The figure shows a quarter circle and an equilateral triangle. What is thearea of the shaded part? Give your answer to 3 significant figures. (Take it= 3.14.)7 cm
Answers
Since the triangle is equilateral, all of its interior angles have a measure of 60º.
Substract the area of the triangle from the area of a circular sector with radius 7cm enclosed by an angle of 60º to find the area of the shaded region.
The area of an equilateral triangle with side length L is:
[tex]A=\frac{\sqrt[]{3}}{4}L^2[/tex]The area of a circular sector of radius r enclosed by an angle of θ degrees is:
[tex]A=\frac{\theta}{360}\times\pi r^2[/tex]Replace θ=60 and r=7cm to find the area of the circular sector:
[tex]A_c=\frac{60}{360}\times3.14\times(7\operatorname{cm})^2=25.643\ldots cm^2[/tex]Replace L=7cm to find the area of the triangle:
[tex]A_T=\frac{\sqrt[]{3}}{4}\times(7\operatorname{cm})^2=21.2176\ldots cm^2[/tex]Then, the area of the shaded region is:
[tex]\begin{gathered} A_C-A_T=25.6433\ldots cm^2-21.2176\ldots cm^2 \\ =4.4257\ldots cm^2 \\ \approx4.43\operatorname{cm}^2 \end{gathered}[/tex]Therefore, the area of the shaded region to 3 significant figures, is:
[tex]4.43\operatorname{cm}^2[/tex]Related Questions
Given that f ( x ) = 3 x − 6 f ( x ) = 3 x - 6 and g ( x ) = 2 − x 2 g ( x ) = 2 - x 2 , calculate
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If it is given f(x) = 3x− 6 and g(x) = 2- x² then f(g(x)) = -6x².
To solve this problem we have to know more about mathematical functions.
What is a mathematical function?
A mathematical function is a such type of mathematical device as it establishes a special type of relation which provides an output concerning an input.
Example: f(x) = x²+ 2 where f(x) is a function of x where x is the input. If x = 3 then the output value of f(x) = 3²- 2 = 9-2 = 7.
Here we have to calculate, f(g(x)) where f is a function of g(x) and g(x) is a function of x.
g(x) = 2- x².
f(x) = 3x - 6.
Therefore,
f(g(x)) = 3( 2- x² ) - 6. [where g(x) = 2- x²]
So, f(g(x)) = 3( 2- x² ) - 6 = 6 -6x² -6 = -6x²
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The complete question:
Given that f(x) = 3x − 6 and g(x) = 2 - x² , calculate f(g(x))
Find the solution.7 · x = 8412139177
Answers
We need to find the value for x using the inverse operation:
Then:
[tex]\begin{gathered} 7-x=84 \\ \end{gathered}[/tex]Let us solve for x:
The x is subtracting, so it will add up to the other side:
[tex]7=84+x[/tex]Now, the 84 is positive, so it will be negative on the other side:
[tex]\begin{gathered} 7-84=x \\ x=-77 \end{gathered}[/tex]Hence, the solution for x is -77.
An air traffic controller spots two planes flying at the same altitude. Their flight paths form a right angle at point P. One plane is 150 miles from point P and is moving at 440 miles per hour. The other plane is 200 miles from point P and is moving at 440 miles per hour. Write the distance s between the planes as a function of time t.
Answers
The distance s as a function of time is s = 50√(162t² -126t +25)
Take miles and hours to be the problem's units.
The distance of the first plane from point p is provided by
x = 150 -450t
The distance of the second plane from point p is given by
y = 200 -450t
The Pythagorean theorem can be used to calculate the distance between them because their flight trajectories are at right angles (s).
s² = x² + y²
s² = (150 -450t) (150 -450t)
² + (200 -450t)² = 22500 -135000t +202500t² +40000 -180000t +202500t²
... s² = 40500t² -315000t +62500 = 2500(162t² -126t +25)
... s = 50√(162t² -126t +25)
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If translation T maps point A(-3, 1) onto point A'(5, 5),
which is the translation T?
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Answer: [tex](x,y) \to (x+8, y+4)[/tex]
==================================================
Explanation:
The x coordinate of A and A' are -3 and 5 respectively.
This is an increase of +8 since -3+8 = 5
Therefore, we shift the preimage 8 units to the right to get the image point.
That explains how x turns into x+8.
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The y coordinates of A and A' are 1 and 5 respectively.
This is an increase of +4, so we shift the preimage up 4 units.
This signals that y turns into y+4
--------------
To recap we found that,
x becomes x+8y becomes y+4Therefore we get to the answer [tex](x,y) \to (x+8, y+4)[/tex]
--------------
To check the answer, let's apply this translation to point A(-3,1) and we should get (5,5) as the result.
