Use the diagram to answer the questions. What is the area of the circle in terms of pi? π units² What is the measure of the central angle of the shaded sector? ° What is the area of the shaded sector rounded to the nearest whole number? units²

Answer:

15.5

Step-by-step explanation:

So the formula here is the square of the tangent length is equal to the product of the exterior part of the secant line and total length of the secant.

So that means we have x^2=10(14+10).

After simplifying the right hand side we have the equation is x^2=10(24) or x^2=240.

To get rid of the square on the x, we square root both sides.

x=sqrt(240)

x=15.49193338

To the nearest tenths, the answer is x=15.5

So 15.5 inches is the length of x.

Answer:

Area of the polygon = 59 in²

Explanation:

From the given diagram, we can note that the given polygon is composed of an upper triangle, a side triangle and a rectangle

Therefore:

Area of polygon =

area of upper triangle + area of side triangle + area of rectangle

1- getting the area of the upper triangle:

We have:

base of triangle = 7 in

height of triangle = 6 in

Therefore:

Area of upper triangle = [tex]\frac{1}{2}*base*height = \frac{1}{2}*7*6=21[/tex] in²

2- getting the area of the side triangle:

We have:

base of triangle = 4 in

height of triangle = 5 in

Therefore:

Area of upper triangle = [tex]\frac{1}{2}*base*height = \frac{1}{2}*4*5=10[/tex] in²

3- getting the area of the rectangle:

We have:

length of rectangle = 7 in

width of rectangle = 4 in

Therefore:

Area of rectangle = length x width = 7 x 4 = 28 in²

4- getting the total area of the polygon:

Area of polygon =

area of upper triangle + area of side triangle + area of rectangle

Therefore:

Area of polygon = 21 + 10 + 28 = 59 in²

Hope this helps :)

Answer:

y=5/4x-4

Step-by-step explanation:

C. y = 5/4x - 4.

One of the three ways we may express a straight line is in slope-intercept form. The other forms are known as point slope form and standard form, however in this section we will mostly use slope-intercept form. The slope-intercept form is used to write a line's equation as y = mx + c.

You may be aware that a point's coordinates on a graph are x and y.

Given two coordinates of a line from that, we can calculate the slope.

slope m = (y₂ - y₁)  /  (x₂- x₁)

m = 5/4

Put the value of m and one coordinate value in the slope-intercept equation

-4 = 5/4 * 0 + c

c = -4

therefore slope-intercept equation of given coordinates is y = 5/4x - 4.

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Answer:

The answer is 6 cups of flour.

To find the amount of flour needed for 3 sticks of butter, a proportion based on the original recipe ratio is used, resulting in 6 cups of flour.

Jermiah's recipe calls for 1 1/2 cups of flour for every 3/4 stick of butter. Therefore, if he uses 3 sticks of butter, we need to find out how many cups of flour that corresponds to.

To determine the amount of flour needed, we set up a proportion, where the original amount of butter and flour are proportional to the new amount of butter and flour.

Since 3/4 stick of butter corresponds to 1 1/2 cups of flour, 3 sticks of butter would be 4 times as much, because 3 divided by 3/4 equals 4. Therefore, he will need 4 times the original amount of flour.

Here is the math: 1 1/2 cups of flour x 4 = 6 cups of flour.

Answer:

4.54%

Step-by-step explanation:

Step 1: Write the data

Total bill = $170

Penalty = $7.72

Percentage of penalty = ?

Step 2: Write the formula to find the percentage of penalty

Percentage of penalty = Penalty/Total bill * 100

Percentage of penalty = 7.72/170 * 100

Percentage of penalty = 4.54%

Therefore, the percent of penalty is 4.54%

!!

Answer:

p - q

Step-by-step explanation:

Given the factors

(x + p)(x - q) ← expanding the factors

= x² - qx + px - pq ← collect like terms

= x² + px - qx - pq ← factor out x in each of the x- terms

= x² + (p - q)x - pq

The coefficient of the x- term is p - q

In a scale model, Figure A has one side measuring 45 units and another side measuring x, while Figure B has corresponding sides of 27 and 18 units. By setting up a proportion, x is determined to be 30 units.

To find the value of x, we can set up a proportion based on the given information:

In Figure A, one side is 45, and in Figure B, it corresponds to a side of 27.

In Figure A, the other side is x, and in Figure B, it corresponds to a side of 18.

