Answers
Answer:
The value of a is 14 unit and the value of b is [tex]6\sqrt{2}[/tex] unit
EXPLANATION:
Draw a perpendicular line from vertex B to DC at E.
Labeling the diagram as shown in the attachment:
Now, as you can see from the Figure as shown in the attachment that [tex]ABDE[/tex] represents the rectangle because a rectangle is a quadrilateral with four right angles and their opposite sides would be parallel.
Therefore, we have the sides [tex]AB=DE=8[/tex] unit , and [tex]AD=BE=6[/tex] unit.
Consider the right triangle BEC
BY 45 45 90 triangle is a special type of isosceles right triangle where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.
therefore, the length of side, [tex]BE=EC=6[/tex] unit
Using trigonometric ratio; to find the value of b:
[tex]\sin \theta =\frac{perpendicular}{Hypotenuse}[/tex]
∴ using trigonometric sine ratio in triangle BEC, we have
[tex]\sin 45^{\circ} =\frac{6}{b}[/tex] or
[tex]\frac{1}{\sqrt{2} }= \frac{6}{b}[/tex]
On Simplify:
[tex]b=6\sqrt{2}[/tex] unit
and the value of a = DC = DE+EC=8+6=14 unit
Therefore, the value of a is 14 unit and b is [tex]6\sqrt{2}[/tex] unit
Related Questions
What is the least common Multiple of 9 and 10? Use prime factorization to solve.
Answers
......................
The area of a rectangle is 54 m^2 , and the length of the rectangle is 3m more than twice the width. find the dimensions of the rectangle.
Answers
Calculate the altitude of a triangle corresponding to its shortest side of it's area is 720cm², perimeter is 180cm and two of its sides are 80cm and 18cm.
Answers
altitude = 80 cm
Explanation:
1- getting the third side:
We are given that:
perimeter of the triangle is 180 cm
Two of its sides are 80 cm and 18 cm
This means that:
180 = 80 + 18 + third side
third side = 180 - (80+18)
third side = 82 cm
2- deducing the shortest side that we will use to get the altitude:
We have the three sides of the triangle 80 cm, 18 cm and 82 cm
It is obvious that the shortest side is 18 cm
We will use this side to calculate the altitude since we are given that the altitude corresponds to the shortest side.
3- getting the altitude:
area of triangle = 0.5 * base * altitude
We have:
area of triangle = 720 cm²
base = 18 cm
Substitute to get the altitude as follows:
720 = 0.5 * 18 * altitude
720 = 9*altitude
altitude = 80 cm
Hope this helps :)
In Mr. Sheldon’s physical education class, each student plays at most 1 sport.
A total of 20 students play soccer or basketball.
Given that 1/3 of the students play soccer, and 8 play basketball, how many students in Mr. Sheldon’s class play neither soccer nor basketball?
I have no idea how to calculate. I will reward the right answer along with explanation of how it was figured. (I attached a pic of the multiple choices) Thanks!
Answers
Given that 1/3 of the students play soccer you can conclude that 1\3 is equal 12 student, then in class totally are 12*3=36 students.
36-20=16 students play neither soccer nor basketball
Answer: Correct choice is B.
Pls help.
Solve (6x^3-1x^2+1)/(2 x+1)
a. -3x^2+2x-1
b. 3x^2-2x+1
c. -3x^2+2x-1
d. 3x^2+2x-1,
Answers
Read the word problem. Hershel buys 5 bags of cookies, 3 bags of granola, and several bags of fruit snacks from a bake sale. In total, he buys 10 bags from the bake sale. How many bags of fruit snacks did Hershel buy? Which type of word problem is shown? part-whole comparison multiplication division
Answers
Final answer:
Hershel bought 2 bags of fruit snacks in a part-whole comparison word problem, where the total (10 bags) minus the sum of known parts (5 bags of cookies and 3 bags of granola) equals the unknown part.
Explanation:
The word problem presented asks how many bags of fruit snacks Hershel bought if he bought a total of 10 bags, including 5 bags of cookies and 3 bags of granola. To solve this, we subtract the known quantities from the total: 10 total bags - 5 bags of cookies - 3 bags of granola = 2 bags of fruit snacks.
The type of word problem shown is a part-whole comparison because it involves figuring out a missing part of a whole based on the other known parts.
which value is a solution of the equation 2-8x=-6 ? ( 1point )
A. 1
B. 1/2
c. -1
d. 8,
Answers
whats the answer to 8n−15=41
Answers
8*7=56
56-15=41
Hope this helped☺☺
+15 +15
8n=56 DIVIDE BY 8
/8 /8
n=7 FINAL ANSWER
In a 30-60-90 triangle, what is the length of the hypotenuse when the shorter leg is 5 cm?
Enter your answer in the box.
Answers
10cm
Because (The 30-60-90 Triangle Theorem)
In a 30-60-90 triangle, the length of the hypotenuse is TWICE the length of the shorter leg.
Thanks Shellbag101
The length of the hypotenuse is 10cm
SOH CAH TOA identityGiven a 30-60-90 triangle where:
Length of the shorter leg = 5cm (adjacent)
The hypotenuse is what we need.
[tex]cos \theta = \frac{adj}{hyp} \\ [/tex]
Substitute the given parameters
[tex]cos 60 = \frac{5}{h}\\ h =\frac{5}{cos 60}\\ h = \frac{5}{0.5}\\ h = 10cm[/tex]
Hence the length of the hypotenuse is 10cm
Learn more on SOH CAH TOA here: https://brainly.com/question/20734777
please help me on this question
and explain.
Answers
So 3/2 is equivalent to 1.5. A negative times a positive is a negative. -8 * 1.5 is -12. -12 + 4 is -8. That makes the ordered pair (-8, -8). To -4, -4 * 1.5 is -6. -6 + 4 is -2. That makes the ordered pair (-4, -2). Now to -2, -2 * 1.5 is -3. -3 + 4 is 1. That makes (-2, 1). If you solve for the other 3 values correctly, you other ordered pairs are (0, 4), (2, 7), and (4, 10). When graphed, the points should be plotted as shown in the attatchment.
prove this trigonometric equation;
- tan^2x + sec^2x = 1,
Answers
- tan²x + sec²x = 1 or 1 + tan²x = sec²x
sin²x + cos²x = 1
Divide the whole by cos²x
[tex] \frac{sin^2x}{cos^2x} + \frac{cos^2x}{cos^2x} = \frac{1}{cos^2x} [/tex]
[tex] \frac{sinx}{cosx} = tanx[/tex] so [tex] \frac{sin^2x}{cos^2x} = tan^2x[/tex]
and
[tex] \frac{1}{cosx} = secx [/tex] so [tex] \frac{1}{cos^2x} = sec^2x[/tex]
Therefore,
tan²x + 1 = sec²x
Take tan²x to the other side {You will have the same answer}
1 = - tan²x = sec²x or sec²x - tanx = 1
At Devon's new job he spent $12.99, $10.50, $9.89, $6.90, and $7.58 on lunch the first week.
In the second week, he spent $2 more in total for the 5 lunches than the first week.
What is the increase in the mean for the second week compared to the first?
Round the answer to the nearest penny.
Enter your answer in the box.
$
Answers
$0.40.
Explanation:
To find the mean of the lunch costs for the first week, we first add together all of the amounts he spent on lunch that week:
$12.99+$10.50+$9.89+$6.90+$7.58 = $47.86.
Now we divide this by the number of lunches, 5:
47.86/5 = $9.572 ≈ $9.57.
The second week he spends a total of $2 more on lunch. Adding this to the first week's total, we have:
47.86+2 = $49.86.
To find the mean, we divide this by the number of lunches in the second week, 5:
49.86/5 = $9.972 ≈ $9.97.
The mean increased from the first week to the second week by 9.97-9.57 = $0.40.
The increase in the mean for the second week compared to the first with the given parameters is; $0.40
Let us first find the mean of the lunch costs for the first week;
Mean for first week = ($12.99 + $10.50 + $9.89 + $6.90 + $7.58)/5 = $9.572
We are told that he spends a total of $2 more on lunch in the second week.
Second week total = $12.99 + $10.50 + $9.89 + $6.90 + $7.58 + $2 = $49.86.
Mean of second week = 49.86/5 = $9.972
The increase in the mean for the second week compared to the first is;
9.972 - 9.572 = $0.40
Read more about average increase at; https://brainly.com/question/11360390
40 POINTS! + BRAINLIEST
What is the measure in radians for the central angle of a circle whose radius is 6 cm and intercept arc length is 5.4 cm?
Make sure to show all calculations.
Answers
Answer:
6.5
Step-by-step explanation:
1. calculate using the equation
Dyann takes a bus to work every day. On Monday the trip took 34 minutes. On Tuesday the trip took 36 minutes. On Wednesday the trip took 35 minutes. On Thursday the trip took 34 minutes. Dyann determines that the trip to work on Friday will take about 35 minutes.
Does her conclusion use inductive, or deductive reasoning?
Answers
Answer:
inductive reasoning
In this question, the conclusion is that the trip to work on Friday will take about 3535 minutes. This conclusion is based on observation of specific examples instead of scientific research.
