A section of a roller coaster track forms a parallelogram ABCD. If m∠ABC = 72°, what is m∠DAB? A) 72° B) 108° C) 144° D) 216°
Answers
Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
A section of a roller coaster track forms a parallelogram ABCD.
If m∠ABC = 72°
We need to find the m∠DAB,
Since ABCD is a parallelogram .
So, "Sum of interior angles on the same side is supplementary":
[tex]m\angle ABC+m\angle DAB=180\textdegree\\\\72\textdegree+m\angle DAB=180\textdegree\\\\m\angle DAB=180\textdegree-72\textdegree\\\\m\angle DAB=108\textdegree[/tex]
Hence, Option 'B' is correct.
Related Questions
What type of solution does the system of linear equations have? 2x - 6y = 8 -x + 3y = 10
Answers
2x - 6y = 8
-x + 3y = 10
Let's use the addition/subtraction method. Multiply the 2nd equation by 2, obtaining
2x - 6y = 8
-2x + 6y = 20
--------------------
0 + 0 = 28
Since this can never be true, the system of linear equations
2x - 6y = 8
-x + 3y = 10
has no solution.
Answer:
No Solution
Step-by-step explanation:
Did the test and got this question correct :>
What was the most direct effect of the establishment of the Queen’s Men?
a. New plays were written every year.
b. The queen visited Whitehall Palace.
c. The Puritans were outraged.
d. Drama received royal approval.
Answers
Answer:
C) The Puritans were outraged.
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
trust
Which shows the correct simplification of product of powers?
1.) 78 · 7-4 = 78· (–4) = 7–32
2.)78 · 7–4 = 78 ÷ (–4) = 7–2
3.)78 · 7–4 = 78 + (–4) = 74
4.)78 · 7–4 = 78 - (–4) = 712
Answers
I can infere that the product intended to simplify is (7^8) * (7^-4)., because that permits you to use the rule of the product of powers with the same base.
That rule is that the product of two powers with the same base is the base raised to the sum of the powers is:
(A^m) * (A^n) = A^ (m+n)
=>(7^8) * (7^-4) = 7^ [8 + (- 4) ] = 7^ [8 - 4] = 7^4, which is the option 3 if the powers are placed correctly.
The answer choice which shows the correct simplification of product of powers is:
78 · 7–4 = 78 + (–4) = 74What is Product of Powers?This refers to the mathematical property which states that when there is a multiplication of two powers that have the same base, then there would be the addition of exponents.
From the given choices, we can see that the powers are not given, so we can solve using inference.
This posits that (7^8) * (7^-4) was the product that was intended to be simplified and this law shows:
(A^m) * (A^n) = A^ (m+n)Hence, if we add the powers, then the correct answer would be option C because they are of the same base.
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If Mr. Khans buys 15 staplers, it would cost him $254.85. How would you write this using function notation?
Answers
254.85 = 15x
254.85/15 = x
16.99 = x.....so each stapler costs $ 16.99
Answer:
f(x) = don't spend more than 200 dollars on staplers
Step-by-step explanation:
Find the prime factorization of the follwing numbers: (write p0 if a prime does not appear in the given number.)
Answers
A gas station operates two pumps, each of which can pump up to 10,000 gallons of gas in a month. the total of gas pumped at the station in a month is a random variable y (measured in 10,000 gallons) with a probability density function (p.d.f.) given by compute e(y)
Answers
[tex]f(y)=\begin{cases} cy, & \text{if} \ \ 0\ \textless \ y\ \textless \ 1 \\ (2-y), & \text{if} \ \ 1\leq y\ \textless \ 2 \\ 0, & \text{elsewhere} \end{cases}[/tex]
Part A:
The value of c that makes f(y) a pdf is obtained as follows:
[tex]F(\infty)= \int\limits^{\infty}_{-\infty} {f(y)} \, dy=1 \\ \\ \Rightarrow \int\limits^1_0 {cy} \, dy +\int\limits^2_1 {(2-y)} \, dy=1 \\ \\ \Rightarrow \left. \frac{cy^2}{2} \right]^1_0+\left[2y- \frac{y^2}{2} \right]^2_1=1 \\ \\ \Rightarrow \frac{c}{2} +4-2-2+ \frac{1}{2} =1 \\ \\ \Rightarrow \frac{c}{2} = \frac{1}{2} \\ \\ \Rightarrow \bold{c=1} [/tex]
Part B:
We compute E(y) as follows:
[tex]E(y)=\int\limits^{\infty}_{-\infty} {yf(y)} \, dy \\ \\ =\int\limits^1_0 {y^2} \, dy +\int\limits^2_1 {(2y-y^2)} \, dy \\ \\ =\left. \frac{y^3}{3} \right]^1_0+\left[y^2- \frac{y^3}{3} \right]^2_1 \\ \\ = \frac{1}{3} +4- \frac{8}{3} -1+ \frac{1}{3} \\ \\ =1[/tex]
Therefore, E(y) = 1.
