What is the value of x?
A. 52
B.60
C.86
D.26

Answer:

x = 90° or π/2 rad

Step-by-step explanation:

4+ 2 sin x=14-8 sin x

2 sin x + 8 sin x  = 14 - 4

10 sin x = 10

sin x = 1

Using a calculator

x = sin[tex]sin^{-1}[/tex]1

x = 90° or π/2 rad

x = 90° or π/2 rad

If you are in high school, take Algebra one or two, Trigonometry, Analytic Geometry, or Precalculus. If you're in college take College Algebra, Trig, or then Calculus.

4+ 2 sin x=14-8 sin x

2 sin x + 8 sin x  = 14 - 4

10 sin x = 10

sin x = 1

Using a calculator

x = sin1

x = 90° or π/2 rad

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Answer:

5

Step-by-step explanation:

The radius is 5.

All I do was think of the center-radius form a circle

(x-h)^2+(y-k)^2=r^2

x^2     + y^2    =25

(x-0)^2+(y-0)^2=5^2

The center is (0,0) and the radius is 5.

So a point on the circle (x,y) has a distance of 5 from the center

and the center's case here is (0,0).

Answer:

[tex]d = \frac{W}{F}[/tex]

Step-by-step explanation:

To do this, we must isolate the variable d.

W = Fd

To isolate d, we must divide the variable F from both sides.

W ÷ F = Fd ÷ F

W ÷ F = d

Now that we have isolated the variable d, we have successfully solved this formula for distance.

[tex]d = \frac{W}{F}[/tex]

Answer:

d = W/F.

Step-by-step explanation:

You simply divide both sides by F:

W / F = Fd / F

W/F = d.

Answer: 14 is 20% of 70

The true statement is the graph of the function crosses the x-axis at x = x = 0, 1.34 and 7.97

The function is given as:

[tex]\mathbf{f(x) = x^5 - 8x^4 + 16x^3}[/tex]

See attachment for the graph of [tex]\mathbf{f(x) = x^5 - 8x^4 + 16x^3}[/tex]

From the attachment, we have the following highlights

Hence, the true statement is (b) above

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The sum of the real numbers x and y is 25 and their difference is 13. To find the value of xy, we need to solve a system of equations. The value of xy is 114.

To solve this problem, we need to set up a system of equations based on the given information. Let's denote x and y as the two real numbers. The sum of x and y is 25, so we can write the equation x + y = 25. The difference between x and y is 13, so the equation becomes x - y = 13. To find the value of xy, we need to solve this system of equations.

First, let's add the two equations together. (x + y) + (x - y) = 25 + 13. This simplifies to 2x = 38. Dividing both sides by 2, we find x = 19.

Now, we can substitute the value of x into one of the original equations (x + y = 25) to solve for y. 19 + y = 25. Subtracting 19 from both sides, we get y = 6.

Therefore, the value of xy is 19 * 6 = 114.

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The increase in price of the stock is $37.50. To find the percent increase, divide the increase (37.50) by the original price (12.50) and multiply by 100, giving a percent increase of 300%.

The question requires us to find the percent increase in the price of a stock. First, to find the increase, we subtract the initial price from the final price. We get $50 - $12.50 = $37.50. This is the increase in price. To find the percentage increase, we divide this increase by the initial price and multiply by 100 to convert it into percent. Therefore, the percentage increase = ($37.50 / $12.50) x 100 = 300%. Therefore, there is a 300% increase in the stock price.

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The value of x in the triangle is 8 and the value of y is [tex]8\sqrt2[/tex]

How to determine the value of x in the triangle

From the question, we have the following parameters that can be used in our computation:

The triangle

Using the Pythagoras theorem, we have:

[tex]x^2 = 10^2 - 8^2[/tex]

This gives

[tex]x^2 = 36[/tex]

take the square root of both sides

x = 8

How to determine the value of y in the triangle

Using the Pythagoras theorem on the second triangle, we have

[tex]y^2 = 8^2 + 8^2[/tex]

This gives

[tex]y^2 = 2(8^2)[/tex]

take the square root of both sides

[tex]y = 8\sqrt2[/tex]

Hence, the value of x is 8 and the value of y is [tex]8\sqrt2[/tex]

Answer:

[tex]SA=144\pi\ ft^2[/tex]

Step-by-step explanation:

We know that the diameter of the sphere is 12 feet.

