if f(x)=x^2 - 12, solve for f (x+4)

Answer:

28 minutes

Step-by-step explanation:

Speed = distance / time

Your speed is 1 lawn / 57 minutes.  Your friend's speed is 1 lawn / 54 minutes.  Working together, your combined speed is:

1/57 + 1/54

So the time it takes working together is:

Speed = distance / time

1/57 + 1/54 = 1 / t

t = 27.7 minutes

Rounded to the nearest whole number, it takes 28 minutes.

The correct answer is C. you multiply the 16x5

Answer:B) 40 sq units

Step-by-step explanation:

use formula [tex]\frac{1}{2}[/tex] base × height

= (0.50)(16) × (5)

= 40 sq units

Answer:

64 in² (Answer B)

Step-by-step explanation:

Note that this rhombus is made up of a large upper triangle and a large lower triangle.  Each of these two triangles has base 2(8 in) (or 16 in) and height 4 in.

The area-of-a-triangle formula is

A = (1/2)(base)(height), which here is

A = (1/2)(16 in)(4 in) = 32 in².

Now double that, because we have an upper triangle of area 32 in² and a lower triangle of the same area 32 in².  So the total area of the rhombus is 64 in²

Answer:

V=2

Step-by-step explanation:

p=8/v

substitute p=4,

4=8/v

multiply both sides by v,

4(v)=8(v)/v

4v=8

divide 8 by 4,

v=2

Answer: choice c. 2 edge 2023

Step-by-step explanation:

Answer:

A bar graph

Step-by-step explanation:

A bar chart will give you the visual understanding of your data.It will clearly show the book with most number of pages and compare the books according to the number of pages.You can formart using different colors for each bar.

The answers are:

Part a: The money in the account is growing.

Part b: The rate of growth is 3%

Part c: The value 250 represents the starting amount of money.

To solve the problem, first, we must remember the structure of the exponential growth or decay function:

[tex]P(t)=StartAmount*(rate)^{t}[/tex]

Where,

- Start Amount, is the starting value or amount

- Rate, is the rate of growth or decay, we must consider the following conditions:

If the rate is greater than 1, the rate is a growth rate.

If the rate is lower than 1, the rate is a decay rate.

- t, is the time elapsed.

Therefore, we are given the following function:

[tex]f(x)=250(1.03)^{x}[/tex]

From the function we can see that:

- Since the rate is 1.03 and it's greater than 1, the money in the account is growing.

- From the function we already know that the rate of growth is equal to 1.03

The rate is calculated by the following formula:

[tex]Rate=1+percent(growth)[/tex]

- The value 250 represents the starting amount of money.

Hence, the answers are:

Part a: The money in the account is growing.

Part b: The rate of growth is 3%

Part c: The value 250 represents the starting amount of money.

Have a nice day!

The exponent represents

An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.

Given

The exponential function [tex]\rm f(x)=250(1.03)^x[/tex]

where x is the number of years.

Part A: The money in the account growing or decaying.

If the power increases the value of the function increases.Since the x can never be negative so it is growing.

Part B: The rate of growth or decay.

The rate of growth is the base of the exponent.

Since the base is 1.03, then the rate will be 1.03.

Part C: The value 250 represents.

250 represents the principal value that was invested initially.

A. The x can never be negative so it is growing.

B. The base is 1.03, then the rate will be 1.03.

C. 250 represents the principal value that was invested initially.

More about the exponent link is given below.

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Answer:

yeeeeeeeeeeeeeeeees

For this case we must find the inverse of the following function:

[tex]f (x) = (x-6) ^ 2 + 7[/tex]

For this we follow the steps below:

Replace f (x) with y:

[tex]y = (x-6) ^ 2 + 7[/tex]

We exchange the variables:

[tex]x = (y-6) ^ 2 + 7[/tex]

We solve the equation for "y", that is, we clear "y":

[tex](y-6) ^ 2 + 7 = x[/tex]

We subtract 7 on both sides of the equation:

[tex](y-6) ^ 2 = x-7[/tex]

We apply square root on both sides of the equation to eliminate the exponent:

[tex]y-6 = \sqrt {x-7}[/tex]

We add 6 to both sides of the equation:

[tex]y = \pm \sqrt {x-7} +6[/tex]

We change y by [tex]f ^ {- 1} (x):[/tex]

[tex]f ^ {- 1} (x) = \pm \sqrt {x-7} +6[/tex]

Answer;

[tex]f ^ {- 1} (x) = \pm \sqrt {x-7} +6[/tex]

If it is a inverse function.

