In the figure shown to the right, two parallel lines are cut by a third line. Find w, x, y, and z.
Answers
So first of all is important to note that angle y and the 113° angle are what is known as corresponding angles. Basically, the sides that define them are parallel which means that they have the same measure. Then:
\(\measuredangle y=113^{\circ}\)y and z are opposite angles. Just like before, one of the sides of y is parallel to one of the sides of z and the remaining sides are also parallel. Then they also have the same measure:
\(\measuredangle z=\measuredangle y=113^{\circ}\)Using the same argument, x and the 113° have the same measure:
\(\measuredangle x=113^{\circ}\)Finally, w and y are interior angles. This means that the sum of their measures must be equal to 180°. Then we get:
\(\measuredangle y+\measuredangle w=113^{\circ}+\measuredangle w=180^{\circ}\)If we substract 113° from both sides of the last equality we get:
\(\begin{gathered} 113^{\circ}+\measuredangle w-113^{\circ}=180^{\circ}-113^{\circ} \\ \measuredangle w=67^{\circ} \end{gathered}\)Then the answers are:
\(\begin{gathered} \measuredangle w=67^{\circ} \\ \measuredangle x=113^{\circ} \\ \measuredangle y=113^{\circ} \\ \measuredangle z=113^{\circ} \end{gathered}\)Related Questions
What is the complementary angle of CFB
Answers
Step-by-step explanation:
CFB reads as twenty five degrees
complementary angle will add to it to sum 90 degrees = sixty five degrees
angle CFD is sixty five degrees
Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.4 years with a standard deviation of 0.8 years.
Step 2 of 2: If a sampling distribution is created using samples of the ages at which 38 children begin reading, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary.
Answers
Answer:
Step-by-step explanation:
The standard deviation of the sampling distribution of sample means is given by the formula:
standard deviation = population standard deviation / sqrt(sample size)
Here, the population standard deviation is 0.8 years, and the sample size is 38. Substituting these values into the formula, we get:
standard deviation = 0.8 / sqrt(38)
standard deviation ≈ 0.13
Rounding to two decimal places, the standard deviation of the sampling distribution of sample means is approximately 0.13 years.
8 cm²12 cm²4 cm²16 cm²Q. What is the area of the shaded region?
Answers
12 cm²
1) Since we have two squares, and the smallest one is located inside the greatest one, then we need to calculate the white square area and subtract from the gray one's area
2) This way:
\(\begin{gathered} A_{\text{gray}}=s^{2} \\ A_{\text{gray square }}=4^2=16cm^2 \\ A_{itesquare}=2^2=4\text{ cm²} \\ A_{\text{shaded}}=16\text{ -4 = 12cm²} \end{gathered}\)3) So the area of the shaded region is 12 cm²
Express the given quantity in terms of the indicated variable.
The area (in ft2) of a rectangle that is four times as long as it is wide; w = width of the rectangle (in ft)
Answers
Answer:
Area of a rectangle equals length times width. A = l x w = 9ft x 7ft = 63ft2
Step-by-step explanation:
5. Find the largest difference between a 3-digit number and a 2-digit number.
Answers
Answer:
989
Step-by-step explanation:
The largest difference could be possible between Largest 3 digit number and smaller two digit number
I.e,
999-10=989
4/9
is the additive inverse of which number?
Answers
Answer:
4/9
Step-by-step explanation:
Find the measures of the angles please help I dont understand this
Answers
Given:
\(\bar{HJ}||\bar{ED}\)Where,
\(m\angle ZUJ=100^0\)Therefore,
\(m\angle ZUH+m\angle ZUJ=180^0\text{ \lparen Sum of angles on a straight line is 180}^0)\)Hence,
\(\begin{gathered} m\angle ZUH+100^0=180^0 \\ m\angle ZUH=180^0-100^0=80^0 \\ \therefore m\angle ZUH=80^0 \end{gathered}\)Hence, the answer is
\(m\angle ZUH=80^0\)If you estimate that a piece of wood measures 5.5cm if it actually measures 5.62cm what is the percent error of the estimate
Answers
The percent error of the estimate is -2.14%
How to determine the percent error of the estimate?In this question, the figures are given as
Estimate = 5.5 cm
Actual = 5.62 cm
The percentage of the error is then calculated using the following equation
Error percentage = (Estimate - Actual)/Actual * 100%
Substitute the known values in the above equation, so, we have the following representation
Error percentage = (5.5 - 5.62)/5.62 * 100%
Evaluate
Error percentage = -2.14%
Hence, the error percentage is -2.14%
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If f(x)=5x-2 and g(x)=2x1 find (f+g)(x)
Answers
Answer:
D
Step-by-step explanation:
5x-2+2x+1
5x+2x+1-2
7x-1
Find the area of the rectangle on this centimetre grid.
