If g(x) is the inverse of f(x) and f(x)=4x+12, what is g(x)?

g(x)=12x+4

g(x)=1/4x-12

g(x)=x-3

g(x)=1/4x-3

Answer:

[tex]y=\frac{1}{4p}x^{2}[/tex]

Step-by-step explanation:

∵ The directrix is y = -p

∵ The focus is (0 , p)

∵ (x , y) is a general point on the parabola

∵ The distance between (x , y) and the directrix = the distance

   between (x , y) and the focus

By using the rule of distance:

∵ (y - -p)² = (x - 0)² + (y - p)²

∴ (y + p)² = x² + (y - p)²

∴ y² + 2py + p² = x² + y² - 2py + p²

∴ 2py + 2py = x²

∴ 4py = x² ⇒ ÷ 4p in both sides

∴ [tex]y=\frac{1}{4p}x^{2}[/tex]

Answer:

x = 32/7, or 4 4/7 meals

Step-by-step explanation:

Write and solve an equation of ratios, as follows:

 7/8 lb           4 meals

------------        -------------

    1 lb                   x

x will be the number of meals necessary for the dog to eat 1 lb of food.

Cross-multiplying, (7/8)x = 4.

Multiplying both sides by 8/7 is an easy way to isolate x:

(8/7)(7/8)x = (8/7)(4)

or

              x = 32/7, or 4 4/7 meals

Answer:

The diagonal  is about 14 m

Step-by-step explanation:

A = s^2

98 = s^2

so

s = √98

diagonal c^2 = 98 + 98

c^2 = 196

c = √196

c  ≈ 14

Answer:

The diagonal  is about 14 m

Answer:

C= 14

Step-by-step explanation:

The side is the square root of the area

S × S = A

S = √98

The diagonal is the hypotenuse of a right triangle formed by the two sides so

a²  + b² = c²

Where C = the diagonal A = √98 , B = √98

so C²= (√98)² + (√98)²

This gives: C²= 98 + 98 or

C² = 196

√C² = √196

C= 14

Answer:

(0, 15) and (11, 48)

Step-by-step explanation:

Given the 2 equations

y = x² - 8x + 15 → (1)

y = 3x + 15 → (2)

Substitute y = x² - 8x + 15 into (2)

x² - 8x + 15 = 3x + 15 ( subtract 3x + 15 from both sides )

x² - 11x = 0 ← in standard form

x(x - 11) = 0 ← in factored form

Equate each factor to zero and solve for x

x = 0

x - 11 = 0 ⇒ x = 11

Substitute these values into (2) for corresponding values of y

x = 0 : y = 0 + 15 = 15 ⇒ (0, 15)

x = 11 : y = 33 + 15 = 48 ⇒ (11, 48)

Solutions are (0, 15), (11, 48)

Answer:   (5n - 8)(n² - 3)

Step-by-step explanation:

You can factor this using the Grouping Method (hint: rearrange the terms)

   5n³ - 8n² - 15n + 24

=  5n³ - 15n   -8n² +24

=  5n(n² - 3)   -8(n² - 3)

= (5n - 8)(n² - 3)

Answer:

80 is the volume

Step-by-step explanation:

l*b*h

5*2*8

80

L*W*H

8*5 = 40

40*2 = 80

The volume is 80 cm^3

Answer:

1000 square feet

Step-by-step explanation:

We are given that Jose is planning to spread fertilizer on his rectangular yard which has a length of 40 ft and width of 25 ft.

We need to find out the amount of fertilizer he needs.

We know that the formula of area of rectangle is given by: [tex]l \times w[/tex]

So substituting in the given values to get:

[tex]40 \times 25 = 1000[/tex] square feet

Answer:

1000 sqare feet

Step-by-step explanation:

LxW=A

40x25=1000

Answer:

Step-by-step explanation:

Objects that float on water have densities less than the density of water; those that do not float on water have densisties greater than the density of water:

Float on water:  d < 0.0361 lb/in³ (where d denotes denisity)

Do not float on water:  d > 0.0361 lb/in³

The densities of objects that float on water are lower than those of objects that don't float.