Therefore, the type of reasoning used is inductive reasoning.
Personal Finance is a dead group.
How does the availability of credit in a community affect the housing market there?
The availability of credit has no affect on the housing market.
The less credit available, the higher the cost of housing.
The availability of credit determines whether or not people put their homes up for sale.
The more credit available, the higher the cost of housing.,
Answers
If (3x + 17) is equivalent to (4x - 8) what is x
Answers
3x + 17 = 4x - 8
3x (-4x) + 17 (-17) = 4x (-4x) - 8 (-17)
-x = -8 - 17
-x = -25
-x(/-1) = -25(/-1)
x = 25
25 is your answer
hope this helps
Solve for x under the assumption that x > 0. Enter your answer in interval notation using grouping symbols.
x−24/x<10,
Answers
The solution for the set would be: x is (0,12).
What is the solution?
To arrive at the solution, we would first move the constant term to the right side as follows;
x - 24/x < 10
x < 10 + 24/x
We then multiply both sides by x to eliminate the fraction:
x² < 10x + 24
Collect all terms to one side;
x² - 10x - 24 < 0
Factorize
(x - 12)(x + 2) < 0
So, x - 12 is positive when x > 12 and negative when x < 12.
x + 2 is positive for all values of x > 0.
This circle graph shows the results of a survey that asked people to identify their favorite type of music.
What percent of people chose rock or country as their favorite type of music?
9%
35%
45%
55%
A circle graph with 5 sections. The first section is labeled Rock 27 percent. The second section is labeled Hip Hop 28 percent. The third section is labeled Jazz 19 percent. The fourth section is labeled Country 18 percent. The fifth section is labeled Other 14 percent.
Answers
Country or rock would be found by adding the two percentages:
18+27 = 45.
(Side note: the percentages on this circle graph add up to 106%....)
Answer: C) 45
Hope Thsi Helps ^_^
Explain why increasing the sample size tends to result in a smaller sampling error when a sample mean is used to estimate a population mean.
A. The above statement is incorrect, the sample size has no effect on the sampling error.
B. The larger the sample size, the more closely the possible values of \bar{x} cluster around the mean of \bar{x}
C. If the sample size is larger, the possible values of \bar{x} are farther from the mean of \bar{x},
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Sampling error is inversely proportional to the sample size which means if the sample size increases the sampling error decreases. Then option B is correct.
What is sampling error?The amount of inaccuracy in the estimating value appears due to the smaller sample size.
The sample size tends to result in a smaller sampling error when a sample mean is used to estimate a population mean.
We know that the formula of the sampling error
[tex]\rm Sampling \ error = z \times \dfrac{\sigma}{\sqrt{n}}[/tex]
Sampling error is inversely proportional to the sample size which means if the sample size increases the sampling error decreases.
More about the sampling error link is given below.
https://brainly.com/question/15375591
Which ordered pairs are solutions to the inequality 2x+3y≥−1?
Answers
Final answer:
To find the ordered pairs that are solutions to the inequality 2x+3y≥−1, we can solve the inequality and substitute different x-values to find corresponding y-values.
Explanation:
To find the ordered pairs that are solutions to the inequality 2x+3y≥−1, we can use a graph or a table of values.
Let's solve the inequality for y:
2x + 3y ≥ -1
3y ≥ -1 - 2x
3y ≥ -2x - 1
y ≥ (-2/3)x - 1/3
Now we can choose some x-values and substitute them into the inequality to find corresponding y-values:
Let's choose x = 0:
y ≥ (-2/3)(0) - 1/3
y ≥ 0 - 1/3
y ≥ -1/3
So one ordered pair that is a solution is (0, -1/3).
Let's choose x = 3:
y ≥ (-2/3)(3) - 1/3
y ≥ -2 - 1/3
y ≥ -7/3
So another ordered pair that is a solution is (3, -7/3).
Could I get the answer, all work and explanation for this problem?
Answers
[tex] = \sqrt{25 \times 2 \times y^2 \times y \times x^{14} \times x} [/tex]
[tex] = 5|x^7y|\sqrt{2xy} [/tex]
ANSWER NOW PLEASE! EXTRA POINTS!
1) Martha is covering this trapezoid-shaped board with fabric. How many square feet of fabric does Martha need?
2) A garden in the shape of a regular hexagon has sides that are each 5 meters long. If the height of each of the congruent triangles within the hexagon is about 4.33 meters,what is the area of the garden?
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2. About 64.95meters or technically 64.95191
hope this helps!! :)
A simple question I can't answer thnks yall
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so the answer would be A
PLEASE HELP ASAP! BRAINLIEST TO BEST/RIGHT ANSWER
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my sister needs help on this?can anyone give an explanation and answer/show work? you'll be brainliest if you do! thank you so much for taking the time :) v
Felicity recorded the number of laps she swam each month for 7 months.Her data is shown.
112,134,150,98,120,68,116
Which is the mean absolute deviation to the nearest whole number of Felicity's lap data?
A.16
B.18
C.20
D.36
Answers
Answer C
to calculate mean absolute deviation, we need to use the formula = (∑|x-mean|)/n
where x is each term given in data set
n is number of terms = 7
mean = sum of terms / n = (112+134+150+98+120+68+116)/7 = 114
now find (∑|x-mean|) = 138
MAD = (∑|x-mean|) / n = 138 /7 = 19.714 = 20
Domain -1,4,5,3,-5 Range n,w,y,n,w is this a function
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If you apply the vertical line test, none of the xs have 2 ys. It does not matter if 2 xs have the same y value.
0.135 written as a fraction is _____.
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hope it helps
The decimal 0.135 can be written as 27/200 in fractions.
What is a Fraction?A fraction is a number that can be expressed as p/q, where q is not equal to zero.
It is defined as part of the whole.
0.135 is a decimal and to convert into a fraction it has to be written as
=135/1000
On simplifying the fraction
=27/200
Therefore, the decimal 0.135 can be written as 27/200 in fractions.
To know more about Fraction
https://brainly.com/question/10354322
#SPJ2
The areas of two similar octagons are 112 in.² and 63 in.². What is the ratio (larger to smaller) of their perimeters?
16/3
4/9
16/9
4/3,
Answers
For the area:
A1 = (k ^ 2) * A2
For the perimeter
P1 = k * P2
Note: The factor k is the same in both cases
Where,
k = growth factor (k> 1) or reduction (k <1)
Substituting values we have:
12 = (k ^ 2) * 63
Let's clear k:
k = root (112/63)
k = 4/3
Answer:
The ratio (larger to smaller) of their perimeters is:
k = 4/3
k = growth factor (k> 1) or reduction (k <1)
Area1= (k ^ 2) * Area2Perimeter1 = k * Perimeter2
Substitute: 12 = (k ^ 2) * 63 k = sqaure root (112/63) k = 4/3
part one: How do you solve a system of equations approximately using graphs and tables?
part 2: A lake has a native population of 1,000 frogs. The native frog population increases at a rate of 200 frogs per year. A new species of 10 frogs migrates to the lake. This new species’ population increases at a rate of 50% per year. When will the two populations equal each other? Select to reveal each frog population’s growth model.
the rest: A system of equations can be created with the two functions to determine when the populations will have the same population output value, y.
y = 200x + 1,000
y = 10(1.5x)
To determine when the populations will be equal, set the equations equal to each other, and solve for x.
200x + 1,000 = 10(1.5x)
This equation is a little more challenging to solve by algebraic methods. In this lesson, you will solve systems of equations like the one above approximately by effectively using technology and tables.
Answers
The answer is posted as an attached image. We see that after about 14.75 years, the invading species will surpass the indigenous population.
If it needs to be solved mathematically and accurately, the math is a little more advanced, using the bisection method, or Newton's method.
However, we can also do that by trial and error, starting from 14.75. It is easier than you might think.
Post if you would like to have more information on one or the other methods.
Note: the scale of y has been shrunk by 1000, so each unit on the y-axis represents 1000 frogs.
How many triangles exist with the given angle measures? 32°, 51°, 97°
Answers
We need to check if these angles satisfy that condition:
32°+51°+97°=180°
They do satisfy. Now we check if any angle has value that is not possible.
32° and 51° angles are OK.
97° angle is also OK. It is obtuse angle.
For each angle measures exactly one triangle exists. In this example we have an obtuse-angle triangle.
The correct answer is 1.
To determine if a set of three angles can form a triangle, we need to check if the sum of the three angles is equal to 180°. If the sum is 180°, then the angles can form a triangle; otherwise, they cannot form a triangle.
Given angles: 32°, 51°, 97°
we can represent the calculation as follows:
[tex]\text{Sum of the given angles} &= 32^\circ + 51^\circ + 97^\circ&= 180^\circ[/tex]
Since the sum of the three given angles is equal to 180°, these angles can form a triangle.
To determine the number of triangles that exist with these angle measures, we need to consider the permutations of the angles. Since the order of the angles does not matter in a triangle, we have:
[tex]\text{Number of triangles} = \frac{3!}{3} = 1[/tex]
Therefore, there exists only one triangle with the given angle measures of 32°, 51°, and 97°.