[tex](\text{x},\text{y})\to(\text{x}+8,\text{y}+4)\\\\(-3,1)\to(-3+8,1+4)\\\\(-3,1)\to(5,5)\\\\[/tex]
This confirms the answer is correct.
What is 3+2? and add 7 then subtract 4
Answers
the answer is 8
add 3+2, that gives u 5, add 7+5 which is 12, do 12-4 its equal to 8
The quadrilateral RSTU is inscribed in the circle shown below. S R U Jake wants to prove the theorem that says that the measure of the quadrilateral's opposite angles add to 180°. He knows that the measure of angle Ris half the measure of are STU and that the measure of angle T is half the measure of arc SRU. Which of the following is an appropriate step to prove that ZR + ZT =180°?
Answers
Arc STU and arc SRU can form the complete circle. Therefore
[tex]Therefore,[tex]\begin{gathered} 2R+2T=360^0 \\ \text{factorize left hand side} \\ 2(R+T)=360^0 \end{gathered}[/tex]Dividing both sides by 2, we have
[tex]Hence, the appropriate steps are: Assume that the measure of arcs STU and SRU add up to 360 degreesAlso, substitute 2 m
pick yes in options 2 and 3
pick no in options 1 and 4
Is -36/6 a integer number
Answers
Answer:
Yes
Step-by-step explanation:
-36/6 = -6
Integers are the whole numbers (0.1.2.3.4.5....) and their opposites ...-4,-3,-2,-1
Here’s the question to solve. Just do the question that has the chart
Answers
Step 1:
Write the equation
[tex]x^4-x^3+3x^2\text{ - 9x }-\text{ 54 = 0}[/tex]Step 2:
Use trial and error to find one the the factor
x - 3 is a factor
Because when you substitute x = 3, the result is zero
Hence, 3 is zero of the polynomial
Step 3
Use the long division
plsssssss i need hdelpppppp plss 20 points on the line
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Answer:d is the correct answer.
Step-by-step explanation:
What is the answer to this question?
Answers
The probability of drawing a blue socks and white socks is 1/12.
Given that, a drawer contains 10 red socks, 6 white socks and 8 blue socks.
What is probability of an event?Probability is a type of ratio where we compare how many times an outcome can occur compared to all possible outcomes.
As we know the probability of an event = Number of favorable outcomes/Total number of outcomes
Total number of outcomes = 10+6+8=24
Probability of getting blue socks = 8/24 = 1/3
Probability of getting white socks = 6/24 =1/4
Now, probability of an event = 1/3 × 1/4 = 1/12
Therefore, the probability of drawing a blue socks and white socks is 1/12.
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I dont know how to solve this , I am not familiar with it and am confused.
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a) We have to calculate the total reimbursement.
We can list the types of lunches and reimbursements for each:
0. Free lunches: the school served 29,000 free lulnches and will receive $2.68 for each one.
,1. Reduced-price lunches: the school served 19,000 reduced-price lunchs and will receiv $2.28 for each one.
,2. Full price lunches: the school seved 51,000 regular-price lunches and will receive $0.25 for each one.
Then, we can calculate the total reimbursement as:
[tex]\begin{gathered} R=29000\cdot2.68+19000\cdot2.28+51000\cdot0.25 \\ R=77720+43320+12750 \\ R=133790 \end{gathered}[/tex]The lunch reimbursement should be $133,790.
b) The milk reimbursement can be estimated as $0.035 per lunch, so it can be calculated as:
[tex]\begin{gathered} M=(29000+19000+51000)\cdot0.035 \\ M=99000\cdot0.035 \\ M=3465 \end{gathered}[/tex]The milk reinbursement is $3,465.
c) We can calculate the total reinbursement as the sum of the lunch reinbursement and the milk reinbursement:
[tex]R+M=133790+3465=137255[/tex]The total reinbursement is $137,255.
d) We can calculate the average reinbursement per lunch dividing the total reinbursement by the number of lunches:
[tex]\frac{T}{L}=\frac{137255}{99000}\approx1.39[/tex]The average reinbursement is $1.39 per lunch.
Model the following problem with a quadratic equation. Then solve.Find the length of a side of a square with an area of 50 ft?.Model the problem with a quadratic equation. Let x be the length of a side of the square.
Answers
The area of a square is equal to the squared of one side.
[tex]A=x^2[/tex]Using the given data, we can have the quadratic equation of
[tex]x^2\text{ -50 = 0}[/tex]We can solve for x in 2 ways
[tex]\begin{gathered} x^2\text{ = 50} \\ x\text{ = }\sqrt[]{50}\text{ = 7.07} \end{gathered}[/tex]Or by using the quadratic formula
[tex]undefined[/tex]Out of 250 tickets in a raffle, one ticket will win a $980 prize, one ticket will win a $680 prize, and one ticket will win a $470 prize. The other tickets will win nothing. If you have a ticket, what is the expected payoff?
