know more about rectangles here:

https://brainly.com/question/2607596

#SPJ1

Correct question:

The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options.

NEED ASAP

Answer choices:

a. y(y + 5) = 750

b. y2 – 5y = 750

c. 750 – y(y – 5) = 0

d. y(y – 5) + 750 = 0

e. (y + 25)(y – 30) = 0

Answer:

Step-by-step explanation:

Answer: 6.3 per bag

Step-by-step explanation:

31.50 divided by 5 is 6.3!!!!

Answer: 6.3

Step-by-step explanation:

Divide 31.50 with 5

[tex]5\sqrt{31.50}[/tex]

5 goes into 3 0 times so you do 31/5. You get 6 with 1 as the remainder since 6x5 is 30. Now you do 15/5 which is 3. You get 63 but you have to add the decimal between the 6 and 3 so you will get 6.3. Hope this helped.

The correct three options are:

Nathan rolled a number cube and recorded the results in a table.

The number cube has six sides, numbered 1 through 6.

The number 4 was rolled more frequently than any other number.

Nathan rolled a number cube and recorded the results in a table.

The number cube has six sides, numbered 1 through 6.

Nathan rolled the number cube a total of 90 times.

The number 4 was rolled more frequently than any other number.

The number 2 was rolled the least frequently of all the numbers.

The total number of rolls for odd numbers is greater than the total number of rolls for even numbers.

The correct statements are:

Nathan rolled a number cube and recorded the results in a table.

The number cube has six sides, numbered 1 through 6.

The number 4 was rolled more frequently than any other number.

To know more about cube visit:

https://brainly.com/question/28134860?

#SPJ1

Answer:

see below

Step-by-step explanation:

The equation y - y₁ = m(x − x₁)

1. y - 7 = -4(x - -3)

y - 7 = -4(x + 3)

y = -4x - 12 + 7

y = -4x - 5

2. y - y₁ = m(x − x₁)

9 - -3 = m(8 - 4)

12 = 4m

m = 12/4 = 3

y = mx + b

-3 = 3(4) + b

b = - 3 - 12

b = -15

y = 3x - 15

Answer:

Step-by-step explanation:

it’s equals 0 I think

Answer:

4)  ∠1 and ∠2,  ∠2 and ∠3

5)  ∠1 and ∠3

6)  x = 10

Step-by-step explanation:

Adjacent angles are two angles that share a common vertex and a common side, but do not overlap.

Therefore, the pairs of adjacent angles in the given diagram are:

Vertical angles are pairs of non-adjacent angles that are formed when two lines intersect.  Vertical angles are congruent,

Therefore, the pair of vertical angles in the given diagram are:

As ∠1 and ∠3 are the same measure:

⇒ m∠1 = m∠3

⇒ (9x)° = 90°

⇒ 9x = 90

⇒ 9x ÷ 9 = 90 ÷ 9

⇒ x = 10

Therefore, the value of x is 10.

Answer:

4)  ∠1 and ∠2,  ∠2 and ∠3.

5)  ∠1 and ∠3.

6)  x = 10.

Step-by-step explanation:

Explanations are given in attachment!

Answer:

we need to add the money Andy earned to the negative balance he had. So, we have:

-$45 + $30 + $25 = $10

Therefore, Andy now has $10 in his checking account.

Answer:

Andy now has $10 in his checking account.

Step-by-step explanation:

Andy starts the week with -$45 in his checking account. When he gets paid $30 for mowing the grass and $25 for vacuuming the house, his total earnings for the week are:

$30 + $25 = $55

To find out how much money he now has in his checking account, we need to add his earnings to his starting balance of -$45. Adding a negative number is the same as subtracting a positive number, so we can write this as:

-$45 + $55 = $10

Therefore, Andy now has $10 in his checking account.

The description of the incident is shown below

One incident that shows how selection works in the process of perception is when you are at a party and you hear your name being mentioned in a conversation across the room. In this situation, your attention is immediately drawn to the conversation, and you focus on it while filtering out other sounds and distractions around you.

This is an example of selective attention, where you choose to focus on a particular stimulus and ignore others.

As for an example of a stereotype that I have, it is that all people who live in a certain region or country behave in a particular way.

For instance, I may have the stereotype that people from a particular country are loud and aggressive.

Read more about selection and perception at

https://brainly.com/question/14314991

#SPJ1

Answer:

Step-by-step explanation:

Just divide the total shape into three shapes one rectangle and two triangles and then calculate the area

Hope this helps: )

Answer:

in the image

Step-by-step explanation:

using the arithmetic formula

a = ao + d(n-1)

we can find the sum of this formula added up 5 times

Answer:

0.5625

Step-by-step explanation:

Rectangle, semi circle, semi circle

Perimeter: 60.8

Area: 64.2

In mathematics, the two key characteristics of two-dimensional forms are area and perimeter. The difference between area and perimeter is how much room each type of shape takes up.

Mathematical concepts like area and perimeter are crucial because they are applied to daily living. Any size and form, whether regular or irregular, can use this. Each design has a unique area and perimeter calculation. Forms like triangles, squares, rectangles, circles, spheres, etc. should be known to you. Here, the boundaries and surfaces of all forms are explained.

perimeter= 60.8

each of the three shapes' perimeters separately, then sum them all up to get 60.8.

area= 64.2

Calculate the area of each of the three shapes separately, then sum them all up to get 64.2.

To know more about Rectangle, visit:

https://brainly.com/question/25292087

#SPJ1

The complete question attached below,

The required size and perimeter of the Area are respectively 27.42 and 64.26 square units.

A shape's perimeter is its circumference. How are perimeters determined? By adding the lengths of each side of a shape, the border may be obtained.

