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2 years ago

3^0·10^(-4)= a)-120 b)1 c)1/10,000

Mathematics

1 answer:

Inessa [10]2 years ago

5 0

Answer:

Step-by-step explanation:

3^0

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Could someone help me rnnn?

GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola: $y=3x^2-4$

Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola: $y=a(x-h)^2+k$

(where (h, k) is the vertex and $a$ is some constant)

Substitute point (0, -4) into the equation:

$\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}$

Substitute point (-2, 8) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$

Substitute point (1, -1) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}$

Equate to find h:

$\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}$

Substitute found value of h into one of the equations to find a:

$\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}$

Substitute found values of h and a to find k:

$\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}$

Therefore, the equation of the parabola in vertex form is:

$\implies y=3(x-0)^2-4=3x^2-4$

So the vertex of the parabola is (0, -4)

5 0

2 years ago

Read 2 more answers

By what percent will the fraction increase if its numerator is increased by 60% and denominator is decreased by 20% ?

seropon [69]

Answer:

100%

Step-by-step explanation:

Start with x.

x = x/1

Increase the numerator by 60% to 1.6x.

Decrease the numerator by 20% to 0.8.

The new fraction is

1.6x/0.8

Do the division.

1.6x/0.8 = 2x

The fraction increased from x to 2x. It became double of what it was. From x to 2x, the increase is x. Since x was the original number x is 100%.

The increase is 100%.

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2 years ago

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18-3<br> -18-3<br> -18-(-3)<br> 18-(-3)

Marina CMI [18]

Answer:

1.) 15

2.) -21

3.) -15

4.) 21

Step-by-step explanation:

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2 years ago

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In one week, Callum collected 1246 rocks from the seashore. Every day, he collected the same number of rocks. In a single day, h

Snezhnost [94]

Answer:

178

Step-by-step explanation:

1246 over a week, (1246/7) in a day. 178 rocks a day

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2 years ago

Which expression represents the distance between 4.7 and −11.2 on the number line?

Cerrena [4.2K]

Answer:

4.7 - ( -11.2)

Step-by-step explanation:

4.7 - ( - 11.2) = 15.9

15.9 is the distance between 4.7 and -11.2

Hopefully this helps you

pls mark brainlest

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2 years ago