Find the area of the shaded circles. Leave your answer in terms of pi or round to the nearest 10th
Answers
step 1
Find out the area of the complete circle
[tex]A=\pi\cdot r^2[/tex]we have
r=10 units
substitute
[tex]\begin{gathered} A=\pi\cdot10^2 \\ A=100\pi\text{ unit2} \end{gathered}[/tex]Remember that the area of the complete circle subtends a central angle of 360 degrees
so
Applying proportion
Find out the area of the circle with a central angle of 330 degrees
100pi/360=x/330
solve for x
x=(100pi/360)*330
x=91.67pi unit2Related Questions
Find the equation of the linear function represented by the table below in slope-intercept form. Answer: y=
Answers
Answer:
y = 2x + 6
Explanation:
The slope-intercept form of a linear equation can be found as:
[tex]y=m(x-x_1)+y_1[/tex]Where m is the slope and it is calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]And (x1, y1) and (x2, y2) are values from the table. So, we can replace (x1, y1) by (0,6) and (x2, y2) by (1, 8):
Then, the slope is:
[tex]m=\frac{8-6}{1-0}=\frac{2}{1}=2[/tex]Therefore, the equation of the line is:
[tex]\begin{gathered} y=2(x-0)+6 \\ y=2x+6 \end{gathered}[/tex]So, the answer is y = 2x + 6
Riley read 1 book in 2 months. If she reads at a constant rate, how many books did she read in one month? Give your answer as a whole number or a FRACTION in simplest form.On the double number line below, fill in the given values, then use multiplication or division to find the missing value.
Answers
To find out the unit rate
Divide the total books by the total months
so
1/2=0.5 books per month
the answer is 0.5 books per monthIn the double number line
we have
books 0 0.5 1
months 0 1 2
In how many ways can 3 students from a class of 23 be chosen for a field trip?aYour answer is:
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SOLUTION:
This is a combination problem.
The number of ways 3 students from a class of 23 be chosen for a field trip is;
[tex]23C_3=\frac{23!}{(23-3)!3!}=1771\text{ }ways[/tex]Stephanie dilated the rectangle below and dimensions of the image were 24 ft by 6ft. What was the scale of the factor used?
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In order to determne the scale factor, calculate the quotient in between the lengths of the sides of the rectangles, as follow:
32 ft/24 ft = 4/3
8 ft/ 6 ft = 4/3
Hence, the scale factor is 4/3
find the area of the composite figures by either adding and subtracting regions
Answers
Explanation:
This figure is a rectangle and a quarter of a circle. We can find their areas and add them to find the total area of the figure.
The area of the rectangle is:
[tex]A_{\text{rectangle}}=17cm\times10\operatorname{cm}=170\operatorname{cm}^2[/tex]The area of a circle is:
[tex]A_{\text{circle}}=\pi\cdot r^2[/tex]Where r is the radius of the circle. In this case we have a quarter of a circle, so its area is a quarter of the area of the circle:
[tex]A_{1/4\text{circle}}=\frac{A_{\text{circle}}}{4}=\frac{\pi\cdot r^2}{4}[/tex]The radius of this circle is 8cm:
[tex]A_{1/4\text{circle}}=\frac{\pi\cdot8^2}{4}=\frac{\pi\cdot64}{4}=\pi\cdot16\approx50.27\operatorname{cm}^2[/tex]The total area of the figure is:
[tex]A_{\text{figure}}=A_{\text{rectangle}}+A_{1/4\text{circle}}=170\operatorname{cm}+50.27\operatorname{cm}=220.27\operatorname{cm}^2[/tex]Answer:
The area is 220.27 cm²
1 Ms. Signer has to buy pencils for her class. She goes to CVS and buys 15 pencils for $2.50. How much did she spend per pencil?*
