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2 years ago

Plz help due tonight

Mathematics

2 answers:

MariettaO [177]2 years ago

6 0

Sum of the interior angles of any triangle equal to 180 degrees thus :

60 + 70 + 8x + 2 = 180

8x + 132 = 180

Subtract both sides 132

8x + 132 - 132 = 180 - 132

8x = 48

Divide both sides by 8

8x ÷ 8 = 48 ÷ 8

denis23 [38]2 years ago

5 0

Answer:

I think I did this right x = 6

Step-by-step explanation:

Since all angles are supposed to add up to 180°, I just added 70° and 60° together to get 130°, and then subtracted it from 180° to get 50. Next I plugged it in to

8x + 2 = <u>50</u>, and from that I subtracted 2 on both sides to get 48 and then divided 8 on both sides, to get x by its self, and that leaves us with x = 6 because 48 ÷ 8 = 6.

I hope this helped :)

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Mario compared the slope of the function graphed below to the slope of the linear function that has an x-intercept of 1 and a y-

Lelu [443]

Answer:

The slope of the function graphed is less than the linear function that has an x-intercept of 1 and a y-intercept of -2.

Step-by-step explanation:

It is given that x-intercept is 1 and y-intercept is -2.

Now, the coordinate of the point is (1,0) and (0,-2).

We know that,

Slope = $\dfrac{y_2-y_1}{x_2-x_1}$

$S_1=\dfrac{-2-0}{0-1}$

$S_1 = \dfrac{-2}{-1}$

$S_1=2$

Now, Slope of the graph given

Co-ordinate is (-5,0) and (1,2).

Using the formula of slope

$S_2 = \dfrac{2-0}{1-(-1)}$

$S_2 = \dfrac{2}{1+1}$

$S_2 = \dfrac{2}{2}$

$S_2 =1$

Now, $S_1>S_2$

Hence, the slope of function graphed is less than linear function that has an x-intercept of 1 and a y-intercept of -2.

7 0

3 years ago

Ms. Moran has started an investment club at BSS. $8000 is invested, some at 10%

labwork [276]

The answer can be readily calculated using a single variable, x:

Let x = the amount being invested at an annual rate of 10%
Let (8000 - x) = the amount being invested at an annual rate of 12%

The problem is then stated as:

(x * 0.10) + ((8000 - x) * 0.12) = 900
0.10(x) + ((8000 * 0.12) - 0.12(x)) = 900
0.10(x) + 960 - 0.12(x) = 900
0.10(x) - 0.12(x) = 900 - 960
-0.02(x) = -60
-0.02(x) * -100/2 = -60 * -100/2
x = 6000 / 2
x = 3000

Thus, $3,000 is invested at 10% = $300 annually; and $8,000 - $3,000 = $5,000 invested at 12% = $600 annually, which sum to $900 annual investment.

6 0

2 years ago

What group of numbers does -2 belong to?

Marizza181 [45]

Answer: Integers and Rational Numbers

Explanation: -2 is an integer because integers include positive an negative numbers. It would not be a whole number or a Naural number because both of those sets only include positive numbers. Here’s a better explanation:

Natural numbers: Natural Numbers are like (1,2,3....). They only include positive numbers. Therefore, -2 does not belong in this category.

Whole Numbers: Whole Numbers are like (0,1,2,3....). They include all the natural numbers with 0. Therefore, -2 does not belong in this set.

Integers: Integers include both positive and negative numbers. They are like (-3,-2,-1,0,1,2,3....). Since they both have positive and negative numbers, -2 would belong in this set.

Rational Numbers: Rational Numbers include ALL the sets that were described. (Natural, Whole, Integer). Since this set also includes positive and negative numbers, -2 would belong in this set.

So, -2 belongs in Integers and Rational Numbers

Hope this helps!

3 0

3 years ago

Write this ratio as a fraction in the simplest form without any units. 8 yards to 15 feet. full anwser.

KATRIN_1 [288]

Answer:

8/3

Step-by-step explanation:

15 feet = 3 yards

8 yards to 3 yards

Your welcome!

Kayden Kohl

8th Grade Student

4 0

2 years ago

Match each vector operation with its resultant vector expressed as a linear combination of the unit vectors i and j.

Cloud [144]

Answer:

3u - 2v + w = 69i + 19j.

8u - 6v = 184i + 60j.

7v - 4w = -128i + 62j.

u - 5w = -9i + 37j.

