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3 years ago

Expand the brackets. 7 ( 5 + g ) 11 ( 3s – 4 ) 4 ( 4 – x ) 8 ( 6 + 4w )

Mathematics

1 answer:

goldfiish [28.3K]3 years ago

6 0

Answer:

See answers below

Step-by-step explanation:

Expand the brackets. 7 ( 5 + g ) 11 ( 3s – 4 ) 4 ( 4 – x ) 8 ( 6 + 4w )

We will expand each of the bracket using distributive property

For the expression 7(5+g)

7(5)+7g

= 35+7g

For the expression 11(3s-4)

= 11(3s)-11(4)

= 33s-44

For the expression 4(4-x)

= 4(4)-4x

= 16-4x

For the expression 8(6+4w)

= 8(6)+8(4w)

= 48+32w

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A teenager who is 5 feet tall throws an object into the air. The quadratic function LaTeX: f\left(x\right)=-16x^2+64x+5f ( x ) =

tia_tia [17]

Answer:

At approximately x = 0.08 and x = 3.92.

Step-by-step explanation:

The height of the ball is modeled by the function:

$f(x)=-16x^2+64x+5$

Where f(x) is the height after x seconds.

We want to determine the time(s) when the ball is 10 feet in the air.

Therefore, we will set the function equal to 10 and solve for x:

$10=-16x^2+64x+5$

Subtracting 10 from both sides:

$-16x^2+64x-5=0$

For simplicity, divide both sides by -1:

$16x^2-64x+5=0$

We will use the quadratic formula. In this case a = 16, b = -64, and c = 5. Therefore:

$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Substitute:

$\displaystyle x=\frac{-(-64)\pm\sqrt{(-64)^2-4(16)(5)}}{2(16)}$

Evaluate:

$\displaystyle x=\frac{64\pm\sqrt{3776}}{32}$

Simplify the square root:

$\sqrt{3776}=\sqrt{64\cdot 59}=8\sqrt{59}$

Therefore:

$\displaystyle x=\frac{64\pm8\sqrt{59}}{32}$

Simplify:

$\displaystyle x=\frac{8\pm\sqrt{59}}{4}$

Approximate:

$\displaystyle x=\frac{8+\sqrt{59}}{4}\approx 3.92\text{ and } x=\frac{8-\sqrt{59}}{4}\approx0.08$

Therefore, the ball will reach a height of 10 feet at approximately x = 0.08 and x = 3.92.

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2 years ago

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FrozenT [24]

Answer:9/6 or simplified 1 1/2

Step-by-step explanation:

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An electrician needs to cut a 49 m piece of wire into two pieces so that one piece is 5 m longer than the other piece. What is t

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The length of the shorter wire that the electrician cuts so that the difference between those two is of 5 m is 22.5.

Given to us

An electrician needs to cut a 49 m piece of wire into two pieces so that one piece is 5 m longer than the other piece.

<h3>What are the two equal parts of the wire?</h3>

We know that the length of the wire is 49 m, therefore, to cut the wire in two equal parts divide the total length of the wire by two,

$\dfrac{49}{2} = 24.5$

Thus, the length of each side will be 24.5.

<h3>What is the length of the shorter piece of wire?</h3>

Since we need to cut the wire such that one side of the wire is 5 less than the other, we already know the length of the equal sides deduct (5/2) from both sides to create a difference between the length of the wire.

Length of the shorter wire = 24.5 -2.5 = 22.5

Length of the longer wire = 22.5 + 5 = 27.5

Hence, the length of the shorter wire that the electrician cuts so that the difference between those two is of 5 m is 22.5.

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All of the following types of graphs are used to represent numerical data except a _____.

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Step-by-step explanation:

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