Given the functions f(x) = 10x 25 and g(x) = x 8, which of the following functions represents f[g(x)] correctly? f[g(x)] = 10x 33 f[g(x)] = 10x2 33 f[g(x)] = 10x 105 f[g(x)] = 10x2 105.

Answer:

C. -2n+3/n-4

Step-by-step explanation:

(n^2+10n+21)/(n^2+3n-28)-(3n/n-4)

(n^2+7n+3n+21)/(n^2+7n-4n-28)-(3n/(n-4)

(n(n+7)+3(n+7))/(n(n+7)-4(n+7))-(3n/n-4)

((n+7)(n+3)/(n+7)(n-4))-(3n/n-4)

(n+3/n-4)-(3n/n-4)

n+3-3n/n-4

-2n+3/n-4

Answer:

Yes, it is a function.

Step-by-step explanation:

We can see that using the vertical line test, none of the x points cross the line more than once, that means that it is a function, since it passes the vertical line test.

Answer:

-2x^2-6x+1

Step-by-step explanation:

-1(2x^2+6x-1)

-2x^2-6x+1

The equation that represent the height of the rectangular prism is h = v / lw, where the value of height is 2.5 inches

where

l = length

w = width

h = height

Therefore,

l = 18 inches

w = 6 1 / 2  = 13 / 2 inches

h  =?

v = 292 1 / 2  = 585 / 2

Therefore,

h = v / lw

h = 585 / 2 × 1 / 18 × 2 / 13

h = 585 / 234

h = 2.5 inches

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Answer:

5x+4

Step-by-step explanation:

Combine like terms: 12x+4-7x

Notice that the 7 is being subtracted, as it's negative

12x+4−7x

5x + 4

answer is 5x + 4

Answer:

value of a is 14

Step-by-step explanation:

Answer:

Step-by-step explanation:

From Daniel's initial location from the campsite given the width of the

stream is 400 feet and Daniel swims to the boat ramp, we have;

1.) Please find attached the drawing of the situation

2.) 3.34 minutes

3.) 1,298.59 feet

4.) 3.69 minutes

1.) Please find attached a labelled diagram of the scenario created with MS Visio

2.) Daniel's average swimming rate (speed) = 150 feet per minute

[tex]The \ distance \ Daniel \ swims = \mathbf{\dfrac{400 \, feet}{sin(53^{\circ})}} \approx 500.85 \, feet[/tex]

The time it takes him to swim to the boat ramp, t, is therefore;

3.) The distance, d₁, downstream of the boat ramp from Daniel is given as follows;

d₁ = √((500.85 feet)² - (400 feet)²) ≈ 301.41 feet

Therefore;

The distance from the boat ramp to the campsite, d₂, is therefore;

d₂ ≈ 1600 feet - 301.41 feet = 1,298.59 feet

The distance from the boat ramp to the campsite, d₂ ≈ 1,298.59 feet                              

4. The time, t₂, it will take Daniel to jog from the boat ramp to the campsite is given as follows;

[tex]t_2 = \mathbf{\dfrac{d_2}{v_2}}[/tex]

Where;

v₂ = The rate at which Daniel can jog, which is 4 mph

Which gives;

[tex]t_2 = \mathbf{\dfrac{1298.59 \, feet}{4 \, mph}} = \dfrac{1298.59 \, feet}{4 \, mph} \approx \dfrac{1298.59 \, feet}{5.866142 \ feet/s} \approx \dfrac{221.37 \, s}{60 \, s/min} \approx 3.69 \, min[/tex]

Therefore;

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Check the picture below.

so, the figure is really one big square, a 10x10, with four triangles in it, now, if we just get the area of the square, well 10x10 is just 100 in², and then get the areas of those three triangles, the yellow, purple and orange ones, and subtract their area from that of the larger square, what's leftover is the shaded triangle.  By subtracting the areas from the larger area, we're in essence making a big hole in the larger area, and what's leftover is what was never subtracted.

[tex]\stackrel{\textit{\Large Areas}}{\stackrel{square}{(10)(10)}~~ - ~~\stackrel{yellow~triangle}{\cfrac{1}{2}(10)(7)}~~ - ~~\stackrel{orange~triagle}{\cfrac{1}{2}(7)(10)}~~ - ~~\stackrel{purple~triangle}{\cfrac{1}{2}(3)(3)}} \\\\\\ 100~~ - ~~35~~ - ~~35~~ - ~~\cfrac{9}{2}\implies \cfrac{51}{2}\implies 25\frac{1}{2}[/tex]

Formula: [tex]A=lw[/tex] where l is the length and w is the width

Whenever we modify any of the side lengths, as in make them longer or shorter, we simply add or subtract from l or w.

When a quadratic equation is organized in standard form, it follows the following format:

[tex]y=ax^2+bx+c[/tex] where a, b and c are numbers

In standard form, all the terms have been simplified and there are no parentheses to expand.

