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shusha [124]
2 years ago
11

Identify the key features of the parabola that is formed by the equation

Mathematics
1 answer:
agasfer [191]2 years ago
6 0

Answer:

  • y-intercept: 58
  • vertex: (2, 78) -- a maximum

Step-by-step explanation:

The negative leading coefficient tells you this parabola opens downward, so the vertex will be a maximum. The constant is the y-intercept, which is 58.

__

The vertex is nicely found using a graphing calculator, but can also be found algebraically. The x-value is ...

  x = -b/(2a) = -19.8/(2·(-4.9)) = 19.8/9.8 = 99/49 ≈ 2.02041

The value of f(99/49) is ...

  f(99/49) = (-4.9(99/49) +19.8)(99/49) +58 = (9.9)(99/49) +58 ≈ 78.002

The location of the vertex is approximately ...

  (x, y) ≈ (2.0204, 78.002) ≈ (2, 78)

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Two mechanics worked on a car. The first mechanic worked for 15
nevsk [136]

Answer: For the sum of 130

First: $90

Second: $40

Step-by-step explanation:

We write equations for each part of this situation.

<u>The Total Charge</u>

Together they charged 1550. This means 1550 is made up of the first mechanics rate for 15 hours and the second's rate for 5 hours. Lets call the first's rate a, so he charges 15a. The second's let's call b. He charges 5b. We add them together 15a+5b=1550.

<u>The Sum of the Rates</u>

Since the first's rate is a and the second is b, we can write a+b=130 since their sum is 130.

We solve for a and b by substituting one equation into another. Solve for the variable. Then substitute the value into the equation to find the other variable.

For a+b=130, rearrange to b=130-a and substitute into 15a+5b=1550.

15a + 5 (130-a)=1550

15a+650-5a=1550

10a+650-650=1550-650

10a=900

a=$90 was charged by the first mechanic.

We substitute to find the second mechanic's rate.

90+b=130

90-90+b=130-90

b= $40 was charged by the second mechanic

5 0
3 years ago
On number 4, how do you figure out if it's an enlargement or a reduction?
aalyn [17]
A and C is enlargement
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7 0
3 years ago
Using the Pythagorean Theorem, give an example of three sides of a right triangle
VikaD [51]

Answer:

Two legs and an hypotenuse

Step-by-step explanation:

Isn’t that what your looking for?

8 0
3 years ago
The temperature fell by 15 degrees Fahrenheit today.
katrin2010 [14]
<h3>Answer is   -15</h3>

We read this out as "negative 15" or you could write "negative fifteen".

The negative indicates the temperature went down. It doesn't necessarily mean that the final temperature is -15 degrees.

For example, if it starts being 50 degrees F, and drops by 15 degrees, then 50+(-15) = 50-15 = 35 degrees is the temperature after that drop. It might help to use a vertical number line.

8 0
3 years ago
Match the following items.
ivann1987 [24]

<u>Given</u>

AC = BC

<u>Substitution</u>

∠1 = ∠3

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∠1 = ∠3

<u>Vertical angles =</u>

∠2 = ∠3

7 0
3 years ago
Read 2 more answers
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