Answer:

15

Step-by-step explanation:

Write a proportion:

60 cups / 12 gallons = x cups / 3 gallons

Cross multiply:

12x = 180

Divide:

x = 15

He should use 15 cups.

Jesse should use 15 cups of mushrooms to make 3 gallons of mushroom soup, based on the restaurant's recipe. Devon will be making 37.5 liters of soup for the party of 100 guests.

To solve Jesse's question about how many cups of mushrooms he should use to make 3 gallons of mushroom soup, we need to find the proportion between the amount used in the restaurant's recipe and the desired amount for Jesse's smaller batch.

The restaurant uses 60 cups of mushrooms to make 12 gallons of soup. To find out how many cups are needed for 1 gallon, we divide the number of cups by the number of gallons:

60 cups / 12 gallons = 5 cups per gallon

Jesse wants to make 3 gallons of soup. Multiplying the amount needed for one gallon by 3 gives us the answer:

5 cups/gallon × 3 gallons = 15 cups of mushrooms.

Devon, on the other hand, is preparing soup for a party. Calculating the total amount for 100 guests using 375 milliliters per person, we get:

375 milliliters/guest × 100 guests = 37500 milliliters.

Since 1 liter is equivalent to 1000 milliliters, we can convert the milliliters to liters:

37500 milliliters / 1000 = 37.5 liters of soup for 100 guests.

Answer:

Step-by-step explanation:

It's a parallelogram.

The formula of an area of a parallelogram:

[tex]A=bh[/tex]

b - base

h - height

We have

[tex]b=17\dfrac{1}{5}yd=17\dfrac{1\cdot2}{5\cdot2}yd=17\dfrac{2}{10}yd=17.2yd\\\\h=12\dfrac{1}{2}yd=12.5yd[/tex]

Substitute:

[tex]A=(17.2)(12.5)=215\ yd^2[/tex]

Answer:

r=25.6

Step-by-step explanation:

[tex]p=-4.8\\q=3.2\\\\r=-3.2p+q^2\\r=-3.2(-4.8)+(3.2)^2\\r=15.36+10.24\\r=25.6[/tex]

Answer: D. AE and BD intersect at point C.

Answer: A AND B

Step-by-step explanation:

Answer:

125 packages of chips.

Step-by-step explanation:

A vending machine sells chips at $0.55

And candy at $0.75

Last month, the vending machine yielded $170.00 with the sale of 260 items.

Let x be the number of chips sold and y be the number of candies sold.

$0.55x + $0.75y = $170.00

x + y = 260

Solving the above simultaneous equations by substitution;

x = 260 - y

Then,

0.55(260 - y) + 0.75y = 170

143 - 0.55y + 0.75y = 170

0.2y = 170 - 143 = 27

y = [tex]\frac{27}{0.2}[/tex] = 135

x = 260 - 135 = 125

So there were 125 packages of chips sold.

Answer:

Part a) The paint needed will be [tex]24\ pints[/tex]

Part b) The weight of the life sized statue  is [tex]896\ lb[/tex]

Step-by-step explanation:

step 1

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z----> the scale factor

x----> surface area of the life sized statue

y----> surface area of the smaller statue

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]z=4[/tex]

substitute

[tex]4^{2}=\frac{x}{y}[/tex]

[tex]x=16y[/tex]

The surface area of the life sized statue  is 16 times the surface area of the smaller statue

therefore

The paint needed will be

[tex]16(1.5)=24\ pints[/tex]

step 2

Find the weight of the life sized statue

we know that

If two figures are similar, then the ratio of its weights (or volumes) is equal to the scale factor elevated to the cube

Let

z----> the scale factor

x----> weight of the life sized statue

y----> weight of the smaller statue

[tex]z^{3}=\frac{x}{y}[/tex]

we have

[tex]z=4[/tex]

[tex]y=14\ lb[/tex]

substitute

[tex]4^{3}=\frac{x}{14}[/tex]

[tex]x=64(14)=896\ lb[/tex]

The life-size statue will need 96 pints of paint since its volume is 64 times larger than the smaller statue.

Step 1: Determine the volume ratio between the life-size statue and the smaller statue.

