Find the surface area of the triangular prism. Be sure to include the correct unit in your answer.

Using the tangent theorem and the inscribed angle theorem, we have:

a. m∠SQT = 74°; b. m∠RQS = 16°.

Angle formed at the point of tangency between the tangent and the radius of a circle = 90 degrees based on the tangent theorem.

The inscribed angle theorem states that, measure of inscribed angle = 1/2(measure of intercepted arc).

a. Find m(SQT):

m∠RQT = 90° [tangent theorem]

m(QR) = 180° [semicircle]

m(QRS) = 212° [given]

m(RS) = m(QRS) - m(QR) = 212 - 180 = 32°

m∠RQS = 1/2[m(RS)] [inscribed angle theorem]

m∠RQS = 1/2(32)

m∠RQS = 16°

m∠SQT = m∠RQT - m∠RQS = 90 - 16

m∠SQT = 74°

b. m∠RQS = 1/2(32)

m∠RQS = 16°

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Answer:

[tex]x=\frac{1}{2}\left(\tan^{-1}{4}+\pi k\right)[/tex], where k is any integer

Step-by-step explanation:

Let's start by getting all the trig functions on one side and all the constants on the other. We can do this by dividing both sides by [tex]\cos{2x}[/tex]:

[tex]\dfrac{\sin{2x}}{\cos{2x}}=4[/tex]

This ratio looks familiar! It just so happens that the tangent function is defined as the ratio of sine to cosine. In our case:

[tex]\dfrac{\sin{2x}}{\cos{2x}}=\tan{2x}[/tex]

Substituting this back into our equation, we have [tex]\tan{2x}=4[/tex]. We can unwrap the 2x by applying the inverse tangent function to both sides, giving us [tex]2x=\tan^{-1}{4[/tex]. Note, this specific solution only accounts for values of 2x between 0 and 2π radians. To make it general, we can add the term πk to the end of the right side, where k is any integer. We use π as a coefficient because the tangent function has a period of π radians, and it repeats its values every period.

Finally, we divide both sides of the equation by 2 to isolate x, giving us

[tex]2x=\tan^{-1}{4}+\pi k\\x=\frac{1}{2}\left(\tan^{-1}{4}+\pi k\right)[/tex]

Answer:

.20

Step-by-step explanation:

Answer:

Using Logic...she is shorter than most children at that level.

Step-by-step explanation:

Ashmita is 63 inches tall which is 5 foot 3. or 5.25 feet

When AP stats starts you should be in Highschool.

Here are the averages of highschool students, in height.

14 years = 5ft 4.5in (163.8 cm)  5ft 2.5in (158.7 cm)

15 years  = 5ft 7in (170.1 cm)  5ft 2.9in (159.7 cm)

16 years  = 5ft 8.3in (173.4 cm)  5ft 4in (162.5 cm)

17 years  = 5ft 9in (175.2 cm)  5ft 4in (162.5 cm)

Answer:

The answer is A.

Step-by-step explanation:

If you put it in Desmos Graphing Calculator it will show the one solution is (-31, -100).

please mark brainliest

The side length (in feet) of the square window which has the cost of making equal to $355 is 30 feet.

A mathematical model is the model which is used to explain the any system, the effect of the components by study and estimate the functions of systems.

The cost (in dollars) of making a square window with a side length is C. the length of side of the window is n.

The model, which represent the cost of window in dollar, is,

C=(n²/5)+175

A window costs $355. Thus, C=355. Put this value in above model as,

355=(n²/5)+175

355-175=(n²/5)

180 x 5=n²

n=√(900)

n=30

Hence, the side length (in feet) of the square window which has the cost of making equal to $355 is 30 feet.

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Answer:

C. 1/3.

Step-by-step explanation:

There are 2 favourable outcomes:

a 5 or a 6.

So that is 2 numbers out of 6.

Therefore the probability is 2/6

= 1/3.

