Answers
The missing terms for the congruent angles are;
Complementary angles
m∠1 + m∠3 = 90°
Transitive property of equality
Subtraction property of equality;
Congruent angles.
How to identify congruent angles?Congruent angles are defined as the angles that have equal measure. Therefore, all the angles that have equal measure are called congruent angles.
We are given that;
∠1 and ∠2 are complementary
∠1 and ∠3 are complementary
Now, we are told that m∠1 + m∠2 = 90°. Complementary angles are defined as the 2 angles that sum up to 90 degrees. Thus, ∠1 and ∠2 are complementary by definition.
Similarly, m∠1 + m∠3 = 90°
By the transitive property of equality, we can say that;
m∠1 + m∠2 = m∠1 + m∠3
By the subtraction property of equality;
m∠2 = m∠3
Thus;
∠2 = ∠3 by definition of congruent angles.
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Related Questions
Please help with algebra. Find the formula for an exponential equation that passes through the points, (0,2) and (1,6). The exponential equation should be of the form y=abx.
Answers
The exponential function has an equation of f(x) = 2(3)^x
How to determine the equation of the exponential function?From the question, we have the following points that can be used in our computation:
(0, 2) and (1,6)
Also, we understand that
Function type = Exponential function
An exponential function is represented as
f(x) = ab^x
At point (0, 2), we have
2 = ab^0
Evaluate
a = 2
Substitute a = 2 in f(x) = ab^x
f(x) = 2b^x
At point (1, 6), we have
6 = 2b^1
This gives
2b = 6
Divide
b = 3
So, we have
f(x) = 2(3)^x
Hence, the equation of the exponential function is f(x) = 2(3)^x
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The demand function for a certain make of replacement cartridges for a water purifier is given by the equation p=−0. 01x2−0. 1x+21 where p is the unit price in dollars and xis the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the market price is set at $9/cartridge. (Round your answer to two decimal places. )
Answers
The demand function for a certain is given by the equation p=−0. 01x2−0. 1x+21 then the determined values will be −50.905557, −0.427737,41.333295.
From the given values,
R=px
9 = (−0. 01x2−0. 1x+21) x
0.01x3+0.1x2−21x−9=0
By reducing the equation,
X = −50.905557, −0.427737,41.333295.
Therefore, the determined values will be −50.905557, −0.427737,41.333295.
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At the bakery, they have 4 and a 1/8 pies for sale. They sell 1⁄4 of a pie for$5. How many pieces do they have to sell, and how much money will they make?
Answers
The number of pieces the bakery will sell is 16 and a half. The total amount of money they will make is $82.5.
What is the number of pieces of pies to be sold?To get the number of pieces of pies that they have to sell, we need to first determine how many 1/4 pies are in 4 and 8 pieces of bread. Going by that, we can see that:
1/4x of 4 = 16.
Also, 1/4x of 1/8 = 1/2.
So, the total number of pies that they have to sell is 16 and a half.
Now if 1/4 of a pie costs $5, then 4 1/8 will be equal to 33/8 × 5 ÷ 1/4.
This is equal to 165/8 × 4 = $82.5
So, the total amount of money that the bakery will make will be $82.5.
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Help pls I'll give you brainliest and 15 points asap.
How does the graph of g(x)=4⌊x⌋ differ from the graph of f(x)=⌊x⌋?
1. Multiplying by 4 shifts the graph of g(x)=4⌊x⌋ up 4 units.
2.Multiplying by 4 shifts the graph of g(x)=4⌊x⌋ down 4 units.
3.Multiplying by 4 stretches the graph of g(x)=4⌊x⌋ vertically by a factor of 4.
4.Multiplying by 4 shifts the graph of g(x)=4⌊x⌋ right 4 units.
Question 2
How does the graph of g(x)=⌊x⌋−3 differ from the graph of f(x)=⌊x⌋?
1.The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted right 3 units.
2.The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted left 3 units.
3.The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted up 3 units.
4.The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted down 3 units.
Answers
Answer:
Question 1: #3 is correct.
