Z

X − y = 4 y − 8 = -x At which point do the given equations intersect each other?

Natali5045456 [20]

Answer:

(6,2)

Step-by-step explanation:

Graph is below

3 0

2 years ago

Which expression is equivalent to

Scilla [17]

The equivalent expression of $\frac{(5ab)^3}{30ab^{-7}}$ is $\frac{25a^{2}b^{10}}{6}$

<h3>How to determine the equivalent expression?</h3>

The expression is given as:

$\frac{(5ab)^3}{30ab^{-7}}$

Expand the numerator

$\frac{(5ab)^3}{30ab^{-7}} =\frac{125a^3b^3}{30ab^{-7}}$

Divide 125 and 30 by 5

$\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^3b^3}{6ab^{-7}}$

Apply the law of indices

$\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^{3-1}b^{3+7}}{6}$

Evaluate the exponent

$\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^{2}b^{10}}{6}$

Hence, the equivalent expression of $\frac{(5ab)^3}{30ab^{-7}}$ is $\frac{25a^{2}b^{10}}{6}$

Read more about equivalent expression at:

brainly.com/question/2972832

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6 0

2 years ago

Katie’s baby sister drinks 4 ounces of apple juice with breakfast every morning. There was a full gallon of juice on the table.

Vlad1618 [11]

Answer: 112 oz

First we have to work with the same units. According to the International System of Units (SI), the Liter (L) is the unit of measurement for liquids, however, we are going to use the ounce (oz) in this case, as it is the unit of measure of the juice that Katie's baby sister drinks.

In addition:

$1L=33.814 oz$ (1)

$1 pint=0.5L\approx 16 oz$ (2)

$1 gallon=3.78 L\approx 128 oz$ (3)

Knowing this, we can calculate how much of apple juice is left for the baby after Katie drank a portion.

In order to do this, we have to substract the amount of juice Katie drank ( $1 pint\approx 16 oz$ ) to the total amount of juice in the full gallon ( $1 gallon\approx 128 oz$ ):

$128 oz-16 oz=112 oz$

This means that there are $112 oz$ left for Katie’s baby sister.

In addition, taking into account the baby drinks $4 oz$ each day, the $112 oz$ left are equivalent to approximately 28 days.

5 0

3 years ago

How many subsets are there of the set N = {1, 42, 65, 12, 31, 27}?

lutik1710 [3]

Answer:

$\boxed{ \bold{ \huge{ \boxed{ \sf{64}}}}}$

Step-by-step explanation:

If ' n ' is the cardinal number of a set, the number of subsets of a given set can be obtained by using the formula 2ⁿ

Given,

N = { 1 , 42 , 65 , 12 , 31 , 27 }

where n ( total number of elements ) = 6

So, the number of possible subsets of set N :

= 2ⁿ

= 2⁶

= 2 × 2 × 2 × 2 × 2 × 2

= 64

Hope I helped!

Best regards!!

4 0

3 years ago

Simplify The following equations

Kryger [21]

Mostly collect like terms
use associative property which is
(a+b)+c=a+(b+c)
and remember that:
you just use a general rule
x+x=2x
x^2+x^2=2x^2
3xy4xy=7xy
3x+4x^2=3x+4x^2
you can only add like terms( like terms are terms that are same name like x or y are differnt, and like terms have same power exg x^2 and x^3 and x^1/2 and such

so first one

3b+11c-4c-c
since they are all c except for the first one term, just assign a number for each so it simplifies to c times(11-1)+b(3-4)=c(10-1b=10c-b or

you just use a general rule
x+x=2x
x^2+x^2=2x^2
3xy4xy=7xy
3x+4x^2=3x+4x^2

second one9a-1+8c-8a+c
group like terms
(9a-8a)+(8c+c)-1=(a)+(9c)-1=a+9c-1

12c+5a+7-13c+4a
group like terms(12c-13c)+(5a+4a)+7
add like terms
-c+9a+7
the solution is 9a-c+7

-15-6c+3b-6c+9-2b
group like terms
(-15+9)+(-6c-6c)+(3b-2b)
-6+(-12c)+b=b-6-12c

the answers are:

10c-b

a+9c-1

9a-c+7

b-12c-6

5 0

3 years ago