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2 years ago

Solve the system of linear equations by elimination. 4x−3y=8 5x−2y=−11

Mathematics

1 answer:

AleksandrR [38]2 years ago

7 0

Answer:

(-7, -12)

Step-by-step explanation:

4x-3y=8

5x-2y=-11

Is there any of the like terms can be added and the result will be 0? No, so we have to multiple one OR both of the equations to make that one number do that.

(I will try to remove the y like terms so i will multiple both of them by the opposite so both of the ys will be 6)

2(4x-3y=8)

-3(5x-2y=-11)

8x-6y=16

-15x+6y=33

(now the easy part… cancel the 6s and add the equations)

8x+(-15x)=-7x

16+33=49

-7x=49

(divide 49 by -7)

x=-7

Replace x in any of the equations and you’ll get the y value.

4x-3y=8

4(-7)-3y=8

-28-3y=8

-3y=36

y=12

Threfore, there is one solution which is….. (-7,-12)

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Suppose that the distribution of IQ's of North Catalina State University's students can be approximated by a normal model with m

konstantin123 [22]

Answer:

The required probability is 0.6517

Step-by-step explanation:

Consider the provided information.

North Catalina State University's students can be approximated by a normal model with mean 130 and standard deviation 8 points.

μ₁ = 130 and σ₁ = 8

Chapel Mountain University's students can be approximated by a normal model with mean 120 and standard deviation 10 points.

μ₂ = 120 and σ₂ = 10

As both schools have IQ scores which is normally distributed, distribution of this difference will also be normal with a mean of μ₁-μ₂ and standard deviation will be $\sqrt{\sigma_1^2+\sigma_2^2}$

Therefore,

μ = 130-120=10

$\sigma = \sqrt{8^2+10^2}=12.806$

Now determine the probability of North Catalina State University student's IQ is at least 5 points higher than the Chapel Mountain University student's IQ:

$z=\frac{\bar x-\mu}{\sigma}$

$z=\frac{5-10}{12.806}\approx-0.39$

Now by using the z table we find the z- score of -0.39 is 0.6517.

Hence, the required probability is 0.6517

6 0

2 years ago

Given: WY=ZX A is the midpoint of WY. A is the midpoint of ZX. Prove: WA =ZA

navik [9.2K]

Answer:

Given information: WY=ZX, A is the midpoint of WY and A is the midpoint of ZX.

To prove : WA =ZA

Proof:

A is the midpoint of WY, it means A divides WY in two equal parts.

$WA=AY$

So, WY is twice of WA.

$WY=2WA$ .... (1)

A is the midpoint of ZX, it means A divides ZX in two equal parts.

$ZA=AX$

So, ZX is twice of ZA.

$ZX=2ZA$ ... (2)

$WY=ZX$ (Given)

Substitute the values from equation (1) and (2).

$2WA=2ZA$

Divide both sides by 2.

$WA=ZA$

Hence proved.

5 0

3 years ago

Derik earns $10.00 per hour. He works 35 hours per week. How much will he earn in two weeks? If he spends $50, how much will Der

Ksenya-84 [330]

Answer:

650

Step-by-step explanation:

so the way I did this was by adding how much he works per week which is 35 per week. so he works 70 hours in 2 weeks. he earns 10 dollars per hour. so 10 times 70 you get 700 but he spends 50. so 700 minus 50. you get 650. he has 650 dollars left.

5 0

2 years ago

At the Olympic Games, a runner won the 26.2 mile marathon race in 2 hr 4 min and 1 second. What was his average speed in mph and

Contact [7]

The average speed of the runner is 12.7 mph and 20.4 km/h

Given that the runner ran 26.2 mile in 2hr and 4 minutes, we start of by converting the time from hours and minutes into minutes and finally hours, since hours is what we need. So, we have

2hr = 120mins

+ 4 mins = 124 mins

124 mins ÷ 60 hour/mins = 2.06 hours.

This means that the runner finished the race in 2.06 hours.

If we are to find the average speed in mile per hour, we have

Average speed = distance ran ÷ time taken

Average speed = 26.2 ÷ 2.06

Average speed = 12.7 mph

From the speed in mph, we can directly convert it to km/hr by saying

1 mph = 1.609 km/h

12.7 mph = 12.7 * 1.609 = 20.4 km/hr

for more, check: brainly.com/question/1989219

4 0

2 years ago

Y = 10x + 100

velikii [3]

Answer:

Step-by-step explanation:

10+100=1000

20+100=2000

5 0

3 years ago

Read 2 more answers