Question 2: #4 is correct.
(Help!)
#8 The tables represent some points on the graphs of lines m and n. Which system of equations is represented by lines m and n?
(A) −6x − y = 8 −3x + 2y = 9
(B)6x + y = −8 3x − 2y = 9
(C) 6x − y = −8 −3x − 2y = 9
(D) 6x − y = 8 3x + 2y = 9
#9 A produce company sells crates filled with a mixture of apples and oranges during the holiday season to grocery stores. Each crate contains a total of 72 pieces of fruit. Suppose that a crate has 8 more apples than oranges.
Which system of linear equations can be used to determine the number of pieces of each kind of fruit in the crate?
(A) a + o = 72 o = a + 8
(B) 8a + o = 72 a + o = 8
(C) a + o = 72 a = o + 8
(D) a + 8o = 72 a + o = 8
#10 The tables represent some points on the graphs of lines r and s. Which system of equations is represented by lines r and s?
(A) −4x + 3y = 12 2x − 5y = −10
(B) −4x − 3y = −12 −2x + 5y = 10
(C) 4x + 3y = −12 2x − 5y = 10
(D) 4x − 3y = −12 −2x − 5y = 10
Answers
The linear functions representing the systems of equations in each case are given as follows:
8. (D) 6x − y = 8 3x + 2y = 9
9. (C) a + o = 72 a = o + 8.
10. (C) 4x + 3y = −12 2x − 5y = 10.
What is a linear function?The slope-intercept representation of a linear function is presented by the rule as follows:
y = mx + b
The coefficients of the function and their meaning are listed as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x increases by one.b is the y-intercept of the function, being the numeric value of the function when the input variable x assumes a value of 0.For the line m, we have that when x increases by 6, y increases by 36, hence the slope is:
m = 36/6 = 6.
Considering the positive slope of 6, at x = 0, the numeric value is 12 less than the numeric value at x = 2, hence the intercept is:
b = 4 - 2 x 6 = -8.
Hence the equation is:
y = 6x - 8.
6x - y - 8.
Thus option d is correct.
For item 9, we use the variables a and o. The total is of 72, hence:
a + o = 72.
Suppose that a crate has 8 more apples than oranges, hence:
a = o + 8.
Thus option c is correct.
For line r in item 10, when x increases by 3, y decays by 4, hence the slope is:
m = -4/3.
When x = 0, y = -4, hence the intercept is:
b = -4.
Thus the equation is:
y = -4x/3 - 4
3y = -4x - 4.
4x + 3y = -12.
Meaning that option c is correct.
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A line segment has endpoints at (–4, –6) and (–6, 4). Which reflection will produce an image with endpoints at (4, –6) and (6, 4)?
Answers
The required expression of the reflection of the point is (-x, y).
Given that,
A line segment has endpoints at (–4, –6) and (–6, 4). Which reflection will produce an image with endpoints at (4, –6) and (6, 4) is to be determined.
The expression is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
A line segment has endpoints at (–4, –6) and (–6, 4) and an image with endpoints at (4, –6) and (6, 4) is produced the equation of the reflection is given as,
(x, y) ----> (-x, y)
Thus, the required expression of the reflection of the point is (-x, y).
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two equal rectangular lots are enclosed by fencing the perimeter of a rectangular lot and then putting a fence across its middle. if each lot is to contain 300 square feet, what is the minimum amount of fence (in ft) needed to enclose the lots (include the fence across the middle)?
Answers
The minimum amount of fence needed to enclose the lots is 120ft.
Adding areas of both fields, the combined area comes about to be 600sq ft.
The dimensions of the new plot are x length and y breadth. According to the question, there is a fence in the middle with y breadth.
g(x, y, z) = xy - 600
g(x, y, z) = 2x + 3y
∇g = ∇ (xy - 600) = (y, x)
∇f = ∇(2x + 3y) = (2, 3)
Now from the Lagrange method,
∇f = λ∇g
2 = λy
3 = λx
Now to get the value of lambda,
(2/y) = (3/x) = λ
x = 1.5y
Solving now we get,
1.5y² = 600
y = 20
x = 1.5 × 20 = 30
Thus after getting (x,y) we can put the value in the function to get the answer as 120ft.
