Answers
Triangles AED and BEC are congruent by AAS rule, so DE ≅ CE by CPCTC
What are congruent triangles?
When corresponding sides and angles of two triangles are congruent, they are said to be congruent triangles.
Given is figure of triangles,
In Δ ADC and Δ BCD,
AD ≅ BC (given)
∠ BCD ≅ ∠ ADC (given)
DC is common segment in both,
Therefore, Δ ADC ≅ Δ BCD by SAS rule
∠ DAE ≅ ∠ CBE by CPCTC
∠ AED ≅ ∠ BEC by vertically opposite angles postulate.
Δ AED ≅ Δ BEC by AAS rule
DE ≅ CE by CPCTC
Hence, Triangles AED and BEC are congruent by AAS rule, so DE ≅ CE by CPCTC
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Related Questions
Four consecutive even integers have a sum of 332. What is the least of these integer
Answers
Answer: 80
Step-by-step explanation:
set the 4 numbers to be x,x+2,x+4,x+6
They add up to 332 so the equation would be
x+(x+2)+(x+4)+(x+6)=332
4x=320
x=80
the rest of the numbers are 82,84,86
smallest is 80
HELP ME OUT OMG THANKS
Answers
Answer: r = 12
Step-by-step explanation:
11 - 23 = 12
YOUR SO WELCOME!!! :D
The perimeter of a triangle is 58 cm. The triangle is isosceles, but if its base were lengthened by 4 cm and each leg were shortened by 7 cm, then it would be equilateral. Find the base of the original
triangle.
A. 12 cm
B. 11 cm
C. 23 cm
D. 16 cm
Answers
The base of the original triangle is 12 centimetres.
How to find the base of the original triangle?A triangle is a polygon with three sides. The perimeter of a triangle is 58 cm. The triangle is isosceles.
An isosceles triangle is a triangle with 2 sides equal to each other and two angles equal to each other.
Therefore, let's find the base of the original triangle when the base were lengthened by 4 cm and each leg were shortened by 7 cm,
Hence,
let
x = length of legs
y = length of the base
Therefore,
2x + y = 58
Hence,
y + 4 = x - 7
x - y = 11
2x + y = 58
x - y = 11
3x = 69
x = 69 / 3
x = 23
-y = 11 - 23
-y = -12
y = 12
Therefore,
base of the original triangle = 12 cm
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A pillar of height 222 ft casts a shadow of 348 ft long.
Find the measure of the angle of elevation of the sun.
Answers
Using tangent of the angle, the angle of elevation is 32.5 degrees
Angle of ElevationThe angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.
In this problem, we have to use the tangent of the angle since we know the opposite and adjacent sides
opposite side = 222adjacent side = 348Tan θ = opposite / adjacent
tanθ = 222 / 348
tan θ = 0.6379
θ = tan⁻¹(0.6379)
θ = 32.5°
The angle of elevation is 32.5 degrees
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Factor the expression.
- 20a-35
The positive GCF of -20a and -35 is 5. Complete each equation with an expression or integer factor.
5x -4a=-20a
5× - 7 = - 35
The expression with 5 factored out is
Answers
Answer:
5(-4a -7) = -20a -35
Step-by-step explanation:
Could anyone help? I have to turn this in tomorrow!
Answers
Answer:
Step-by-step explanation:
5 is D
6 is also D
help meee please for a lot of points it gotta be to answer choices
Answers
Answer:
B and D
Step-by-step explanation: I got it right
What is the distance between point p and q
- P(-5,7) Q(6,7)
Answers
The distance between the two points P(-5, 7) and Q(6, 7) is 11 units.
What is the distance formula?The distance formula between two points (x₁, y₁) and (x₂, y₂) is,
D = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex].
Two points are given P(-5, 7) and Q(6, 7).
∴ D = [tex]\sqrt{(6 + 5)^2 + (7 - 7)^2[/tex].
D = [tex]\sqrt{(11)^2[/tex].
D = 11 units.
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Alan purchased three types of pipe for a plumbing job: foot of PVC pipe, foot of copper pipe, and 2 feet of cast iron
pipe. How many total feet of pipe did he purchase? (Simplify your answer and state it as a mixed number.)
O2 feet
Answers
Answer: 4 feet of pipe
Step-by-step explanation:
1(f)+1(f)+(2(f)=4(f)
f=feet
Solve for x and the missing measures given QS = 34 and TS = 3x + 2
Answers
Answer:
x = 5
TS = 17
QT = 17
Step-by-step explanation:
The tick marks show us that line segment QT is equal to TS.
