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3 years ago

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Mathematics

1 answer:

amm18123 years ago

3 0

Answer:

The solution of this system of equations is (3 , -8)

Step-by-step explanation:

The given system is

x + 2y = -13

12x + 5y = -4

We make x the subject of the first equation and put it into the second:

$x = - 13 - 2y$

We put this expression for x into the second equation

12(-13-2y)+5y=-4

-156-24y+5y=-4

-24y+5y=-4+156

-19y=152

y=-8

We substitute y=-8 into x=-13-2y to get:

$x = - 13 - 2( - 8) = 3$

The solution of this system of equations is (3 , -8)

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Brandi solved 16 / 5 by using a related multiplication expression. What multiplication expression did she is?

klemol [59]

The given question is wrong.

Question:

Brandi solved $\frac{1}{6}\div 5$ by using a related multiplication expression. What multiplication expression did she is?

Answer:

The related multiplication expression is $$\frac{1}{6}\times \frac{1}{5}$ .

Solution:

Given expression is $\frac{1}{6}\div 5$ .

We can write 5 as a fraction with denominator 1.

$$ \frac{1}{6}\div5=\frac{1}{6}\div \frac{5}{1}$

Using the fraction rule $$\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}$ ,

$$\frac{1}{6}\div \frac{5}{1}=\frac{1}{6}\times \frac{1}{5}$

Now multiply the fractions using the rule $$\frac{a}{b}\times \frac{d}{c}=\frac{a\times d}{b\times c}$ ,

$$\frac{1}{6}\times \frac{1}{5}=\frac{1\times1}{6\times5}$

Let us multiply the numbers in the numerator and denominator separately, we get

$$\frac{1\times1}{6\times5}=\frac{1}{30}$

Hence the related multiplication expression is $$\frac{1}{6}\times \frac{1}{5}$ .

8 0

3 years ago

Find the area. The figure is not drawn to scale.

jok3333 [9.3K]

Answer:

A = 1/2 (13) ( 9 +9)

A = 1/2 (13) (18)

A = 117

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3 years ago

Guided Practice

Fittoniya [83]

y=17,000 · 0.90xy equals 17,000 times 0.90 superscript x baseline

Step-by-step explanation:

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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

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

$AC^2=202$

$AC=\sqrt{202}\ units$

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

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

Help help help please please please

slavikrds [6]

Answer:

(-2,2)(5,-6)(5,2)

Step-by-step explanation:

just did this problem

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3 years ago