Given:
In triangle ACD, BE||CD, AB = 20 cm, BC = 5 cm, CD = 18 cm, AE = 26 cm.
To find:
(a) The length of ED.
(b) The length of BE.
Solution:
In triangle ABE and ACD,
BE||CD, so angle ABE and angles ACD are corresponding angles. So, their measure are equal.
[tex]m\angle ABE=m\angle ACD[/tex] (Corresponding angles)
[tex]m\angle BAE=m\angle CAD[/tex] (Common angle)
Now,
[tex]\Delta ABE\sim \Delta ACD[/tex]
Corresponding sides of similar triangles are proportional.
[tex]\dfrac{AB}{AC}=\dfrac{BE}{CD}=\dfrac{AE}{AD}[/tex]
(a)
[tex]\dfrac{AB}{AC}=\dfrac{AE}{AD}[/tex]
[tex]\dfrac{20}{20+5}=\dfrac{26}{AD}[/tex]
[tex]\dfrac{20}{25}=\dfrac{26}{AD}[/tex]
[tex]0.8=\dfrac{26}{AD}[/tex]
Isolate AD.
[tex]0.8AD=26[/tex]
[tex]AD=\dfrac{26}{0.8}[/tex]
[tex]AD=32.5[/tex]
Now,
[tex]AD=AE+ED[/tex]
[tex]32.5=26+ED[/tex]
[tex]32.5-26=ED[/tex]
[tex]6.5=ED[/tex]
Therefore, the length of ED is 6.5.
(b)
[tex]\dfrac{AB}{AC}=\dfrac{BE}{CD}[/tex]
[tex]\dfrac{20}{25}=\dfrac{BE}{18}[/tex]
[tex]0.8=\dfrac{BE}{18}[/tex]
Multiply both sides by 18.
[tex]14.4=BE[/tex]
Therefore, the length of BE is 14.4.
What is the median in this set of data?
14, 19, 26, 28, 18, 21, 30, 27
Answer:24
Step-by-step explanation:
Since the numbers in the middle are 21 and 27, you add both and divide by 2 to get the number in the middle of those 2.
Answer:
24
Step-by-step explanation:
it is the median in the set.
Tell whether the equation has one solution, no solution, or infinitely many solutions. 3x - 7 = 3(x - 3) + 2
Answer:3x-7=3(x-3)+2
3x-7=3x-9+2
3x-7=3x-7
Group like terms
3x-3x=-7+7
0=0
Step-by-step explanation: the above calculations implies that, the equation has no solution, since all the unknown variables also vanish to zero.
which two expressions are equivalent?
A) 5x-5 and 5(x-5)
B) 5(x-5) and 5x-25
C) 5x-1 and 5(x-5)
D) 5x(x-1) and 5x-5
I need help asap thank you :)
Answer:
b
Step-by-step explanation:
please help, urgent. picture shown.
Answer: 80
Step-by-step explanation:
First, find the area of the square by doing 12 x 12. (Which = 144)
Then, find the area of the circle. This is found by using the formula of 1/4 • π • 9 squared.
This should get you 63.62, or 64 when rounded up.
You then subtract 64 from 144 and get 80 for your answer.
good night all ✨
[tex] {\boxed{\tt 1.}} \: \: \tt 24 + 5 \times 14 \div 2 = [/tex]
[tex]{\boxed{2.}} \: \: \: \tt 200 \div 4 \times 6 = [/tex]
must accompany "step by step"! :)
Answer:
1. 24+5*14/2=
step 1. 24+5=29
step 2: 14/2=7
step 3: 29*7=59!
2. 200/4*6=
step 1: 4*6= 24
step 2: 25/200= 300!
Step-by-step explanation:
hope this helps did step by step explanation! brainliest?
1. 24+(5×14)÷2
=24+70÷2
=24+35
=59
2. 200÷4×6
=50×6
=300
PLS help!!
Function 1 is defined by the equation d=-3/7t-4
Function 2 is defined by the following table.
Which Function has a more negative slope?
O function 1
O function 2
O both have the same slope
Answer:
function 2
Step-by-step explanation:
Answer:
Function 2
Step-by-step explanation:
Find the slope of the line whose equation is 7x - 2y = 4.
-2
7/2
4/7
HELP PLEASE!!! NOW :(
PLEASE HELP ME FAST!!! Monica's bicycle wheel has a radius of 16 inches. Kevin's tricycle wheel has a radius of 8 inches. How many times larger is the circumference of Monica's wheel that the circumference of Kevin's tricycle wheel? Show your work
Answer:
50.2 inches
Step-by-step explanation:
The wheel of a tricycle is circular in shape.
The circumference of a circle = 2πr
For Monice
Monica's bicycle wheel has a radius of 16 inches.