So, we can set up the following proportion:

(45 / 27) = (x / 18)

Now, cross-multiply and solve for x:

45 * 18 = 27x

810 = 27x

Now, divide by 27 to find the value of x:

x = 810 / 27

x = 30

So, the value of x is 30.

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Answer:

58.6667

Step-by-step explanation:

if you see there are 5280 ft in 1 mile so use ur brain

Answer:

58.67 feet per second.

Step-by-step explanation:

We have been given that Jackrabbit are capable of reaching speeds up to 40 miles per hour. We are asked to represent this speed in feet per second.

We know that 1 mile equals 5280 feet.

We also know that 1 hour equals 3600 seconds.

[tex]\text{Speed of jackrabbit}=\frac{\text{40 miles}}{\text{Hour}}\times \frac{\text{5280 feet}}{\text{Mile}}\times \frac{\text{1 hour}}{\text{3600 sec}}[/tex]

[tex]\text{Speed of jackrabbit}=\frac{40 \times\text{5280 feet}}{\text{3600 sec}}[/tex]

[tex]\text{Speed of jackrabbit}=\frac{211200\text{ feet}}{\text{3600 sec}}[/tex]

[tex]\text{Speed of jackrabbit}=\frac{58.67\text{ feet}}{\text{3600 sec}}[/tex]

Therefore, the speed of jackrabbit is 58.67 feet per second.

Answer:

[tex]\large\boxed{(b)\ \dfrac{x+2}{x-3}}[/tex]

Step-by-step explanation:

[tex]\dfrac{1}{x+1}+\dfrac{x}{x-3}-\dfrac{-x-5}{x^2-2x-3}=(*)\\\\x^2-2x-3=x^2-3x+x-3=x(x-3)+1(x-3)=(x-3)(x+1)\\\\(*)=\dfrac{1(x-3)}{(x+1)(x-3)}+\dfrac{x(x+1)}{(x+1)(x-3)}+\dfrac{-(-x-5)}{(x+1)(x-3)}\\\\=\dfrac{x-3+x^2+x+x+5}{(x+1)(x-3)}=\dfrac{x^2+(x+x+x)+(-3+5)}{(x+1)(x-3)}\\\\=\dfrac{x^2+3x+2}{(x+1)(x-3)}=\dfrac{x^2+2x+x+2}{(x+1)(x-3)}=\dfrac{x(x+2)+1(x+2)}{(x+1)(x-3)}\\\\=\dfrac{(x+2)(x+1)}{(x+1)(x-3)}\qquad\text{cancel (x + 1)}\\\\=\dfrac{x+2}{x-3}[/tex]

The answer is:

To find the x-interception of the given function, we just need to isolate the variable "x", by making the function (y) equal to 0.

So, we are given the function:

[tex]F(x)=y=Log_{0.71}(x)[/tex]

Now, making y equal to 0, to isolate "x", we have:

[tex]y=Log_{0.71}(x)\\\\0=Log_{0.71}(x)[/tex]

[tex]0=Log_{0.71}(x)\\\\0.71^{0}=0.71^{Log_{0.71}(x)}} \\\\1=x[/tex]

We have that the x-intercept of the logarithmic function is located at (1,0)

Hence, the correct answer is:

B. (1,0).

Have a nice day!

Note: I have attached a picture for better understanding.

Answer:

A

Step-by-step explanation:

3y (-5)(y+2)

3y(-5y-10)

3y-5y-10

-2y-10

-2y-10

3y - 5(y +2)

Use the distributive property:

3y - 5y +10

Combine like terms:

-2y+10

The answer is B.

Answer:

(x, y ) → (x + 4, y - 3 )

Step-by-step explanation:

A translation of 4 units to the right is a positive shift in the x- direction, that is,

The x- coordinate of the image is the original + 4

A translation of 3 units down is a negative shift in the y- direction, that is

The y- coordinate of the image is the original - 4

Putting the 2 together

(x, y ) → (x + 4, y - 3 )

To find the exact value of cos(127.5), we can use the half angle identity for cosine. By substituting the angle into the half angle identity and simplifying, we find that cos(127.5) is approximately ±0.99992.

The cosine function is a trigonometric function that relates the angle of a right triangle to the ratio of the adjacent side to the hypotenuse. To find the exact value of cos(127.5), we can use the half angle identity for cosine. This identity states that cos(θ/2) = ±√((1 + cos(θ))/2), where θ is the original angle.

In this case, we have θ = 255 degrees (since 127.5 is half of 255). Using the half angle identity, we can calculate cos(127.5) as follows:

Therefore, the exact value of cos(127.5) is approximately ±0.99992.

