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2 years ago

How many solutions does the system have?

Mathematics

1 answer:

EastWind [94]2 years ago

3 0

Answer:

A:One Solution

Step-by-step explanation:

First substitute the y in the first equation with the second equation to get

-2x-4=3x+3

since theres a variable of both sides, you subtract the variable with the least coefficient, in this case, you add 2x to both sides to get

-4=5x+3

subtract the constant on both sides to get

-1=5x

divide both sides by 5

x= -0.2 or -1/5

it's A, one solution

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Grace cut 3 pieces of ribbon; each piece was 2/5 of a foot long.How many feet of ribbon does she have in all?

ser-zykov [4K]

Answer:

6/5 or 1 1/5

Step-by-step explanation:

Each piece is 2/5 so you add it up 3 times or multiply by 3 to get 6/5 or 1 and 1/5.

8 0

2 years ago

Question 4 plz show ALL STEPS

scoray [572]

Part (a)

Locate x = -1 on the x axis. Draw a vertical line through this x value until you reach the f(x) curve. Then move horizontally until you reach the y axis. You should arrive at y = 4. Check out the diagram below to see what I mean.

Since f(-1) = 4, this means we can then say

g( f(-1) ) = g( 4 ) = 4

To evaluate g(4), we'll follow the same idea as what we did with f(x). However, we'll start at x = 4 and draw a vertical line until we reach the g(x) curve this time.

<h3>Answer: 4</h3>

==========================================================

Part (b)

We use the same idea as part (a)

f(-2) = 5

g( f(-2) ) = g(5) = 6

<h3>Answer: 6</h3>

==========================================================

Part (c)

Same idea as the last two parts. We start on the inside and work toward the outside. Keep in mind that g(x) is now the inner function for this part and for part (d) as well.

g(1) = -2

f( g(1) ) = f(-2) = 5

<h3>Answer: 5</h3>

==========================================================

Part (d)

Same idea as part (c)

g(2) = 0

f( g(2) ) = f( 0 ) = 3

<h3>Answer: 3</h3>

6 0

2 years ago

What is the effect on the graph of the function f(x) = |x| when f(x) is changed to f( 3/4 x)?

bulgar [2K]

Answer:

Whats The Answer Choice?

Step-by-step explanation:

4 0

3 years ago

A filter filled with liquid is in the shape of a vertex-down cone with a height of 9 inches and a diameter of 6 inches at its op

Alina [70]

Answer: Level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

Step-by-step explanation:

Since we have given that

Height = 9 inches

Diameter = 6 inches

Radius = 3 inches

So, $\dfrac{r}{h}=\dfrac{3}{9}=\dfrac{1}{3}\\\\r=\dfrac{1}{3}h$

Volume of cone is given by

$V=\dfrac{1}{3}\pi r^2h\\\\V=\dfrac{1}{3}\pi \dfrac{1}{9}h^2\times h\\\\V=\dfrac{1}{27}\pi h^3$

By differentiating with respect to time t, we get that

$\dfrac{dv}{dt}=\dfrac{1}{27}\pi \times 3\times h^2\dfrac{dh}{dt}=\dfrac{1}{9}\pi h^2\dfrac{dh}{dt}$

Now, the liquid drips out the bottom of the filter at the constant rate of 4 cubic inches per second, ie $\dfrac{dv}{dt}=-4\ in^3$

and h = 2 inches deep.

$-4=\dfrac{1}{9}\times \pi\times (2)^2\dfrac{dh}{dt}\\\\-9\pi =\dfrac{dh}{dt}\\\\-28.28=\dfrac{dh}{dt}$

Hence, level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

7 0

2 years ago

6x^2+x-12 in factored form

pychu [463]

6x²+x-12

the first thing we need to do is find 2 numbers that add up to equal the middle term (1) but multiply together to get a product of -72 (-12*6)

two numbers that would fit this is 9 and -8
so now we placed 9x and -8x in place of the middle term

6x²+9x-8x-12

now we look for whats common between the first two numbers and divide them out

6x²+9x = 3x(2x+3)

now we do the same with the last two numbers

-8x-12 = -4(2x+3)

notice how the numbers in brackets are the same (2x+3)
we will keep (2x+3) and then combine the numbers on the outside

once we do that you should get an answer of

(3x-4)(2x+3)

hope this helped!

5 0

2 years ago