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3 years ago

Explain in detail how to find the vertex: y=-2x^2 + 2x + 3

1 answer:

7 0

$\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-2}x^2\stackrel{\stackrel{b}{\downarrow }}{+2}x\stackrel{\stackrel{c}{\downarrow }}{+3} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)$

$\bf \left(-\cfrac{2}{2(-2)}~~,~~3-\cfrac{2^2}{4(-2)} \right)\implies \left( \cfrac{1}{2}~~,~~3+\cfrac{4}{8} \right)\implies \left(\cfrac{1}{2}~~,~~\cfrac{28}{8} \right) \\\\\\ \left(\cfrac{1}{2}~~,~~\cfrac{7}{2} \right)\implies \left(\frac{1}{2}~,~3\frac{1}{2} \right)$

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How do I solve and whats the answer?

8090 [49]

Answer:

x = -6

Step-by-step explanation:

Here we have an equilateral triangle. All three sides have the same length, 2. Therefore, the interior angles are all equal to 60 degrees.

Therefore, 6 - 9x = 60, and -9x = 54. Dividing both sides by -9 results in

x = -54/9, or x = -6.

8 0

3 years ago

P, Q, V, and K are collinear with V between K and P, and Q between V and K. If VP = 14x + 4, PK = x + 630, VQ = 17x + 6, and KQ

Ierofanga [76]

It's given in the question,

P, Q, V and K are collinear.

VP = 14x + 4

PK = x + 630

VQ = 17x + 6

KQ = 11x + 5

By segment addition postulate,

KQ + VQ + VP = KP

Substitute the values in the expression,

(11x + 5) + (17x + 6) + (14x + 4) = x + 630

(11x + 17x + 14x) + (5 + 6 + 4) = x + 630

42x + 15 = x + 630

42x - x = 630 - 15

41x = 615

x = $\frac{615}{41}$

x = 15

Therefore, value of VP = (14x + 4)

= 14(15) + 4

= 214 units

Learn more,

brainly.com/question/628239

3 0

2 years ago

Jessie estiments the weight of her cat to be 10 pounds the actual weight of the cat is 13.75 pounds fine the percent error

GarryVolchara [31]

Answer:

The percent error would be 27.27%

Step-by-step explanation:

percent error = \frac{measured - actual}{actual} x 100%

3 0

3 years ago

You have a piggy bank made of only dimes and quarters. There are 42 coins and their value is $6.75. How many dimes and quarters

babunello [35]

There are 23 quarters and 19 dimes

7 0

3 years ago

If x and y in the equations

Brums [2.3K]

We can let
a = 1/(x-1)
b = 1/(y+2)
and rewrite the equations as
2a - b = 10
a + 3b = -9
Using the first to write an expression for b, we get
b = 2a - 10
Substituting this into the second equation gives
a + 3(2a -10) = -9
7a -30 = -9 . . . . . . . . simplify
7a = 21 . . . . . . . . . . .add 30
a = 3
b = 2·3 - 10 = -4

Now, we can find x and y.
   3 = 1/(x -1)
   x - 1 = 1/3
   x = 1 1/3 = 4/3

  -4 = 1/(y +2)
  y +2 = -1/4
  y = -2 1/4 = -9/4

Then the desired sum is
  x + y = 4/3 -9/4 = (16 -27)/12
x + y = -11/12

The appropriate choice is ..
c. -11/12

5 0

3 years ago