By definition the radius of the sphere is:

[tex]r =\frac{d}{2}[/tex]

Where d is the diameter of the sphere

Then

[tex]r =\frac{12}{2}[/tex]

[tex]r =6\ ft[/tex]

Now we calculate the surface area of the sphere using the formula

[tex]SA=4\pi r^2[/tex]

[tex]SA=4\pi (6)^2[/tex]

[tex]SA=4\pi(36)[/tex]

[tex]SA=144\pi\ ft^2[/tex]

Answer:

The result of 36 divided by 3 is 12

Answer:

12 is  the answer

Step-by-step explanation:

the asnwer is most likey 12x^4-32x^3+24x^2

Answer:

Last option:  [tex]8x^4-32x^3+24x^2[/tex]

Step-by-step explanation:

Given the expression [tex]4x^2(2x^2-8x + 6)[/tex], you need to remember the Product of powers property, which states the following:

 [tex](a^m)(a^n)=a^{(m+n)}[/tex]

Knowing this, you can apply the Distributive property. Therefore, you get:

[tex](4x^2)(2x^2)-(8x)(4x^2) +(6)(4x^2)=8x^{(2+2)}-32x^{(1+2)}+24x^2=8x^4-32x^3+24x^2[/tex]

You can observe that this matches with the las option.

Answer:

Step-by-step explanation:

A pie weighs n pounds.  How much would one serving weigh if the entire pie were to be shared equally among 12 people?

Answer:

57.12cm²

Step-by-step explanation:

From the attached picture, you will notice that you can fill in the 4 corners of the hexagon with 4 triangles (i.e shaded areas) to form a rectangle.

Area of each shaded corner (triangle) = [tex]\frac{1}{2}[/tex] x 4 x 2.14 = 4.28 cm²

Area of 4 shaded corners = 4 x 4.28 = 17.12cm²

Area of rectangle = 9.28 x 8 = 74.24 cm²

Area of hexagon

= Area of rectangle - Area of 4 shaded corners

= 74.24 - 17.12

= 57.12cm²

Answer:

The answer is y = -12x - 42

Step-by-step explanation:

First distribute -12 into the paranthesis.

y - 6 = -12x - 48

Then add 6 to both sides.

y = -12x - 42

That's your final answer. I hope this helps love! :)

Answer:

[tex]x = \frac{ - 1}{12} y + \frac{ - 7}{2} \\ c. \: y = - 12x - 42[/tex]

Step-by-step explanation:

[tex] 1. \: - 12x - 48 = y - 6 \\ 2. \: - 12x = y + 42 \\ 3. \: \frac{12x}{ - 12} = \frac{y + 42}{ - 12} \\ x = \frac{ - 1}{12} y + \frac{ - 7}{2} [/tex]

Answer:

no

Step-by-step explanation:

a line is better for a more constant and organized data. this data is unorganized and is scattered. this would be best for this type of dara

Answer:

1). sin x  and csc x

2). cos x and sec x

3).tan x and cot x

Step-by-step explanation:

Points to remember

Trigonometric ratios

Sin θ  = Opposite side/Hypotenuse

Cos θ = Adjacent side/Hypotenuse

Tan θ = Opposite side/Adjacent side

Csc θ = Hypotenuse /Opposite side

Sec θ = Hypotenuse /Adjacent side

Cot θ = Adjacent side/Opposite side

To find the correct answers

From the above points we get reciprocal of functions are,

1). sin x  and csc x

2). cos x and sec x

3).tan x and cotx

Option (1) will be the answer.

        [tex]\frac{\text{sinA}}{a}= \frac{\text{sinB}}{b}= \frac{\text{sinC}}{c}[/tex]

        Where [tex]a,b,c[/tex] are the opposite sides of ∠A, ∠B and ∠C.

Given in the question,

Apply sine rule in the triangle given in the picture,

[tex]\frac{\text{sin(40)}^\circ}{y}= \frac{\text{sin(75)}^\circ}{25}[/tex]

   Therefore, expression given in option (1) will be the answer.

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Answer:

y=5x+1

Step-by-step explanation:

step 1

Find the slope of the given line

we have

(0,1) and (5,0)

m=(0-1)/(5-0)

m=-1/5

step 2

Find the slope of the perpendicular line to the given line

we know that

If two lines are perpendicular, then the product of their slopes is equal to -1

m1*m2=-1

m1=-1/5

substitute

(-1/5)*m2=-1

m2=5

step 3

Find the equation of the line with slope m=5 and y-intercept (0,1)

The equation of the line into slope intercept form is equal to

y=mx+b

we have

m=5

b=1

substitute

y=5x+1

Answer:

C

Step-by-step explanation:

ANSWER

The answer is B.

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

EXPLANATION

The graph represents a rational function.

This rational function has a hole at x=1 and a vertical asymptote at x=-3.

This implies that the denominator of the rational function in factored form is

[tex](x + 3)(x - 1)[/tex]

When we expand this, we get:

[tex] {x}^{2} + 2x - 3[/tex]

This tells us that the answer must be option B.

This graph also has a horizontal asymptote at y=1.

The numerator must therefore have leading term that is quadratic with the coefficient being unity or 1.

Therefore the function is actually

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

Answer:

-5

Step-by-step explanation:

We have two points.  We can find the slope m using

m = (y2-y1)/ (x2-x1)

   = (8--2)/ (1-3)

      (8+2)/(1-3)

     10/-2

   -5

The slope is -5

Answer:

-5

Step-by-step explanation:

Answer:

128 degrees, so C is again the answer.

Step-by-step explanation:

Since angles 3 and 11 are corresponding(from your previous question), angles 1 and 11 will add up to 180 degrees, since a line is that long. Therefore your answer is 180-(degrees of angle 1)= 180-52= 128

m∠11 = 128°.

A line that cuts three parallel lines forms congruent angles which means they measure the same.

In this problem m∠1 = 52° = m∠4 = m∠5 = m∠8 = m∠9 = m∠12, and  m∠2 = m∠3 = m∠6 = m∠7 = m∠10 = m∠11.

To calculate m∠11, we know that m∠12 = m∠1 = 52°, the sum of the angle of m∠11 and m∠12 is 180°. Then:

m∠11 + m∠12 = 180°, with m∠1 = 52° = m∠12

m∠11 + 52° = 180°

m∠11 = 180° - 52°

m∠11 = 128°

Answer:

A and B, A and C

Step-by-step explanation:

A and B touch at T same as A and C. The tangent is in between the two circles but through the touching points. B and C share the tangent but externally since at T it does not pass in between them.

Answer:

- x² + x - 1

Step-by-step explanation:

(f / g)(x)

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

divide each term on the numerator by - x²

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

=  - [tex]x^{4-2}[/tex] + [tex]x^{3-2}[/tex] - [tex]x^{2-2}[/tex]

= - x² + x - [tex]x^{0}[/tex] = - x² + x - 1

Check the picture below.

since the vertical distance, namely the y-coordinate, is twice as much as the horizontal, then if the horizontal is "x", the vertical one must be 2x.

let's find the hypotenuse first.

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{x}\\ b=\stackrel{opposite}{2x}\\ \end{cases} \\\\\\ c=\sqrt{x^2+(2x)^2}\implies c=\sqrt{x^2+4x^2}\implies c=\sqrt{5x^2}\implies c=x\sqrt{5} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf sin(\theta )=\cfrac{\stackrel{opposite}{2~~\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }}{\stackrel{hypotenuse}{~~\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ \sqrt{5}}}\implies \stackrel{\textit{and rationalizing the denominator}~\hfill }{\cfrac{2}{\sqrt{5}}\cdot \cfrac{\sqrt{5}}{\sqrt{5}}\implies \cfrac{2\sqrt{5}}{(\sqrt{5})^2}\implies \cfrac{2\sqrt{5}}{5}}[/tex]

The value of Sin θ for a given circle and given condition is (2√5)/5.

A circle is the set of all points in the plane that are a fixed distance (the radius) from a fixed point (the center). Any interval joining a point on the circle to the center is called a radius.

Here, let the horizontal side be x.

         vertical side be y

then as per the given condition

Vertical distance = 2 X horizontal distance

      y = 2x

By Pythagoras Theorem,

      r = [tex]\sqrt{x^2+y^2}[/tex]

      1 = [tex]\sqrt{x^2+(2x)^2}[/tex]

      1 = x² + 4x²

      5x² = 1

       x² = 1/5

      x = 1/√5

then, y = 2/√5

Now, Sin θ = perp. / Hypo.

         Sin θ = y/1

           Sin θ  = 2/√5

or        Sin θ  = (2√5)/5

Thus, the value of Sin θ for a given circle and given condition is (2√5)/5.

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The equation 3 • (10 • 12) = (3 • 10) • 12 is justified by the associative property of multiplication, stating that the grouping of numbers in multiplication does not change the outcome.

The equation 3 • (10 • 12) = (3 • 10) • 12 can be justified using the property of associative property of multiplication. This property states that when three or more numbers are multiplied, the way in which the numbers are grouped does not change the product. In simpler terms, no matter how we place the parentheses in a multiplication equation, the result will always be the same.

For example, let's take three numbers, a, b, and c. The associative property of multiplication tells us that (a • b) • c = a • (b • c). Applying this to the given equation, 3 • (10 • 12) is the same as (3 • 10) • 12 because, according to the property, the grouping of numbers does not affect the outcome. This demonstrates why the original equation holds true.

The answer is 12

a² = c² - b²

a² = 15² - 9²

a² = 225 - 81

a² = 144

a = √144

a = 12

Answer:

12 ft

Step-by-step explanation:

The diagonal divides the flag into 2 right triangles.

Using Pythagoras' identity on the right triangle.

The square on the hypotenuse (diagonal ) is equal to the sum of the squares on the other 2 sides.

let x be the length, then

x² + 9² = 15²

x² + 81 = 225 ( subtract 81 from both sides )

x² = 144 ( take the square root of both sides )

x = [tex]\sqrt{144}[/tex] = 12

The length of the flag is 12 ft

Answer:

1344 ft^2

Step-by-step explanation:

From the picture we can see that 4w = 3l, which means that l = (4/3)w.  Since w = 12 ft, l = (4/3)(12 ft) = 16 ft.  Then the total area of the floor is

(length of floor)(width of floor) = (48 ft)(12 ft + 16 ft) = 1344 ft^2

Answer:

y=1/4 x +11

Step-by-step explanation:

So this is a word problem but it isn't too bad to figure what they want:  They are looking for a line that is perpendicular to y=-4x-6 and goes through (-4,10).

So we are looking for an equation whose slope is the opposite reciprocal of the given equation's slope.

The given equation has a slope of -4

The opposite reciprocal of -4 is 1/4 so that is the slope of our new line.

So we know our equation is in the form of y=1/4 x+b

Now we are given that this line should go through (-4,10) so plug it in to find b.

10=1/4 * (-4)+b

10=-1+b

11=b

So the equation is y=1/4 x+11

Answer: [tex]y=\frac{1}{4}x+11[/tex]

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

Given the equation of the line [tex]y= -4x - 6[/tex], you can identify that the slope is:

[tex]m=-4[/tex]

By definition, the slopes of perpendicular lines are negative reciprocals, then the slope of equation  of the line that represents the new path which will be built perpendicular to other path, is:

[tex]m=\frac{1}{4}[/tex]

Knowing that the path will intersect at the point (-4 ,10), you  need to substitute the slope and this point into  [tex]y=mx+b[/tex] and solve for "b":

[tex]10=\frac{1}{4}(-4)+b\\\\10+1=b\\\\b=11[/tex]

Therefore, the equation that represents the new path is:

 [tex]y=\frac{1}{4}x+11[/tex]

Answer:

The answer is 57 degrees Fahrenheit

Step-by-step explanation:

The  temperature in degrees Fahrenheit is 57.2°F

The Fahrenheit temperature scale is used in the United States; the Celsius, or centigrade, scale is employed in most other countries and for scientific purposes worldwide.

The conversion formula for a temperature that is expressed on the Celsius (°C) scale to its Fahrenheit (°F) representation is:

°F = (9/5 × °C) + 32.

Given:

temperature= 14 C

using formula,

F=9/5C+32,

F= 9/5 * 14+32

F= 126/5+32

F= 25.2+32

F= 57.2

Hence, the temperature in degrees Fahrenheit is 57.2°F.

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Answer:

[tex]\large\boxed{b=0}[/tex]

Step-by-step explanation:

[tex]4b+6=2-b+4\qquad\text{combine like terms}\\\\4b+6=(2+4)-b\qquad\text{add}\ b\ \text{to both sides}\\\\5b+6=6\qquad\text{subtract 6 from both sides}\\\\5b=0\qquad\text{divide both sides by 5}\\\\b=0[/tex]

Hello!

Answer:

[tex]\boxed{b=0}\checkmark[/tex]

The answer should have a positive sign.

Step-by-step explanation:

First, switch sides and group like terms.

4b+6=-b+2+4

Then, add numbers from left/right.

2+4=6

4b+6=-b+6

Subtract by 6 both sides of an equation.

4b+6-6=-b+6-6

Simplify.

4b=-b

Next add b both sides of an equation.

4b+b=-b+b

Simplify.

5b=0

Therefore, you divide by 5 from both sides of an equation.

5b/5=0/5

Finally, you simplify and solve to find that answer is.

0/5=0

b=0 is the correct answer.

Hope this helps!

Have a nice day! :)

-Charlie

Thank you so much!