Answers
Solution:
We are given an irregular pentagon. To calculate the area, we will have to break the pentagon into component shapes
We can break the pentagon into a trapezium and a triangle
The dimensions of the trapezium are :
1st base = 3 units
2nd base = 4 units
Height = 3 units
\(\begin{gathered} Area\text{ of the trapezium = }\frac{1}{2}(a+b)h \\ =\frac{1}{2}(3+4)(3) \\ =10.5\text{ square unit} \end{gathered}\)The dimensions of the triangle are:
Base= 4 units
Height=2 units
\(\begin{gathered} Area\text{ of the triangle = }\frac{1}{2}\text{ x base x height} \\ =\frac{1}{2}\text{ x 4 x 2} \\ =4\text{ square units} \end{gathered}\)Area of the polygon = area of trapezium + area of triangle
= 10.5 square unit + 4 square unit = 14.5 square unit
The answer is 14.5 square units
Related Questions
∫0πsinmπxsinnπxdx={0,,m=nm=n ∫−ππsinnxsinnxdx={0,m=n
Answers
The required integral is:\(∫0πsinmπxsinnπxdx={0,,m=nm=n∫−ππsinnxsinnxdx={0,m=n\)
Given the integral:
∫0πsinmπxsinnπxdx={0,,m=nm=n
∫−ππsinnxsinnxdx={0,m=n
We need to prove the integral equal to zero for all m and n.
For m ≠ n:
∫0πsinmπxsinnπxdx
Now use trigonometric identity:
sinA sinB = (1/2)[cos(A-B)-cos(A+B)]
Substituting A= mπx and B = nπx, we have:
∫0πsin(mπx)sin(nπx)dx= (1/2)
∫0πcos[(m-n)πx]dx= 0
because cos[(m-n)πx] is an odd function and the limits of integration are symmetric about the origin.
For m = n: ∫-ππsinn2x dx
Here, we use the identity:
cos2x= 2cos^2 x -1
⇒cos^2 x= (1/2)(1+cos2x)
Substituting this value in the integral, we get:
∫-ππ(1/2)(1-cos2x)n dx= (1/2)
∫-ππ(1-cos2x)n dx
Expanding the binomial:
∫-ππ1 - ncos2x + ... dx= π- n
∫-ππcos2x dx= π
if n is odd, and 0 if n is even.
Hence, the required integral is:∫0πsinmπxsinnπxdx={0,,m=nm=n∫−ππsinnxsinnxdx={0,m=n.
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find the missing side of the right angle round to the nearest tenth if necessary triangle is 6 meters by 12m
Answers
To get x, we will use the Pythagoras theorem
With the hypotenuse equal to 12m
\(\begin{gathered} x^2=12^2-6^2 \\ x^2\text{ = 144 - 36} \\ x^2\text{ = 108} \end{gathered}\)\(\begin{gathered} x\text{ = }\sqrt[]{108\text{ }}=\text{ 10.39} \\ \text{ x = 10. 4m (to the nearest tenth)} \end{gathered}\)
At noon, Trevor and Kim start running from the same point. Trevor runs east at a speed of 8 km/h and Kim runs west at a speed of 6 km/h. At what time will they be 21 km apart?
Answers
Trevor and Kim will be situated 21 kilometers apart from each other at 1:30 PM. They will be separated by a distance of 21 km when the clock strikes 1:30 in the afternoon.
To determine at what time Trevor and Kim will be 21 km apart, we can set up a distance-time equation based on their relative speeds and distances.
Let's assume that t represents the time elapsed in hours since noon. At time t, Trevor would have traveled a distance of 8t km, while Kim would have traveled a distance of 6t km in the opposite direction.
Since they are running in opposite directions, the total distance between them is the sum of the distances they have traveled:
Total distance = 8t + 6t
We want to find the time when this total distance equals 21 km:
8t + 6t = 21
Combining like terms, we have:
14t = 21
To solve for t, we divide both sides of the equation by 14:
t = 21 / 14
Simplifying, we find:
t = 3 / 2
So, they will be 21 km apart after 3/2 hours, which is equivalent to 1 hour and 30 minutes.
Therefore, Trevor and Kim will be 21 km apart at 1:30 PM.
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Which statement about the reflection below is true? On a coordinate plane, Triangle A B C is reflected across a line to form triangle A prime B prime C prime. A red dotted line goes from point C prime to C and crosses the line of reflection at point P.
Answers
To understand the concept of reflection, it is important to know that it is a transformation in which a shape is flipped over a line called the line of reflection.
In this case, Triangle A B C is reflected across a line to form triangle A prime B prime C prime. The line of reflection is not given in the question, but we know that it is a straight line that passes through point P and is perpendicular to the red dotted line that connects points C prime and C. The fact that the red dotted line crosses the line of reflection at point P tells us that point P is the midpoint of the segment that connects point C and its reflection, C prime. This is because the line of reflection is the perpendicular bisector of this segment.
Moreover, we can also conclude that points A and A prime, as well as B and B prime, are equidistant from the line of reflection. This is because the reflection preserves the distance between any point and the line of reflection. Finally, we can answer the original question, which asks us to determine which statement about the reflection is true. Based on the information given, we can conclude that the statement "The red dotted line goes from point C prime to C and crosses the line of reflection at point P" is true.
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The ratio of yellow marbles to purple marbles was 13 to 4. If there were 102 marbles in the bag, how many were yellow marbles?
Answers
The number of yellow marbles based on the given ratio will be 78.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Suppose, the number of yellow marbles is Y while purple marbles are P.
As per the given,
The ratio Y/P = 13/4
Total Y + P = 102
(13/4)P + P = 102
13P + 4P = 408
17P = 408
P = 24
And, Y = 102 - 24 = 78
Hence "The number of yellow marbles based on the given ratio will be 78".
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At 106°F, a certain insect chirps at a rate of 67 times per minute, and at 108°F, they chirp 83 times per minute. Write an equation in slope-intercept form that represents the situation.
Answers
Answer:
\(y=8x-781\)
Here, \(x\) represents temperature and \(y\) denotes rate of chirping per minute.
Step-by-step explanation:
Let \(x\) represents temperature and \(y\) denotes rate of chirping per minute.
At \(106\)°F, a certain insect chirps at a rate of \(67\) times per minute.
Take \((x_1,y_1)=(106,67)\)
At \(108\)°F, they chirp \(83\) times per minute.
Take \((x_2,y_2)=(108,83)\)
Slope intercept form:
\(y-y_1=(\frac{y_2-y_1}{x_2-x_1})(x-x_1)\)
\(y-67=(\frac{83-67}{108-106})(x-106)\\\\y-67=(\frac{83-67}{108-106})(x-106)\\\\y-67=(\frac{16}{2})(x-106)\\\\y-67=8(x-106)\\y-67=8x-848\\y=8x+67-848\\y=8x-781\)
The two lines graphed below are not parallel. How many solutions are there to
the system of equations?
A. Zero
B. Infinitely many
C. Two
D. One
O
Answers
Answer:
D. One.
Step-by-step explanation:
Agatha drives 73 1/2 miles through two towns in 2 1/3 hours. What is her average speed in miles per hour?
Answers
Answer:
31 1/2
Step-by-step explanation:
average speed = distance/time
average speed = (73 1/2 miles)/(2 1/3 hours)
= (147/2 miles)/(7/3 hours)
= 147/2 * 3/7 miles/hour
= 441/14 miles/hour
= 31 1/2 miles/hour
math question help me
Answers
Answer:
i give you my best wishes
Step-by-step explanation:
-a-b³+ab if a=-3 and b=2
Answers
Answer:
-11
Step-by-step explanation:
Lets rewrite the equation with the values
-(-3) - 2³ + ab
3 - 8 + (-3*2)
-5 + -6 = -11
-11
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
-11
Step-by-step explanation:
Simply plug in a=-3 and b=2 into the equation provided. Remember the signs (+/-) and be careful with your calculations.
