Answers
The values of x, y and z in the angles are as follows
x = 30 degreesy = 15z = 150 degreesHow to find the angles on parallel line cut by a transversal?When parallel lines are cut by a transversal line, angle relationship are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles.
The parallel lines forms angles relationships.
Therefore,
x = 2y (alternate angles)
z = 2x + 90 (alternate angles)
Using substitution,
z = 2(2y) + 90
z = 4y + 90
x + 2x + 90 = 180 (sum of angles on a straight line)
3x = 180 - 90
3x = 90
x = 90 / 3
x = 30°
Hence,
30 = 2(y)
y = 30 / 2
y = 15
z = 4(15)+ 90
z = 60 + 90
z = 150°
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Related Questions
The length of a rectangle id 5 meters more than its width. the perimeter is 66 meters. find the dimensions of the rectangle.
Answers
The dimension(width and length) of the rectangle are 14 meters and 19 meters respectively.
How to find the dimension of rectangles?A rectangle is a quadrilateral that has opposite sides equal to each other. The opposite sides are parallel to each other.
Therefore, the rectangles length is 5 meters more than its width. The perimeter is 66 meters.
Hence,
perimeter of a rectangle = 2(l + w)
where
l = lengthw = widthTherefore,
l = 5 + w
Hence,
66 = 2(5 + w + w)
66 = 2(5 + 2w)
66 = 10 + 4w
66 - 10 = 4w
56 = 4w
w = 56 /4
w = 14 meters
l = 5 + 14 = 19 meters
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Determine if 0. 7653765376537653. 0. 7653765376537653. Is rational or irrational and give a reason for your answer.
Answers
The number 0. 7653765376537653 is rational number.
What is rational and irrational number?
Perfect squares like 4, 9, 16, 25, and other integers are included in the category of rational numbers. Surds like 2, 3, 5, 7, and so forth are examples of irrational numbers. Rational numbers have whole integers for both their numerator and their denominator, meaning that their denominator is not equal to zero. All whole numbers, fractions, and decimal numbers that finish or repeat are considered rational numbers. Any number that is not rational—that is, any number that cannot be divided by a fraction—is considered to be irrational.
Here the given number is
=>0.7653765376537653
It consists repeated numbers and we can also convert into fraction value.
Hence it is a rational number.
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Select the correct answer.
Which function is the inverse of f(x) = (x − 3)³ + 2?
O A.
f¹(x)=√x-2 +3
O B.
f¹(x)=√x +3 - 2
O c.
f¹(x)=√x+2 - 3
O D.
f¹(x)=√x-3 +7
Answers
The inverse of the function is 3+[tex]\sqrt[3]{x\x-2}[/tex].
What is inverse of the function?
An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f-1 or F-1. One should not confuse (-1) with exponent or reciprocal here.
Given, f(x) = (x − 3)³ + 2
replace f(x) with y
y = (x − 3)³ + 2
y-2 = (x − 3)³
∛y-2 = x-3
∛y-2 +3 = x
Put y =x
we get
∛x-2 +3 =y
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Hi can someone check my work and make sure I got it all right? I got a decimal on number 5 which is why I’m unsure If I got it right or wrong
Answers
All the answers are correct, but the 5th one is wrong, the correct answer for the 5th question is y = 6.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.
A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
The answer of 5th question,
The given expression is,
(5y - 3)/63 = 9/21
105y -63 = 567
105y = 630
y = 630/105
y = 6.
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If p is a number between -1 and 0, which of the following operations would result in the SMALLEST number?
Answers
Finding Angle Measures When Parallel Lines Are Cut By a Transversal
Answers
Answer:
180° - 87° = 93° Supplementary angles with 287° Given87° Vertical angles with 293° Vertical angles with 193° Corresponding angles with 187° Alternate interior angles with 387° Vertical angles with 693° Vertical angles with 5Let us consider the points with an integer y-coordinate from (-1) to 1 and with an integer x-coordinate from (-20) to 20. How many lines are there parallel to the line y=2x and passing through any of these points? PLEASE HELP I NEED THE ANSWER!!!!
Answers
There are infinite linear functions that are parallel to y = 2x passing through these two points.
What is a linear function?The slope-intercept representation of a linear function is presented by the equation shown as follows:
y = mx + b
The coefficients of the the linear function, along with their meaning, are described as follows:
m is the slope of the function, representing the unit rate of change of the output y in relation to the input x.b is the y-intercept of the function, which is value of y at which the linear function crosses the y-axis.What defines two parallel linear functions is that they have the same slope.
The slope of the line y = 2x is of 2, hence we will have an infinity number of linear functions in the following format:
y = 2x + b.
In which b is the y-intercept of the function.
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find the annual salary of a person who is paid $3,800.00 per month and show working for the this question
Answers
Answer:
$45600.00
Step-by-step explanation:
Year is synonm to annual
As there is 12 months in a year
we times $3,800 by 12 which is $45600.00
Pls give me brainliest
pls:(
a deck of cards has only red cards and black cards. the probability of a randomly chosen card being red is 1 3 . when 4 black cards are added to the deck, the probability of choosing red becomes 1 4 . how many cards were in the deck originally?
Answers
Answer: The answer is (264)×(261)(525), because (264)×(261) are the possibilities for choosing 4 red cards and 1 black card from a deck of 52 cards, while (525) are the possibilities for choosing 5 cards from a deck of 52 cards.
So, your first solution is almost correct. On why your second solution is wrong, you'll have to explain your thought process.
Step-by-step explanation:
Given the figure below find if fgh is an equalateral triangle then choose from the answer choices
Answers
Answer: Triangle FGH is an equilateral with values of x as 9.
Step-by-step explanation: The triangle given is an equilateral because all the given side are equal. The value of x is 9.
I don’t know if the question is messed up but adding up all three side after plugging in 9 for x does not give you 180 even though a triangle must be 180 degrees. However, I did try all choices and that was the best one.Answer:
x = 9
Step-by-step explanation:
if x = 2 then
4x + 1 = 93x + 10 = 165x - 8 = 2 (not equal)If x = 22.25 then
4x + 1 = 913x + 10 = 77.5 5 x - 8 = 102(not equal)if x = 180 then
4x+1= 7213x + 10 = 5505x - 8 = 892(not equal)If x = 9 then
4x + 1 = 373x + 10 = 375x - 8 = 37(equal!)Zayne wants to join a gym.
Get Fit Gym charges a $140 enrollment fee and $50 per month.
Fit R Us charges a $245 enrollment fee and $35 a month.
He thinks Get Fit Gym is the better deal. Do you agree or disagree? Explain you're answer
Answers
Zayne is right as Get Fit Gym is the better deal.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have Zayne who wants to join a gym. Get Fit Gym charges a $140 enrollment fee and $50 per month. Fit R Us charges a $245 enrollment fee and $35 a month. He thinks Get Fit Gym is the better deal.
The price for one month at Get Fit Gym will be -
C[G] = 140 + 50 x 1 = 140 + 50 = $190
The price for one month at Fit R Us will be -
C[F] = 245 + 35 x 1 = 245 + 35 = $280
Therefore, Zayne is right, Get Fit Gym is the better deal.
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Find the missing angle
Answers
Answer:
60
Step-by-step explanation:
All of the angles of a trapezoid add up to 360 degrees so,
2h+2h+h+h=360 degrees
6h=360 degrees
h = 60 degrees
2h=120degrees
a bag contains 11 counters.
5 of the counters are white.
a counter is taken at random from the bag and is not replaced.
a 2nd counter is taken out of the bag by random.
calc probability that only one of the counters is white.
Answers
The probability that only one of the counters is white is the fraction 6/11 or 0.55 considering that the first take is without replacement
Probability of an event without replacementThe probability for an event without replacement implies that once an item is taken, then we do not replace it back to the sample space before taking a second item.
Given that there are 11 counters in the bag, with 5 of them being white;
The probability of taking a white counter = 5/11
The probability of not taking a white counter = 6/11
The probability of taking a white counter first without replacement and not taking it the second time = (6/11) × (5/10)
The probability of not taking a white counter first without replacement and taking it the second time = (5/11) × (6/10)
The probability that only one of the counters is white = (6/11) × (5/10) + (5/11) × (6/10)
The probability that only one of the counters is white = (30/110) + (30/110)
Therefore, probability that only one of the counters is white = 6/11 [by simplification]
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PLS HELP
Find the missing term
b) 3:7= : __ 42
Answers
The missing term is 18.
How to find denominator ?The lower number in a fraction is known as the denominator. It demonstrates the equal division of something into portions. Four would be the denominator, for instance, if the fraction was 3/4.Making ensuring your denominators are the same is always the first step when adding or subtracting fractions. This implies that you must identify the common factor. The numerators may then be easily added or subtracted after you have determined the common denominator.Equations with identical denominators are simple to solve because you don't need to identify their shared denominator. The lowest common denominator is known. For instance: 1/4 + 2/4 = 3/4The common denominator in this equation is 4, thus. As a result, you may add the numerators together and place 4 at the bottom of the fraction. You now have 3/4.From given details : 3:7= : __ 42
Here's a little tip for you. Any numbercan be converted to fraction if you
use 1 as the denominator: = 3 / 7 = 42 / 1
= 3 x 42 / 7 x 1 = 126 / 7
= 18
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question is in the pic
Answers
The ordered pair that shows the dilation of the square ABCD, located at A(-10, -2), B(-5, -2), C(-5, -7), and D(-10, -7), by a scale factor of 5 about the origin is option B
B. A'(-50, -10), B'(-25, -10), C'(-25, -35), and D'(-50, -35)
What is a dilation transformation?A dilation transformation is in which the sizes of the sides of the pre image or original figure is changes proportionately to get the image.
The vertex of the preimage ABCD are; A(-10, -2), B(-5, -2), C(-5, -7), and D(-10, -7)
A dilation by a scale factor of 5 is found using the formula;
(x, y) Dilation by scale factor of 5 about the origin ⇒ (5·x, 5·y)
Therefore, the coordinates of the square ABCD following a dilation by a scale factor of 5 is therefore;
A'(5 × -10, 5 × -2), B'(5 × -5, 5 × -2), C'(5 × -5, 5 × -7), and D'(5 × -10, 5 × -7)
Which gives;
A'(-50, -10), B'(-25, -10), C'(-25, -35), and D'(-50, -35)
Checking the lengths of the sides gives;
AB = 5
A'B' = -25 - (-50) = 25
BC = 5
B'C' = -10 - (-30) = 25
CD = 5
C'D' = -25 - (-50) = 25
AD = 5
A'D' = -10 - (-35) = 25
Therefore, the lengths of the sides of A'B'C'D' are 5 times the lengths of the sides of the square ABCD
The correct option is therefore option B
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Use the elimination method to solve the system of equation.
7x+4y=39
2x+4y=14
Answers
x=5 and y=1
Step-by-step explanation:
You treat this as a subtraction problem first noticing which variables are the same between both equations which is 4y.
We set up the subtraction between 7x+4y=39 and 2x+4y=14
7x+4y=39
-(2x+4y=14)
----------------
We subtract and now we get 5x=25
We solve for x and get 5.
Now we plug in the x value into one of the equations to get the y value.
2(5)+4y=14
10+4y=14
4y=4
y=1
Answer:
x=5, y=1
Step-by-step explanation:
you subtract to get rid of 'y' in the equation like you are subtracting two numbers
7x+4y=39
2x +4y =14
5x=25
simplify to get 'x'
x=5
to get 'y' substitute the value of 'x' in one of the equations
2x+4y=14
(2x5)+4y=14
10+4y=14
subtract 10 to get 'y' on its own
4y= 4
simplify to get 'y'
y= 1
Look at the picture and answer the four questions
Answers
Answer:
First Picture is a rotation
Second Picture is a rotation
Third Picture is a vertical translation
The last Picture is a reflection
Step-by-step explanation:
Answer:
First is rotation
Second is rotation
Third is translation
Fourth is reflection
4 times the sum of a number and -6 equals 20
Answers
Answer:
The number is 11.
Step-by-step explanation:
Step one: Convert to algebraic equation
4 x ( a -6 ) = 20
Step two: Simplify both sides of the equation.
4 (a −6) = 20
(4)(a) +(4)(−6) = 20 (Distribute)
4a +−24 = 20
4a −24 = 20
Step three: Add 24 to both sides.
4a −24 +24 = 20 +24
4a = 44
Step four: Divide both sides by 4.
(4a /4) = (44 /4)
a = 11
The number of home runs by player A and player B for a season are consecutive odd integers whose sum is 108.
Determine the number of home runs hit by player A and player B.
The number of home runs hit by player A is (?) The number of home runs hit by player B is (?)
Answers
The number of home runs hit by player A nd player B are respectively 53 and 55which are consecutive odd integers.
Let the number of home runs hit by A is x.
Therefore the number of home runs hit by B is x+2 as they are consecutive odd numbers.
If x is odd then x + 1 is even and x+2 is odd.
The sum of their home runs is 108.
We will form a linear equation in x to represent this situation.
x + (x+2) = 108
now we will solve this equation to find the value of x.
or, 2x + 2 = 108
or, x + 1 = 54
or, x = 53
Hence the number of home runs hit by A is 53 .
Number of home runs hit by B = 53+2 = 55
Therefore the number of homeruns hit by players A and B are 53 and
55.
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A discount of 25 % is allowed on an article marked at rs 17 500. calculate the discount.
Answers
Answer:
$4375
Step-by-step explanation:
25 percent *17500 =
(25:100)*17500 =
(25*17500):100 =
437500:100 = 4375
How do you do this………. Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 8 people took the trip. She was able to purchase coach tickets for $230 and first class tickets for $950. She used her total budget for airfare for the trip, which was $6160. How many first class tickets did she buy? How many coach tickets did she buy?
Answers
Answer: SO WHAT YOU HAVE TO DO IS
Step-by-step explanation:
Two beetles sit at the top edge of the house roof. The roof has two faces. The first face is such that the horizontal shift by 3 cm along this face means 2 cm shift vertically. Simultaneously the beetles start moving downwards, the first beetle by the first face, the second -- the second face of the roof. The first beetle moves twice as fast as the second beetle. Find the altitude of the second beetle above the first beetle when they will be 72 cm apart horizontally, if the second face of the roof is perpendicular to the first face?
Answers
Answer:
9 cm
Step-by-step explanation:
Given two beetles on a roof with a first face having a slope of -2/3 and the second face perpendicular to it. The first beetle travels down the first face twice as fast as the second beetle travels down the second face. You want to know their vertical separation when their horizontal separation is 72 cm.
SeparationIn a given unit of time, the first beetle will travel 2×3 = 6 cm horizontally, and 2×(-2) = -4 cm vertically. The second beetle will travel 2 cm horizontally and -3 cm vertically in the same time, a perpendicular distance half as far.
After that one unit of time, the separation between the beetles is ...
horizontally: 6 +2 = 8 cm
vertically: -3 -(-4) = 1 cm
ScaleWe notice the vertical separation is (1 cm)/(8 cm) = 1/8 of the horizontal separation. When the horizontal separation is 72 cm, the vertical separation will be ...
(1/8)(72 cm) = 9 cm
The second beetle is 9 cm above the first when their horizontal separation is 72 cm.
__
Additional comment
The rise/run for the first face is given as (-2 cm)/(3 cm) = -2/3. The second face is perpendicular, so will have a rise/run = -1/(-2/3) = 3/2. That is, for a run of -2 cm, the rise will be -3 cm.
We note that the right triangles with legs "rise" and "run" are congruent for the two beetles. Traveling at the same speed, each beetle will cover a hypotenuse length in a given unit of time, hence the lengths "rise" and "run" on their respective roof faces. Since beetle 1 travels twice as fast, its distance will be 2·rise and 2·run in each time unit.
The attached diagram shows the geometry of the problem. The measures show beetle 1 has traveled twice as far as beetle 2 when they are separated horizontally by 72 cm. The grid is set so you can see the slopes are -2/3 and 3/2.
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Find the missing factor.
• 200 = 36,000
Answers
Answer:
180
Step-by-step explanation:
this can be turned into
200x=36,000
Divide 200 to both sides of this equation
x=180
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In order to determine an interval for the mean of a population with unknown standard deviation a sample of 61 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for reading the t value is.
