in the given figure ab cd and p q. find the measure of x y and z
Answers
The measures of x, y and z are 40⁰, 90⁰ and 50⁰
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
We know that co-interior angles are supplementary.
∠APQ+∠CPQ=180⁰
x+∠CPQ=180⁰
x+140⁰=180⁰
x=40⁰
∠BPR+∠PRD=180⁰
z+130⁰=180⁰
z=50⁰
Now, angles x, y and z form a line, hence they sum up to 180∘.
x+y+z=180⁰
40⁰+y+50⁰=180⁰
y=90⁰
Hence, the measures of x, y and z are 40⁰, 90⁰ and 50⁰
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The question is not complete, similar kind of question is given below.
In the given figure, AB || CD. Find the measure of x, y and z.
Related Questions
In the diagram below,
m∠CIH=100 and m∠BGD=42 Find m∠FHG.
Answers
m∠FHG is given as 120 degrees
How to solve for the angle100 + ∠FJG = 180 degrees
∠FJG = 80 degrees
∠BGD = ∠AGJ They are vertically opposite
∠HGI + ∠GIH + ∠IHG = 180
40 + 80 + ∠IHG = 180
∠IHG = 60 degrees
∠IHG + m∠FHG = 180 degrees
60 + m∠FHG = 180
m∠FHG = 120 degrees
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Real World Application
Cody and Aliyah are selling wrapping paper for a school fundraise.
Customers can buy rolls of plain wrapping paper and rolls of
holiday wrapping paper. Cody sold 5 rolls of plain wrapping paper
and 8 rolls of holiday wrapping paper for a total of $174. Aliyah
sold 5 rolls of plain wrapping paper and 10 rolls of holiday
wrapping paper for a total of $210. What is the solution to the
system of equations? What is the cost each of one roll of plain
wrapping paper and one roll of holiday wrapping paper?
Roll of plain wrapping paper: $
Roll of holiday wrapping paper: $
Answers
Using a system of equations, the unit cost of one roll of plain wrapping paper and one roll of holiday wrapping paper is as follows:
Roll of plain wrapping paper: $6.00Roll of holiday wrapping paper: $18.What is a system of equations?A system of equations is two or more equations solved at the same time, concurrently, or simultaneously.
A system of equations is otherwise known as simultaneous equations.
Plain Wrapper Holiday Wrapper Total Cost
Cody sales 5 8 $174.00
Aliyah 5 10 $210.00
Let the unit cost of Plain Wrapper = x
Let the unit cost of Holiday Wrapper = y
Equations:5x + 8y = 174... Equation 1
5x + 10y = 210... Equation 2
Subtract Equation 1 from Equation 2:
5x + 10y = 210
-
5x + 8y = 174
2y = 36
y = 18
y = $18
Substitute y = 18 in either equation:
5x + 8y = 174
5x + 8(18) = 174
5x +144 = 174
5x = 174 - 144
5x = 30
x = 6
x = $6
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three vectors have equal magnitudes and make 120° with each other. we can say that
Answers
the magnitude of the resultant is [tex]\sqrt{2}[/tex] times the magnitude of each individual vector, not one-third.
No, that is incorrect. The magnitude of the resultant of three vectors having equal magnitudes and making an angle of 120 degrees with each other is not one-third the magnitude of the component vectors.
The magnitude of the resultant of three vectors depends on the angle between them, as well as their magnitudes. In general, the magnitude of the resultant of three vectors can be calculated using the law of cosines, which states that the square of the magnitude of the resultant (R^2) is equal to the sum of the squares of the magnitudes of the individual vectors ([tex]A^2, B^2, and C^2[/tex]), plus twice the product of the magnitudes of two of the vectors multiplied by the cosine of the angle between them.
For three vectors of equal magnitude (A = B = C = m), the magnitude of the resultant can be calculated as:
[tex]R^2 = 3m^2 + 2m^2 * cos(120) = 3m^2 - m^2 = 2m^2[/tex]
[tex]R = \sqrt{2} * m[/tex]
Therefore, the magnitude of the resultant is sqrt(2) times the magnitude of each individual vector, not one-third.
