What are the trigonometric ratios of a right triangle ABC that has its right angle at C? AC=12 and BC=5

Answers

Answer 1

There are 3 trigonometric ratios:
Sine = opposite/hypotenuse,
Cosine = adjacent/hypotenuse and
tangent = opposite/adjacent
Since in the question we have not been given the hypotenuse, we calculate it first.
So, hypotenuse = √(12²+5²) = √(144+25) = √169 = 13.

Now we can find the trigonometric ratios;
Sin A = Cos B = 5/13
Sin B = Cos A = 12/13
Tan A = 5/12
Tan B= 12/5

Related Questions

What is the value of w?

w + 3
4
=
w - 2
2

Answers

The answer to the value of W would be (W = -3/2 = -1.500).

PLEASE HELP ME WITH THIS ILL MARK AS BRAINIEST

What is the value of h when the function is converted to vertex form?

Note: Vertex form is f(x)=a(x−h)2+k .

f(x)=x2+10x+35

Enter your answer in the box.

Answers

Please use "^" to indicate exponentiation:

f(x)=x^2+10x+35

Complete the square: f(x)=x^2+10x+25-25+35 = (x+5)^2 +10

or y-10=(x+5)^2, so the vertex is at (-5,10). h has the value -5.

Answer:

h = -5

Step-by-step explanation:

An insect flies 20 feet in 1 second. how fast does the insect fly in miles per hour?

Answers

[tex] \frac{20 ft}{sec} ( \frac{60 sec}{min} )( \frac{60 min}{hr})( \frac{1 mi}{5280 ft}) [/tex]

All of the units cancel other than miles divided by hours which is what we need.

Now we do (20 * 60 * 60 * 1) / 5280 which is 13.636363 (repeating) or 13.6364 miles per hour.

Part A: Factor 5x2b2 + 14xb2 − 3b2. Show your work.
Part B: Factor x2 − 18x + 81. Show your work.
Part C: Factor x2 − 121. Show your work.

Answers

Part A:
We have the following expression:
5x2b2 + 14xb2 - 3b2
Rewriting we have:
b2 (5x2 + 14x - 3)
b2 (5x-1) (x + 3)

Part B:
We have the following expression:
x2 - 18x + 81
Rewriting we have:
(x-9) (x-9)
(x-9) ^ 2

Part C:
We have the following expression:
x2 - 121
Rewriting we have:
(x-11) (x + 11)

What is the excluded value of the rational expression: x-4/6 divided by x+1/7?
A. -1
B. 4
C. -7
D. None of the above

Answers

For this case we have the following expression:
((x-4) / (6)) / ((x + 1) / (7))
Rewriting we have:
7 (x-4) / 6 (x + 1)
We observe that the expression is not defined for the values where the denominator is equal to zero.
We have then:
x + 1 = 0
x = -1
Answer:
The excluded value of the rational expression is:
A. -1

Pollsters take a survey of people at a ball game to collect and analyze data about favorite leisure activities of star city’s residents. Would this study be biased Why or why not?

Answers

Answer:

Yes, it will be a biased study.

Step-by-step explanation:

Given is that -

Pollsters take a survey of people at a ball game to collect and analyze data about favorite leisure activities of star city’s residents.

This study will be biased and it will produce biased results.

Firstly, few people at ball game do not represent the whole population of the city and it is not necessary that all the people at ball park will respond to the question in the survey.

Answer:

Yes, it is biased. The sample of people at the ball park is not representative of Star City’s residents.

The answer is D.

A circular mirror has a diameter of 12 inches. part a what is the area, in square inches, of the mirror?
a. 6 π
b. 12 π
c. 36 π
d. 72 π part b a circular frame that is 3 inches wide surrounds the mirror. what is the combined area, in square inches, of the circular mirror and the frame?
a. 9 π
b. 18 π
c. 54 π
d. 81 π

Answers

1st part is c
2nd part is d

I BELIEVE

Final answer:

The area of the circular mirror is 36π square inches, and the combined area of the mirror and frame is the difference between the total area with the frame (81π square inches) and the mirror alone, resulting in 45π square inches.

Explanation:

Part A: Area of the Circular Mirror

To find the area of the circular mirror, we use the formula for the area of a circle, which is A = πr², where r is the radius of the circle. Since the diameter of the mirror is given as 12 inches, the radius would be half of that, which is 6 inches. Plugging the radius into the formula, we get:

A = π(6 inches)² = 36π square inches

Part B: Area of the Circular Mirror and Frame

The frame adds 3 inches to the radius on all sides, making the overall radius of the mirror and frame 9 inches (6 inches + 3 inches). Using the area formula again, A = π(9 inches)² = 81π square inches.

