Answers
I hope this helps!
The required pairs of triangles in A and D are congruent triangles.
What are congruent triangles?Congruent triangles are two triangles that have the same shape and size. In other words, they are identical in every way, including their angles and side lengths. When two triangles are congruent, their corresponding sides and angles are equal.
Here,
Congruent triangles are important in geometry because they have many useful properties and can be used to solve a variety of problems. For example, if two triangles are congruent, then any corresponding parts (such as their altitudes, medians, or angle bisectors) will also be congruent. This can be helpful in finding missing side lengths or angles of a triangle.
Thus, from the above definitions Pairs of triangles in A and D are congruent triangles.
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Related Questions
A polynomial expression is shown below.
(mx³ + 3)(2x² + 5x + 2) - (8x⁵ + 20x⁴)
The expression is simplified to 8x³ + 6x² + 15x + 6. What is the value of m?
Answers
if it is reduced to 8x^3+6x²+15x+6, so we can find the value of m
(mx^3+3)(2x²+5x+2)-(8x^5+20x^4) = 8x^3+6x²+15x+6
2mx^5+5mx^4+2mx^3+6x²+15x+6-8x^5-20x^4=8x^3+6x²+15x+6
2mx^5+5mx^4+2mx^3=8x^3+6x²+15x+6-6x²-15x-6+ 8x^5+20x^4
= 8x^5+20x^4+8x^3= 4(2x^5+5x^4+2x^3)
finally
m(2x^5+5x^4+2x^3)=4(2x^5+5x^4+2x^3), and after simplification
C: m=4
4. When the expression is factored x²-3x-18 completely,
one of its factor is x-6
x²-3x-18=0
D= 9-4(-18)= 81, sqrtD=9 x=3-9/2= -6/2= -3, and x=3+9 / 2= 6
so x²-3x-18= (x-6)(x+6)
The value of the m in the polynomial expression for which the simplified expression is 8x³ + 6x² + 15x + 6 is 4.
What is the simplified form of a equation?Simplified form of an equation is the simplest way of expression the equation, which is obtained by applying the required operations of mathematics.
A polynomial expression is shown below.
[tex](mx^3 + 3)(2x^2 + 5x + 2) - (8x^5 + 20x^4)[/tex]
The expression is simplified to the following expression,
[tex]8x^3 + 6x^2 + 15x + 6[/tex]
As the equation is a simplified expression of the given polynomial. Thus, both the equation are same.
[tex](mx^3 + 3)(2x^2 + 5x + 2) - (8x^5 + 20x^4)=8x^3 + 6x^2 + 15x + 6[/tex]
Open the brackets and simplify it further,
[tex]2mx^5+5mx^4+2mx^3+6x^2+15x+6-8x^5-20x^4=8x^3 + 6x^2 + 15x + 6\\2mx^5+5mx^4+2mx^3=8x^3+6x^2+15x+6-6x^2-15x-6+ 8x^5+20x^4\\m(2x^5+5x^4+2x^3)= 8x^5+20x^4+8x^3 \\m(2x^5+5x^4+2x^3)=4(2x^5+5x^4+2x^3)[/tex]
On comparing both side of the equation, the value of m we get is,
[tex]m=4[/tex]
Thus, the value of the m in the polynomial expression for which the simplified expression is 8x³ + 6x² + 15x + 6 is 4.
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What is 15% higher than 60?
A.9
B.24
C.69
D.75
Answers
.15 x 60 = 9 + 60 = 69
Two cars start at the same time, but travel in opposite directions. One car's average speed is 30 miles per hour (mph). At the end of 4 hours, the two cars are 400 miles apart. Find the average speed in mph of the other car.
Answers
Final answer:
The average speed of the second car is calculated by subtracting the distance traveled by the first car from the total distance after both cars have traveled in opposite directions for the same amount of time. The second car's average speed is found to be 70 mph.
Explanation:
To find the average speed of the second car, we first need to establish the total distance covered by both cars. Since they are moving in opposite directions, we can add their distances together to determine the total distance.
Let's designate the distance the first car travels as D1 and the distance the second car travels as D2. The average speed of the first car is given as 30 mph, and both cars travel for 4 hours. Therefore, D1 can be calculated as follows:
D1 = average speed of first car × time = 30 mph × 4 h = 120 miles
Since we know that the combined distance D1 + D2 is 400 miles, we can find D2 by subtracting D1 from the total distance:
D2 = total distance - D1 = 400 miles - 120 miles = 280 miles
Now, to find the average speed of the second car, we divide D2 by the time, which is 4 hours:
Average speed of the second car = D2 / time = 280 miles / 4 h = 70 mph
Therefore, the average speed of the second car is 70 mph.
