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3 years ago

Translate each equation into slope-intercept form. Then, state the slope and y-intercept . 4y=2x+20

Mathematics

1 answer:

likoan [24]3 years ago

5 0

Answer:

The slope-intercept form of the equation: y = 0.5x + 5

The slope: m = 0.5

The y-intercept: b = 5

Step-by-step explanation:

Slope-intercept form is y = mx + b, where m is the slope and b is y-intecept

4y = 2x + 20 {divide both sides by 4}

y = 0.5x + 5 ⇒ m = 0.5 and b = 5

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What is the solution of y − 4x = 0 and 3x + 6y = 9?

Elden [556K]

You solve this by plugging one equation into the other. Usually you have to rewrite one equation to make this work. In this case I choose to rewrite y-4x=0 as y=4x.

After plugging it into the second, you get:

3x + 6*4x = 9 => 27x = 9 => x=1/3

Putting this solution back into y=4x gives us y=4/3

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2 years ago

A 4-pack of greeting cards costs $7.40. What is the unit price?pls answer fast

densk [106]

Answer:

The unit price of the problem is that one pack of greeting cards costs $1.85

Step-by-step explanation:

In order to find the unit rate, you have to divide the price by the quantity of the product. So, we will divide 7.40 by 4 so we can see the price of one pack.

7.40 ÷ 4 = 1.85

So, one pack of greeting cards costs $1.85 which is also our unit price.

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3 years ago

Find the measure of the combined angle.

Dmitry [639]

138% is the combined answer of this equation

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1 year ago

The strength of an aluminum alloy is normally distributed with mean 10 gigapascals (GPa) and standard deviation 1.4 GPa. What is

tensa zangetsu [6.8K]

Answer:

The first quartile of the strengths of this alloy is 9.055 GPa.

Step-by-step explanation:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The strength of an aluminum alloy is normally distributed with mean 10 gigapascals (GPa) and standard deviation 1.4 GPa.

This means that $\mu = 10, \sigma = 1.4$

What is the first [lower] quartile of the strengths of this alloy?

This is the 100/4 = 25th percentile, which is X when Z has a pvalue of 0.25, so X when Z = -0.675.

$Z = \frac{X - \mu}{\sigma}$

$-0.675 = \frac{X - 10}{1.4}$

$X - 10 = -0.675*1.4$

$X = 9.055$

The first quartile of the strengths of this alloy is 9.055 GPa.

3 0

2 years ago

Solve the system of equations.

emmainna [20.7K]

$x = \frac{ 419 }{ 113 } ~,~y = -\frac{ 208 }{ 113 } ~,~z = \frac{ 21 }{ 113 }$

<h2>Explanation:</h2>

We have the following system of three linear equations:

$\begin{array}{ cccc }2~ x&+~~4~ y&+~~32~ z&~=~6\\5~ x&+~~8~ y&+~~~~ z&~=~4\\4~ x&+~~5~ y&+~~2~ z&~=~6\end{array}$

Let's use elimination method in order to get the solution of this system of equation, so let's solve this step by step.

Step 1: Multiply first equation by $-5/2$ and add the result to the second equation. So we get:

$\begin{array}{ cccc }2~ x&+~~4~ y&+~~32~ z&~=~6\\&-~~~2~ y&-~~~79~ z&~=~-11\\4~ x&+~~5~ y&+~~2~ z&~=~6\end{array}$

Step 2: Multiply first equation by −2 and add the result to the third equation. So we get:

$\begin{array}{ cccc }2~ x&+~~4~ y&+~~32~ z&~=~6\\&-~~~2~ y&-~~~79~ z&~=~-11\\&-~~~3~ y&-~~~62~ z&~=~-6\end{array}$

Step 3: Multiply second equation by −32 and add the result to the third equation. So we get:

$\begin{array}{ cccc }2~ x&+~~4~ y&+~~32~ z&~=~6\\&-~~~2~ y&-~~~79~ z&~=~-11\\&&+~~\frac{ 113 }{ 2 }~ z&~=~\frac{ 21 }{ 2 }\end{array}$

Step 4: solve for z.

$\begin{aligned} \frac{ 113 }{ 2 } ~ z & = \frac{ 21 }{ 2 } \\ z & = \frac{ 21 }{ 113 } \end{aligned}$

Step 5: solve for y.

$\begin{aligned}-2y-79z &= -11\\-2y-79\cdot \frac{ 21 }{ 113 } &= -11\\y &= -\frac{ 208 }{ 113 } \end{aligned}$

Step 6: solve for x by substituting $y=-\frac{208}{113}$ and $z = \frac{21}{113}$ into the first equation:

$2x+4(-\frac{208}{113})+32(\frac{21}{113})=6 \\ \\ 2x-\frac{832}{113}+\frac{672}{113}=6 \\ \\ 2x=6+\frac{832}{113}-\frac{672}{113} \\ \\ 2x=\frac{838}{113} \\ \\ x=\frac{319}{113}$

Finally:

$x = \frac{ 419 }{ 113 } ~,~y = -\frac{ 208 }{ 113 } ~,~z = \frac{ 21 }{ 113 }$

<h2>Learn more:</h2>

Solving System of Equations: brainly.com/question/13121177

#LearnWithBrainly

7 0

3 years ago