To find the combined area of the mirror and frame, we subtract the area of the mirror from the total area. Hence, combined area = 81π square inches - 36π square inches = 45π square inches.

15 Points!

Describe how to transform the graph of f into the graph of g.

A) Shift the graph of f left 3 units.
B) Shift the graph of f right 7 units.
C) Shift the graph of f right 3 units.
D) Shift the graph of f left 7 units.

Answers

[tex]f(x)=\sqrt{x-2}\\\\g(x)=\sqrt{x+5}=\sqrt{x+7-2}=\sqrt{(x+7)-2=f(x+7)[/tex]

Answer:
D) Shift the graph of f left 7 units.

Look at the picture.

YO!NEED THIS!!!!!POINTS!!!!!!WILL GIVE THE BRAIN!!!!

Answers

The graph is falling on the left hand side and rising on the right hand side.

Since the two ends of graph are in opposite direction, the exponent of variable has to be odd. For an even exponent of leading term, the two ends are in same direction.

Since the graph is falling on left and rising on right, this indicates that the coefficient of leading term is positive.

So, the leading term must have:
1) Odd exponent
2) Positive Coefficient

Thus, option Fourth is the correct answer

A number is mutiplied by 10. Then 32 is added to the product. This sum is then devised by 4. The answer is 28. What was the original number?

Answers

The Answer is 8 because you take 28 and multiply 4, then you subtract 32, and lastly, you divide by 10 and you get 8.

8 is your original number.

I went in a did the opposite of what it said (so I multiples 28 by 4, subtracted 32, and then divided by 10). Hope this helps!

A number is less than 20 units away from 7 on the number line. What numbers are within these parameters? Choose the inequality that represents the situation.

Answers

Answer:

For the pull out menu it was B

Step-by-step explanation:

What is the y-intercept of x^2+2x+6

Answers

The y-intercept occurs when x = 0.
y = x^2 + 2x + 6
Let x = 0
y = 0^2 + 2 * 0 + 6
y = 6
Answer: 6

y-intercept is a point when x=0,
so
y=x²+2x+6=0²+2*0+6=6
y=6
So y-intercept is (0,6)

use the formulas to find the lateral area and the surface area of the given prism round your answer to the nearest whole number 5.39m 26m 5m 2m
the choices for the answer is
322m2 327m2
296m2 342m2
296m2 332m2
322m2 332m2

Answers

The Answer is 296m2 342m2

Answer:

for connexus 322m^2, 332m^2

Step-by-step explanation:

what is the area of the circle if DF=20 in.

Answers

we know that

DF is the diameter of the circle
so
radius r=DF/2----->20/2-----> r=10 in

area of the circle=pi*r²------> pi*10²-----> 100*pi in²-----> 314 in²

the answer is

100*pi in² or 314 in²

YOOOOOO!!!!!!NEEEED HELP!!!WILL GIVE BRAIN!!!!!!PART2!!!!

Answers

For this case we have the following main function:
f (x) = x ^ 3
We have the following transformation of functions:
Expansions and vertical compressions:
To graph y = a * f (x)
If a> 1, the graph of y = f (x) is expanded vertically by a factor a. (It lengthens)
If 0 <a <1, the graph of y = f (x) is compressed vertically by a factor a. (Shrinks)
We have then:
h (x) = ((1/4) x) ^ 3
h (x) = (1/64) * (x) ^ 3
h (x) = (1/64) * f (x)
0 <1/64 <1
The graph f (x) shrinks,
Answer:
f (x) = x ^ 3
option A

Solve the system of equations. { 13x−y=90 y=x^2−x−42

Answers

There are two possible answers:
(6, -12)
(8, 14)

You can get these by taking the second equation and plugging it in for y in the first equation. Then solve using the quadratic formula.

Write each of the equations below in standard form (i.e. y = ax^2+bx+c y=ax 2 +bx+c):
a. y = 3(x-7)(x+4) y=3(x−7)(x+4)
b. y = 2(x-3)^2 + 5 y=2(x−3) 2 +5
c. y = -2(x+3)(x+5) y=−2(x+3)(x+5)
d. y = -3(x-4)^2 + 8y=−3(x−4) 2 +8

Answers

C . Is the answer
Hope it helps

Irma needs to rent a car for a business trip from phoenix to san jose (720 miles one way). she will drive round trip and will be gone a total of 8 days. the car rental company charges $65.00 per day and allows for 1,600 miles for irmas's trip. there will be an additional charge of $0.24 per mile over the 1,600 miles allowed. how many total miles can she drive without exceeding her budget of $600.00?

Answers

To find the number of miles Erma can drive, you will write and equation and solve it to find the amount of miles that can be driven on $600 over the 1600 miles that are allowed.

Daily rate + cost per mile over 1600 = total cost
(65 x 8) + 0.24m = 600
520 + 0.24m = 600
-520 -520
0.24m = 80
0.24 0.24
m = 333.33... miles

The maximum number of whole miles she can drive would be 1933 miles (1600 + 333).

A. 99
B. 100
C. 121
D. Cannot be determined

Answers

B. 100
Corresponding parts of congruent figures

The size of a television is given by the length ofthe diagonal of the screen. the ratio of the height to the width of wide flat-screen tv is 8:15. find expressions for the width and height of a wide-screen tv in terms of the length of its diagonal.\

Answers

Using the ratios,
suppose:
width=8x
length=15x
let d be the diagonal
thus; using Pythagorean theorem:
d^2=(8x)^2+(15x)^2
=64x^2+225x^2
=289x^2
d=17x

or x=d/17

width=8x=8d/17
length=15x=15d/17

Find the slope and the y-intercept of the line with equation y=-5/4x+5

Answers

In an equation with the form y = mx + b, the m is slope and the b is y-intercept.

Therefore, your slope, m, is -5/4 and your y-intercept, b, is 5.

Another question for math. ill give mad points, the question is in attachment

Answers

For this case we have the following points:
y = (- 2, 5)
z = (1, 3)
Therefore, the vector yz is given by:
yz = z - y = (1, 3) - (-2, 5)
yz = ((1 - (- 2)), (3-5))
yz = ((1 + 2), -2)
yz = (3, -2)
Then, the magnitude is given by:
lyzl = root ((3) ^ 2 + (-2) ^ 2)
lyzl = root (9 + 4)
lyzl = root (13)
Answer:
yz = (3, -2)
lyzl = root (13)
option A

Akikos dogs has three puppies. They weigh 2.6pounds, 2.74 pounds, and 3.1 pounds. How much more does the heaviest puppy weigh than the lightest puppy?

Answers

the answer is 0.5 pounds

9. WILL GIVE BRAINLIEST IF CORRECT

Answers

Answer is: A;
Re-arrange formula to give: sin q = -1/square root of 2
Now, sin (3 pie/4) = sin(135) = -1/square root of 2
Also, sin(5 pie/4) = sin(235) = -sin(45) = -1/square root of 2

rearrange the equation we get;

sinq = -2/2sqrt(2) = -1/sqrt(2)

answer is letter A. 3pi/4 , 5pi/4

Hope this helps your question! Goodluck

If EFGH is a parallelogram, what is the value of x?

Answers

to be a parallogram the 2 angles shown need to equal 180 degrees

so we have: 34 + (4x-2) = 180

now we can solve for x

34 + 4x -2 = 180

simplify the left side by subtracting 2 from 34

32+4x =180

subtract 32 from each side:

4x = 148

divide both sides by 4 to get x

x = 148 / 4

x = 37

The answer is B

A quadrilateral in which opposite sides are parallel is called a parallelogram. The value of x is 37.

What is a parallelogram?

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

For a parallelogram, any two adjacent angles are always supplementary. Therefore, we can write the sum of the two angles as,

(4x-2)° + 34° = 180°

4x - 2 + 34 =180

4x + 32 =180

4x = 180 - 32

4x = 148

x = 37

Hence, the value of x is 37.

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Use graphs and tables to find the limit and identify any vertical asymptotes of the function.

Answers

Lim x→8- [1/(x-8)]=1/(8-8)=1/(-0)→Lim x→8- [1/(x-8)]=-Infinite

Vertical asymptote: x=8

Answer:

The limit of the function is [tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty[/tex] and the vertical asymptotes is x=8.

Step-by-step explanation:

The given function is

[tex]f(x)=\frac{1}{x-8}[/tex]

We need to find the value of

[tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}[/tex]

The graph of the function f(x) is attached below.

From the graph it is clear that the function approaches to -∞ as x approaches to 8 from left. So, by the graph we can say that

[tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty[/tex]

The table of values is attached below. From the table it is clear that the value of f(x) decreasing as the value of x is closed to 8 from left. So, by the table we can say that

[tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty[/tex]

To find the vertical asymptotes equate denominator, equal to 0.

[tex]x-8=0[/tex]

[tex]x=8[/tex]

Therefore the limit of the function is [tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty[/tex] and the vertical asymptotes is x=8.

What is the radius of the circle given the equation x2 - 6x + y2 + 10y - 2 = 0?

Answers

[tex]\text{Equation of the circle in standard form:}\\\\(x-h)^2+(y-k)^2=r^2\ \text{where}\\\\\text{(h; k) - coordinates of the center of the circle}\\\\\text{r-the radius}[/tex]

[tex]\text{We have:}\\\\x^2-6x+y^2+10y-2=0[/tex]

[tex]\text{Use:}\ (a\pm b)^2=a^2\pm2ab+b^2[/tex]

[tex]\underbrace{x^2-2\cdot x\cdot3+3^2}_{(x-3)^2}-3^2+\underbrace{y^2+2\cdot y\cdot5+5^2}_{(y+5)^2}-5^2-2=0\\\\(x-3)^2+(y+5)^2-9-25-2=0\\\\(x-3)^2+(y+5)^2-36=0\ \ \ \ |+36\\\\(x-3)^2+(y+5)^2=36[/tex]

[tex]\text{coordinates of the center of the circle (3; -5)}\\\\\text{a radius}\ r=\sqrt{36}=6[/tex]

A gardener wants to plant 122500 trees in his field in such a way that the number of trees in a row is equal to the number of rows .How many trees will he plant in each row?

Answers

Given that the gardener wants the number of trees in each raw to be equal to the number of rows, then let the number of in each row be x this means that the number of rows will be x.
Thus the total number of trees will be:
Total=(number of rows)*(number of trees in each row)
hence:
122500=x×x
122500=x²
hence
x=√122500
x=350
thus the number of rows will be 350 and the number of trees in each row will be 350

The first painter can finish a paint job in 2 hours. The second painter can finish the same job in 8 hours. How long would it take them to finish the job if they were working together?

Answers

Final answer:

If two painters who can individually finish a painting job in 2 hours and 8 hours respectively work together, they will be able to finish the job in 1.6 hours.

Explanation:

The question is about determining how fast two painters can finish a paint job if they work together, given their individual working speeds. This is related to the field of mathematics and specifically to the concept of rates. The first painter can finish the job in 2 hours, so, his rate of working is 1/2 of the job per hour. The second painter can finish the job in 8 hours, so his rate of working is 1/8 of the job per hour. When they work together, their rates are added together. So, the combined rate of both painters is 1/2 + 1/8 = 5/8 of the job per hour. To find out how long it would take them to finish the job together, we take the reciprocal of this, which gives us 8/5 or 1.6 hours.

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Final answer:

Working together, the two painters would take approximately 1.6 hours or 1 hour and 36 minutes to finish the job.

Explanation:

To find how long it would take the two painters to finish the job together, we can use the concept of work rates. The first painter can finish the job in 2 hours, so they have a work rate of 1/2 job per hour. Similarly, the second painter can finish the job in 8 hours, so their work rate is 1/8 job per hour.

When the two painters work together, their combined work rate is the sum of their individual work rates. So, the total work rate when they work together is 1/2 + 1/8 = 5/8 job per hour.

To find the time it would take them to finish the job, we can use the formula time = 1 / work rate. Substituting in the combined work rate of 5/8 job per hour, we get:

time = 1 / (5/8) = 8/5 = 1.6

Therefore, it would take the two painters approximately 1.6 hours or 1 hour and 36 minutes to finish the job if they were working together.

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Find the volume of each sphere or hemisphere. Round to the nearest tenth.

sphere: circumference of a great circle = 26m

Answers

we know that
volume of a sphere=(4/3)*pi*r³

in this problem
circumference=26 m
circumference=2*pi*r
so
26=2*pi*r----------> r=26/(2*pi)----> 4.14 m

volume of a sphere=(4/3)*pi*(4.14)³---> 297.08 m³------> 297.1 m³

the answer is
volume of a sphere is equal to 297.10 m³

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