Answers
Answer: The required values are
u = 140, v = 28, w = 40, x = 40 and y = 20.
Step-by-step explanation: We are given to find the values of u, v, w, x and y from the figure shown.
We see that
the lines AB and CD are parallel to each other and PS is a transversal.
So, we must have
[tex]u^\circ=140^\circ~~~~\textup{[alternate interior angles]}\\\\\Rightarrow u=140.[/tex]
Now, we also have
[tex]u^\circ=5v^\circ~~~~~\textup{[vertically opposite angles]}\\\\\Rightarrow u=5v\\\\\Rightarrow 140=5v\\\\\Rightarrow v=\dfrac{140}{5}\\\\\Rightarrow v=28.[/tex]
Now, from the property of linear pair, we get
[tex]u^\circ+x^\circ=180^\circ\\\\\Rightarrow u+x=180\\\\\rightarrow 140+x=180\\\\\Rightarrow x=180-140\\\\\Rightarrow x=40.[/tex]
Since angles of measure w° and x° are alternate interior angles, so
[tex]w^\circ=x^\circ=40^\circ\\\\\Rightarrow w=40.[/tex]
Again, by using the property of linear pair, we get
[tex]2y^\circ+140^\circ=180^\circ\\\\\Rightarrow 2y+140=180\\\\\Rightarrow 2y=40\\\\\Rightarrow y=\dfrac{40}{2}\\\\\Rightarrow y=20.[/tex]
Thus, the required values are
u = 140, v = 28, w = 40, x = 40 and y = 20.
Related Questions
The telephone pole is _____ feet tall (Round to the nearest whole number)
14 ft
85 ft
42 ft
33 ft
Answers
Answer:
[tex]33\ ft[/tex]
Step-by-step explanation:
Let
y-----> the height of the telephone pole
we know that
In the right triangle of the figure
The sine of angle of 67 degrees is equal to divide the opposite side of angle of 67 degrees by the hypotenuse
[tex]sin(67\°)=\frac{y}{36}[/tex]
solve for y
[tex]y=(36)sin(67\°)=33\ ft[/tex]
Tickets to a local circus cost $5 for students and $8 for adults. A group of 9 people spent a total of $60. How many adults were in the group?
Answers
Final answer:
By setting up a system of equations based on the provided information and solving them, we can determine that there were 5 adults in the group that attended the circus.
Explanation:
To determine how many adults were in the group at the circus, let's use variables to represent the number of students and adults in the group. Let x be the number of students and y be the number of adults. We know there are a total of 9 people, so we have the equation:
x + y = 9
The total cost for all tickets is $60, and considering the cost for students is $5 and for adults is $8, we have the equation:
5x + 8y = 60
We now have a system of equations that can be solved using the substitution or elimination method. If we solve for x in the first equation (x = 9 - y) and substitute into the second equation:
5(9 - y) + 8y = 60
45 - 5y + 8y = 60
3y = 15
y = 15 / 3
y = 5
There are 5 adults in the group. Now, we can find the number of students by substituting y back into the first equation:
x + 5 = 9
x = 9 - 5
x = 4
So, there are 4 students in the group.
Please helppp Omg pleaseee
Answers
Answer:
3/4 3/6 5/12
Step-by-step explanation:
the bottom goes from least to greatest
Please help me asap!! 200 points !!!!!!!! Find the area of the trapezoid given the coordinates: -3,3 -1,-3 1,-2 3,-3
Answers
Answer:
Area 6
Hope This Helps! Have A Nice Day!!
Area 6
Hope This Helps! Have A Nice Day!!
Select the correct answer. A number is selected at random from the set {2, 3, 4, ... 10}. Which event, by definition, covers the entire sample space of this experiment? A. The number is greater than 2. B. The number is not divisible by 5. C. The number is even or less than 12. D. The number is neither prime nor composite. E. The square root of the number is less than 3.
Answers
Answer:
c
Step-by-step explanation:
Answer:
C. The number is even or less than 12.
Step-by-step explanation:
Let's analyze each event:
A. The number is greater than 2.
This doesn't cover the case when we get number 2. Because 2 is equal to 2, not greater.
B. The number is not divisible by 5.
10 and 5 are divisible by 5, so this doesn't cover the entire sample space.
C. The number is even or less than 12.
Let's notice that every number from {2, 3, 4, ... 10} is less than 12, so the even part of the event doesn't play any role. This covers the entire sample space.
