Can anyone give a step-by-step guide on how to answer these types of questions? I'm really struggling with similar shapes so thank you in advance.
Answers
Answer:
a) 8cm
b) 19.8cm
Step-by-step explanation:
The key to these types of questions is to keep proportions in mind.
To solve the first question, you want to find the proportion of the smaller triangle to the bigger triangle. The length of AE is 6cm, but the length of AD is (6+4) = 10cm. So the proportion of the bigger triangle to the smaller triangle is 10/6. So to find the lengths of the sides of the bigger triangle, we want to keep this number in mind.
The BE side is parallel to CD, so we have to use length of BE multiplied by the proportion in order to get the length of CD.
CD = 4.8 * (10/6) = 8
CD = 8cm
For the second question, you use the same concept to find all the other side lengths. The only one you need left for the shape EBCD is side BC. Do the same thing you did before, take the length of the side of the smaller triangle that corresponds with side AC on the bigger triangle. In this case, it's AB, which is 4.5cm. Multiply this by 10/6 to get AC.
AC = 4.5 * (10/6) = 7.5
AC = 7.5
But we're not done. We just found the length of AC, but we need the length of BC to calculate the perimeter. To do this, we want to take the length of AC - the length of AB.
7.5 - 4.5 = 3
So the length of BC is 3cm. Now, to find the perimeter, just add all the sides of EBCD together.
4.8 + 4 + 8 + 3 = 19.8cm.
Hope this helps.
Answer:
a) CD = 8 cm
b) Perimeter of EBCD is 19.8 centimeters
Step-by-step explanation:
For this question, you can assume that ΔABE and ΔACD are similar. That's proven by BE ║ CD, but that's not directly relevant to the question so I won't explain it unless you would like me to.
In 2 similar triangles, all corresponding angles are congruent and all corresponding sides have the same scale factor.
For example, in ΔABC and ΔXYZ:
[tex]\frac{AB}{XY} =\frac{AC}{XZ} =\frac{BC}{YZ}[/tex]
Using those relationships, you can solve for any side in one triangle given the corresponding side in the other triangle.
A)
In the given triangles ΔABE and ΔACD, CD corresponds to BE, so:
[tex]\frac{CD}{BE} =\frac{AD}{AE}[/tex]
where AD is just 6 + 4 = 10.
[tex]\frac{CD}{4.8} =\frac{10}{6} \\\\\frac{CD}{4.8} =1.6667\\\\CD=8[/tex]
CD = 8cm
B)
Doing the same thing as above, now find the length of AC:
[tex]\frac{AC}{AB} =\frac{AD}{AE} \\\\\frac{AC}{4.5} =\frac{10}{6}\\\\\frac{AC}{4.5} =1.6667\\\\AC=7.5[/tex]
Now, to find BC:
[tex]BC=AC-AB\\BC=7.5-4.5\\BC=3[/tex]
Finally, add up the sides to find the perimeter of EBCD:
[tex]4.8+3+8+4\\19.8[/tex]
Perimeter of EBCD is 19.8 centimeters
Related Questions
Monica deposits $300 into a savings account that pays a simple interest rate of 3.9%. Paul deposits 400$ into a savings account that pays a simple interest rate of 3.2%. Monica says that she will earn more interest in 1 year because her interest rate is higher. Is she correct? Justify your response.
Answers
Answer:
For Monica : Principle = $300 rate : 3.4% time 1 yr
Simple interest = Prt/100 = 300*3.4*1/100 = 1020/100= $ 10.2
For Paul : Principle = $400 rate : 2.8% time 1 yr
Simple interest = Prt/100 = 400*2.8*1/100 = 1120/100= $ 11.2
Step-by-step explanation:
and side q has a
In the 30-60-90 triangle below, side s has a length of
length of
30°
g
10
90°
60°
S
A. 5.10.15
B. 10.13.20
C. 105: 105
Answers
Answer:
E
Step-by-step explanation:
Using the cosine and sine ratios in the right triangle and the exact values
cos60° = [tex]\frac{1}{2}[/tex] , sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{s}{10}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2s = 10 ( divide both sides by 2 )
s = 5
------------------------------
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{q}{10}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2q = 10[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
q = 5[tex]\sqrt{3}[/tex]
–
2.8,
–
2
1
4
, and
–
2.45 in order from least to greatest
Answers
Answer: -2.8, -2.45, -2, 1, and 4.
Step-by-step explanation:
Larger negatives go first so -2.8 is the largest and you continue using that method until 1 where the smaller number go first. Positives.
