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Find sinx2, cosx2, and tanx2 from the given information.sin(x) = 513, 0° < x < 90°

It is 180 degrees.....

Related Questions

Posted in Mathematics

Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the top of the dam to be 26º. Scarlett's height is 1.65 meters, so the height of the dam is

Make a drawing with a right triangle.

The opposite side, y, is the height of the dam less 1.65 m

The base or adjacent side is 90 m

The angle between the two sides is 90 m.

Then tan (26) = y / 90

y = 90 tan(26) = 90 (0.4877) = 43.90 m

The height of the dam is 43.90m + 1.65m = 45.55 m

Posted in Mathematics

For f(x)=2x+1 and g(x)=x^2-7, find (f-g)(x)

I hope this helps you

(f-g)(x)=2x+1-(x^2-7)

(f-g)(x)=2x+1-x^2+7

(f-g)(x)= -x^2+2x+8

Posted in Mathematics

A quadratic equation is shown below: 9x2 - 36x + 36 = 0 Part A: Describe the solution(s) to the equation by just determining the discriminant. Show your work. (3 points) Part B: Solve 2x2 - 9x + 7 = 0 using an appropriate method. Show the steps of your work and explain why you chose the method used.(4 points)

For part A:
9x² - 36x + 36 = 0
9(x² - 4x + 4) = 0
9(x-2)(x-2) = 0
Radicand = Discriminant = 36² - 4(9)(36) = 0
there is 1 real zero that repeats itself)

zero is x=2.

Use factoring. Factors of 7 are 1 and 7
2x²-9x+7 = 0

(2x-7)(x-1) = 0
2x-7 = 0              (x-1)=0
2x = 7x=1
x = 7/2
Your solutions are x = 1 and x = 7/2

I hope my answers helped you

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Posted in Mathematics

Anastasia uses the equation p = 0.7(rh + b) to estimate the amount of take-home pay, p, for h hours worked at a rate of r dollars per hour and any bonus received, b. What is an equivalent equation solved for h? h = (– b)÷ r h = – b ÷ r h = ÷ r – b h = ÷ r

For the answer to the question above, first we must enlist the given

p = take home pay
r = rate of dollars per hour
h = number of hours worked
b = bonus

So now we can find h and let us start with the formula.

p = 0.7(rh + b)

p = 0.7*r*h + 0.7b

p - 0.7b = 0.7rh

So the answer for this problem is

h = (p-0.7b)/0.7r

Posted in Mathematics

A triangle has side lengths measuring 3x cm, 7x cm, and h cm. Which expression describes the possible values of h, in cm? 4x < h < 10x 10x < h < 4x h = 4x h = 10x

In a triangle sum of two sides , should always be greater than the third side.

Sides of the given triangle are, 3 x cm, 7 x cm and h cm.

1.

3 x + 7 x > h

→ 10 x > h

2.

3 x+ h > 7 x

→h > 7 x -3 x

→h> 4 x

3.

7 x + h > 3 x, which will be always true.

Combining 1, 2 and 3 we get

→4 x < h < 10 x

Option A

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What is f(x) = 2x2 + 28x – 5 written in vertex form?

To convert a quadratic from y = ax2 + bx + c form to vertex form, y = a(x - h)2+ k, you use the process of completing the square. We do as follows:

f(x) = 2x^2 + 28x – 5
f(x) = 2(x^2 + 14x) – 5
f(x) = 2(x^2 + 14x + 49) – 5 - 98
f(x) = 2(x + 7)^2 – 103

Hope this answers the question. Have a nice day.

Posted in Mathematics

Given f(x)=17-x^2, what is the average rate of change in f(x) over the interval [1, 5]?

For the answer to the question above, I'll show my to solution to the answer below.
average rate of change is
(f(5) - f(1))/(5 - 1) =

(17 - 5^2 - (17 - 1^2))/4 =

(17 - 25 - 17 + 1)/4 =
So the answer for this problem is
-6
I hope my answer helped you. Feel free to ask for more questions.

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Match Term Definition Line Segment A) a series of points that extend in two directions without end Plane B) two lines that intersect at 90° angles Perpendicular Lines C) lines that lie in the same plane and do not intersect Line D) a flat surface that extends infinitely and has no thickness Parallel Lines E) part of a line that has two endpoints

The correct matches are as follows:

Line Segment
E) part of a line that has two endpoints

Plane
D) a flat surface that extends infinitely and has no thickness

Perpendicular Lines
B) two lines that intersect at 90° angles

Line
A) a series of points that extend in two directions without end

Parallel Lines
C) lines that lie in the same plane and do not intersect

Hope this answers the question. Have a nice day.

