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Morgarella [4.7K]

4 years ago

15

Simplify the following expression by combining like terms.

1 answer:

Dima020 [189]4 years ago

5 0

Answer: The answer should be 16x^2-4x

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Dot plots are often used for what 2 sets of data

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categorical or quantitative data

Step-by-step explanation:

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3 years ago

Find the x- and y-intercepts of the graph of 4x + 10y = 36. State your answers as

svetoff [14.1K]

Answer:

Step-by-step explanation:

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3 0

3 years ago

Simplify y-2/3/y+1/5

liberstina [14]

Answer:

$\frac{15y-10}{15y-3}$

Step-by-step explanation:

First at all, we need to use $a=\frac{a}{1}$ to convert this expression into a fraction, like:

$y-\frac{2}{3}$ to convert into $\frac{y}{1} -\frac{2}{3}$ .

Expand the fraction to get the least common denominator, like

$\frac{3y}{3*1}-\frac{2}{3}$

Write all numerators above the common denominator, like this:

$\frac{3y-2}{3}$

The bottom one used the same way to became simplest form, like this:

$y+\frac{1}{5}$

$\frac{y}{1} +\frac{1}{5}$

$\frac{5y}{5*1}+\frac{1}{5}$

$\frac{5y+1}{5}$

And it became like this:

$\frac{3y-2}{3}/\frac{5y+1}{5}$

Now, we are going to simplify this complex fraction. We can use cross- multiply method to simplify this fraction.

$\frac{3y-2}{3}*\frac{5y+1}{5}$

3y-2(5) and 5y-1(3)

and it will becomes like this in function form:

$\frac{3y-2(5)}{5y+1(3)}$

Then, we should distribute 5 through the parenthesis

$\frac{15y-10}{5y+1(3)}$

$\frac{15y-10}{15y+3}$

And.... Here we go. That is the answer.

7 0

3 years ago

9. A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

SSSSS [86.1K]

Answer:

Part 4) $r=84\ units$

Part 9) $sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) $sin(\theta)=-\frac{9\sqrt{202}}{202}$

Step-by-step explanation:

Part 4) A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

we know that

The circumference of a circle subtends a central angle of 360 degrees

The circumference is equal to

$C=2\pi r$

using proportion

$\frac{2\pi r}{360^o}=\frac{56\pi}{120^o}$

simplify

$\frac{r}{180^o}=\frac{56}{120^o}$

solve for r

$r=\frac{56}{120^o}(180^o)$

$r=84\ units$

Part 9) Given cos(∅)=-2/3 and ∅ lies in Quadrant III. Find the exact value of sin(∅) in simplified form

Remember the trigonometric identity

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

we have

$cos(\theta)=-\frac{2}{3}$

substitute the given value

$(-\frac{2}{3})^2+sin^2(\theta)=1$

$\frac{4}{9}+sin^2(\theta)=1$

$sin^2(\theta)=1-\frac{4}{9}$

$sin^2(\theta)=\frac{5}{9}$

square root both sides

$sin(\theta)=\pm\frac{\sqrt{5}}{3}$

we know that

If ∅ lies in Quadrant III

then

The value of sin(∅) is negative

$sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) The terminal side of ∅ passes through the point (11,-9). What is the exact value of sin(∅) in simplified form?

see the attached figure to better understand the problem

In the right triangle ABC of the figure

$sin(\theta)=\frac{BC}{AC}$

Find the length side AC applying the Pythagorean Theorem

$AC^2=AB^2+BC^2$

substitute the given values

$AC^2=11^2+9^2$

$AC^2=202$

$AC=\sqrt{202}\ units$

so

$sin(\theta)=\frac{9}{\sqrt{202}}$

simplify

$sin(\theta)=\frac{9\sqrt{202}}{202}$

Remember that

The point (11,-9) lies in Quadrant IV

then

The value of sin(∅) is negative

therefore

$sin(\theta)=-\frac{9\sqrt{202}}{202}$

5 0

3 years ago

Using the section of the graph shown, which of

RSB [31]

Step-by-step explanation:

STEP1:Equation at the end of step 1

(((2 • (x3)) + 32x2) - 6x) - 40

STEP 2 :

Equation at the end of step2:

((2x3 + 32x2) - 6x) - 40

STEP3:Checking for a perfect cube

3.1 2x3+9x2-6x-40 is not a perfect cube

Trying to factor by pulling out :

3.2 Factoring: 2x3+9x2-6x-40

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: -6x-40

Group 2: 2x3+9x2

Pull out from each group separately :

Group 1: (3x+20) • (-2)

Group 2: (2x+9) • (x2)

I thing it will help you

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5 0

2 years ago