QS = QT + TS and QT and TS are the same length
34 = 2(3x + 2) Distribute the 2
34 = 6x + 4 Subtract 4 from both sides
30 = 6x Divide both sides by 6
5 = x
Substitute in 5 for x
3x + 2
3(5) + 2
15 + 2 = 17
TS is 17
QT is 17
Graph the equation.
y
=
−
4
(
x
+
2
)
2
−
1
y=−4(x+2)
2
−
Answers
Answer:
see instructions
Step-by-step explanation:
1. (x + 2) = 0 gives us x = -2 = x coordinate of vertex; and
the -1 at the end gives us the y coordinate.
Move the vertex of the parabola to the point (-2,-1)
2. The -4 in front of the (x+2)² gives the direction and stretch of the parabola. FROM the Vertex, position the other point Down 4 and Right 1 (at (1,-5)).
use the parallax formula to complete the following statements correctly.
A star with a parallax angle of 0.1 arcsecond is ___ away from us:
A star with a parallax angle of 0.01 arcsecond is ___ away from us:
A star with a parallax angle of 0.001 arcsecond is _____ away from us.
A star with a parallax angle of 0.0001 arcsecond is ____ away from us.
Answers
The distance between us and a star with a parallax angle of 0.1 arcsecond is 3.26 light years.
The distance between us and a star with a parallax angle of 0.01 arcsecond is 326 light years.
The distance between us and a star with a parallax angle of 0.001 arcsecond is 3260 light years.
The distance between us and a star with a parallax angle of 0.0001 arcsecond is 32600 light years.
How do you determine distances?The distance at which an object has a parallax of 1 arcsecond is known as a parsec. 3.26 light years are about how far this is.
The length of one parsec is 3.26 light years.
One arcsecond is equal to one parsec, which is equal to 3.26 light years.
We determine the other provided arcseconds based on this comparison.
3.26 light years make up a parsec.
0.1 arcsecond = 10 parsec
= 10 * 3.26 light years
= 32.6 light years
0.01 arcsecond = 100 parsec
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Every day, Garrett's burrito stand uses 1 7/10 bags of tortillas. How many days will 8 1/2 bags of tortillas last?
Answers
Answer: 5 days.
Step-by-step explanation: To solve this problem, we first need to convert 1 7/10 bags of tortillas to a decimal number. We can do this by dividing the numerator of the fraction (7) by the denominator (10) and adding the result to the whole number (1) to get 1 + 7/10 = 1.7 bags of tortillas.
Next, we can divide the number of bags of tortillas that Garrett's burrito stand uses per day (1.7 bags) into the total number of bags of tortillas that are available (8.5 bags) to find out how many days the tortillas will last: 8.5 bags / 1.7 bags/day = 5 days
Therefore, the 8 1/2 bags of tortillas will last for 5 days.
Solve w=1/2x^2y for x
Answers
Answer : x= [tex]\sqrt{2wy}[/tex]/ y
Step-by-step explanation:
Dr. Hill charges $30 for a tutoring session, plus $0.25 per problem.
Write an equation to represent the problem.
Then, determine how many problems he helped with if he charged $47.75
Answers
Part B: 71 problems
A recipe called for the ratio of sugar to flour to be 7 : 3. If you used 63 ounces of sugar, how many ounces of flour would you need to use? Solve by using equivalent fractions.
_________________ounces of flour (write just the number)
Answers
Correct answer is:
27
Answer:
There would be 27 ounces of flour
Step-by-step explanation:
The ratio is 7:3 for sugar to flour.
I divided the 63 ounces of sugar by 7 to earn 9
Now, I multiplied 9 by 3 to get 27
Now thee ratio is 63:27
If you divide 7 and 3 you will get 2.3 repeating
If you divide 63 and 27 you will also get 2.3 repeating
Hope that makes sense! ;)
The length of a rectangle is 8 inches more than it’s width. It’s area is 308 square inches. The length is?
Answers
Answer:38.5
Step-by-step explanation:
308/8 =38.5
Answer: 8ft
Step-by-step explanation:
the length of the room is 8fr
What angles are linear pairs? Check all that apply.
Answers
Answer:
show the choices please.
Step-by-step explanation:
Old Navy had $940 worth of orders for shirts. The prices for the shirts were categorized by style: $10 for tank tops, $14 for graphic tees, and $22 for polos. The number of polos ordered was one more than half the number of graphic tees, and the number of graphic tees ordered was eight less than twice the number of tank tops. Determine the number of each type of shirt ordered.
Answers
The number of each type of shirt ordered are as follows;
number of graphic tees = 29number of tanks tops = 19number of polos = 15How to find the number of each type of shirt ordered?Old Navy had $940 worth of orders for shirts.
The prices for the shirts were categorized by style: $10 for tank tops, $14 for graphic tees, and $22 for polos.
The number of polos ordered was one more than half the number of graphic tees, and the number of graphic tees ordered was eight less than twice the number of tank tops.
let
x = number of graphic tees
Hence,
number of polos = 1 + 1 / 2 x
Number of tank tops = 1 / 2 x + 4
Therefore, the total
14x + 10(1 / 2 x + 4) + 22(1 + 1 / 2 x) = 940
14x + 5x + 40 + 22 + 11x = 940
30x + 62 = 940
30x = 878
x = 29.266667
x = 29
number of polos = 1 + 1 / 2 (29) ≈ 15
Number of tank tops = 1 / 2 (29) + 4 ≈ 19
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The microwave oven uses only 1000 watts of electricity. Does this allow you to have both the microwave oven and the toaster plugged into the circuit at the same time? Explain your reasoning.
Answers
watts
Load of microwave=1000
watts
Load of the toaster=800
watts
Load of microwave+
load of toaster<
maximum load allowed in circuit
1000+800<1800
1800<1800
, this is not true because1800
is equal to1800
and not less than that.
Leila's vegetable garden has an area of 400 ft. It is the shape of a rectangle with a length of 40 ft and a width of She has decided to expand the garden to make room for several new varieties of lettuce. The new garden will be a larger rectangle. She plans on making the new length 2 times the current length and the new' width 4 times the current width.
(a) Fill in the blanks to describe the size of Leila's new garden.
___ ft x ___ ft = ___ ft²
(b) How will the expansion change the area of the garden?
The area of the new garden will be _____ times the area of the current garden.
(c) Leila's friend Keiko also wants to expand her rectangular garden. Keiko wants her new garden to be a rectangle that has 20 times the area of her current garden. She goes to Leila for advice. Fill in the blank so that Leila's advice to Keiko is correct.
Make the new length 5 times the current length, and make the new width _____times the current width.
Answers
The answers of all the blanks are as:
a) 3200ft².
b) 8 times.
c) 100ft.
What is the area of the rectangle?
When calculating a rectangle's area, we multiply the length by the width of the rectangle.
we have,
length = 40ft
width = 10ft
Leila's vegetable garden has an area of 400 ft.
a)
new length = 40 * 2 =80ft
new width = 10 * 4 = 40ft
Therefore, this describes the size of Leila's new garden :
= 80 * 40 = 3200ft²
b)
3200 / 400 = 8
The expansion changes the area of the garden:
The area of the new garden will be 8 times the area of the current garden.
c)
Leila's friend Keiko wants to expand her rectangular garden by 20 times the area of her current garden:
400 * 20 = 8000ft²
Keiko's garden length would be 5 times the current length:
40 * 5 = 80ft
and the new width would be the current width :
new width of Keiko's garden = 8000 / 80 = 100ft.
Hence, the answers of all the blanks are as:
a) 3200ft².
b) 8 times.
c) 100ft.
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two packages of cookies cost $9.50. How much do seven packages cost?Try using a proportion to solve or finding unit rate?
Answers
Answer:
$33.25
Step-by-step explanation:
Two packages cost $9.50
Divide $9.50 by two get the cost for one package
$4.75 per package
$4.75 * 7 to get the cost for 7 packages
$33.25
Solve for y. y ≥ 10 y ≥ -10 y ≤ -10 y ≤ 10
Answers
The solution for y in the inequality is (a) y ≥ 10
How to determine the solution for x?From the question, we have the following inequality expression that can be used in our computation:
42≤4.2y
Rewrite the expression properly
So, we have the following representation
42 ≤ 4.2y
Divide both sides of the inequality by 4.2
So, we have
42/4.2 ≤ 4.2y/4.2
Evaluate the quotients
So, we have the following representation
10 ≤ y
Rewrite the expression as
y ≥ 10
Hence, the solution is y ≥ 10
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Possible question
Solve for y. 42≤4.2y
y ≥ 10 y ≥ -10 y ≤ -10 y ≤ 10
FIRST ANSWER WILL GET 100 PTS!
What mixed number is equivalent to 21 ÷ 4?
Answers
Answer:
Step-by-step explanation:
5 1/4
Answer:là
5
với số dư
1
.
5
1
4
Step-by-step explanation:
PLEASE HELP ASAP!!!! FULL ANSWER ONLY!!!
A person standing close to the edge on top of a 72-foot building throws a ball vertically upward. The quadratic function h = − 16 t^2 + 84 t + 72 models the ball's height above the ground, h , in feet, t seconds after it was thrown.
a) What is the maximum height of the ball? ____________ feet
b) How many seconds does it take until the ball hits the ground? ____________ seconds
Answers
The time taken by the ball to hit the ground is 9 seconds in quadratic equation .
What does quartic equation mean?
