Answers
Answers:
DE = 1.1DF = 1.6BC = 4.8===========================================================
Explanation:
I recommend drawing the two triangles as shown below. The diagram isn't to scale, but all that matters is that we get the general idea down.
Your teacher gave you this info:
angle A = angle E (red angles)angle C = angle F (blue angles)These two pieces of info are enough to prove that triangle ABC is similar to triangle EDF. Use the angle angle (AA) similarity theorem to do this proof. The order of the lettering matters because it helps us see how the letters pair up.
A and E go firstB and D in the middleC and F go lastSince the triangles are similar, the scale factor to go from ABC to EDF is EF/AC = 2/6 = 1/3
In other words, the side lengths of triangle EDF are exactly 1/3 that of the corresponding lengths of ABC. Or we can reverse things to say the sides of ABC are 3 times longer than the sides of EDF.
----------------------
Use this scale factor to help determine the missing length ED.
(ED)/(AB) = scale factor
(ED)/(AB) = 1/3
(ED)/(3.3) = 1/3
ED = (1/3)*(3.3)
ED = 1.1
Note how ED/AB = (1.1)/(3.3) = 11/33 = 1/3
----------------------
While we don't know how long sides BC or DF are, we are told that DF is 3.2 units shorter compared to BC.
This means
DF = BC - 3.2
DF = x - 3.2
Then we can say,
(DF)/(BC) = scale factor
(x-3.2)/(x) = 1/3
3(x - 3.2) = x*1
3x - 9.6 = x
3x - x = 9.6
2x = 9.6
x = (9.6)/2
x = 4.8
So BC is x = 4.8 units long and DF is x-3.2 = 4.8-3.2 = 1.6 units long
Related Questions
james cuts his neighbor's lawn the first is 1000 m long and 100 m wide what is the area
Answers
Answer:
100,000 m²
Step-by-step explanation:
the area = l x w = 1000 x 100 = 100,000 m²
what is the mass of raisins in a package
Answers
Answer:
Step-by-step explanation:
12
Find the interior angle sum for the following polygon
Answers
Im not really sure but I think this is it
Really hope this helps
15) The sum of one-fourth, one-ninth and one- third of a number is 25. Find the number.
Answers
Answer:
Step-by-step explanation:
(1/4 + 1/9 + 1/3)x = 25.
x = 36
Answer:
Let the number be x
(1/4 + 1/9 + 1/3) * x = 25
25/36 * x = 25
25x = 25*36
x = 25*36/25
x = 36
Step-by-step explanation:
determine the dimension of cube when the volume is 1.468mcube
Answers
Answer:
1.137 m
Step-by-step explanation:
The volume of a cube is given as the cube of the side. A cube is a 3 dimensional shape with equal sides and 6 faces. If the volume is V and the side is s then
V = s * s * s
Given that the volume is 1.468mcube then
s^3 = 1.468
s = cube root of 1.468
= 1.137 m
PLEASE HELP! DUE TODAY :))
Answers
Step-by-step explanation:
do like the picture I sent
What is 200% of 20? Thanks!
Answers
40
Step-by-step explanation:
200% of 20 = 200 • 0.20 = 40
Answer:
40
Step-by-step explanation:
200% x 20
200/100 x 20
(200 ÷ 100) x 20
200 x 20 ÷ 100
4,000 ÷ 100 = 40
find k so that x^2+2x+k is a factor of 2x^4+x^3-14x^2+5x+6. also find all the zeroes of the two polynomial
Answers
Compute the quotient and remainder,
[tex]\dfrac{2x^4+x^3-14x^2+5x+6}{x^2+2x+k} \\\\ = 2x^2 - 3x - (8+2k) + \dfrac{(21+7k)x+(6+8k+2k^2)}{x^2+2x+k}[/tex]
The remainder upon dividing [tex]2x^4+x^3-14x^2+5x+6[/tex] by [tex]x^2+2x+k[/tex] should leave no remainder, which means
[tex]21+7k = 0 \implies 21 = -7k \implies k=-3[/tex]
and
[tex]6+8k+2k^2 = 0 \implies 2(k+3)(k+1)=0 \implies k=-3\text{ or }k=-1[/tex]
Only k = -3 makes both remainder terms vanish.
