1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Blababa [14]
3 years ago
8

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

Mathematics
2 answers:
xxTIMURxx [149]3 years ago
5 0

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)

aev [14]3 years ago
4 0

Answer: A is correct

Step-by-step explanation: b must equal 7 and a second solution to the system must be located at the point (2, 5).

You might be interested in
List the angles of triangle ABC in order from smallest to largest measure if AB=9, AC=11, and BC=10
nadezda [96]
The angles go in the same order as the sides across from them.
AB is the smallest side so angle C is across from it.
BC is the middle length so angle A is the middle angle. AC is the longest side so angle B is the largest angle.
3 0
2 years ago
Solve each equation:
omeli [17]
You sure seem to be asking a lot of questions lately. I'd like to see that you've been trying with these problems at least because if you can't get that first one it's almost like you missed the whole lesson.

1. 20 = 4b + 7 + 5
Add the 7 and 5.
20 = 4b + 12
Subtract 12 from each side.
8 = 4b
Divide each side by 4.
2 = b

2. 7 = 6k - 7k
6k - 7k = -1k. (the k acts as a sort of unit)
7 = -1k
Divide each side by -1.
-7 = k

3. 3.23 - 2m = 3 - 2(5m - 2)
Distribute the ×-2 to each term inside the parentheses.
3.23 - 2m = 3 - 10m + 4
Add the 3 and 4.
3.23 - 2m = 7 - 10m
Add 10m to each side.
3.23 + 8m = 7
Subtract 3.23 from each side.
8m = 3.77
Divide by 8.
m = 0.47125

4. -88/45=1/3r+2/5r
To get rid of the fractions, let's multiply everything by 45.
-88 = 15 + 18r
Subtract 15 from each side.
-103 = 18r
Divide by 18.
-103/18 = r
As a mixed number, r = -5 and 13/18
As a decimal, r = -5.7222...
6 0
3 years ago
Find a number if: 3/7 of it is 2 1/4
Sergeeva-Olga [200]

Answer:

x=5 1/4

Step-by-step explanation:

2 1/4= \frac{9}{4}---> \frac{9}{4} divided by 3 to find 1/7x----> \frac{3}{4}=1/7x---> x=21/4---> x=5 1/4

8 0
3 years ago
Read 2 more answers
A local boutique sells water bottles for a set price, plus an additional fee for each letter that customers would like engraved
lesantik [10]

Answer:

y = 0.35x + 18.99

5 0
2 years ago
How do you write 76% as a fraction​
padilas [110]

Answer:

76/100 or simplified into 19/25

4 0
2 years ago
Other questions:
  • Diet cola was on sale last week; it cost $10 for every 4 packs of diet cola.
    7·1 answer
  • I need help class almost over
    10·1 answer
  • Find the values of x and y. 4y 112° 7x +7° ​
    14·2 answers
  • Plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
    6·1 answer
  • The answer below thanks
    15·1 answer
  • 7x= -56<br> Im stumped plz help ;-;
    12·1 answer
  • Select the equations in which
    9·1 answer
  • Tell me if its blurry
    14·1 answer
  • Please help me on this!!
    12·1 answer
  • How many miles will she bike in 1/2 hour?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!