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VikaD [51]
4 years ago
13

What are the solutions of the following system?

Mathematics
1 answer:
Andreyy894 years ago
3 0
X^2 + y^2 = 25
2x + y = -5.....y = -2x - 5

x^2 + (-2x - 5)^2 = 25
x^2 + (-2x - 5)(-2x - 5) = 25
x^2 + (4x^2 + 20x + 25) = 25
5x^2 + 20x + 25 = 25
5x^2 + 20x = 0
5x(x + 4) = 0

5x = 0         2(0) + y = -5
x = 0            y = -5

x + 4 = 0      2(-4) + y = -5
x = -4           -8 + y = -5
                     y = 3

solutions are : x = 0, y = -5.....and x = -4, y = 3

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Kim is making a bouquet for her friend. She used x tulips and some daffodils in the bouquet. The number of daffodils is equal to
zzz [600]

Kim used 4 tulips in the bouquet.

Step-by-step explanation:

Tulips used = x

Daffodils used = x²

Total flowers in bouquet = 20

According to given statement;

x^2+x=20\\x^2+x-20=0

Factorizing the Eqn

x^2+5x-4x-20=0\\x(x+5)-4(x+5)=0\\(x+5)(x-4)=0

Either,

x+5=0        => x= -5

Or,

x-4=0        => x = 4

As the number of flowers cannot be negative, therefore,

x = 4 (Where x is the number of tulips used)

Kim used 4 tulips in the bouquet.

Keywords: factorization, subtraction

Learn more about factorization at:

  • brainly.com/question/3614284
  • brainly.com/question/3799248

#LearnwithBrainly

3 0
4 years ago
If quadrilateral MNPO is reflected over the x-axis, what are the coordinates of
jenyasd209 [6]

<em>Note: you have not added the image, so I am assuming the quadrilateral MNOP with coordinates M(-4, 0), N(5, -3), P(2, 6) and O(-5, 7). It will anyhow clear your concept as I would explain the concept of reflection over the x-axis.</em>

Step-by-step explanation:

Considering the quadrilateral MNPO with assumed vertices

  • <em>M(-4, 0)</em>
  • <em>N(5, -3)</em>
  • <em>P(2, 6)</em>
  • <em>O(-5, 7)</em>

<em />

<em>THE RULE OF REFLECTION </em>states that when we tend to reflect a point let say (x, y), across the x-axis, the x-coordinate does not change or transform, but the y-coordinate is changed into its opposite sign i.e. (x,-y).

So, the coordinates of the point in the image after quadrilateral MNPO is reflected over the x-axis will be:

<h3>(x, y)                      (x, -y)</h3>

<em>M(-4, 0)                     M'(-4, 0)</em>

<em>N(5, -3)                     N'(5, 3)</em>

<em>P(2, 6)                      P'(2, -6)</em>

<em>O(-5, 7)                   O'(-5, -7)</em>

Hope, it will help you clear your concept regarding reflection of an object over the x-axis. Using this understanding, you can solve any other question related to this topic.

6 0
4 years ago
You are planning a trip of 900 miles. Your car gets about 21 mpg. Gasoline costs $1.59 per gallon. How much should you budget fo
monitta

Answer:

$64.3

Step-by-step explanation:

Given the following

Total distance = 900miles

Rate per gallon = 21miles per gallon

rate = distance/time

Get the number of gallons used;

Number of gallons used = 900/21

Number of gallons = 42.857gallons

If coost of 1 gallon is $1.50

42.857gallons will cost 42.857 * 1.50

42.857gallons will cost $64.3

Hence he should budget $64.3 for the trip

6 0
3 years ago
GEOMETRY. I need help Is this right or not?
meriva

Answer:

Step-by-step explanation:

yea...................

5 0
3 years ago
What is the implied service rate per service counter employee at an airport automobile rental counter if customer demand is 36 c
mart [117]

Answer:

24 customers per hour

Step-by-step explanation:

The service rate is given by the demand of customers per hour per employee divided by the labor utilization.

If there are two service counter employees on duty, the demand of customers per hour per employee is:

D=\frac{36}{2}=18\ customers/hour

Assuming a 75% labor utilization, the service rate is:

S =\frac{18}{0.75}=24\ customers/ hour

8 0
3 years ago
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