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3 years ago

The sides of a triangle have lengths 3, 3, and 5. what kind of triangle is it ?

Mathematics

1 answer:

nlexa [21]3 years ago

4 0

Two sides are the same. One side is different.

Isosceles triangle.

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This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form?

creativ13 [48]

Answer:

Part a) The function’s equation written in vertex form is

$f(x)=2(x-2)^2-8$

Part b) The function’s equation written in factored form is equal to

$f(x)=2x(x-4)$

Step-by-step explanation:

Part a) What is the function’s equation written in vertex form?

we know that

The equation of a vertical parabola written in vertex form is equal to

$f(x)=a(x-h)^2+k$

where

a is a coefficient

(h,k) is the vertex

Looking at the graph

The vertex is the point (2,-8)

substitute

$f(x)=a(x-2)^2-8$

Find the value of the coefficient a

take one point from the graph

(0,0)

substitute in the equation

$0=a(0-2)^2-8\\0=4a-8\\4a=8\\a=2$

therefore

The function’s equation written in vertex form is

$f(x)=2(x-2)^2-8$

Part b) What is the function’s equation written in factored form?

we know that

The equation of a vertical parabola written in factored form is equal to

$f(x)=a(x-x_1)(x-x_2)$

where

a is a coefficient

x_1 and x_2 are the zeros or x-intercepts of the function

Remember that the x-intercept is the value of x when the value of the function is equal to zero

Looking at the graph

The zeros or x-intercepts of the function are

x=0 and x=4

$f(x)=a(x-0)(x-4)$

$f(x)=ax(x-4)$

Find the value of the coefficient a

take one point from the graph

(2,-8)

substitute

$-8=a(2)(2-4)\\-8=-4a\\a=2$

therefore

The function’s equation written in factored form is equal to

$f(x)=2x(x-4)$

4 0

3 years ago

Value of the y-intercept of the graph of f(x) = e1–x – 1?

frozen [14]

Answer:

(0, e-1) or (0, 1.718) to the nearest thousandth.

Step-by-step explanation:

The y-intercept occurs when x = 0 so here we have:

y = e^(1 - 0) - 1

= e - 1

So the y-intercept is the point (0, e-1)

5 0

3 years ago

Jack was 99 years older than priscilla. together their ages totaled 167167 years. what were their ages?

faust18 [17]

Priscilla's age was 83,534 while Jack's age was 83,633.

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3 years ago

Which equation represents a line which is parallel to x = 0

levacccp [35]

I really don’t no so sorry hope u find the asset if you haven’t

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What is the equation of the line in slope-intercept form?

Bingel [31]

Y= Mx+b

In the equation of a straight line,the slope is the number "m" that is multiplied on the x, and "b" is the y-intercept (that is, the point where the line crosses the vertical y-axis).

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3 years ago

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