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3 years ago

Use distributive property to simplify 5(s-5t)

Mathematics

2 answers:

Norma-Jean [14]3 years ago

8 0

the answer is 5s- 25t

steps

1. distribute the 5 out, (5*s)+(5*5t)

2. solve and combine, (5s)+(25t)

3. answer 5s+25t

Fofino [41]3 years ago

6 0

5(s-5t) =5s -25t ...distributive property

hope it helps

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URGENT 50 PTS

Len [333]

Point c

explanation:

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2 years ago

Let U = {q, r, s, t, u, V, W, x, y, z}

Alexus [3.1K]

Answer:

B'=U-B={q, r, s, t, u, V, W, x, y, z}-{q, s, y, z}={r,t, u, V, W, x, y}

A'=U-A={q, r, s, t, u, V, W, x, y, z}-{q, s, u, w, y}={r,t,v,w,x,z}

B'UC={r,t, u, V,W, x, y}U{v, w, x, y, z).={{r,t, u, V,W, x, y,z}

Step-by-step explanation:

(B'U C) U A'={{r,t, u, V,W, x,y,z}U{r,t,v,w,x,z}={{r,t, u, V,W, x,y,z}

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3 years ago

working together, paul and dan can pick forty bushels of apples in 4.95 hours. Had he done it alone it would have taken dan 9 ho

Leya [2.2K]

Answer:

Step-by-step explanation:

If Daniel does 1/9 of the job in one hour

let x = Paul's rate

Paul does 1/x of the job in one hour

They both do the job in 4.95hrs

(1/9)(4.95) + (1/x)(4.95) = job completion

multiply both sides by 9x

(9x)(1/9)(4.95) + (9x)(1/x)(4.95) = 9x(1)

4.95x + 9*4.95 = 9x

4.95x + 44.55 = 9x

9x - 4.95x = 44.55

4.05x = 44.55

x = 44.55/4.05

x = 11 hours i.e time it takes for Paul to pick the 40 bushels alone

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3 years ago

Help! Prove the equality arccos √(2/3) - arccos (1+√6)/(2*√3) = π/6

stealth61 [152]

Answer:

Proof in the explanation

Step-by-step explanation:

Trigonometric Equalities

Those are expressions involving trigonometric functions which must be proven, generally working on only one side of the equality

For this particular equality, we'll use the following equation

$\displaystyle cos(x-y)=cos\ x\ cos\ y+sin\ x\ sin\ y$

The equality we want to prove is

$\displaystyle arccos\ \sqrt{\frac{2}{3}}-arccos\left(\frac{1+\sqrt{6}}{2\sqrt{3}}\right)=\frac{\pi}{6}$

Let's set the following variables:

$\displaystyle x=arccos\ \sqrt{\frac{2}{3}},\ y=arccos(\frac{1+\sqrt{6}}{2\sqrt{3}})$

And modify the first variable:

$\displaystyle x=arccos\ \frac{\sqrt{6}}{3}}=>\ cos\ x= \frac{\sqrt{6}}{3}}$

Now with the second variable

$\displaystyle y=arccos\ \frac{1+\sqrt{6}}{2\sqrt{3}}=>cos\ y=\frac{1+\sqrt{6}}{2\sqrt{3}}=\frac{\sqrt{3}+3\sqrt{2}}{6}$

Knowing that

$sin^2x+cos^2x=1$

We compute the other two trigonometric functions of X and Y

$\displaystyle sin \ x=\sqrt{1-cos^2\ x}=\sqrt{1-(\frac{\sqrt{6}}{3})^2}=\sqrt{1-\frac{6}{9}}=\frac{\sqrt{3}}{3}$

$\displaystyle sin\ y=\sqrt{1-cos^2y}=\sqrt{1-\frac{(\sqrt{3}+3\sqrt{2})^2}{36}}}$

$\displaystyle sin\ y=\sqrt{\frac{36-(3+6\sqrt{6}+18)}{36}}=\sqrt{\frac{15-6\sqrt{6}}{36}}$

Computing

$15-6\sqrt{6}=(3-\sqrt{6})^2$

Then

$\displaystyle sin\ y=\frac{3-\sqrt{6}}{6}$

Now we replace all in the first equality:

$\displaystyle cos(x-y)=\frac{\sqrt{6}}{3}.\frac{\sqrt{3}+3\sqrt{2}}{6}+\frac{\sqrt{3}}{3}.\frac{3-\sqrt{6}}{6}$

$\displaystyle cos(x-y)=\frac{3\sqrt{2}+6\sqrt{3}}{18}+\frac{3\sqrt{3}-3\sqrt{2}}{18}$

$\displaystyle cos(x-y)=\frac{9\sqrt{3}}{18}=\frac{\sqrt{3}}{2}=cos\ \pi/6$

Thus, proven

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3 years ago

Harry measures the big prize wheel on a game show and calculates that it has an area of 12.56 square yards. What is the prize wh

Alex_Xolod [135]

Answer:

The prize wheel diameter is 4.00 yards

Step-by-step explanation:

Area (A) = πd^2/4

πd^2 = 4A

d^2 = 4A/π

d (diameter) = √(4A/π)

A = 12.56 square yards, π = 3.142

d = √(4×12.56/3.142) = √15.99 = 4.00 yards

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3 years ago