XZ is the perpendicular bisector of segment WY. Solve for k. Enter a NUMBER only.
Answers
Given that XZ is the perpendicular bisector of segment WY, the numerical value of k is 6.
What is the numerical value of K?A bisector divides a segment or angle into two equal halves.
Given the data in the question;
XZ is the perpendicular bisector of segment WYSegment WX = 3k + 17Segment XY = 7k - 7Value of k = ?Since XZ is a perpendicular bisector of segment WY,
Segment WX is equal to Segment XY
Segment WX = Segment XY
Plug in the given values and solve for k.
3k + 17 = 7k - 7
Collect like terms
3k - 7k = -7 - 17
-4k = -24
Divide both sides by the coefficient of k
-4k/-4 = -24/-4
k = 6
Given that XZ is the perpendicular bisector of segment WY, the numerical value of k is 6.
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Related Questions
prove that the sequence {Xn ] Such that
Xn Converges to Zero
Answers
The sequence or pattern [[tex]x_{n}[/tex]] [tex]x_{n}[/tex] Converges to Zero, meaning that the power, limit, and final solution all get closer to zero.
What do you mean by mathematical sequence?A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts. The length of the series is the number of elements (potentially infinite).Unlike a set, a sequence may contain the same things more than once at different locations, and unlike a set, the sequence's order is crucial.
According to given information;
First put;
[tex]x_{n}[/tex]−1=−√(1+x[tex]_n_-_2[/tex]+1)
into
[tex]x_{n}[/tex]=(−1+x[tex]_n_-_1[/tex]+1)
You'll notice a general form:
[tex]x_{n}[/tex]=−1+(x[tex]_n_-_r[/tex]+1)^2^−r
Then put r = n-1, and take the limit of both sides with n tending to infinity. On the right hand side, you have
−1 +[tex]\lim_{n \to \infty}[/tex](x+1)^[tex]\frac{1}{2n-1}[/tex]
n→∞
he power approaches 0, the limit approaches 1 and the final answer approaches 0.
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The price of 3 citrons and 4 fragrant wood apples is 51 units. The price of 4 citrons and 3 fragrant wood apples is 54 units. Find the price of a citron and the price of a wood apple.
Answers
Answer:9 citronella and 6 fragrant wood apples
Step-by-step explanation:
Which of the following numbers is irrational? -4.8237, pi/2, the square root of 4 to the third power, or 4 + the square root of 25
Answers
Answer:
Did you already get the answer?
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs. Match the equations and their solutions.
Answers
The solutions of given equations are x = 0,b = -3,y = 2 and c = 5 respectively.
What is the equation?A formula known as an equation uses the same sign to denote the equality of two expressions.
The equation must be constrained by =,< or >.
Given the equations,
01) x/4 + 2x/3 - 4 = - 4 + 5x/2
(3x + 8x)/12 = 5x/2
x = 0
02) 3.2b + 10 = -1.7b - 4.7
2.2b + 1.7b = -4.7 - 10
b = -3
03) 6.6y + y + 6.5 = y - 6.7
5.5y = -6.7 - 6.5
y = 2
04) 2c - 7c + 8 = -17
-5c = -25
c = 5
Hence "The solutions of given equations are x = 0,b = -3,y = 2 and c = 5 respectively".
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Given n(J) = 255, n(K) = 186 and n(J ∪ K) = 429, find n(J ∩ K).
Answers
Answer:
12
Step-by-step explanation:
[tex]n(J \cap K)=n(J)+n(K)-n(J \cup K) \\ \\ =255+186-429 \\ \\ =12[/tex]
For her 1st birthday, Ruth's grandparents invested $1500 in an 18-year certificate for her that pays 12% compounded annually. How much will the certificate be worth on
Ruth's 19th birthday? (Round your answer to the nearest cent.)
Answers
The certificate will be worth of $11534.9 on Ruth's 19th birthday.
Compound Interest is calculated using the formula.
[tex]Amount=P*(1+\frac{r}{n} )^{nt}[/tex]
where , P=principal
r = rate of interest
n= number of times interest is compounded
t = no of years
In the given question ;
Principal = $1500
n=1 ...(as it is compounded annually)
t= 18 years ...(as on 19th birthday Ruth will complete 18 years)
r=12%=0.12
Substituting the values of P,n,t,r in the formula we get,
[tex]Amount=P*(1+\frac{r}{n} )^{nt}[/tex]
[tex]=1500*(1+\frac{0.12}{1} )^{1*18}[/tex]
On solving further we get
=[tex]1500*(1.12)^{18}[/tex]
=1500*7.6899
=11534.85
Therefore , On Ruth's 19th birthday the certificate will be of worth $11534.9 .
