Find the surface area of the composite solid.

Answer:

Part 1) The measure of the angle is 47°

Part 2) The measure of the angle is 52°

Step-by-step explanation:

Part 1)

we know that

The inscribed angle is half that of the arc it comprises.

we have that

(12y-1)°=(9y+11)° ----> because the arc that the inscribed angles comprise is the same

Solve for y

12y-9y=11+1

3y=12

y=4°

Find the measure of the angle

(12y-1)°=12(4)-1=47°

Part 2)

we know that

The inscribed angle is half that of the arc it comprises.

we have that

2(3m+2)°=(4m+20)° ----> because the arc that the inscribed angles comprise is the same

Solve for m

6m+4=4m+20

6m-4m=20-4

2m=16

m=8

Find the measure of the angle

(4m+20)°=4(8)+20=52°

Answer:

[tex]\$5,828.28[/tex]

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=5\ years\\ P=\$4,900\\ r=0.035\\n=2[/tex]  

substitute in the formula above  

[tex]A=\$4,900(1+\frac{0.035}{2})^{2*5}[/tex]  

[tex]A=\$4,900(1.0175)^{10}=\$5,828.28[/tex]

Answer:

5,828.28

Step-by-step explanation:

1)when we know x+y=90* the sine of x is equal to cosine of y , so the solution of the first is 0.6 again!

Answer:

Left diagram cos(y) = 0.6

Right diagram x = 5 makes the equation true.

Step-by-step explanation:

Left diagram

Both the sin(x) and the Cos(y) use the same side as the non hypotenuse side.

Therefore they most be equal.

So if sin(x) = 0.6, then cos(y) = 0.6

=========================

Right diagram

You can factor this to get the answer.

From the first 2 terms, take out x^2. From terms 3 and 4 take out 2.

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

Take out the common factor of (x - 5)

(x^2 +2)(x - 5)

x^2 + 2 yields a complex answer (which doesn't matter for this question)

x - 5 = 0

x = 5

[tex]\bf \textit{Product to Sum Identities} \\\\sin(\alpha)cos(\beta)=\cfrac{1}{2}[sin(\alpha+\beta)\quad +\quad sin(\alpha-\beta)] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(5\theta )cos(2\theta )\implies \cfrac{1}{2}[sin(5\theta +2\theta )+sin(5\theta -2\theta )]\implies \cfrac{sin(7\theta )+sin(3\theta )}{2}[/tex]

The required value of trigonometry expression is the product as a sum [sin(7θ) + sin(3θ)] / 2.

The product-to-sum formulae are used to represent the sum of the sine and cosine functions. These are generated from trigonometry's sum and difference formulae.

sin A cos B = (1/2) [ sin (A + B) + sin (A - B) ]

The trigonometry expression is given in the question

sin (5θ) cos (2θ)

According to  the product to sum Identities

sin A cos B = (1/2) [ sin (A + B) + sin (A - B) ]

Here A = 5θ and B = 2θ

sin (5θ) cos (2θ) = (1/2) [sin(5θ + 2θ) + sin(5θ - 2θ)]

sin (5θ) cos (2θ) = (1/2) [sin(7θ) + sin(3θ)]

sin (5θ) cos (2θ) =  [sin(7θ) + sin(3θ)] / 2

Thus, the required value of trigonometry expression is the product as a sum [sin(7θ) + sin(3θ)] / 2.

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Answer:  6 nickels and 9 dimes

Step-by-step explanation:

15 coins - 3 extra dimes = 12

12 / 2 = 6

6 nickels

6 + 3 = 9 dimes

Answer:

First option

x = 9.1, AB  = 16.5, CD = 14.1

Step-by-step explanation:

5 * x = 13 * 3.5

5x = 45.5

x = 9.1

AB = 3.5 + 13 = 16.5

CD = 5 + 9.1 = 14.1

The value of x and the length of each chord is x = 9.1, AB  = 16.5, CD = 14.1. Thus first option is correct.

If the considered circle has center O and chord AB, then if there is perpendicular from O to AB at point C, then that point C is bisecting(dividing in two equal parts) the line segment AB.

Or

|AC| = |CB|

Let x be the measure of the length of ED.

[tex]5 \times x = 13 \times3.5\\5x = 45.5\\x = 9.1[/tex]

Therefore,

AB = 3.5 + 13 = 16.5

CD = 5 + 9.1 = 14.1

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I think the answer is six

(1,1) , (2,2) , (3,3) , (4,4) , (5,5) , (6,6)

The mean is the average. The outlier is a number way bigger or smaller than the rest of the data. The outlier here would be 17. If you remove 17 and then find the average again, it will be smaller because all the numbers left are around the same range.