A fourth-degree equation, also known as a quartic equation, is one that reduces a quartic polynomial to zero and has the formula: where a 0. A quartic function's derivative is a cubic function.
a) The maximum height of the ball can be obtained by differentiating the given quadratic function, h = -16t² + 136t + 72.
Differentiating both sides.
δh/δt = -32t + 136
-32t + 136 = 0
or, t = 136/32 = 4.5.
To check whether the value of h is maximum/minimum at t = 4.5, we differentiate
δh/δt = -32t + 136
δh/δt = -32
which is < 0, which that implies, h is maximum at t = 4.5.
the maximum height, by putting in t = 4.5, in the equation, to get:
h = -16(4.5)² + 136(4.5) + 72,
or, h = -16(20.25) + 612 + 72,
or, h = -324 + 684 = 360
Therefore, The maximum height of the ball is 360 feet.
b) the quadratic function h = -16t² + 136t + 72, as the height of the ball at the ground is 0.
Therefore, it can be written as:
0 = -16t² + 136t + 72.
or, 16t² - 136t - 72 = 0.
Solving this using the quadratic equation, we get
t = - ( -136)± √(-136)² - 4( 16 ) ( -72)/2 * 16
t = 136 ± √18496 + 4608/32
t = 136 ± √23104/32
t = 136 ± 52/32
Therefore, either t = (136+152)/32 = 9,
or, t (136 - 152)/32 = -0.5.
Since t represents time, we won't take the negative value, and hence t = 9.
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When loaded with bricks, a lorry has a mass of 11600 kg. If the mass of the bricks is three times that of the empty lorry, find the mass of the bricks.
Answers
Answer:
8700kg
Step-by-step explanation:
b = mass of bricks
l = mass of lorry
b+l = total mass = 11600kg
b = 3l ==> l = b/3
substitute: b + b/3 = 11600
multiply every term by 3 to get rid of denominator: 3b + b = 34800
simplify and solve: 4b = 34800 ==> b = 8700
check: l = 8700/3 = 2900
2900 + 8700 = 11600? YES
In a certain board game, players spin a spinner to determine how many spaces they advance. The odds in favor of advancing five spaces are 3/10. Find the probability of advancing five spaces.
(b)Ravi has a box of candies with different flavors. He will randomly choose one piece of candy. The probability that he chooses a strawberry-flavored piece is 6/19. What are the odds against him choosing a strawberry-flavored piece?
Answers
The probability of advancing five spaces is 3/13 and the odds against is 13 : 6
How to determine the probability and the odds?The board game
From the question, we have the odds to be
Odds in favour = 3/10
This can be rewritten as
Odds in favour = 3 : 10
For an odd represented as a : b, the probability is
Probability = a/a + b
Using the above as a guide, we have
Probability = 3/13
The box of candies
From the question, we have the probability to be
Probability = 6/19
For a probability represented as a/b, the odds against is
Odds = b - a : a
Using the above as a guide, we have
Odds = 19 - 6: 6
Evaluate
Odds = 13 : 6
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17. Write 2 numbers that are less than -1000?
Answers
Answer: -1001, -1002
Step-by-step explanation:
Solve one and three-fourths times two-fourths equals blank.
fourteen-sixteenths
fifteen-sixteenths
one and one-sixteenth
one and two-sixteenths
Answers
Answer:
fourteen-sixteenths or seven eights = 7/8 or 14/16
Step-by-step explanation:
Which ordered pairs in the form (x, y) are solutions to the equation
7x−5y=28?
Select each correct answer.
Responses
(7, 9)
Begin ordered pair 7 comma 9 end ordered pair
(4, 10)
Begin ordered pair4 comma 10 end ordered pair
(−1, −7)
Begin ordered pair negative 1 comma negative 7 end ordered pair
(−6, −14)
Answers
The ordered pair (-1, -7) is the solution to the equation 7x - 5y = 28.
Define solutions of linear equations.The collection of variable values in linear equations that yields all feasible solutions is referred to as the solution of a linear equation. In order to describe real-world issues, linear equations contain unknown values in the form of one or more variables. The collection of values for each variable in a system of linear equations is referred to as the solution set.
Consider the equation,
7x - 5y = 28
Now put the values from options, the pair values at which LHS = RHS that will be the solution to the equation.
Put x = 77, y = 9 in the equation
7(7) -5(9)
= 49 - 45
= 4
This is not a solution.
Put x =4, y= 10
7(4) - 5(10)= 28 - 50
= -32
This is not a solution.
Put x= -1, y = -7
7(-1) - 5 (-7)
= -7 + 35
= 28
So, this is the solution to the equation as LHS = RHS
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Answer:
C. the ordered pair (1.5, 10)
Step-by-step explanation: