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3 years ago

How do you use numerical expression to solve real word problem

Mathematics

1 answer:

Yuki888 [10]3 years ago

3 0

I really don’t know

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Four times the larger of two numbers is equal to seven times the smaller. The sum of the numbers is 22. Find the numbers

kompoz [17]

The answers should be 8 and 14

4 0

3 years ago

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

Read 2 more answers

Yani has a box of pencils: 5 pencils are green, 12 are brown, 6 are yellow, and 4 are blue. If he selects a pencil at random, wh

dexar [7]

It would be blue I believe

8 0

3 years ago

Jenny is dog sitting for 13 dogs. One runs away, and she is not sure which one. There were 3 Labradors (L), 2 Golden Retrievers

Softa [21]

Answer:

Step-by-step explanation:

It is 5 because she originally had 13. There are 5 types of dogs she was dog-sitting. There are 5 possible types of dogs that ran away.

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3 years ago

PLEASE HELP!! OFFERING 39 POINTS

jenyasd209 [6]

I hope you understand it. Also pay attention to if the line is dotted or not because they do matter.

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4 years ago