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postnew [5]
2 years ago
9

A triangular prism has a volume of 2500 cubic feet. What is the length of the prism if its triangular bases are right triangles,

each with perpendicular sides of 10 and 20 feet
Mathematics
1 answer:
seraphim [82]2 years ago
5 0

Answer:

25 ft

Step-by-step explanation:

V = AH, where A = area of the base, and H = height (length) of the prism

A = bh/2 for a triangle

V = bh/2 × H

2500 = (10)(20)/2 × H

2500 = 100H

H = 25

Answer: 25 ft

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Which real-world situation can be represented by the expression 12n – 5?
madam [21]

Answer:

It would be D, because you have 12 students who have tickets worth n amount, and all of them get a discount of $5.00 off. You would there have 12 times the number of tickets (n) minus $5.00 off from your discount

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Solve for -2<-3-3x<0
gregori [183]

-3 from all ends to get 1<-3x<3 then divide by -3 on all ends to get -1/3>x>-1 you flip the sign because of the negative,


8 0
3 years ago
Find the six trig function values of the angle 240*Show all work, do not use calculator
-BARSIC- [3]

Solution:

Given:

240^0

To get sin 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, sin 240 will be negative.

sin240^0=sin(180+60)

Using the trigonometric identity;

sin(x+y)=sinx\text{ }cosy+cosx\text{ }siny

Hence,

\begin{gathered} sin(180+60)=sin180cos60+cos180sin60 \\ sin180=0 \\ cos60=\frac{1}{2} \\ cos180=-1 \\ sin60=\frac{\sqrt{3}}{2} \\  \\ Thus, \\ sin180cos60+cos180sin60=0(\frac{1}{2})+(-1)(\frac{\sqrt{3}}{2}) \\ sin180cos60+cos180sin60=0-\frac{\sqrt{3}}{2} \\ sin180cos60+cos180sin60=-\frac{\sqrt{3}}{2} \\  \\ Hence, \\ sin240^0=-\frac{\sqrt{3}}{2} \end{gathered}

To get cos 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, cos 240 will be negative.

cos240^0=cos(180+60)

Using the trigonometric identity;

cos(x+y)=cosx\text{ }cosy-sinx\text{ }siny

Hence,

\begin{gathered} cos(180+60)=cos180cos60-sin180sin60 \\ sin180=0 \\ cos60=\frac{1}{2} \\ cos180=-1 \\ sin60=\frac{\sqrt{3}}{2} \\  \\ Thus, \\ cos180cos60-sin180sin60=-1(\frac{1}{2})-0(\frac{\sqrt{3}}{2}) \\ cos180cos60-sin180sin60=-\frac{1}{2}-0 \\ cos180cos60-sin180sin60=-\frac{1}{2} \\  \\ Hence, \\ cos240^0=-\frac{1}{2} \end{gathered}

To get tan 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, tan 240 will be positive.

tan240^0=tan(180+60)

Using the trigonometric identity;

tan(180+x)=tan\text{ }x

Hence,

\begin{gathered} tan(180+60)=tan60 \\ tan60=\sqrt{3} \\  \\ Hence, \\ tan240^0=\sqrt{3} \end{gathered}

To get cosec 240 degrees:

\begin{gathered} cosec\text{ }x=\frac{1}{sinx} \\ csc240=\frac{1}{sin240} \\ sin240=-\frac{\sqrt{3}}{2} \\  \\ Hence, \\ csc240=\frac{1}{\frac{-\sqrt{3}}{2}} \\ csc240=-\frac{2}{\sqrt{3}} \\  \\ Rationalizing\text{ the denominator;} \\ csc240=-\frac{2}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}} \\  \\ Thus, \\ csc240^0=-\frac{2\sqrt{3}}{3} \end{gathered}

To get sec 240 degrees:

\begin{gathered} sec\text{ }x=\frac{1}{cosx} \\ sec240=\frac{1}{cos240} \\ cos240=-\frac{1}{2} \\  \\ Hence, \\ sec240=\frac{1}{\frac{-1}{2}} \\ sec240=-2 \\  \\ Thus, \\ sec240^0=-2 \end{gathered}

To get cot 240 degrees:

\begin{gathered} cot\text{ }x=\frac{1}{tan\text{ }x} \\ cot240=\frac{1}{tan240} \\ tan240=\sqrt{3} \\  \\ Hence, \\ cot240=\frac{1}{\sqrt{3}} \\  \\ Rationalizing\text{ the denominator;} \\ cot240=\frac{1}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}} \\  \\ Thus, \\ cot240^0=\frac{\sqrt{3}}{3} \end{gathered}

5 0
1 year ago
A central angle measuring 150° intercepts an arc in a circle whose radius is 6. What is the area of the sector of the circle for
katovenus [111]

Answer: 15

Step-by-step explanation: its 15

4 0
3 years ago
Btw John makes 9$ an hour and amber makes 8$ an hour. REMEMBER TO ANSWER IN MINUTES NOT HOURS.
yarga [219]
Hello there! Provided the information, we know that the nearest multiple of 8 and 9 has to be greater than 50. 8 and 9 do not go into 50.

$9 • 6 hours = $54

$8 • 7 hours = $56

There are 60 minutes in an hour, so we can multiply accordingly:

60 minutes • 6 hours = 360 minutes

60 minutes • 7 hours = 420 minutes

Your final answers are:

It will take John 360 minutes to earn $50.

It will take Amber 420 minutes to earn $50.

(P.S. It takes Amber one more hour to earn $50 than it does for John to earn $50.)

Hope this helps!
8 0
2 years ago
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