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KatRina [158]
3 years ago
15

PLEASE HELP find the vertex of f(x)=x^2+2x+3 (make sure you show your work)

Mathematics
1 answer:
kotegsom [21]3 years ago
4 0

Answer:

(- 1, 2)

Step-by-step explanation:

Given a quadratic in standard form y = ax² + bx + c : a ≠ 0

Then the x- coordinate of the vertex is

x_{vertex} = - \frac{b}{2a}

f(x) = x² + 2x + 3 ← is in standard form

with a = 1 and b = 2, hence

x_{vertex} = - \frac{2}{2} = - 1

Substitute x = - 1 into f(x) for corresponding value of y

f(- 1) = (- 1)² + 2(- 1) + 3 = 1 - 2 + 3 = 2

vertex = (- 1, 2 )

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Identify the angles that each have a measure of 124º.
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Answer:

Angle 1, angle 3 and angle 7 will be the equal angles.

Step-by-step explanation:

In the figure attached,

Two lines are parallel and a transversal line is intersecting these parallel lines.

Congruent angles to the angle measuring 124° will be,

m(∠7) = 124° [Vertical angles]

m(∠1) = 124° [Corresponding angles]

m(∠3) = 124° [Alternate interior angles]

Therefore, ∠1, ∠7 and ∠3 will measure the same as 124°.

6 0
3 years ago
Sixty-three people participated in a study to see if they were left-brain dominant or right-brain dominant. In the study, the pe
Cloud [144]
The two-way table is attached.

We know that 63 people took the survey, and 22 of them were left-handed.  This means that 63-22=41 of them are right handed.

Out of the 63 total, 37 are left brain dominant; this means that 63-37=26 are right brain dominant.

Of the 26 that are right brain dominant, 21 are right handed; this means 26-21=5 are left handed.

Of the 22 left-handed people, 5 are right brain dominant; this means 22-5 = 17 are left brain dominant.

Of the 37 left brain dominant people, 17 are left handed; this means 37-17=20 are right handed.

8 0
3 years ago
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Please help me on this problem
kirill115 [55]

Answer:

y=-1/2x-3

Step-by-step explanation:

sorry if wrong form, there are like 6, but that is correct if in the right form

7 0
2 years ago
Help fast please who ever answer correct i will rate them excellent,
GaryK [48]

1. x =5

2. x = 7

3. p = 12

4. m=2

5. z = 10

5 0
2 years ago
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The dimensions of a rectangular prism are shown below: Length: 1 and 1 over 3 feet Width: 1 foot Height: 2 and 1 over 3feet The
Andreas93 [3]

9514 1404 393

Answer:

  • 84 small cubes
  • 3 1/9 unit cubes

Step-by-step explanation:

A cube that is 1/3 ft on a side will fit 3 in a foot. In terms of the 1/3 ft small cube, the dimensions of the prism are ...

  1 1/3 ft = 4 small cubes

  1 ft = 3 small cubes

  2 1/3 ft = 7 small cubes

Then the volume in terms of small cubes is ...

  V = LWH = (4)(3)(7) = 84 small cubes

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There are 3×3×3 = 27 small cubes in a 1-ft unit cube, so the prism volume in terms of unit cubes is ...

  84/27 = 3 1/9 . . . unit cubes

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<em>Additional comment</em>

The largest dimension of the prism is just over 2 ft, so the maximum number of unit (1 ft) cubes that will fit is 2. To fill the volume with 3 1/9 unit cubes, those would have to be cut and fit into the space.

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