Use a trigonometric function to find the value of x

Answer:

A)

58/3 = 19.33 hours

B)

84.00 hours

C)

2074.29 miles

Step-by-step explanation:

Under the assumption the earth is a perfect circle, then in a complete rotation ( 24 hours) the earth will rotate through  360 degrees or 2π radians.

A)

In one day or 24 hours the earth rotates through 360 degrees. We are required to determine the duration it takes to rotate through 290 degrees. Let x be the duration it takes the earth to rotate through 290 degrees, then the following proportions hold;

(24/360) = (x/290)

solving for x;

x = (24/360) * 290 = 58/3 = 19.33 hours

B)

In 24 hours the earth rotates through an angle of 2π radians. We are required to determine the duration it will takes the Earth to rotate through 7π radians. Let x be the duration it takes the earth to rotate through 7π radians, then the following proportions hold;

(24/2π radians) = (x/7π radians)

Solving for x;

x = (24/2π radians)*7π radians = 84 hours

C)

If the diameter of the earth is 7920 miles, then in a day or 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle;

circumference = 2*π*R = π*D

                         = 7920*3.142

                         = 24891.43 miles

Therefore a point on the equator covers a distance of 24891.43 miles in 24 hours. This will imply that the speed of the earth is approximately;

(24891.43miles)/(24 hours) = 1037.14 miles/hr

The distance covered by the point in 2 hours will thus be;

1037.14 * 2 = 2074.29 miles

Answer:

3120

Step-by-step explanation:

step 1:multiply 8 with 0 and 7 with 0

step 2:add a 0 in the end and multiply 8 with 4 . you get 32. take 2 and carry over 3. multiply 7 with 4. you get 28 . add 3 you get 31. now add. you get 3120

Answer:

3120

Explanation:

Step 1: 0 multiply by 8 give 0

Step 2: 0 multiply by 7 give 0

Step 3: put the number 0 in the right side

Step 4: 4 multiply by 8 give 32

Step 5: add the number 3 to the answer we are going to get for 4 multiply by 7 which is 28+3=31

Answer:

The area of the base is [tex]10\pi m^2[/tex]

Step-by-step explanation:

The volume of a cylinder is calculated using the formula:

[tex]Volume=\pi r^2h[/tex]

The volume is given to be:

[tex]V=140\pi m^3[/tex]

The height of the cylinder is h=14 meters.

We substitute these values into the formula to obtain;

[tex]140\pi=\pi r^2\times 14[/tex]

Divide both sides by 14.

[tex]\frac{140\pi}{14}=\pi r^2[/tex]

[tex]10\pi=\pi r^2[/tex]

The area of the base is a circle which is [tex]\pi r^2=10\pi m^2[/tex]

So what I would do is plug in the point into each system:

#1:

y > 0        (-3,0) since y = 0, plug in 0 for y

0 > 0       This can't be true because they are = to each other, so you would need to have a sign of either ≤ or ≥ (less/greater than or equal to) for the point to be a solution to the system

#2 is the same "0 < 0" can't be true

#3

0 ≤ 0 this is true

y > x + 9     Plug in the point (-3,0)

0 > -3 + 9   Simplify

0 > 6 This is false because 0 is not greater than 6

#4

0 ≥ 0    This is true

0 < -3 + 9

0 < 6     This is true because 0 is less than 6

---->       4th option is your answer

Answer:

x=11, y=8/3

Step-by-step explanation:

Consider quadrilateral LMNO. If this quadrilateral MUST BE a parallelogram, then

LM=NO

and

LO=MN

Thus,

[tex]\left\{\begin{array}{l}4x+4=5x-7\\ \\x-7=3y-4\end{array}\right.[/tex]

Solve this system of two equations. From the first equation:

[tex]4x-5x=-7-4\\ \\-x=-11\\ \\x=11[/tex]

Substitute it into the second equation:

[tex]11-7=3y-4\\ \\3y-4=4\\ \\3y=4+4\\ \\3y=8\\ \\y=\dfrac{8}{3}[/tex]

Answer:

B. 34

Step-by-step explanation:

Perimeter= 42+42+x+x

First add the 42 together

42+42 =  84

Then subtract the number away because this was added to the total

152 - 84 = 68

68 is not your missing number

Dividing 68 by 2 which gives you 34

So,

Perimeter = 42+42+34+34 = 152

Answer:

  (B) isosceles

Step-by-step explanation:

An isosceles triangle is one that has two sides of equal length.

___

If the distance between the legs were the same as the leg length, then the triangle would be equilateral. There is nothing in the problem statement suggesting this is the case.

The figure is separated into triangles.

The triangle has a base of 8 inches and a hypotenuse of 10 inches.

Using the Pythagorean theorem solve for the height of the triangle:

10^2 = 8^2 + x^2

100 = 64 + x^2

x^2 = 100-64

x^2 = 36

x = √36

x = 6

The height of the triangle is the width of the rectangle and the length of  the rectangle is 2 triangle bases ( 8 * 2 = 16)

Area of a rectangle is L x W = 6 x 16 = 96 square inches.

Answer:

c

Step-by-step explanation:

16X12.49=199.84

For this case we can raise a rule of three:

$ 12.49 ---------------> 1 yard

x -------------------------> 16 yards

Where the variable "x" represents the cost of the 16 yards.

[tex]x = \frac {16 * 12.49} {1}\\x = 199.84[/tex]

Thus, the cost of the 16 yards will be 199.84 dollars.

Answer:

Option C

Answer:

Option C. [tex]784\pi\ units^{2}[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z-----> the scale factor

x----> surface area of the sponge ball

y----> surface area of a plastic ball

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]z=2[/tex]

[tex]y=196\pi\ units^{2}[/tex]

substitute and solve for x

[tex]2^{2}=\frac{x}{196\pi}[/tex]

[tex]x=4*(196\pi)=784\pi\ units^{2}[/tex]

Answer:

$3.52 or $3.53

Step-by-step explanation:

We know that he is paying $2.35 per pound, and that he is buying 1.5 pounds worth of pears. Simply multiply 2.35 times 1.5 to get your answer, depending on how far you round, which is 3.52 or 3.53.

1 pound = $2.35

Leo bought 1 pound and 0.5 of a pound (half of a pound). To find how much 0.5 of a pound costs divide 2.35 (the cost of one full pound) by two

2.35 ÷ 2 = 1.18

so...

1 + 0.5 = 1.5

and

2.35 + 1.18 = 3.53

Leo spent $3.53 on 1.5 pounds of pears

Hope this helped!

~Just a girl in love with Shawn Mendes

ANSWER

A,B, and C

EXPLANATION

If

[tex]f(g(x))=g(f(x))=x[/tex]

then f and g are inverse functions.

A.

[tex]f(x) = \frac{x + 1}{6} [/tex]

[tex]g(x) = 6x - 1[/tex]

[tex]f(g(x)) = \frac{6x - 1 + 1}{6} = \frac{6x}{6} = x[/tex]

B.

[tex]f(x) = \frac{x - 4}{19} [/tex]

[tex]g(x) = 19x + 4[/tex]

[tex]f(g(x)) = \frac{19x + 4 - 4}{19} = \frac{19x}{19} = x[/tex]

C.

[tex]f(x) = {x}^{5} [/tex]

[tex]g(x) = \sqrt[5]{x} [/tex]

[tex]f(g(x)) = (\sqrt[5]{x})^{5} = x[/tex]

D.

[tex]f(x) = \frac{x}{x + 20 } [/tex]

[tex]g(x) = \frac{20x}{x - 1} [/tex]

[tex]f(g(x)) = \frac{ \frac{20x}{x - 1} }{ \frac{20x}{x - 1} + 20} = \frac{20x}{40x - 20} = \frac{x}{2x - 1} [/tex]

The correct answers are A, B , C

Answer:

Option A.

Step-by-step explanation:

The given sequence is 1.5, 3, 6............

We will check first whether the the given sequence is arithmetic or geometric.

For arithmetic sequence

[tex]a_{2}-a_{1}=3-1.5=1.5[/tex]

[tex]a_{3}-a_{2}=6-3=3[/tex]

1.5 ≠ 3, therefore, the given sequence is not an arithmetic sequence.

For geometric sequence

[tex]\frac{a_{2} }{a_{1} }=\frac{3}{1.5}=2[/tex]

[tex]\frac{a_{3} }{a_{2} }=\frac{6}{3}=2[/tex]

2 = 2, therefore, sequence is geometric.

For geometric sequence explicit formula is defined as

[tex]a_{n}=a_{1}(r)^{n-1}[/tex]

[tex]a_{7}=1.5(r)^{7-1}[/tex]

              = [tex]1.5(2)^{6}=96[/tex]

Therefore, Option A. is the answer.

Answer:

A, 96 have an amazing day!!!

Step-by-step explanation:

They had 54 twos and 62 threes.

54 + 62 = 116 outcomes of either 2 or 3

The probability is the number of outcomes divided by the total number of rolls.

116 / 360 = 0.32

The answer is A.

Answer:

0.32.

Step-by-step explanation:

Prob(Rolling a 2) = number of 2's rolled / total number of rolls

=  54/360 = 0.15

Similarly Prob(rolling a 3) =  62/360 = 0.17.

So the probability of a 2 or a 3 = 0.15 + 0.17 = 0.32.

Answer:

-6718464

Step-by-step explanation:

-4x-6=24

24x-6=-144

and keep on doing times -6 6 more times

Answer: The sum is 25220

Step-by-step explanation:

1) -4

2) -4*-6 =24

3) 24*6 = 144

4) 114*-6 = -864

5) -864*6 = -5184

6) -5184*-6= 31104

The sum is: 25220

To solve the problem, we need to find the area of the triangle, and then find 2/3 of that triangle.

The equation to find the area of a triangle is bh1/2 or base*height*1/2.

Now substitute the known values.

24*16*1/2

Solve

24*8

192.

Now, the easiest way to find 2/3 of a number is to divide that number by 3 and multiply the answer by 2.

192/3=64

64*2=128

Omar kept 128 square centimeters of the flag.

Hope this helps!

[tex] \frac{16 \times 24}{2} = \frac{384}{2} = 192[/tex]

192 is the total area of the triangle; since he kept 2/3 of the flag divide the area by three and times it by two:

[tex]192 \div 3 = 64 \times 2 = 128[/tex]

answer is 128cm^2

Answer:

The amount of rainfall increases as an exponential function of time.

Step-by-step explanation:

Answer:

C ;
Here is the picture if the letter changes! Sorry, it was hard to screenshot proof!

☆
EDGE2023; Good Luck :3!!

Answer:approximatly 800 inches is the distance between Scott and Steve

Step-by-step explanation: 40 revolutions * 20 inches

The approximate distance between Scott and Steve is 2513.27 inches.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

Each revolution of the bicycle tire covers a distance equal to the circumference of the tire, which is equal to pi times the diameter of the tire.

The distance travelled by the bicycle tire for 40 full revolutions is:

Distance = 40 x π x 20 inches

Distance ≈ 2513.27 inches

Therefore, the approximate distance between Scott and Steve is 2513.27 inches.

To know more about an expression follow

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Answer:it is 2 since it include3s all possible answers for both heads & tails.

Step-by-step explanation:

you can get a H1-4 & a T1-4 since you have 4 parts one the spinner & 2 things on a coin (Heads & tails) you can just times 4*2 & know that you have 8 possible answers.

Answer:

H-1 H-2 H-3 H-4, T-1 T-2 T-3 T-4

Answer:

(y + 1)

Step-by-step explanation:

Given

5y² + 4y - 1

To factorise the quadratic

Consider the factors of the product of the coefficient of the y² term and the constant term which sum to give the coefficient of the y- term

product = 5 × - 1 = - 5 and sum = + 4

The factors are + 5 and - 1

Use the factors to split the y- term

5y² + 5y - y - 1 ( factor the first/second and third/fourth terms )

= 5y(y + 1) - 1(y + 1) ← factor out (y + 1) from each term

= (y + 1)(5y - 1)

Mode means the number that appears most often in the data. Below I provided a tally of how many each of the numbers appear

59: twice

57: once

56: once

50: once

58: once

51: once

54: once

59: once

55: once

52; once

53: once

As you can see 59 appears the most often, being listed twice in the data set, and is therefore the mode

Hope this helped!

Answer:

your answer would be 59 scenice it goes twice i hope this helps have a great day

Step-by-step explanation:

8 units

First, find the area of the 4 by 16 rectangle. 4 times 16 is 64, so that is the area.

The area of a square is calculated with A = S^2, where A is the area and S is the side length.

So, set 64 to be the area and solve for S. 64 = S^2

The opposite of squaring something is finding the square root. So, find the square root of both sides.

square root of 64 = S

Now, what is the square root of 64? Well, what number when multiplied by itself equals 64? There are actually two possibilities here: -8 and 8. However, -8 cannot be the answer since distance cannot be negative, so 8 is the length of the side.

Answer:

2) 33

Explanation:

First, identify x.

3x+1=17

3x=16

X=16/3

Then substitute x in the expression.

6x+1=?

6(16/3)+1=?

32+1=?

33=?

So, the answer is #2.

When the equation 3x + 1 equals 17, the value of x is 16/3. Substituting this value of x into the expression 6x + 1 results in an answer of 33.

The subject of the question is Mathematics and it appears to be at a High School level. Given the equation 3x + 1 = 17, we can first solve for x by subtracting 1 from both sides resulting in 3x = 16 and then dividing both sides by 3 which gives x = 16/3. Then we can substitute this value of x in the expression 6x + 1 giving us 6*(16/3) + 1 which simplifies to 32 + 1 = 33. So, the value of the expression 6x + 1 is 33 when the value of the expression 3x + 1 is 17.

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Answer:

D. 22

Step-by-step explanation:

Let O be the origin, then we can use the Pythagoras Theorem to obtain:

[tex]|AB|^2=|AO|^2+|OB|^2[/tex]

This implies that;

[tex]|AB|^2=14^2+16^2[/tex]

[tex]|AB|^2=196+256[/tex]

[tex]|AB|^2=452[/tex]

Take positive square root to get:

[tex]|AB|=\sqrt{452}[/tex]

[tex]|AB|=\sqrt{113}[/tex]

[tex]|AB|=21.26029163[/tex]

We round to the nearest whole number to get

[tex]|AB|=21[/tex] units

The closes is 22

X axes are supposed to be positive and the y is negative.

[tex]\bf q^7\div q^{26}q^7\div q^{26}\implies \cfrac{q^7}{1}\div \cfrac{q^{26}q^7}{1}\div \cfrac{q^{26}}{1}\implies \cfrac{\begin{matrix} q^7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }{1}\cdot \cfrac{1}{q^{26}~~\begin{matrix} q^7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }\cdot \cfrac{1}{q^{26}} \\\\\\ \cfrac{1}{q^{26}q^{26}}\implies \cfrac{1}{q^{26+26}}\implies \cfrac{1}{q^{52}}\implies q^{-52}[/tex]

ANSWER

Rewrite and make substitution.

EXPLANATION

Since Harriet calculated 27 divided 4 and had 6.75.

This means that:

[tex] \frac{27}{4} = 6.75[/tex]

Now we want to find

[tex] \frac{270}{4} [/tex]

without divide.

Therefore we need to rewrite the expression so in terms of

[tex] \frac{27}{4} [/tex]

so that we can substitute.

This will give us;

[tex] \frac{270}{4} = \frac{27}{4} \times 10[/tex]

This implies that,

[tex]\frac{270}{4} = 6.75 \times 10[/tex]

[tex]\frac{270}{4} = 67.5[/tex]

ANSWER

[tex]p(x) =( x - 3)(2{x} + 1)(x + 2)[/tex]

EXPLANATION

The given polynomial is

[tex]2 {x}^{3} - {x}^{2} - 13x - 6[/tex]

If 3 is a root of this polynomial, then

[tex]x - 3[/tex]

is a factor.

We use long division to obtain the quotient as shown in the attachment.

We can the factor the polynomial as:

[tex]p(x) =( x - 3)(2{x}^{2} + 5x + 2)[/tex]

The complete factored form is:

[tex]p(x) =( x - 3)(2{x} + 1)(x + 2)[/tex]

ANSWER

D. 13

EXPLANATION

We have

[tex]f(x) = \frac{2x + 1}{x - 4} [/tex]

To find

[tex] {f}^{ - 1} (3)[/tex]

means we want to find an x-value whose image is 3.

[tex]\frac{2x + 1}{x - 4} = 3[/tex]

We cross multiply,

[tex]2x + 1 = 3(x - 4)[/tex]

Expand:

[tex]2x + 1 = 3x - 12[/tex]

Combine like terms,

[tex]3x - 2x = 12 + 1[/tex]

[tex]x = 13[/tex]

[tex] \therefore{f}^{ - 1} (3)= 13[/tex]

Answer:

Option D is correct.

Step-by-step explanation:

[tex]f(x)= \frac{2x+1}{x-4} \,\,find \,\,value\,\,of\,\, f^{-1}(3)[/tex]

We know that f(a) =b ⇔ f^-1 (b) =a

Using this,

We are given [tex]f^{-1}(3)=x => f(x)=3[/tex]

and [tex]f(x)= \frac{2x+2}{x-4}[/tex]

putting value of f(x)

[tex]3= \frac{2x+1}{x-4}\\3(x-4) = 2x+1\\3x-12 = 2x+1\\Adding\,\,like\,\,terms\,\,\\3x-2x = 12+1\\x=13\\So, f^{-1}(3) = 13[/tex]

Option D is correct.

Consider a striking deviation as an outlier (Something that stands out in a pattern, EX: 2, 3, 4, 4, 4, 5, 5, 10 where the outlier would be 10.) Because there is a piece of data at 25-30 minutes that deviates (Or, separates, in a way), it would be considered an outlier (Or, a Striking deviation). Using this information, we can conclude that the answer would be A: 25-30 minutes.