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BlackZzzverrR [31]
3 years ago
9

Explain how you can determine the number of real number solutions of a system of equations in which one equation is linear and t

he other is quadratic–without graphing the system of equations.
Mathematics
2 answers:
DerKrebs [107]3 years ago
4 0

Isolate one variable in the system of equations. Use substitution to create a one-variable equation. Then, set the quadratic equation equal to zero and find the discriminant. If the discriminant is negative, then there are no real number solutions. If the discriminant is zero, then there is one real number solution. If the discriminant is positive, then there are two real number solutions.

fenix001 [56]3 years ago
4 0

Answer:

e2020

Step-by-step explanation:

Use substitution to create a one-variable equation.

Set the quadratic equation equal to zero and find the discriminant.

The value of the discriminant will tell you how many real number solutions the system of equations has

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A new carpet cleaning company claims that they can clean 3 times as many carpets in 1 week as another company. If both companies
inna [77]

Answer:

The number of carpets cleaned by new company per week  is 249

Step-by-step explanation:

Let us assume :

The number of carpets cleaned by old company in 1 week = m

So, the number of carpets cleaned by new company in 1 week

= 3 x ( Number of carpets cleaned by old company)

 = 3 (m) = 3 m

Total carpet cleaned altogether in a week  = 332

So, Total Carpets cleaned by both companies in 1 week

= Number of carpets cleaned by ( Old + New) company in 1 week.

=  m + 3  m =  4 m

⇒  4  m = 332

or, m = 332 / 4 = 83  , or m = 83

Hence number of carpets cleaned by old company per week = m = 83

The number of carpets cleaned by new company per week

= 3 m =  3 x 83= 249

8 0
3 years ago
If a car travels at an average speed of x miles per hour, how far would the car travel in 90 minutes ?
antiseptic1488 [7]

Answer:

(1.5)x

Step-by-step explanation:

90 minutes = 1.5 hours therefore

if car travels x miles in 1 hour

then the care has to travel (1.5)x miles in 90 minutes

6 0
3 years ago
Read 2 more answers
F(x)=2^x evaluate f(5)
Helen [10]

Hey there!

To solve this, we will first replace x with 5 anytime we see it in the equation.

f(5) = 2^5

Now, we simplify 2^5.

The base is 2 and the exponent is 5 in this case.

The exponent is the number of times you multiply the base by itself. In oour case:

2 x 2 x 2 x 2 x 2 = 32

f(5) = 32

Hope this helps!

3 0
3 years ago
If possible, factor 9x2 − 625y2.
Igoryamba

Answer:

(3x - 25y)(3x + 25y)

Step-by-step explanation:

9x² - 625y² ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

Given

9x² - 625y²

= (3x)² - (25y)²

= (3x - 25y)(3x + 25y)

3 0
3 years ago
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One-Step Equations:
erastova [34]
9. X=7. 7-8=-1

8. X=18. 18-7=11
3 0
3 years ago
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