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3 years ago

Rewrite, using the distributive property. 5(2x – 3y) = [?]* - [ ]y

Mathematics

1 answer:

olchik [2.2K]3 years ago

7 0

Answer:

10x-15y

Step-by-step explanation:

So, when they say use the distrubutive property, they basically mean turning this:

a(b+c)

Into this:

ab+ac

So in this case, it would be:

5(2x-3y)

And we will turn it into:

10x-15y

ANother way to think about it is we are multiplying 2x by 5, and -3y by 5. So:

2x*5

10x

And

-3y*5

-15y

Then we can combine these two:

10x-15y

Hope this helps!

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15y+31=61 how do I solve this

Setler79 [48]

15y + 31 = 61
15y = 61 - 31
15y = 30
y = 30 ÷ 15
y = 2

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4 years ago

Fill in the missing operator where the blank is (-40)__(8)=-5 please I need help

Aleks04 [339]

Answer:

The operator would be division

Step-by-step explanation:

-40/8=-5

4 0

3 years ago

If a plant manufacturing carpet backing has a cylindrical tank that is 3 meters high and is 6 meters in diameter, what is the vo

Oksi-84 [34.3K]

Volume of a cylinder = cross sectional area * height
so...
height = 3m
cross sectional area = pi × radius^2
radius = 1/2 diameter
radius = 1/2 × 6 = 3
3.14 × 3^2
= 3.14 × 9
= 28.26
therefore...
volume of cylinder = 28.26 × 3
= 84.78 m^3

8 0

3 years ago

Read 2 more answers

Rewrite without absolute value for the given conditions: y=|x−5|+|x+5|, if x>5

julia-pushkina [17]

Answer:

$y=2x$ if $x>5$

Problem:

"Rewrite without absolute value for the given conditions: y=|x−5|+|x+5|, if x>5"

Step-by-step explanation:

Let's figure out when the insides of the absolute values are positive and negative, and then see where the given condition that x>5 fits into that.

$|x-5|=x-5$ if $x-5$ is positive or 0, $\ge 0$ .

$x-5 \ge 0$

Add 5 on both sides:

$x \ge 5$ .

$|x-5|=-(x-5)$ if $x-5$ is negative or zero, $\le 0$ .

$x-5 \le 0$

Add 5 on both sides:

$x \le 5$

Since $x>5$ then we will choose $|x-5|=x-5$ .

---

$|x+5|=x+5$ if $x+5$ is positive or 0, $\ge 0$ .

$x+5 \ge 0$

Subtract 5 on both sides:

$x \ge -5$ .

$|x+5|=-(x+5)$ if $x+5$ is negative or zero, $\le 0$ .

$x+5 \le 0$

Subtract 5 on both sides:

$x \le -5$

Since $x>5$ then we will choose $|x+5|=x+5$ .

$y=|x−5|+|x+5|$ with $x>5$ :

$y=(x-5)+(x+5)$

$y=(x+x)+(-5+5)$

$y=(2x)+(0)$

$y=2x+0$

$y=2x$

6 0

3 years ago

PLSS HELP ME I NEED IT ASAPP TYSM ILY

Hatshy [7]

Answers:

He needs 310 grams of the 99% cocoa brand
He needs 590 grams of the 70% cocoa brand

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

Explanation:

Let's label the two brands of chocolate as A and B

Brand A is 99% cocoa
Brand B is 70% cocoa

Furthermore, define these variables

x = amount of brand A
y = amount of brand B

The amounts are in grams.

The two amounts must add to 900 grams, so x+y = 900. This can be solved to y = 900-x which we'll use later.

Since we have x grams of brand A, and brand A has 99% cocoa, this means 0.99x represents the amount of pure cocoa from brand A.

Similarly, brand B contributes another 0.70y grams of pure cocoa

Overall, we're dealing with 0.99x+0.70y grams of pure cocoa from the two brands mixed together.

---------------

Rolf needs 900 grams of final product. He wants it to be 80% cocoa, which means 80% of the 900 is going to be pure cocoa

80% of 900 = 0.80*900 = 720

Rolf wants 720 grams of pure cocoa after mixing the two brands together.

So this leads to the second equation: 0.99x+0.70y = 720

---------------

Let's apply substitution to replace y with 900-x

0.99x+0.70y = 720

0.99x+0.70( y ) = 720

0.99x + 0.70( 900-x ) = 720

At this point, we have a single variable in which we can isolate x fully.

0.99x + 0.70( 900-x ) = 720

0.99x + 0.70( 900) + 0.70(-x) = 720

0.99x + 630 - 0.70x = 720

0.29x = 720-630

0.29x = 90

x = 90/(0.29)

x = 310.344827586 which is approximate

Rounding to the nearest full gram, we get x = 310

Use this x value to find y

y = 900-x

y = 900-310.344827586

y = 589.655172414 which is also approximate

y = 590 when rounding to the nearest whole number

---------------

In summary, we have

x = 310
y = 590

Meaning that Rolf will need 310 grams of brand A to mix with 590 grams of brand B.

If we plugged those values into x+y = 900, then that equation works out.

If we tried the second equation, then,

0.99x+0.70y = 720

0.99*310+0.70*590 = 720

719.9 = 720

The slight discrepancy is due to the fact we rounded those approximate x and y values to the nearest whole number. We would get better accuracy if we rounded to say the nearest tenth or hundredth.

8 0

2 years ago