The value of y so that WX ⊥ YZ is y = 4 .
In the question ,
it is given that
the line WX is perpendicular to line YZ
and the end points of WX is W(2,-3) and X(-4,9)
and the end points of YZ is Y(5,y) and Z(-1,1) .
let the slope of line WX = m₁
and slope of line YZ = m₂ .
we know that when two lines are perpendicular , then
m₁ * m₂ = -1
m₁ = (9-(-3))/(-4-2)
and m₂ = (1-y)/(-1-5)
Substituting the values of m₁ and m₂ in the equation m₁ * m₂ = -1 ,
we get
(9-(-3))/(-4-2) * (1-y)/(-1-5) = -1
(9+3)/(-6) * (1-y)/(-6) = -1
12/(-6) * (1-y)/(-6) = -1
-2* (1-y) = 6
-2 + 2y = 6
2y = 6+2
2y = 8
y = 4
Therefore , the value of y is = 4 .
The given question is incomplete , the compete question is
Given W(2, -3) X(-4, 9) Y(5, y) and Z(-1, 1) . find the value of y so that WX ⊥ YZ ?
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(2x - 5)(x-3)
Please help!!
Step-by-step explanation:
(2x - 5)(x-3)
FOIL method: multiply first, outer, inner, and last of the pairs
[tex]2x^2-6x-5x+15\\\\2x^2-11x+15[/tex]
Answer:
Step-by-step explanation:
A shipping container will be used to transport several 150-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 6800 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine xx, the number of 150-kilogram crates that can be loaded into the shipping container.
The greatest number of 150-kilogram crates that can be loaded into the shipping container are 138
Greatest weight that can be loaded = 27500 kilograms
Weight of each crate = 150 kilogram
Weight of other shipments = 6800 kilograms
Let c be the greatest number of 150 kilogram crates that can be loaded.
The required inequality
27500 ≥ 6800 + 150c
27500 - 6800 ≥ 150c
20700 ≥ 150c
c ≥ 20700/150
c ≥ 138
Hence, the maximum number of crates are 138.
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Please solve these radical expressions
The simplified form of given radical expression :
1) √216k⁴ = 6√6k²
2) √28x³y³ = 2xy√(7xy)
3) √192n³ = 8n√(3n)
4)∛40n² = 2∛n²n^(2/3)
5) ∛216x³ = 6x
6) ⁴√128x⁶y⁸ = 2xy8^(1/4)√(yx)
7) √252a³b^4 = 6ab²√(7a)
We need to solve given radical expressions.
1) √216k⁴
= √216 × √k⁴
= √(6 × 36) × √(k²)²
= 6√6 × k²
= 6√6k²
2) √28x³y³
= √(7 * 4) × √x³ × √y³
= 2√7 * x√x * y√y
= 2√7 * xy√(xy)
3) √192n³
= √(64 × 3) * √n³
= 8√3 * n√n
= 8n√(3n)
4)∛40n²
= ∛(8 × 5) * ∛n²
= ∛2³ * ∛5 * ∛n²
= 2∛n²n^(2/3)
5) ∛216x³
= ∛216 * ∛x³
= ∛6³ * ∛x³
= 6 * x
= 6x
6) ⁴√128x⁶y⁸
= ⁴√128 * ⁴√x⁶ * ⁴√y⁸
= ⁴√(16 × 8) * x(⁴√x²) * y(⁴√y²)
= 2 * 8^(1/4) * xy (x²y²)^(1/4)
= 2xy8^(1/4)√xy
7) √252a³b^4
= √(36 × 7) * √a³ * √b^4
= 6√7 * a√a * b²
= 6ab²√(7a)
Therefore, the simplified form of given radical expression :
1) √216k⁴ = 6√6k²
2) √28x³y³ = 2xy√(7xy)
3) √192n³ = 8n√(3n)
4)∛40n² = 2∛n²n^(2/3)
5) ∛216x³ = 6x
6) ⁴√128x⁶y⁸ = 2xy8^(1/4)√(yx)
7) √252a³b^4 = 6ab²√(7a)
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Marie will earn $15 Per hour at a new job. During training, she will earn $10 per hour.
What percent of Marie's regular hourly rate will she earn during training
The percent that Marie will earn during her training is 66.67%.
