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3 years ago

8. Solve the system of equations using substitution.

Mathematics

1 answer:

Elodia [21]3 years ago

8 0

Answer:

Step-by-step explanation:

In order to solve this we need to plug in the answer choices and make sure they work for BOTH answers!

Let us start with option A. (6,3) 3 = 4(6) + 6 = 3 = 30 This is automaticly wrong because 3 doesnt equal 30. There is no need to try it on the second equation since the first one was wrong.

Next answer choice, B (3,6) 6 = 2(3) = 6=6. The second equation works perfect for this. Now we have to make sure that it works for the first one as well. 6 = 4(3) + 6 = 6 = 18 which is wrong.

Next, C. (1,2) 2 = 2(1) = 2=2 Right now lets check the other equation.

2 = 4(1) + 6 = 2=10. Wrong

Last, D. (-3, -6) -6 = 2(-3) = -6 = -6 Right now lets check the other equation.

-6 = 4(-3) + 6 = -6 = -6. CORRECT. Answer choice D works for both equations.

Sorry for the wait of response.

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

Is 4y^2 + 9 = -4 a linear equation?

bekas [8.4K]

Answer:

No.

Step-by-step explanation:

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6 0

3 years ago

Purchasing A regional survey found that 70% of all families who indicated an intention to buy a new car bought a new car within

zheka24 [161]

Answer:

If a family chosen at random bought a car, we need to find the probability that the family had not previously indicated an intention to buy a car = P(I'|B) = 0.3362

Step-by-step explanation:

Let the event that a family that intends to buy a car be I

Let the event that a family does not intend to buy a car be I'

Let the event that a family buys a car in those 3 months be B

Let the event that a family does not buy a car in those 3 months be B'

Given,

P(B|I) = 0.70

P(B|I') = 0.10

P(I) = 0.22

P(I') = 1 - P(I) = 1 - 0.22 = 0.78

If a family chosen at random bought a car, we need to find the probability that the family had not previously indicated an intention to buy a car = P(I'|B)

The conditional probability P(A|B), is given as

P(A|B) = P(A n B) ÷ P(B)

So,

P(B|I) = P(B n I) ÷ P(I)

P(B n I) = P(B|I) × P(I) = 0.70 × 0.22 = 0.154

P(B|I') = P(B n I') ÷ P(I')

P(B n I') = P(B|I') × P(I') = 0.10 × 0.78 = 0.078

P(B) = P(B n I) + P(B n I') = 0.154 + 0.078 = 0.232

P(B') = 1 - 0.232 = 0.768

P(I'|B) = P(B n I') ÷ P(B)

= 0.078 ÷ 0.232 = 0.3362

Hope this Helps!!!

8 0

3 years ago

This question is down below. The picture attached below. <br> Thanks.

Ostrovityanka [42]

The vendor has to sell 88 gingerbread houses to earn a profit of $665.60 and there is no chance that the vendor will earn $1500.

Given an equation showing profits of A Christmas vendor as

P=-0.1 $g^{2}$ +30g-1200.

We have to find the number of gingerbread houses that the vendor needs to sell in order to earn profit of $665.60 and $1500.

To find the number of gingerbread houses we have to put P=665.60 in the equation given which shows the profit earned by vendor.

665.60=-0.1 $g^{2}$ +30g-1200

0.1 $g^{2}$ -30g+1200+665.60=0

0.1 $g^{2}$ -30g+1865.60=0

Divide the above equation by 0.1.

$g^{2}$ -300g+18656=0

Solving for g we get,

g=[300± $\sqrt{(300)^{2}-4*1*18656 }$ ]/2*1

g=[300± $\sqrt{90000-74624}]/2$

g=[300± $\sqrt{15376}$ ]/2

g=(300±124)/2

g=(300+124)/2 , g=(300-124)/2

g=424/2, g=176/2

g=212,88

Because 212 is much greater than 88 so vendor prefers to choose selling of 88 gingerbread houses.

Put the value of P=1500 in equation P=-0.1 $g^{2}$ +30g-1200.

-0.1 $g^{2}$ +30g-1200=1500

0.1 $g^{2}$ -30g+1500+1200=0

0.1 $g^{2}$ -30g+2700=0

Dividing equation by 0.1.

$g^{2}$ -300g+27000=0

Solving the equation for finding value of g.

g=[300± $\sqrt{300^{2} -4*1*27000}$ ]/2*1

=[300± $\sqrt{90000-108000}] /2$

=[300± $\sqrt{-18000}$ ]/2

Because $\sqrt{-18000}$ comes out with an imaginary number so it cannot be solved for the number of gingerbread houses.

Hence the vendor has to sell 88 gingerbread houses to earn a profit of $665.60 and there is no chance that the vendor will earn $1500.

Learn more about equation at brainly.com/question/2972832

#SPJ1

7 0

1 year ago