Then the previous result reduces to
[tex]\dfrac{2x^4+x^3-14x^2+5x+6}{x^2+2x-3} = 2x^2 - 3x - 2[/tex]
so that
[tex]2x^4+x^3-14x^2+5x+6 = (x^2+2x-3) (2x^2 - 3x - 2) \\\\ 2x^4+x^3-14x^2+5x+6 = (x+3)(x-1)(2x + 1)(x-2)[/tex]
and so the zeroes of the quartic polynomial are x = -3, x = 1, x = -1/2, and x = 2.
¿Cual es el resultado de dividir 164.64 entre 8
Answers
Answer: 20.58
Step-by-step explanation:
An airplane travels 4020 kilometers against the wind in 6 hours and 4800 kilometers with the wind in the same amount of time. What is the rate of the plane in still air and what is the rate of the wind?
Answers
Answer:
Rate of plane 735 km/hr
Rate of wind 65 km/hr
Step-by-step explanation:
Calculation to determine the rate of the plane in still air
Let Va represent the velocity of the airplane
Let Vw represent the velocity of the wind
When flying with the wind:
(Va+Vw)*(6 hours) = 4800
6Va + 6Vw = 4800
6Vw = 4800 - 6Va
Vw=4800/6-Va
Vw = 800 - Va
When flying against the wind:
(Va-Vw)*(6 hours) = 4020 km
6Va - 6Vw = 4020
Substitute 800-Va for Vw and solve for Va:
6Va - 6(800-Va) = 4020
6Va -4800 + 6Va = 4020
12Va = 8820
Va=8820/12
Va = 735 km/hr
Therefore the rate of the plane in still air is 735 km/hr
Calculation to determine the rate of the wind
Rate of wind:
Vw = 800 - Va
Vw= 800 -735
Vw= 65 km/hr
Therefore the rate of the wind is 65 km/hr
is 23/17 a rational number?
Answers
Answer:
rational number
Step-by-step explanation:
a rational number can be written as a/b where a and b are integers
23/17 = a/b where a = 23 and b = 17
This is a rational number
hlpppppp plesaseeeeeeeeeeeeeeeee
Answers
Answer:
50
Step-by-step explanation:
Given,
96 + 2² / 2
96 + 4 / 2
100 / 2
50
cho tam giác ABC vuông tại A < góc B=a chứng minh: a) 1+[tex]tan^{2}[/tex]a=[tex]\frac{1}{sin^{2}a }[/tex]
làm giúp mình với
Answers
[tex]\\ \sf\longmapsto 1+tan^2A[/tex]
[tex]\boxed{\sf tanA=\dfrac{sinA}{cosA}}[/tex]
[tex]\\ \sf\longmapsto 1+\dfrac{sin^2A}{cos^2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{cos^2A+sin^2A}{cos^2A}[/tex]
[tex]\boxed{\sf cos^2A+sin^2A=1}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{cos^2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{1-sin^2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{1}-\dfrac{1}{sin^2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{sin^2A}[/tex]
Hence verified
Find the shortest side of a triangle whose perimeter is 64 if the ratio of two of its sides is 4:3 and the third side is 20 less than the sum if the other two
Answers
Answer:
The shortest side of the triangle is 18
Step-by-step explanation:
Let the sides the triangle be x, y and z.
From the question, the perimeter of the rectangle is 64, that is
x + y + z = 64 ...... (1)
Also, the ratio of two of its sides is 4:3, that is x:y = 4:3, then we can write that x/y = 4/3 ⇒ 3x = 4y ...... (2)
The third side, z, is 20 less than the sum of the other two, that is
z + 20 = x + y ...... (3)
Substitute equation (3) into (1)
Then,
z + 20 + z = 64
2z +20 = 64
2z = 64 - 20
2z = 44
z = 44/2 k
z = 22
From equation (3)
z + 20 = x + y
Then, k
22 + 20 = x +y
42 = x + y
x = 42 - y ...... (4)
Substitute this into equation 2
3x = 4y
3(42-y) = 4y
126 - 3y = 4y
4y + 3y = 126
7y = 126
y = 126/7
y = 18
Substitute this into equation (4)
x = 42 - y
x = 42 - 18
x = 24
∴ x = 24, y = 18 and z = 22
Hence, the shortest side of the triangle is 18.
Monica plans to buy markers and colored pencils at an office supply store A box of markers cost $3.85 and a a box of colored pencils cost $1.85. She has $40 to spend Which inequality best represents how many boxes of markers m and colored pencils c she can buy
Answers
Answer:
Step-by-step explanation:
m=7
c=5
balance=26.802
HELP OVER HERE LOL !!
Find the measure of the intercepted arc
Answers
Answer:
arc GH = 74°
Step-by-step explanation:
The inscribed angle GFH is half the measure of the intercepted arc aGH, then
arc GH = 2 × 37° = 74°
Find the area of the shaded regions:
Answers
Answer:
84.78
Step-by-step explanation:
Used calculator and formula
90/360 * (3.14)(36)
= 28.26
I need help solving this
Answers
Answer:
E. 248
Step-by-step explanation:
1 to 500 in set A, 250 to 750 in set B
500 - 250 = 250
100 and 200 are divisible by 100.
250 - 2 = 248
(4,-5) with slope of 2
Answers
that's a point slope form so
y +5 = 2(x -4)
In the adjoining fig. In a circle with centre C and chord DE ,ahe CF perpendicular to chord DE.If diameter of a circle is 20cm and DE=16cm,then CF=?GIVE REASON
Answers
DC=CF
Diameter=20cmRadius=20/2=10cmWe know
[tex]\boxed{\sf L=\dfrac{\theta}{180}\times πr}[/tex]
[tex]\\ \large\sf\longmapsto L=\dfrac{90}{180}\times \dfrac{22}{7}\times 10[/tex]
[tex]\\ \large\sf\longmapsto L=\dfrac{1}{2}\times \dfrac{220}{7}[/tex]
[tex]\\ \large\sf\longmapsto L=\dfrac{110}{7}[/tex]
[tex]\\ \large\sf\longmapsto L=15.5[/tex]
Now
[tex]\\ \large\sf\longmapsto CF=L+r-DE[/tex]
[tex]\\ \large\sf\longmapsto CF=15.7+10-16[/tex]
[tex]\\ \large\sf\longmapsto CF=25.7-16[/tex]
[tex]\\ \large\sf\longmapsto CF=9.7cm[/tex]
[tex]\large\sf\red{⟼L=18090×722×10}[/tex]
[tex]\begin{gathered}\\ \large\sf\red{ ⟼ L=\dfrac{1}{2}\times \dfrac{220}{7}}\end{gathered}[/tex]
[tex]\begin{gathered}{ \large\sf\red{⟼ L=\dfrac{110}{7}}\end{gathered}[/tex]
⟼ L=15.5
Now
⟼ CF=L+r−DE
⟼ CF=15.7+10−16
⟼ CF=25.7−16
⟼CF=9.7cmYou draw a red marble out of a bag and give it your friend. You draw another marble out of the bag. Are the events independent? Explain.
No; the red marble was not replaced, so it has an effect on drawing a second marble.
Yes; you may not get a red marble again.
No; you do not know which marble you will draw next.
Yes; the red marble was kept out, so you can not draw it again.
Answers
Answer:
the red marble was kept out so you can not draw it again
Answer:
Yes; you may not get a red marble again.
Step-by-step explanation:
there is a chance to get a red marble but it is not high
porfavor ayudenme con esta radicacion no la entiendo√81 ∙ 49
Answers
Answer:
441
Step-by-step explanation:
sqrt81=9
9 x 49=441
Answer:
441
Step-by-step explanation:
√ 9 ^2 ⋅ 49
9 ⋅ 49 = 441
1. Write three different solutions of 4x - 2y = 8. plzz answer fast
Answers
Answer:
y=-4+2x
x=(4+y)/2
2x-y=4
4(1)-2y=8
-2y=8-4
-2y=4
y=-2
ii)x=2
4(2)-2y=8
8-2y=8
y=0
iii)x=3
4(3)-2y=8
12-2y=8
2y=12-8
2y=4
y=2
Hope it helps!
Using two independent samples, two population means are compared to determine if a difference exists. The population standard deviations are equal. The number in the first sample is fifteen and the number in the second sample is 12. How many degrees of freedom are associated with the critical value
Answers
Answer:
Hence the degrees of freedom are associated with the critical value is 25.
Step-by-step explanation:
Using two independent samples, two population means are
compared to determine if a difference exists, the population standard deviation is equal.
sample size 1 = [tex]n_{1}[/tex]= 15 and sample size 2 = [tex]n_{2}[/tex] = 12
since, population standard deviations are equal, required degrees of freedom
[tex]= n_{1} + n_{2} - 2 \\= 15 + 12 - 2\\ = 25[/tex]
Let g(x) = f (x+1) - 2, find when g(x) = 12
I don't know how to evaluate this since I have both g(x) and an f(x).
Answers
Answer:
f(x +1 ) =14
Step-by-step explanation:
12= f(x +1) -2
f(x +1) = 12 +2
f (x+1 ) = 12
Find the missing segment in the image below
Answers
Answer:
Step-by-step explanation:
Single adults: According to a Pew Research Center analysis of census data, in 2012, 20% of American adults ages 25 and older had never been married. Suppose that we select random samples from this population of American adults ages 25 and older. For each sample we then calculate the proportion that had never been married.
For which of the following sample sizes will the sampling distribution be approximately normal?
Wang, W., and Parker, K. (2014). Record Share of Americans Have Never Been Married. Pew Research Center. http://www.pewsocialtrends.org/2014/09/24/record-share-of-americans-have-never-married/
A) 25
B) 50
C) 75
Answers
Answer:
B. 50
Step-by-step explanation:
Central limit theorem is used to calculate the sampling distribution of the given case. The number of adults who are 25 years of age or above and not married is 20% of the samples selected. The standard deviation is 0.06 while the sample size should be 50 to conclude the results.
please help asap!!! i dont understand it
Answers
Answer:
a
Step-by-step explanation:
A perpendicular bisector, intersects a line at its mid point and is perpendicular to it.
Calculate slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 7, 1) and (x₂, y₂ ) = (9, 13)
m = [tex]\frac{13-1}{9-(-7)}[/tex] = [tex]\frac{12}{9+7}[/tex] = [tex]\frac{12}{16}[/tex] = [tex]\frac{3}{4}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{4} }[/tex] = - [tex]\frac{4}{3}[/tex] ← slope of perpendicular bisector
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
([tex]\frac{x_{1}+x_{2} }{2}[/tex], [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
using (x₁, y₁ ) = (- 7, 1) and (x₂, y₂ ) = (9, 13) , then
midpoint = ( [tex]\frac{-7+9}{2}[/tex], [tex]\frac{1+13}{2}[/tex] ) = ( [tex]\frac{2}{2}[/tex], [tex]\frac{14}{2}[/tex] ) = (1, 7 )
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - [tex]\frac{4}{3}[/tex] , then
y = - [tex]\frac{4}{3}[/tex] x + c ← is the partial equation
To find c substitute the midpoint (1, 7) into the partial equation
7 = - [tex]\frac{4}{3}[/tex] + c ⇒ c = [tex]\frac{21}{3}[/tex] + [tex]\frac{4}{3}[/tex] = [tex]\frac{25}{3}[/tex]
y = - [tex]\frac{4}{3}[/tex] x + [tex]\frac{25}{3}[/tex] ← equation of perpendicular bisector
Which lists all of the shapes that are in a two-dimensional net of a square pyramid? 6 squares 4 triangles 1 square and 3 triangles 1 square and 4 triangles
Answers
Answer:
4 triangles and 1 square
Step-by-step explanation:
Required
The shapes in two-dimensional net of a square pyramid
To do this, I will attach an attachment of a 2D net of a square pyramid (see attachment)
From the attachment, we can see that:
The 2d shape of the pyramid is made of 4 triangles and 1 square
Answer:
D
Step-by-step explanation:
f(x) = x+3
g(x) = 2x^2-4
find (f times g) (x)
Answers
Step-by-step explanation:
(f*g) (x)=f(x) * g(x)
=(x+3)(2x^2-4)
=2x^3-4x+6x^2-12