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Question: Three Vectors Have Equal Magnitudes And Make 120° With Each Other. We Can Say That The Magnitude Of The Resultant Is One-Third The Magnitude Of The Component Vectors. The Resultant Is Zero. The Magnitude Of The Resultant Is Equal To The Magnitude Of The Component Vectors. The Magnitude Of The Resultant Is More Than Three Times The Magnitude Of Each component Vector.
PLEASE HELP !!!!!
Function g is graphed here. If function f is the parent exponential function (). what is the equation of transformed function g in terms of f?
Answers
Therefore , the solution of the given problem of function comes out to be f(x) = 1.1f(x + 1) is the solution for the graph.
What is function?The study of mathematics includes looking at numbers, their variables, the world around us, buildings, and both real and imagined places. An illustration of the relation between the quantity of inputs and the appropriate outputs for each is called a function. A function, simply described, is a group of inputs who, when combined, provide distinct outputs for each input. Every function has a city, province, or scope—also referred to as a domain—assigned to it. Functions are usually indicated with the letter f. (x). The input contains an x.
Here,
Given:
The parent function f(x) is translated left by one unit and slightly stretched vertically to form g(x).
=>g(x) is:
=> f(x) = 1.1f(x + 1)
Thus , f(x) = 1.1f(x + 1) is the given function which is graphed here.
Therefore , the solution of the given problem of function comes out to be f(x) = 1.1f(x + 1) is the solution for the graph.
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Show how 15 + 5n and 5(3 + ) are equivalent
Answers
Answer: 5n+30
( The problem was incomplete on my end )
( Hope this helps )
Match the exponent expression with it's correct solution.
Answers
According to algebra property of power of a power, the following results are listed below:
Case 1: (x⁵)³ = x¹⁵ (Correct choice: 1)
Case 2: (x⁸)⁷ = x⁵⁶ (Correct choice: 4)
Case 3: (x⁷)¹⁰ = x⁷⁰ (Correct choice: 2)
Case 4: (x¹⁴)³ = x⁴² (Correct choice: 3)
How to apply power properties
In this question we find four cases of power of a power, whose solution is described by the following algebra property:
(xᵃ)ᵇ = xᵃᵇ, where x, a and b are real numbers.
Now we proceed to determine the solution to each case:
Case 1
(x⁵)³ = x¹⁵
Case 2
(x⁸)⁷ = x⁵⁶
Case 3
(x⁷)¹⁰ = x⁷⁰
Case 4
(x¹⁴)³ = x⁴²
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Juan went to the store to buy a plant for his mother, but forgot to ask which kind to get. Out of 30 plants, six of them are a kind that his mother would want. If Juan chooses one randomly, what is the probability that he will choose a kind that his mother would want? You will need to change your probability to a decimal and then to a percent.
Answers
The probability that Juan will choose a kind of plant his mother would want is 6/30, which is equal to 0.2 or 20%
To calculate the probability that Juan will choose a kind of plant his mother would want, out of 30 plants, six of them are a kind that his mother would want, first divide the number of plants his mother would want (6) by the total number of plants (30). This will give you a decimal, 0.2. To turn this decimal into a percent, multiply it by 100. This will give you 20%, or a 20% chance of Juan choosing a kind of plant his mother would want. To summarize, therefore, the probability that Juan will choose a kind of plant his mother would want is 0.2 or 20%.
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last year, 20 percent of all teenagers purchased a new iphone. this year, a sample of 260 randomly chosen teenagers showed that 39 had purchased a new iphone. to test whether the percentage has decreased, the p-value is:
Answers
The p-value is 0.063, which indicates that there is not strong evidence to reject the null hypothesis that the percentage has stayed the same.
The p-value can be calculated by using a one-proportion z-test. The null hypothesis would be that the percentage has stayed the same from last year, and the alternative hypothesis is that the percentage has decreased.
The formula for the z-score is (x-p)/√(p(1-p)/n), where x is the observed proportion (39/260), p is the expected proportion (0.20), and n is the sample size (260). The p-value is then calculated using the z-score and the cumulative distribution function.
Therefore p-value, in this case, is 0.063, which indicates that there is not strong evidence to reject the null hypothesis that the percentage has stayed the same.
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find the radius and diameter of a circle whose area is 15400 mm²
Answers
Solution:
Area=15400mm^2
Now,
Area=pi×r^2
or,15400=22/7×r^2
or,15400×7=22×r^2
or,107800=22r^2
or,107800/22=r^2
or,4900=r^2
or,r=70
Also,
Diameter (d)=r×2
=70×2
=140
q. The graph shows the change in temperature
in Monterey, CA over several hours. Is the
between the number of hours and
relationship between
temperature linear or non-linear? Explain.
Answers
Answer:
Non-linear
Explanation below
Step-by-step explanation:
The relationship is clearly non-linear
If it where a linear relationship then the temperature change per hour would be constant throughout the time period when the observations were made.
The resultant graph would be a straight line
Here the graph rises at a decreasing rate until it almost flattens out. This means the temperature reaches a maximum and stays at that maximum.
Which expression does not have a solution of 12, if w = 4?
Options :
3 w
w + 8
4 w
16 - w
Answers
Elsa is building a fence around her garden. For every 4 feet of fencing, the cost is $2
Complete the table below showing the length of the fence and the cost.
Length of fencing (feet)
Cost ($)
Explanation
Pls help
Answers
Answer:
Step-by-step explanation:
4ft : $24 -> 1ft = $6
so 7ft = 6X7 = $42
and 6X10 = $60
histograms can be used to multiple select question. observe the spread or the variability of the data. observe individual data points. construct a pie chart. determine the shape of the data.
Answers
Histograms are commonly used to visualize the distribution of a dataset by grouping the data into bins and representing the frequency of each bin by the height of a bar.
They are useful for observing the spread or variability of the data and determining the shape of the data, such as whether it is symmetrical or skewed. They cannot be used to observe individual data points, but they provide a good visual representation of the overall pattern of the data. Histograms are not appropriate for multiple choice questions as they do not display individual data points in a clear manner. To display parts of a whole, pie charts are a better choice as they show the proportion of each category as a sector of a circle
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A gardener has 600ft of fencing to fence in a rectangular garden. One side of the garden is boarded by a river and so it does not need any fencing.
What dimensions would guarantee that the garden has the greatest possible area?
Shorter side:
Longer side:
Greatest possible area:___ft^2 (square feet)
Answers
Answer:
To find the dimensions that would guarantee the greatest possible area, we can use the formula for the area of a rectangle, which is A = l * w, where l is the length and w is the width.
Since one side of the garden is already boarded by a river, we only need to use 600ft of fencing for the other three sides. This means that the length and width of the garden must add up to 600ft. We can write this as:
l + w = 600
Since we want to find the dimensions that would give us the greatest possible area, we want to maximize l * w. Using the formula for the area of a rectangle, we can write this as:
A = l * w = l * (600 - l) = 600l - l^2
To find the maximum area, we can differentiate this equation and set it equal to zero:
dA/dl = 600 - 2l = 0
Solving for l, we get:
l = 300/2 = 150ft
So, the shorter side is 150ft and the longer side is 450ft (600 - 150).
Finally, we can use the formula for the area of a rectangle to find the greatest possible area:
A = 150 * 450 = 67,500ft^2
Therefore, the greatest possible area for the garden is 67,500ft^2 when the shorter side is 150ft and the longer side is 450ft.
Step-by-step explanation:
A square has an area of 64 square meters. What is the lenht of each side
Answers
Answer:
8 m
Step-by-step explanation:
All the sides of a square are equal.
let x = length of one side
A = x² = 64 m²
√x² = x = √64 = 8
PLEASE HELP ME ASAP
Answers
Answer:
the answer is E
Step-by-step explanation:
your welcome
−3/4(x+2)=[tex]-3/4(x+2)=6[/tex]6
Answers
The value of x for the equation is -10.
What is simplification?To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common factors from the numerator and denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.
Given equation,
-3/4(x + 2) = 6
both sides multiply by -4/3
-3/4(x + 2) * -4/3 = 6 * -4/3
x + 2 = -8
subtract 2 from both sides
x + 2 - 2 = -8 - 2
x = -10
Hence the value of x is -10.
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how far away is the puddle from the house? angle of depression is 40 degree
Answers
Answer: 29.8 feet
Step-by-step explanation:
To solve this, the first step is to make the imaginary triangle (look at the picture below). Now, we use the basic trigonometry functions. Since we have to find tge base part of the triangle (which is the adjacent one to the angle, and we already have the opposite to the angle. So, now we know we have to use the tan ratio. We now solve it with the following method:
[tex]tan(Angle) = \frac{Opposite}{Adjacent} \\[/tex]
Now we sub in our values and use the calculator to solve it:
[tex]tan(40) = \frac{25}{x}\\\\x = \frac{25}{tan(40)} \\\\x = 29.8 (1 d.p)[/tex]
Create a flowchart proof of a two column proof. If HG = KG and HI || KJ, prove that HI = KJ
Answers
Answer:
Both triangles are congruent by S A S congruent.
Step-by-step explanation:
Congruent triangles:In ΔHIG & ΔKJG,
HG = KG Given
∠GHI ≅ ∠GKJ Alternate interior angles, HI // KJ and KH is transversal
HI = KJ Given
ΔHIG ≅ ΔKJG Side Angle Side congruency
A right triangle is drawn on the coordinate plane. Which is a dilation of this triangle with respect to the origin by a factor of ?
Answers
The correct response is A since this triangle has a dilatation of (0,0),(1,0),(1,1)) by a factor of 1/3 with respect to the origin.
What is the process of dilation?A figure will dilate if its sides are scaled (multiplied) by the same amount. The scale factor of that dilatation is the name given to that figure.
It is also known as scaling a figure, but since coordinates are involved, it also requires the center of a dilation, which is similar to a pinned point and remains in the same location after dilation.
It appears as though we are adjusting the size of the figure (or leaving it the same when the scale factor is 1).
According to question:The positions (0, 0), (3, 0), (3,3)
1/3 scale factor
Now
the GPS coordinates;
(0,0),(1,0),(1,1)
Thus, required dilation is (0,0),(1,0),(1,1).
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Complete question:
A right triangle is drawn on the coordinate plane. Which is a dilation of this triangle with respect to the origin by a factor of 1/3?
Answer:
The positions (0, 0), (3, 0), (3,3)
1/3 scale factor
Now
the GPS coordinates;
(0,0),(1,0),(1,1)
Thus, required dilation is (0,0),(1,0),(1,1).
Step-by-step explanation:
option a
Gerry is shopping for clothes at the mall. He buys 4 new shirts for $6. 0. What is the unit rate for the shirts
Answers
The unit rate of the shirt is $1.50 per shirt.
Unit rate is a measure of the relationship between two quantities, where the second quantity is expressed as a unit of one. It is often expressed as a ratio, with the unit of the second quantity being 1. Unit rate helps us compare different quantities and make sense of their relative sizes.
The unit rate for the shirts can be calculated by dividing the total cost by the number of shirts. In this case, the unit rate would be:
$6.00 ÷ 4 shirts = $1.50/shirt
So, the unit rate for the shirts is $1.50 per shirt.
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help me baaaaaaaaaaaaaaaalls
Answers
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Answer:
The correct scale faction the first pentagon dilated by to create the second pentagon is 1.25.
Step-by-step explanation:
Since the second pentagon is a dilation of the first pentagon, we can conclude these pentagons are similar, meaning the shape retained all of its previous angles, and all the corresponding sides are dilated by a common scale factor. Since we know the values of a pair of corresponding sides, we can use those to find the scale factor of dilation.
The corresponding side of the original pentagon is 4 units, and the corresponding side of the dilated pentagon is 5 units. Since the first pentagon dilated to become the second, in order to solve the scale factor the pentagon dilated by, we'd have to divide the side given on the second pentagon by the corresponding side of the first, which will be 5 ÷ 4 = 1.25. Therefore, that will be the scale factor the pentagon dilated by.
Have a great day! Feel free to let me know if you have any more questions :)
what is 10% of £7.50
Answers
Answer: 0.75 :D Hope this helps
Step-by-step explanation:
4. VOLUME The volume of one column of the Lincoln Memorial is approximated by the expression (x³ +37x²-110x + 400). If the height of the column is x + 40 feet, find the expression that approximates the area of the base of the column in terms of x and pi.
Answers
To find the area of the base of the column, we need to find the expression for the radius of the column, r, in terms of x.
The volume of a column can be calculated as V = πr²h, where r is the radius, h is the height, and π is pi.
Using the given expression for the volume of the column, we can write:
πr²h = x³ + 37x² - 110x + 400
Since h = x + 40, we can substitute to get:
πr²(x + 40) = x³ + 37x² - 110x + 400
Dividing both sides by π(x + 40) gives us:
r² = (x³ + 37x² - 110x + 400) / (π(x + 40))
Finally, taking the square root of both sides gives us the expression for the radius in terms of x:
r = √((x³ + 37x² - 110x + 400) / (π(x + 40)))
So, the expression that approximates the area of the base of the column in terms of x and π is:
A = πr² = π √((x³ + 37x² - 110x + 400) / (π(x + 40)))²
Solve the following
i} p+ 3 = 205 ii} 2x/7 = 4 iii} 3y - 6 = 9
Answers
Answer:
[tex]1) p = 205 - 3 = 202 \ 2)2x \div 7 = 4 \\ 2x = 28 \\ x = 14 \\ \\ 3)3y - 6 = 9 \\ 3y = 9 + 6 \\ 3y = 15 \\ y = 5[/tex]
2. after 15 hours and 12 minutes a tsunami from krakatau hit port elizabeth, south africa, 7546 kilometers away. find the average speed of the tsunami.
Answers
The average speed of the tsunami was approximately 496.45 km/hr.
To find the average speed of the tsunami, we need to know the distance it traveled (7546 kilometers) and the time it took to travel that distance (15 hours and 12 minutes).
First, we need to convert the time to a single unit of measurement. For this calculation, we'll use hours. To do this, we'll convert the minutes to hours:
15 hours + 12 minutes ÷ 60 minutes/hour
= 15.2 hours
Next, we can divide the distance traveled by the time it took:
7546 km ÷ 15.2 hours
= 496.45 km/hr
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2n × r × 2 × 1 × s
for n = 2, r = 2, and s = 1.
Answers
What is the arc measure of major arc BAC in degrees?
Answers
Answer:
arc BAC = 276°
Step-by-step explanation:
the sum of the angles around point D is 360°
sum the central angles and equate to 360
7n + 12 + 6n + 13n - 16 = 360
26n - 4 = 360 ( add 4 to both sides )
26n = 364 ( divide both sides by 26 )
n = 14
Then
∠ ADB = 7n + 12 = 7(14) + 12 = 98 + 12 = 110°
∠ ADC = 13n - 16 = 13(14) - 16 = 182 - 16 = 166°
• the arc of a circle is equal to the central angle it subtends
arc BA = ∠ ADB = 110°
arc AC = ∠ ADC = 166°
Then
arc BAC = arc BA + arc AC = 110° + 166° = 276°
streets that form a square block. The length of each side of the block is 221 m. Find the area of the square defined by this city block.
Answers
The area of the square block is 48,881 m2, which is calculated by multiplying the length of each side (221 m) by itself.
The area of a square can be calculated by multiplying the length of one side by itself. In this case, the length of each side is 221 m. To find the area of the square block, we need to multiply 221 m by itself. This gives us 48,881 m2 as the final answer. To summarize, the area of the square can be found by multiplying the length of one side by itself. In this case, the length of each side of the block was 221 m, so 221 m multiplied by 221 m results in a total area of 48,881 m2.
The complete question: In one city there are four straight streets that form a square block. The length of each side of the block is 221 m. Find the area of the square defined by this city block.
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Laura ha comprado una falda y una blusa por 66 euros ambas tenian el mismo precio pero en la falda le han hecho un 20% de rebaja y en la blusa solo un 15% ¿cuanto costaba cada prenda?
Answers
The cost of the skirt and blouse after the discount would be -
$52.8 and $56.1 respectively.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Laura has bought a skirt and a blouse for 66 euros, both had the same price but they have given her a 20% discount on the skirt and only 15% on the blouse.
The cost skirt would be -
${x} = 66 - {20% of 66}
${x} = 66 - {20/100 x 66}
${x} = 66 - {66/5}
${x} = 66 - 13.2
${x} = 52.8
The cost of blouse would be -
${y} = 66 - {15% of 66}
${y} = 66 - {15/100 x 66}
${y} = 66 - {3/20 x 66}
${y} = 66 - 9.9
${y} = 56.1
Therefore, the cost of the skirt and blouse after the discount would be -
$52.8 and $56.1 respectively.
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{Question in english -
Laura has bought a skirt and a blouse for 66 euros, both had the same price but they have given her a 20% discount on the skirt and only 15% on the blouse. How much did each item cost??