Which of these reasons would John not need to use in his proof
Answers
Use the slope formula and state what is the slope of a line with the following two points: (-2, 7) and (8, -9)?
Answers
Answer:
m = -8/5
Step-by-step explanation:
[tex]m=\frac{-9-7}{8-(-2)} =\frac{-16}{10} =-\frac{8}{5}[/tex]
Hope this helps
The arithmetic sequence 2, 4, 6, 8, 10,. . . Represents the set of even natural numbers. What is the 100th even natural number? a100 = What is the sum of the first 100 even natural numbers? S100 = Complete the sentence below with less than, greater than, or equal to. The sum of the first 100 even natural numbers is the sum of the first 101 odd natural numbers.
Answers
The 100th even natural number is 200
Given the sequence 2, 4, 6, 8, 10....
The nth term of the sequence is expressed as:
Tn = a + (n - 1)d
a is the first term = 2
d is the common difference = 4 - 2 = 6 - 4 = 2
n is the number of terms
Substitute the given parameters into the formula
Tn = 2(n-1)2
Tn = 2+(2n - 2)
Tn = 2n
Get the 100th term
T10= 2(100) = 200
Hence the 100th even natural number is 200
Learn more on AP here: https://brainly.com/question/24072079
Answer:
1)
200
2)
10100
3)
less than
Step-by-step explanation:
on god
12 + (-4) - 2/5j - 4/5j + 5
Answers
12+ 5= 17
17+(-4) -2/5= 12.6
Answer:
-6j+65/5
Step-by-step explanation:
PLEASE GIVE ME THE BRAINLIEST ANSWER
Is this a function?
Answers
Answer:
Yes
Step-by-step explanation:
Yes, the graph represents a function because it passes the vertical line test: Any vertical line drawn through this graph intersects this graph only once.
Work out the circumference of this circle.
Take it to be 3.142 and write down all the digits given by your calculator.
10 cm.
Answers
Answer:
62.84
Step-by-step explanation:
pie=3.142
c=pie * diameter
r=10cm
d=2r
d=2(10)=20cm
c=3.142 * 20
c=62.84
Step-by-step explanation:
Formula for the Circumference of a circle = 2πr
C = 2πr
C = (2 * 3.142) * 10
C = 6.284 * 10
C = 62.84cm
Dorit wants to make farmer’s cheese. She knows that for 2 gallons of milk, she will need 14 teaspoon of rennet. She only has 12 gallon of milk. Which statement(s) describe the step(s) Dorit can take to determine how much rennet, in teaspoons, she will need to make cheese?
Answers
Answer:
to do this you need to Multiply 14 by 6 to satisfy the fact she has 6 times the amount of milk for 14 teaspoons of rennet
if someone would me it would meaqn alott
Answers
Answer:
ration of bream to tench to carp
12: 7: 21
Step-by-step explanation:
12/40 = bream
28/40 = not bream
(28/40) x (1/4) = tench
(28/40) x (3/4) = carp
tench = (28/40) x (1/4)
= 7/40
carp = (28/40) x (3/4)
= 21/40
ration of bream to tench to carp
12: 7: 21
Answer:
12:7:21
Step-by-step explanation:
If you have 40 total, the non-bram are (40-12) = 28. One quarter of them, or 7 (since 7x4=28)are trench. It leaves 28-7= 21 carps. The total ratio is: 12:7:21. Since the three numbers are co-primes (ie, they don't share a divisor between all 3) there is no way to simplify the ratio (or, if you prefer, their sum, 40, is the minimum ammount of fishes you need to have a whole number of fishes in the pond).
AABC-ADEF so if BC = 10, EF = 25 and AB = 20, then DE =
Answers
7.2.....................................
URGENT!!!! UNIT 4 CONGRUENT TRIANGLES
HOMEWORK 6 PROVING TRIANGLES CONGRUENT: ASA AAS AND HL
Answers
As per the question there are four congruent tringles and these congruency is that all sides are equal in length and size.
The four triangles are ASA, AAS and HL. The ∠BD divides ∠ABD. ∠BDA is equal to ∠BCD as given. In second, ST is parallel to UN and congruent to VU. That is also given. In the third statement the FH bisects the ∠EHG. FRH is congruent to FGH. Hence given.Learn more about the PROVING TRIANGLES CONGRUENT: ASA AAS AND HL.
brainly.com/question/25544949.
Work out the equation of
the line that goes through
(3, 2) and (-1, 10)
Answers
Answer:
[tex]The\,\,equation\,\,will\,\,be\,\,2x+y=8[/tex]
Step-by-step explanation:
Let, A=(3,2)
B=(-1,10)
So, The equation will be
[tex]\frac{x-x_{1} }{x_{1} -x_{2} } =\frac{y-y_{1} }{y_{1} -y_{2} } \\=>\frac{x-3 }{3-(-1) } =\frac{y-2 }{2-10} \\=>\frac{x-3 }{4} =\frac{y-2 }{-8}\\=>-8x+24=4y-8\\=>8x+4y=32\\=>2x+y=8[/tex]
Hope you have understood this.....
ask me if you have any confusion.....
if you liked it pls mark it as the brainliest
Answer:
y = - 2x + 8
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 2 ) and (x₂, y₂ ) = (- 1, 10 )
m = [tex]\frac{10-2}{-1-3}[/tex] = [tex]\frac{8}{-4}[/tex] = - 2 , then
y = - 2x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (3, 2 )
2 = - 6 + c ⇒ c = 2 + 6 = 8
y = - 2x + 8 ← equation of line
What can i multiply 2/3 by to make a product of 1? Explain how you know.
Answers
Answer:
[tex]\mathsf{\frac{3}{2}}[/tex]
Step-by-step explanation:
In order to get a product of 1, you must multiply [tex]\mathsf{\: \frac{2}{3}}[/tex] with another fraction that will result in the same value for the numerator and the denominator, which is its reciprocal.
In other words, [tex]\mathsf{\frac{2}{3} \:\times\frac{3}{2}\:=\:\frac{6}{6}\:=\:1}[/tex].
Therefore, you could multiply [tex]\mathsf{\: \frac{2}{3}}[/tex] by [tex]\mathsf{\frac{3}{2}}[/tex] to make a product of 1.
Pls can someone pls help me
Please show your work
Answers
Answer:
x = 8
I dunno what the question is in the first place, but I assume you are solving for x.
Step-by-step explanation:
The two given angles are equivalent because they are parallel and they have a line that intersects.
The line creates two angles on each side of each line, which is 120 or 60 because there are 180 degs on a straight line.
The obtuse side is 120, and the -8 + 16x is also on an obtuse angle, showing that they are equal.
120 = -8 + 16x
128 = 16x
8 = x
x = 8
Simplify this expression 3(2h + 5)
Answers
Explaination: cause I’m a genius
Explanation: use the distributive property.
3 x 2h = 6h
3 x 5 = 15
Choose the angles that are adjacent to <3
Answers
Answer:
<2 & <4
Step-by-step explanation:
yeah-ya........ right?
Read the scenario. 1. The temperature at 6 A.M. was -5°F. By noon the temperature had risen by 5°F. What was the temperature at noon? Represent these values with integers and model them on a number line. + + + 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 Read the scenario. 2. A diver was 8 feet below sea level. The diver swam back up 8 feet. What is the location of the diver? Represent these values with integers and model them using integer tiles.
Answers
Answer:
mm
Step-by-step explanation:
Jordan and Ben exercise at the same gym. The table below shows the number of calories they burned in each of their last 5 workouts.
How many calories would ben need to burn in his next workout to have the same average as Jordan?
Answers
Answer: The answer is 55 more calories than jordan in the next session
Step-by-step explanation: So sorry, I am bad at explaining :(
Answer:
760 calories
Step-by-step explanation:
Jordan's average is ...
(850 +674 +729 +658 +614)/5 = 705
Then the total number of calories Ben needs to burn in 6 sessions is ...
705×6 = 4230
So far, Ben has burned ...
716 +635 +802 +687 +630 = 3470 . . . calories
So, in his next session, Ben must burn ...
4230 -3470 = 760 . . . calories
To have the same average after 6 sessions that Jordan now has after 5 sessions, Ben must burn 760 calories in his 6th session.
If the output number y is -52 (y=5x-2) what is the input number? SHOW WORK
Answers
Answer:
the input number is -10
Step-by-step explanation:
output is always y
input is always x
so instead of y, put -52
-52=5x-2 add 2 to each side to ger 5x by itself
-50=5x divide both sides by 5 to get x by itself
-10=x
x is the input so the input is -10
Haley has 48 colored pencils and 3 cups (A, B, C). Cup A holds one more colored pencil than cup C. Cup B holds 2 more colored pencils than cup C. How many pencils does cup B contain?
Answers
Answer:
17 pencils
Step-by-step explanation:
Assume that cup C holds x pencils. In this case, cup A holds x + 1 pencils, and cup B holds x + 2 pencils. We know that all of the cups together hold 48 pencils. If we add what we got together, we would get x + x + 1 + x + 2 = 48. 2x + 1 + x + 2 = 48. 2x + x + 1 + 2 = 48. 3x + 1 + 2 = 48. 3x + 3 = 48. 3x = 48 - 3. 3x = 45. x = 45 / 3. x = 15. Now, we know that cup C holds 15 pencils, and from here, we can find the number of pencils in cup B by adding 2 to 15 and getting 17, and that would be your answer.
Tell me if I'm wrong :)
Answer:
12
Step-by-step explanation:
7. Ashok gets an increase of 4% in his weekly salary. In addition to that, he gets ? 75 per week. If his present salary is 2,500 per week, what will be his new salary next week?
a. 2600
b. 2675
c. 2700
d. 2765
Answers
B.
I think B will make more B make more sense because you say he gets 75 a week.
Follow the steps to finish solving the equation -3x +18 = 7x
1. Add 3x to both sides to isolate the variable term.
2. Divide both sides by 10.
x=
Answers
Answer:
x = 9/5 or 1.8
Step-by-step explanation:
Answer: Or 9/5 Have a great day :)
Step-by-step explanation:
-3x+18= 7x
18+= 10x
x= 18/10
x= 9/5
The black graph is the graph of
y = f(x). Choose the equation for the
red graph.
a. y = f(x + 3)
b. y = f(x – 3)
C. y + 3 = f(x)
d. y - 3 = f(x)
Answers
Answer:
C
Step-by-step explanation:
When
f(x+3) would indicate a Shift 3 units to the left
f(x-3) indicates a Shift 3 units to the right
y+3=f(x) indicates a Shift 3 units up
y-3=f(x) indicates a Shift 3 units down
Because the graph is shifted 3 units up, it would be y+3=f(x), which is option C
PLEASE HELP! 20 POINTS
What is the x-intercept of the line with this equation -2x+1/2y=18?
Enter your answer in the box
( ,0)
Answers
Answer:
x - intercept = - 9
Step-by-step explanation:
To find the x- intercept, let y = 0 in the equation and solve for x
- 2x + [tex]\frac{1}{2}[/tex] (0) = 18
- 2x + 0 = 18
- 2x = 18 ( divide both sides by - 2 )
x = - 9 or (- 9, 0 ) in coordinate form
b)
Here is another number machine.
Input
Output
х
4x + 5
Answers
Answer:
collect like terms x=5-4=1
what is the prime factorization of 252
1. 2^2x7x9
2. 2x7x27
3.2^2×3^2×7
4.2^3×3×7
Answers
Answer:
Prime factorization: 2x2x3x3x7
Exponential form: = 2^2 x 3^2 x 7
Step-by-step explanation:
a toy car costing 500.00 is reduced by 10% in the sale how much does it cost now?
Answers
After the 10% reduction in the price of the toy car, the car costs 450.
In order to determine the cost of the toy car after the price was reduced by 10%, the first step is to determine what 10% of $500 is.
10% x 500
0.1 x 500 = 50.
The second step is to subtract the value of the 10% price reduction from the original cost of the toy car.
500 - 50 = 450
To learn more about how to calculate discounts, please check: https://brainly.com/question/9350849?referrer=searchResults
The area of the regular hexagon is 169. 74 ft2. A regular hexagon has an apothem with length 7 feet and an area of 169. 74 feet squared. What is the perimeter, rounded to the nearest tenth? 24. 2 ft 28. 3 ft 48. 5 ft 56. 8 ft.
Answers
The perimeter of the hexagon is the sum of its side lengths
The perimeter of the hexagon is 48.5 ft
The given parameters are:
[tex]\mathbf{Area = 169.74}[/tex] --- the area of the hexagon
[tex]\mathbf{a = 7}[/tex] -- the apothem
Let the perimeter of the hexagon be p.
So, the area is calculated as:
[tex]\mathbf{Area = \frac 12 pa}[/tex]
Substitute values for Area and (a)
[tex]\mathbf{169.74 = \frac 12 \times p \times 7}[/tex]
Multiply both sides by 2
[tex]\mathbf{339.48= p \times 7}[/tex]
Divide both sides by 7
[tex]\mathbf{48.5= p }[/tex]
Rewrite as:
[tex]\mathbf{p = 48.5}[/tex]
Hence, the perimeter of the hexagon is 48.5 ft
Read more about perimeter and areas at:
https://brainly.com/question/1969956
