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bagirrra123 [75]
3 years ago
8

What should be added to both sides of the equation below to complete the square?

Mathematics
1 answer:
Sveta_85 [38]3 years ago
8 0

Answer:

Step-by-step explanation:

x² + 6x = 8

Coefficient of the x term: 6

Divide it in half: 3

Square it: 3²

Add 3² to both sides of the equation to complete the square and keep the equation balanced:

x² + 6x + 3² = 8 + 3²

(x+3)² = 17

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Can someone help me with this? 20 points
lawyer [7]

Answer:

Step-by-step explanation:

Triangle ABC is a 45-45-90 right triangle. That means that segment BC also measures 10.

The big triangle as a whole is a 30-60-90. The side length across from the 30 degree angle is 10, so the whole length of BD is 10√3. However, since we already have the length of BC as 10, then segment CD measures

10√3 -10 which is 7.32

4 0
2 years ago
he owner of a local supermarket wants to estimate the difference between the average number of gallons of milk sold per day on w
stellarik [79]

Answer:

90% confidence interval is ( -149.114, -62.666   )

Step-by-step explanation:

Given the data in the question;

Sample 1                                Sample 2

x"₁ = 259.23                            x"₂ = 365.12

s₁  = 34.713                              s₂ = 48.297

n₁ = 5                                       n₂ = 10

With 90% confidence interval for μ₁ - μ₂ { using equal variance assumption }

significance level ∝ = 1 - 90% = 1 - 0.90 = 0.1

Since we are to assume that variance are equal and they are know, we will use pooled variance;

Degree of freedom DF = n₁ + n₂ - 2 = 5 + 10 - 2 = 13

Now, pooled estimate of variance will be;

S_p^2 = [ ( n₁ - 1 )s₁² + ( n₂ - 1)s₂² ] / [ ( n₁ - 1 ) + ( n₂ - 1 ) ]

we substitute

S_p^2 = [ ( 5 - 1 )(34.713)² + ( 10 - 1)(48.297)² ] / [ ( 5 - 1 ) + ( 10 - 1 ) ]

S_p^2 = [ ( 4 × 1204.9923) + ( 9 × 2332.6 ) ] / [  4 + 9 ]

S_p^2 = [ 4819.9692 + 20993.4 ] / [  13 ]

S_p^2 = 25813.3692 / 13

S_p^2 = 1985.64378

Now the Standard Error will be;

S_{x1-x2 = √[ ( S_p^2 / n₁ ) + ( S_p^2 / n₂ ) ]

we substitute

S_{x1-x2 = √[ ( 1985.64378 / 5 ) + ( 1985.64378 / 10 ) ]

S_{x1-x2 = √[ 397.128756 + 198.564378 ]

S_{x1-x2 = √595.693134

S_{x1-x2 = 24.4068

Critical Value = t_{\frac{\alpha }{2}, df = t_{0.05, df=13 = 1.771  { t-table }

So,

Margin of Error E =  t_{\frac{\alpha }{2}, df × [ ( S_p^2 / n₁ ) + ( S_p^2 / n₂ ) ]

we substitute

Margin of Error E = 1.771 × 24.4068

Margin of Error E = 43.224

Point Estimate = x₁ - x₂ = 259.23 - 365.12 = -105.89

So, Limits of 90% CI will be; x₁ - x₂ ± E

Lower Limit = x₁ - x₂ - E = -105.89 - 43.224 = -149.114

Upper Limit = x₁ - x₂ - E = -105.89 + 43.224 = -62.666

Therefore, 90% confidence interval is ( -149.114, -62.666   )

3 0
3 years ago
1. The manager of FrozonAir Refrigerator factory notices that on Monday it cost the company a total of $25,000 to build 30 refri
Vinvika [58]

Answer:

The fixed costs per day for the factory is $10,000 and marginal cost of one refrigerator for $500

Step-by-step explanation:

Let

Cost per refrigerator (marginal cost) = r

Fixed costs per day for the factory = f

Total cost = variable cost + fixed cost

Monday

25,000 = 30r + f

Tuesday

30,000 = 40r + f

Using Monday,

f = 25000 -30r

Substitute f = 25000 - 30r into Tuesday

30,000 = 40r + f

30,000 = 40r + (25,000 -30r)

30,000 = 40r + 25,000 - 30r

Collect like terms

30,000 - 25,000 = 40r - 30r

5,000 = 10r

Divide both sides by 10

r = 5,000 / 10

= 500

r = $500

Substitute r= 500 into Monday equation

f = 25,000 -30r

= 25,000 - 30(500)

= 25,000 - 15,000

= 10,000

f = $10,000

Therefore, the fixed costs per day for the factory is $10,000 and marginal cost of one refrigerator for $500

7 0
3 years ago
To get into shape, Miles ran for 1 minute on Monday, 3 minutes on Tuesday, 6 minutes on Wednesday, and 10 minutes on Thursday. I
Eduardwww [97]

Answer:

15 minutes??

I guess?

Step-by-step explanation:

Im really not sure

There's a pattern!!

You just need to count how many numbers passed by!

Clear?

3 0
3 years ago
What number do we divide by -9 to get 8?
Darya [45]

Answer:

-72 i notice you're having trouble message me and ill help you

7 0
3 years ago
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