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Ludmilka [50]
4 years ago
14

Write a division problem involving the division of a decimal by a whole number with an estimated quotient of 7?

Mathematics
1 answer:
stellarik [79]4 years ago
7 0
Ummmmmmmmmmmmmmmmmmmmmmmmmmmm
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PLZ HELP OOOOHHH<br><br> Solve for X<br><br> -1/5(x-4)= -2<br><br> x=[_]
zavuch27 [327]

Answer:

X = 10 + 4   Simplified: X = 14

Step-by-step explanation:

-1/5 (x - 4) = -2

distributive property

(-1/5 · x) + (-1/5 · -4) = -2

simplify

-1/5x + 0.8 = -2

multiply each side by -5

X + -4 = 10

simplify

X - 4 = 10

an

5 0
3 years ago
Read 2 more answers
Please help prove these identities!
lord [1]
<h3>Hi! It will be a pleasure to help you to prove these identities, so let's get started:</h3>

<h2>PART a)</h2>

We have the following expression:

tan(\theta)cot(\theta)-sin^{2}(\theta)=cos^2(\theta)

We know that:

cot(\theta)=\frac{1}{cot(\theta)}

Therefore, by substituting in the original expression:

tan(\theta)\left(\frac{1}{tan(\theta)}\right)-sin^{2}(\theta)=cos^2(\theta) \\ \\ \\ Simplifying: \\ \\ 1-sin^2(\theta)=cos^2(\theta)

We know that the basic relationship between the sine and the cosine determined by the Pythagorean identity, so:

sin^2(\theta)+cos^2(\theta)=1

By subtracting sin^2(\theta) from both sides, we get:

\boxed{cos^2(\theta)=1-sin^2(\theta)} \ Proved!

<h2>PART b)</h2>

We have the following expression:

\frac{cos(\alpha)}{cos(\alpha)-sin(\alpha)}=\frac{1}{1-tan(\alpha)}

Here, let's multiply each side by cos(\alpha)-sin(\alpha):

(cos(\alpha)-sin(\alpha))\left(\frac{cos(\alpha)}{cos(\alpha)-sin(\alpha)}\right)=(cos(\alpha)-sin(\alpha))\left(\frac{1}{1-tan(\alpha)}\right) \\ \\ Then: \\ \\ cos(\alpha)=\frac{cos(\alpha)-sin(\alpha)}{1-tan(\alpha)}

We also know that:

tan(\alpha)=\frac{sin(\alpha)}{cos(\alpha)}

Then:

cos(\alpha)=\frac{cos(\alpha)-sin(\alpha)}{1-\frac{sin(\alpha)}{cos(\alpha)}} \\ \\ \\ Simplifying: \\ \\ cos(\alpha)=\frac{cos(\alpha)-sin(\alpha)}{\frac{cos(\alpha)-sin(\alpha)}{cos(\alpha)}} \\ \\ Or: \\ \\ cos(\alpha)=\frac{\frac{cos(\alpha)-sin(\alpha)}{1}}{\frac{cos(\alpha)-sin(\alpha)}{cos(\alpha)}} \\ \\ Then: \\ \\ cos(\alpha)=cos(\alpha).\frac{cos(\alpha)-sin(\alpha)}{cos(\alpha)-sin(\alpha)} \\ \\ \boxed{cos(\alpha)=cos(\alpha)} \ Proved!

<h2>PART c)</h2>

We have the following expression:

\frac{cos(x+y)}{cosxsiny}=coty-tanx

From Angle Sum Property, we know that:

cos(x+y)=cos(x)cos(y)-sin(x)sin(y)

Substituting this in our original expression, we have:

\frac{cos(x)cos(y)-sin(x)sin(y)}{cosxsiny}=coty-tanx

But we can also write this as follows:

\\ \frac{cosxcosy}{cosxsiny}-\frac{sinxsiny}{cosxsiny}=coty-tanx \\ \\ Simplifying: \\ \\ \frac{cosy}{siny}-\frac{sinx}{cosx} =coty-tanx \\ \\ But: \\ \\ \frac{cosy}{siny}=coty \\ \\ \frac{sinx}{cosx}=tanx \\ \\ Hence: \\ \\ \boxed{coty-tanx=coty-tanx} \ Proved!

<h2>PART d)</h2>

We have the following expression:

\ln\left|1+cos \theta\right|+\ln\left|1-cos \theta\right|=2\ln\left|sin \theta\right|

By Logarithm product rule, we know:

log_{b}(x.y) = log_{b}(x) + log_{b}(y)

So:

\ln\left|1+cos \theta\right|+\ln\left|1-cos \theta\right|=\ln\left|(1+cos \theta)(1-cos \theta)\right|

The Difference of Squares states that:

a^2-b^2=(a+b)(a-b) \\ \\ So: \\ \\ (1+cos \theta)(1-cos \theta)=1-cos^2 \theta

Then:

\ln\left|(1+cos \theta)(1-cos \theta)\right|=\ln\left|1-cos^{2} \theta\right|

By the Pythagorean identity:

sin^2(\theta)+cos^2(\theta)=1 \\ \\ So: \\ \\ sin^2 \theta = 1-cos^2 \theta

Then:

\ln\left|1-cos^{2} \theta\right|=\ln\left|sin^2 \theta|

By Logarithm power rule, we know:

log_{b}(x.y) = ylog_{b}(x)

Then:

\ln\left|sin^2 \theta|=2\ln\left|sin \theta|

In conclusion:

\boxed{\ln\left|1+cos \theta\right|+\ln\left|1-cos \theta\right|=2\ln\left|sin \theta\right|} \ Proved!

4 0
3 years ago
Complete the ordered pairs so that each is a solution of the given linear equation. Then graph the equation. x=6+y
Sav [38]
x=6+y&#10;\\y=x-6&#10;\\x=0 \Rightarrow y=-6&#10;\\x=-2 \Rightarrow y=-8&#10;\\x=6 \Rightarrow y=-0&#10;\\&#10;\\(0,-6),(-2,-8),(6,0)

6 0
3 years ago
How do you distribute: 2 ( x + 5 )
Kisachek [45]

Answer:10x

Step-by-step explanation:

4 0
3 years ago
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What is the solution to 8•g=-32?
Anni [7]
8 x -4 = -32... good luck
5 0
4 years ago
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