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Evaluate the following expression: (3x+2)+5
Answers
Answer:
3x + 7
Step-by-step explanation:
Hope this helps you :)
A lacrosse field is rectangular with a length of 110 yards and a width of 60 yards. Which side lengths could be used to create a scale drawing of the field?
Answers
The side lengths could be used to create a scale drawing of the field is 6600 yard².
What is rectangle?A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.
Given:
A lacrosse field is rectangular with a length of 110 yards and a width of 60 yards.
According to given question we have
We know that
Area of rectangle= Length × width
Area of rectangle= 110 × 60
Area of rectangle= 6600 yard².
Scale ratio can be 1:55
Therefore, the side lengths could be used to create a scale drawing of the field is 6600 yard².
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the sum of three consecutive odd integers is 321. what are the three consecutive odd integers?
define in words variables for the unknown values
create an equation
solve using algebra
Answers
The consecutive odd numbers that sum up to 321 are 105, 107 and 109.
How to find the three consecutive odd numbers?The sum of three consecutive odd integers is 321.
Odd numbers are numbers that when divided by 2 produces a remainder.
let
x = first odd numbers
Therefore,
x + x + 2 + x + 4 = 321
combine the like terms
x + x + x + 2 + 4 = 321
add the like terms
x + x + x + 2 + 4 = 321
3x + 6 = 321
subtract 6 from both sides
3x + 6 = 321
3x + 6 - 6 = 321 - 6
3x = 315
divide both sides by 3
x = 315 / 3
x = 105
Therefore, the consecutive odd numbers that sum up to 321 are 105, 107 and 109.
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the information in the following table for the next few questions. The following statistics represent samples of copper wire submitted by two companies for tensile strength testing (psi).
Statistic Company A Company B
Arithmetic Mean 500 600
Median 500 500
Mode 500 300
Standard Deviation 40 20
Mean Absolute Deviation 32 16
Quartile Deviation 25 14
Range 240 120
Sample Size 100 80
The middle 95% of the wires from Company A tested between _____ and _____ . Record ONLY the lower limit as a whole number.
The middle 50 percent of the wires of Company A tested between _____ and _____. Record ONLY the lower limit as a whole number.
Which company's distribution has the larger dispersion (answer either 'A' or 'B')?
The variance for Company A is _____? (whole numbers only)
Answers
Using the normal distribution, we have that:
A.
The middle 95% of the wires from Company A tested between 420 and 580 psi.The middle 50% of the wires of Company A tested between 473 psi and 527 psi.B. Due to the higher coefficient of variation, Company A has the larger dispersion.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For Company A, the mean and the standard deviation are given as follows:
[tex]\mu = 500, \sigma = 40[/tex]
The Empirical Rule is applicable for a normal variable, meaning that 95% of the measures are within 2 standard deviations of the mean, hence:
500 - 2 x 40 = 420.500 + 2 x 40 = 580.The middle 95% of the wires from Company A tested between 420 and 580 psi.
The middle 50% is the measures between the 25th percentile(X when Z = -0.675) and and the 75th percentile(X when Z = 0.675), hence:
25th percentile:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
-0.675 = (X - 500)/40
X - 500 = -0.675(40)
X = 473.
75th percentile:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
0.675 = (X - 500)/40
X - 500 = 0.675(40)
X = 527.
The middle 50% of the wires of Company A tested between 473 psi and 527 psi.
Which Company had the larger dispersion?The company with the larger dispersion has the highest coefficient of variation, given by the standard deviation divided by the mean.
Hence:
Company A: 40/500 = 0.08.Company B: 20/600 = 0.033.Hence Company A has the larger dispersion.
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Write a formula for the perimeter of the rectangle in terms of its length, l.
Answers
a formula for the perimeter of the rectangle in terms of its length, l will be given as l = P / 2 - b.
We know that the perimeter of rectangle is given by:
Perimeter ( P ) = 2 ( l + b )
Now, we need to represent this formula in terms of length that is l.
