Answers
The values of x and y from the figure are 22.5 and 10 respectively
Vertical anglesThe angles that meet at a point X are equal and vertically opposite
From the diagram shown
6x - 5 = 8x - 50
6x - 8x = -50 + 5
-2x = -45
x = 22.5
Similarly
2y + 30 = 3y + 20
2y - 3y = 20 - 30
-y = -10
y = 10
Hence the values of x and y from the figure are 22.5 and 10 respectively
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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
Since the two lines intersects each other we can conclude that :
6x - 5 = 8x - 50and
2y + 30 = 3y + 20[ That's because they form vertical opposite angle pair ]
So, let's solve for x and y ~
[tex]\qquad \sf \dashrightarrow \:6x - 5 = 8x - 50[/tex]
[tex]\qquad \sf \dashrightarrow \:8x - 6x = - 5 + 50[/tex]
[tex]\qquad \sf \dashrightarrow \:2x = 45[/tex]
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{45}{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:x = 22.5[/tex]
And
[tex]\qquad \sf \dashrightarrow \:2y + 30 = 3y + 20[/tex]
[tex]\qquad \sf \dashrightarrow \:3y - 2y = 30 - 20[/tex]
[tex]\qquad \sf \dashrightarrow \:y = 10[/tex]
I hope the steps are clear ~ let me know if you have doubts ~
Related Questions
3. The probability of winning a balloon dart game is 0.25. The odds of winning a ring toss game are 2:7. Which game gives you a better chance of winning?
Please help
Answers
Answer:
Ring toss game
Step-by-step explanation:
[tex]2:7[/tex] can be rewritten as [tex]\frac{2}{7}[/tex], which is [tex]\approx0.286[/tex].
We can now compare the probabilities of winning for each game.
[tex]0.286 > 0.25[/tex]
This means the odds of winning the ring toss game ([tex]0.286[/tex]) are higher than the odds of winning the balloon dart game [tex](0.25)[/tex].
A rectangle is divided into 4 equal rows with 4 squares in each row. mark says 1 square is 1/4 of the whole rectangle. kareem says 1 row of the whole rectangle.
Answers
Kareem is correct
4 rows = each row is 1/4 of the rectangle
Match each pair of rational numbers with their sum
Answers
The match each pair of rational numbers with their sum is:
[tex]\frac{2*(a-b)}{a^2b^2} = \frac{-2}{a^2b}+\frac{2}{ab^2}[/tex]
[tex]\frac{a-b^2}{a^2b^3} }=\frac{1}{ab^3} +\frac{-1}{a^2b}[/tex]
[tex]\frac{2ab-1}{4a^2b^2} }=\frac{1}{2ab} +\frac{-1}{4a^2b^2}[/tex]
[tex]\frac{2*(1-ab^2)}{a^2b^3} =\frac{2}{a^2b^3}+\frac{-2}{ab}[/tex]
FactoringIn math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization. One of them is a factor out a common term for example: x²-x= x(x-1), where x is a common term.
When you factor an expression using the rule a factor out a common term, it is possible simplify an expression
Then, you should factor and simplify each given algebraic expression.
[tex]\frac{2*(a-b)}{a^2b^2} =\frac{2a-2b}{a^2b^2}=\frac{2a}{a^2b^2} -\frac{2b}{a^2b^2} =\frac{2}{ab^2} +\frac{-2}{a^2b}[/tex][tex]\frac{a-b^2}{a^2b^3} }=\frac{a}{a^2b^3} -\frac{b^2}{a^2b^3} =\frac{1}{ab^3} +\frac{-1}{a^2b}[/tex][tex]\frac{2ab-1}{4a^2b^2} }=\frac{2ab}{4a^2b^2} -\frac{1}{4a^2b^2} =\frac{1}{2ab} +\frac{-1}{4a^2b^2}[/tex][tex]\frac{2*(1-ab^2)}{a^2b^3} =\frac{2-2ab^2}{a^2b^3}=\frac{2-2ab^2}{a^2b^3}=\frac{2}{a^2b^3}+\frac{-2}{ab}[/tex]
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Given lines l, m,n are parallel and cut by two transversal lines, find the value of x. Round your answer to the nearest tenth if necessary.
Answers
Answer: 50.5
Step-by-step explanation:
[tex]\frac{30}{22}=\frac{x}{37}\\x=(30/22)(37) \approx \boxed{50.5}[/tex]
What is the product of the fractions below?
1/8 * 4/5
Answers
Answer: 1/10
Step-by-step explanation:
(1 x 4)/(8x5)
4/40
1/10
Hello, can someone help with this problem?
The graph shows the probability distribution of a random variable.
What is the value of P(4≤X≤8)?
0.40
0.45
0.50
0.55
Answers
Answer:
P(5 ≤ X ≤ 8) = a rectangle with a width of 3 and height of .15 = 3(.15) = .45
P( 4 ≤ X ≤ 5) = a triangle with a base of 1 and a height of (0.15 -0.05) = .10
So....this area = (1/2)(1)(.10) = .05
And another rectangle with a width of 1 and height of .05 = (1) (.05) = .05
So
Adding these areas
P( 4 ≤ X ≤ 8 ) = .45 + .05 + .05 = .55
Step-by-step explanation:
Hoped this helped!
Type the correct answer in each box. a race car is driven by a professional driver at 99 . what is this speed in and ? 1 mile = 1.61 kilometers 1 hour = 60 minutes express the answers to the correct number of significant figures. the speed is equivalent to , or .
Answers
The speed of the car in kilometres per minutes is 2.6565 km/minutes
How to find speed in km/minutes?The car speed is 99 miles per hours.
Therefore,
1 miles = 1.61 km
99 miles = ?
cross multiply
distance = 159.39 km
Therefore,
1 hour = 60 minutes
Hence,
speed = 159.39 / 60
speed = 2.6565
speed = 2.6565 km/minutes
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Sana's mother bought produce for Sunday dinner. She bought one more pound of peaches than pounds of tomatoes. She bought 3 times as many pounds of tomatoes as pounds of mushrooms. If peaches cost $6 per lb, tomatoes cost $3 per lb, and mushrooms cost $10 per lb, how many of each did Sana's mother buy for $80?
Answers
Using a system of equations, it is found that Sana's mother bought 6.72 pounds of peaches, 5.72 pounds of tomatoes and 2.24 pounds of mushrooms for $80.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given as follows:
Variable x: Number of pounds of peaches.Variable y: Number of pounds of tomatoes.Variable z: Number of pounds of mushrooms.She bought one more pound of peaches than pounds of tomatoes, hence:
x = y + 1.
y = x - 1.
She bought 3 times as many pounds of tomatoes as pounds of mushrooms, hence:
x = 3z.
y = x - 1 = 3z - 1.
She spent a total of $80, hence considering the cost per pound of each product we have that:
6x + 3y + 10z = 80.
Considering the values of x and y as function of z and replacing in the equation, we have that:
6(3z) + 3(3z - 1) + 10z = 80
18z + 9z - 3 + 10z = 80.
37z = 83.
z = 83/37
z = 2.24.
Then:
x = 3z = 3 x 2.24 = 6.72.
y = x - 1 = 3z - 1 = 6.72 - 1 = 5.72.
Hence, she bought 6.72 pounds of peaches, 5.72 pounds of tomatoes and 2.24 pounds of mushrooms for $80.
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7 lbs peaches, 6 lbs tomatoes, 2 lbs mushrooms
yum!
Which table represents a linear function?
X
X
y
1
1
1
2
2
1
2
3
4
34
O
122
1/7/2
O
y
1
121314
X
1
2
3
4
X
1
2
3
14
O
y
7
9
13
21
y
0
6
16
30
Answers
the third one
Step-by-step explanation:
What are the answers for the first page????
Answers
Answer:
which first pagee???There is no any first page????
A graph shows the number of texts, numbered 10 to 100, on the x-axis, and the total cost in dollars, numbered 3 to 27, on the y-axis. A straight red line with a positive slope, labeled Emilia, begins at (0, 10), and a straight blue line with a positive slope, labeled Hiroto, begins at (0, 20). Both lines intersect at point (50, 22.5).
Hiroto’s texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia’s plan costs $10 per month and $0.25 per text. Using the graph below, which statement is true?
Answers
(50, 22.5) is the solution of the system of equations, therefore, the true statement would be: Both plans cost the same when 50 texts are sent.
What is the Solution of a System of Linear Equations?A solution to the system of linear equations is the point of intersection where both line of each equation meet.
The solution to the system of linear equations given in the graph attached below is (50, 22.5).
(50, 22.5) implies that both plans will cost the total amount when 50 text are sent.
The true statement using the graph would be: Both plans cost the same when 50 texts are sent.
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Answer:
Both plans cost the same when 22 texts are sent
Step-by-step explanation:
on edge
Which answer choice has the set of numbers
ordered correctly from least to greatest?