A shape comprised of two circles and a rectangle has been provided.

the size of a circle = 12 - 6 = 6

then radius = 3 units

Perimeter = 3+3+3+3+3+3+π(3)

= 18 + 3.14(3)

= 18 + 9.42

= 27.42 units

and

Area = area of rectangle + area of two half circles

= 12(3) + π(3)²

= 36 + 28.26

= 64.26 sq units.

Therefore, the shape's needed area and perimeter are respectively 27.42 and 64.26 square units.

To know more about Area, visit:

brainly.com/question/2254372

#SPJ1

A) The FPCF for this sample is 0.899. B) The sample size is about 12% of the population size, which is relatively large.

A) The FPCF (Finite Population Correction Factor) is used to adjust for the impact of a finite population on the sampling distribution. The formula for the FPCF is:

FPCF = [tex]\sqrt{((N-n)/(N-1))}[/tex]

where N: size of the population and n: size of the sample.

In this case, the population size is N = 199, and the sample size is n = 24. Therefore, the FPCF can be calculated as follows:

FPCF = [tex]\sqrt{((199-24)/(199-1))}[/tex] = 0.899

So, the FPCF for this sample is 0.899.

B) In general, a population can be considered effectively infinite when the sample size is no more than 5-10% of the population size. In this case, the sample size is n = 24, and the population size is N = 199. Therefore, the sample size is about 12% of the population size, which is relatively large.

Learn more about fpcf here:

https://brainly.com/question/10098164

#SPJ1

Answer:

yes

Step-by-step explanation:

john has 34 marbles

Answer:

38/15

Step-by-step explanation:

4 1/5 - 5/3

4 1/5 = 21/5

21/5 - 5/3 = 63/15 - 25/15 = 38/15

So, the answer is 38/15

The tax rate of a house valued at $115,000 with a property tax of $1265 is 110%. or $110 per $1,000 of property value.

The property tax is the levy imposed on the assessed value of the property of an individual or corporation.

Property tax is usually levied as a percentage of the assessed value.

Property tax = $1265

House value - $115,000

Tax rate = 110% [tex](\$1265\div\$115000 \times 100)[/tex]

Thus, the tax rate of a house valued at $115,000 with a property tax of $115,000 is 110%. or $110 per $1,000 of property value.

Learn more about property tax at

https://brainly.com/question/5428406

Answer:

The answer is 6x + 2

Step-by-step explanation

I did all the work and I passed on this test so i know this is the answer.

The calculated key features of the quadratic functions 1 to 6 are listed below

Function 1: y = 1/2(x + 4)(x - 2)

Expand

y = x^2/2 + x - 4

From the function, we have

a = 1/2 (coefficient of x^2 term)

p = -b/2a (x-coordinate of the vertex)

p = -(1)/2(1/2)

p = -1

q = f(p) (y-coordinate of the vertex)

q = 1/2(1 + 4)(1 - 2)

q = -5/2

From the function, we have

x-intercepts = (-4, 0) and (2, 0)

This also means that the axis of symmetry is

x = -1

The quadratic function opens up because the coefficient of the x^2 term is positive.

Next, we have

Vertex = (-1, -5/2)

For the y-intercept, we have

y-intercept = f(0)

y-intercept = 1/2(0 + 4)(0 - 2)

y-intercept = -4

Slope to a point one unit from the vertex can be found by taking the derivative of the function:

f(x) = x^2/2 + x - 4

f'(x) = x + 1

At x = -2 (one unit to the left of the vertex), the slope is -1

i.e. f'(-2) = -2 + 1 = -1

At x = 0 (one unit to the right of the vertex), the slope is 1.

i.e. f'(0) = 0 + 1 = 1

When the above steps is repeated for the remaining functions, we have the following results:

Function 2: y = 1/2x(x - 8)

The features are:

Function 3: y = (x + 2)(x - 2)

The features are:

Function 4: y = -1/3(x + 1)(x - 5)

The features are:

Function 5: y = 4(x + 2)(x + 1)

The features are:

Function 6: y = -(x - 3)(x - 3)

The features are:

Read more about quadratic functions at

https://brainly.com/question/30660734

#SPJ1

Answer:

13

Step-by-step explanation:

Student: 80 * 55% = 44

Adult: 50 * 98% = 49

49-44=5

Answer: Algebra Examples

Logarithm base 4 of 4 is 1.

Step-by-step explanation:

unity

The value of log 4 to the base 4 is equal to unity. The Antilogarithm of the logarithmic value of 4 is equal to 4.

[tex] \angle3 \: and \: \angle4 [/tex] are complementary.

What is Complementary angle?

If sum of two angles is 90° then we can say that those angles are complementary.

For example, if [tex] \angle \: a + \angle \: b = {90}^{o} [/tex] then angle a and angle b are complementary.

Here are some examples of complementary angles:

Here given,

[tex] \angle1 \: and \angle2[/tex] are complimentary.

So,

[tex] \angle1 + \angle2 = {90}^{o} [/tex]

It is clear that [tex] \angle1, \angle2, \angle3, \angle4[/tex] are making a straight angle.

So, we can write,

[tex] \angle1 + \angle2 + \angle3 + \angle4 = {180}^{o} \\ {90}^{o} + \angle3 + \angle4 = {180}^{o} \\ \angle3 + \angle4 = {180}^{o} - {90}^{o} \\ \angle3 + \angle4 = {90}^{o} [/tex]

Here sum of angle 3 and angle 4 is 90°.

According to definition angle 3 and angle 4 are complimentary angles.

Learn more about angles:

https://brainly.com/question/30147425

#SPJ1