Posted in Mathematics

What is the solution to the system of equations? y = 1.5x – 4 y = –x a. (–1.6, 1.6) b. (–1.5, 1.5) c. (1.5, –1.5) d. (1.6, –1.6)

I believe the correct answer from the choices listed above is option D. The solution to the system of equations given above would be (1.6, –1.6). We can use the substitution method to solve this. We do as follows:

-x = 1.5x – 4
4 = 2.5x
x = 1.6
y = -x = -1.6

Posted in Mathematics

A certain forest covers an area of 2,000 square kilometers. Suppose that each year this area decreases by 6%. What is the function that best represents the area of the forest each year and how much area remains after 12 years? Round your answer to the nearest square kilometer. Hint: Use the formula, f(x) = P(1 + r)x

For the answer to the question above, I think the formula you is wrong. The x must be in exponential form. It must look like this

f(x) = P(1 + r)^x
Now we can solve.

Given:
P = 2000
r = -0.06

f(x)  =  2000 (1 - 0.06)^x
=  2000 (0.94)^x

2000 (0.94)¹² =

2000 (0.476)  =
951.8 square kilometers.

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If the equilibrium interest rate in the money market is 5%, then at an interest rate of 2% sellers of interest-bearing financial assets _____ interest rates to find willing buyers.

If the equilibrium interest rate in the money market is 5%, then at an interest rate of 2% sellers of interest-bearing financial assets greater than interest rates to find willing buyers.

Posted in Mathematics

Which ordered pair is a solution of the equation 2x − y = 9 (-4,1) (-2,5) (5,1) (6,-3)

In order to confirm if which ordered pair is a solution of the given equation above, we can just simply plug in the values.
So based on my solution, the correct answer would be the third option: (5,1)
So let us try to plug in the values.
2(5) - 1 = 9
10 -1 = 9
9 = 9

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Posted in Mathematics

What is the range of the function f(x) = 3x2 + 6x – 9

I have a solution here however with a slight change in the equation:

f(x)=3x^2-6x+1

My solution is:

The domain is all real numbers--there are no restrictions like a square root or variable in the denominator

this is a U shape parabola and you want to find the bottom point, it is at the vertex

x=-b/2a =- (-6) /2 (3) =1
f(1) =3(1)^2 -6(1) +1 =3-6+1 =-2
the minimum is (1, -2)
so the range is all real numbers >= -2

By examining my solution, you could just answer the problem on your own! I hope it helps!

Posted in Mathematics

Find the multiplicative inverse of 6 + 2i.

The solution to the problem is as follows:

First thing to do is get rid of the i. Multiplying by 6 - 2i will do this

( 6 + 2i)(6 - 2i) = 6^2 - (2i)^2 = 36 - 4(-1) = 36 + 4 = 40

Dividing by 40 gets you 1

(6 + 2i) (6-2i)/40 = 1

The answer is (6 - 2i)/40 = (3 - i)/20

I hope my answer has come to your help. God bless and have a nice day ahead!

Posted in Mathematics

Solve the equation for y 2x+6y=13

So here is how we are going to solve for y for the given equation above:
2x+6y=13
Next, transfer 2x to the right side and it will look like this:
6y=13-2x
Now, divide both sides by 6, and it will look like this:
y=13-2x
--------
6
So, this is the final answer for y.

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Posted in Mathematics

The price of a cup of coffee was \$2.65 yesterday. today, the price fell to \$2.50 . find the percentage decrease. round your answer to the nearest tenth of a percent.

We must find the difference between prices. \$2.65 - \$2.50 = \$0.15. Now we need to calculate what percent \$0.15 is of \$2.65. It is 5.7%! The price decreased, so it is a 5.7% decrease!

Posted in Mathematics

How to solve this problem 14-6= 10-6=?

I really don't think you wrote the question properly. Or maybe you did, but this question doesn't make any sense! :/

Posted in Mathematics

Algebraic terms are separated by ______. Choose all that apply. 1)= 2)+ 3)x 4)÷ 5)-

1)=

2)+

5)-

Explanation

When letter or numbers are separated by multiplication or division can be combined to make one term.

In an algebra equation, terms are separated by an addition sign, subtraction sign or an equal sign. For example,

3a + 7b = 21.

This equation have 3 terms.

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Let P be a point between points S and T on 2004-01-01-02-00_files/i0120000.jpg. If ST = 21, SP = 3b – 11, and PT = b + 4, solve for b. A. –7 B. 7 C. 14 D. 32

The best and most correct answer among the choices provided by your question is the third choice or letter C.

If ST = 21, SP = 3b – 11, and PT = b + 4, the value of b would be 14.

I hope my answer has come to your help. God bless and have a nice day ahead!

Posted in Mathematics

If np >5 and nq>5 estimate P (fewer than 4) with n=13 p=0.4 by using normal distribution as an approximate to the binomial distribution if np <5 or nq< then state that the normal approximation is not suitable.

The Normal approximation to the binomial

is as follows

mean=13(.5)=6.5
variance=6.5(.5)=3.25
Pr[fewer than 4]=
Pr[N<=3] Apply the continuity correction
Pr[N<=3.5]~=Pr[Z<3.5-6.5/sqrt(3.25)]=

Pr[Z<-1.66]=0.048457226

I hope my answer has come to your help. God bless and have a nice day ahead!

Posted in Mathematics

6 times the square root of 2.25 and then minis 4.23 =

________________

6√(2.25)  - 4.23 = ?
__________________
6√(2.25)  - 4.23 =
______________________
6*(1.5)  - 4.23 =
_______________
9 - 4.23 =
_______________
4.77

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Posted in Mathematics

A car travel 90 Km in 2 1/2 hours. How much time is required to cover 30 Km and find the distance cover in 2 hours

90:2 1/2
90/3 : (2 1/2)/3
30 : (2 1/2)/3
30 : (5/2)/(3/1)
30 : 5/2*1/3
30 : 5/6
30km in 50 mins

90 : 2 1/2
90/(2 1/2) : (2 1/2) / (2 1/2)
90/(2 1/2) : 1
(90/1)/(5/2) : 1
(90/1)*(2/5) : 1
180/5 :1
36:1
Multiply each side by 2:
72:2
72 km in 2 hours

Hope this helps :)

Posted in Mathematics

The public library has fewer than 4,000 books. Let b represent the number of books in the library. Which inequality describes the number of books? b < 4,000 b > 4,000 b ≤ 4,000 b ≥ 4,000

Answer:  The correct option is (A) b < 4000.

Step-by-step explanation:  Given that the public library has fewer than 4,000 books.

We are to select the inequality that describes the number of books in the library.

The number of books in the library is represented by b.

According to the given information, the inequality hat describes the number of books in the library is given by

Thus, (A) is the correct option.

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Sophia is saving money for a new bicycle. The bicycle will cost at least \$623. Sophia makes \$8.22 per hour. Which inequality could be used find the number of hours Sophia needs to work to make enough money to buy a new bicycle? \$8.22h > \$623 \$8.22h ≤ \$623 \$8.22h ≥ \$623 \$8.22h < \$623

C.\$ 623

Step-by-step explanation:

We are given that Sophia is saving money for a new bicycle.

The bicycle will  cost atleast \$623.

Sophia makes \$8.22 per hour.

We have to find the inequality that could be used to find the number of hours Sophia needs to work to make enough money to buy a new bicycle.

Let Sophia works h hours to make enough money to buy a new bicycle.

Sophia makes money per hour =\$8.22

Total money made by Sophia in h hours =

According to question

\$623

Hence, option C is true.

Posted in Mathematics

Solve the inequality. p – 9 < –9

I hope this helps you

p-9 < -9

p-9+9 < -9+9

p <0

Posted in Mathematics

Solve for x. round to nearest tenth if needed. 1. 7r-7=2r+18 a.r=-5 b.r=5 c.r=2.2 d.r=1.2 2. 2x+12=18-x a.x=3 b.x=10 c.x=6 d.x=2 3. 8x-3=15x+18 a.x=-3 b.x=3 c.x=2.1 d.x=0.9 4. 6y-6=4y+16 a.y=2.2 b.y=-2.2 c.y=11 d.y=5 5. 3(x-4)=5(x+2) a.x=11 b.x=-11 c.x=1 d.x=-1

1)  The answer is: [B]: r = 5 .
__________________________
Explanation:
__________________________
Given: 7r − 7 = 2r + 18 ; Round your answer to the nearest tenth, if necessary.
____________________________
Since "r" is the only variable given, let us assume we want to solve for "r" (instead of "x").
___________________________
→ Subtract "2r" from EACH SIDE of the equation; and & add "7" to EACH SIDE of the equation:
_____________
→ 7r − 7 − 2r + 7 = 2r + 18 − 2r + 7 ;  to get: → 5r = 25 ;
_____________
→ Now, divide EACH SIDE of the equation by "5"; to isolate "r" on one side of the equation; and to solve for "r" :
______________
→ 5r / 5 = 25 / 5 → r = 5 → which is: "Answer choice: [B]".
_________________
Let us check our answer, by plugging in "5" for "r" in the original equation:
_________________
→ 7r − 7 = 2r + 18 ;  →  7(5) − 7 =? 2(5) + 18? ;
______________________
→ 35 − 7 =? 10 + 18 ?;     → 28 =? 28? Yes!
______________________
2) The answer is: [D]: x = 2 .
_____________
Explanation:
_____________
Given: 2x + 12 = 18 − x ; Solve for "x" (round to nearest tenth, if necessary).
_______________
→ Add "x" to EACH SIDE of the equation, & subtract "12" from EACH SIDE of the equation:  → 2x + 12 + x − 12 = 18 − x + x − 12 ;
______________
→ To get: 3x = 6 ;  → Divide EACH SIDE of the equation by "3";
to isolate "x" on one side of the equation; and to solve for "x":
_____________
→ 3x / 3 = 6 / 3 ; → x = 2 ; which is: "Answer choice: [D]".
______________
Let us check our answer, by plugging in "2" for "x" in the original equation:
________________
→ 2x + 12 = 18 − x ; → 2(2) + 12 =? 18 − 2 ?
________________
→ 4 + 12 =? 18 − 2 ? ;   → 16 =? 16?  Yes!
________________________________
3)  The answer is: [A]: x = -3 .
_____________
Explanation:
________________
Given:  8x − 3 = 15x + 18 ; Solve for "x". Round your answer to the nearest tenth, if necessary.
_________________
→ Subtract "8x" from EACH SIDE of the equation, & add "3" to EACH SIDE of the equation:
_______________
→ 8x − 3 − 8x + 3 = 15x + 18 − 8x + 3 ; to get:
_______________
→ 0 = 7x + 21 ; → Subtract "21" from EACH SIDE of the equation;
_______________
→ 0 − 21 = 7x + 21 − 21 ; to get:
_______________
→  -21 = 7x ; Now divide EACH SIDE of the equation by "7";
to isolate "x" on one side of the equation; & to solve for "x":
_______________
→ = -21 / 7 = 7x / 7 ; →  -3 = x ; which is "Answer choice: [A]."
_________________
Let us check our answer, by plugging in "-3" for "x" in the original equation:
________________
→  8x − 3 = 15x + 18 ;  → 8(-3) − 3 =?  15(-3) + 18 ?;
________________________
→ -24 − 3 =?  -45 + 18 ? ;   →  -27 =? -27?  Yes!
___________________________
4)  The answer is: [C]: y = 11 .
_____________
Explanation:
____________
Given: 6y − 6 = 4y + 16 ; Solve for "y"; Round to the nearest tenth, if necessary.
____________
(Note: Since "y" is the only variable given; assume we are to solve for "y" instead of "x").
____________
→ Subtract "4y" from EACH SIDE of the equation, & add "6" to EACH SIDE of the equation; → 6y − 6 − 4y + 6 = 4y + 16 − 4y + 6 ; to get:
_______________
→ 2y  = 22 ; Now, divide EACH SIDE of the equation by "2"; to isolate "y" one side of the equation; and to solve for "y" ;
_______________
→ 2y / 2 = 22 / 2 ; →  y = 11 → which is "Answer choice: [C]".
_______________________________
Let us check our answer, by plugging in "11" for "y" in the original equation:
___________________
→  6y − 6 = 4y + 16 ; → 6(11) − 6 =? 4(11) + 16 ?
_______________________
→ 66 − 6  =? 44 + 16 ?  → 60 =? 60 ?  Yes!
__________________
5)  The answer is: [B]: x = -11 .
_____________________
Explanation:
_________________
Given: 3(x − 4) = 5(x + 2) ; Solve for "x". Round to the nearest tenth, if necessary.
___________
→Note the "distributive property of multiplication":
_____________
a*(b + c) = ab + ac ;  and: a*(b − c) = ab − ac ;
_______________
→ Let us expand EACH SIDE of our given equation.
____________
3(x − 4) = (3*x)  − (3*4) = 3x − 12;
______________________________
→Now let us expand the "right-hand side" of the given equation:
____________
→  5(x + 2) = (5*x) + (5*2) = 5x + 10 ;
______________
→Now, we can rewrite the original equation:
_______________
→ 3(x − 4) = 5(x + 2) ; by substituting the expanded values for EACH SIDE of the question:   →  3x − 12 = 5x + 10 ;
__________________
→ Subtract "3x" from EACH SIDE of the equation; and add "12" to EACH SIDE of the equation: →  3x − 12 − 3x + 12 = 5x + 10 − 3x + 12 ; to get:
________________
→  0 = 2x + 22;  → Now subtract "22" from EACH SIDE of the equation:
______________
→  0 − 22 = 2x + 22 − 22 ; to get:  →  -22 = 2x ;
__________
→ Divide EACH SIDE of the equation by "2"; to isolate "x" on one side of the equation; & to solve for "x" ;
_____________
→  -22 / 2 = 2x /2 ;  →  -11 = x ; which is "Answer choice: [B]".
______________
Let us check our answer, by plugging in "-11" for "x" in the original equation:
___________
→ 3(x − 4) = 5(x + 2) ; →  3(-11 − 4) =? 5(-11 + 2) ? ;
_______________________
→3(-15) =? 5(-9) ? ; → -45 =? -45 ?  Yes!
_____________________________________________

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