It is defined as the mass-to-volume ratio. The density indicates the object's density and is represented by the symbol. The density is measured in kilograms per cubic meter.

We have:

Water has a density of about 0.0361 pounds/cubic inch.

Let d be the density:

Float on water:  d < 0.0361 lb/in³

Do not float on water:  d > 0.0361 lb/in³

The densities of objects that float on water are lower than those of objects that don't, which have densities higher than those of water.

Thus, the densities of objects that float on water are lower than those of objects that don't float.

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Answer:

x : y = 2 : - 3

Step-by-step explanation:

given

[tex]\frac{2}{3}[/tex]  = [tex]\frac{x}{3x+y}[/tex] ( cross- multiply )

3x = 2(3x + y) ← distribute

3x = 6x + 2y ( subtract 6x from both sides )

- 3x = 2y ( divide both sides by y )

- 3[tex]\frac{x}{y}[/tex] = 2 ( divide both sides by - 3 )

[tex]\frac{x}{y}[/tex] = [tex]\frac{2}{-3}[/tex]

Answer:

In my opinion I would say Tax Dollars

Hope This Helps!     Have A Nice Day!!      

Whether public goods should be paid for through taxes or individual fees depends on various factors, including the nature of the good and one's income level. For many public goods and services, a combination of tax funding and user fees is used. The decision between the two is a matter of public policy and individual preference.

The decision on whether to pay for public goods through taxes or individual fees depends on various factors. In essence, this relates to the discussion on public provision versus personal pay-per-use. Some public goods, like parks, are free to use, but the government charges for certain services, such as parking or reserving picnic areas. This is a mixture of public provision at no charge along with fees for some purposes.

On the other hand, taxes are paid by most working people and by consumers when they buy goods and services. These taxes fund public services like roads, bridges, schools, and public safety functions. Thus, some may prefer public goods to be funded through taxes so everyone contributes to these community-supporting services.

Nonetheless, there are also 'toll goods', like cable TV and private schools, that are open to everyone but require users to pay a fee. The choice between taxes versus individual fees can also depend on one's income level, as those with more discretionary income might prefer pay-per-use to avoid potential higher taxes.

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Answer:

The answer is $7.50.

Step-by-step explanation:

First you have to find the price of the souvenirs which were $2.25, just by doing each common price. Then you just do the answer you got divided by two.

The one ticket for this basketball game is $ 7.50, and one ticket for a souvenir is $2.25.

It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.

If in the linear equation one variable is present then the equation is known as the linear equation in one variable.

Let's suppose the price of the one ticket = $x

And the price of the one souvenir = $y

We have:

2x + y = 17.25 ....(1)

5x + 2y = 42.00 ....(2)  (from the quetion)

From the equation (1):

y = 17.25 - 2x

Put the value of y in the equation (2), we get:

5x +2(17.25 -2x) = 42

5x + 34.5 - 4x = 42

x = 42 - 34.5

x = $ 7.50

and y = 17.25 - 2x ⇒ 17.25 - 2(7.5) ⇒ $2.25

Thus, the one ticket for this basketball game is $ 7.50, and one ticket for a souvenir is $2.25.

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Answer:

2, 29

Step-by-step explanation:

The prime numbers are 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89, and 97.

Check the picture below.

so, the reference angle, will be the angle made by it with the x-axis, namely 75°.

Step-by-step explanation:

Divide the circumference by pi to get diameter, which is 14. Divide 14 by 2 for the radius, which is 7. Now square the radius to get 49, and multiply by pi for the area.

Area is 49pi.

The area of the circle in terms of π with a circumference of 14π is 49π units².

Given a circle.

Also, given that:

Circumference of the circle = 14π

It is required to find the area of the circle.

It is known that:

Circumference of a circle is:

C = 2πr, where r is the radius.

So, here,

2πr = 14π

2r = 14

r = 7

So, the radius of the circle is 7.

So, the area of the circle is:

A = πr²

  = π(7)²

  = 49π

Hence, the area is 49π.

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Here is your answer 651 2/12

hope this helps.

Please mark me as brainliest.

Answer:

651  2/12

Step-by-step explanation:

Answer:

angle 2 is 43 as the opposite side of the angle is always equal angle 1 and 3 are:

step 1

43+43=86

step 2

360-86=274

step 3

274÷4=68.5

we subtracted 86 with 360 because 360 is the sum of all the angles we then divided  the answer by 2 as we were suppose to find two angles angle 1 and 3 are opposite angles so they both will be same

      hope this information helps u :)

Answer:

see explanation

Step-by-step explanation:

∠1 and 43° form a straight angle = 180°, hence

∠1 = 180° - 43° = 137°

∠2 = 43° ( vertical to 43° )

∠3 = 137° ( vertical to ∠1 )

2²=4 2×2

3²=9 3×3

4²=16 4×4

5²=25 5×5

6²=36 6×6

7²=49 7×7

8²=64 8×8

9²=81 9×9

10²=100 10×10

11²=121 11×11

Answer:

2²=4 2×2

3²=9 3×3

4²=16 4×4

5²=25 5×5

6²=36 6×6

7²=49 7×7

8²=64 8×8

9²=81 9×9

10²=100 10×10

11²=121 11×11

525

Because the nearest tenth is the number after the decimal point but then nine rounds up. If you don’t want the nine rounded up leave it as 524.9

In given number 524.95, place value of 9 is tenth. So, the nearest ten is 525.0

The place value is the position of each digit in a number.

The nearest tenth is the number after the decimal point but then nine rounds up. If you don’t want the nine rounded up leave it as 524.9

524.9 = 525.0

Therefore, the answer is 525.0

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Answer:

A

Step-by-step explanation:

To calculate the slope m use the slope formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 3, - 7) and (x₂, y₂ ) = (9, 1) ← 2 points on the line

m = [tex]\frac{1+7}{9+3}[/tex] = [tex]\frac{8}{12}[/tex] = [tex]\frac{2}{3}[/tex]

Answer: 2:1

Step-by-step explanation:

Answer:

The answer is 195 :)))

Step-by-step explanation:

the measure is 140, I basically summed all of the angles of a polygon of “n”, which is 7, then I did 7-2 times 180 (900) so I can finally add up all of your measurements

The seventh angle of the given Heptagon is 140 degrees.

A heptagon is a polygon that has seven sides. It is a closed figure having 7 vertices. A heptagon is also sometimes called Septagon.

Given, six angles of a heptagon measure 107, 139, 131, 110, 145. and 128.

Since, Sum of all angles of Heptagon is 900°

Let "x" be the seventh angle of Heptagon

thus,

107 + 139 + 131  + 110 + 145 + 128 + x = 900

760 + x = 900

x = 140

Therefore, The seventh angle of the given Heptagon is 140 degrees.

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So y = 1/3x + 7, therefore the gradient is 1/3 and the y-intercept is 7.

Answer:

54

Step-by-step explanation:

add all of the numbers then subtract from 100

Answer:

y = 1/2 x

Step-by-step explanation:

slope = 1/2 and y-intercept = 0

so equation

y = 1/2 x

1 Use Integration by Parts on \int \sec^{3}x \, dx∫sec

​3

​​ xdx.

Let u=\sec{x}u=secx, dv=\sec^{2}xdv=sec

​2

​​ x, du=\sec{x}\tan{x} \, dxdu=secxtanxdx, v=\tan{x}v=tanx

2 Substitute the above into uv-\int v \, duuv−∫vdu.

\sec{x}\tan{x}-\int \tan^{2}x\sec{x} \, dxsecxtanx−∫tan

​2

​​ xsecxdx

3 Use Pythagorean Identities: \tan^{2}x=\sec^{2}x-1tan

​2

​​ x=sec

​2

​​ x−1.