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She bought pencils for her class. She bought 25 pencils for $2.50 . The amount for each pencil can be computed below
[tex]\begin{gathered} 25\text{ pencils = \$2.50} \\ 1\text{ pencil = ?} \\ \text{cross multiply} \\ \cos t\text{ of each pencil=}\frac{2.50}{25} \\ \text{ cost of each pencil = \$}0.1 \end{gathered}[/tex]Given a regular octagon and a regular nonagon, which one has the greater interior angle?(Type your answer as the name of the polygon)
Answers
Answer:
Nonagon
Explanation:
Each of the interior angles of a polygon is calculated using the formula:
[tex]\frac{180^0\mleft(n-2\mright)}{n}[/tex]An Octagon has 8 sides, therefore:
[tex]\begin{gathered} Each\; \text{Interior Angle=}\frac{180^0(8-2)}{\square} \\ =\frac{180\times6}{8} \\ =\frac{1080^0}{8} \\ =135^0 \end{gathered}[/tex]A Nonagon has 9 sides, therefore:
[tex]\begin{gathered} Each\; I\text{nterior Angle=}\frac{180^0(9-2)}{9} \\ =\frac{180\times7}{9} \\ =\frac{1260^0}{9} \\ =140^0 \end{gathered}[/tex]Therefore, the nonagon has a greater interior angle.
11) What is the area of the composite figure? *7 points6 ftT T2 ft5 ft3ft220O 212223
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Answer: 22
Step-by-step explanation:
Solve the inequality and write the solution using:
the inequality
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IF G and R denote the grade and the radian measure of an angle, then prove that G/200 = R/pie
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Solution:
Given;
IF G and R denote the grade and the radian measure of an angle, i.e.
Where
[tex][/tex]Here are the exam scores for the 15 students in Mr. Kirk's statistics class:
72 75 75 78 81 83 85 89 90 90 90 91 95 95 98
Karen was at the 20th percentile of the distribution. What score did Karen earn on the exam?
(A) 75
(B) 78
(C) 81
(D) 83
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Determine the functions value when x= -1?a. g(-1) = -3b. g(-1) = 0c. g(-1) = 1d. g(-1) = 27
Answers
Problem
Determine the functions value when x= -1?
a. g(-1) = -3
b. g(-1) = 0
c. g(-1) = 1
d. g(-1) = 27
Solution
For this case we just need to find the value of g when x= -1 and if we look at the table we got:
g(-1)= (-1)^3 + 6(-1)^2 +12(-1) +8
g(-1)= -1 +6 -12+8 = 5-12+8= 1
And then the solution for this case would be:
c. g(-1) = 1
What is the value of x in the proportion2 1/4 = 1 1/2_________x = 3 3/5A. 2 2/5B. 5 2/5C. 8 1/10D. 12 3/20
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First, we transform the mixed fractions
[tex]\begin{gathered} 2\frac{1}{4}=2+\frac{1}{4}=\frac{8}{4}+\frac{1}{4}=\frac{9}{4} \\ 1\frac{1}{2}=1+\frac{1}{2}=\frac{2}{2}+\frac{1}{2}=\frac{3}{2} \\ 3\frac{3}{5}=3+\frac{3}{5}=\frac{15}{5}+\frac{3}{5}=\frac{18}{5} \end{gathered}[/tex]Then, we use cross multiplication
[tex]\begin{gathered} \frac{\frac{9}{4}}{x}=\frac{9}{4}\times\frac{1}{x}=\frac{9}{4x} \\ \frac{\frac{5}{2}}{\frac{18}{5}}=\frac{3}{2}\times\frac{5}{18}=\frac{15}{36} \end{gathered}[/tex]so, we have
[tex]\frac{9}{4x}=\frac{15}{36}[/tex]Finally, we solve for x, we multiply x on both sides
[tex]\begin{gathered} \frac{9}{4x}x=\frac{15}{36}x \\ \frac{15}{36}x=\frac{9}{4} \\ x=\frac{\frac{9}{4}}{\frac{15}{36}} \\ x=\frac{9}{4}\times\frac{36}{15} \\ x=\frac{9\times9\times4}{15\times4} \\ x=\frac{81}{15} \\ x=\frac{27}{5} \end{gathered}[/tex]Since 27/5 = 5+2/5.Then,
[tex]x=5\frac{2}{5}[/tex]Then the answer is the second one.
A radio tower is located 250 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 31∘ and that the angle of depression to the bottom of the tower is 29∘
How tall is the tower? ____________ feet.
Answers
Given a radio tower of 250 feet and angles of 31 and 29 degrees, the height of the tower is given as 308.58 ft
What is angle of depression?This is the term that is used to refer to the angle that lies between the horizontal line and the object that would be observed from the horizontal line.
In the question we have the following data
b = 250 feet
angles = 31 degrees, 29 degrees
for the top α = 31 degrees, β = 59
For the bottom α = 29 degrees, β = 61 degrees
We have the formula as
a /sin α = b / sin β = c
tan ∅ = opp / adj
for ΔOCA
h1 = 250 x tan 39 degrees
= 250 x 0.8098
= 202.45
h2 = OCB
= 250 x tan 23
= 250 x 0.4245
= 106.125
The height h = h1 + h2
= 202.45 + 106.125
= 308.58
The height of the tower is 308.58 ft
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What’s the correct Answer answer asap for brainlist please
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Answer:
A. accuracy
Step-by-step explanation:
precise means to be accurate
use properties of operations to write an equivalent expression. will sand image
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Use properties of operations to write equivalent expressions
WRITING EQUIVALENT EXPRESSIONS USING PROPERTIES
Commutative Property of Addition :
When adding, changing the order of the numbers does not change the sum. ...
Commutative Property of Multiplication : ...
Associative Property of Addition : ...
Associative Property of Multiplication : ...
Distributive Property :
2.8 w + 5.6
= 2.8 ( w + 2 ) ----------- OPTION B
you can make pancakes with just bananas and eggs : serves 4 people with 6 eggs 2 bananas. how many eggs and bananas do u need to serve 6 people?
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Given:
To prepare a pancake that serves 4 people, we need 6 eggs and 2 bananas.
Required:
The number of eggs and bananas that serves 6 people
By comparison,
If we need 6 eggs to prepare a pancake that serves 4 people, the number of people that 1 egg would serve is:
[tex]\begin{gathered} k\text{ = }\frac{4\text{ people}}{6\text{ eggs}} \\ =\text{ }\frac{2}{3}\text{ people/ egg} \end{gathered}[/tex]Similarly, If we need 2 bananas to prepare a pancake that serves 4 people, the number of people that 1 banana would serve is:
[tex]\begin{gathered} k_2\text{ = }\frac{4\text{ people}}{2\text{ bananas}} \\ =\text{ 2 people/banana} \end{gathered}[/tex]The number of eggs that serves 6 people:
[tex]\begin{gathered} =\text{ 6 people }\times\frac{3}{2}\text{ egg/people} \\ =\text{ 9 eggs} \end{gathered}[/tex]The number of bananas that serves 6 people:
[tex]\begin{gathered} =\text{ 6 people }\times\text{ }\frac{1}{2}\text{ banana/ people} \\ =\text{ 3 bananas} \end{gathered}[/tex]Answer:
9 eggs are needed
3 bananas are needed
HelppppppFunction f is a(n)functionThe graph is a reflection in thewith a verticaland atranslationunits:The domain of f isThe domain of the parent function is;The range of f isThe range of the parent function is
Answers
Answer:
In order of appearance of boxes
quadraticx-axisstretch3 (units)upall real numbersall real numbersy ≤ 3y ≥ 0Step-by-step explanation:
The given function f(x) = -2x² + 3 belongs to the quadratic family of equations. A quadratic equation has a degree of 2. The degree is the highest power of the x variable in the function f(x)
The parent f(x) = x²
Going step by step:
2x² ==> graph x² is vertically stretched by 2. For any value of x in x², the new y value is twice that the old value. For example, in the original parent function x², for x = 2, y = 4. In the transformed function 2x², for x = 2, y = 2 x 4 = 8 so it has been stretched vertically. It becomes skinnier compared to the original
-2x² => graph is reflected over the x-axis. It is the mirror image of the original graph when viewed from the x-axis perspective
-2x² + 3 ==> graph is shifted vertically up by 3 units
Domain is the set of all x-input values for which the function is defined. For both x² and -2x² + 3 there are no restrictions on the values of x. So the domain for both is the set of all real numbers usually indicated by
-∞ < x < ∞
The range is the set of all possible y values for a function y = f(x) for x values in domain.
