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3 years ago

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Mathematics

1 answer:

kobusy [5.1K]3 years ago

3 0

The equation of the line is y - 3 = 5(x - 8) ⇒ c

Step-by-step explanation:

The point-slope form of the linear equation is $y-y_{1}=m(x-x_{1})$ , where:

m is the slope of the line
$(x_{1},y_{1})$ is a point on the line

∵ The line passes through point (8 , 3)

∴ $x_{1}$ = 8 and $y_{1}$ = 3

∵ The slope of the line is 5

∴ m = 5

- Substitute these values in the form of the equation below

∵ $y-y_{1}=m(x-x_{1})$

∴ y - 3 = 5(x - 8)

The equation of the line is y - 3 = 5(x - 8)

Learn more:

You can learn more about the linear equations in brainly.com/question/1284310

#LearnwithBrainly

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Match the following rational expressions to their rewritten forms.

Nookie1986 [14]

Answer:

Answer image is attached.

Step-by-step explanation:

Given rational expressions:

$1.\ \dfrac{x^2+x+4}{x-2}\\2.\ \dfrac{x^2-x+4}{x-2}\\3.\ \dfrac{x^2-4x+10}{x-2}\\4.\ \dfrac{x^2-5x+16}{x-2}$

And the rewritten forms:

$(x-2)+\dfrac{6}{x-2}\\(x+3)+\dfrac{10}{x-2}\\(x+1)+\dfrac{6}{x-2}\\(x-3)+\dfrac{10}{x-2}$

We have to match the rewritten terms with the given expressions.

Let us consider the rewritten terms and let us solve them one by one by taking LCM.

$(x-2)+\dfrac{6}{x-2}\\\Rightarrow \dfrac{(x-2)^{2}+6 }{x-2}\\\Rightarrow \dfrac{x^2-4x+4+6 }{x-2}\\\Rightarrow \dfrac{x^2-4x+10}{x-2}$

So, correct option is 3.

$(x+3)+\dfrac{10}{x-2}\\\Rightarrow \dfrac{(x+3)(x-2)+10}{x-2}\\\Rightarrow \dfrac{(x^2+3x-2x-6)+10}{x-2}\\\Rightarrow \dfrac{x^2+x+4}{x-2}$

So, correct option is 1.

$(x+1)+\dfrac{6}{x-2}\\\Rightarrow \dfrac{(x+1)(x-2)+6}{x-2}\\\Rightarrow \dfrac{x^{2} +x-2x-2+6}{x-2}\\\Rightarrow \dfrac{x^{2} -x+4}{x-2}$

So, correct option is 2.

$(x-3)+\dfrac{10}{x-2}\\\Rightarrow \dfrac{(x-3)(x-2)+10}{x-2}\\\Rightarrow \dfrac{x^2-3x-2x+6+10}{x-2}\\\Rightarrow \dfrac{x^2-5x+16}{x-2}$

So, correct option is 4.

The answer is also attached in the answer area.

7 0

2 years ago

Express 80 inches in standard notation using feet and inches.

Vladimir79 [104]

80 inches in standard notation using feet and inches would be expressed as 6 ft 8 inches by converting inches into feet and inches.

The solution to the given problem is to use some standard conversion units that are:

1 foot = 12 inches

1 inch = 0.8333 feet

Solution:

As mentioned above that one inch is equal to 0.8333 foot therefore

1 foot = 12 inches

then,

80 inches would be equal to

= $\frac{80}{12}$ ft

= $\frac{20}{3}$ ft

= 6ft 8 inches

= 6' 8"

Thus, 80 inches in standard notation using feet and inches would be expressed as 6 ft 8 inches by converting inches into feet and inches.

Learn more:

brainly.com/question/884268

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3 years ago

a cylindrical can of juice has a height of 5 inches and a radius of 1.25 inches. Which is closest to the total volume, in cubic

makvit [3.9K]

$\bf \textit{volume of a cylinder}\\\\
V=\pi r^2 h\quad 
\begin{cases}
r=radius\\
h=height\\
------\\
r=1.25\\
h=5
\end{cases}\implies V=\pi \cdot 1.25^2\cdot 5$

4 0

3 years ago

Read 2 more answers

Armando’s home insurance has

igomit [66]

Answer:

a. Armando pays 2500

b The insurance pays 16900

Step-by-step explanation:

Armando has to pay 2500 always and the insurance company will pay all thats left to pay is what i understand by the question and the total payment both have to do is 19400.

19400

2500 = 16900

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1 year ago

What is i + 6i? You have to simplify

marissa [1.9K]

$i=1i\\\\i+6i=1i+6i=(1+6)i=\boxed{7i}$

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3 years ago