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Bill wants to save for his son’s college expenses. He knows what tuition will cost in 18 years and knows the interest rate on the bank account. What he doesn’t know is how much to deposit each month to save enough for his son’s college expenses. Which Excel formula would you use?
Answers
The Excel formula that Bill would use is PMT.
How to illustrate the information?From Bill's situation, he has the following information:
time = NPER = number of periods = 18 years
RATE of the bank
FV = future value = cost of tuition
PMT, is a financial function, computes the loan payment based on constant payments and a constant interest rate. The Excel PMT function is a financial function that computes loan payments based on a fixed interest rate, the number of periods, and the loan amount. The function's name is derived from the acronym "PMT," which stands for "payment."
In conclusion, the correct option is PMT.
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Complete question
Bill wants to save for his son’s college expenses. He knows what tuition will cost in 18 years and knows the interest rate on the bank account. What he doesn’t know is how much to deposit each month to save enough for his son’s college expenses. Which Excel formula would you use? Choose from FV, PV, PMT, NPER, or RATE.
Round 45.4673
off each number
to two (2) Decimal Place
Answers
Answer:
45.47
Step-by-step explanation:
examples of linear equation
Answers
Y=x^1 +b
Y=4x+3
Y=-5x+2/3
Y=4.5x+2
Y=x
What is the solution set for ly-9| ≤122
O y23 ory≤21
O
-35y≤21
O y2-3 ory$21
0 35ys21
Answers
The solution set for the inequality is.
-113 ≤ y ≤ 131
What is the solution set for the inequality?Here we have the following inequality:
|y - 9| ≤ 122
Any absolute value inequality can just be decomposed as follows:
|y - 9| ≤ 122
to:
-122 ≤ y - 9 ≤ 122
Now we can solve this for y by adding 9 in all places:
-122 + 9 ≤ y - 9 + 9 ≤ 122 + 9
-113 ≤ y ≤ 131
That is the solution set.
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A soft drink manufacturer has a daily production cost of C = 70,000 - 120x + 0.055x ^ 2 , where C is the total cost (in dollars) and x is the number of units produced. How many units should they produce each day to yield a minimum cost?
Show all work please.
Answers
The minimum cost will be 1091 units.
Define Vertex Formula.
When the graph crosses its symmetry axes, the vertex formula aids in determining the vertex coordinate of a parabola. The vertex point is often represented by (h, k).
We are aware that a parabola's conventional equation is y=ax²+bx+c. The vertex in this case should be near the base of the U-shaped curve if the coefficient of x² is positive. The vertex should be at the peak of the U-shaped curve if the coefficient of x² is negative.
Given expression is,
C = 70,000 - 120x + 0.055x²
For this equation, the graph will be parabola opening upward.
For that, the vertex will be the minimum cost
x = (-b) / 2a
Here, a = 0.055 , b = -120
Now, plug in the values and find 'x'
minimum cost (x) = ( -(-120) ) / ( 2 * 0.055 )
= 120 / 0.11
= 120 / 0.11
= 1090.90 or 1091 units
Therefore, the minimum cost will be 1091 units.
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Solve the double-ended inequality:
2x-5<4x+2<2x-3
Answer: _ _ x _ _
Answer with a number in the first box, inequality in the second box, than after the x an inequality in the 3rd box and a number in the last box.
EG 5 > x > 18
Answers
The solution of the double-ended inequality is -7/2 < x < -5/2
Solving Linear InequalitiesFrom the question, we are to solve the doubled ended inequality.
The given inequality is
2x - 5 < 4x + 2 < 2x -3
From the inequality, we can write that
2x - 5 < 4x + 2 and 4x + 2 < 2x - 3
Now, we will solve each of the inequalities separately
Solving 2x - 5 < 4x + 2
Add 5 to both sides
2x - 5 + 5 < 4x + 2 + 5
2x < 4x + 7
Subtract 4x from both sides
2x - 4x < 4x - 4x + 7
-2x < 7
Divide both sides by -2 and reverse the sign
x > -7/2
-7/2 < x
Solving 4x + 2 < 2x - 3
Subtract 2x from both sides of the equation
4x - 2x + 2 < 2x - 2x -3
2x + 2 < -3
Subtract 2 from both sides
2x + 2 -2 < -3 - 2
2x < -5
Divide both sides by 2
x < -5/2
Putting the two solutions together, we get
-7/2 < x and x < -5/2
-7/2 < x < -5/2
Hence, the solution is -7/2 < x < -5/2
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everyone can someone help me here please (complete solution and graph)
Answers
Answer:
1: x^2+y^2-6x-4y-3=0
2: x^2+y^2-10x+4y=0
3: x^2+y^2-10x+2y+1=0
is the number 1.41421356 rational
Answers
The number 1.41421356 is not a rational number.
What is a rational number?
A number that can be expressed as a ratio is called a rational number. This indicates that it may be expressed as a fraction, where the numerator (the number on top) and denominator (the number on the bottom) are both whole numbers.
The given number is 1.41421356
The square root of 2 has the approximate value of 1.41421356
The number is non-terminating and non-repeating decimals.
That's why the given number is not a rational number.
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find the surface area of a rectangle prism that has the following deminsions.
length : 2ft
width : 14in
height : 11in
surface area : in 2
Answers
Answer:
SA(surface area) of the rectangular prism is 1,510 in inches
Step-by-step explanation:
SA=2(lh+lw+hw)
2inch=24ft
lh=264
lw=336
wh=154
755*2=1,510
3.472 divided by ____=0.112 free 25 points!!
Answers
When the divisor is missing, you divide the dividend (3.472) by the quotient (0.112)
So, we will do 3.472 divided by 0.112
3.472/0.112 = 31
Another method is multiplication. Multiplication is the opposite of division. We'd multiply 0.112 by 31.
0.112 x 31 = 3.472
In conclusion,
3.472/31 = 0.122
If you need extra help, use this video as a reference
https://youtu.be/9ui8Yh0bwCI?t=83
Answer: 3.472/31 = 0.122
Step-by-step explanation: I hope this helps:)
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Answers
The number of bicycles that must be manufactured to minimize the cost of 250 and the minimum cost is $11,500.
In the given question,
The cost C in dollars of manufacturing x bicyles at a production plant is given by the function shown below;
C(x) = 3x^2-1500x+199,000
(a) In the given question we have to find the number of bicyles that must be manufactured to minimize the cost.
The given function is
C(x) = 3x^2-1500x+199,000
To find the maximum or minimum value we firstly find the value of f'(x).
C'(x) = 6x-1500
Now put f'(x)=0
6x-1500=0
Add 1500 on both side, we get
6x=1500
Divide by 6 on both side we get
x=250
Hence, the number of bicycles that must be manufactured to minimize the cost of 250.
(b) Now finding the value of function at x=250
C(250) = 3(250)^2-1500*250+199,000
C(250) = 3*62,500-375,000+199,000
C(250) = 187,500-375,000+199,000
C(250) = 11,500
The minimum cost is $11,500.
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a tire manufacturer wishes to investigate the tread life of its tires. a sample of 10 tires driven 50,000 miles revealed a sample mean of 0.32 inches of tread remaining with a sample standard deviation of 0.09 inches. construct a 95% confidence interval for the population mean.
Answers
The confidence interval for the population mean is 0.2896 , 0.3505)
The sample mean is x = 0.32
The sample standard deviation is s = 0.09
The sample size is n = 10
The population standard deviation is unknown and sample size is atleast 10.
Thus use the t distribution.
Replacing the values in the following formula, determine the 95% confidence interval.
95% C.I = x ± t₀.₉₅,ₙ₋₁ . Sm
= x ± t₀.₀₅/₂,₁₀₋₁ . s/√n
= 0.32 ± 2.03 . 0.09/√10
= (0.2896 , 0.3505)
Hence the confidence interval for the population mean is 0.2896 , 0.3505)
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a fair coin is tossed 28 times. what is the probability that at most 25 tails occur? a) 0.99998628 b) 0.00000152 c) 0.99999848 d) 0.00001220 e) 0.01001372 f) none of the above.
Answers
The probability that at most 25 tails occur is 0.99999848.
We know that,
P(x = x) = ⁿCₓ × pˣ × [tex]q^{n-x}[/tex]
p = probability of success = 0.5
n = number of trials = 28
q = 1 - p = 0.5
The probability of the tail occurring at most 25 times can be written as
P(X ≤ 25) = P (X = 0) + P(X = 1) + ..... + P(X = 25)
Using a binomial probability calculator,
P(X ≤ 25) = 0.99999848
Therefore the probability that at most 25 tails occur is 0.99999848
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an instructor gives a course grade of b to students who have total score on exams and homeworks between 800 and 900, where the maximum possible is 1000. if the total scores have approximately a normal distribution with mean 830 and standard deviation 50, about what proportion of the students receive a b?
Answers
Let x denote the score. Assuming x follows normal distribution with
mean m = 70 and SD = 5 ,
we first calculate P( x < or = 80)
The SNV is z = (x — m) /SD
When x = 80, Z = ( 80 — 70)/5 = 2
So, P( x < or= 80)
= P( z < or= 2)= Area under the standard normal curve on LHS of z = 2=0.5000 + 0.4772=0. 9772, which is the relative frequency of x < or = 80Given that total number of students is
N = 1000. Let f be the number of students who have scored < or equal to 80,Then f/N = relative frequency = 0.9772Hence f = 0.9772 X N = 0.9772 X 1000 = 977learn more about binomial distrubution click here:
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The perimeter of a rectangle can be found using the equation P = 2L + 2W, where P is the perimeter, L is the length, and W is the width of the rectangle.
Solve the equation for the variable w
When you have done that
state the value of 'w' if the perimeter of the rectangle is equal to 37 feet and the length is equal to 4 feet.
hurrryyyy pls
Answers
Answer:
14.5 feet
Step-by-step explanation:
To make subject as 'w' and solving:To make the subject as 'w', isolate w.
To isolate 'w', subtract 2L from both sides .2L + 2W =P
2W = P - 2L
Now, divide both sides by 2.[tex]\sf W = \dfrac{P-2L}{2}\\\\W =\dfrac{P}{2}-\dfrac{2L}{2}\\\\ \boxed{W = \dfrac{P}{2}-L}[/tex]
P = 37 feet
L = 4 feet
[tex]\sf W =\dfrac{37}{2}-4\\\\[/tex]
= 18.5 - 4
W = 14.5 feet
What is the quotient (x2 − 9x + 20) ÷ (x − 4)? (1 point) x − 5 x − 4 x + 4 x + 5
Answers
Answer:
The guy under me is correct
Step-by-step explanation:
Answer:
x - 5
Step-by-step explanation:
Factor the expressions that are not already factored
(x^2 - 9x + 20) / (x - 4)
Cancel out x - 4 in both numerator and denominator
[tex]\frac{(x-5)(x-4)}{x-4}[/tex]
x - 5
a student in public administration wants to estimate the mean monthly earnings of city council members in large cities. she can tolerate a margin of error of $100 in estimating the mean. she would also prefer to report the interval estimate with a 95% level of confidence. the student found a report by the department of labor that reported a standard deviation of $1,000. what is the required sample size? (hint: round your answer up to the nearest whole number)
Answers
the required sample size for the interval estimate with a 95% level of confidence is 385
since we are given the margin of error which is f $10 and a standard deviation which is $1,000, and we are also given the level of confidence which is 95%
so the formula we are referring to calculate the sample size is :
n=z(0..95)*s²/ E
here, E is the margin of error, S is the standard deviation
so z score of 0.95 is 1.96
so n = 1.96*1000^2/100
= 384.16 ,which is almost 385
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Choose the linear equation that is parallel to the following line y =−1/4 x − 1
Answers
Answer:
Any equation that has the same slope as this line will be parallel to it. The slope is -1/4, so whichever equation has -1/4 x in it will be parallel to the line.
A sample survey of 54 discount brokers showed that the mean price charged for a trade of 100shares at 50 per share was $33. 77 (AAII Journal, February 2006). The survey is conducted annually. With the historical data available, assume a known population standard deviation of $15.
a. Using the sample data, what is the margin of error associated with a 95% confidence interval?
b. Develop a 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share
Answers
a) The margin of error associated with a 95% confidence interval is 4.
b) The 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77,$37.77)
a) We are given with the information that the mean for 54 discount brokers is $50 for 100 shares is $33.77 Also the population standard deviation is $15.
The formula for margin of error is Z = zα/2 σ √ n
Now we know from our z-table that value of zα/2 for 95% confidence interval is 1.96
So, the value of error margin is zα/2 σ √ n =1.96 (15/√54) = 1.96 x 2.04
= 4
b) We know from part a that margin of error is 4.
Also, the mean price charged for a trade of 100shares at 50 per share was $33. 77
The value of confidence interval for population mean is,
x ± zα/2 σ √ n = 33.77 ± 4 = (29.77,37.77)
Thus, the 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77,$37.77)
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Answer it now bois now
Answers
Answer:
Answer is [tex](\frac{4}{-1})[/tex] option D is correct
Kaela wants to purchase a pair of shoes at Macy’s that cost $80. If Macy’s charges a
6% sales tax, how much will Kaela pay for the shoes, including tax?
Answers
Answer: $84.80
Step-by-step explanation:
The actual sales tax was 4.80 because 6% of 80 is 4.80
Then add the 4.80 to the 80 to get your total
Hope this helped :)
Could someone help quick
Answers
The constant of proportionality is known to be the ratio of two proportional values that is said to be in a constant value.
What is the constant of proportionality?The constant of proportionality is a term that is defined as the rate or the ratio of two proportional values which are known to be at the same value.
constant of proportionality = 2.5
Given : y = 2.5x.
To find : What is constant of Proportionality in the equation.
Solution : We have given
y = 2.5x.
On comparing with equation of proportionality : y = kx,
Where, k is the constant of proportionality.
On comparing y = 2.5 x by y = kx .
We get k = 2.5
So, constant of proportionality = 2.5
Therefore, constant of proportionality = 2.5
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The value of constant proportionality is 2.5. The constant of proportionality is known to be the ratio of two proportional values that is said to be in a constant value.
What is the constant of proportionality?The constant of proportionality is a term that is defined as the rate or the ratio of two proportional values which are known to be at the same value.
constant of proportionality = 2.5
Given : y = 2.5x.
To find : What is constant of Proportionality in the equation.
Solution : We have given
y = 2.5x.
On comparing with equation of proportionality : y = kx,
Where, k is the constant of proportionality.
On comparing y = 2.5 x by y = kx .
We get k = 2.5
So, constant of proportionality = 2.5
Therefore, constant of proportionality = 2.5
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13) Mr. Harrington wants to buy a new TV for $500. He has a 10% off coupon and knows the tax
be 13.5%. How much money will he need to save to buy the TV?
a) $510.75
c) $450
b) $432.50
d) $567.50
Answers
Mr. Harrington will need $510.75 to buy the TV
The correct answer is an option (a)
In this question, Mr. Harrington wants to buy a new TV for $500
He has a 10% off coupon.
After applying this coupon, the cost of TV would be,
500 - (10 percent of $500)
= 500 -[ (10/100) * 500]
= 500 - 50
= 450
He knows the tax be 13.5%.
13.5 percent of 450 would be,
(13.5/100) * 450
= 60.75
So, the amount he will need to save to buy the TV,
$450 + $60.75 = $510.75
Therefore, Mr. Harrington will need $510.75 to buy the TV
The correct answer is an option (a)
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