The range of f(x) = x² is x≥ 0 since x² can never be negative
Range of -2x² + 3 is x ≤ 3 : Range of -2x² is y ≤ 0 since y cannot be negative and therefore range of -2x² + 3 is y ≤ 3
Lisa played 42 of thepossible 60 minutes of asoccer game. Whatpercent did she notplay?
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Lisa played 42 minutes of a 60 minutes match. This means that she didn't play 18 minutes of the game; to find what percent this represents we can use the rule of three:
[tex]\begin{gathered} 60\rightarrow100 \\ 18\rightarrow x \end{gathered}[/tex]Then:
[tex]\begin{gathered} x=\frac{18\cdot100}{60} \\ =30 \end{gathered}[/tex]Therefore, Lisa didn't play 30% of the game.
The table shows the cost for a clothing store to buy jeans and khakis. The total cost for Saturday's shipment, $1,800, is represented by the equation 15x + 20y = 1,800. Use the x- and y-intercepts to graph the equation. Then interpret the x- and y-intercepts.
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A number multiplied by 2/5 is 3/20, Find the number
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Answer:
3/8
Explanation:
Let the number be x.
A number multiplied by 2/5 = (2/5)x
Therefore:
[tex]\frac{2}{5}x=\frac{3}{20}[/tex]To solve for x, first, we cross-multiply.
[tex]\begin{gathered} 2x\times20=3\times5 \\ 40x=15 \end{gathered}[/tex]Next, we divide both sides of the equation by 40.
[tex]\begin{gathered} \frac{40x}{40}=\frac{15}{40} \\ x=\frac{3}{8} \end{gathered}[/tex]The number is 3/8.
The points (-6, -10) and (23, 6) form a line segment.
Write down the midpoint of the line segment.
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A line segment has the endpoints at (-6, -10) and (23, 6) then the midpoints of the line segment will be (17, -2).
What is meant by line segment?An area or portion of a line with two endpoints is called a line segment. A line segment, in contrast to a line, has a known length. A line segment's length can be estimated by utilizing either metric measurements like millimeters or centimeters, or conventional measurements like feet or inches.
A line segment has the endpoints at (-6, -10) and (23, 6).
Mid point of the line segment is given by [tex]$\left(\frac{x_1+x_2}{2}\right),\left(\frac{y_1+y_2}{2}\right)$[/tex]
The midpoints of the line segment will be
= [tex]$\frac{23+-6}{2}[/tex], [tex]$\frac{-10+6}{2}}[/tex]
= 17, -2
Therefore midpoints of the line segment will be (17, -2).
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Looking to receive assistance on the following problem, thank you!
Answers
Given:
[tex]\begin{gathered} v=3i-4j \\ u=-2i-7i \\ w=5j \end{gathered}[/tex]So the value is:
(a)
[tex]\begin{gathered} u=-2i-7j \\ 2u=2(-2i-7j) \\ 2u=-4i-14j \end{gathered}[/tex][tex]\begin{gathered} 2u-v=-4i-14j-(3i-4j) \\ =-4i-14j-3i+4j \\ =-7i-10j \end{gathered}[/tex](b)
[tex]\begin{gathered} w=5j \\ 3w=3\times5j \\ 3w=15j \end{gathered}[/tex][tex]\begin{gathered} u=-2i-7i \\ 4u=4(-2i-7j) \\ 4u=-8i-28j \end{gathered}[/tex][tex]\begin{gathered} 3w+4u=15j+(-8i-28j) \\ =15j-8i-28j \\ =-8i-13j \end{gathered}[/tex](c)
The dot product of v and u.
