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zavuch27 [327]
2 years ago
12

30 POINTS!!! Louie is trying to find a rectangular canvas for his art project. Its diagonal must measure 23.3 inches and form a

31° angle with the bottom of the canvas. What is the height of the canvas? Round your answer to the nearest inch. 12 inches 14 inches 24 inches 27 inches
Mathematics
2 answers:
Lisa [10]2 years ago
7 0

Answer:

12 inches

Step-by-step explanation:

Given

\theta = 31^{\circ}

diagonal = 23.3\ in

Required

Determine the height of the canvas

The question is illustrated using the attached image.

Using the attachment as a point of reference, the height is calculated from

sin \theta = \frac{opp}{hyp}

This gives:

sin 31^{\circ}= \frac{h}{23.3}

Make h the subject

h = 23.3 * sin(31^{\circ)

h = 23.3 * 0.5150\\

h = 11.9995

h = 12\ inches

zysi [14]2 years ago
5 0

Answer:

A 12 Inches

Step-by-step explanation:

I got it right on the test

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What are the x and y intercepts of f(x) = x2-x-12/x2+5x+6 and is there a hole? ​
stiv31 [10]

Answer:

There are no holes. The VAs are x=4 & x=-4  the HA is  x=2 the x intercepts are  (-3,0) & (3,0)  and the y intercept is (0,9/8).

Step-by-step explanation:

Given  f ( x ) =2 x ^2 − 18/x^2-16

find all asymptotes, holes and intercepts.

Factor the numerator and denominator.

f ( x ) =2 ( x ^2 − 9 )/( x + 4 ) ( x − 4 )

f ( x ) =2 ( x +3 ) ( x − 3 )/( x + 4 ) ( x − 4 )

A hole exists when the numerator and denominator contain the same factor (a factor "cancels out"). This function has no holes.

To find the vertical asymptote(s) (VA), find the values of  x

which make the denominator equal zero. The function is undefined at these values of  x

because you cannot divide by zero.

Set each factor of the denominator equal to zero and solve.

x + 4 = 0  and x − 4 = 0

x = − 4  and  x = 4

These are the VAs.

To find the horizontal asymptote(HA), compare the degree of the numerator and denominator. If the degrees are the same, the HA is the ratio of the leading coefficients.

For  f ( x) =2 x ^2 − 18/x^2-16

the degree in both numerator and denominator is  2

and the ratio of the leading coefficients is 2/1=1

The HA is  x = 2

The  x  intercept is the value at which the function (or "y") equals zero. If the numerator is zero, the function equals zero.

2 ( x + 3 ) ( x − 3 ) = 0

x + 3 = 0    x − 3 = 0

x = − 3   and  x = − 3

The  x  intercepts are  ( − 3 , 0 )  and  ( 3 , 0 ) .

The  y  intercepts are found by setting  x = 0 .

f ( 0 ) = 2 ( 0 ) ^2 − 18/( 0 )^2 − 16 = 9 /8

The  y  intercept is  ( 0 , 9/ 8 ) .

graph{(2x^2-18)/(x^2-16) [-10.04, 9.96, -3.56, 6.44]}

HOPE THIS HELPS YOU!!!!

        =)

4 0
3 years ago
The distances of a port from 20 differ- ent locations form an AP. If the farthest distance is 300 km, and the nearest distance i
Mkey [24]

Answer:

Required difference = 270/19 km

Step-by-step explanation:

If we consider the AP of distances to be

a, a + r, a + 2r, ..., a + 19r,

where a is the distance of the nearest location from the port and r is the difference between any two successive location.

Given that,

a + 19r = 300 .....(1)

a = 30 ..... (2)

Using (2), from (1), we get

30 + 19r = 300

or, 19r = 300 - 30

or, 19r = 270

or, r = 270/19

Therefore the distance between any two successive location is 270/19 km.

5 0
2 years ago
PLEASE HELP FAST! WILL MARK AS BRAINLIEST IF GIVEN GOOD ANSWER!
S_A_V [24]

Answer:

8y=8 or 4y=-4

Step-by-step explanation:

1.)-2(x+3y=-1)

   2x+2y=6

2.)-2x+6y=2

     2x+2y=6

3.)6y=2  

   2y+6

4.)8y=8 (If adding) or 4y=-4 (If subtracting)

5 0
3 years ago
Can someone please help me with math.
krek1111 [17]

Answer:

Step-by-step explanation:

1) Number of nickels = x

Number of quarter = y

x + y = 7   ----------------------(I)

x = 7 - y ------------------------(II)

0.05x + 0.25y = 0.55 -----------(III)

Substitute s = 7 - y in equation (III)

0.05*(7 - y)  + 0.25y = 0.55

0.05*7 - 0.05*y + 0.25y = 0.55

0.35 <u>- 0.05y + 0.25y</u>  = 0.55            {Combine like terms}

0.35  + 0.20y  = 0.55          {Subtract 0.35 from both sides}

  0.2y = 0.55 - 0.35

   0.2y = 0.2       {Divide both sides by 0.2}

        y = 0.2/0.2

y = 1

Substitute y =1 in equation (II)

x = 7 - 1

x = 6

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2) Number of children tickets = x

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2x + 5y = 170 -----------------(III)

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2*(40-y) + 5y = 170

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80 + 3y = 170                {Subtract 80 from both sides}

       3y = 170 - 80

       3y = 90       {Divide both sides by 3}

         y = 90/3

y = 30

Substitute y = 30 in equation (II)

x  = 40 - 30

x = 10

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Number of adult tickets =30

3 0
3 years ago
What is the square root of pi
san4es73 [151]

Answer:

The square root of pi is 1.7724

8 0
2 years ago
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