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Anna71 [15]
3 years ago
15

How many solutions does the system have? {y=−2x+2y=x2−3x Enter your answer in the box.

Mathematics
1 answer:
navik [9.2K]3 years ago
3 0
ANSWER

The system has two solutions.

EXPLANATION

The given equations are

y=-2x + 2

and

y={x}^{2} - 3x

We equate both equations to obtain;

{x}^{2} - 3x =-2x + 2

This implies that,

{x}^{2} - 3x +2x - 2 = 0

{x}^{2} - x - 2 = 0

where a=1, b=-1,c=-2.

We find the discriminant, D=b²-4ac of this equation to be;

D = {(-1)}^{2} - 4(1)( - 2) = 9

Since the discriminant is greater than zero, it means the two functions intersected at two distinct points.


Hence the system has two solutions.
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Find the vertex of the graph of the function.
lapo4ka [179]

Answer: The correct options are  (1) (5,10), (2) (3,-3), (3) x = -1, (4) y=(x+2)^2+3, (5) 21s and (6) 0, -1, and 5.

Explanation:

Te standard form of the parabola is,

f(x)=a(x-h)^2+k        .....(1)

Where,  (h,k) is the vertex of the parabola.

(1)

The given equation is,

f(x)=(x-5)^2+10

Comparing this equation with equation (1),we get,

h=5 and k=10

Therefore, the vertex of the graph is (5,10) and the fourth option is correct.

(2)

The given equation is,

f(x)=3x^2-18x+24

f(x)=3(x^2-6x)+24

To make perfect square add (\frac{b}{2a})^2, i.e., 9. Since there is factor 3 outside the parentheses, so subtract three times of 9.

f(x)=3(x^2-6x+9)+24-3\times 9

f(x)=3(x-3)^2-3

Comparing this equation with equation (1),we get,

h=3 and k=-3

Therefore, the vertex of the graph is (3,-3) and the fourth option is correct.

(3)

The given equation is

f(x)=4x^2+8x+7

f(x)=4(x^2+2x)+7

To make perfect square add (\frac{b}{2a})^2, i.e., 1. Since there is factor 4 outside the parentheses, so subtract three times of 1.

f(x)=4(x^2+2x+1)+7-4

f(x)=4(x+1)^2+3

Comparing this equation with equation (1),we get,

h=-1 and k=3

The vertex of the equation is (-1,3) so the axis is x=-1 and the correct option is 2.

(4)

The given equation is,

y=x^2+4x+7

To make perfect square add (\frac{b}{2a})^2, i.e., 2^2.

f(x)=x^2+4x+4+7-4

f(x)=x^2+4x+4+7-4

f(x)=(x+2)^2+3

Therefore, the correct option is  4.

(5)

The given equation is,

h=-16t^2+672t

It can be written as,

h=-16(t^2-42t)

It is a downward parabola. so the maximum height of the function is on its vertex.

The x coordinate of the vertex is,

x=\frac{b}{2a}

x=\frac{42}{2}

x=21

Therefore,  after 21 seconds the projectile reach its maximum height and the correct option is first.

(6)

The given equation is,

f(x)=3x^3-12x^2-15x

f(x)=3x(x^2-4x-5)

Use factoring method to find the factors of the equation.

f(x)=3x(x^2-5x+x-5)

f(x)=3x(x(x-5)+1(x-5))

f(x)=3x(x-5)(x+1)

Equate each factor equal to 0.

x=0,-1,5

Therefore, the zeros of the given equation is 0, -1, 5 and the correct option is 2.

3 0
3 years ago
Cameron has decided to diversify his investments in the following way $3000 in an account earning 2.7% simple interest $5000 in
jolli1 [7]
A=3000(1+3*0.027)=3,243
Interest earned 243
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Interest earned 274.89
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Interest earned 617.41

Total interest 243+274.89+617.41=1,135.3
Total amount Amount after 3 years
3,243+5,274.89+5,617.41=14,135.3
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M with the exponent 2 written as an equivalent expression
alexandr402 [8]
M² is equivalent to the expression  M x M .
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What percent of 23 is 51 ?
krek1111 [17]

Answer:

I think its 45.1

Step-by-step explanation:

You can go online to the percent calculator and look.

8 0
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The histogram shows the ages of people in a community chorus. How many people in the chorus are 50 or older? Enter your answer i
Vilka [71]

Answer:

13

Step-by-step explanation:

The computation of the number of people in the chorus are 50 or older is as follows

According to the attached figure

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Hence, the no of people would be 13

The same is relevant

3 0
3 years ago
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