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evablogger [386]
3 years ago
15

5(x+4)+10-2x+3(2x+9)

Mathematics
1 answer:
qwelly [4]3 years ago
4 0

Answer:

x = (-19)/3

Step-by-step explanation:

Solve for x:

10 - 2 x + 5 (x + 4) + 3 (2 x + 9) = 0

5 (x + 4) = 5 x + 20:

10 - 2 x + 5 x + 20 + 3 (2 x + 9) = 0

3 (2 x + 9) = 6 x + 27:

6 x + 27 + 5 x - 2 x + 10 + 20 = 0

Grouping like terms, 6 x + 5 x - 2 x + 10 + 20 + 27 = (-2 x + 5 x + 6 x) + (10 + 20 + 27):

(-2 x + 5 x + 6 x) + (10 + 20 + 27) = 0

-2 x + 5 x + 6 x = 9 x:

9 x + (10 + 20 + 27) = 0

10 + 20 + 27 = 57:

9 x + 57 = 0

Subtract 57 from both sides:

9 x + (57 - 57) = -57

57 - 57 = 0:

9 x = -57

Divide both sides of 9 x = -57 by 9:

(9 x)/9 = (-57)/9

9/9 = 1:

x = (-57)/9

The gcd of 57 and 9 is 3, so (-57)/9 = (-(3×19))/(3×3) = 3/3×(-19)/3 = (-19)/3:

Answer: x = (-19)/3

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A cylindrical swimming pool has a diameter of 20 feet and a height of 3.5 feet. How many gallons of water can the pool contain?
kvasek [131]

Answer:

The swimming pool will contain approx 8243\ gal of water.

Step-by-step explanation:

Given the swimming pool is in a cylindrical shape.

And the dimensions are 20\ feet diameter with a height of 3.5\ feet.

Also, 1\ ft^3 =7.5\ gal

First, we will find the volume of the swimming pool.

The swimming pool is in cylindrical shape.

So, the volume would be \pi r^2h

The height (h) is given as 3.5\ feet. To calculate radius (r) we will divide the diameter by two.

The radius of the cylinder would be \frac{20}{2}=10\ feet

Plug these values in the formula we get,

\pi r^2h\\=\pi\times 10^2\times 3.5\\=3.14\times 100\times 3.5\\=1099\ ft^3

Now, it is given 1\ ft^3 =7.5\ gal

So, 1099\ ft^3 =1099\times 7.5\ gal=8242.5\ gal

The swimming pool will contain approx 8243\ gal of water.

6 0
3 years ago
The thickness of a plastic film (in mils) on a substrate material is thought to be influenced by the temperature at which the co
statuscvo [17]

Answer:

Step-by-step explanation:

Hello!

The objective is to test if rising the process temperature reduces the thickness of the plastic film that coats a substrate material To do so, two samples of substrates are coated at different temperatures:

Sample 1

X₁: Thickness of the plastic film after the substrate is coated at 125F

n₁=11

X[bar]₁= 101.28

S₁= 5.08

Sample 2

X₂: Thickness of the plastic film after the substrate is coated at 150F

n₂= 13

X[bar]₂= 101.70

S₂= 20.15

Does the data support this claim? Use the P-value approach and assume that the two population standard deviations are not equal.

Now if the higher the heat, the thinner the thickness of the plastic coating, then the average thickness of the coating done at 150F should be less than the average thickness of the coating done at 125F, symbolically: μ₂ < μ₁

Then the hypotheses are:

H₀: μ₂ ≥ μ₁

H₁: μ₂ < μ₁

α:0.05 (there is no α level stated so I've chosen the most common one)

Assuming that both variables have a normal distribution since the population standard deviations are not equal, the statistic to use is the Welch's t-test:

t= \frac{(X[bar]_2-X[bar]_1)-(Mu_1-Mu_2)}{\sqrt{\frac{S^2_1}{n_1} +\frac{S^2_2}{n_2} } } ~~t_w

t_{H_0}= \frac{(101.7-101.28)-0}{\sqrt{\frac{(20.15)^2}{13} +\frac{(5.08)^2}{11} } } = 0.072

This test is one-tailed to the left, meaning that you'll reject the null hypothesis at small values of t. The p-value is also one-tailed and has the same direction as the test. To calculate it you have to first calculate the degrees of freedom of the Welch's t:

Df_w= \frac{(\frac{S^2_1}{n_1} +\frac{S^2_2}{n_2} )^2}{\frac{(\frac{S^2_1}{n_1})^2 }{n_1-1}+\frac{(\frac{S^2_2}{n_2} )^2}{n_2-1}  }

Df_w= \frac{(\frac{5.08^2}{11} +\frac{20.15^2}{13} )^2}{\frac{(\frac{5.08^2}{11})^2 }{10} +\frac{(\frac{20.15^2}{13} )^2}{12} } = 13.78

The distribution is a Student's t with 13 degrees of freedom, then you can calculate the p-value as:

P(t₁₃≤0.072)= 0.4718

Using the p-value approach, the decision rule is:

If the p-value ≤ α, the decision is to reject the null hypothesis.

If the p-value > α, the decision is to not reject the null hypothesis.

The p-value is greater than the significance level, so the decision is to nor reject the null hypothesis.

Using a significance level of 5%, there is no significant evidence to support the claim that the average thickness pf the plastic coat processed at 150F is less than the average thickness pf the plastic coat processed at 125F.

I hope you have a SUPER day!

4 0
3 years ago
The increase in a person’s body temperature T(t), above 98.6ºF, can be modeled by the function T(t)=4t/t^2+1, where trepresents
elena-14-01-66 [18.8K]
The meaning of the horizontal asymptote is that the increase in a person's body temperature is a constant value when long time passes.

You can obtain that value by calculating the limit of the function when t → ∞:

                 4t
T(t) =  ------------- => Lim T(t) when t → +∞ = 0.
             t^2 + 1

That means that at long term the Temperature tends to remain at 98.6°F.
7 0
2 years ago
Rebecca needs 10 1/2 yards of fabric to make quilt. She has one piece of fabric that is 2 1/2 yards and another piece of fabric
ASHA 777 [7]

Answer:

-15/4

Step-by-step explanation:

Add 2 1/2 and 4 1/4

Take that fraction and subtract it from 10 1/2

6 0
3 years ago
Can someone pls pls help me ?
Yakvenalex [24]

9514 1404 393

Answer:

  a = 9 meters

Step-by-step explanation:

The perimeter is the sum of the side lengths:

  28 m = a + 2m + a + 8m

  18 m = 2a . . . . . . . . . . . . . . . . subtract 10m, collect terms

  9 m = a . . . . . . . . . . . . . . . divide by 2

The value of a is 9 meters.

8 0
2 years ago
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