What is percentage?
Percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Given,
She earns working in new job = $15
She earns while training = $10
percentage she will earn during her training
= earing during training/earning during job multiplied by 100.
= 10/15(100)
=66.67%
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The stemplot displays 26 students' scores on a 90-point
statistics test.
Which of the following best describes the shape of the distributor test scores
Bimodal and symmetric
Slightly skewed left
Slightly skewed right
Heavily skewed right
Answer:
I think C is correct
Step-by-step explanation:
I am not really sure
a political candidate has asked you to conduct a poll to determine what percentage of people support her. if the candidate only wants a 2% margin of error at a 90% confidence level, what size of sample is needed?
Size of sample needed to determine the percentage of people with give margin of error is equal to 1691.
As given in the question,
Margin of error = 2%
= 0.02
Sample proportion 'p' = 0.5
⇒ (1 - p) = 1 - 0.5
= 0.5
Let 'n' represents the sample size
Z- value at confidence interval 90% = 1.645
Formula used
Margin of error = z-value √ [p( 1-p)/n]
Substitute the value we get,
0.02 = 1.645 √ (0.5)(0.5)/n
Squaring on both the side
0.0004 = 2.706025 ( 0.25/n)
⇒ n = ( 2.706025 × 0.25 )/ 0.0004
⇒ n = 1691.26
⇒ n ≈ 1691
Therefore, size of sample needed with given margin of error is equal to 1691.
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the mean of this sample is 264.4 yards. his driving distance is known to be normally distributed with a population standard deviation of 20 yards. test jean's claim that jack's driving distance is less than 275 yards at a 0.05 significance level. calculate the test statistic to 2 decimal places.
After solving, the test statistic value of z is -2.65.
In the given question,
Sample Mean x=264.4
Population standard deviation σ=20
sample size (n) = 25
significance level α=0.05
To test Jean's claim that Jack's driving distance is less than 275 yards
The null and alternative hypothesis are
H(0): μ=275
H(α): μ<275
Test Statistic Z is:
Z = (x-μ)/(σ/√n)
Z = (264.4-275)/(20/√25)
Z = -10.6/(20/5)
Z = -10.6/4
Z = -2.65
Hence, the test statistic value of z is -2.65.
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The right question is:
Jack tells Jean that his average drive of a golf ball is 275 yards. Jean is skeptical, she thinks he has overstated is driving distance and asks for substantiation. So Jack takes a random sample of 25 of his drives. The mean of this sample is 264.4 yards. His driving distance is known to be normally distributed with a population standard deviation of 20 yards. Test Jean's claim that Jack's driving distance is less than 275 yards at a 0.05 significance level. Calculate the test statistic to 2 decimal places.
if you have 2, 6 sided cubes and you can add any numbers to them, which numbers do you put on them so that you can display every day of the month?
Answer: its 12 and 8 10 12 14 16 either of those
Step-by-step explanation:
Lines f and g are graphed on top of each other below.Does the system of linear equation on the below graph represent infinitely many solution?
True or False
The required answer is True.
What are Graphing Systems of Linear Equations?
There exists an endless number of valid solutions for both equations if the graphs of the equations are identical.
For the given graph,
The equations are simply multiples or rearrangements of one another if graph lines meet. Every set of numbers that satisfies one of the equations also satisfies the other.
Hence, the system of the linear equation on the below graph represents infinitely many solutions and it is True.
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What is mean absolute deviation in math example?.
The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data collection. A measure of variance in a data collection is the mean absolute deviation. We can determine how "spread out" the values in a data set are by looking at the mean absolute deviation.
What is mean absolute deviation?The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data collection. A measure of variance in a data collection is the mean absolute deviation. We may determine how "spread out" the values in a data collection are by looking at the mean absolute deviation. Take the absolute value of each digit in the data set, then deduct the mean. Next, add up the absolute values. The mean absolute deviation is then calculated by dividing the aforementioned sum by the total number of values in the data set. Finally, tenths should be rounded.
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Given (x – 7)2 = 36, select the values of x
Answer:
A. x = 13
B. x = 1
And the next equation answers are:
C. x = 1-5√2
D. x = 1+5√2
Step-by-step explanation:
Just took it. Edg 2020. Hope this helps :)
sin A = 3/5, cos B = 8/17 and A and B are acute angles, determine the exact value of tan A tan B
According to the Pythagoras theorem, the exact value of tan A is 3/4 and the value of tan B is 15/8
Pythagoras Theorem
Pythagoras theorem defines that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“
Given,
Here we have the value of sin A = 3/5, cos B = 8/17 and A and B are acute angles.
And we need to find the value of tan A and tan B.
According to the Pythagoras theorem,
If the value of sin A = 3/5, then we have the value of the right angle triangle of hypotenuse and the opposite.
So, the adjacent value is calculated based on the theorem is,
=> 5² = ad² + 3²
=> 25 = ad² + 9
=> ad² = 25 - 9
=> ad = √16
=> ad = 4
Therefore, the value of tan A is written as,
=> tan A = opposite/ adjacent
=> tan A = 3/4
Similarly, the value of tan B is calculated as,
If the value of cos B = 8/17, then we have the value of the right angle triangle of hypotenuse and the adjacent.
So, the opposite value is calculated based on the theorem is,
=> 17² = 8² + op²
=> 289 = 64 + op²
=> op² = 289 - 64
=> op = √225
=> op = 15
Therefore, the value of tan B is written as,
=> tan B = opposite/ adjacent
=> tan B = 15/8
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What is the value of x?
Enter your answer in the box.
X =??
Answer:
x = 9
Step-by-step explanation:
Triangles are similar due to AAA (all angles are congruent due to shared angle and corresponding angles). Thus, the sides are proportional, and we can set up a proportion with corresponding sides:
9/(72 + 9) = (3x - 20)/(3x - 20 + 56)
9/81 = (3x - 20)/(3x + 36)
(1/9) * (3x + 36) = 3x - 20
(3x + 36)/9 = 3x - 20
3x + 36 = (3x - 20)*9
3x + 36 = 27x - 180
36 + 180 = 27x - 3x
216 = 24x
x = 9
Communicate and Justify In Example 5, Pedro finds applesauce that comes in packages of 8, but now he finds juice bottles only in packages of 3. Will the LCM change? Explain.
*If answer given on next 3-8 hours will give brainliest.*
Yes, the LCM changed for the two terms. Because there is no common term in the 3 and 8.
What is LCM?It is defined as the common number of two integers, which is the lowest number that is a multiple of two or more numbers. The full name of LCM is the least common multiple.
It is given that Pedro finds applesauce that comes in packages of 8, but now he finds juice bottles only in packages of 3.
The factor of 8,
8=2×2×2×1
The factor of 3,
3=3×1
There are no common terms in both the given integers as a result the LCM changes.
Thus, the LCM changed for the two terms. Because there is no common term in the 3 and 8.
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martin is making four milkshakes if the recipe calls for 2/3 cup of milk how many cups of milk does he need
Answer:
[tex]2\frac{2}{3}[/tex] cups of milk
Step-by-step explanation:
The problem is [tex]\frac{2}{3}[/tex] of a cup per milkshake times 4 milkshakes. Keeping in mind that we can write any number over 1 without changing its value, our math problem is:
[tex]\frac{2}{3}[/tex] × [tex]\frac{4}{1}[/tex]
We multiply numerator times numerator and denominator times denominator to get [tex]\frac{8}{3}[/tex]. If we convert that improper fraction to a mixed number fraction we get [tex]2\frac{2}{3}[/tex].
The number of cups of milk would be 2 2/3 needed in the four milkshakes.
What is Ratio?A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other
We have been given that martin is making four milkshakes. The recipe calls for 2/3 cup of milk.
We have to determine the number of cups of milk he needs
Let the number of cups of milk would be x in the four milkshakes.
As per the given situation, we can write the ratio would be as:
1 milkshakes : 2/3 cup of milk = 4 milkshakes : x cup of milk
⇒ 1 / (2/3) = 4/x
Reciprocal the term in the numerator,
⇒ 3/2 = 4/x
Apply the cross-multiplication operation,
⇒ 3x = 8
⇒ x = 8/3
⇒ x = 2 2/3
Thus, the number of cups of milk would be 2 2/3 in the four milkshakes.
