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3 years ago

Find an equation of a plane that satisfies the given conditions

Mathematics

1 answer:

guajiro [1.7K]3 years ago

3 0

The conditions are needed to be able to answer the question

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Triangle J is shown below. James drew a scaled version of Triangle J using a scale factor of 4 and labeled it

Novay_Z [31]

Answer:

The area of triangle K is 16 times greater than the area of triangle J

Step-by-step explanation:

we know that

If Triangle K is a scaled version of Triangle J

then

Triangle K and Triangle J are similar

If two triangles are similar, then the ratio of its areas is equal to the scale factor squared

Let

z -----> the scale factor

Ak ------> the area of triangle K

Aj -----> the area of triangle J

$z^{2}=\frac{Ak}{Aj}$

we have

$z=4$

substitute

$4^{2}=\frac{Ak}{Aj}$

$16=\frac{Ak}{Aj}$

$Ak=16Aj$

therefore

The area of triangle K is 16 times greater than the area of triangle J

4 0

3 years ago

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1 1/3 x 5/8 <br> Please help, no links or out of context answers, thank you!

natta225 [31]

Answer:

so, i have a method of multiplying fractions, but im not going to strait give you the answer

Step-by-step explanation:

multiply the whole number (1) by the denominator (3) and then add it to the numerator (1).

you multiply the fractions from there.

this is a very fun way of doing fraction multiplying with mixed numbers!

have a good day! :D

5 0

2 years ago

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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

3 years ago

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Kieth bought 165 crayons that came in packs of 15. There were 9 colors of crayons how many packs of crayons did Kieth buy?

Andrej [43]

Answer:

11 packs

Step-by-step explanation:

165/15 = 11

6 0

3 years ago

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Simplify 123 over 3

igor_vitrenko [27]

Answer:

The answer is 41

Step-by-step explanation:

5 0

3 years ago

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