The figure shows two parallel lines AB and DE cut by the transversals AE and BD:
Which statement best explains the relationship between Triangle ABC and Triangle EDC ?
A. Triangle ABC is similar to triangle EDC , because m∠2 = m∠6 and m∠1 = m∠5
B. Triangle ABC is similar to triangle EDC , because m∠3 = m∠6 and m∠1 = m∠4
C. Triangle ABC is congruent to triangle EDC , because m∠3 = m∠4 and m∠1 = m∠5
D. Triangle ABC is congruent to triangle EDC , because m∠3 = m∠6 and m∠1 = m∠4
Answers
Related Questions
What is the distance between the points (3,8) (-9,8)
A)5
B)10
C)15
D)20
Answers
So the distance is simply 3 - -9 = 12.
So all answers are wrong or you made a typo!
The distance between the points (3,8) and (-9,8) is 12. The correct answer is option B) 10.
Explanation:The distance between two points can be found using the distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2). In this case, the coordinates of the two points are (3,8) and (-9,8). Plugging these values into the formula, we get:
d = √((-9 - 3)^2 + (8 - 8)^2)
d = √((-12)^2 + (0)^2)
d = √(144 + 0)
d = √144
d = 12
Therefore, the distance between the points (3,8) and (-9,8) is 12. The correct answer is option B) 10
Learn more about Distance between points here:https://brainly.com/question/15958176
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solve The quantity 2 x minus 10 divided by 4 = 3x
Answers
(2x-10)/4=3x multiply both sides by 4
2x-10=12x subtract 12x from both sides
-10x-10=0 add 10 to both sides
-10x=10 divide both sides by -10
x=-1
To solve the equation 2x - 10 / 4 = 3x, multiply both sides by 4, simplify, and solve for x to find its value as -1.
Step 1: Multiply both sides of the equation by 4 to get rid of the fraction:
4 * (2x - 10) / 4 = 4 * 3x
Step 2: Simplify the equation:
2x - 10 = 12x
Step 3: Rearrange the equation to solve for x:
2x - 12x = 10
-10x = 10
x = -1
It takes 113 pounds of seed to completely plant a 12 -acre field. how many acres can be planted per pound of seed?
Answers
It takes about 9lbs of seed to plant 1-acre, so to find the answer divide 12/113 and you get how many acres 1lb of seed could cover.
Hope this helps :-)
Ten is no more than 4 times the sum of twice a number and 3? Equation?
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[tex]Ten: 10 \\ NoMore: less \\ 4times: 4 And Multiply \\ sum: + (add) \\ twice: 2 \\ number: a \\ 3: 3 \\ \\ \\ \\ \\ \\ Answer: 10 \leq 4 (2a + 3) \\ \\ \\ \\ Good\\ luck\\ on \\ your \\ assignment \\ \\ enjoy \\ your \\ day \\ \\ \\ \\ MeIsKaitlyn :)[/tex]
A gardener has 27 pansies and 36 daisies he ants an equal number of each type of flower in each row what is the greatest possible number of pansies in each row
Answers
The possible rows that will contain equal numbers of pansies are
1 row, 27 pansies in the row, or
3 rows, 9 pansies per row, or
9 rows, 3 pansies per row.
There are 36 daisies.
The possible rows that will contain equal numbers of daisies are
1 row, 36 daisies in the row,
2 rows, 18 daisies per row, or
3 rows, 12 daisies per row, or
4 rows, 9 daisies per row, or
6 rows, 6 daisies per row, or
9 rows, 4 daisies per row, or
12 rows, 3 daisies per row, or
18 rows, 2 daisies per row.
The only common row combination is 3 rows, with 9 pansies and 12 daisies per row.
Answer: 9 pansies in each row.
If 3 is added to a number and the sum is tripledtripled, the result is 27 more than the number. find the number.
Answers
To solve this problem, let us say that the number is called x and let us do this step by step.
1st step: 3 is added to the number, therefore:
x + 3
2nd step: the sum is tripled, therefore:
3 (x + 3)
3rd step: the result in the 2nd step is equal to 27 more than the original number, therefore:
3 (x + 3) = x + 27
4th step: find for the value of x using the equation
3 x + 9 = x + 27
3 x – x = 27 – 9
2 x = 18
x = 9
Answer:
The number is 9
Jane Marko buys a car for $43,900. In three years, the car depreciates 48% in value. How much is the car worth in 3 years
Answers
How do you use the slope to prove lines are parallel or perpendicular?
How do you write an equation of a line so that it is parallel or perpendicular to a given point?