So, we get that:
P = 2 l + 2 b
Now subtract 2 b from both the sides:
P - 2 b = 2 l + 2 b - 2 b
P - 2 b = 2 l
2 l = P - 2 b
Divide both the sides by 2:
2 l / 2 = (P - 2 b) / 2
l = P / 2 - b
Therefore, we get that, a formula for the perimeter of the rectangle in terms of its length, l will be given as l = P / 2 - b.
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1. A rectangle has area 48cm². a) What might its perimeter be?
Answers
There are multiple but here are 2
13+13+11+11 = 42
10+10+14+14 = 42
Samir measured a boarding school and made a scale drawing. He used the scale 10 millimeters = 2 meters. What is the scale factor of the drawing?
Answers
The scale factor of the drawing is 1 / 200 or 0.005.
What is scale factors?Scale factor is used to scale shapes in different dimensions.
In other words, Scale factor is described as the number or the conversion factor which is used to change the size of a figure without affecting its shape.
Therefore, scale factor can be represented mathematically as follows:
Scale factor = dimensions of the new shape ÷ dimensions of the original shape.
Hence he uses the scale 10 millimetres equals to 2 meters.
We have to convert metres to millimetres to get the scale.
10millimetres = 2meters
Therefore,
1 meter = 1000 millimetres.
2 meters = ?
cross multiply
length = 2 × 1000 = 2000 millimetres
Therefore, the scale factor of the drawing is as follows:
scale factor = 10 / 2000
scale factor = 1 / 200
scale factor = 0.005
Therefore, the scale factor of the drawing is 1 / 200 or 0.005.
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Write a function g whose graph is a reflection in the x-axis of the graph of f(x)=|x|−5
Answers
The function g(x) reflected along x-axis is |x| + 5.
What is a mod function ?A modulus function always outputs positive values, hence the outputs are greater than or equal to zero,f(x) ≥ 0.
When a graph is reflected along x-axis f(x) becomes -f(x).
∴ The function f(x) = |x| - 5 when reflected along x-axis it will become
f(x) = - (|x| - 5).
f(x) = - |x| + 5.
Or
g(x) = - |x| + 5.
Graph of g(x) is shown in the image attached.
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. Rewrite Y = √4x+16 +5 y to make it easy to graph using a translation. Describe the graph.
Answers
Answer:
The graph of [tex]y=\sqrt{4x+16}+5[/tex] is the graph of [tex]y=\sqrt{x}[/tex] translated 4 units left, stretched horizontally by a factor of 1/4, and translated 5 units up.
Step-by-step explanation:
Transformations
[tex]\textsf{For }a > 0[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
Given function
[tex]y=\sqrt{4x+16}+5[/tex]
Parent function
Parent functions are the simplest form of a given family of functions.
[tex]y=\sqrt{x}[/tex]
The graph of the parent function is related to the graph of the given function by a series of transformations. To determine the series of transformations, work out the steps of how to go from the parent function to the given function.
Factor the expression under the square root sign:
[tex]y=\sqrt{4(x+4)}+5[/tex]
Transformations
Parent function:
[tex]f(x)=\sqrt{x}[/tex]
Translated 4 units left:
[tex]f(x+4)=\sqrt{x+4}[/tex]
Horizontally stretched by a factor of 1/4 (compressed by a factor of 4):
[tex]\begin{aligned}f(4(x+4)) & =\sqrt{4(x+4)}\\ & = \sqrt{4x+16} \end{aligned}[/tex]
Translated 5 units up:
[tex]f(4x+16)+5=\sqrt{4x+16}+5[/tex]
Therefore, the graph of [tex]y=\sqrt{4x+16}+5[/tex] is the graph of [tex]y=\sqrt{x}[/tex] translated 4 units left, stretched horizontally by a factor of 1/4, and translated 5 units up.
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A = P(1+r)tn
The formula above is used to calculate compound interest. A represents the amount of money accumulated after n years, including interest; P is the initial principal amount (i.e.,
the initial amount deposited); stands for the annual rate of interest as a decimal; and t
represents the number of years and in the number of times the interest is compounded, per
year. If Serina deposits $500 in an account earning 5% interest compounded semiannually and keeps the money in her account for three years, how much money will she have at the end of the five years? Round your answer to the
nearest dollar.
