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3 years ago

A triangle has side lengths of 24 in., 32 in., and 40 in. Is the triangle acute, obtuse, or right? A) right. B) obtuse. C) acute

1 answer:

8 0

The answer is: [A]: "right [triangle]" .
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Explanation:
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Given: Side lengths:
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" 24 in., 32 in., and 40 in " ;
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Divide each side length by "8" ;

24 in. / 8 = 3 in. ;

32 in. / 8 = 4 in. ; and

40 in. / 8 = 5 in. .
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3 in . , 4, in, 5 in. ; is a "right triangle" ;

since: 3² + 4² = 5² ;

→ 9 + 16 = 25 ;

according to the Pythagorean theorem: " a² + b² = c² " .
_________________________________________________

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A movie Theater charges $6.50 for morning tickets and $8.75 for night tickets the theater sold 378 tickets for a total amount of

Xelga [282]

Answer:

The number of sold morning tickets are 168.

Step-by-step explanation:

Given,

Total number of tickets = 378

Total earned amount = $2929.50

Charge of each morning ticket = $6.50

Charge of each night ticket = $8.75

Solution,

Let the number of morning tickets be 'x'.

And also let the number of night tickets be 'y'.

So, the total number of tickets is the sum of number of morning tickets and number of evening tickets.

So, framing in equation form, we get;

$x+y=378\ \ \ \ equation\ 1$

Again, Total earned amount is the sum of number of morning tickets multiplied with charge of each ticket and number of evening tickets multiplied with charge of each ticket.

So, framing in equation form, we get;

$6.50x+8.75y=2929.50\ \ \ equation\ 2$

On multiplying equation 2 by 100 on both side, we get;

$100(6.50x+8.75y)=2929.50\times100\\\\650x+875y=292950\ \ \ \ equation\ 3$

Now multiplying equation 1 by '650', we get;

$650(x+y)=378\times650\\\\650x+650y=245700\ \ \ \ equation\ 4$

Now subtracting equation 4 from equation 3, we get;

$(650x+875y)-(650x+650y)=292950-245700\\\\650x+875y-650x-650y=47250\\\\225y=47250\\\\y=\frac{47250}{225}=210$

Now substituting the value of'y' in equation 1, we get;

$x+y=378\\\\x+210=378\\\\x=378-210=168$

Hence The number of sold morning tickets are 168.

Whereas The number of sold night tickets are 210.

5 0

3 years ago

Amber is an engineer designing a suspension bridge. She has a tower at each end of the bridge that will hang four diagonal cable

Usimov [2.4K]

Answer

she should find the length from where the tower begins to where the cable touches the ground, and use that number to be leg B, with the hight of the tower being constant and being leg A. then she uses the two numbers to find the hypotenuse of the new triangle. Repeat this with the other 3 cables and you have the answer! (Note: leg A's length will remain constant, but leg B's length will not because it is reliant on how far away the cables contact the ground in relation to the tower.)

Step-by-step explanation:

Hope tis helps :)

3 0

3 years ago

In the diagram, GB = 2x + 3.. What is GB?

tia_tia [17]

Answer:

GB = 15

Step-by-step explanation:

DC, EB and FA are the medians of the triangle.

The point G where the medians intersect is the centroid.

On each median the distance from the vertex to the centroid is twice as long as the distance from the centroid to the midpoint, hence

FG = 2GA, that is

5x = 2(x + 9)

5x = 2x + 18 ( subtract 2x from both sides )

3x = 18 ( divide both sides by 3 )

x = 6

Hence

GB = 2x + 3 = (2 × 6) + 3 = 12 + 3 = 15

6 0

3 years ago

If g(x) = 2x - 5 and h(x) = 3x + 7, then g(h(x)) = ?

Anarel [89]

Answer:

Step-by-step explanation:

g(h(x))=g(3x + 7). Since h(x)=3x + 7

g(h(x))= 2(3x + 7) - 5

g(h(x))= 6x + 14 -5

=6x +9

3 0

3 years ago

C U12122 Write a Sum or Difference as a Product A 8 Questions 1. Use the GCF to rewrite the sum as a product. 30 + 16 a) 8 (3+2)

Alex73 [517]

Answer:

2(15+8)

Step-by-step explanation:

Given the expression 30+16

We are to use GCF to rewrite the sum as a product.

Get the factor of each value first as shown;

30 = 2 * 15

16 = 2 * 8

substitute the factors back into the expression:

30+16 = (2*15)+(2*8)

Since 2 is common to both terms, then:

30+16 = 2(15+8)

Hence the required sum of product of the terms is 2(15+8)

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2 years ago