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IrinaVladis [17]
1 year ago
7

Shannon made a scale drawing of a farm. the scale she used was 1 centimeter : 9 meters. the actual length of the goat pen is 18

meters. how long is the pen in the drawing?
Mathematics
1 answer:
Hitman42 [59]1 year ago
5 0

Answer:

2 meters

Step-by-step explanation:

18/9=2, so 2 centimeters

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Please help me on this
IrinaVladis [17]

Answer:

Step-by-step explanation:

coordinate of O(2,1),Y(3,-2),T(-3,-3)

let the reflected points are O',Y',T'

distance of O from y=2 is 1 unit.

∴ ordinate of O' =1+2(1)=3

or O' is (2,3)

distance of Y from y=2 is2+2=4

ordinate of Y'=-2+2(4)=6

so coordinate of Y' is (3,6)

distance of T from y=2 is (2+3)=5

so ordinate of T' =-3+2(5)=7

coordinate of T' is(-3,7)

3 0
2 years ago
1. Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.
german

Answer:

Step-by-step explanation:

1.

To write the form of the partial fraction decomposition of the rational expression:

We have:

\mathbf{\dfrac{8x-4}{x(x^2+1)^2}= \dfrac{A}{x}+\dfrac{Bx+C}{x^2+1}+\dfrac{Dx+E}{(x^2+1)^2}}

2.

Using partial fraction decomposition to find the definite integral of:

\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}dx

By using the long division method; we have:

x^2-8x-20 | \dfrac{2x}{2x^3-16x^2-39x+20 }

                  - 2x^3 -16x^2-40x

                 <u>                                         </u>

                                            x+ 20

So;

\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}= 2x+\dfrac{x+20}{x^2-8x-20}

By using partial fraction decomposition:

\dfrac{x+20}{(x-10)(x+2)}= \dfrac{A}{x-10}+\dfrac{B}{x+2}

                         = \dfrac{A(x+2)+B(x-10)}{(x-10)(x+2)}

x + 20 = A(x + 2) + B(x - 10)

x + 20 = (A + B)x + (2A - 10B)

Now;  we have to relate like terms on both sides; we have:

A + B = 1   ;   2A - 10 B = 20

By solvong the expressions above; we have:

A = \dfrac{5}{2}     B =  \dfrac{3}{2}

Now;

\dfrac{x+20}{(x-10)(x+2)} = \dfrac{5}{2(x-10)} + \dfrac{3}{2(x+2)}

Thus;

\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}= 2x + \dfrac{5}{2(x-10)}+ \dfrac{3}{2(x+2)}

Now; the integral is:

\int \dfrac{2x^3-16x^2-39x+20}{x^2-8x-20} \ dx =  \int \begin {bmatrix} 2x + \dfrac{5}{2(x-10)}+ \dfrac{3}{2(x+2)} \end {bmatrix} \ dx

\mathbf{\int \dfrac{2x^3-16x^2-39x+20}{x^2-8x-20} \ dx =  x^2 + \dfrac{5}{2}In | x-10|\dfrac{3}{2} In |x+2|+C}

3. Due to the fact that the maximum words this text box can contain are 5000 words, we decided to write the solution for question 3 and upload it in an image format.

Please check to the attached image below for the solution to question number 3.

4 0
2 years ago
A 25,000-gallon swimming pool needs to be completely drained for maintenance purposes.
egoroff_w [7]

Answer:

A: 1800h-25,000

B: Yes, he would have time.

Step-by-step explanation:

A:

Lets turn 30 gallons/minute into hours so we can make it easier.

18000h-25000

Then plug in h which is hours. To get your answer

B:

From May 7 at 8:00 a.m. to May 8 at 12 p.m. would be 28 hours.

So we plug in 28 for h and get our answer of 25400 gallons/hour

8 0
3 years ago
There are 3200 students at Lake High School and 2/5 of these students are sophomores. If 3/8 of the sophomores are opposed to th
svet-max [94.6K]

Answer:

4

Step-by-step explanation:

2/5*3000 = 1200 seniors

then

3000 - 1200 = 1800 students not seniors

therefore

4/5* 1200 = 960 do not like rock climbing

and

9/10** 1800 = 1620 also do not like it:

"how many students are in favor of this idea?"

subtract the "don't likes" from 3000

3000 - (960+1620) = 420 like rock climbing:

3x-x+2=4

5 0
3 years ago
Read 2 more answers
when two fractions refer to the same whole and have the same denominators explain why you can compare only the numerators​
Mars2501 [29]

Answer:

If the two fractions simplify to fractions with a common denominator, you can then compare numerators. If the denominators are different, you can find a common denominator first and then compare the numerators. Two fractions are equivalent fractions when they represent the same part of a whole.

Hope This Helps!    Have A Nice Day!!

7 0
2 years ago
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