We're given:

If we're expanding each side by x, we're simply adding x to each side length:

10 ft by 10 ft ⇒ (x + 10) ft by (x + 10) ft

Now to find the area, we can use the area formula:

[tex]A=(x+10)(x+10)[/tex]

This expression can be simplified as l = w:

[tex]A=(x+10)^2[/tex]

Putting it into standard form:

We can do this by expanding the parentheses:

[tex]A=(x+10)^2[/tex]

⇒ Because this is a perfect square, we can use the following rule to help us expand this equation:

[tex]A=x^2+20x+100[/tex]

Therefore, the expression in standard form that represents the area of the new expanded garden is [tex]x^2+20x+100[/tex].

Answer:

54 inch²

Step-by-step explanation:

the cube has six surface. so we calculate the area of a surface and then multiple in six.

area of a surface: 3×3 = 9 inch²

area of the cube: 6×9 inch² = 54 inch²

Answer:

(x+3) (x+1)

Step-by-step explanation:

write 4r as a sum of 3r+r

r^2+3r+r+3

factor out r from the expression

r(x+3) + r + 3

factor out x+3 from the expression

(x+3) (x+1)

Answer:

your sample in statistics has to represent or be pulled from the population you are interested in.  If your population was all the drivers on highway 10 it wouldn't make sense to draw a sample from the local grocery store.  The sample has to be pulled from the population

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

Area is found by doing two length x width. Because ethics is a square all side lengths are equal. Therefore I did the square root of 625 in order to determine what 2 numbers (length and width) would be multiplied by each other to get 625. Hope this helps

The measures that will form right angles are 14, 48 and 50 AND 35, 120 and 125

For the sides of a triangle to be right-angled, the sum of the square of the longest side must be equal to the measure of the sum of the square of the other two sides

According to the question, we are to select the sides of the triangle that will form a right angle.

The measures that will form right angles are 14, 48 and 50 AND 35, 120 and 125

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Answer:

6x²+20y²+7xy

Step-by-step explanation:

Answer:

3.14 + 3.14 × 3.14 + 3.14 ÷ 3.14 is equal to 13.9996

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem

(leg of big Δ )² = (part of hypotenuse below it ) × ( whole hypotenuse )

x² = 20 × (20 + 36) = 20 × 56 = 1120 ( take square root of both sides )

x = [tex]\sqrt{1120}[/tex] = [tex]\sqrt{16(70)}[/tex] = [tex]\sqrt{16}[/tex] × [tex]\sqrt{70}[/tex] = 4[tex]\sqrt{70}[/tex]

Answer:

W=12 cm.

Step-by-step explanation:

If the total area is 180 sq. cm., and you multiply length times width to find area, this time it is inversed. So you do 180/15=12

Answer:

12 cm

Step-by-step explanation:

The area of a rectangle = length × width

We know that the length is 15 cm and the area is 180 cm² so we can substitute this into the equation:

180 cm² = 15 cm × width

Finally, we can divide both sides by 15 to find the width:

width = 180 ÷ 15

width = 12 cm

Hope this helps!

Answer:

, volume = [(3√3)/2]a2h cubic units

Step-by-step explanation:

The formula for the volume of a hexagonal prism is, volume = [(3√3)/2]a2h cubic units where a is the base length and h is the height of the prism.

Answer:

54 lbs. of meat

Step-by-step explanation:

7x6=42

4x3=12

42+12=54

Answer:

The answer is -4s + 14

Step-by-step explanation:

First what you want to do is add the -6s to 2s they have the same variables then add 4 to 10 which equals 14. I hope that helped! :)

Answer:

To reflect the shape in the line y = 1:

(-4, 4) → (-4, -2)

(-1, 4) → (-1, -2)

(-1, 2) → (-1, 0)

Answer:

[tex]\sf A . \sf \frac{3}{-7}[/tex]

[tex]\sf E. \sf -( \frac{-3}{-7} )[/tex]

This above options makes the expression true.

Answer:

20.5

25.5

hope this helps

Answer:

90 minutes or 1 1/2 hours

Step-by-step explanation:

One mile = 15 minutes

6 x 1 miles = 15 x 6 minutes

6 miles = 90 minutes or 1 1/2 hours

Answer: s = -4

Step-by-step explanation:

s/4 + 15 = 14

We can subtract 15 from both sides:

s/4 = -1

We can multiply both sides by 4:

s = -4

Answer:118

Step-by-step explanation:

Y= mx-b ....substitute the values of m,x,b

Y=(5×6)-12

y= 30-12

Y=118

A central angle means an angle that is at the center of a circle and whose legs are intersecting the circle.

Your information is incomplete as the data is not given. Therefore, an overview will be given.

Central angles are shaped by an arc between the two points. When a central angle and the inscribed angle intercept the same arc, then the central angle would be the double of the inscribed angles while the inscribed angle will be half of the central angle.

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Answer:

Step-by-step explanation:

Find the difference between year 4 and year 5 salary.

32,625 - 31,900 = 725 (rate of change)

Multiply 4 x 725 then subtract that number from 31,900 to find out base salary

4x 724 = 2900

31,900 - 2,900 = 29,000

That's the constant.

So,

f(n) = 725n + 29,000