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3 years ago

From the equations below, let's find the value of x.x=y=2zxyz=256

Mathematics

1 answer:

Shtirlitz [24]3 years ago

6 0

Answer:

x=8

Step-by-step explanation:

xyz=256

x=y=2z

Replace y with x and z with x/2

x * (x) *(x/2) =256

x^3 /2 = 256

x^3 = 512

Take the cubed root of each side

(x^3) ^(1/3) = (512) ^ (1/3)

x=8

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A pair of shoes costs $30.99 and the state sales tax is 5%. Use the formula C = p + rp to find the total cost of the shoes, wher

liberstina [14]

First, write the rate as a decimal by moving the decimal point two places to the left from the percent.

r = 5% = 0.05

C = p + rp

C = 30.99 + 0.05 * 30.99

C = 30.99 + 1.55

C = 32.54

Answer: The total cost is $32.54

5 0

3 years ago

Find -4A+8B (Picture provided)

Anarel [89]

Answer:

Option C

Step-by-step explanation:

We are given two matrices A and B and we have to calculate the value of the expression -4A + 8B. Each element of matrix A will be multiplied by -4 and each element of matrix B will be multiplied by 8. The corresponding elements of the resulting matrices will be added.

$-4A+8B=-4\times\left[\begin{array}{ccc}-4&-4&1\\1&4&7\\2&3&3\end{array}\right] +8\times\left[\begin{array}{ccc}2&9&-9\\8&8&-2\\4&10&1\end{array}\right] \\\\\\ -4A+8B=\left[\begin{array}{ccc}16&16&-4\\-4&-16&-28\\-8&-12&-12\end{array}\right] +\left[\begin{array}{ccc}16&72&-72\\64&64&-16\\32&80&8\end{array}\right]\\\\ \\ -4A+8B=\left[\begin{array}{ccc}32&88&-76\\60&48&-44\\24&68&-4\end{array}\right]$

Therefore, option C gives the correct answer.

8 0

3 years ago

Convert 5.82% to an equivalent decimal

lisov135 [29]

5.82% = 0.0582 in decimal form.

7 0

3 years ago

Read 2 more answers

Why was this amendment necessary?

N76 [4]

The answer to this B.

5 0

3 years ago

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If sin θ = cot θ, then, what is the value of cos θ + 2 cos^2 θ + 2 cos^3 θ + cos^ 4 θ ?

VARVARA [1.3K]

Notice that

cos(θ) + 2 cos²(θ) + 2 cos³(θ) + cos⁴(θ)

= cos(θ) (1 + 2 cos(θ) + 2 cos²(θ) + cos³(θ))

= cos(θ) ([1 + cos(θ)] + [cos(θ) + cos²(θ)] + [cos²(θ) + cos³(θ)])

= cos(θ) ([1 + cos(θ)] + [cos(θ) (1 + cos(θ))] + [cos²(θ) (1 + cos(θ))])

= cos(θ) (1 + cos(θ)) (1 + cos(θ) + cos²(θ))

Given that sin(θ) = cot(θ), by definition of cotangent this tells us that

sin(θ) = cos(θ)/sin(θ) ⇒ cos(θ) = sin²(θ)

and by the Pythagorean identity

cos²(θ) + sin²(θ) = 1

it follows that

cos(θ) = sin²(θ) = 1 - cos²(θ)

Substituting these results into the factorization above gives

cos(θ) (1 + cos(θ)) (1 + cos(θ) + cos²(θ))

= cos(θ) (1 + cos(θ)) (1 + [1 - cos²(θ)] + cos²(θ))

= 2 cos(θ) (1 + cos(θ))

= 2 sin²(θ) (1 + cos(θ))

= 2 (1 - cos²(θ)) (1 + cos(θ))

= 2 (1 + cos(θ) - cos²(θ) - cos³(θ))

= 2 (cos(θ) + cos(θ) - cos³(θ))

= 2 (2 cos(θ) - cos³(θ))

= 2 cos(θ) (2 - cos²(θ))

= 2 cos(θ) (1 + cos(θ))

= 2 (cos(θ) + cos²(θ))

= 2 (1 - cos²(θ) + cos²(θ))

= 2

7 0

3 years ago

From the equations below, let's find the value of x.x=y=2zxyz=256​

From the equations below, let's find the value of x.x=y=2zxyz=256