\sec{x}\tan{x}-\int (\sec^{2}x-1)\sec{x} \, dxsecxtanx−∫(sec

​2

​​ x−1)secxdx

4 Expand (\sec^{2}x-1)\sec{x}(sec

​2

​​ x−1)secx.

\sec{x}\tan{x}-\int \sec^{3}x-\sec{x} \, dxsecxtanx−∫sec

​3

​​ x−secxdx

5 Use Sum Rule: \int f(x)+g(x) \, dx=\int f(x) \, dx+\int g(x) \, dx∫f(x)+g(x)dx=∫f(x)dx+∫g(x)dx.

\sec{x}\tan{x}-\int \sec^{3}x \, dx+\int \sec{x} \, dxsecxtanx−∫sec

​3

​​ xdx+∫secxdx

6 Set it as equal to the original integral \int \sec^{3}x \, dx∫sec

​3

​​ xdx.

\int \sec^{3}x \, dx=\sec{x}\tan{x}-\int \sec^{3}x \, dx+\int \sec{x} \, dx∫sec

​3

​​ xdx=secxtanx−∫sec

​3

​​ xdx+∫secxdx

7 Add \int \sec^{3}x \, dx∫sec

​3

​​ xdx to both sides.

\int \sec^{3}x \, dx+\int \sec^{3}x \, dx=\sec{x}\tan{x}+\int \sec{x} \, dx∫sec

​3

​​ xdx+∫sec

​3

​​ xdx=secxtanx+∫secxdx

8 Simplify \int \sec^{3}x \, dx+\int \sec^{3}x \, dx∫sec

​3

​​ xdx+∫sec

​3

​​ xdx to 2\int \sec^{3}x \, dx2∫sec

​3

​​ xdx.

2\int \sec^{3}x \, dx=\sec{x}\tan{x}+\int \sec{x} \, dx2∫sec

​3

​​ xdx=secxtanx+∫secxdx

9 Divide both sides by 22.

\int \sec^{3}x \, dx=\frac{\sec{x}\tan{x}+\int \sec{x} \, dx}{2}∫sec

​3

​​ xdx=

​2

​

​secxtanx+∫secxdx

​​  

10 Original integral solved.

\frac{\sec{x}\tan{x}+\int \sec{x} \, dx}{2}

​2

​

​secxtanx+∫secxdx

​​  

11 Use Trigonometric Integration: the integral of \sec{x}secx is \ln{(\sec{x}+\tan{x})}ln(secx+tanx).

\frac{\sec{x}\tan{x}+\ln{(\sec{x}+\tan{x})}}{2}

​2

​

​secxtanx+ln(secx+tanx)

​​  

12 Add constant.

\frac{\sec{x}\tan{x}+\ln{(\sec{x}+\tan{x})}}{2}+C

​2

​

​secxtanx+ln(secx+tanx)

​​ +C

To integrate sec³(x), use integration by parts and trigonometric identities, ultimately resulting in the integral: 1/2 * (sec(x) * tan(x) + ln|sec(x) + tan(x)|) + C.

To integrate sec³(x), we can use integration by parts. Let’s denote the integral by I:

I = ∫ sec³(x) dx

First, we use the identity:

We know that sec²(x) = 1 + tan²(x), so:

Now, we use integration by parts:

Then, du = sec(x) * tan(x) dx and v = tan(x).

Using integration by parts formula ∫ u dv = uv - ∫ v du, we get:

Which simplifies to:

We already know sec²(x) = 1 + tan²(x), so:

Answer:

100

Step-by-step explanation:

sqrt[y] = 10

Apply both side a ^2

then

y = 100

Best regards

Answer:   b. 100

Step-by-step explanation:

[tex]\sqrt y-7=3\\\\\sqrt y=10\qquad added\ 7\ to\ both\ sides\\\\(\sqrt y)^2=(10)^2\\\\y=100\\\\\\Check:\\\sqrt{100}-7=3\\\\10-7=3\ \checkmark[/tex]

Answer: third option

Step-by-step explanation:

You have the following information given in the problem:

- The dimensions of Kyra's bed is:

[tex]4feet*5feet[/tex]

- The scale factor she used was: [tex]\frac{1}{5}[/tex]

Therefore, keeping the above on mind, you can find the the dimensions of the model bed she built by multipliying the dimensions of her bed by the scale factor:

[tex]\frac{1}{5}*4ft=0.80ft\\\\\frac{1}{5}*5ft=1.00ft[/tex]

Then, the answer is:

[tex]0.80ft*1.00ft[/tex]

Answer:

Refer to Step-by-step

Step-by-step explanation:

1. Circle P

Because the name of the circle is named by the central point of the circle.

2. Radius AP or PB

The radius is the measurement of the center of the circle to the circumference of the circle.

3. Chord DE

A chord is a line segment where both endpoints lie on the circle.

4. Diameter AB

The diameter is a line segment that goes straight across the center of a circle and the endpoints reach the circumference of the circle.

5. 12.73ft

[tex]d = \dfrac{C}{\pi }[/tex]

[tex]d = \dfrac{40}{\pi }[/tex]

[tex]d=12.73ft[/tex]

6. 4.97m

[tex]d = \dfrac{C}{\pi }[/tex]

[tex]d = \dfrac{15.62}{\pi }[/tex]

[tex]d = 4.97m

[/tex]

7. 132.7cm

[tex]a^{2}+b^{2} =c^{2}[/tex]

a = 5 cm

b = 12 cm

c = ?

[tex]5^{2}+12^{2} =c^{2}[/tex]

[tex]25+144=c^{2}[/tex]

[tex]c^{2}=169[/tex]

[tex]\sqrt{c^{2}}=\sqrt{169}[/tex]

[tex]c=13cm[/tex]

r = diameter/2

r = 13cm

r = 6.5cm

[tex]C=\pi r^{2}[/tex]

[tex]C=\pi 6.5^{2}[/tex]

[tex]C=132.7cm[/tex]

8. 128.7in

[tex]a^{2}+b^{2} =c^{2}[/tex]

a = 9in

b = 9in

c = ?

[tex]9^{2}+9^{2} =c^{2}[/tex]

[tex]81+81=c^{2}[/tex]

[tex]c^{2}=162[/tex]

[tex]\sqrt{c^{2}}=\sqrt{162}[/tex]

[tex]c=12.7in[/tex]

r = diameter/2

r = 12.7in/2

r = 6.4in

[tex]C=\pi r^{2}[/tex]

[tex]C=\pi 6.4^{2}[/tex]

[tex]C=128.7in[/tex]

Before we proceed, let's solve for the missing arcs UT, PQ, and RQ

Arc UT = 180° - (40° + 40° + 50°)

Arc UT = 50°

Now since Arc PQ is half of the diameter, then:

Arc PQ = 90°

The same applies for Arc QR

Arc QR = 90°

9. 275°

Arc UPQ = 40°+50°+180°

Arc UPQ = 275°

10. 90°

Arc UTS = 50°+40°

Arc UTS= 90°

11. 140°

Arc RSU = 50°+40°+50°

Arc RSU = 140°

12. 270°

Arc PQS = 40°+50°+180°

Arc PQS = 270°

13. 180°

Arc PQR = 90° + 90°

Arc PQR = 180°

14. 50°

15. 130°

Arc STP = 40°+50°+40°

Arc STP = 130°

16. 320°

Arc PRU = 180° + 50° + 40° + 50°

Arc PRU = 320°