Since the dimensions of the life-size statue are four times those of the smaller statue, the volume ratio is [tex]\(4^3 = 64\)[/tex]. This means the life-size statue will have 64 times the volume of the smaller statue.

Step 2: Calculate the amount of paint needed for the life-size statue.

If 1.5 pints of paint are needed for the smaller statue, then the life-size statue will require [tex]\(1.5 \times 64 = 96\)[/tex] pints of paint.

Step 3: Write the final answer.

Therefore, 96 pints of paint will be needed to paint the life-sized statue.

Answer:

Step-by-step explanation:

A function has a root only if cuts the x axis .

If it cuts once it means it has one real root, if twice then two roots and so on .

Here in the graph of G(x) shown ,it never crosses the x axis so we can say that there is no real root of the given function G(x).

It means the option A which states G(x) has zero roots is correct.

progress prior to 1980. if n is an integer greater than two (n > 2)

Final answer:

Fermat's Last Theorem is an extension of the Pythagorean Theorem, with the latter being a special case where n=2 in the general form of equations proposed by Fermat.

Explanation:

The familiar theorem that Fermat's Last Theorem is an extension of is the Pythagorean Theorem. The Pythagorean Theorem, which states that in a right-angled triangle the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (a² + b² = c²), can be seen as the case n=2 in a series of equations of the form a⁴ + b⁴ ≠ c⁴ for any integer value of n greater than 2, which is what Fermat's Last Theorem addresses. The conviction behind mathematical postulates, as well as the certainty and consistency of mathematical proofs, contribute to the trust we place in mathematical theorems, just as repeated verification confirms theories in physics when the correct postulates are chosen.

[tex]255.35 \div 5 = 51.07 [/tex]

[tex]51.07 \times 2 = 102.14[/tex]

Answer:

102.14

Step-by-step explanation:

1/3

2 of the books are math books and there are 6 books. This is 2/6. Now, divide both sides of the fraction by 2 to simplify it. This gives you a final answer of 1/3.

Answer:

y=0

Step-by-step explanation:

For the x axis, the value of y is zero

y=0

The insurance company's payment is $1,680.00 and Bill's share of the charge is $670.00.

To calculate the insurance company's payment, we first need to determine the amount after the deductible is applied. Since the bill was $2,350.00 and the deductible is $250, we subtract the deductible from the bill: $2,350.00 - $250 = $2,100.00. The insurance company covers 80% of this amount, so we multiply $2,100.00 by 80%: $2,100.00 x 80% = $1,680.00. Therefore, the insurance company's payment is $1,680.00.

Bill's share of the charge is calculated by subtracting the insurance company's payment from the total bill: $2,350.00 - $1,680.00 = $670.00. Therefore, Bill's share of the charge is $670.00.

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Answer:

The answer is ± 5i

Let [tex]v[/tex] be the speed of train A, and let's set the origin in the initial position of train A. The equations of motion are

[tex]\begin{cases}s_A(t) = vt\\s_B(t) = -\dfrac{8}{7}vt+450\end{cases}[/tex]

where [tex]s_A,\ s_B[/tex] are the positions of trains A and B respectively, and t is the time in hours.

The two trains meet if and only if [tex]s_A=s_B[/tex], and we know that this happens after two hours, i.e. at [tex]t=2[/tex]

[tex]\begin{cases}s_A(2) = 2v\\s_B(2) = -\dfrac{16}{7}v+450\end{cases}\implies 2v = -\dfrac{16}{7}v+450[/tex]

Solving this equation for v we have

[tex]2v = -\dfrac{16}{7}v+450 \iff \dfrac{30}{7}v=450 \iff v=\dfrac{450\cdot 7}{30} = 105[/tex]

So, train A is travelling at 105 km/h. This implies that train B travels at

[tex]105\cdot \dfrac{8}{7} = 15\cdot 8=120 \text{ km/h}[/tex]

train A travels at 210 km/h and train B travels at 240 km/h.

The student's question involves finding the speeds of two trains moving towards each other when certain conditions are provided. We know that the two trains are 450 km apart and meet after 2 hours. Train B travels at 8/7 the speed of train A.

Let's denote the speed of train A as v km/h. Then, the speed of train B would be 8/7 * v km/h. Since they meet after 2 hours, we can add their distances to equal the total distance between them.

Speed of train A: v km/h
Speed of train B: 8/7 × v km/h
Total distance: 450 km
Time to meet: 2 hours

The total distance both trains cover can be expressed as:
(Speed of train A + Speed of train B) × Time = (v + 8/7 × v) × 2 hours

Since the sum of the two distances covered by the trains is the initial distance between them which is 450 km, we get:
(1 + 8/7)v * 2 = 450 km

We simplify this equation to find the value of v. The equation becomes:
15/7  v × 2 = 450 km
v = (450 × 7) / (15 × 2)
v = 210 km/h

Now, we find the speed of train B by multiplying the speed of train A by 8/7:
Speed of train B = 8/7 × 210 km/h = 240 km/h

Therefore, train A travels at 210 km/h and train B travels at 240 km/h.

Answer:

The function is a linear function

The function is translated 3 units to the left,then stretched vertically

by factor 2, then translated 5 units down

Step-by-step explanation:

* Lets revise some transformation

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

- If the function f(x) stretched vertically, then g(x) = k · f(x), where

 k > 1 (multiplying each of its y-coordinates by k)

- If the function f(x) compressed vertically, then g(x) = k · f(x), where

 0 < k < 1 (multiplying each of its y-coordinates by k)

* Now lets solve the problem

∵ f(x) = 2(x + 3) - 5

- The greatest power of the function is 1 (degree of the function)

∴ f(x) is linear function

- The parent function f(x) = x

∵ f(x) changed to f(x + 3)

∴ f(x) translated 3 units to the left

# Each x-coordinate of the points on the function subtracted by 3

∵ f(x + 3) changed to 2f(x + 3)

∵ 2 > 1

∴ f(x + 3) stretched vertically by factor 2 (k = 2)

# Each y-coordinate of the points on the function multiplied by 2

∵ 2f(x + 3) changed to 2f(x + 3) - 5

∴ 2f(x + 3) translated 5 units down

# Each y-coordinate of the points on the function subtracted by 5

Answer:

4

Step-by-step explanation:

In a 45-45-90 triangle, the length of the hypotenuse is √2 times the legs.

s√2 = 4√2

s = 4

Each leg is 4 units long.

Each length of the side of the triangle is 4 units long.

We have given that side is s and hypotenuse is 4root2.

and also the angle is 45-45-90degrees.

We have to determine the length of the sides

In a 45-45-90 triangle, the length of the hypotenuse is √2 times the legs.

45°−45°−90° triangle is a commonly encountered right triangle whose sides are in the proportion 1:1:√2 .

s√2 = 4√2

s = 4

Therefore each length of the side of the triangle is 4 units long.

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The recursive rule tells you that

[tex]t_2=t_1+3[/tex]

[tex]t_3=t_2+3=(t_1+3)+3=t_1+2\cdot3[/tex]

[tex]t_4=t_3+3=(t_1+2\cdot3)+3=t_1+3\cdot3[/tex]

and so on, with the general rule

[tex]t_n=t_1+(n-1)\cdot3[/tex]

Then with [tex]t_1=1[/tex], you have

[tex]t_n=1+3(n-1)\implies\boxed{t_n=3n-2}[/tex]

Answer:

0.525 %

Step-by-step explanation:

there is a total of 80 students and 42 received a A or B so 42/80 = 0.525

Hope this helps!

Answer:

The surface area is [tex]1,536\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The surface area is equal to

[tex]SA=B+PH[/tex]

where

B is the area of the ceiling

P is the perimeter of the base

H is the height of the walls

substitute the given values

[tex]SA=(20)(24)+2(20+24)(12)[/tex]

[tex]SA=480+1,056=1,536\ ft^{2}[/tex]

Mrs. Karabin will be painting a total of 1536 square feet in her garage. This includes 1056 square feet for the walls and 480 square feet for the ceiling.

To solve this, we need to calculate the surface area for the walls and ceiling of the garage. Because all sides of this garage are rectangular, we can find the area by multiplying the length by times width for each side.

For the walls: There are two walls that are 12 feet high and 24 feet long and two walls that are 12 feet high and 20 feet wide. So, we calculate (12x24)x2 + (12x20)x2 = 576 + 480 = 1056 square feet.

For the ceiling: The ceiling is 20 feet wide and 24 feet long, so we calculate 20x24 = 480 square feet.

Adding these together, Mrs. Karabin will be painting 1056 (for the walls) + 480 (for the ceiling) = 1536 square feet in total.

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Answer:

to the full amount

Step-by-step explanation: