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marysya [2.9K]
2 years ago
7

Help me with this problem!

Mathematics
1 answer:
kipiarov [429]2 years ago
8 0

Answer:

y = -(2/3)x + 3  

C

Step-by-step explanation:

The slope of the equation that was given is - 2/3

The slope in a slope intercept equation is the number in front of the x when the value of the number in front of the y = 1 and x and y are on opposite sides of the equal sign. Let's translate that.

The original equation is y = -(2/3)x + 5/3

  • y and x have to be on opposite sides of the equal sign [They are]
  • The slope is the number in front of the x. That's (-2/3).  That makes A incorrect.

Now you need to use the given point

The point is (-3 , 5) Put this into the equation that you have so far

y = (-2/3)x + b

y = 5

x = -3

5 = (-2/3)(-3/1) + b Substitute in the givens

5 = (-2 * -3)/3 + b Multiply -2 * - 3 = 6

5 = 6/3  + b          Divide the 6 by 3

5 = 2 + b               Divide

5 - 2 = b                Subtract 2 from both sides

3 = b                      Switch sides

b = 3

Answer y = (-2/3)x + 3 or C


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Answer: B

Step-by-step explanation:

The range of a function is the set of all possible values for the function's dependent variable. In this case, that variable is y, so we can look at the graph to observe what possible y-values fit in the range.

There are no y-values below -1 on the chart, and the function goes upwards to infinity, so the correct answer is B, y is greater than or equal to -1.

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What is the solution of the equation x2 − 2x = −2?
RSB [31]

Answer:

-2

Step-by-step explanation:

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2 years ago
Roxanne has 1/2 as many beads as Sherrie. The number of beads Sherrie has is 4/5 that of Ting Ting's. Ting Ting has 165 beads. H
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165 Ting Ting's beads* (4 Sherrie's beads/ 5 Ting Ting's beads)= 132 Sherrie's beads.
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Read 2 more answers
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)

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h=-16t^2+672t

It can be written as,

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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}

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(6)

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

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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.

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