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Semenov [28]
3 years ago
5

a square painting has an area of 81x^2-90x-25. A second square painting has an area of 25x^2+30x+9. What is an expression that r

epresent the difference of the area of the paintings? show two ways to find the solution
Mathematics
1 answer:
galina1969 [7]3 years ago
4 0

Answer:

The answer in the procedure

Step-by-step explanation:

Let

A1 ------> the area of the first square painting

A2 ---->  the area of the second square painting

D -----> the difference of the areas

we have

A1=81x^{2}-90x-25

A2=25x^{2}+30x+9

case 1) The area of the second square painting is greater than the area of the first square painting

The difference of the area of the paintings is equal to subtract the area of the first square painting from the area of the second square painting

D=A2-A1

D=(25x^{2}+30x+9)-(81x^{2}-90x-25)

D=(-56x^{2}+120x+34)

case 2) The area of the first square painting is greater than the area of the second square painting

The difference of the area of the paintings is equal to subtract the area of the second square painting from the area of the first square painting

D=A1-A2

D=(81x^{2}-90x-25)-(25x^{2}+30x+9)

D=(56x^{2}-120x-34)

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3 years ago
Two ships leave the same port in different directions, forming a 120° angle between them. One ship travels 70 mi. and the other
kondaur [170]

Answer : Distance between the ships to the nearest miles = 106.03 ≈ 106 mi.

Explanation :

Since we have shown in the figure below :

a=70 mi.

b=52 mi.

c=x mi.

\text{Since two ships leaves the same port in different directions forming a }120\textdegree\text{angle between them.}

So, we use the cosine rule , which states that

 c^2=a^2+b^2-2ab.cosC\\\\x^2=70^2+52^2-2\times 70\times 52\times cos(120\textdegree)\\\\x^2=4900+2704-7280\times (-0.5)\\\\x^2=7604+3640\\\\x^2=11244\\\\x=\sqrt{11244}\\\\x=106.03

So, c = x= 106.03 mi.

Hence, distance between the ships to the nearest miles = 106.03 ≈ 106 mi.


8 0
3 years ago
Savannah has a 22 ounce soda. She drinks 13 ounces. Enter the percentage of ounces Savannah has left of her soda. Round your ans
Kaylis [27]

Answer:

59%

Step-by-step explanation:

13/22=.59 or 59%

Take the amount she drank and divide by the total size of soda.

4 0
3 years ago
What is the value of 10C3?
Zigmanuir [339]
The answer is B. 120

nCr = n! / ((r! * (n - r)!)

n = 10
r = 3

10C3 = 10! / ((3! * (10 - 3)!)
         = 10! / ((3! * 7!)
         = (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (3 * 2 * 1 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
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3 years ago
2.6.5 A plant physiologist grew birch seedlings in the green-house and measured the ATP content of their roots. (See Example 1.1
Ilya [14]

Answer:

(a)\ \bar x = 1.19

(b)\ \sigma_x = 0.18

Step-by-step explanation:

Given

n = 4

x: 1.45\ 1.19\ 1.05\ 1.07

Solving (a): The mean

This is calculated as:

\bar x = \frac{\sum x}{n}

So, we have:

\bar x = \frac{1.45 + 1.19 + 1.05 + 1.07}{4}

\bar x = \frac{4.76}{4}

\bar x = 1.19

Solving (b): The standard deviation

This is calculated as:

\sigma_x = \sqrt{\frac{\sum(x - \bar x)^2}{n - 1}}

So, we have:

\sigma_x = \sqrt{\frac{(1.45 -1.19)^2 + (1.19 -1.19)^2 + (1.05 -1.19)^2 + (1.07 -1.19)^2}{4 - 1}}

\sigma_x = \sqrt{\frac{(0.1016}{3}}

\sigma_x = \sqrt{0.033867}

\sigma_x = 0.18

4 0
2 years ago
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