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Arlecino [84]
2 years ago
7

Directions: Solve each problem. Show how you found each answer.

Mathematics
1 answer:
Misha Larkins [42]2 years ago
8 0

Answer:

8 and a half hours

Step-by-step explanation:

Time arthur went to bed = 9:30 pm
Time arthur woke up = 6 am
Hours arthur was asleep = 24 - (9 and half + 6)
                                         = 24 - 15 and a half
                                         = 8 and a half

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$120-$78= m (how much money you need to save)
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3 years ago
Tom determines that the system of equations below has two solutions, one of which is located at the vertex of the parabola.
xxTIMURxx [149]

Answer:

Option A: b must equal 7 and a second solution to the system must be located at the point (2, 5)

Step-by-step explanation:

<u><em>The complete question is</em></u>

Tom determines that the system of equations below has two solutions, one of which is located at the vertex of the parabola.

Equation 1: (x – 3)2 = y – 4

Equation 2: y = -x + b

In order for Tom’s thinking to be correct, which qualifications must be met?

A: b must equal 7 and a second solution to the system must be located at the point (2, 5).

B: b must equal 1 and a second solution to the system must be located at the point (4, 5).

C: b must equal 7 and a second solution to the system must be located at the point (1, 8).

D: b must equal 1 and a second solution to the system must be located at the point (3, 4).

step 1

Find the vertex of the quadratic equation

The general equation of a vertical parabola in vertex form is

y=a(x-h)^2+k

where

(h,k) is the vertex

we have

(x-3)^{2}=y-4

so

y=(x-3)^{2}+4

The vertex is the point (3,4)

step 2

Find out the value of b in the linear equation

we know that

If the vertex is a solution of the system of equations, then the vertex must satisfy both equations

substitute the value of x and the value of y of the vertex in the linear equation

y=-x+b

For x=3, y=4

4=-3+b\\b=7

so

y=-x+7

step 3

Find out the second solution of the system of equations

we have

y=(x-3)^{2}+4 -----> equation A

y=-x+7 ----> equation B

solve the system of equations by graphing

Remember that the solutions are the intersection points both graphs

The second solution of the system of equations is (2,5)

see the attached figure

therefore

b must equal 7 and a second solution to the system must be located at the point (2, 5)

5 0
3 years ago
Read 2 more answers
Which angles are adjacent to each other ? select all that apply
sukhopar [10]

Step-by-step explanation:

1st one

2nd

4th

8 0
3 years ago
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The andersons can set up 6 tables in 1 hour how many tables can they set up in 5 hours
Talja [164]

They can set up total 30 tables in 5 hours.

<h3>How is a multiplication explained?</h3>

Multiply in mathematics refers to the continual addition of sets of same size.

2 × 3 = 6

It can be interpreted this way:

Three times two equals six.

Three times two equals six.

Six is two threes.

Given,

Andersons can set up 6 tables in 1 hour

Tables they can set up in 5 hours = 5 × 6

= 30

To learn more about multiplication from given link

brainly.com/question/4721701

#SPJ9

7 0
1 year ago
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Have a nice day/night <3
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3 years ago
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