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2 years ago

What is the y-value of the solution to the system of equations? 3x + 5y = 1 7x + 4y = −13

1 answer:

6 0

3x + 5y = 1 . . . . . . . . (1)
7x + 4y = -13 . . . . . . .(2)
(1) x 7: 21x + 35y = 7 . . (3)
(2) x 3: 21x + 12y = -39 .(4)
(3) - (4) = 23y = 46
y = 46/23 = 2

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Factorise 9w² - 100<br><br><br>

ohaa [14]

Answer:

$9\, w^{2} - 100 = (3\, w - 10) \, (3\, w + 10)$ .

Step-by-step explanation:

Fact:

$\begin{aligned} & (a - b)\, (a + b)\\ =\; & a^{2} + a\, b - a\, b - b^{2} \\ =\; & a^{2} - b^{2} \end{aligned}$ .

In other words, $(a^{2} - b^{2})$ , the difference of two squares in the form $a^{2}$ and $b^{2}$ , could be factorized into $(a - b)\, (a + b)$ .

In this question, the expression $(9\, w^{2} - 100)$ is the difference between two terms: $9\, w^{2}$ and $100$ .

$9\, w^{2}$ is the square of $3\, w$ . That is: $(3\, w)^{2} = 9\, w^{2}$ .
On the other hand, $10^{2} = 100$ .

Hence:

$9\, w^{2} - 100 = (3\, w)^{2} - (10)^{2}$ .

Apply the fact that $a^{2} - b^{2} = (a - b) \, (a + b)$ to factorize this expression. (In this case, $a = 3\, w$ whereas $b = 10$ .)

$\begin{aligned}& 9\, w^{2} - 100 \\ =\; & (3\, w)^{2} - (10)^{2} \\ = \; & (3\, w - 10)\, (3\, w + 10)\end{aligned}$ .

8 0

2 years ago

A cone has a 4 radius and a 8 height what is the volume

Marta_Voda [28]

Hey there! I'm happy to help!

To find the volume of a cone, you multiply the base by the height and then divide by three.

First, we need to find the base. A cone has a circle for the base. To find the area of a circle, we square the radius and multiply it by pi (we will use 3.14).

4²=16

16×3.14= 50.24

Now, we multiply our base by the height.

50.24×8=401.92

Finally, we divide by three.

401.92÷3≈133.973 (to nearest thousandth)

Therefore, the volume of the cone is about 133.973 units cubed. If you were to use exact pi, it would be more like 134 because of all those decimals after pi!

Now you can find the volume of cones!

I hope that this helps! Have a wonderful day!

8 0

2 years ago

Which of the following expressions is not equivalent to 12x + 18y?

Fed [463]

Answer:

3(4x + 18y)

..................

8 0

1 year ago

At the mall Julie finds a sale at her favorite store. Two pair of pants will cost $42. If she wants to buy 5 pair, how much will