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3 years ago

Systems of Equations: Solve each system by setting the equations equal to each other and solving.

2 answers:

8 0

Since ' x ' and '-x ' are both equal to ' y ', they must be equal to each other.

 x = -x

Add ' x ' to each side: 2x = 0

Divide each side by 2 : x = 0
whence  y = 0 .

That's the only possible solution to the system [ y = x and y = -x ] .

Papessa [141]3 years ago

8 0

Since x and -x both equal y they must be equal to each other:
x= -x
+x +x (add x to both sides)
2x=0
x=0
when x=0, y=0

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Identify the lateral area and surface area of a regular triangular pyramid with base edge length 14 cm and slant height 15 cm.

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3 years ago

What is the solution to x 4 + 4x 3 ≤ 12x 2?

andriy [413]

Answer:

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Step-by-step explanation:

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3 years ago

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Two years ago, Sally had 5,000 dogs in her dog shelter. Now she has 24,575 dogs. What is the

vodomira [7]

Two years ago, Sally had 5,000 dogs in her dog shelter. Now she has 24,575 dogs. The rate of change is 391.5 % increase

Solution:

Given that Two years ago, Sally had 5,000 dogs in her dog shelter

Now she has 24,575 dogs

To find: rate of change

A rate of change is a rate that describes how one quantity changes in relation to another quantity

<h3>Steps to follow:</h3>

First: work out the difference (increase) between the two numbers you are comparing.

Increase = New Number - Original Number.

Then: divide the increase by the original number and multiply the answer by 100.

% change = Increase ÷ Original Number x 100

$\text {rate of change }=\frac{\text { new value }-\text {original value}}{\text {original value}} \times 100$

$\begin{array}{l}{\text { rate of change }=\frac{24,575-5000}{5000} \times 100} \\\\ {\text { rate of change }=\frac{19575}{5000} \times 100=391.5}\end{array}$

Thus the rate of change is 391.5 % increase

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3 years ago

What are the Values of h and k?

lawyer [7]

Answer:

$h=4, k=-2$

Step-by-step explanation:

we know that

In the function f(x) the inflection point is at $(0,0)$

In the function g(x) the inflection point is at $(4,-2)$

the rule of the translation of f(x) to g(x) is equal to

$(x,y)-----> (x+4,y-2)$

That means-----> the translation is $4$ units to the right and $2$ units down

The equation of g(x) is equal to

$g(x)=(x-4)^{3} -2$

therefore

$h=4, k=-2$

5 0

3 years ago

Determine the equation of the parabola shown in the diagram in factored form. (check picture below)

krok68 [10]

Answer:

$(x+1)(x-3)$

Step-by-step explanation:

A quadratic in factored form is usually expressed as: $a(x\pm a)(x \pm b)$ where the sign of a and b depends on the sign of the zero. And I said "usually" since sometimes the x will have a coefficient. Anyways in the quadratic there are two zeroes at x=-1 and x=3. This can be written as: $a(x+1)(x-3)$ . Notice how the signs are different? This is because when you plug in -1 as x you get a factor of (-1+1) which becomes 0 and it makes the entire thing zero since when you multiply by 0, you get 0. Same thing for the x-3 if you plug in x=3. Now a is in front and it can influence the stretch/compression. To find the value of a, you can take any point (except for the zeroes, because it will make the entire thing zero, and you can technically input anything in as a)

I'll use the point (1, -4) the vertex

-4 = a(1+1)(1-3)

-4 = a(2)(-2)

-4 = -4a

1 = a. So yeah the value of a is 1

So the equation is just: $(x+1)(x-3)$

6 0

2 years ago