Write an expression that shows how to multiply 7 x 256 using the expanded form and the Distributive Property.
Answers
1. Write the greater factor in expanded form, and
2. Record partial products by using Distributive property.
Step 1.
7 x 256 = 7 x (200 + 50 + 6)
Step 2.
7 x (200 + 50 + 6) = 7 x 200 + 7 x 50 + 7 x 6
Hence, the complete expression should look like:
7 x 256 = 7 x (200 + 50 + 6) = 7 x 200 + 7 x 50 + 7 x 6
What’s 36/1000 (fraction) Simplified
What’s 506/1000 simplified (fraction)
Answers
506/1000 simplified in fraction form is 253/500.
2. 253/500
These are the simplified versions of the fractions.
Shawn has been hired as a sales associate Horizon Mobile Phone Company. He has two salary options. He can either receive a fixed salary of $750.00 per week or a salary of $400.00 per week plus an 8% commission of his weekly sales. Which solution set among the options below represents the dollar amount of sales that he must generate each week in order for the option with commission to be the better choice?
Answers
Cause he gets a base salary of 400.00 plus the 0.08 commision (8%)
He would need at least 5,000 in sales to get 8 percent which would be 400, making his salary
400+400 = 800, better than the other option of 750
25=2y-5 solve the equation for y
Answers
+5 +5
30 = 2y
/2 /2
y=15
Karl participated in a two-day charity walk. His parents donated money for each mile he walked. Karl walked 3 1/4 miles on the first day and 5 1/2 miles on the second day. His parents donated $175. How much money did his parents pay for each mile
Answers
3.25+5.5=8.75
Then we will divide 175 by the number of miles walked which in this case is 8.75.
Then we get 20 which is the amount of money that his parents donated for every mile that he walked.
10 ways to divide 96 into equal groups
Answers
These are the ten ways to divide 96 into equal groups:
96 divided by 2 = 2 groups of 48
96 divided by 48 = 48 groups of 2
96 divided by 12 = 12 groups of 8
96 divided by 8 = 8 groups of 12
96 divided by 32 = 32 groups of 3
96 divided by 3 = 3 groups of 32
96 divided by 24 = 24 groups of 4
96 divided by 4 = 4 groups of 24
96 divided by 6 = 6 groups of 16
96 divided by 16 = 16 groups of 6
the local bakery uses 1.75 cups of flour in each batch of cookies. The bakery used 5.25 cups this morning. How many batches of cookies did the barkey make?
Answers
divide total by amount needed for each batch
5.25 / 1.75 = 3
they made 3 batches of cookies
Ivan has a piece of lumber 104 inches long. He is sawing it into 12-inch lengths to make fence posts. He says he can get about 9 fence posts out of the board.
Answers
12 x 8 = 96 leaving him 8 more inches of board.
12 x 9 = 108 meaning he would need 4 more inches of lumber to make his last fence post uniform with the rest.
Each small square on the grid is 1 ft².
Which estimate best describes the area of this figure?
25 ft²
35 ft²
50 ft²
65 ft²
Answers
Answer:
50 ft²
Step-by-step explanation:
As you can see the polygon on the grid is not a regular polygon, so to calculate the area would be very complicated without having the right tools, what we can doo is to draw a squre that covers the whole height but not the total length, that way we can take a close estimate of the area, the closest square that can be formed would be a 6x9 square, and the estimated area would be 54, that would be the maximun area, so the answer would be 50 squared feet.
At a car repair shop, the cost of repair depends on the time the mechanic works. Which of the following shows this idea in function notation?
Pleas show all work.
A. number of cars (time)
B. time(cost)
C. time(number of cars)
D. cost(time)
Answers
The mechanic would charge x amount per hour,
so it would look like:
x(time)
So lets say every hour was $5 and he worked on it for 5 hours, then it would be
$5(5)
hope this helps!
i hope this helped and have a wonderful day!!
if 2/3 of the girls in class have brown eyes and 1/4 of the girls have blue eyes, what fraction of the girls in class have neither blue or brown eyes.
Answers
8/12 + 3/12 = 11/12
11/12 of the girls have blue and brown eyes. That leaves 1/12 of the girls who have neither blue nor brown eyes.