Answers
The number of degree of freedom for reading the t values is 60 , the correct option is (c) .
In the question ,
it is given that ,
number of items in the sample = 61 items
the mean of the sample is given as 23 ,
we have to find the degree of freedom(df) ,
the degree of freedom(df) can be solved using the formula
degree of freedom(df) [tex]=[/tex] (number of observations) - 1
Substituting the values in the formula ,
we get ,
degree of freedom = 61 - 1
= 60
Therefore , The number of degree of freedom for reading the t values is 60 , the correct option is (c) .
The given question is incomplete , the complete question is
In order to determine an interval for the mean of a population with unknown standard deviation a sample of 61 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for reading the t value is ?
(a) 22
(b) 23
(c) 60
(d) 61
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in 2020 summer camp registration was $15 more than it was in 2021. in 2020, registration was $285 by what percentage did the summer camp registration decrease in 2021
Answers
If in 2020, registration was $285.The percentage that the summer camp registration decrease in 2021 is 5.26%%.
How to calculate the decrease in percentageUsing this formula to find the decrease in percentage
Decrease in percentage = [2020 registration cost - (2020 registration cost - 2020 summer registration)] / 2020 registration cost
Let plug in the formula
Decrease in percentage = [285 - (285 -15)] /285
Decrease in percentage =285 - 270 / 285
Decrease in percentage = 15 /285
Decrease in percentage =0.0526× 100
Decrease in percentage =5.26%
Therefore 5.26% is the decrease in percentage .
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(Algebra 1) please help
Answers
The domain for plotting the growth function will be [0, 5].
A function's domain is the set of its possible inputs or the set of input values for which the function is defined. The domain is the set of objects that the machine will accept as inputs in the function machine metaphor.
If the f(n) = 11.04 cm
By substituting the value in the equation,
11.04 = 10(1.02)n
(1.02)n = 11.04/10
(1.02)n = 1.104
Take log on both the sides,
log(1.02)n = log(1.104)
n[log(1.02)] = log(1.104)
n = 4.996 ≈ 5 years
Therefore, the span of the study was 0–5 years.
As a result, the domain for plotting the growth function will be [0, 5].
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You estimate that there are 42 marbles in a jar. The actual amount is 67 marbles. Find the percent error. Round to the nearest tenth of a percent if necessary.
Answers
If the actual amount is 67 marbles. the percent error is 37%.
How to find the percent error?Using this formula to find the percent error
Percent error = Actual value -Estimated value/ Estimated value
Where:
Actual value = 67
Estimated value = 42
Let plug in the formula
Percent error = 67 - 42 /67
Percent error = 25/67 × 100
Percent error = 37%
Therefore the percent error is 37%.
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An elephant can’t drink up to 6400 fluid ounces of water a day how many gallons of water can an elephant drink per day
Answers
The number of gallons of water can an elephant drink per day is 50 gallons.
Given that, an elephant can’t drink up to 6400 fluid ounces of water a day.
What is metric conversion?Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.
We know that, there are 128 fluid ounces in 1 gallon.
Now, 6400/128
= 50 gallons
Hence, the number of gallons of water can an elephant drink per day is 50 gallons.
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.04/70.8deion saves 15% of his paycheck every month. last month he saved $219. how much was his paycheck? use p for your variable.
Answers
If deion saves 15% of his paycheck every month. last month he saved $219. then his paycheckwould have been $1460
deion saves 15% of his paycheck every month. last month he saved $219. how much was his paycheck
Let his paycheck be p
Then 15 % of p is equal to 219
(15/100 ) p = 219
p = 219 (100/15)
p = 1460
Therefore, if deion saves 15% of his paycheck every month. last month he saved $219. then his paycheck would have been $1460
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Of the 50 students in ski club, 14 are freshmen. What percent of the
members are not freshmen?
Answers
Answer:
72% are not freshmen.
Step-by-step explanation:
The not freshmen students are,
→ 50 - 14
→ 36 students
Then percent of not freshmen,
→ (36/50) × 100
→ 0.72 × 100
→ 72%
Hence, the answer is 72%.