[tex]\begin{gathered} v=3i-4j \\ u=-2i-7i \end{gathered}[/tex]dot product is:
[tex]\begin{gathered} vu=(3i-4j)\cdot(-2i-7j) \\ =-6(i\cdot i)-21(i\cdot j)+8(j\cdot i)+28(j\cdot j) \end{gathered}[/tex]The doat product (i.i = 1) and ( j.j=1) and ( i.j=0) and ( j.i = 0)
[tex]\begin{gathered} =-6(1)-21(0)+8(0)+28(1) \\ =-6+28 \\ =22 \end{gathered}[/tex]I need help with this problem.
Answers
Using tangent function:
[tex]\begin{gathered} \tan (\theta)=\frac{opposite}{adjacent} \\ \tan (T)=\frac{16}{32}=\frac{1}{2}=0.5 \end{gathered}[/tex]Pls help with my hw pls
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Use the table to find the slope of the line.Round your answer out to two decimal places
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Given:
The points are (8, -3) and (-5, 1).
To find the slope of the line:
The slope formula is,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{1-(-3)}{-5-8} \\ =\frac{1+3}{-13} \\ =-\frac{4}{13} \\ =-0.30769 \\ \approx-0.31 \end{gathered}[/tex]Hence, the slope of the line is -0.31 (rounded to the nearest two decimal places).
I'm trying to simplify negative 5/8 divided by negative 3/4 how do I do that?
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Determine the missing coordinates in the ordered pair (-1,?) so that it will satisfy the given equation
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we have the equation
2x-3y=4
Remember that
if the ordered pair is a solution of the given equation, then the ordered pair must satisfy the given equation
we have the ordered pair (-1,a)
substitute the given coordinates in the equation
2(-1)-3(a)=4
-2-3a=4
solve for a
3a=-2-4
3a=-6
a=-2
therefore
the missing coordinate is -2
Use the graph of the function y= f(x) below to answer the questions
Answers
a)
We need to find the value of f(-3), that means we need to find the value of the y-coordinate when the x-coordinate is -3
As we can see in the graph
f(-3)=-5
Therefore f(-3) is negative
The answer for this part is NO
b)
if f(x)=0, that means that we are looking for the x-intercepts
x=-2
x=1
x=4
The answer is -2,1,4
c)
We need to know for what values of x f(x)<0
In this case in interval notation
[tex]\lbrack-3,2)\cup(1,4)[/tex]I have a practice problem that I need help on.These are included in the problem as well Where did Arjun make errors?Explain his errors and the properties of logarithms that leads to the answer. State the correct answer.
Answers
Arjun applied the wrong laws of logarithms.
The question can be solved as shown below:
[tex]\log _7x+\log _7y+\log _7z[/tex]Step 1: Apply the addition rule of logarithm given as
[tex]\log _am+\log _an=\log _a(m\cdot n)[/tex]Thus, we have:
[tex](\log _7x+\log _7y)+\log _7z=\log _7(x\cdot y)+\log _7z[/tex]Step 2: Apply the subtraction rule of logarithm given as
[tex]\log _am-\log _an=\log _a(\frac{m}{n})[/tex]Thus, we have:
[tex]\log _7(x\cdot y)+\log _7z=\log _7(\frac{x\cdot y}{z})[/tex]Therefore, the correct answer is:
[tex]\log _7x+\log _7y+\log _7z=\log _7(\frac{xy}{z})[/tex]