A $515.00
B $530.00
C $670.05
D$710.10
Answers
Answer:
670.05
Step-by-step explanation:
Rounding to the nearest dollar, Serina will have $515 at the end of five years. Therefore, correct option is A.
To calculate the amount Serina will have at the end of five years, we can use the formula for compound interest:
A = [tex]P(1 + r)^{(nt)[/tex]
Where:
A = the future value of the investment/loan, including interest
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years the money is invested for
In this case, Serina deposits $500 with an annual interest rate of 5%, compounded semiannually (n = 2), and keeps the money in her account for three years (t = 3).
Plugging in the values, we get:
A = 500(1 + 0.05)⁶
A = 500(1.005)⁶
A ≈ 500(1.030)
A ≈ $515
Therefore, correct option is A.
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Translate the point (5, -3) 3 units left and 1 unit up.
The image point is located at ____.
Answers
Answer:
(2,-2)
Step-by-step explanation:
17. In the number below,
which digit is in the
thousandths place?
7459.31890
Answers
Answer:
hey from where are you...
Write a function g whose graph represents a vertical shrink by a factor of 1/2 of the graph of f(x)= 2x + 6
Answers
Answer:
f(x)= x + 3
Step-by-step explanation:
Find the measure of the missing angle
Answers
Answer:
a = 115°
Step-by-step explanation:
Two angles are supplementary angles because they make a straight line.
The sum of two angles is equal to 180° then to find the measure of the missing angle we simply subtract 65 from 180:
180 - 65 = 115
(3x-5) + (x +1) = 180
Answers
Answer:
46
Step-by-step explanation:
4x-4=180
4x=184
x=46
Answer:
x=46
Step-by-step explanation:
used by scientific calculator.
I need help with this
Answers
Answer:
1. He get get to school 10 minutes faster riding by hisself than ridding with Christina.
Step-by-step explanation:
Christina is 22 minutes - Luis 12 minutes = 10 minutes.
Write the English phrase as an algebraic expression. Let the variable X represent the number
The sum of 15 divided by a number and that number divided by 15.
The expression is: ???
Answers
Answer:
(15 ÷ n) + (n ÷ 15)
Step-by-step explanation:
The sum of 15 divided by a number and that number divided by 15.
15 divided by a number
= (15 ÷ n)
15 is being divided by an unknown number (put n as a variable)
that number divided by 15
= (n ÷ 15)
An unknown number (put n as a variable) is being divided by 15.
The sum
Add (15 ÷ n) and (n ÷ 15)
(15 ÷ n) + (n ÷ 15)
Hope this helped and have a lovely rest of your day! :)
An aspiring business owner is planning their college course of study and would like to know whether they should pursue a doctoral degree before they open their own business. Explain what you would recommend to them using two specific examples from the bar graph to support your response.
Answers
Answer:
Yes
Step-by-step explanation:
true or false 3:7=3/7
Answers
true, 3:7 is a ratio and is equal to 3/7
A point is plotted on the number line at 2. A second point is plotted at 4.
What is the length of a line segment joining these points?
Enter your answer as a simplified mixed number in the box.
units
units
Answers
what’s the answer to area=11in2
Answers
A computer programmer had two flies with a total size of 77.56 gigabytes if one of the files was 45.46 gigabytes how big is the second file
Answers
Answer:
Step-by-step explanation:
32.1 gb is answer
77.56
-45.46
second file would be 32.10 gb
Write each number in standard form.
2. eight and fifty-nine hundredths
3. seven and three thousandths
1
4.3 +2× +4×
1,000
Answers
The values given in standard form are 8.59 and 7.003
Writing in standard formThe standard form of a number is a way of writing the number in a form that follows certain rules. Any number that has exponents and decimals is said to be a standard notation.
Given the following statements
eight and fifty-nine hundredths
8 + 59/100
8 + 0.59
8.59
For the expression seven and three thousandths
7 + 3/1000
7 + 0.003
7.003
Hence the values given in standard form are 8.59 and 7.003
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Raphi buys 1 rubber and 1 pen for £1.25.
Dylan buys 4 rubbers and 3 pens for £4.75.
Work out the cost of one rubber and one pen.
rubber: £
pen: £
Submit Answer
Answers
Answer:
Step-by-step explanation:
Cost of one rubber = $1
Cost of one pen = 0.25