16
13, √, 1.71, 9
3
√. 12, 16, 1.71
4
3
16
1.71, 12, 1
9
O
16.1.71,√, 12
3
9
Answers
Answer:
0
3
3
3
8
9
12,161.71√
I think his is the best order
Find the amplitude of this function.
Answers
The amplitude is 2.5
Equation:
the equation to find the amplitude is (max-min) / 2.
using this equation, it would be (4 - (-1)) / 2
5 / 2 = 2.5
The first steps in determining the perimeter of triangle ABC are shown.
To the nearest whole unit, what is the perimeter of triangle ABC?
6 units
8 units
14 units
16 units
Answers
Answer:
C) 14 Units
Step-by-step explanation:
E2020
can someone help me to number 2,4&5.
just 2,4&5 that's all thank you.
Answers
Answer:
See below ~
Step-by-step explanation:
ACTIVITY #1
Try It!
A. Write the definition, property, postulate or theorem that will prove each of the given statements.
Answers
What completes the proof are:
1. LC ≅ CU; CU ≅ UK
2. Given
3. Unequal angle theorem (Aa → Ss)
What is the Unequal Angle Theorem?The unequal angle theorem states that the longer side of a triangle will always be directly opposite the largest angle measure. This implies that, if an angle that is opposite a side is greater than another another, the side it is opposite will also be longer than the side opposite the other angle (Aa → Ss).
From the image given, statement 1 was given as well as statement 2.
Statement 1 would be: LC ≅ CU; CU ≅ UK.
The reason for statement 2 will also be "given".
Then, UL > CK using the unequal angle theorem (Aa → Ss).
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A 12 m ladder propped against a wall forms an angle of 60° with the ground. Determine
how far the top of the ladder is from the ground. Include a diagram.
Answers
Answer:
the top of the ladder is approx 8.485 meters off the ground
written explanation included
Step-by-step explanation:
I should probably write this out in one note but bear with me, please.
Assuming the ground and the wall meet at a 90° angle
therefore the angles of the triangle formed are 90°, 30°, and 60°
Solve system of equation using elimination by addition.
Will give brainliest!!
Answers
Answer:
x = -8
y = 0
Step-by-step explanation:
The two shown equations can be added together:
x + 4y = -8
+ ( x - 4y = -8 )
The two x's would combine to make two x, the 4y and -4y cancel out to zero, and -8 added to -8 is -16:
2x = -16
Therefore, x = -8. We can plug this into the first equation to get:
-8 + 4y = -8
Subtracting 8 on both sides yields:
4y = 0
Now divide by 4 on both sides to get
y = 0
We can check these values by plugging them into the second equation:
(-8) - 4(0) = -8
-8 - 0 = -8
-8 = -8
Since -8 always equals -8, the answer is correct.
!!20 POINTS AND BRAINLIEST!!! HELP ASAP!!!
How much ribbon would be needed to go around a package that had a length 2x^2+3x-5/x^2+x-3 centimeters and width x^2-x-5/x^2+x-3 centimeters?
(show work)
Answers
Answer:
23cm
Step-by-step explanation:
If you multiply like terms you will get the answers. Then you add last to get 23cm
The required length ribbon needed to go around the package is 2(3x^2 + 2x -10) / (x^2 + x - 3).
Given that,
Package that had a length of 2x^2+3x-5/x^2+x-3 centimeters and width x^2-x-5/x^2+x-3.
How much ribbon would be needed to go around the package in centimeters is to be determined.
Perimeter is the measure of the figure on its circumference.
The rectangle is a four-sided polygon whose opposites sides are equal and has an angle of 90° between its sides.
Quantity of ribbon = perimeter of the rectangular package
= 2 * length + 2* width
= 2 * (2x^2+3x-5/x^2+x-3) + 2(x^2-x-5/x^2+x-3)
= 2 (3x^2 + 2x -10) / (x^2 + x - 3)
Thus, the required length of ribbon needed to go around the package is 2(3x^2 + 2x -10) / (x^2 + x - 3).
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Evaluate (cant write it out, picture included)
Answers
Let's solve this problem step-by-step:
⇒ with our knowledge of PEMDAS
⇒ (look at the image attached)
Let's solve:
Let's first plug n's value[tex]\frac{9}n}+4 = > \frac{9}{-3}+4[/tex]
Let's first do the division[tex]\frac{9}{-3}+4=-3+4[/tex]
Now let's add[tex]-3+4=1[/tex]
Answer: 1
Hope that helps!
