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2 years ago

14

Find the measures of two supplementary angles m and n if m=6x+3 and n=2x-7

1 answer:

nataly862011 [7]2 years ago

3 0

When two angles are supplementary, their angle measures add up to 180°. That means that the angles measures of angle m and angle n should add up to 180. With this information, you can set up the equation m + n = 180. You can find the value of x by substituting m and n with their values and solving algebraically.

6x + 3 + 2x - 7 = 180 Add up like values (6x and 2x) (3 and -7)
8x - 4 = 180 Add 4 to both sides
8x = 184 Divide both sides by 8
x = 23

Now to find the measures of angles m and n, substitute the x value into both of the equations and solve.

m = 6x + 3 Substitute
m = 6(23) + 3 Multiply
m = 138 + 3 Add
m = 141°

-----------------------------------------------

n = 2x - 7 Substitute
n = 2(23) - 7 Multiply
n = 46 - 7 Subtract
n = 39°

You can check your work by adding the two angle measures to make sure hey are supplementary.

141° + 39° = 180°

So angle m is 141° and angle n is 39°.

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Need help with my homework

Volgvan

Answer:

$\displaystyle y=\frac{16-9x^3}{2x^3 - 3}$

$\displaystyle y=-\frac{56}{13}$

Step-by-step explanation:

<u>Equation Solving</u>

We are given the equation:

$\displaystyle x=\sqrt[3]{\frac{3y+16}{2y+9}}$

i)

To make y as a subject, we need to isolate y, that is, leaving it alone in the left side of the equation, and an expression with no y's to the right side.

We have to make it in steps like follows.

Cube both sides:

$\displaystyle x^3=\left(\sqrt[3]{\frac{3y+16}{2y+9}}\right)^3$

Simplify the radical with the cube:

$\displaystyle x^3=\frac{3y+16}{2y+9}$

Multiply by 2y+9

$\displaystyle x^3(2y+9)=\frac{3y+16}{2y+9}(2y+9)$

Simplify:

$\displaystyle x^3(2y+9)=3y+16$

Operate the parentheses:

$\displaystyle x^3(2y)+x^3(9)=3y+16$

$\displaystyle 2x^3y+9x^3=3y+16$

Subtract 3y and $9x^3$ :

$\displaystyle 2x^3y - 3y=16-9x^3$

Factor y out of the left side:

$\displaystyle y(2x^3 - 3)=16-9x^3$

Divide by $2x^3 - 3$ :

$\mathbf{\displaystyle y=\frac{16-9x^3}{2x^3 - 3}}$

ii) To find y when x=2, substitute:

$\displaystyle y=\frac{16-9\cdot 2^3}{2\cdot 2^3 - 3}$

$\displaystyle y=\frac{16-9\cdot 8}{2\cdot 8 - 3}$

$\displaystyle y=\frac{16-72}{16- 3}$

$\displaystyle y=\frac{-56}{13}$

$\mathbf{\displaystyle y=-\frac{56}{13}}$

8 0

2 years ago

Criterion: Identify IV, DV, and hypotheses and evaluate the null hypothesis for an independent samples t test. Data: Use the inf

Papessa [141]

The table is missing in the question. The table is provided here :

Group 1 Group 2

34.86 64.14 mean

21.99 20.46 standard deviation

7 7 n

Solution :

a). The IV or independent variable = Group 1

The DV or the dependent variable = Group 2

b).

$H_0: \mu_1 = \mu_2$

$H_a:\mu_1 < \mu_2$

Therefore, $t = \frac{\bar x_1 - \bar x_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{S_2^2}{n_2}}}$

$t = \frac{34.86 - 64.14}{\sqrt{\frac{21.99^2}{7}+\frac{20.46^2}{7}}}$

t = -2.579143

Now, $df = min(n_1 - 1, n_2 - 1)$

df = 7 - 1

= 6

Therefore the value of p :

$=T.DIST(-2.579143,6,TRUE)$

= 0.020908803

The p value is 0.0209

$p< 0.05$

So we reject the null hypothesis and conclude that $\mu_1 < \mu_2$

7 0

2 years ago

i will give brainliest to first correct answer!! what is the length of YZ? i will report if you give a fake answer

luda_lava [24]

Answer:

25

Step-by-step explanation:

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2 years ago

Infants who weigh less than 2,500 grams (5 1/2 pounds) at birth are called

Whitepunk [10]

Low-birthweight i believe.

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2 years ago

A number is chosen at random from 1 to 10. Find the probability of selecting factors of 4 and factors of 6

disa [49]

4,6,8 because 4 times 2 is 8 and 6 times 1 equals 6 and 1 times 4 equals 4

5 0

2 years ago