The circumference of her bicycle wheel = 2 × π × 16
= 100.53096491 inches
Approximately = 100.5 inches
For Kevin
Kevin's tricycle wheel has a radius of 8 inches.
The circumference of his wheel =
2 × π × 8
= 50.265482457 inches
Approximately = 50.3 inches
How many times larger is the circumference of Monica's wheel that the circumference of Kevin's tricycle wheel?
This is calculated as:
Circumference of Monica's wheel - Circumference of Kevin's wheel
= 100.5 inches - 50.3 inches
= 50.2 inches
Hence: Monica's wheel is 50.2 inches larger than Kevin's wheel
Answer: All I know is I got a 1/2 points on my open ended question. Monica’s bicycle wheel is 2 times larger than Kevin’s.
Step-by-step explanation: I think you add or multiply or divide. I gotta figure it out myself.
-4 + -7 ?
HELLPP
Can somebody explain to me please
Answer:
−4−7
=−4+−7
=−11
Step-by-step explanation:
if its the same sign add, different signs keep the sing of the larger number
g(x)=-3x - 2
f(x) = 3x + 1
Find g(x) ÷ f(x)
Answer:
15
Step-by-step explanation:
Anyone know the answer?!
Answer:
the correct answer is C) x - 6y = 14
Write an equation of a line that has a slope of 7/2 and passes through the point (14,-3). Convert it to slope-intercept form.
Answer:
y = ⁷/₂x - 52Step-by-step explanation:
The point-slope form of the equation is y - y₀ = m(x - x₀), where (x₀, y₀) is any point the line passes through and m is the slope:
m = ⁷/₂
(14, -3) ⇒ x₀ = 14, y₀ = -3
So, the point-slope form of the equation:
y + 3 = ⁷/₂(x - 14)
So::
y + 3 = ⁷/₂x - 49 {subtract 3 from both sides}
y = ⁷/₂x - 52 ← the slope-intercept form of the equation
1206.37 ROUNDED TO NEARST HUNDRETH
Answer:
It is already rounded
Step-by-step explanation:
What are like terms? (Pls give an example of one too)
Answer:
Step-by-step explanation:
Like terms are terms that have the same variable raised to the same exponent. For example, 7z and 2z are like terms because they have the same variable, z, and are raised to the same exponent, 1. 5x² and 10x are not though, because the first one is raised to a power of 2, whereas the latter is only raised to a power of 1. And numbers with different variables, like 7x and 3z, are not either.
Answer: like terms are terms that have the same variables and powers
For example: 3x and 4x are like terms because they both are x and only x. 12xy and 4y would not be like terms because they don’t share the same variable. if it was 5x ² and 8x ² they would be like terms. i hope this helps!
"Five times a number minus seven is equal to the opposite of eleven."
Answer:
- 4/5
Step-by-step explanation:
5X-7 = -11
+7 = -11+7
5X = -4
Divide 5 on both sides
= - 4/5
the mail slot is 24cm in width and 7cm in length what is the maximum width of the mail slot
Answer:
24 cm
Step-by-step explanation:
it says that the mail slot is 24 cm in width
Answer:
Step-by-step explanation:
14cm
Find the length of the third side to the nearest tenth. 3 3
Answer:
4.2
Step-by-step explanation:
Hypotenuse ² = opposite ² + adjacent ²
Opposite = 3
Adjacent = 3
Hypotenuse ² = opposite ² + adjacent ²
Hypotenuse ² = 3² + 3²
Hypotenuse ² = 9 + 9
Hypotenuse ² = 18
Find the square root of both sides
√Hypotenuse² = √18
Hypotenuse = √18
Hypotenuse = 4.2426406871192
Hypotenuse = 4.2 to the nearest tenth
If it takes eight men ten hours to build a wall, how long would it take four men?
Answer:
20 bc if 8 men took 10 hours then 4 men would take double the time
Answer:
ha ha is it math question seriously or riddle if riddle the wall is already built by men they non time is taken by men.
What is the length of an arc that subtends an angle of 60° at the centre of radius ½m?
a) 0.5238 b) 0.53
c) 0.357 d) 0.25
Pls help!!!!!