The expected value E(y) cannot be computed without the given probability density function for the random variable y. The computation involves integrating the product of the variable and its probability density over its range. An example has been provided for how to compute the expected value with a hypothetical p.d.f.
Explanation:To answer the student's question, it appears there may be a missing probability density function (p.d.f.) for the random variable y, which represents the total amount of gas pumped at the station in a month. Without the actual function, we cannot compute E(y), which is the expected value (mean) of the random variable y. In general, if we had the p.d.f., we would compute the expected value by integrating the product of the variable and its probability density over its range.
An example of how to compute the expected value if we had a p.d.f. f(y) might look like this:
E(y) = ∫ y × f(y) dy
For instance, if the p.d.f. were f(y) = ay (a being a constant) over the interval [0, 1], then:
Integrate the product of y and the p.d.f. over the interval:E(y) = ∫01 y × ay dy = a × ∫01 y² dyAfter computing the integral you would find the expected value E(y).However, without the p.d.f. provided, we can only state the method, not the actual expected value.
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which number is greater 67.89 and 67.98
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so 67.98 is greater than 67.89
answer
67.98 is greater
Ignore the bottom...the top question is what I’m struggling with
Answers
so, an approximation could just be 48,000,000.
Use the chinese remainder theorem to solve the systems of congruences:
a. find x mod 77 if x ≡ 2 (mod 7) and x ≡ 4 (mod 11).
b. x ≡ 2 (mod 3), x ≡ 3 (mod 4), x ≡ 1 (mod 5).
Answers
[tex]x=2+4=6[/tex]
Modulo 7, we're left with [tex]x\equiv2+4\pmod7=6\mod7[/tex], but we want a remainder of 2, so multiply 4 by 7 to assure that that remainder vanishes. So now
[tex]x=2+4\cdot7=30[/tex]
and [tex]x\equiv2\pmod7[/tex], but modulo 11, we have [tex]x=\equiv2+28\equiv2+4\equiv6\pmod{11}[/tex]. But we want the remainder to be 4, so multiply the first term by 11 to guarantee this. So we write
[tex]x=2\cdot11+4\cdot7=50[/tex]
but now, we get a remainder of 1 modulo 7 and 6 modulo 11. To fix the first case, multiply the first term by 2. For the second case, first find the inverse of 6 modulo 11. We have [tex]2\cdot6=12[/tex], and [tex]12\equiv1\pmod{11}[/tex], so the inverse is 2. Multiply the second term by 2, so that the second term's remainder modulo 11 becomes 1. Then multiply by 4, so that now
[tex]x=2\cdot11\cdot2+4\cdot7\cdot2\cdot4=268[/tex]
We have
[tex]x=268=3\cdot77+37\implies x\equiv37\pmod{77}[/tex]
(b) This is done similarly. Modulo 3, we want a remainder of 2, so we can start with
[tex]x=2+3+3=8[/tex]
Then taken modulo 4, we need to multiply the first term by 2 and the third term by 4 to ensure the remainder becomes 3. The second term can be left alone.
[tex]x=2\cdot2+3+3\cdot4=19[/tex]
Now taken modulo 5, we can multiply the first two terms by 5 and the third term by the inverse of [tex]3\times2\equiv12\equiv2\pmod5[/tex]. We have [tex]3\cdot2\equiv6\equiv1\pmod5[/tex], so we multiply by 3.
[tex]x=2\cdot2\cdot5+3\cdot5+3\cdot4\cdot3=71[/tex]
Now
[tex]x=71=1\cdot(3\cdot4\cdot5)+11=1\cdot60+11[/tex]
which means the smallest positive solution for the system would be [tex]x=11[/tex].
jake said he has 8/100 of a dollar in his pocket Margie said that the decimal for 8/100 is 0.8 what error did she make. what is the decimal form for 8/100?
Answers
A theater can seat 864 people. The number of rows is 5 less than the number of seats in each row. How many rows of seats are there?
Answers
Final answer:
To determine the number of rows in a theater that can seat 864 people, with the number of rows being 5 less than the number of seats per row, we set up the equation x(x-5)=864. Solving this quadratic equation, we find that there are 31 rows of seats.
Explanation:
To solve for the number of rows in the theater, let's denote the number of seats in each row as x and the number of rows as x - 5. Since the product of the number of seats in each row and the number of rows will give us the total seating capacity, we can write down the equation:
x(x - 5) = 864
Expanding the equation, we get:
x2 - 5x - 864 = 0
Using the quadratic formula or factoring, we find that x = 36. Therefore:
The number of rows is x - 5 = 36 - 5 = 31.
So, the theater has 31 rows of seats.
linear graphing y= -2x
Answers
This gives you one point.
Then let x = 1. What do you get for y.
This gives you a second point.
an airplane approaching its destination has begun it's final descent into the airport. if the plane descends at a rate of 300 feet per minute. what is the change in altitude of the plane after 4 minutes?
Answers
you have descended 1200 feet in 4 minutes
a few questions i need help with.
Answers
The first step is getting rid of the denominators by multiplying all terms by 3. This is done using multiplicative property.
The second step is getting rid of the brackets using the distributive property.
The third and fourth steps are isolating the term containing the x on one side of the inequality using addition or subtraction property of order
The last step is getting rid of the coefficient of the x using the division property of order.
So, the correct order of choices is:
1- multiplicative property..
2- distributive property.
3- addition or subtraction property of order
4- addition or subtraction property of order
5- division property of order.
question 2:
The first step is getting rid of the brackets using the distributive property.
The second and third steps are isolating the term containing the x on one side of the inequality using addition or subtraction property of order
The last step is getting rid of the coefficient of the x using the division property of order.
So, the correct order of choices is:
1- distributive property.
2- addition or subtraction property of order
3- addition or subtraction property of order
4- division property of order.
At 1pm, there was 16 seagulls on the beach. At 3pm, there were 60 seagulls. What is the constant rate of change
Answers
Cross Multiply
48/60=4/5
The constant rate of change is 4/5
Students can take MATH 080 between one and four times. The student's tuition for MATH 080 is $ 548.00 If the tuition is increased 6% AFTER 2 ATTEMPTS, what is the student's one semester tuition after the 2nd attempt? In this situation what is the total tuition for taking MATH 080 the allowed four times
Answers
for the 3rd attempt 6% extra of that, (6/100) * 580.88, is 34.8528, so the price is 615.7328.
4th attempt is 6% extra of that, (6/100) * 615.7328, 36.943968, adding that will give us 652.676768.
What is the slope of the line represented by the equation y = 1/4x – 3?
Answers
what is the answer ×-(-150)=200
Answers
x + 150 = 200
x + 150 (-150) = 200 (-150)
x = 200 - 150
x = 50
hope this helps
Joanne is depositing money into a bank account. After 3 months there is $150 in the account. After 6 months there is $300 in the account. Determine the constant rate of change of the account.
Answers
Answer:
The constant rate of change of the account is $50 or Increasing by $50 per month.
Step-by-step explanation:
Consider the provided information.
Joanne is depositing money into a bank account. After 3 months there is $150 in the account. After 6 months there is $300 in the account.
Rate of change is known as how one quantity change in relation to other.
The rate of change can be calculated as:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Now use the above formula to calculated the rate of change.
[tex]\frac{300-150}{6-3}[/tex]
[tex]\frac{150}{3}[/tex]
[tex]50[/tex]
Hence, the constant rate of change of the account is $50 or Increasing by $50 per month.
a pump is running at 6.4 quarts per minute. how many gallons per hour is this?
