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3 years ago

If (x) = x+8 and g(x) = -4x-3, find (f+ g)(x).

Mathematics

1 answer:

Ede4ka [16]3 years ago

8 0

Answer:

Answer=B

(f+g)(x)=-3x-5

Step-by-step explanation:

f(x)=x+8.

g(x)=-4x-3.

(f+g)(x) means f(x)+g(x),So

(x+8)+(-4x-3)

(add all same terms together)

=(x+(-4x))+(8+(-3))

=-3x+5

so,

(f+g)(x)=-3x+5

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Erik drives 19.2 miles in 16 minutes.

Katen [24]

Answer:

Erik's average speed exceeds the speed limit by 6.91 miles per hour.

Step-by-step explanation:

Let suppose that Erik travels at constant speed. Hence, the speed ( $v$ ), measured in miles per hour, is determined by following equation of motion:

$v = \frac{s}{t}$ (1)

Where:

$s$ - Distance, measured in miles.

$t$ - Time, measured in hours.

Please notice that a hour equals 60 minutes. If we know that $s = 19.2\,mi$ and $t = 0.267\,h$ , then the speed of Erik is:

$v = \frac{19.2\,mi}{0.267\,h}$

$v = 71.910\,\frac{mi}{h}$

Which is 6.91 miles per hour above the speed limit.

6 0

2 years ago

Find the arc length of the given curve between the specified points. x = y^4/16 + 1/2y^2 from (9/16), 1) to (9/8, 2).

lutik1710 [3]

Answer:

The arc length is $\dfrac{21}{16}$

Step-by-step explanation:

Given that,

The given curve between the specified points is

$x=\dfrac{y^4}{16}+\dfrac{1}{2y^2}$

The points from $(\dfrac{9}{16},1)$ to $(\dfrac{9}{8},2)$

We need to calculate the value of $\dfrac{dx}{dy}$

Using given equation

$x=\dfrac{y^4}{16}+\dfrac{1}{2y^2}$

On differentiating w.r.to y

$\dfrac{dx}{dy}=\dfrac{d}{dy}(\dfrac{y^2}{16}+\dfrac{1}{2y^2})$

$\dfrac{dx}{dy}=\dfrac{1}{16}\dfrac{d}{dy}(y^4)+\dfrac{1}{2}\dfrac{d}{dy}(y^{-2})$

$\dfrac{dx}{dy}=\dfrac{1}{16}(4y^{3})+\dfrac{1}{2}(-2y^{-3})$

$\dfrac{dx}{dy}=\dfrac{y^3}{4}-y^{-3}$

We need to calculate the arc length

Using formula of arc length

$L=\int_{a}^{b}{\sqrt{1+(\dfrac{dx}{dy})^2}dy}$

Put the value into the formula

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4}-y^{-3})^2}dy}$

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4})^2+(y^{-3})^2-2\times\dfrac{y^3}{4}\times y^{-3}}dy}$

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4})^2+(y^{-3})^2-\dfrac{1}{2}}dy}$

$L=\int_{1}^{2}{\sqrt{(\dfrac{y^3}{4})^2+(y^{-3})^2+\dfrac{1}{2}}dy}$

$L=\int_{1}^{2}{\sqrt{(\dfrac{y^3}{4}+y^{-3})^2}dy}$

$L= \int_{1}^{2}{(\dfrac{y^3}{4}+y^{-3})dy}$

$L=(\dfrac{y^{3+1}}{4\times4}+\dfrac{y^{-3+1}}{-3+1})_{1}^{2}$

$L=(\dfrac{y^4}{16}+\dfrac{y^{-2}}{-2})_{1}^{2}$

Put the limits

$L=(\dfrac{2^4}{16}+\dfrac{2^{-2}}{-2}-\dfrac{1^4}{16}-\dfrac{(1)^{-2}}{-2})$

$L=\dfrac{21}{16}$

Hence, The arc length is $\dfrac{21}{16}$

6 0

2 years ago

Rectangle EFGH is similar to rectangle JKLM. Which proportion can be used to

Dominik [7]

*See attached picture for the diagrams being referred to

Answer:

C. ⁵/12= ²/x

Step-by-step Explanation:

Given that rectangle EFGH is similar to rectangle JKLM, it means the corresponding sides of both rectangles are similar, and as such the ratios if the corresponding sides of rectangle EFGH and rectangle JKLM would be equal.

Thus, EF/JK = FG/KL

Since, EF = 5; JK = 12; FG = 2; and KL= x, therefore, the proportion to use in finding x would be:

⁵/12= ²/x

6 0

2 years ago

David needs 36 gallons of punch for a party and has two different coolers to carry it in. the bigger cooler is 5 times as large

serg [7]

The little cooler can contain = 6 gallons.

The large cooler can contain is = 30 gallons.

<h3>What is volume surface area?</h3>

Any particular object's surface area is the space that the object's surface takes up. Volume, however, refers to the quantity of space a thing has. Different shapes and sizes exist in geometry, including spheres, cubes, cuboid shapes, cones, and cylinders, among others. Both the surface area and the volume are unique to each shape.

<h3>According to the given information:</h3>

The number of gallons that a small cooler can hold is: x gallons.

and a larger cooler can hold: 5x the number of gallons.

(Because it was noted:

In comparison to the smaller cooler, the larger cooler is five times bigger.

Additionally, a party requires 36 gallons of punch in total.

The result is:

x+5x=36

i.e. 6x=36

Divide both sides by 6, and the result is:

x=6

In light of this, the little cooler can contain 6 gallons.

and how many gallons the large cooler can contain is: 5 x 6 = 30 gallons.

To know more about volume surface area visit:

brainly.com/question/12446369

#SPJ4

6 0

1 year ago

What is the remainder when 6x+12 is divided by 2x-8.

bagirrra123 [75]

Answer:

4(3x-2)

Step-by-step explanation

6x+12/2x-8

6x+6x-8

12x-8

4(3x-2)

7 0

2 years ago

Read 2 more answers