Answers
Final answer:
To prove lines are parallel, their slopes must be equal, and to prove they are perpendicular, their slopes must be negative reciprocals. To write an equation for a parallel line, use the same slope as the original; for a perpendicular line, use the negative reciprocal of the original line's slope. Manipulating a line involves changing either its slope or intercept.
Explanation:
To use slope to prove that lines are parallel or perpendicular, you need to compare their slopes. Two lines are parallel if their slopes are equal. Conversely, two lines are perpendicular if their slopes are negative reciprocals of each other, meaning that one slope is the negative inverse of the other (e.g., the slope of one line is 2 and the other is -1/2).
To write an equation of a line so that it is parallel to a given line, you must use the same slope as the given line. If the equation of the given line is y = mx + b, then the equation of a parallel line will be y = mx + c, where c is a different y-intercept. To write an equation of a line so that it is perpendicular to a given line, you use the negative reciprocal of the slope of the given line. If the slope of the given line is m, then the slope of the perpendicular line will be -1/m.
For example, consider a line with the equation y = 3x + 9, which signifies a slope of 3 and a y-intercept of 9 based on Figure A1. A parallel line would have a slope of 3 but could have a different y-intercept, such as y = 3x + 4. A perpendicular line would have a slope of -1/3, so it could be something like y = -1/3x + 5.
Manipulating a line involves changing its slope (m) or intercept (b). Changing the slope will tilt the line, while changing the intercept will shift the line up or down on the graph. Understanding how to read and manipulate a graph is crucial for visualizing these changes.
Each triangle is a 30-60-90 triangle, and the hypotenuse of one triangle is the longer leg of an adjacent triangle. the hypotenuse of the larger triangle is 16 centimeters. what is the number of centimeters in the length of the longer leg of the smaller triangle?
Answers
The length of the longer leg of the smaller triangle is 8[tex]\sqrt{3}[/tex] centimeters.
In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows:
- The length of the shorter leg is x.
- The length of the longer leg is x[tex]\sqrt{3}[/tex].
- The length of the hypotenuse is 2x.
Given that the hypotenuse of the larger triangle is 16 centimeters, we can set up the equation:
2x = 16
Solving for x:
x = [tex]\frac{16}{2}[/tex] = 8
Now, we know that the length of the longer leg of the larger triangle is x[tex]\sqrt{3}[/tex] = 8[tex]\sqrt{3}[/tex] centimeters.
Since the hypotenuse of the larger triangle becomes the longer leg of the smaller triangle, the longer leg of the smaller triangle is 8[tex]\sqrt{3}[/tex] centimeters.
The question is:
There are two triangles. Each triangle is a 30-60-90 triangle, and the hypotenuse of one triangle is the longer leg of an adjacent triangle. the hypotenuse of the larger triangle is 16 centimeters. What is the number of centimeters in the length of the longer leg of the smaller triangle?
Sasha sets a goal to read 5 minutes longer than each previous day for 30 days. On the first day, Sasha reads for 20 minutes. The expression mc018-1.jpg represents the total number of minutes Sasha reads during the 30 days. How many total minutes does she read?
Answers
Final answer:
Sasha reads a total of 2775 minutes over 30 days, calculated using the formula for the sum of an arithmetic sequence.
Explanation:
To calculate the total number of minutes Sasha reads over 30 days, we note that she starts with 20 minutes on the first day and reads 5 minutes more each subsequent day. This is an arithmetic sequence where the first term (a1) is 20 minutes, the common difference (d) is 5 minutes, and the number of terms (n) is 30.
We can use the formula for the sum of an arithmetic sequence: Sn = n/2 (2a1 + (n - 1)d).
Plugging in the given values gives us S30 = 30/2 (2(20) + (30 - 1)(5)).
Now we calculate: S30 = 15(40 + 29(5)) = 15(40 + 145) = 15(185) = 2775 minutes.
Therefore, Sasha reads a total of 2775 minutes over the course of 30 days.
Simplify 8 − (14)
1. −22
2. −6
3. 6
4. 22
Answers
Answer:
2
Step-by-step explanation:
-6
A coin is tossed 72 times. Find the standard deviation for the number of heads that will be tossed
Answers
The probability of obtaining heads (success) is p = 1/2.
In n tosses, the expected statistical parameters are
m = np, the mean
σ = √[np(1-p)]
In 72 tosses of the coin, the standard deviation for the number of heads obtained is
σ = √[72*(0.5)*(0.5)]
= 4.243
Answer: 4.243
The standard deviation for the number of heads that will be tossed is [tex]\boxed{4.24}.[/tex]
Further Explanation:
The random variable X follows binomial distribution.