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Final answer:

To simplify (f+g)(2) with given functions f(x)=x+1 and g(x)=x^2-x, calculate the functions' values at x=2 and sum them, resulting in (f+g)(2) = 5.

Explanation:

To find and simplify the expression (f+g)(2), you first need to determine the individual functions f(x) and g(x) at the value x = 2, and then sum them.

The function f(x) is given by f(x) = x + 1. At x = 2, f(2) = 2 + 1 = 3.

The function g(x) is given by g(x) = x2 - x. At x = 2, g(2) = 22 - 2 = 4 - 2 = 2.

Adding these two results together, we get (f+g)(2) = f(2) + g(2) = 3 + 2 = 5.

Answer:

The correct option is A

Step-by-step explanation:

Lets suppose that the third side is hypotenuse.

We will apply Pythagorean theorem:

c²= a²+b²

where,

a=12 inches

b=15 inches

Now substitute the values in the theorem:

c²=(12)²+(15)²

c²=144+225

c²=369

Take square root on both sides:

√c²=√369

c= 19.2 inches.

Now assume that the third side is a leg:

Here we will find the value of b.

a=12 inches

c= 15 inches.

b= ?

Now substitute the values in the theorem:

c²=a²+b²

(15)²=(12)²+b²

225=144+b²

Move the constant to the L.H.S

225-144=b²

81=b²

Take square root on both sides:

√81=√b²

9=b

Now we will find the difference of the third sides:

19.2-9 = 10.2

Thus the length of the third side is 10.2 inches

The correct option is A....

Answer:

A.

Step-by-step explanation:

Answer: [tex]AC=10.5[/tex]

Step-by-step explanation:

Assuming that [tex]b=AC[/tex] and given the following equation:

 [tex]tan(55\°)=\frac{15}{b}[/tex]

You need to solve for "b" in order to find the lenght of AC asked in the exercise.

 Therefore, with this procedure you get that the lenght of AC is the following:

[tex]\frac{15}{tan(55\°)}=b[/tex]

[tex]b=AC=10.5[/tex]

Answer:

The sum is [tex]9,331[/tex]

Step-by-step explanation:

we have

[tex]1,6,36,...[/tex]

we have

[tex]a1=1[/tex]

[tex]a2=6[/tex]

[tex]a3=36[/tex]

Find the common ratio r

[tex]a2/a1=6/1=6[/tex]

[tex]a3/a2=36/6=6[/tex]

The common ratio is r=6

The formula to calculate the sum in a geometric sequence is equal to

[tex]S=a1\frac{(1-r^{n})}{(1-r)}[/tex]

where

n is the number of terms

r is the common ratio

a1 is the first term

we have

[tex]n=6[/tex]

[tex]a1=1[/tex]

[tex]r=6[/tex]

substitute

[tex]S=(1)\frac{(1-(6)^{6})}{(1-6)}[/tex]

[tex]S=\frac{(1-(6)^{6})}{(-5)}[/tex]

[tex]S=9,331[/tex]

Answer:

The mode is 10.

Step-by-step explanation:

A mode is basically the number that occurs most in a data set, so first to make it easier you can list the number least to greatest. After that look at the data set and see what number occurs the most. In this situation it is 10 because it occurs 3 times.

In a data set, the mode is the value that appears the most frequently. A set of data can have just one mode, multiple modes, or none at all.

To solve mode given series is

[tex]10\\16\\15\\14\\8\\21\\10\\5\\19\\18\\4\\5\\16\\12\\10\\9\\[/tex]

Rearranging series we get

[tex]4\\5\\5\\8\\9\\10\\10\\10\\12\\14\\15\\16\\16\\18\\19\\21\\[/tex]

hence, mode is number with highest frequency which is 10 in this series

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Answer:

[tex]\large\boxed{y=\dfrac{1}{2}x+1}[/tex]

Step-by-step explanation:

[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{We have:}\ m=\dfrac{1}{2}\ \text{and the point}\ (6,\ 4).\\\\\text{The equation:}\ y=\dfrac{1}{2}x+b.\\\\\text{Put the coordinates of the point to the equation:}\\\\4=\dfrac{1}{2}(6)+b\\\\4=3+b\qquad\text{subtract 3 from both sides}\\\\1=b\to b=1\\\\\text{Finally:}\\\\y=\dfrac{1}{2}x+1[/tex]

Answer:

D

Step-by-step explanation:

Since GH and JK  are congruent then the central angles are congruent, that is

∠KOJ = ∠HOG = 68° → D

The  measure of KOJ = 68 degree.

