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Lemur [1.5K]
3 years ago
8

If m∠ABC=7x-2 and ∠CDE=5x+16 are congruent, find m∠ABC?

Mathematics
2 answers:
aliina [53]3 years ago
6 0

Answer: m∠ABC = 61°

Step-by-step explanation: Since angles are congruent, make the equation

7x-2 = 5x + 16

7x-5x = 16 +2

2x = 19

x = 9

Substitute 9 for x

7(9) -2 = m∠ABC .    and      5(9) + 16 = m∠CDE

63-2 = 61° = m∠ABC             45 + 16 = 61   True!

max2010maxim [7]3 years ago
3 0

Answer:

idk im dumb i just need points

Step-by-step explanation:

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The table lists how poverty level income cutoffs​ (in dollars) for a family of four have changed over time. Use the midpoint for
frez [133]

The poverty level cutoff in 1987 to the nearest dollar  was $10787.

<h3>How to find a midpoint?</h3>

The midpoint as the point that divides the line segment exactly in half having two equal segments. Therefore, the midpoint presents the same distance between the endpoints for the line segment. The midpoint formula is: \mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right).

For solving this exercise, first you need plot the points in a chart. See the image.

Your question asks to approximate the poverty level cutoff in 1987 to the nearest dollar using the midpoint formula. Note that the year 1987 is between 1980 and 1990, thus you should apply the midpoint formula from data for this year (1987).

\mathrm{Midpoint\:of\:}\left(1980,8429),\:\left(1990,13145):\quad \left(\frac{1990+1980}{2},\:\:\frac{13145+8429}{2}\right)\\\\ \\

\mathrm{Midpoint\:of\:}\left(1980,8429)\:=\left(\frac{1990+1987}{2},\:\frac{13145+3843}{2}\right)\\ \\ =\left(\frac{3977}{2},\:\frac{21574}{2}\right)

\mathrm{Midpoint\:of\:}\left(1980,8429)\:=\=(\frac{3977}{2},10787)

The answer for your question will be the value that you calculated for the y-coordinate. Then, the poverty level cutoff in 1987 to the nearest dollar  was $10787.

Read more about the midpoint segment here:

brainly.com/question/11408596

7 0
2 years ago
What is the form of the Difference of Cubes identity?
scoray [572]

Solution:

The difference of cubes identity is

if a and b are any two real numbers, then difference of their cubes , when taken individually:

→a³ - b³= (a-b)(a² + a b + b²)→→→Option (D) is true option.

I will show you , how this identity is valid.

Taking R H S

(a-b)(a² +b²+ab)

= a (a² +b²+ab)-b(a² +b²+ab)

= a³ + a b² +a²b -b a² -b³ -ab²

Cancelling  like terms , we get

= a³ - b³

= L H S



4 0
3 years ago
Read 2 more answers
Test the claim that the proportion of people who own cats is larger than 40% at the 0.025 significance level. The null and alter
Alecsey [184]

Answer:

H 0 : p ≤ 0.4 H a : p > 0.4

And based on the alternative hypothesis we can conclude that we have a right tailed test

Step-by-step explanation:

Data given

n=300 represent the random sample size

\hat p=0.45 estimated proportion of people with cats

p_o=0.40 is the value that we want to test

\alpha=0.025 represent the significance level

z would represent the statistic

p_v represent the p value

Null and alternative hypothesis

We want to test if the true proportion of people with cats is higher than 0.4, so then the best alternative is:  

Null hypothesis:p\leq 0.4  

Alternative hypothesis:p > 0.4  

H 0 : p ≤ 0.4 H a : p > 0.4

And based on the alternative hypothesis we can conclude that we have a right tailed test

The statistic is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

Replacing we got:

z=\frac{0.45 -0.4}{\sqrt{\frac{0.4(1-0.4)}{300}}}=1.768  

5 0
3 years ago
A bag of sugar contains 420g. A
faltersainse [42]

Answer:

63g extra

Step-by-step explanation:

420 x 0.15 =63 g

6 0
3 years ago
Work out the missing numbers:<br>a) 1.5 x__=10.5<br>b)__X 1.3 = 1.56​
Andreyy89

Answer:

a) 7

b)1.2

Step-by-step explanation:

10.5÷1.5=7

1.56÷1.3=1.2

7 0
3 years ago
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