Answers
Answer:
A = 35 cm²
Step-by-step explanation:
the area (A) of a rectangle is calculated as
A = length × width
by counting the squares on the sides
length = 7 cm and width = 5 cm , then
A = 7 × 5 = 35 cm²
Question 4 of 5
Drag each label to the correct location on the triangle. Not all labels will be used.
Find the unknown measurements. Round all values to the nearest tenth.
cm
8.9 cm
65°
Answers
Answer:
long side: 19.1 cmmissing angle: 25°hypotenuse: 21.1 cmStep-by-step explanation:
You can use this information to "guess" at the answers without doing any "work."
The sum of angles in a triangle is 180°.The shortest side is opposite the smallest angle.__
qualitative solutionThe missing angle is the complement of the marked acute angle in the right triangle, so is ...
C = 90° -65° = 25°
This angle is opposite the side of length 8.9 cm. The next-smallest angle is 65°, which is more than double the smallest angle. Hence the side opposite 65° will not be either of 3.8 or 9.8.
Of the two remaining measures, the longer one, 21.1, will be the hypotenuse, BC. The shorter of those, 19.1, will be the long side, AC.
Our solution is ...
AC = 19.1 cmC = 25°BC = 21.1 cm__
quantitative solutionThe mnemonic SOH CAH TOA reminds you of the relations between trig functions and right triangle sides. Here, we're given an angle and the length of its adjacent side. We are asked for the opposite side and for the hypotenuse. This suggests useful relations might be ...
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
Solving the first of these for the hypotenuse gives ...
hypotenuse = adjacent/cos(65°)
BC = 8.9 cm/cos(65°) ≈ 21.059 cm ≈ 21.1 cm
Solving the second relation above for the opposite side gives ...
opposite = adjacent×tan(65°)
AC = 8.9 cm×tan(65°) ≈ 19.086 cm ≈ 19.1 cm
As above, the missing angle is the complement of the given one:
C = 90° -65° = 25°
Then the quantitative solution is ...
AC = 19.1 cmC = 25°BC = 21.1 cm_____
Additional comment
If AC were 9.8 cm, the angle at B would be about 48°. That is, the two acute angles in the triangle would be very nearly equal.
We know that the side ratios in a 30°-60°-90° right triangle are 1 : √3 : 2. This triangle has a larger angle greater than 60°, so its longer side will be more than √3 times the short side. That means a length of 9.8 cm is way too short.
The bakery sold
1,240 cupcakes over 4 days.
What is the unit rate?
Answers
Answer:
310 cupcakes per day
Step-by-step explanation:
divide 1240 by the 4 days to find out how many they sell in one day
if this is wrong idc im just gathering points so i can put my questions
Which expression is equivalent to 2(x + 7) -18x + 4/6
A)20x + 74/5
B) 20x + 139/5
C) - 16x + 74/5
D) - 16x + 139/5
Answers
Answer:
i got -16x+44/3 so i guess c?
Step-by-step explanation:
hope this helps
Find the median of the data.
93, 81, 94, 71, 89, 92, 94,99
Find the mode(s) of the data.
Pls help
Answers
Answer:
92.5Step-by-step explanation:
The data given:
93, 81, 94, 71, 89, 92, 94, 99Put the data in the ascending order:
71, 81, 89, 92, 93, 94, 94, 99Since the data size is even, the median is the average of middle two:
median = (92 + 93)/2 = 92.5Which triangle is similar to △JKH?
1. △MKN
2. △JOG
3. △MQL
4. All triangles are similar to △JKH
Answers
Given that Line a is parallel to Line b (Line a ║ Line b), the triangle that is similar to ΔJKH is 1. ΔMKN
What are similar triangles in geometry?Similar triangles are triangles that have congruent corresponding angles, and in which all three corresponding sides are proportional.
The given parameter is Line a is parallel to Line b, which gives: a║b
Two triangles are similar if they satisfy the following conditions:
Two angles in one triangle are equal to two angles in the other triangle.Each of the three corresponding sides of the two triangles are proportional.Two sides of one triangle are proportional to the corresponding two sides on the other triangle, and the included angle between the specified two sides in both triangles are congruent.According to alternate angles theorem, the angles ∠JHK in ΔJKH is congruent to the ∠KNM in triangle ΔMKN
Similarly, the angle ∠HJK in ΔJKH is congruent to the ∠KMN in ΔMKN
Therefore, ΔJKH is similar to ΔMKN by Angle-Angle, AA similarity postulate.
The correct option for the triangle similar to ΔJKH is option 1. ΔMKN
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Please I need help really badly
Answers
Answer:
with what
Step-by-step explanation:
I can't really see the question
Write a numerical expression for the word expression. The product of 7 and 12
Answers
Answer:
7x12
Step-by-step explanation:
product is multiplication
2
Select the correct answer.
If the graph of f(x) = 4x is shifted 7 units to the left, then what would be the equation of the new grap
O A.
О в.
O C.
O D.
g(x) = 4(x-7)
g(x) = 4x + 7
g(x) = 4(x+7)
g(x) = 4x - 7
Reset
Next
Answers
If the graph of f(x) = 4x is shifted 7 units to the left then the equation be 4(x+7).
What is meant by translation?A translation in Euclidean geometry is a geometric transformation that shifts each point of a figure, shape, or space by the same amount in one direction. Another way to think of a translation is as the addition of a constant vector to each point or as a change in the coordinate system's origin.
A sort of transformation called a translation involves moving each point in a figure the same distance in the same direction.
Translation in geometry refers to shifting a shape into a different position without altering it in any manner. Shape translation is introduced to students in Year 5 by providing them shapes on squared paper, which must then be moved a specific number of squares up, down, left, or right.
1) {f(x) + a} is f(x) shifted up (a) units
2) {f(x) – a} is f(x) shifted down (a) units
3) {f(x + a)} is f(x) shifted left (a) units.
4) {f(x – a)} is f(x) shifted right (a) units.
Let the given function be f(x) = 4x
When exists shifted 7 units to the left, we should apply rule (3) where a = 7
f(x + 7) = 4(x+7) = 4x +28
Therefore, the correct answer is option c) g(x) = 4(x+7).
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Complete the table of values
Answers
Answer:
x = 0 —> y = 0 —> ( 0 , 0 )
x = 1 —> y = – 2 —> ( 1 , – 2 )
x = 5 —> y = – 10 —> ( 5 , – 10 )
x = -3 —> y = 6 —> ( -3 , 6 )
Step-by-step explanation:
x = 0 —> y = -2x = -2(0)=0
x = 1 —> y= -2x = -2(1) = -2
x = 5 —> y = -2x = -2(5) = -10
x = -3 —> y = -2x = -2(-3) = 6
I hope I helped you^_^
A rectangular room is
1.5
times as long as it is wide, and its perimeter is
35
meters. Find the dimension of the room.
The length is :
meters and the width is
meters.
Answers
The dimensions of the room are approximately 7 meters by 10.5 meters.
The length is 10.5 meters and the width is 7 meters.What are dimensions?In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape. A rectangle has length and width as its dimensions that define the area of a rectangle.
Let's start by using algebra to represent the information given in the problem. Let x be the width of the rectangular room, then the length is 1.5 times the width or 1.5x.
The perimeter of a rectangle is the sum of the lengths of all its sides, which can be expressed as:
\(\text{Perimeter} = 2(\text{length} + \text{width})\)
Substituting the values we have for length and width, we get:
\(\rightarrow35 = 2(1.5\text{x} + \text{x})\)
Simplifying the equation, we get:
\(\rightarrow35 = 2(2.5\text{x})\)
\(\rightarrow35 = 5\text{x}\)
\(\rightarrow\text{x}=\dfrac{35}{5}\)
\(\rightarrow\bold{x\thickapprox7}\)
So the width of the room is 7 meters.
To find the length, we can substitute x into the expression we have for the length:
\(\rightarrow\text{Length} = 1.5\text{x}\)
\(\rightarrow\text{Length} = 1.5(7)\)
\(\rightarrow\bold{Length=10.5}\)
So the length of the room is 10.5 meters.
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Pls I don't understand
Answers
The unit rate of the relationship will be 10/3. The correct option is C.
The given equation is,
y = 10/3x + 8
The general form of an equation of the line is,
y = mx + c
here, the slope will be 10/3
Slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for a given change in the independent variable.
The slope of a line is represented by the ratio of the change in the y-axis (vertical) to the change in the x-axis (horizontal) between any two points on the line. It can also be interpreted as the rate of change of the dependent variable with respect to the independent variable.
A positive slope indicates an upward trend, while a negative slope indicates a downward trend. The slope of a line is often denoted by the letter m.
The unit relationship will be 10/3.
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A college statistics class conducted a survey of how students spend their money. They asked 25 students to estimate how much money they typically spend each week on fast food. They determined that the mean amount spent on fast food each week is $31.52 and the median is $32. Later they realized that a value entered as $2 should have been $20. They recalculate the mean and the median. Which of the following is true? Group of answer choices
a. The mean and median will increase.
b. The mean will increase, but the median will remain the same.
c. The mean will stay the same, but the median will increase.
d. Both the mean and median will remain the same.
Answers
Answer:
Option B, The mean will increase, but the median will remain the same.
Step-by-step explanation:
Given
Mean value is \(31.52\) dollars
Median Value is \(32\) dollar.
Mean is the average of all the units in a given set of data. Change in any of the number will change the mean.
Here the mean is 31.25
Total money would be \(31.25 * 25 = 781.25\\\)
A number is changed from 2 to 20 , i.e addition of 18 dollars
the new mean would be 781.25 + 18/25 = 31.97
However, the median value is the value of the unit at the center of the arrangement. Hence, it will not change.
Option B is correct
Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of y plus StartFraction one-half EndFraction equals 3 left-parenthesis x minus 2 right-parenthesis.?
y + 2 =y plus 2 equals StartFraction one-third EndFraction left-parenthesis x plus 3 right-parenthesis.(x + 3)
y – 2 = y minus 2 equals StartFraction one-third EndFraction left-parenthesis x minus 3 right-parenthesis.(x – 3)
y + 3 = y plus 3 equals StartFraction one-third EndFraction left-parenthesis x plus 2 right-parenthesis.(x + 2)
y – 3 = y plus StartFraction one-half EndFraction equals 2 left-parenthesis x minus 3 right-parenthesis.(x – 2)
Answers
The equation that shows the point-slope form of the line passing through (3, 2) with a slope of (1/2) is:
y - 2 = (1/2)(x - 3)
In the point-slope form of a linear equation, the formula is y - y1 = m(x - x1), where (x1, y1) represents a point on the line, and m represents the slope of the line. By substituting the given values into the formula, we can determine the correct equation.
In this case, the given point is (3, 2) and the slope is (1/2). Plugging these values into the formula, we get:
y - 2 = (1/2)(x - 3)
This equation represents the line passing through the point (3, 2) with a slope of (1/2). It is in the point-slope form, which allows us to easily determine the equation of a line based on a given point and slope.
Therefore, the correct equation is y - 2 = (1/2)(x - 3).
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Answer: B
Step-by-step explanation:
Please help!!! Brainliest given!!
1. Which of the following polynomial equations are valid identities?
A. m3 - 1 = (m - 1) (1 + m + m2)
B.(n + 3)2 + 2n = 81 +13
A. Only B
B. Only A
C. Neither A nor B
D. Both A and B
2. Select the polynomial that has (x-3) as a factor.
A. p(x)=x^4-2x^3-25
B. p(x)=x^3+3x^2-2x-6
C. p(x)=x^3-2x^2-4x+3
D. p(x)=x^4-20x-23
3. Find the remainder when x^4-2x^3+x^2-5x+3 is divided by x+1
A. 3
B. 8
C. 12
D. -2
Answers
Answer:
1: A
2: C
3: I have no clue (Sorry)
Step-by-step explanation:
Answer:
1. A2. C3. CStep-by-step explanation:
1. ................................................
A. m^3 - 1 = (m - 1)( 1 + m + m^2)
When we open parenthesis we get both sides equal. YESB. (n + 3)^2 + 2n = 81 + 13
Left side has variables, right side not. NO2. Polynomial that has (x - 3) as a factor
A. p(x)=x^4-2x^3-25
x^4 - 3x^3 + x^3 - 27 + 2x^3(x-3) + (x - 3)(x^2 + 3x + 9) + 2It can' be factored without remainder. NOB. p(x)=x^3+3x^2-2x-6
x^2(x+3) -2(x+3).It has (x+3) as a factor. NOC. p(x)=x^3-2x^2-4x+3
x^3 - 3x^2 + x^2 - 3x - x +3 =x^2(x - 3) + x(x - 3) - (x - 3)It has a (x - 3) as a factor. YESD. p(x)=x^4-20x-23
x^4 - 27 x + 7 x - 23 =x(x-3)(x+3x + 9) + 7( x - 3) - 2It can' be factored without remainder. NO3. x^4-2x^3+x^2-5x+3 is divided by x+1, find remainder
x^4 + x^3 - 3x^3 - 3x^2 + 4x^2 + 4x - 9x - 9 + 12=x^3 (x + 1) - x^2(x + 1) + 4x(x + 1) - 9(x + 1) + 12The remainder is 12. Option C
Select the correct answer.
Which number has a repeating decimal form?
b.11/25
c.3/20
d.2/6
Answers
Answer:
d.2/6 has a repeating decimal form
Answer:
[D. 2/6]
Step-by-step explanation:
For edmentum users (Please check your answers before placing the answer to avoid low grades and misconfusion.)
A random sample of 10 employees of a company was selected to estimate the mean one-way commute time for all employees at the company. The mean and standard deviation of the sample were 38 minutes and 6 minutes, respectively. Assuming all conditions for inference are met, which of the following is the margin of error, in minutes, for a 95 percent confidence interval for the population mean one-way commute time?
1.812 (6/√10)
1.833 (6/√10)
1.96 (6/√10)
2.228 (6/√10)
2.262 (6/√10)
Answers
Margin of error can be calculated by using sample size, standard deviation and z-value. Here the margin of error is found to be 2.262×(6/√10). So option 5 is correct.
The values that are given are,
Mean = 38
Standard deviation= 6
Confidence interval = 95%
Sample size = 10
Margin of error is the degree of deviation from the mean value. The maximum acceptable error can be found out using this. It can be calculated using the formula,
E = \(z_{y}\) × σ/√n
Here the value corresponding to 95% in the z-table is 2.262
So the margin of error, E = 2.262× (6/√10)
So option 5 is correct.
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Skylar goes to a school which has 1000 students in it.She asks 40 random students whether they like the new 8.30 am start to the day. 30 of them say ‘no’ they do not like it. Use this information to estimate how many students in the whole school dislike the 8.30 am start
Answers
Answer:
Step-by-step explanation:
30 out of 40 could be used to estimate that 750 out of 1000 would say 'no'
30/40 equals 3/4
3/4 of 1000 is 750
Use the matrix tool to solve the system of equations. Choose the correct
ordered pair.
4x - 7y = -5
-6x+ 5y = 2
PLEASE HELP
Answers
Graph 5x + 3y = 15 on a graph
Answers
Answer is y=-5/3x+5
Brainliest?
Please help me thank you I appreciate it
Answers
Answer:35 degrees
Step-by-step explanation:
Answer:
angle KLN° + angle NLM° =180° ( l.p)
angle NLM°=180°-145°
angle NLM=35°