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2 years ago

Use the graphing calculator to locate the solutions of this system of equations:

2 answers:

7 0

Hello,

y=(x-2)²-15
y=5x-1

==> 5x-1=x²-4x+4-15
==> x²-9x-10=0
Δ=9²+4*10=11²
x=(9+11)/2 or x=(9-11)/2
==>(x=10 and y=5*10-1=49) or (x=-1 and y=5*(-1)-1=-6)

1) A (-1,-6)
2) C (10,49)

Law Incorporation [45]2 years ago

4 0

Answer:

Option A (-1, -6)

Option C (10, 49)

Step-by-step explanation:

Two equations are given as y = (x - 2)² - 15 ----------(1)

and -5x + y = -1

y = -1 + 5x ------(2)

We put the value of y from equation 1 in equation 2.

(x -2)² - 15 = 5x - 1

x² + 4 - 4x - 15 = 5x - 1

x²- 4x - 11 = 5x - 1

x² - 4x - 11 - 5x + 1 = 0

x² - 9x - 10 = 0

x² - 10x + x - 10 = 0

x(x - 10) + 1(x - 10) = 0

(x + 1)(x - 10) = 0

x = -1 , 10

Now we put the value of x in equation 2

y = 5(-1) - 1

y = -5 -1 = -6

For x = 10

y = 5×10 - 1 = 50 - 1 = 49

So solutions are (-1, -6) and (10, 49)

First solution is Option A. (-1, -6) and second solution is Option C.(10, 49)

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Ester's choir wants to learn a new song for the school concert in 7 weeks. The song has 3016 lines. The choir learns an equal nu

andriy [413]

Hello!

We are asked to find the number of lines the choir has to learn in time for a concert.

We're given that the concert is in 7 weeks, but they learn new lines each day, so we have to convert it to days. We know that there is 7 days in a week, we would multiply 7 weeks by 7 days, which is 49 days.

Now, we would take the total number of lines, which is 3016, and divide that by 49 days.

3016 lines / 49 days ≈ 61.55 lines/day

Since this is a real-world situation, we should round our answer is to nearest whole number, which would be 62 lines/day.

Therefore, Ester's choir needs to learn about 62 lines per day in time for the concert.

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2 years ago

Owen is making lemonade from concentrate. The number of quarts of water he needs is 4 times the number of quarts of concentrate.

tiny-mole [99]

Answer:

The system of equation that models the situation is:

w = 4c

w + c = 100

And c = 20 quarts, 4c = 80 quarts and w = 80 quarts.

Step-by-step explanation:

1. Let's review the information given to us to answer the problem correctly:

Owen wants to make 100 quarts of lemonade

Number of quarts of water 4 times the number of quarts of concentrate

2. Which of the following systems of equations models this situation?

c = number of quarts of concentrate

w = number of quarts of water

Like the alternatives of systems of equations that model the situation were not given, let's write them by ourselves, this way:

w = 4c (Number of quarts of water 4 times the number of quarts of concentrate)

w + c = 100 (Owen wants to make 100 quarts of lemonade)

Now, let's solve for c and w, this way:

w = 100 - c

Substituting w in the first equation, we have:

100 - c = 4c

100 = 5c

c = 20 ⇒ 4c = 20 * 4 = 80

w = 4 * 20

w = 80

The system of equation that models the situation is:

w = 4c

w + c = 100

And c = 20 quarts, 4c = 80 quarts and w = 80 quarts.

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2 years ago

Chen completed the division problem below. 0.9 StartLongDivisionSymbol 192.6 EndLongDivisionSymbol right arrow 9 StartLongDivisi

tatuchka [14]

Answer:

He should have multiplied both numbers by 100

Step-by-step explanation:

Given

See Attachment for given

Required

What's Chen error

Chen error is at step 2 where he changed 0.9 to 9.

Any changes made on the divisor must also be made on the dividend

He got 9 by multiplying 0.9 by 10;

So, his mistake is that he should have multiplied both numbers by the same number.

From the list of given options, the option that best answer this question is He should have multiplied both numbers by 100

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2 years ago

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2 years ago

If it takes 10 seconds for 10 printers to print out 10 pages of paper, how many seconds will it take 50 printers to print out 50

Fed [463]

Lets use the formula $RWT=J$ to solve this, where,

R is the rate
W is the number of workers/things
T is time
J is number of jobs/things

"If it takes 10 seconds for 10 printers to print out 10 pages of paper" - here -

W is 10 printers, T is 10 seconds, and J is 10 pages. We can write:

$R(10)(10)=10\\R(100)=10\\R=\frac{10}{100}\\R=0.1$

"how many seconds will it take 50 printers to print out 50 pages of paper" - here we use $R=0.1$ (previously found) to figure out T.

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So it will take 10 seconds for 50 printers to print 50 pages.

ANSWER: 10 seconds

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2 years ago

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