Answers
Kurt and Maria’s high school is having a newspaper drive.The goal is to collect 3,585 pounds of newspapers. So far, 21% of the goal has been reached. Kurt estimated the number of pounds of newspapers collected by finding 10% of 3,600 and then multiplying the result by 2. Maria estimated the number of pounds of newspapers collected by finding mc006-1.jpg of 3,600. Who is right, and why?
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Determine whether the variable is qualitative or quantitative. explain your reasoning. miles per gallon that a car gets for highway driving
Answers
Carly is making 3 1/2 batches of biscuits. If one batch calls for 2 1/3 cups of floor, how much flour will she need?
Answers
1 batch of biscuit= 2 1/3 cups of flour
Then 3.5 batches of cookies would be:
3.5 batches of biscuit * (2 1/3 cups of flour/ batch of biscuit)= 49/6 cups of flour= 8.16 cups of flour
an equation is shown below. 3x-10x+5=5x+17 what is the value of x that makes the equation true?
Answers
collect like terms;
3x-10x=-7x
-7x+5=5x+17
move the variable to the left and change sign
-7x+5=5x+17
move the constant to the right and change sign
-7x-5x+17-5
collect the like terms
-12x=17-5
subtract the numbers
-12x=12
divide both sides by -12
your answer is: x= -1
Graph the line y+3=2(x-1) first identify the slope of the line
Answers
y + 3 = 2(x - 1)
y + 3 = 2x - 2
Then you need to put that into slope-intercept form (y = (slope)x + (y intercept))
y + 3 = 2x - 2
-3 -3
y = 2x - 5
The slope is the coefficient of x, so 2 is the slope of the line.
perform the following conversions convert 5.0 cm to m
Answers
To convert 5.0 cm to m, use the conversion factor of 1 m = 100 cm to get the result of 0.05 m.
Convert 5.0 cm to m:
1 m = 100 cm, which means 1 cm is 0.01 m.
Therefore, 5.0 cm is equal to 5.0 x 0.01 m = 0.05 m.
Suppose you buy a piece of office equipment for $17,000. After 3 years you sell it for a scrap value of $3,000. The equipment is depreciated linearly over 3 years. The rate of depreciation of the piece of equipment is
Answers
Depreciation amount = $17,000 - $3,000
Depreciation amount = $14,000
depreciation rate = $14,000/3 years
depreciation rate= $4667.67
The rate of depreciation of the piece of equipment is 27.45%.
Given that,
The cost of office equipment is $17,000.The number of years is 3And, the scrap value is $3,000.Based on the above information, the depreciation should be
= (Office equipment cost - scrap value) ÷ (Office equipment cost × number of years)
= ($17,000 - $3,000) ÷ ($17,000 × 3)
= $14,000 ÷ $51,000
= 27.45%
Therefore we can conclude that the rate of depreciation of the piece of equipment is 27.45%.
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Your favorite football team has three games left to finish the season. the outcome of each game can be win, lose or tie. the number of possible outcomes is ____.
Answers
Since there's three more games, they've had 13 so far.
There are 27 combinations of outcomes.
There are 27 possible outcomes for your favorite football team's remaining three games.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
If each game can have one of three possible outcomes (win, lose, or tie), then the total number of possible outcomes for all three games can be calculated by multiplying the number of possible outcomes for each individual game.
Since each game has three possible outcomes, the total number of possible outcomes for all three games is:
3 x 3 x 3 = 27
So there are 27 possible outcomes for your favorite football team's remaining three games.
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Is the subset w = {(x, y, z) | z = 1} ⊂ r 3 a vector subspace of r 3 ? explain why or why not?
Answers
Which equation has no solution?
A) 2.3y + 2 + 3.1y = 4.3y + 1.6 + 1.1y + 0.4
B) 32x + 25 - 21x = 10x
C) 5/8 x + 2.5 = 3/8 x + 1.5 + 1/4 x
D) 1/3 + 1/7 y = 3/7 y
PLEASE HELP!!
| THANK YOU SO MUCH |
Answers
Answer: c
Step-by-step explanation: