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mylen [45]
2 years ago
9

If the graph below corresponds to the equation y = x2 + bx + c, what are the values of b and c?

Mathematics
1 answer:
Viktor [21]2 years ago
4 0

Answer:

C. b = -1, c = -2

Step-by-step explanation:

2 roots: x = -1 and x = 2

(x+1)(x-2) = 0

y = x² - x -2

b= -1 , c = -2

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ABCD is a rectangle. The measure of angle BCE is 4x-23 and the angle measure of angle DCE is 5+5x. Find the measure of angle BEC
Temka [501]
<h2>Explanation:</h2><h2></h2>

The diagram for this problem is shown below. Point E is the intersection of the two diagonals and we know that:

\angle BCE=\beta \\ \\ \angle DCE=\theta

Every internal angle of any rectangle measures 90 degrees, so:

\beta +\alpha=90 \\ \\ (4x-23)+(5+5x)=90 \\ \\ \\ Isolating \ x: \\ \\ (4x+5x)+(5-23)=90 \\ \\ 9x-18=90 \\ \\ 9x=108 \\ \\ x=\frac{108}{9}=12

So:

\beta=4x-23=4(12)-23=25^{\circ}

So the measure of angle BEC can be found as follows:

We know that triangle ΔCEB is an isosceles triangle because the diagonals of any rectangle measure the same. So

\angle EBC=\beta

The sum of internal angles of any triangle add up to 180 degrees, so:

\beta + \beta+\angle BEC=180^{\circ} \\ \\ 2\beta+\angle BEC=180^{\circ} \\ \\ \angle BEC=180^{\circ}-2\beta \\ \\ \angle BEC=180^{\circ}-2(25^{\circ}) \\ \\ \angle BEC=180^{\circ}-50^{\circ} \\ \\ \boxed{\angle BEC=130^{\circ}}}

7 0
3 years ago
James asks 60 pupils which drink they liked best from cola milk and water 32 boys were in the survey 12 of the boys said they li
adelina 88 [10]

Answer:

Students altogether liked cola the best 26

Step-by-step explanation:

Total no of pupils = 60

Boys = 32

girls = 28

we will make a table

Gender         cola             milk               water       total

Boys             12                                         4              32

Girls                                                          9                28

we can find the missing numbers

Let x be for milk

In boys  12 + x + 4 = 32

                 x  = 16

In girls

          as 21 liked milk altogether

so girls = 21 - 16 = 5

Gender         cola             milk               water       total

Boys             12                 16                      4              32

Girls                                   5                      9                28

For cola let y

in girls

y + 5 + 9 = 28

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Gender         cola             milk               water       total

Boys             12                 16                      4              32

Girls              14                   5                      9            28

Altogether cola = 14 + 12 = 26

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