D. The number is neither prime nor composite.
The definition of prime number is exactly the opposite of composite number, so there can't be a number that's neither both. This event doesn't cover any number of the set.
E. The square root of the number is less than 3.
This doesn't cover number 10, because the square root of 10 is approx. 3,16 that's greater than 3.
Help! Help! I need to study for tomorrow's math exam. Plz also explain how u got ur answer
Answers
Answer:
5,1 is correct
Step-by-step explanation:
you go over one then up two for G. For H, you go down one and over two.
5,1 because they are both the same distance from F
What is a radical equation
Answers
Answer:
is an equation in which a variable is under a radical
Answer:
An equation where the radical is under the equation...
Step-by-step explanation:
Right?
the sum of the series below is 10900 how many numbers n are in the series 19+20.5+22+23.5+...+181
Answers
Consecutive terms differ by 1.5, so this is an arithmetic sequence given by
[tex]\begin{cases}a_1=19\\a_n=a_{n-1}+1.5&\text{for }n>1\end{cases}[/tex]
So we have
[tex]a_2=a_1+1.5[/tex]
[tex]a_3=a_2+1.5=a_1+2\cdot1.5[/tex]
[tex]a_4=a_3+1.5=a_1+3\cdot1.5[/tex]
and so on, up to
[tex]a_n=a_1+1.5(n-1)=17.5+1.5n[/tex]
The sum of the first [tex]N[/tex] terms is 10,900:
[tex]\displaystyle\sum_{n=1}^Na_n=\sum_{n=1}^N(17.5+1.5n)=17.5N+1.5\dfrac{N(N+1)}2=10,900[/tex]
[tex]\implies17.5N+0.75N(N+1)=10,900[/tex]
[tex]\implies0.75N^2+18.25N-10,900=0[/tex]
[tex]\implies N=109[/tex] (we ignore the negative solution)
so there are 109 terms in the series.
Answer:
109Step-by-step explanation:
[tex]19,\ 20.5,\ 22,\ 23.5,\ ...,\ 181\\\\\text{It's the arithmetic sequence with:}\\\\a_1=19,\ a_n=181.\\\\\text{The sum of n terms of this sequence is equal to 10,900.}\\\\\text{the formula of a sum of n terms of an arithmetic sequence:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\text{Substitute:}\ S_n=10,900,\ a_1=19,\ a_n=181:\\\\\dfrac{19+181}{2}\cdot n=10,900\\\\\dfrac{200}{2}n=10,900\\\\100n=10,900\qquad\text{divide both sides by 100}\\\\n=109[/tex]
Which of the following are considered measures of variability?
I. mean
II. interquartile range
III. mean absolute deviation
Answers
Answer:
the answers are interquartile range and mean absolute deviation
Step-by-step explanation:
In statistics, measures of variability are Interquartile Range and Mean Absolute Deviation, which indicate the degree of spread in a data set. However, the Mean is a measure of central tendency, not variability.
Explanation:
In the context of statistics, measures of variability are statistical data that highlight the degree of the spread in a data set. These are measures that can help us to identify how much the values in the data set differ from their mean value. Out of the options provided, II. Interquartile Range and III. Mean Absolute Deviation can be classified as measures of variability.
The Interquartile Range (IQR) is a measure of statistical dispersion and is calculated as the difference between the 75th and 25th percentiles. It’s the range within which the center half of a data set lies. The Mean Absolute Deviation (MAD) is the average distance between each data value and the mean.
However, I. Mean is not a measure of variability but rather a measure of central tendency. It helps to identify the central point or typical value of a data set but does not represent the dispersion of data points.
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Which of the following represents 3x 5/7
Answers
2.14 is the answer!!!
Answer:
Step-by-step explanation:
3*5 / 7 is the way I'm guessing it is.
15/7 one way it can be represented.
2 1/7 is another way.
2.1428 is yet another way.
Plzz help me ASAP plz plz!!
Which expression is equivalent??
Answers
Answer:
THe 3rd one
Step-by-step explanation:
Number 3 should be the answer
Solution of 0.5x = -1.
first correct answer gets brainliest!!!
Answers
Answer:
x = - 2
Step-by-step explanation:
0.5x = - 1
(0.5/0.5 ) x = -1/0.5
Use your calculator
1
÷
0.5
=
You should get 2. But there is a minus sign on the right. The answer is -2
If two sides of a triangle are 9 cm and 15 cm in length, which COULD be the measure of the third side?
A) 23 cm
B) 24 cm
C) 25 cm
D) 26 cm
Answers
Answer:
Its A) 23
Step-by-step explanation:
Its right, trust me
The possible value of the third side of the triangle is 23.
What is the range of the third side when two sides of a triangle are known?The range of third side c when two sides a and b of a triangle are known is given by the inequality:
[tex]a-b < c < a+b[/tex]
It is given that:
a =15
b = 9
So, by the triangle inequality
[tex]15-9 < c < 15+9[/tex]
6 <c <24
The third side will take the value between 6 and 24.
so, the possible value of the third side of the triangle i.e. c is 23.
Therefore, the possible value of the third side of the triangle is 23.
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Evaluate the expression when n= 3
Answers
what expression?
if you have an expression then I could probably help you.
Mary tutors english. For each hour that she tutors she earns 40 dollars. Let E be her earnings (in dollars) after tutoring for H hours. Write an equation relating E to H. Then use this equation to find marys earnings after tutoring for 13 hours
Answers
Answer:
A.) 40(t) = E
B.) 520
Step-by-step explanation:
t is for time, E is the total, H is the hourly rate.
plug in the numbers to get 40(13) = h and solve for H and you get 520
-- Brainliest answer is much appreciated! :)
An equation is formed of two equal expressions. Mary's earnings after tutoring for 13 hours is $520.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that for each hour that Mary tutors she earns 40 dollars. Therefore, the equation to find marys earnings after tutoring for H hours can be written as,
Earnings = Hourly rate of tutoring × Number of hours
E = 40 × H
E = 40H
Now, Mary's earnings after tutoring for 13 hours will be,
E = 40(13)
E = 520
Hence, Mary's earnings after tutoring for 13 hours is $520.
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which scale drawing of the parallelogram has a scale factor of 1/3 if the original parallelogram has lengths 6 cm and 15 cm
Answers
Answer:
2 and 5
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
What is the median of the data shown in the box plot below?
A:23
B:28
C:30
D:35
Answers
Answer:
It has to be 25 it is the middle number
Answer:
C which is 30.
*will give brainlist**okay so u want to know how much diapers u will use for 3 years basically and then the details to help u each box cost 30$ and u need 1,500 of diapers a year how much will u spend in 3 years in total???
Answers
ok so divide 1500 by 250 to determine how many boxes you need to by in 1 year
so that equals 6 then you multiply that by $30 to find the total cost of all the diapers per year so the is $180 per year and then multiply that by 3 to find the cost of all 3 years
So the answer is you will spend $540 in total
Answer: you will spend $540 on diapers total.
Which segment is parallel to BC
Answers
Line DF is parallel
In triangle ABC with midpoints D, E, and F on sides AB, BC, AC, respectively, segment DF is parallel to BC based on the Midline Theorem
In triangle ABC, if D, E, and F are the midpoints of sides AB, BC, and AC, respectively, then the line segment DE is parallel to BC as per the Midline Theorem.
This theorem states that if a line segment connects the midpoints of two sides of a triangle, that segment is parallel to (and half the length of) the third side of the triangle.
Considering our given scenario, the midpoints of AB and AC are D and F and the line segment formed is DF.
Following the Midline Theorem, this segment DF would be parallel to the third side of the triangle, i.e., BC.
So, the answer to the question 'which segment is parallel to BC?' is DF.
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The probable question may be:
In triangle ABC, Point D, E and F are midpoint of triangle ABC.
which segment us parallel to BC?
A. AB
B. DF
C. AC
D. DE
A square has a perimeter of 36 units. One vertex of the square is located at (3,5) on the coordinate grid. What could be the x- and y- coordinates of another vertex of the square?
Answers
Answer:
3,-4
Step-by-step explanation:
Answer: (9,11)
Explanation: if you plot (9,11) on a grid you can see that the length between 3 and 9 is 6. And the length between 9 and 11 is 6. 6 times 6 is 36. The two length have to be equal to each other because it is a square.
Find the measure of the central angle of an arc if its length is 14pi and 12 is the radius.
Answers
[tex]\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\[-0.5em] \hrulefill\\ s=14\pi \\ r=12 \end{cases}\implies 14\pi =12\theta \implies \cfrac{14\pi }{12}=\theta \\\\\\ \stackrel{\textit{radians}}{\cfrac{7\pi }{6}}=\theta ~\hspace{10em}\stackrel{\textit{in degrees}}{210^o}[/tex]
Can some one answer this ASAP 15points sorry about the scribbles please give answers
Answers
Answer: THEIR HIDEOUT MUST BE CLOSE TO THE SCHOOL
Step-by-step explanation: U= 1 L=0 R= -2 I=24 M=17 H= -3 E=100 S= -439 O=11 B= -6 T= -41 D= 19 C=206
need help plz .You have $2500 to invest in two different accounts. In order to save the money you need for college, you need to average 7% interest. If the two accounts pay 7.5% and 6% interest, how much should you invest in each account? Round to the nearest dollar amount.
