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2 years ago

Find the equation of the para bola that has zeros of x = -2 and x = 3 and a y-intercept of (0,-30)

Mathematics

1 answer:

lana [24]2 years ago

7 0

Answer:

y = 5x^2-5x-30

Step-by-step explanation:

A parabola with x-intercepts at (-2,0) and (3,0) has the equation

y = a(x+2)(x-3)

where a is to be determined.

We know that it passes through the point (0,-30), so

-30 = a(0+2)(0-3) = -6a

Therefore solve for a to get

a = 5

y = 5(x+2)(x-3)

y = 5(x^2-x+6)

y = 5x^2-5x-30

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I need to find the greatest common factor of <img src="https://tex.z-dn.net/?f=40s%5E3t%5E5" id="TexFormula1" title="40s^3t^5" a

solong [7]

Answer:

$\large\boxed{GCF(40s^3t^5,\ 2s^4t^4,\ 14s^6t^6)=2s^3t^4}$

Step-by-step explanation:

$40s^3t^5=\boxed2\cdot2\cdot2\cdot5\cdot \boxed{s\cdot s\cdot s}\cdot \boxed{t\cdot t\cdot t\cdot t}\cdot t\\\\2s^4t^4=\boxed2\cdot \boxed{s\cdot s\cdot s}\cdot s\cdot \boxed{t\cdot t\cdot t\cdot t}\\\\14s^6t^6=\boxed2\cdot7\cdot \boxed{s\cdot s\cdot s}\cdot s\cdot s\cdot s\cdot \boxed{t\cdot t\cdot t\cdot t}\cdot t\cdot t\\\\GCF(40s^3t^5,\ 2s^4t^4,\ 14s^6t^6)=\boxed2\cdot \boxed{s\cdot s\cdot s}\cdot\boxed{t\cdot t\cdot t\cdot t}=2s^3t^4$

7 0

2 years ago

Over what interval is the graph of f(x) = –(x + 8)2 – 1 decreasiang help

Degger [83]

Please use " ^ " to denote exponentiation:

f(x) = –(x + 8)^2 – 1
Find the first derivative: f '(x) = -2(x+8)(1)
Set this = to 0: -2(x+8) = 0
solve for x: x = -8
Divide the number line into subintervals based upon x=-8:

(-inf, -8) and (-8, inf)

Choose a test value for x from each interval, e. g., -10 from the first interval and 20 from the second.

Subst. this test value into the derivative, shown above.

If the result is + the function is incr on that interval; if - the fn. is decr.

Questions welcome!

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2 years ago

Which of the following is equivalent to the expression below?

pentagon [3]

I think the answer is a

4 0

2 years ago

Read 2 more answers

The members of a population are numbered 150. Use the table linked below to obtain a simple random sample of size 6 from the pop

Nady [450]

Answer:

Number of 2 digit number: 10 to 99, 90 numbers. Hence,P(selecting a 2 digit number) = 1/90 = .

Step-by-step explanation:

8 0

2 years ago

Use formulas to find the lateral area and surface area of the given prism. Round

tatuchka [14]

Answer:

136 m²: 188 m²

Step-by-step explanation:

I think your question missed key information, allow me to add in and hope it will fit the orginal one. Please have a look at the attached photo

My answer:

Given the information:

The height: 4m
The lenght: 13m
The width 4m

The lateral area:

As we know, the lateral area can be calculated by the following formula:

= the perimeter of the base* the height

= (13 + 4 + 13 + 4)*4

= 136 m²

The surface area:

As we know, the lateral area can be calculated by the following formula:

= The lateral area + thhe base area + the top area

= 136 + 13*4 + 13*4

= 136 + 52 + 52

= 240 m2

3 0

2 years ago