-(-3) - (2)^3 + (-3)(2) = -11
15 < -5x
Help I need it for khan academny
Answers
\(\huge \boxed{\sf x < -3} \\\\\\ \displaystyle \sf 15 < -5x \\\\ Divide\ each\ side\ by\ -5\ and\ switch\ the\ symbol. \\\\ \frac{15}{-5} > \frac{-5x}{-5} \\\\-3 > x\)
Answer this question and show me how to check it
Answers
In order to rewrite these values in the standard form, let's calculate the product with the power of 10 from each number.
For the length, we have:
\(\begin{gathered} 8\cdot10^4 \\ =8\cdot10000 \\ =80000\text{ meters} \end{gathered}\)For the thickness, we have:
\(\begin{gathered} 5\cdot10^{-6} \\ =5\cdot0.000001 \\ =0.000005\text{ meters} \end{gathered}\)What is the forecast for May using a five-month moving average?(Round answer to the nearest whole number.) Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47
A. 43 B. 47 C. 52 D. 38 E. 39
Answers
The forecast for May using a five-month moving average is 39 (Option E).
Moving average is used for smoothing out time series data to find any trends or cycles within the data. A five-month moving average is the average of the past five months. To calculate the moving average, add up the sales for the previous five months and divide it by five.
According to the question, the sales for the previous five months are: Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47
We have to add the sales of these five months, which gives:
27 + 40 + 42 + 41 + 47 = 197
To find the moving average for May, we divide this sum by 5:
197 / 5 = 39.4
Since we have to round the answer to the nearest whole number, we round 39.4 to 39, which is option E.
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Solve for x. 7x=28 4x=48
Answers
Answer: x=4
x=12
Step-by-step explanation:
7x=28
divide 7 on both sides
28/7=4
x=4
4x=48
divide 4 on both sides
48/4=12
x=12
x=4 for the first one because you have to separate the 7 from x so to do that you would have to divide 7 from both sides to get x by itself. Same for the second one, x would = 12 because when you divide 4 from 48 in order to get x by itself.
find the mean of the data set 2,5,5,6,8,9,13,14,15,18
Answers
Answer:
106142400
Step-by-step explanation:
2*5*5*6*8*9*13*14*15*18=1061424000
1061424000/10=106142400
Find 3.5⋅(−1.2). Write your answer as a decimal.
Answers
Answer: 3.5⋅(−1.2)=4.2
Does this table represent a function ? Why or why not
Answers
Me ayudan explicándome esto o igual nose algunas respuestas
Answers
Answer:
Step-by-step explanation:Subscribe to my channel thatgirl.christinak for a giveaway
Find a positive coterminal angle less than 360°.
With the given angle -450
Answers
======================================================
Explanation:
The angle -450 is not between 0 and 360. Add on 360 so that we do one full revolution to get -450+360 = -90.
The angle -90 isn't between 0 and 360 either. We repeat the last step by adding on 360 to get -90+360 = 270.
The result 270 is between 0 and 360, so we stop here.
The angle -450 and 270 both point in the same direction. Both point directly south. This is why they are considered coterminal angles.
As an estimation we are told 5 miles is 8 km.
Convert 92 km to miles.
Answers
Answer:
105 miles
Step-by-step explanation:
Change 20 5/9 to an
improper fraction.
Answers
Answer:
185/9
Step-by-step explanation:
20 5/9
Multiply 20 by the 9 (the denominator), and you''ll get 180.
Add the 5 (the numerator) to 180, and you'll get 185.
Then, place 185 over the denominator which is 9 and you get 185/9!
Answer:
\(\frac{185}{9}\)
Step-by-step explanation:
This is the answer because:
1) The formula of changing mixed fractions to improper fractions is denominator times the whole number plus the numerator
2) Denominator = 9
Whole number = 20
Numerator = 5
9 x 20 + 5 = 185
Therefore, the answer is \(\frac{185}{9}\)
Hope this helps!
Find the area of the triangle.
12 ft 13 ft
The area of the triangle is
ft2.
Answers
Answer:
156 ft
Step-by-step explanation:
area formula is:
length x width
(A= l*w)
12 x 13 = 156
Bailey can read an average of 16 pages during a 30 minute reading period at school. At this rate, approximately how many hours will it take her to read a 336-page book? *
10.5
With a proportion, please
Answers
Answer:
10.5 hours for 336 pages
Step-by-step explanation:
16 pgs : 30 mins
336 pgs: __ hours
16+16=32 pages: 30+30=1 hour
for every 1 hour, Bailey reads 32 pages.
Simplify the exponential expression.
Answers
The simplification form of the provided expression is g . 6² . p⁴ option (B) g . 6² . p⁴ is correct.
What is an integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
It is given that:
The expression:
\(= \rm \dfrac{(g^3)(6^3)(p^7)}{(6)(g^2)(p^2)(p)}\)
After using the properties of integer exponent:
\(\rm =\dfrac{g^3\cdot \:6^2p^7}{g^2p^2p}\)
\(\rm =\dfrac{g\cdot \:6^2p^5}{p}\)
= g . 6² . p⁴
Thus, the simplification form of the provided expression is g . 6² . p⁴ option (B) g . 6² . p⁴ is correct.
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Nate buys 2,560 shares of an income stock from a moving company. The company pays a dividend of $0.99 per share. If the moving company pays Nate the dividends quarterly, how much money does he receive each quarter?
Answers
Answer:
102.4 im pretty sure this is it forgive me if its wrong
Step-by-step explanation:
What is the length of ST?
Answers
The length of ST using the theorem of intersecting chords is 13 units
How to calculate the length of ST?From the question, we have the following parameters that can be used in our computation:
The cicles
Using the theorem of intersecting chords, we have
(x - 4) * 8 = 4 * 10
Divide both sides by 8
So, we have
x - 4 = 5
Add 4 to both sides
x = 9
Recall that
ST = 8 + x - 4
So, we have
ST = 8 + 9 - 4
Evaluate the like terms
ST = 13
Hence, the length of ST is 13 units
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Solve each system by graphing. y=6x+3 and y=x−2
Answers
Answer:
y=6x+3
slope 6
y-intercept 0,-3
x y
0 -3
1 3
y=x−2
slope 1
y-intercept -2
x y
0 -2
1 -1
Step-by-step explanation:
solve and show your complete solution.
-thank you
Answers
Answer:
4x
Step-by-step explanation:
Given
\(\frac{\frac{2x^3}{3y} }{\frac{x^2}{6y} }\)
= \(\frac{2x^3}{3y}\) ÷ \(\frac{x^2}{6y}\)
Leave the first fraction, change division to multiplication, turn the second fraction upside down, that is
\(\frac{2x^3}{3y}\) × \(\frac{6y}{x^2}\)
Cancel 3y and 6y by 3y and 2x³ and x² by x²
= \(\frac{2x}{1}\) × \(\frac{2}{1}\)
= 2x × 2
= 4x
Algebra 1 Q. Checkpoint: Function concepts HWA The organizers of the Clark County Fair keep track of daily revenue from ticket sales. The function f(x) gives the revenue from ticket sales on day x of the fair. The revenue is measured thousands of dollars. What does f(4) > f(1) tell you? The revenue from ticket sales on day 4 was greater than $1,000. The fair had greater revenue from ticket sales on day 4 than on day 1. On day 1, the revenue from ticket sales was less than $4,000. $4,000 in ticket revenue is greater than $1,000 in ticket revenue. Submit.
Answers
1000*1.40=482892 algebra 6x+73=8228
Answer:
The fair had greater revenue from ticket sales on day 4 than on day 1.
Step-by-step explanation:
5r-8=9r-12 answer this plsss
Answers
Answer:
R=1
Step-by-step explanation:
5
−
8
+
8
=
9
−
1
2
+
8
ask you teacher how to solve linear equation he or she could help with that