A)$1667 in 7.5%, $833 in 6%
B)$1833 in 7.5%, $667 in 6%
C)$667 in 7.5%, $1833 in 6%
D)$833 in 7.5%, $1667 in 6%
Answers
Answer:
A)$1667 in 7.5%, $833 in 6%
Step-by-step explanation:
You need to average 7% interest.
initial investment = $2500
7% of $2500 = [tex]\frac{7}{100}[/tex] × 2500 ⇒ (0.07 ) × (2500) ⇒ $175
so the combined interest from both accounts should be $175
Checking options:
A)$1667 in 7.5%, $833 in 6% ∵ 7.5 % = 0.075
(1667 × 0.075) + (833 × 0.06) 6 % = 0.06
125.025 + 49.98 ⇒ 175.005
B) $1833 in 7.5%, $667 in 6%
(1833 × 0.075) + (667 × 0.06)
137.475 + 40.02 ⇒ 177.495
C)$667 in 7.5%, $1833 in 6%
(667 × 0.075) + (1833 × 0.06)
50.025 + 109.98 ⇒ 160.005
D)$833 in 7.5%, $1667 in 6%
(833 × 0.075) + (1667 × 0.06)
62.475 + 100.02 ⇒ 162.495
Option A is the closest to average7% interest of $2500, which is $175.
9 grams =
milligrams
Answers
Answer:
9000 milligrams
Step-by-step explanation:
1 gram = 1000 milligrams
( × 9 on both sides to get 9 grams )
9 grams = 9000 milligrams
Answer:
9000 milligram
Step-by-step explanation:
multiply the mass value by 1000
simplify 15c3 please
Answers
Answer:
455.
Step-by-step explanation:
Yes. You require the number of combinations of 3 from 15.
15C3
The formula for this is 15! / 12! 3! or you can do itr as follows
15C3 = 15*14*13/3*2*1
= 5*7*13
= 35*13
= 455.
7/3x = 2/(x+5) the solution
Answers
Hi, if we are using the quadratic formula to solve this, then here is a good answer.
The solution to the equation 7/3x = 2/(x+5) is found by cross-multiplication and simplifying, ending with the result x = -35.
Explanation:To solve the given equation 7/3x = 2/(x+5), the first step is to cross-multiply. This gives us 7*(x+5) = 2*3x. Simplifying this results in 7x + 35 = 6x. Subtract 6x from each side and you get x + 35 = 0. And thus, x = -35 is the solution of the equation.
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Evaluate the expression. 0.3+0.2×0.5
Answers
Answer:
The answer is 0.4
Step-by-step explanation:
Since we do multiplication first, we do 0.2*0.5. That equals 0.1.
Next, we do addition. 0.3+0.1 is 0.4.
Answer:
.4
Step-by-step explanation:
First, multiply .2 by .5 which is .1
add this to .3 and you get .4
Your answer is .4
Keiko spent $6 on the fruit at a grocery store. she spent a total of $40 at the store. what percentage of total did she spend on fruit?
Answers
Answer:
15%
Step-by-step explanation:
15% of 40 is 6.
5(3x+8) simplify this equation please that would help a lot thanks.
Answers
[tex]5(3x + 8) \\ 15x + 40[/tex]
Hope that helped
Answer:
15x+40
Step-by-step explanation:
Use the Distributive Property
The equation for the best fit line is y=5.2x+18. It says if the observed value when x=10 was y=62, then which of the following represents the value of the residual for this point. The options are 52, 8,-8,&-10. i need help please!!
Answers
The residual value is -8
What is a residual value?A residual value is the difference between the observed y-value and the predicted y-value( from the regression equation ) .
Here, the given regression equation of the line,
y = 5.2 x +18
Thus, for x = 10, the predicted value of
y = (5.2 × 10) +18
y = 52 + 18
y = 70
Now, by the given question,
For x = 10, the observed value of y = 62,
Hence, the residual for 10 = Observed value of y for 10 - Predicted value of y for 10
= 62 - 70
= -8
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