ANSWER:

Answer:

$2552

Step-by-step explanation:

First you have to find Justin's monthly salary.  You do this by dividing his annual salary by 12 months.  48000/12 = 4000  This means Justin makes $4000 each month.  Next we have to find what 5% of that is, in order to know how much his retirement plan contribution costs.  To do this you divide 4000 by 100 to know how much 1% of his monthly salary is, and then you multiply that by 5 to know how much 5% of his monthly salary is.  4000/100 = 40  40x5 = 200 .We now know his retirement plan contribution each month costs $200.  Now we need to know how much to subtract from his monthly salary to get his net pay for the month.   We can do this by adding all of his monthly expenses together and then subtracting that total from 4000.  650+248+350+200 = 1448  4000-1448 = 2552  Justin's net pay for the month is $2552  

Answer:

Step-by-step explanation:

(d). V ≈ 3016

S.A. ≈ 2261

Answer:

3:1.

Step-by-step explanation:

21:7

= 3:1.

Answer: 8 meters

Step-by-step explanation: 72/9 = 8

Answer:

8 meters

Step-by-step explanation:

Since there is so little information given, I'm assuming this is just the area of a rectangle. The formula you used to find the area of a rectangle is "area = length * width" or "A = l*w".

We are given the area and the length, so we can fill in those spaces in the formula-

72 = 9 * w

Now, in order to find the width. we have to undo in reverse order. We have to divide 72 by 9.

72 (/ 9) = 9 * w (/ 9)

8 = w

Therefore, the width is 8 meters. I hope this helps! Have a lovely day!! :)

Answer:

y=0, x=4

Step-by-step explanation:

2x+2y=8 --- (1)

4x+3y=16 --- (2)

Multiply the coefficient of x in equation (1) across the variables in equation (2), and multiply the coefficients of x in equation (2) across the variables in equation (1).

8x+8y=32 ---- (3)

8x+6y=32 ---- (4)

Subtract equation (3) from (4)

2y=0, y=0/2, y=0.

Substitute the solution for y=0 into equation (1)

2x+2(0)=8

2x=8

x=4

Answer:

slope m = - [tex]\frac{7}{3}[/tex]

Step-by-step explanation:

Answer:

k = 9

y = 9x

Step-by-step explanation:

Variation Constant Formula :

Equation :

Answer:

[tex]y = x \\ the \: constant \: k \: will \: be \: y = kx \\ therefore \: if \: y = 9 \: and \: x = 1 \\ the \: equation \: will \: be \: 9 = k(1) \\ this \: gives \: k = 9 \\ therefore \: to \: represent \: in \: equation \: it \: will \: be \\ y = 9x[/tex]

The value of x is from negative infinity to negative 3/7 and 29 to positive infinity.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality equations are given below.

a)  - 9x + 7 > 16 + 12x

b)  18 + 13x < 14x - 11

Then

a)  - 9x + 7 > 16 + 12x

Solving for x, we have

21x < -9

  x < -3/7

The value of x is less than the negative of 3/7.

b)  18 + 13x < 14x - 11

Solving for x, we have

x > 29

The value of x is greater than 29.

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Answer:

ST = 7

Step-by-step explanation:

Answer:

A is the answer Have a great day

Step-by-step explanation:

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's calculate its surface area ~

[tex] \sf SA = Area (2 × \triangle) + Area ( three \: \square)[/tex]

[tex] \sf SA =(2 \cdot \dfrac{1}{2} \cdot8 \cdot6 ) + (7 \cdot10) + (7 \cdot 8) + (7 \cdot6)[/tex]

[tex] \sf SA =(48 ) + (7 0) + (56) + (42)[/tex]

[tex] \sf SA =216 \: m {}^{2} [/tex]

Answer:

..................................

Step-by-step explanation:

Answer:

..................................

Step-by-step explanation:

No clear question so the answer is the question

Answer:

the last (4th) option

Step-by-step explanation:

the easiest way to find the right answer :

which of the 4 answers would deliver infinity for x = 5 ?

and that is only answer 4, as x = 5 creates 0 in the denominator of the fraction, which leads to the infinity break at that point in the functional curve.

other indications :

the smaller x, the more the denominator goes to -infinity, and the bigger x, the more the denominator goes to +infinity.

and that means the whole fraction goes to 0. and we are left for the function limit with the constant added at the end of the function.

looking at the graph, this has to be +3.

and again, only the 4th answer has "+3" at the end.