What is the median of the following distribution?
26, 26, 28, 29, 31, 33, 35, 36, 37, 38, 40, 42, 43, 46, 48
OA. 33
OB. 37
O C. 56
OD. 43
OE. 36
Answers
please answer, much appreciated!!!!!
Answers
Answer:
i don't understand your question
Step-by-step explanation:
Select the correct answer from each drop-down menu.
Consider the function f(x) = 3x4 − 5x2.
This function is
1. even
2. odd
3. neither even or odd
because
1. f(x)-f(x)
2. f(x)=f(x)
3. -f(x)=f(-x)
Answers
Using the classification for even and odd functions, it is found that the function is even, because f(-x) = f(x).
How we verify if the function is even, odd, or neither?If for all values of x, f(x) = f(-x), the function is even.If for all values of x, f(-x) = -f(x), the function is odd.If neither of these statements are true, the function is neither even nor odd.Graphing the function [tex]f(x) = 3x^4 - 5x^2[/tex], for every value of x, f(x) = -f(x), that is, the function is symmetric over the y-axis, hence it is even.
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A tub of water is emptied at a rate of 3 gallons per minute. The equation y –12 = –3(x – 1) models the amount of water remaining, where x is time (in minutes) and y is the amount of water left (in gallons). Analyze the work shown below to determine the initial amount of water.
1. Solve for the y-variable.
y – 12 = –3(x – 1)
y – 12 = –3x + 3
y = –3x +15
2. Write the equation using function notation.
f(x) = –3x +15
The tub started with
gallons of water.
Answers
The initial amount of the water is 15 gallons
Linear functionsThese are functions that has a leading degree of 1. Given the equation that represents the amount of water remaining after x minutes;
y - 12 = -3(x- 1)
y -12 = -3x + 3
y = -3x +3 + 12
y = -3x + 15
In order to determine the initial amount of water, we will substitute x =0 into the function
y = -3(0) + 15
y = 15
Hence the initial amount of the water is 15 gallons
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Answer:
15
Step-by-step explanation:
Find the indicated conditional probability
using the following two-way table:
Grade
Drive to school Take the bus
Walk
Sophomore
2
25
3
Junior
13
20
2
Senior
25
5
5
P(Take the bus | Junior) = [?]
Round to the nearest hundredth.
Answers
Using it's concept, it is found that the desired probability is given by:
P(Take the bus | Junior) = 0.5714 = 57.14%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that out of the 13 + 20 + 2 = 35 Junior students, 20 take the bus, hence the probability is given by:
P(Take the bus | Junior) = 20/35 = 0.5714 = 57.14%.
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In the following exercises, translate into an equation and solve
Kindergarten Connie’s kindergarten class has 24 children. She wants them to get into 4 equal groups. How many children will she put in each group?
Answers
Answer: 6 children
Step-by-step explanation:
Given:
Children - 24
Groups - 4
Number of children per group - x
Solve:
24 ÷ 4 = x
x = 6
Hope it helps!!! Please mark as brainliest. Thanks :D
If x and y are supplementary angles, then x is _____ obtuse.
answer choices - always, sometimes, or never.
Answers
Answer:
sometimes
Step-by-step explanation:
a supplementary angle is "either of two angles whose sum is 180°".
So, x or y could be any degree, (less than 180 of course) and either one could be obtuse (>90) or acute (<90).
Area of a rectangular playground in residential society is 2 2/5 km square and one of its sides is 1 2/5 km/ find the length of the other side
Answers
Step-by-step explanation:
area of a rectangle is
length × width
so, in our case
2 2/5 km² = 1 2/5 × width (or length, it does not matter)
12/5 km² = 7/5 × width
width = 12/5 / 7/5 = 12×5 / 7×5 = 12/7 = 1 5/7 km
DL is a perpendicular bisector of chord GA. Identify the diameter.
Answers
A circular grass lawn has an area of 314 square metres.
12.
Find the circumference of the lawn.
Answers
Answer:
[tex]C= 62.8m[/tex]
Step-by-step explanation:
Let's round [tex]\pi = 3.14[/tex]. Area of a circle if [tex]\pi r^2[/tex]. In our case, we can easily find out the radius[tex]\pi r^2 = 100\pi \rightarrow r=10m^[/tex]. At this point, it's easy to find the length of the circumference by doubling it and multiplying again by [tex]\pi[/tex]:
[tex]C= 2\pi r = 62.8 m[/tex]