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2.085x10^5 in standard form
Answer:
?jsp?3×4=5/6(9÷43)=2×3=45/_<7<78>(56)
What is the average of 17 multiple of 7?.
The average of 17 multiple of 7 is 63 average is computed by adding a set of numbers and then dividing by the total number of those numbers.
Do you mean total by average?By dividing the total number of values by the total number of numbers, the average can be computed. A mean is the mathematical average of a set of two or more data items. Common names for average include mean and mathematical mean. The term "mean" simply represents the average of the sample.
How would you define average?
The average of a list of data represents the fundamental value of a group of data mathematically. The ratio of the total number of data points to the total number of units in the list is how it is technically defined. In statistics, the term "mean" also denotes the average of a certain set of numerical data.
To calculate average=
7+14+21+28+35+42+49+56+63+70+77+84+91+98+105+112+119/17
= 1071/17
=63
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Erin recycles milk bottles, soda cans, and newspapers. If the following items are in the trash bin, what percent of the items can be recycled?
2 milk bottles, 1 banana peel, 3 newspapers, 2 soda cans, 12 apple cores
A. 35%
B. 7%
C. 100%
D. 25%
Option A. The percentage of items that can be recycled is 35%
How to solve for percentageWe are first to determine the objects that can be recycled and those that cannot be recycled.
The recyclable objects that we have here are:
milk bottles = 2
soda cans = 2
newspapers = 3
The total number of recyclables = 7
The items that can not be recycled are:
1 banana peel
12 apple cores
The total number of recyclables = 13
The total number of objects = 7 + 13 = 20
The percentage of recyclables would be 7 / 20 * 100
= 35%
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A toy company makes wooden blocks. A carton holds 87 blocks.
How many blocks can 15 cartons hold?
The cartons can hold
blocks.
The cartons hold 1305 blocks.
What are Comparing quantities?
- Finding an unknown quantity that has a relationship with a certain condition associated to it is the process of comparing quantities.
- One or more quantities with their units will be provided to us, and we will be required to determine the value of the same quantity in other units (i.e. in higher values or in lower values).
We given that,
A carton holds 87 blocks.
It means, 1 carton holds = 87 blocks
So find 15 cartons holds how much of blocks.
15 cartons holds = 15 * 87
= 1305 blocks
Hence, we can say that the cartons hold 1305 blocks.
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If the area of a circle is 114 cm2, what is its circumference?
Answer: ≈ 18.91 cm
Step-by-step explanation:
r²= 114 ÷ pi/3.14 = 5700/157
r = √r²
≈ 6.025
Circumference = r × pi/3.14
≈ 18,91 cm
calculate the number of waffles produced if you start with 15 eggs, assuming you have enough of all other ingredients? given: 4 cups flour 6 eggs 2 tbsp oil 8 waffles
The number of waffles can be made from 15 eggs are, 20 waffles.
the waffles can be calculates as follows
4 cups of fluor + 6 eggs +2 tbsp oil = 8 waffles
we need 6 eggs to make 8 waffles
So, the waffles can we make from 15 eggs = [tex]\frac{8}{6} X 15 = 20[/tex] waffles
Hence, the number of waffles can be made from 15 eggs are 20 waffles.
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the basis for a statistical process control chart is a(the) multiple choice process capability. sampling distribution. control limit. sample range. sample mean.
The correct statement is 'the basis for a statistical process control chart is a(the) sampling distribution'
In this question, we have been given a statement.
We need to select the correct option to complete the given statement.
Given statement:
the basis for a statistical process control chart is a(the) ............
We know that statistical process control chart or graph is used to study how a process changes over time with data plotted.
A statistical process control chart is nothing but a line graph showing a measure in consecutive order, with the measure on the y-axis and time or observation number on the horizontal x-axis. The use of statistical process control chart in the monitoring and maintaining of the quality found in a sample.
Therefore, the correct statement is 'the basis for a statistical process control chart is a(the) sampling distribution'
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(-2,-1) and (0,1) slope intercept
(stuck on it)
Slope intercept form of (-2,-1) and (0,1) is y = 3/2x +1.
Define slope intercept form.The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The slope, m, is a measure of how steep a line is. Simply put, the slope-intercept form is the way to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible. This form is frequently known as the y = mx + b form.
Given,
Coordinates = (-2,-1) and (0,1)
For slope:
m = y₂ - y₁/ x₂ - x₁
m = 1 + 2/0 + 2
m = 3/2
Slope intercept form:
y = mx + b
y = 3/2x +1
Slope intercept form of (-2,-1) and (0,1) is y = 3/2x +1.
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15. Which is an equation of the line with slope of that passes through (5,-5)?
3
Ay-5= -²(x+5)
Cy+5=-(x - 5)
By-5=-(x-5)
Dy+5=-x-5
A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
What is meant by slope of line?A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.The equation of a line is given by the expression:
(y-y1)=m(x-x1)
in the given problem the slope is m=1 and the point (x1, y1) is (5, 3), so substituting those values we have:
(y-3)=1(x-5)
simplifying:
y-3=x-5
isolating "y":
y=x-5+3
y=x-2
The complete questions is,
Which is the equation of a line that has a slope of 1 and passes through point (5, 3)? A.y = x – 2
B.y = x + 2 C.y = x + 3
D.y = x – 5
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Problem 2
The metal rim of a magnifying glass is inches around.
What is the area of the surface of the glass inside?
The area of the glass inside the 10 inches metal rim is 25/π square inches
What is the area of a plane shape?The area of a geometric shape or figure is a measure of the flat surface the shape occupies.
The dimension in the question, obtained from a similar question online are;
The length of the metal rim around the magnifying glass = 10 inches around
Required; The surface area of the glass inside the rim
The metal rim around the magnifying glass indicates the circumference of the glass inside;
Therefore;
The circumference of the glass inside the rim = 10 inches
The formula for the circumference of a circle = 2·π·r
Where;
r = The radius of the circle;
Therefore;
r = Circumference ÷ (2×π)
The radius of the glass inside is therefore;
r = 10 inches/(2·π) = 5/π inches
The area of a circle = π × r²
The area of the glass, A = π × (5/π)² = 25/π
The area of the glass inside is A = 25/π square inches
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Please someone help me out with my math homework .
Answer:
you see that Square on the corner of B use that unit box and trace it and then go to E and Trace two unit boxes at the top
PLS HELP I WILL GIVE BRAINIEST TO WHOEVER ANSWERS BOTH OF THESE CORRECTLY
Answer:
Step-by-step explanation:
What is the change to the graph of y=−3x−2 when the slope is changed to −1/3?
The slope of the graph will be changed. The graph is still a straight line, But it becomes steep.
The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.
Slope of a Line :
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
As a result, m = change in y/change in x = y/x is the formula for the change in y-coordinate with respect to the change in x-coordinate.
where "m" represents a line's slope.
The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.
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One leg of a right triangle is 8 units long, and its hypotenuse is 12 units long. What is the length of the other leg? Round to the nearest whole number.
4 units
9 units
10 units
20 units
The length of the other leg is 9 units. Therefore, option B is the correct answer.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
Given that, one leg of a right triangle is 8 units long, and its hypotenuse is 12 units long.
Let the length of the other leg be x.
12²=8²+x²
144=64+x²
x²=144-64
x²=80
x=√80
x=8.94
x≈9 units
Therefore, option B is the correct answer.
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identify the center and the radius of a circle that has a diameter with endpoints at (5, 8) and (7, 6).
The center of the circle is (6,7) and the radius of the circle is 1.414 units
The diameter with endpoints = (5, 8) and (7, 6)
The mid point of the diameter = The center of the circle
The center of the circle = [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Substitute the values in the equation
The center of the circle = ( (5+7)/2 , (6+8)/2 )
= (12/2 , 14/2)
= (6, 7)
The radius of the circle = The distance between (6, 7) and (7, 6)
The distance between two points = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The distance between (6, 7) and (7, 6) = [tex]\sqrt{(7-6)^2+(6-7)^2}[/tex]
= [tex]\sqrt{1^2+(-1)^2}[/tex]
= [tex]\sqrt{1+1}[/tex]
= [tex]\sqrt{2}[/tex]
= 1.414 units
Hence, the center of the circle is (6,7) and the radius of the circle is 1.414 units
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