1-(8/12+3/12)
1-11/12
1/12
1/12 of girls the class has neither blue nor brown eyes.
You have to add the two fractions (2/3 and 1/4) together to get the fraction of the girls in the class that have blue or brown eyes and subtract that by one to get the fraction of the girls in the class that have neither brown nor blue eyes.
Hope this helps :)
A used electronics store pays $30 for each cell phone, spends $20 refurbishing the phone, and sells the refurbished phone to a customer for $115.
a. Write an expression in simplest form that represents the company's earnings (in dollars) from buying, processing, and selling cell phones. Use x to represent the number of cell phones they sell.
An expression is ([answer]) dollars.
Answers
I am subtracting the amount it took to make the phone, from the amount they sell the phone to a customer for.
115-(30+20)=x
115-50=x
65=x
Charlie made four out of 23 free-throw shots. What percentage of shots does he make? Round to the nearest whole number
Answers
He attempts a total of 23 shots.
His accuracy is 4/23 * 100, or 400/23 %.
He makes 17.39% of his shots.
Two families are sharing the cost of vacation home for one week. The cost to rent the home is $3,513 plus a $351.30 deposit. What is each family’s fair share of the home plus deposit?
$1756.50
$1128.10
$1932.15
.
$1432.15
Answers
The answer is $1932.15
3,513+351.30=3864.30
3864.30÷2=1932.15
Hope this helps!
whats 603X4 estimate go math
Answers
Multiply 600 and 4.
=2400
603 X 4≈2400
600 x 4 = 2,400
A motorcross rider is in the air for 2.5 seconds. Your camera can take a picture very 0.125 second. Your friend's camera can take a picture every 0.15 second.
a. How many times faster is your camera than your friend's camera?
b. How many more pictures cna you take while the rider is in air?
Answers
b. 3 and 1/3 more pictures
Which point represents the fraction 3/6???
A
B
C
or
D
????
PLEASE HELP
Answers
c is 1/2 of 1
The point that represents the fraction 3/6 is point B.
Explanation:The point that represents the fraction 3/6 is point B.
When we simplify the fraction 3/6, we obtain 1/2.
To represent a fraction on a number line, we divide the line segment between 0 and 1 into equal parts. Since the denominator is 2, we divide the segment into 2 equal parts. The numerator, 1, represents the number of parts we need to take from the line (starting from 0) to reach the fraction. Thus, we locate point B on the number line to represent the fraction 3/6.
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Jason works at least 5 hours but not more than 10. He earns $15.30 per hour. The function f (t) = 15.3t represents the money he earns for working t hours. What is the practical range? Show all your work.
1. Correctly determine the minimum and maximum money earned.
2. Correctly identify the practical range as inclusive or exclusive.
3. Correctly state the practical range.
Answers
1. The minimum number of hours is 5 hours, so the minimum money earned is:
minimum money = 15.30 * 5 = $76.50
The maximum number of hours is 10 hours, so the maximum money earned is:
maximum money = 15.30 * 10 = $153
2. Since the words “at least” and “not more than” are used, hence this is inclusive.
3. The practical range is:
$76.50 ≤ f(t) ≤ $153
Answer:
$76.50 ≤ f(t) ≤ $153
Step-by-step explanation:
Alicia and Elena each earned $135 doing telephone surveys. Alicia did her surveys in 12 hours. It took Elena 75% as long to do her surveys. How much money did Elena earn per hour? A. $7 B. $11 C. $12 D. $15
Answers
Alicia worked for 12 hours.
Elena worked for 75% of 12 hours = 0.75*12 = 9 hours.
Elena's earning rate is
($135)/(9 hours) = $15 per hour.
Answer: D. $15
Answer:
d 15
Easy. As that
write the addition sentence illustrated by each figure
Answers
32. The answer is -2+9=7
33. -11+9=-2
34. -6+(-3)=-9
Jennifer has 3 1/2 cups of jelly beans to share with 7 friends how many cups does each person get
Answers
=3 1/2 ÷7
=1/2
each person gets 1/2 cup
In the diagram shown, ∠2 measures 77 degrees. What is the measure of ∠4?
Answers
A skydiver jumps out of an airplane. After 0.8 seconds, she has fallen 100 feet. After 3.1 seconds, she has fallen 500 feet. Emtiaz says that the skydiver should fall about 187.5 feet in 1.5 seconds. Is his answer reasonable? Explain.
Answers
g = 32 ft/s², acceleration due to gravity.
Ignore air resistance.
The distance fallen after t seconds is
s = (u ft/s)*(t s) + (1/2)*(32 ft/s²)*(t s)² = ut + 16t²
When t = 0.8 s,
s = 0.8u + 16*0.8² = 0.8u + 10.24
Because s = 100 ft, therefore
u = (100 - 10.24)/0.8 = 112.2 ft/s
When t = 3.1 s,
s = 112.2*3.1 + 16*3.1² = 501.6 ft
This compares favorably with 500 ft.
When t = 1.5 s, then
s = 112.2*1.5 + 16*1.5² = 204.3 ft
This disagrees with the specified value of 187.5 ft
Answer:
The answer is not reasonable.
Reason:
The answer does not obey the equation
s = u + (1/2)gt²
the temperature on monday was -1.5°C. The temperature on Tuesday was 2.6°C less than the temperature on Monday.what was the temperature on Tuesday?
Answers
[tex]-1.5+(-2.6)[/tex]
So then the temperature on Tuesday is -4.1.
Gas is $2.09 per gallon; how much will it cost to get 10 gallons of gas?
$20.90
$12.09
$7.91
$4.10
Answers
$2.09 * 10 gallons= $20.90
Remember that to multiply by 10, you can just move the decimal one place value to the left.
Final answer: $20.90
A softball is thrown straight up, reaching a maximum height of 20 meters, what is the ball's approximate vertical speed when it hits the ground?
Answers
Velocity is the rate of change of distance over time.
The ball's approximate vertical speed when it hits the ground is 19.8m/s
The maximum height of an object, thrown up is calculated as:
[tex]\mathbf{h_{max} = \frac{v^2}{2g}}[/tex]
Where:
[tex]\mathbf{h_{max} = 20m}[/tex] --- the maximum height
[tex]\mathbf{v = ??}[/tex] --- final velocity
[tex]\mathbf{g = 9.8ms^{-2}}[/tex] --- acceleration due to gravity
So, we have:
[tex]\mathbf{h_{max} = \frac{v^2}{2g}}[/tex]
[tex]\mathbf{20 = \frac{v^2}{2 \times 9.8}}[/tex]
Solve for v^2
[tex]\mathbf{v^2 = 2 \times 9.8 \times 20}[/tex]
[tex]\mathbf{v^2 = 392}[/tex]
Take square roots of both sides
[tex]\mathbf{v = 19.8ms^{-1}}[/tex]
Hence, the ball's approximate vertical speed when it hits the ground is 19.8m/s
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When a softball is thrown straight up and reaches a maximum height of 20 meters, the approximate vertical speed when it hits the ground can be determined by taking into account the initial vertical velocity and the time it takes to reach the maximum height and fall back down. Using the given information, the initial vertical velocity is calculated using the equation v0y = sqrt(2gh), where g is the acceleration due to gravity and h is the maximum height. Substituting the values, the approximate vertical speed is 19.80 m/s.
Explanation:When a softball is thrown straight up and reaches a maximum height of 20 meters, its approximate vertical speed when it hits the ground can be determined using the principles of projectile motion. The vertical speed of the ball when it hits the ground can be calculated by taking into account the initial vertical velocity and the time it takes for the ball to reach its maximum height and then fall back down. In this case, since the ball is thrown straight up, the vertical speed when it hits the ground will be equal to the initial vertical speed.
Using the given information, we know that the ball reaches a maximum height of 20 meters. We can calculate the time it takes for the ball to reach this height using the equation for vertical displacement:
h = v0yt + (1/2)gt2
Where:
h is the vertical displacement (20 meters in this case)v0y is the initial vertical velocity (which we need to find)t is the time it takes to reach the maximum heightg is the acceleration due to gravity (approximately 9.8 m/s2)Since we know the maximum height and the acceleration due to gravity, we can rearrange the equation to solve for the initial vertical velocity:
v0y = sqrt(2gh)
where:
sqrt represents the square rootg is the acceleration due to gravity (approximately 9.8 m/s2)h is the maximum height (20 meters in this case)Substituting the values into the equation, we get:
v0y = sqrt(2 * 9.8 * 20)
Simplifying further:
v0y = sqrt(392)
v0y ≈ 19.80 m/s
Therefore, the approximate vertical speed of the ball when it hits the ground is 19.80 m/s.
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Solve for x. The triangles in each pair are similar.