[tex]\boxed{X \sim {\text{Bin}}\left( {n,p} \right)}[/tex]
Here, n represents the total number of experiments and p denotes the probability of the event.
Apply central limit theorem.
[tex]\boxed{X \sim {\text{Normal}}\left( {np,np\left( {1 - p} \right)} \right)}[/tex]
The mean of the binomial distribution can be calculated as follows,
[tex]\boxed{{\text{Mean}} = n \times p}[/tex]
The standard deviation of binomial distribution can be calculated as follows,
[tex]\boxed{{\text{Standard deviation}} = \sqrt {np\left( {1 - p} \right)} }[/tex]
Given:
Coin is tossed 72 times.
Explanation:
Consider X is the random variable that head will occur.
The probability of head occur is [tex]p = \dfrac{1}{2}.[/tex]
The mean can be calculated as follows,
[tex]\begin{aligned}{\text{Mean}}&= 72\times \frac{1}{2}\\&= 36\\\end{aligned}[/tex]
The standard deviation of the number of heads can be calculated as follows,
[tex]\begin{aligned}{\text{Standard deviation}}&= \sqrt {72 \times \frac{1}{2}\left( {1 - \frac{1}{2}} \right)} \\&= \sqrt {72 \times\frac{1}{2} \times \frac{1}{2}}\\&=\sqrt{\frac{{72}}{4}}\\&= \sqrt {18}\\&= 4.24\\\end{aligned}[/tex]
Hence, the standard deviation for the number of heads that will be tossed is [tex]\boxed{4.24}.[/tex]
Learn more:
1. Learn more about normal distribution https://brainly.com/question/12698949
2. Learn more about standard normal distribution https://brainly.com/question/13006989
3. Learn more about confidence interval of mean https://brainly.com/question/12986589
Answer details:
Grade: College
Subject: Statistics
Chapter: Binomial Distribution
Keywords: coin, tossed 72 times, number of heads, binomial distribution, standard normal distribution, standard deviation, test, measure, probability, low score, mean, repeating, indicated, normal distribution, percentile, percentage, proportion, empirical rule.
A group of men and women were asked what their favorite pet was, and the results of the survey were tabulated.Petey is considering investing $19 in a certain company. Financial advisors forecast that there is a 30% chance that the stock will increase in value by 10%, and a 70% chance he will lose his initial investment. Determine if Petey should make the investment, and find the expected value of the investment.
Answers
For the first part:
A group of men and women were asked what their favorite pet was, and the results of the survey were tabulated.
[tex]\begin{center} \begin{tabular} {|c|c|c|c|c|} & Cats & Dogs & Other & Total \\ [1ex] Male & 42 & 58 & 6 & 106 \\ Female & 52 & 48 & 2 & 102 \\ [1ex] Total & 94 & 106 & 8 & 208 \end{tabular} \end{center}[/tex]
Let event A be defined as randomly choosing someone who picked cats or dogs as their favorite pet. Let event B be defined as a randomly chosen person being male.
Find P(B| NOT A).
P(A) = P(choosing cat) + P(choosing dog) = [tex] \frac{94}{208} + \frac{106}{208} = \frac{200}{208} = \frac{25}{26}[/tex]
P(NOT A) = [tex]1- \frac{25}{26} = \frac{1}{26} [/tex]
P(B and NOT A) = P(males that did not choose cat or dog) = [tex] \frac{6}{208} = \frac{3}{104} [/tex]
P(B | NOT A) = [tex] \frac{P(B \, and \, NOT \, A)}{P(NOT \, A)} = \frac{ \frac{3}{104} }{ \frac{1}{26} } =\frac{3}{104}\times26= \frac{3}{4} [/tex]
For the second part of the question.
Petey is considering investing $19 in a certain company. Financial advisors forecast that there is a 30% chance that the stock will increase in value by 10%, and a 70% chance he will lose his initial investment. Determine if Petey should make the investment, and find the expected value of the investment.
If his investment increases by 10%, the value of the investment will be 1.1 x $19 = $20.90 with a probability of 30% or 0.3
The expected value of the investment is given by
[tex]\$20.90\times0.3+(-\$19\times0.7)=\$6.27-\$13.30=-\$7.03[/tex]
Therefore, Petey should not make the investment as there is an expectation of a loss from the investment.
Identify the property that justifies the statement: If 4x-3=7, then 4x=10
Answers
The equation shown above is showing the Addition Property of Equation where the number “3” is added to both of its sides. This is shown below,
4x - 3 = 7
4x - 3 + 3 = 7 + 3
4x = 10
I need help finding ac, cb, and ab
Answers
CB is 3x-4
AB= 2x+1+3x-4
A carpenter is assigned a job of installing a spa into a pre-existing deck. The dimensions of the deck are (5x + 2) wide by (3x + 1) long. The dimensions of the spa are (2x + 3) wide by (x + 2) long.
Write the polynomial that represents the remaining area of the deck after the carpenter cut the hole out for the spa.
Find the area of the new deck if x = 2 feet.
Answers
The area of the deck is
A₁ = (5x + 2)(3x + 1)
= 15x² + 5x + 6x + 2
= 15x² + 11x + 2
Answer: 15x² + 11x + 2
The dimensions of the spa are (2x + 3) wide by (x + 2) long.
The area of the spa is
A₂ = (2x + 3)(x + 2)
= 2x² + 4x + 3x + 6
= 2x² + 7x + 6
Answer: 2x² + 7x + 6
The area remaining after the hole for the spa has been cut from the deck(the area of the new deck) is
A = A₁ - A₂
= 15x² + 11x + 2 - (2x² + 7x + 6)
= 15x² - 2x² + 11x - 7x + 2 - 6
= 13x² + 9x - 4
Answer: 13x² + 9x - 4
If x = 2 feet, the area of the new deck is
A(2) = 13*2² + 9*2 - 4 = 78 ft²
Answer: 78 ft²
For a daily airline flight between two cities, the number of pieces of checked luggage has a mean of 380 and a standard deviation of 20. What number of pieces of checked luggage is 3 standard deviations above the mean?
Answers
Answer:
The answer is 440 pieces of checked luggage
Step-by-step explanation:
Mean = 380
Standard deviation = 20
No. of pieces of checked luggage for 1 standard deviation = 20 pieces
Therefore, Mean for 3 standard deviations above the mean = 3 × 20 = 60
Now, number of pieces of checked luggage 3 standard deviations above the mean = Mean for 1 standard deviation + Mean for 3 standard deviations above the mean
⇒ 380 + 60 = 440 pieces
What is the final transformation in the composition of transformations that maps pre-image ABCD to image A"B"C"D"?
Answers
a 270-degree rotation about point B
A store manager is looking at past jewelry sales to determine what sizes of rings to keep in stock. The list shows the ring sizes purchased by the last ten jewelry customers.
9, 7, 6.5, 7.5, 7, 8, 5, 6, 7.5, 8
What is the variance of the data? Round to the nearest hundredths.
Answers
Mean = 9 + 7 + 6.5 + 7.5 + 7 + 8 + 5 + 6 + 7.5 + 8 / 10
Mean = 6.4
Squared of the sum of the differences = (9-6.4)^2 + (7-6.4)^2 + (6.5-6.4)^2 + (7.5-6.4)^2 + (7-6.4)^2 + (8-6.4)^2 + (5-6.4)^2 + (6-6.4)^2 + (7.5-6.4)^2 + (8-6.4)^2 = 17.15
Variance = 17.15 / 10 = 1.715
I REALLY NEED HELP ON THESE EQUATIONS THE LAST PIC AND THIS ONE PLEASEEE IM IN DANGER OF FAILING
Answers
so, we know the boat is going at a rate of "x", and the current has a rate of "y".
ok... from A to B, the boat is going downstream, the speed of the boat is not really "x", is " x + y ", because, is going with the stream and thus the current is adding "y" to its speed.
now, from B to A, the boat is going upstream, against the current, is not really going "x" fast either, is going " x - y ", because the current is eroding/subtracting from it's speed.
ok... since, since the towns A and B didn't really move, unless they're floating towns, but they're not, so, the distance from A to B is the same distance from B to A, say they're at a distance "d".
[tex]\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ downstream&d&x+y&3\\ upstream&d&x-y&3.6 \end{array} \\\\\\ \begin{cases} \boxed{d}=(x+y)3\\ d=(x-y)3.6\\ \boxed{3(x+y)}=3.6(x-y) \end{cases} \\\\\\ 3(x+y)=3.6(x-y)\implies 3x+3y=3.6x-3.6y \\\\\\ 3y+3.6y=3.6x-3x\implies 6.6y=0.6x\implies y=\cfrac{0.6x}{6.6} \\\\\\ y=\cfrac{1}{11}x\implies \textit{y is }\frac{1}{11}x\textit{ or about }9\%\textit{ the speed of \underline{x}}[/tex]
In the past ten years, the population of a city decreased from 90,000 to 75,000 Find the percent decrease.
Answers
((75,000−90,000)÷90,000)×100
=−16.7%
Please HELP. Thank you
Answers
I would go with A because the lengths of the sides don't abide by the pythagorean theorem rule: A^2 + B^2 = C^2
Point C to Point B appears to have a slope of 2/3, 3 blocks apart (in width) and 2 blocks apart (in height). Using a^2 + b^2 = c^2 will help where ^2 means (squared).
(2 x 2) + (3 x 3) = 13
Line CB is (square root) of 13.
Point A and B are 2 blocks apart (width) and 3 blocks apart (height), so using what we did in the last step...
(3 x 3) + (2 x 2) = 13
Line AB is (square root) of 13.
So now... With Line AB and Line CB being the square root of 13, the line AC should be (square root) (13 + 13), so (square root) 26. If it does equal this, then it is a right-triangle.
Point C and A are 1 block apart (width) and 5 blocks apart (height) so...
(1 x 1) + (5 x 5) = 26
Square root of 26...
In conclusion, the Triangle IS a Right-angle and you should pick "D"
What is the area of the triangle?
Answers
answer
first one.
24 square units
If M is the midpoint of FG and MG = 7x-15, FG = 33, X = ?
Answers
The given expression gives x = 4.5.
If M is the midpoint of FG, this means that M divides FG into two equal segments. Therefore, FM = MG. We are given that MG = 7x - 15 and the total length of FG = 33. Hence, FM = MG = (1/2) * (FG).
Step-by-step solution:
Set up the equation for FM: FM = MG = (1/2) * 33.
This simplifies to FM = MG = 16.5.
Since MG = 7x - 15, we set 7x - 15 equal to 16.5.
Solve for x: 7x - 15 = 16.5.
First, add 15 to both sides: 7x = 31.5.
Finally, divide both sides by 7: x = 4.5.
Therefore, the value of x is 4.5.
16x+9=9y−2x
solve for y
I am confused on how to solve for y, I learned it but I forgot how to can some one please help me?
Answers
16x + 9 = 9y - 2x
Add 2x to both sides to isolate y (get it by itself on one side of the equation).
16x + 2x = 18x
-2x + 2x = 0
18x + 9 = 9y
Divide both sides by 9 to solve for y.
18x / 9 = 2x
9 / 9 = 1
9y / 9 = y
We are now left with:
2x + 1 = y
I hope this helps!
A stock can go up, go down, or stay unchanged. how many possibilities are there if you own 66 stocks?
Answers
Use cavalieri's principle to a circular pillar candle is 2.8 inches wide & 6 inches tall. find the volume of the candle.
Answers
The volume of the cylinder is Area(base)*height =
[tex] \pi R^{2} *H=3.14* (1.4)^{2}*6= 37[/tex] (in cubed)
According to Cavalieri's principle, the volume of the candle is equal to the volume of the cylinder we described.
Answer: 37 in cubed
You have 12 balloons to blow up for a party. You blow up 1313 of them, and your friend blows up 5 of them. What fraction of the balloons still need blowing up?
Answers
u blow up 1/3.....1/3(12) = 12/3 = 4....so u blow up 4 out of 12...thats 4/12
ur friend blows up 5...he blows up 5 out of 12....thats 5/12
so 4/12 + 5/12 = 9/12....9/12 are blown up.....that leaves 3/12 or 1/4 left to blow up
Answer:
The Answer Is 1/4
Step-by-step explanation:
Ur brain xd
The formula a = 118e^0.024t models the population of a particular city, in thousands, t years after 1998. when will the population of the city reach 140 thousand?
Answers
So, substituting the values:
140 = 118 e^0.024t
140/118 = e^0.024t
Taking the natural logarithm, ln, on both sides,
ln (140/118) = lne^0.024t
ln(140/118) = 0.024t
t = ln(140/118) ÷ 0.024
t = 7.12 years
So, that would be approximately 7 years after 1998. The population would reach 140 thousand in year 2005.
Final answer:
To find when the population of the city will reach 140 thousand, the formula a = 118e⁰.⁰²⁴t must be solved, resulting in approximately 3.52 years after 1998.
Explanation:
The formula a = 118e^0.024t models the population of a city, in thousands, t years after 1998. To find when the population reaches 140 thousand, set the formula equal to 140 and solve for t:
a = 118e⁰.⁰²⁴t
140 = 118e⁰.⁰²⁴t
t = (ln(140/118)) / 0.024 ≈ 3.52 years after 1998.
(02.06 MC)
What is the measure of angle x?
A pair of parallel lines is cut by a transversal. An exterior angle on the left of the transversal is labeled as 40 degrees. An interior angle on the right of the transversal, which is not vertically opposite to the 40 degree angle, is labeled as x.
40 degrees
80 degrees
130 degrees
140 degrees