Answers
The expected value is given as:
[tex]E(x)=\sum ^{}_{}xP(x)[/tex]then in this case we have:
[tex]\begin{gathered} E(x)=980(\frac{1}{250})+680(\frac{1}{250})+470(\frac{1}{250}) \\ =8.52 \end{gathered}[/tex]therefore the expected payoff is $8.52
PLS HELP!!!!!
TRUE OR FALSE:
A single cube with a side of 1cm has the same surface-to-volume ratio as a structure containing 8 cubes with sides that equal 1cm (remember that surface of a cube with a side A is 6A2cm2 and the volume is A3cm3).
Answers
Answer:
the answer is true
Step-by-step explanation:
What shape is generated when SABC is rotated around the vertical linethrough B and C?4ABA. PrismB. PyramidC. CylinderD. Cone
Answers
A triangle, when rotated about one of its sides will generate a solid in a form of a Cone.
The cone could be a hollow one or a solid-filled one, depending on the properties of the triangle being rotated.
Therefore, the shape generated is a cone.
Answer: D.
Help need please!!!!!!!factorize 36a-12b-60c
Answers
Solution:
Given:
[tex]36a-12b-60c[/tex]The greatest common factor (GCF) is factored out of the expression.
The GCF is 12.
Hence,
[tex]36a-12b-60c=12(3a-b-5c)[/tex]Therefore, the factorization of the given polynomial 36a - 12b - 60c is;
[tex]12(3a-b-5c)[/tex]Victor earns 19% commission as a salesperson. He sold a microscope that cost $368.84. How much commission did Victor earn? Round your answer to the nearest cent: $
Answers
Victor earns 19% commission
He sold a microscope that cost $368.84.
so, the commission = 19% of $368.84 = 0.19 * 368.84 = 70.0796
Rounding to the nearest cent
So,
the commission = $70.08
jermey wants to buy a new computer the sales woman says that he can make a down payment and then pay for the computer in installments here is the formula for this scex=t-yzx= amount down y=money each month z=number of months t= total price rewrite the formula to solve for the total price of the computer
Answers
ANSWER:
[tex]t=x+yz[/tex]STEP-BY-STEP EXPLANATION:
We have the following formula for the statement
[tex]x=t-yz[/tex]They ask us to rewrite this formula solving for the total price of the computer, it would be like this:
[tex]\begin{gathered} t-yz=x \\ t-yz+yz=x+yz \\ t=x+yz \end{gathered}[/tex]Number 6. Find the missing measure and round to nearest 10th
Answers
Note that Cosine law can be used if three sides of the triangle are given in order to get the angles.
For example, in getting the measurement of angle C
[tex]\cos C=\frac{a^2+b^2-c^2}{2ab}[/tex]Then take the arccos to get the angle C.
From the problem, we have :
We need to find the measurement of angle F using the same formula above.
[tex]\begin{gathered} \cos F=\frac{16^2+12^2-18^2}{2(16)(12)} \\ \cos F=\frac{19}{96} \end{gathered}[/tex]Taking the arc cosine :
[tex]\begin{gathered} \angle F=\arccos (\frac{19}{96}) \\ \angle F=78.58 \end{gathered}[/tex]The answer rounded to the nearest 10th is
#3 TV Aspect RatioUsing your knowledge of aspect ratios, find the difference between the actualscreen size or area of an older style TV with an aspect ratio of 4:3 and a newer TVwith an aspect ratio of 16:9. Assume that both TV's are 52 inches in height. Whatis the difference in the areas of the two TV's? (show all work and justify youranswer) (8 points)
Answers
3:4 ratio
height: 52 in
width: height * 4/3 = 52*4/3 = 208/3 in
Area of the TV: height*width = 52*208/3 = 3605 1/3 square inches
9:16 ratio
height: 52 in
width: height * 16/9 = 52*16/9 = 832/9 in
Area of the TV: height*width = 52*832/9 = 4807 1/9 square inches
Then, the difference in the areas is: 4807 1/9 - 3605 1/3 = 1201 7/9 square inches
p and q are both prime numbers. They are each less than 22 Give an example where p + q is odd but not prime. You must only write the two numbers in the answer box. Type here to search O RI e Total ma
Answers
Answer:
See below
Step-by-step explanation:
2 + 7 = 9 2 and 7 are prime the answer is odd but not prime
Describe a series of transformations Matt can perform to device if the two windows are congruent
Answers
Congruent shapes are produced by combining the three different transformations—rotations, reflections, and translations. Actually, by combining one or more of these three transformations, any pair of congruent shapes can be matched to one another.
What are transformations?A point, line, or geometric figure can be transformed in four different ways, each of which alters the shape and/or placement of the object. While Image refers to the position and ultimate shape of the object, Pre-Image refers to the shape of the thing as it was before alteration.
Given Data
We now understand that the size and shape of the figures are preserved during stiff transformations (reflections, translations, and rotations). The pre-image and the actual image concur all the time.
The following Matt's transformational skills:
Reflection
Since the reflection maintains its original shape, The line of reflection remains the same distance away from comparable points from the pre-image to the image.
As a Congruence Transformation, rotations
Rotating a figure causes it to twist. Even though the figure is the same size and shape as before, it appears to have toppled over. A clock is a fantastic example of how the earth actually rotates. Every hour or every day, the clock's connecting arms revolve around their axis. A rotation's degree determines what it is, and common rotations include 90, 180, and 270 degrees. Before going back to its original position, the figure rotates a full 360 degrees. the direction of a rotation, whether it is counterclockwise or clockwise. It is possible to determine the degree, amount, and the revolution's direction.
Transformation based on translational congruence
When an object or shape is transported from one location to another without changing its size, shape, or orientation, the movement is referred to as a translation. During a translation, also known as a slide, every point on an object or shape is moved by the same amount and in the same direction.
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What is the volume, in cubic inches, of a rectangular prism with a height of 19in, a width of 8in, and a length of 17in?
Answers
The volume of a rectangular prism is given by
[tex]V=L\times W\times H[/tex]Where L is the length, W is the width, and H is the height of the rectangular prism.
For the given case, we have
Length = 17 in
Width = 8 in
Height = 19 in
Let us substitute these values into the above formula
[tex]\begin{gathered} V=L\times W\times H \\ V=17\times8\times19 \\ V=2584\: in^3 \end{gathered}[/tex]Therefore, the volume of the given rectangular prism is 2584 cubic inches.
please help me out fr
Answers
Christian, this is the solution to the problem:
p = 2l + 2w
Solving for l, we have:
2l = p - 2w
Dividng by 2 at both sides:
2l/2 = (p - 2w)/2
l = (p - 2w)/2
The correct answer is D.
Write the value of 17 tens in three different ways. Use the largest unit possible.
Answers
Answer:
1 and 7 and 0
Step-by-step explanation:
Pls help I really need this!!!
For what values of x is the function
positive?
y = |x +4|-1
Answers
Answer: x > -3 or x < -5
Step-by-step explanation:
The function is positive when y > 0.
So if we make this function into an inequality, we can solve for the values of x.
0 < |x + 4| -1
1 < | x + 4 |
Absolute values make the answer always positive despite the sign so now we have to solve for x when x + 4 > 1 and when x + 4 > -1.
x = 1 - 4 = -3
x = -1 -4 = -5
So for the function to be positive,
x > -3 or x < -5
Solve the trigonometric equation for all values 0 ≤ x < 2π.tan x - 1 = 0
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Point B is located at (-5, -5) on the coordinate plane. Point B is reflected over thex-axis to create point B'. What ordered pair describes the location of B'?
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SOLUTION
If a coordinate is refleted over the x-axis, the formula to apply is
[tex](x,y)\rightarrow(x,-y)[/tex]So for B(-5, -5), this becomes
[tex]\begin{gathered} B\mleft(-5,-5\mright)\rightarrow(-5,-(-5) \\ \\ the\text{ answer becomes } \\ \\ B(-5,-5)\rightarrow B^{\prime}(-5,5) \end{gathered}[/tex]111 pointFind cot(1.570/7.3). Round to 3 decimal places.Type your answer...
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how do I put 5/7-i in standard form?
Answers
To put
[tex]\frac{5}{7-i}[/tex]In the standard form, we must multiply the numerator and denominator by the complex conjugate of (7-i), it means
[tex]\frac{5}{7-i}\cdot\frac{7+i}{7+i}[/tex]And now we solve it, therefore
[tex]\frac{5}{7-i}\cdot\frac{7+i}{7+i}=\frac{5(7+i)}{7^2-i^2}[/tex]Remember that
[tex]i^2=-1[/tex]Then
[tex]\begin{gathered} \frac{5(7+i)}{7^2-i^2}=\frac{5(7+i)}{49+1} \\ \\ \frac{5(7+i)}{49+1}=\frac{5(7+i)}{50} \end{gathered}[/tex]Now we can simplify it
[tex]\frac{5(7+i)}{50}=\frac{7+i}{10}[/tex]And we have it in the standard form
[tex]\frac{7}{10}+\frac{1}{10}i[/tex]