A sector is formed by two radii and the intercepted arc on the circle.

The angle subtended by the sector at the center is called Central Angle.

It is given that the

sector , GH and JK are congruent.

As they are congruent the angle subtended by them at the center will be equal.

The measure of ∠GOH = 68 degree

∠KOJ = ∠GOH = 68 degree

Therefore , The  measure of KOJ = 68 degree.

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The slope is [tex]-10[/tex] and the y-intercept is [tex]1[/tex].

This function is written in slope-intercept form, which is [tex]y=mx+b[/tex].  In this form, [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.

In this case, [tex]m=-10[/tex] and [tex]b=1[/tex], so those are the answers to this problem.

For this case we have that by definition, the equation of a line of the slope-intersection form is given by:

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

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We have the following equation:

[tex]y = -10x + 1[/tex]

So we have to:

[tex]m = -10\\b = 1[/tex]

Answer:

[tex]m = -10\\b = 1[/tex]

Answer:

The probability a person will ace a test given that the person got a

good night's sleep the previous night.

Step-by-step explanation:

A conditional probability is a probability that something will occur given that something else has happened.

C The probability a person will ace a test given that the person got a

good night's sleep the previous night.

Answer:

30√3 - 21 √6

Step-by-step explanation:

The given expression is:

3√2 (5√6 -7√3)

We cannot subtract the values inside the bracket because the values inside the radicals are not same.

So multiply 3√2 with the bracket.

=3*5√2*6 -  3*7√2*3

=15√12 - 21√6

Now break √12

=15√4*3 - 21√6

write √4*3 separately:

=15√4 *√3 - 21√6

We know that √4 = 2

=15*2*√3 - 21√6

=30√3 - 21 √6

Therefore the answer is 30√3 - 21 √6 ....

Answer:

The slope is -4.

Step-by-step explanation:

Slope formula:

[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}=\frac{rise}{run}[/tex]

[tex]\displaystyle \frac{(-9)-(-5)}{1-0}=\frac{-4}{1}=-4[/tex]

Therefore, the slope is -4, and the correct answer is -4.

Hope this helps!

Answer:

TRUE:

When x≈2.7, the graphs of f(x) and g(x) intersect

f(x)=g(x) when x=0

Step-by-step explanation:

The graphs of two function y=f(x) and y=g(x) are shown in attached diagram.

These two graphs intersect at two points (0,-3) and about (2.7,2.3). This means that

f(0)=g(0)=-3

and

f(2.7)=g(2.7)=2.3

So, x=0, y=-3 is the solution to the system (the solution to the system is ordered pair (x,y), not only x)

Points (1.5,0) and (2,0) are not solutions, because they are not points of graphs intersection.

When x≈2.7, the graphs of f(x) and g(x) intersect (TRUE)

f(x)=g(x) when x=0 (TRUE)

Answer:

f(x)=g(x) when x=0.

x=0 is a solution to the system.

When x≈2.7, the graphs of f(x) and g(x)intersect because they are equal to each other at that value.

Answer:

The area of the shaded region is [tex]11.6\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The area of the shaded region is equal to the area of the sector of circle of angle 68.9 degrees minus the area of the isosceles triangle

step 1

Find the area of sector of the circle

The area of circle is equal to

[tex]A=\pi r^{2}[/tex]

assume

[tex]\pi =3.14[/tex]

[tex]r=9.28\ cm[/tex]

substitute

[tex]A=(3.14)(9.28)^{2}[/tex]

[tex]A=270.41\ cm^{2}[/tex]

Remember that the area of a circle subtends a central angle of 360 degrees

so

using proportion Find out the area of a sector with a central angle of 68.90 degrees

Let

x -----> the area of a sector

[tex]270.41/360=x/68.90\\\\x=68.90*270.41/360\\\\x=51.75\ cm^{2}[/tex]

step 2

Find the area of the isosceles triangle

Applying the law of sines

The area is equal to

[tex]A=(1/2)r^{2}sin(68.90)[/tex]

we have

[tex]r=9.28\ cm[/tex]

substitute

[tex]A=(1/2)(9.28)^{2}sin(68.90)=40.17\ cm^{2}[/tex]

step 3

Find the area of the shaded region

[tex]51.75-40.17=11.58\ cm^{2}[/tex]