The function represented by the graph is y = 1(x - 5) + 3.

Option D is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The equation y = 1/(x - 5) + 3 represents a rational function with a vertical asymptote at x = 5.

This means that the graph of the function gets closer and closer to the vertical line x = 5, but never touches or crosses it.

The graph of the function also has a horizontal asymptote at y = 3.

This means that as x approaches infinity or negative infinity, the value of the function approaches 3.

The function has a y-intercept at (0, -4), where x = 0 and y = 1/(-5) + 3 = -4.

Thus,

The function represented by the graph is y = 1(x - 5) + 3.

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Answer:

60.

Step-by-step explanation:

P = 2( 17 + 13)

= 2 * 30

= 60

Answer:

Therefore, Peter is 21 years old.

Step-by-step explanation:

    [tex]\bf{ x+11=\dfrac{(x-13)^2}{2} \ \Longrightarrow \ 2x+22=x^2-26x+169 }[/tex]

          [tex]\bf{ 0=x^2-28x+147=(x-21)(x+7) }[/tex]

Answer:

23.33

Step-by-step explanation:

The sum of the internal angles of a triangle is 180°, which is given by The Angle Sum Property of Triangles.

⇒ 3x - 17 + 2x + 5 + x + 52 = 180

⇒ 6x + 40 = 180

⇒ 6x = 140

⇒ x = 140/6

⇒ x = 70/3

⇒ x = 23.33

Answer: x = 23.333

In any triangle, all the three angles will ALWAYS add up to 180°. According to that:

▪ 180° = <a + <b + <c

(2x + 5) + (3x - 17) + (x + 52) = 180

2x + 5 + 3x - 17 + x + 52 = 180

Rearrange according to like terms

2x + 3x + x + 52 - 17 + 5 = 180

6x + 40 = 180

Now we'll find the value of x

6x = 180 - 40

x = 140/6

By cross cancellation we get

x = 70/3

You could change it into decimal as well

x = 23.333 answer

therefore, the third option that says 23.33 is correct.

Hope that helps...

Step-by-step explanation:

there are just some big words trying to confuse you.

it just means that there is a right-angled triangle :

there is the point on the ground, where the surveyor is standing.

then there is the elevated point up there, where the surveyor was measuring the angle to.

and then there is the point on the ground directly under this elevated point. at this point in the ground we have the right angle (90°).

this height of the elevated point above this ground point is what we are looking for, and it is one leg of the right-angled triangle.

the ground distance from the surveyor to the ground point under the elevated point is 5 miles and the second leg.

the direct line of sight from the surveyor to the elevated point is inclined up by 20°, and is the Hypotenuse (baseline opposite of the 90° angle) of the triangle.

remembering that the sum of all angles in a triangle is always 180°, we also know the angle at the elevated point :

180 - 90 - 20 = 70°

now we are using the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

where the sides are always opposite to their associated angles.

so, we have in our triangle

height/sin(20) = 5/sin(70)

height = 5×sin(20)/sin(70) = 1.819851171... miles

so, the elevated point is 1.819851171... miles above the elevation of the surveyor.

Answer:

About 969 dollars

Step-by-step explanation:

I kind of did it the long way. I divided $1,404 by 100 and multiplied by 19. Did the same thing with 12. Added the product of those together and subtracted from 1,404.

(1,404÷100)19 + (1,404÷100)12 = 435.24

1,404 - 435.24 = 968.76

Since it was an estimate I rounded it to the nearest whole number and got 969

Hope this helps. There are probably better methods to solve this problem but this was my way.

Negative when subtracted is counted as positive because negative multiplied with negative gives positive

-10-(-6)

-10+6

-4 answer

Answer:

-4

Step-by-step explanation:

(-10)-(-6)=

-10 + 6=

-4

hope this helps

have a good day

Answer:

answer  in picture

Step-by-step explanation:

Answer:

1. 175

2. 28

Step-by-step explanation:

If you're converting from another base, just multiply each digit, then add up the numbers:

ones digit × 8^0,

tens digit × 8^1

hundreds × 8^2

see image.

The second problem gives you a new operation. Follow the rule by squaring the first number and taking away the first×second. Do the parenthesis first!

see image.