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LuckyWell [14K]
3 years ago
14

Solve each word problem using a system of equations. Use substitution or elimination.

Mathematics
1 answer:
nasty-shy [4]3 years ago
4 0

Answer:

Step-by-step explanation:

x + 3y = 24.....multiply by -1

5x + 3y = 36

------------------

-x - 3y = -24 (result of multiplying by -1)

5x + 3y = 36

------------------add

4x = 12

x = 12/4

x = 3 <=======

x + 3y = 24

3 + 3y = 24

3y = 24 - 3

3y = 21

y = 21/3

y = 7 <========

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Find the volume of the given solid. Under the surface z = 6xy and above the triangle with vertices (1, 1), (4, 1), and (1, 2)
Leya [2.2K]

he volume of the solid under a surface  

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and above a region D is given by the formula  

∫

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Here  

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Here is a sketch of the triangle:

Intersecting Region

The inequalities that describe D are given by the sketch as:  

1

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−

x

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Therefore, volume is

V

=

∫

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1

∫

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x

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3

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6

x

y

d

y

d

x

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6

x

[

y

2

2

]

−

x

3

+

7

3

1

d

x

=

3

∫

4

1

x

[

y

2

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−

x

3

+

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3

1

d

x

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1

x

[

49

9

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14

x

9

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x

2

9

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1

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d

x

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3

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4

1

40

x

9

−

14

x

2

9

+

x

3

9

d

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[

40

x

2

18

−

14

x

3

27

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x

4

36

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4

1

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3

[

(

640

18

−

896

27

+

256

36

)

−

(

40

18

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14

27

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4 0
3 years ago
What is the distance between coordinates (-6.25,5) and (-3.75,2)
Oksi-84 [34.3K]

Answer:

\sqrt{15.25}

Step-by-step explanation:

To find the distance, we can use the distance formula:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} when the given points are (x_1,y_1) and (x_2,y_2)

Plug in the points (-6.25,5) and (-3.75,2)

d=\sqrt{(-6.25-x_1)^2+(5-y_1)^2}\\d=\sqrt{(-6.25-(-3.75))^2+(5-2)^2}\\d=\sqrt{(-6.25+3.75)^2+(5-2)^2}\\d=\sqrt{(-2.5)^2+(3)^2}\\d=\sqrt{6.25+9}\\d=\sqrt{15.25}

Therefore, the distance between the two coordinates is \sqrt{15.25}, or approximately 3.91.

I hope this helps!

6 0
3 years ago
Write the equation in slope intercept form<br> 2x+y=6
Rina8888 [55]

Answer: the slope intercept form of 2x+y=6 is y=-2+6

Step-by-step explanation:

2x+y=6  (subtract 2x from both sides)

-2x    -2x  (the -2x and the 2x cancel leaving...)

<u><em>y=-2x+6</em></u>  →( y equals negative two x plus six)

3 0
3 years ago
What values of c and d make the equation true?
saul85 [17]

Answer:

Third option.

Step-by-step explanation:

You need to cube both sides of the equation. Remember the Power of a power property:

(a^m)^n=a^{mn

\sqrt[3]{162x^cy^5}=3x^2y(\sqrt[3]{6y^d})\\\\(\sqrt[3]{162x^cy^5})^3=(3x^2y(\sqrt[3]{6y^d}))^3\\\\162x^cy^5=27x^6y^36y^d

According to the Product of powers property:

(a^m)(a^n)=a^{(m+n)

Then. simplifying you get:

162x^cy^5=162x^6y^{(3+d)}

Now you need to compare the exponents. You can observe that the exponent of "x" on the right side is 6,  then the exponent of "x" on the left side must be 6. Therefore:

c=6

You can notice that the exponent of "y" on the left side is 5,  then the exponent of "x" on the left side must be 5 too. Therefore "d" is:

3+d=5\\d=5-3\\d=2

4 0
3 years ago
By hiring 45 new employees, a department store increased its help by 18% during the Christmas season. How many employees did the
bagirrra123 [75]
Hi!

We can set up a proportion then cross multiply to solve this.

\frac{45}{x}  \frac{18}{100}

45 x 100 = 4500
4500/18 = 250

The answer is 250

Hope this helps! :)
7 0
3 years ago
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