Round to the nearest tenth

[tex]11.58=11.6\ cm^{2}[/tex]

The calculated area of the shaded region is 11.6 square cm

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

The circle

The area of the shaded region is calculated as

Area of shaded region = Area of sector - Area of triangle

Using the respective formulas, we have

Area of shaded region = 68.9/360 * 3.14 * 9.28 * 9.28 - 1/2 * 9.28 * 9.28 * sin(68.9)

Evaluate

Area of shaded region = 11.6

Hence, the area of the shaded region is 11.6 square cm

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Answer:

A) 12,14,16

B) 3x+1=16

Step-by-step explanation:

A)

They already gave you the equation to solve:

n+(n+2)+(n+4)=42

n+n+2+n+4=42

Put like terms together:

n+n+n+2+4=42

Combine the like terms:

3n+6=42

Subtract 6 on both sides:

3n=42-6

Simplify:

3n=36

Divide both sides by 3:

n=36/3

Simplify:

n=12

If n=12,

then

n+2=14 and

n+4=16.

Check the addition of those numbers: 12+14+16=26+16=42.

B)

There is a lot of equations that have a solution of 5.

It might be good start with x=5.

Then just remember whatever you do to one side, you must do to the other.

x=5

Multiply both sides by 3:

3x=15

Add 1 on both sides:

3x+1=16

An example of equation that solution 5 is 3x+1=16.

Answer:

That may be one of the answers but it is check all that apply

Step-by-step explanation:

Answer:

See explanation

Step-by-step explanation:

Triangle ABC ha vertices at: A(-3,6), B(0,-4) and (2,6).

Let us apply 90 degrees clockwise about the origin twice to obtain 180 degrees clockwise rotation.

We apply the 90 degrees clockwise rotation rule.

[tex](x,y)\to (y,-x)[/tex]

[tex]\implies A(-3,6)\to (6,3)[/tex]

[tex]\implies B(0,4)\to (4,0)[/tex]

[tex]\implies C(2,6)\to (6,-2)[/tex]

We apply the 90 degrees clockwise rotation rule again on the resulting points:

[tex]\implies (6,3)\to A''(3,-6)[/tex]

[tex]\implies (4,0)\to B''(0,-4)[/tex]

[tex]\implies (6,-2)\to C''(-2,-6)[/tex]

Let us now apply 90 degrees counterclockwise  rotation about the origin twice to obtain 180 degrees counterclockwise rotation.

We apply the 90 degrees counterclockwise rotation rule.

[tex](x,y)\to (-y,x)[/tex]

[tex]\implies A(-3,6)\to (-6,-3)[/tex]

[tex]\implies B(0,4)\to (-4,0)[/tex]

[tex]\implies C(2,6)\to (-6,2)[/tex]

We apply the 90 degrees counterclockwise rotation rule again on the resulting points:

[tex]\implies (-6,-3)\to A''(3,-6)[/tex]

[tex]\implies (-4,0)\to B''(0,-4)[/tex]

[tex]\implies (-6,2)\to C''(-2,-6)[/tex]

We can see that A''(3,-6), B''(0,-4) and C''(-2,-6) is the same for both the 180 degrees clockwise and counterclockwise rotations.

Triangle ABC ha vertices at: A(-3,6), B(0,-4) and (2,6).

Let us apply 90 degrees clockwise about the origin twice to obtain 180 degrees clockwise rotation.

We apply the 90 degrees clockwise rotation rule.

(x,y) --- (y, -x)

A(-3, 6) > (6, 3)

B(0, 4) > (4, 0)

C(2, 6) > (6, -2)

We apply the 90 degrees clockwise rotation rule again on the resulting points:

(6, 3) > A'(-3, 6)

(4, 0) > B'(0, -4)

(6, -2)> C'(-2, -6)

Let us now apply 90 degrees counterclockwise  rotation about the origin twice to obtain 180 degrees counterclockwise rotation.

We apply the 90 degrees counterclockwise rotation rule.

(x,y) --- (-y, x)

A(-3, 6) > (-6, -3)

B(0, 4) > (-4, 0)

C(2, 6) > (-6, 2)

We apply the 90 degrees counterclockwise rotation rule again on the resulting points:

(-6, -3) > A'(3, -6)

(-4, 0) > B'(0, -4)

(-6, 2) > C'(-2, -6)

We can see that A'(3,-6), B'(0,-4) and C'(-2,-6) is the same for both the 180 degrees clockwise and counterclockwise rotations.

Ez why to copy