Answer: It will decrease

Answer:

3 hours and 30 minutes

Step-by-step explanation:

Since both of these times are in the P.M., each hour has 60 minutes and 2:30 is half, add 30 minutes to get 3:00 P.M. and then add 3 hours to get 6:00 P.M. . 3 hours and 30 minutes added to 2:30 P.M. equals 6:00 P.M. :)

Answer:

3 hours and 30 minutes

Step-by-step explanation:

Kylie started basketball practice at 2:30

Kylie finished basketball practice at 6:00

Time duration = 3 hours and 30 minutes

2 : 30 → 3 : 00

( 30 minutes )

3 : 00 → 6 : 00

( 3 hours )

3 hours + 30 minutes = 3 hours and 30 minutes

Answer:

20°

Step-by-step explanation:

40=2x,x=20°

Answer:

Step-by-step explanation:

Use the sum of angle formula:

  cos(a+b) = cos(a)cos(b) -sin(a)sin(b)

This gives you ...

  cos(x)cos(-π/6) -sin(x)sin(-π/6) = 1 + cos(x)cos(π/6) -sin(x)sin(π/6)

Subtracting the right-side trig function terms and factoring, we have ...

  cos(x)(cos(-π/6) -cos(π/6)) -sin(x)(sin(-π/6) -sin(π/6)) = 1

Since the cosine is an even function, cos(-π/6) = cos(π/6). Since the sine is an odd function, sin(-π/6) = -sin(π/6). This gives us ...

  cos(x)·0 -sin(x)(-2sin(π/6)) = 1

  sin(x) = 1/(2·sin(π/6)) = 1/(2·1/2) = 1

  x = arcsin(1)

  x = π/2

_____

When solving these by using a graphing calculator, it is convenient to subtract one side of the equation so you have a function of x that you want to find the zeros of. Here, we subtracted the right side. The graph shows the result is zero for x=π/2, as we know.

Answer:

Option C. [tex]y = (x-8) ^ 2[/tex]

Step-by-step explanation:

If we have a parent function f(x) and we want to make a transformation that translates the graph of f(x) horizontally then we do

[tex]y = f (x + h)[/tex]

Where h is a constant such that:

If [tex]h> 0[/tex] then the graph of f(x) moves h units to the left

If [tex]h <0[/tex] then the graph of f(x) moves h units to the right.

In this case we have the function [tex]y = x ^ 2[/tex] and we know that 8 units are moved to the right. If you move 8 units to the right This means that

[tex]h <0[/tex] and [tex]h = -8[/tex]

So if [tex]f(x) = x ^ 2[/tex] the transformed function will be:

[tex]y = f(x -8)[/tex]

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

Final answer:

To locate the person who moved from (0, 1) with a slope of -4, we need to know the specific horizontal distance they moved. Without this, we can only say they moved downward 4 units for every 1 unit they moved to the right.

Explanation:

The student's question involves determining the position of a person who has moved along a slope on a coordinate plane. Since the individual started at the point (0, 1) and moved to the right with a slope of -4, we can assume they are moving in the negative y-direction (downward), as the negative slope indicates a decrease in y for every increase in x. The specific horizontal distance isn't given, so we cannot provide an exact new coordinate without more information. However, if we had a specific horizontal distance the person moved, we could calculate the new position using the slope (-4), which means for every 1 unit moved horizontally to the right, the person would move 4 units down.

Answer:

  (x +8)² +(y +1)² = 9

Step-by-step explanation:

The formula for a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

Filling in your given numbers gives ...

  (x -(-8))² +(y -(-1))² = 3²

Simplifying that results in ...

  (x +8)² +(y +1)² = 9

Answer:

N/A

Step-by-step explanation:

Not enough context is given for the problem.

Just remember, though:

And = Multiplication

Or = Addition

1/8 chance for each section

Answer:

(A) P(gray), P(green)

Step-by-step explanation:

Notice that there are 2 tiles in each, so it should be A as the answer.

Please mark me brainiest!

Hope you have a good day!

Answer:

3w + 52 ≥ 90

Step-by-step explanation:

If she volunteers 3 hours per week for w weeks, then the number of hours from tutoring is 3w.  Add the 52 hours from her summer volunteering, and her total hours is 3w + 52.  This needs to be at least 90 hours for her to graduate, so:

3w + 52 ≥ 90

The answer is 8......

Answer:

The answer is 8

Step-by-step explanation:

Just add the rest of the numbers and then subtract from the answer

Answer:

[tex]3,744.45\ m^{2}[/tex]

Step-by-step explanation:

we know that

The area of a sector is equal to

[tex]A=\frac{\theta}{360\°}\pi r^{2}[/tex]

where

[tex]\theta[/tex] ------> is the angle in degrees

r is the radius of the circle

In this problem we have

[tex]r=45\ m[/tex]

[tex]\theta=212\°[/tex]

assume

[tex]\pi =3.14[/tex]

substitute the values

[tex]A=\frac{212\°}{360\°}(3.14)(45)^{2}[/tex]

[tex]A=3,744.45\ m^{2}[/tex]

Answer:

[tex]x=1[/tex]

Step-by-step explanation:

Remember:

[tex](\sqrt[n]{a})^n=a\\\\(a+b)=a^2+2ab+b^2[/tex]

Given the equation [tex]\sqrt{17-x}=x+3[/tex], you need to solve for the variable "x" to find its value.

You need to square both sides of the equation:

[tex](\sqrt{17-x})^2=(x+3)^2[/tex]

[tex]17-x=(x+3)^2[/tex]

Simplifying, you get:

[tex]17-x=x^2+2(x)(3)+3^2\\\\17-x=x^2+6x+9\\\\x^2+6x+9+x-17=0\\\\x^2+7x-8=0[/tex]

Factor the quadratic equation. Find two numbers whose sum be 7 and whose product be -8. These are: -1 and 8:

[tex](x-1)(x+8)=0[/tex]

Then:

[tex]x_1=1\\x_2=-8[/tex]

Let's check if the first solution is correct:

[tex]\sqrt{17-(1)}=(1)+3[/tex]

[tex]4=4[/tex] (It checks)

Let's check if the second solution is correct:

[tex]\sqrt{17-(-8)}=(-8)+3[/tex]

[tex]5\neq-5[/tex] (It does not checks)

Therefore, the solution is:

[tex]x=1[/tex]

the only solution is x = 1.

To solve the equation sqrt(17-x) = x+3, we first eliminate the square root by squaring both sides of the equation. Doing so yields:

17 - x = (x + 3)2

17 - x = x2 + 6x + 9

Next, we rearrange the equation to set it equal to zero, thus forming a quadratic equation:

x2 + 6x + 9 + x - 17 = 0

x2 + 7x - 8 = 0

Now, we factor the quadratic:

(x + 8)(x - 1) = 0

Hence, the solutions are:

x = -8

x = 1

To verify that these solutions satisfy the original equation, we perform a check by substituting them back into the original equation. However, we notice that the solution x = -8 does not work because it would result in taking the square root of a negative number, which is not possible in real numbers. So the only solution is x = 1.

Answer

the rectangle

Step-by-step explanation:

the cylinder folds like a circle but it is not a circle.

A rectangular shape can be rotated about an axis to form a cylinder.

A cylindrical shape is a three-dimensional geometrical shape consisting of two parallel circular bases which are connected by some height h.

We know that cylinder has some height h and two base circles.

If we compare the curved part of the cylinder then we can see that its shape is similar to a rectangle.

The length of the rectangle is similar to the circumference of the circular base of a cylinder and the height of the cylinder with the breadth of the rectangle.

Thus, a rectangular shape can be rotated about an axis to form a cylinder.

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f(x)=3x^2-18x+10

a = 3, b = -18 and c = 10

The vertex of a parabola is in form a(x+d)^2 + e

d = b/2a = -18/2(3) = -18/6 = -3

e = c-b^2/4a = 10 - -18^2/4(3) = 10-27 = -17

Now the vertex form of the parabola becomes 3(x-3)^2 -17

Use the vertex form of the parabola in the vertex form of y = a(x-h)^2 +k

Where a = 3, h = -3 and k = -17

Now you have y = 3(x-(-3))^2 +(-17)

Simplify: y = 3(x+3)^2 -17

The vertex becomes the h and k values of (3,-17)

There are 126 slices of sausage pizza sold

15/17. The value (ratio) of cos A is 15/17.

The trigonometric ratios of an acute angle are, basically, the sine, the cosine and the tangent. They are defined from an acute angle, α, of a right triangle, whose elements are the hypotenuse, the leg contiguous to the angle,  and the leg opposite the angle.

-The sine of the angle is the opposite leg divided by the hypotenuse.

-The cosine of the angle is the adjacent leg divided by the hypotenuse.

-The tangent of the angle is the opposite leg divided by the adjacent leg or, which is the same, the sine of the angle divided by the cosine of the angle.

cos A = adjacent leg/hypothenuse = BC/AC = 15/17

Answer:

210.06 feet

Step-by-step explanation:

This is a classic right triangle trig problem.  The distance from the launch pad is the measure of the base of the right triangle.  The angle of elevation, 35, is the base angle (not the right angle).  How high the fireworks go up is the height of the triangle.  You have the reference angle of 35, the side adjacent to it, 300, and you're looking for the side length across from it, y.  The trig ratio that relates a reference angle to the sides opposite it and adjacent to it is the tangent ratio.  Setting that up:

[tex]tan(35)=\frac{y}{300}[/tex]

Solving for y:

y = 300 tan(35)

On your calculator in degree mode find y to be 210.06 feet.