plssss helppp ok really needed it
Answer:
[tex]y^{6}[/tex]
Step-by-step explanation:
Using the rules of exponents
[tex]a^{m}[/tex] × [tex]x^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]
[tex]\frac{a^{m} }{a^{n} }[/tex] ⇔ [tex]a^{(m-n)}[/tex] , then
[tex]\frac{y^4 y^7}{^5}[/tex]
= [tex]\frac{y^{(4+7)} }{y^5}[/tex]
= [tex]\frac{y^{11} }{y^5}[/tex]
= [tex]y^{(11-5)}[/tex]
= [tex]y^{6}[/tex]
Part A: What is the ratio of the number of students receiving a C and the number of students receiving an A? * 1:4 6:1 4:1 3:1 Part B: Complete the statement: For every student receiving a D, ______ students received a B. * Part C: What is the ratio of the number of students receiving a C and the number of students receiving an D? 1:4 6:1 4:1 3:1
Answer:
a. 4 : 1
b. 2 students
c. 3 : 1
Step-by-step explanation:
a. There were 12 students who got a C and 3 students who got As. The ratio is therefore:
12 : 3
Take it to the lowest form by dividing both sides by 3:
= 4 : 1
b. There were 4 students with a D grade and 8 with a B. The ratio is:
= 4 : 8
Taken to the lowest form that would be:
= 1 : 2
This means that for every student receiving a D, 2 students received an A.
c. 12 students received a C and 4 students received a D. That ratio is therefore:
= 12 : 4
Take to the lowest form by dividing both sides by 4:
= 3 : 1
Jane babysits for $8 per hour. She earned $240 last week. This equation represents the number of hours, h, Jane babysat last week.
Answer: the equation would be 8h=240
h=30
Step-by-step explanation:
Stir-fry is Felix's favorite food to cook, but it always makes a lot of smoke! Felix needs to know the volume of his kitchen so he can buy a fan that is the right size. Felix's kitchen has a floor area of 85 square feet. The height of the ceiling is 8 feet. What is the volume of Felix's kitchen?
Answer:
680
Step-by-step explanation:
85x8
Answer: 680 cubic feet
Step-by-step explanation:
V = B * hV = 85 * 8V = 680 cubic fett
Find the equation of the straight line which passes through the point (2,3) and is
inclined at 30° to the positive direction of the x-axis.
Answer: y = 1.73*x - 0.46
Step-by-step explanation:
For a linear equation of the form:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we have an angle of A degrees with respect to the x-axis, the slope of the function can be calculated as:
Tan(A) = a.
in this case, we have we have an inclination of 30° to the positive x-axis (measured from the positive y-axis) and we know that the angle between the positive x-axis and the positive y-axis is 90°, then the angle measured from the positive axis will be such that:
A + 30° = 90
A = 90° - 30° = 60°
Then the slope is:
a = Tan(60°) = 1.73
Then we have the equation:
y = 1.73*x + b
And we know that this line passes through the point (2, 3) then we can replace x by 2 and y by 3 in the equation, and find the value of b.
3 = 1.73*2 + b
3 - 1.73*2 = b = -0.46
Then the equation is:
y = 1.73*x - 0.46
help pleaseeeeeeeeeeeeee
Luke bought a computer for $525 and two computer games for $34.99 each. The sales tax rate was 6.25%. How much sales tax was Luke charged?
Luke charged an amount of $37.18 in sales tax which is determined by the evaluation of 6.25% of 595.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
For example, If Saima obtained a score of 57% on her exam, that corresponds to 67 out of 100. It is expressed as 57/100 in fractional form and as 57:100 in ratio form.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
Luke bought a computer for $525 and two computer games for $34.99 each. The sales tax rate was 6.25%.
⇒ 525 + 2×34.99 = 595
We have to determine the evaluation of 6.25% of 595.
⇒ 6.25% of 595
6.25% is expressed as 6.25/100 in fractional form
⇒ (6.25/100)(595)
6.25/100 is expressed as 0.0625 in decimal form
⇒ (0.0625 )(595)
Apply the multiplication operation, and we get
⇒ 37.18
Therefore, Luke charged an amount of $37.18 in sales tax.
Learn more about the percentages here:
brainly.com/question/24159063
#SPJ6
What effect does inflation have on the prices of goods and services?
A. Prices decrease
B. Prices double
C. Prices increase
D. Prices stay the same
Answer:
C, price increases
Step-by-step explanation:
this is correct I promise you.
Answer:
C
Step-by-step explanation:
Prices increase because there is a higher demand for the product, but it does not double because each individual seller can set their price.
Which equation is equivalent to 8x + 2y = 10?
Answer:
y=-4x+5
Step-by-step explanation:
8x+2y=10
2y=10-8x
divide by 2
y=5-4x
y=-4x+5
Can someone pls help me!!
A. 5 inches
B. 16 inches
C. 13 inches
D. 19 inches
Answer:
c. 13
Step-by-step explanation:
[tex]c=\sqrt{a^{2}+b^{2}} = \sqrt{12^{2}+4^{2}}[/tex] ≈ [tex]12.64911[/tex] ≈ [tex]13[/tex]
I found my VibeBuddy ong im too happy!!!!!!!!!!!!
Answer: OMG i hope they are nice to you
Step-by-step explanation: