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2 years ago

What is the point of intersection of these two lines? -4x + y = 8 2x - y = 4 (2, 0)

Mathematics

1 answer:

kotykmax [81]2 years ago

7 0

Answer:

(- 6, - 16 )

Step-by-step explanation:

Given the 2 equations

- 4x + y = 8 → (1)

2x - y = 4 → (2)

Adding the 2 equations term by term will eliminate the term in y

- 2x = 12 ( divide both sides by - 2 )

x = - 6

Substitute x = - 6 into either of the 2 equations and soilve for y

Substituting x = - 6 into (2)

2(- 6) - y = 4

- 12 - y = 4 ( add 12 to both sides )

- y = 16 ( multiply both sides by - 1 )

y = - 16

Solution is (- 6, - 16 )

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A cosmetic company makes three bottles of scented lotion using the recipe shown. Each bottle holds a different amount of lotion.

seropon [69]

Answer:

Part 1) Bottle 1 (vanilla=1,almond=3,pineapple=4)

Part 2) Bottle 2 (vanilla=2,almond=6,pineapple=8)

Part 3) Bottle 3 (vanilla=1 1/2,almond=4 1/2,pineapple=6)

Step-by-step explanation:

Let

x ----> the amount of vanilla sent

y ----> amount of almond sent

z ----> the amount of pineapple sent

we know that

$x:y:z=\frac{1}{8}:\frac{3}{8}:\frac{1}{2}$

$\frac{x}{y}=\frac{1}{8}:\frac{3}{8}$

$\frac{x}{y}=\frac{1}{3}$

$x=\frac{y}{3}$ -----> equation A

$\frac{x}{z}=\frac{1}{8}:\frac{1}{2}$

$\frac{x}{z}=\frac{1}{4}$

$x=\frac{1}{4}z$ -----> equation B

$\frac{y}{z}=\frac{3}{8}:\frac{1}{2}$

$\frac{y}{z}=\frac{3}{4}$

$y=\frac{3}{4}z$ -----> equation C

Part 1) Bottle 1

vanilla=?

almond=?

pineapple=4

we have

$z=4$

Find the value of x

substitute the value of z in equation B

$x=\frac{1}{4}(4)$

$x=1$

Find the value of y

substitute the value of z in equation C

$y=\frac{3}{4}(4)$

$y=3$

therefore

Bottle 1

vanilla=1

almond=3

pineapple=4

Part 2) Bottle 2

vanilla=?

almond=6

pineapple=?

we have

$y=6$

Find the value of x

substitute the value of y in equation A

$x=\frac{6}{3}=2$

Find the value of z

substitute the value of x in equation B

$2=\frac{1}{4}z$

solve for z

$z=8$

therefore

Bottle 2

vanilla=2

almond=6

pineapple=8

Part 3) Bottle 3

vanilla=1 1/2

almond=?

pineapple=?

we have

$x=1\frac{1}{2}$

convert to an improper fraction

$x=1\frac{1}{2}=\frac{1*2+1}{2}=\frac{3}{2}$

Find the value of y

substitute the value of x in equation A

$\frac{3}{2}=\frac{y}{3}$

$y=\frac{9}{2}$

convert to mixed number

$y=\frac{9}{2}=\frac{8}{2}+\frac{1}{2}=4\frac{1}{2}$

Find the value of z

substitute the value of x in equation B

$\frac{3}{2}=\frac{1}{4}z$

$z=6$

therefore

Bottle 3

vanilla=1 1/2

almond=4 1/2

pineapple=6

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2 years ago

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amm1812

Answer:

Step-by-step explanation:

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2 years ago

4/7 of the children in a pool are girls. What is the ratio of girls to boys?

marshall27 [118]

4/7 of the children in the pool are girls
3/7 of the children in the pool are boys
4/7:3/7
4:3 is the ratio of girls to boys

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2 years ago

A group of n people enter an elevator in a building with k floors. Each person independently selects a floor uniformly at random

____ [38]

Answer:

Hence the person stop at floor by at least one person will be

E(X)=(summation from K=1 to k)[1-{(k-1)/k}^n]

Step-by-step explanation:

Given:

There are n peoples and k floors in a building.

Selects floor with 1/k probability .

To find :

Elevator stop at each floor by at least one person.

Solution:

Now

let K= number of floor at which at least one person will be stopping.

For getting E(X)

consider a variable Ak =1 if a least one person get of the elevator

and values for k=1,2,3.....k

K=(summation From k=1 to k)Ak

E(K)=((summation From k=1 to k) E[Ak]

=(summation From k=1 to k)[ $1-{(k-1/k)^n$

Hence the person stop at floor by at least one person will be

E(K)=(summation from K=1 to k)[1-{(k-1)/k}^n]

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Big Ideas Math 7.4 Practice A 8th grade

ziro4ka [17]

Answer:

What do you mean

Step-by-step explanation:

I don’t understand

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2 years ago

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