By using basic trigonometry, specifically the tangent of the viewing angle, we can determine that the height of the fireworks when they explode is approximately 210 feet.

You are asking how to use trigonometry to find the height of the fireworks when they explode. If we combine your conditions that the launch was vertical and the viewing angle was 35°, we can use the tangent of that angle to find the height of the fireworks. The tangent of an angle in a right triangle is the opposite side (height in this case) divided by the adjacent side (distance from the launch, 300 feet in this case). So setting up the equation, we have: tan(35°) = height / 300. Solving for 'height', we get: height = 300 * tan(35°). Using a calculator, we find that tan(35°) is roughly 0.70021. Multiplying that by 300, we find that the height of the fireworks when they explode is approximately 210 feet.

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Answer:

The measures of angles of triangle EFQ are

1) [tex]m\angle EFQ=100\°[/tex]

2) [tex]m\angle FEQ=66\°[/tex]

3) [tex]m\angle EQF=14\°[/tex]

Step-by-step explanation:

step 1

Find the measure of arc QD

we know that

The inscribed angle is half that of the arc it comprises.

[tex]m\angle DFQ=\frac{1}{2}(arc\ QD)[/tex]

substitute the given value

[tex]10\°=\frac{1}{2}(arc\ QD)[/tex]

[tex]20\°=(arc\ QD)[/tex]

[tex]arc\ QD=20\°[/tex]

step 2

Find the measure of arc FQ

we know that

[tex]arc\ QD+arc\ FQ+arc\ EF=180\°[/tex] ---> because ED is a diameter (the diameter divide the circle into two equal parts)

substitute the given values

[tex]20\°+arc\ FQ+28\°=180\°[/tex]

[tex]arc\ FQ=180\°-48\°=132\°[/tex]

step 3

Find the measure of angle EFQ

we know that

The inscribed angle is half that of the arc it comprises.

[tex]m\angle EFQ=\frac{1}{2}(arc\ QD+arc\ ED)[/tex]

substitute the given value

[tex]m\angle EFQ=\frac{1}{2}(20\°+180\°)=100\°[/tex]

step 4

Find the measure of angle FEQ

we know that

The inscribed angle is half that of the arc it comprises.

[tex]m\angle FEQ=\frac{1}{2}(arc\ FQ)[/tex]

substitute the given value

[tex]m\angle FEQ=\frac{1}{2}(132\°)=66\°[/tex]

step 5

Find the measure of angle EQF

we know that

The inscribed angle is half that of the arc it comprises.

[tex]m\angle EQF=\frac{1}{2}(arc\ EF)[/tex]

substitute the given value

[tex]m\angle EQF=\frac{1}{2}(28\°)=14\°[/tex]

Answer:

No.

Step-by-step explanation:

The square root of an integer is rational only if that integer is a square number. The closest squares to 8 are 2^2 = 4 and 3^2 = 9. 8 is not a square number, so has an irrational square root.

The square root of 8 is an irrational number.

A square root is a mathematical operation that, when applied to a number, finds a value that, when multiplied by itself, equals the original number. For example, the square root of 25 is 5 because 5 x 5 = 25. It is denoted by the √ symbol. Whether the square root of 8 is a rational number or not can be determined by finding the square root and checking if it can be expressed as a fraction.

The square root of 8 is approximately 2.828, which is an irrational number because it cannot be expressed as a fraction. To further prove that it is irrational, we can use the prime factorization method and show that 8 does not have a perfect square factor.

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Answer

[tex]\frac{121}{4} \pi mm^2[/tex]

Explanation

Find the radius

11/2 = 5.5

The formula to find the area of a circle is [tex]\pi r^2[/tex]

[tex]\pi 5.5^2[/tex] = [tex]30.25\pi[/tex]

Convert number into fraction.

[tex]30.25 \rightarrow \frac{121}{4} \pi[/tex]

Area = [tex]\frac{121}{4} \pi mm^2[/tex]

Answer:

30.25π mm²

Step-by-step explanation:

The area (A) of a circle is calculated using the formula

A = πr² ← r is the radius

here diameter = 11 and radius is half of the diameter. thus

r = 5.5

A = π × 5.5² = 30.25π mm²

Answer:

  72

Step-by-step explanation:

Exhaustive search shows the numbers to be 12, 24, 36. The sum of these three numbers is 72.

Answer:

25 possible outcomes

19 non-red outcomes

Step-by-step explanation:

there are 25 cards. if you remove the 6 red card outcomes you have 19.

Answer:

A

Step-by-step explanation:

Diagonals of a parallelogram bisect each other.

3x = 3

x = 1

y = x

y = 1

In a parallelogram, the parts in which each diagonal cuts the other are congruent.

This means that we must have

[tex]\begin{cases}3=3x\\x=y\end{cases}[/tex]

From the first equation we can deduce x=1, and thus y=x=1.