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vaieri [72.5K]
3 years ago
9

Solve the following system of equations and show all work. y = -x^2 + 4 y = 2x + 1

Mathematics
1 answer:
Pavel [41]3 years ago
8 0
-x^2 + 4 = 2x + 1
-x^2 - 2x + 4 - 1 = 0
-x^2 - 2x + 3 = 0
(x + 3)(-x + 1)= 0

x + 3 = 0           -x + 1 = 0
x = -3                -x = -1
                          x = 1

so x = -3 and x = 1
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Given: ABCD is a trapezoid, AB=CD, MN is a midsegment, MN=30, BC=17, AB=26 Find: m∠A, m∠B, m∠C, and m∠D
enyata [817]

Answer:

The measures of angle ∠A, ∠B, ∠C, and ∠D are 60, 120, 120 and 60 degree respectively.

Step-by-step explanation:

Given information:AB=CD, MN is a midsegment, MN=30, BC=17, AB=26

Since two opposites sides are equal, therefore we can say that two no parallel sides are equal.

The length of midsegment is average of length of parallel lines.

MN=\frac{AD+BC}{2}

30=\frac{AD+17}{2}

60=AD+17

43=AD

Draw perpendiculars on AD from B and C. Let angle A be θ. D

AD=AE+EF+FD

Since ABCD is an isosceles trapezoid, therefore AE=FD and EF=BC

AD=AE+EF+AE

43=2(AE)+17

26=2(AE)

13=AE

\cos\theta=\frac{base}{hypotenuse}

\cos\theta=\frac{AE}{AB}

\cos\theta=\frac{13}{26}

\cos\theta=\frac{1}{2}

\theta=\cos^{-1}\frac{1}{2}

\theta=60

Since ABCD is an isosceles trapezoid, therefore angles A and D are same. Angle B and C are same.

\angle A=\angle D=60^{\circ}

The sum of two consecutive angles of a trapezoid is 180 degree by consecutive interior angle theorem.

\angle A+\angle B=180^{\circ}

60^{\circ}+\angle B=180^{\circ}

\angle B=120^{\circ}

\angle B=\angle C=120^{\circ}

Therefore measures of angle ∠A, ∠B, ∠C, and ∠D are 60, 120, 120 and 60 degree respectively.

3 0
3 years ago
The table shows the amount of money Justin earns for mowing lawns. Is the relationship proportional? Why or why not?
djverab [1.8K]
It is not proportional because 3 should be 45, since it is 3x15
5 0
3 years ago
10 6 4 15 6 8 6 15 4 find the median range of the data if necessary round to the nearest tenth
Lelu [443]

Reorder from least to greatest.

4, 4, 6, 6, 6, 8, 10, 15, 15

                /\

                 |

Median is the middle number.

This would be 6.

---

hope it helps

8 0
2 years ago
Can i get some help with this question please <br><br>​
viva [34]
Which question do you need to be answered?
4 0
2 years ago
Read 2 more answers
△KLM
Yuki888 [10]
It is <span>reflection across y = x
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3 years ago
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