Step-by-step explanation:

Note that there are multiple ways to denote a vector. For example, vector u can be written either in bold typeface "u" or with an arrow above it $\vec{u}$ . This explanation uses both representations.

$\displaystyle \vec{u} = \langle 11, 12\rangle =\left(\begin{array}{c}11 \\12\end{array}\right)$ .

$\displaystyle \vec{v} = \langle -16, 6\rangle= \left(\begin{array}{c}-16 \\6\end{array}\right)$ .

$\displaystyle \vec{w} = \langle 4, -5\rangle=\left(\begin{array}{c}4 \\-5\end{array}\right)$ .

There are two components in each of the three vectors. For example, in vector u, the first component is 11 and the second is 12. When multiplying a vector with a constant, multiply each component by the constant. For example,

$3\;\vec{v} = 3\;\left(\begin{array}{c}11 \\12\end{array}\right) = \left(\begin{array}{c}3\times 11 \\3 \times 12\end{array}\right) = \left(\begin{array}{c}33 \\36\end{array}\right)$ .

So is the case when the constant is negative:

$-2\;\vec{v} = (-2)\; \left(\begin{array}{c}-16 \\6\end{array}\right) =\left(\begin{array}{c}(-2) \times (-16) \\(-2)\times(-6)\end{array}\right) = \left(\begin{array}{c}32 \\12\end{array}\right)$ .

When adding two vectors, add the corresponding components (this phrase comes from Wolfram Mathworld) of each vector. In other words, add the number on the same row to each other. For example, when adding 3u to (-2)v,

$3\;\vec{u} + (-2)\;\vec{v} = \left(\begin{array}{c}33 \\36\end{array}\right) + \left(\begin{array}{c}32 \\12\end{array}\right) = \left(\begin{array}{c}33 + 32 \\36+12\end{array}\right) = \left(\begin{array}{c}65\\48\end{array}\right)$ .

Apply the two rules for the four vector operations.

$\displaystyle \begin{aligned}3\;\vec{u} - 2\;\vec{v} + \vec{w} &= 3\;\left(\begin{array}{c}11 \\12\end{array}\right) + (-2)\;\left(\begin{array}{c}-16 \\6\end{array}\right) + \left(\begin{array}{c}4 \\-5\end{array}\right)\\&= \left(\begin{array}{c}3\times 11 + (-2)\times (-16) + 4\\ 3\times 12 + (-2)\times 6 + (-5) \end{array}\right)\\&=\left(\begin{array}{c}69\\19\end{array}\right) = \langle 69, 19\rangle\end{aligned}$

Rewrite this vector as a linear combination of two unit vectors. The first component 69 will be the coefficient in front of the first unit vector, i. The second component 19 will be the coefficient in front of the second unit vector, j.

$\displaystyle \left(\begin{array}{c}69\\19\end{array}\right) = \langle 69, 19\rangle = 69\;\vec{i} + 19\;\vec{j}$ .

$\displaystyle \begin{aligned}8\;\vec{u} - 6\;\vec{v} &= 8\;\left(\begin{array}{c}11\\12\end{array}\right) + (-6) \;\left(\begin{array}{c}-16\\6\end{array}\right)\\&=\left(\begin{array}{c}88+96\\96 - 36\end{array}\right)\\&= \left(\begin{array}{c}184\\60\end{array}\right)= \langle 184, 60\rangle\\&=184\;\vec{i} + 60\;\vec{j} \end{aligned}$ .

$\displaystyle \begin{aligned}7\;\vec{v} - 4\;\vec{w} &= 7\;\left(\begin{array}{c}-16\\6\end{array}\right) + (-4) \;\left(\begin{array}{c}4\\-5\end{array}\right)\\&=\left(\begin{array}{c}-112 - 16\\42+20\end{array}\right)\\&= \left(\begin{array}{c}-128\\62\end{array}\right)= \langle -128, 62\rangle\\&=-128\;\vec{i} + 62\;\vec{j} \end{aligned}$ .

$\displaystyle \begin{aligned}\;\vec{u} - 5\;\vec{w} &= \left(\begin{array}{c}11\\12\end{array}\right) + (-5) \;\left(\begin{array}{c}4\\-5\end{array}\right)\\&=\left(\begin{array}{c}11-20\\12+25\end{array}\right)\\&= \left(\begin{array}{c}-9\\37\end{array}\right)= \langle -9, 37\rangle\\&=-9\;\vec{i} + 37\;\vec{j} \end{aligned}$ .

7 0

2 years ago