The areas of similar triangles ΔABC and ΔDEF are equal. If the longest side of ΔDEF measures 25 units, what is the length of the longest side of ΔABC?

A.
5 units

B.
25 units

C.
75 units

D.
50 units

Answer:

[tex]\mathrm{C)\:}x=15,\:-7[/tex]

Step-by-step explanation:

For [tex]|a-b|=c[/tex], there are two possible cases:

[tex]\begin{cases}a-b=c\\a-b=-c\\\end{cases}[/tex]

Solving for both cases, we get:

[tex]\begin{cases}x-4+6=17, \:x+2=17, \: \fbox{$x=15$}\\-(x-4)+6=17,\: -x+10=17, \: -x=7, \:, \fbox{$x=-7$}\\\end{cases}[/tex]

Answer:

x = 2°

Step-by-step explanation:

x + 2x + 30 = 180°

3x + 30 = 180°

3x = 180°/30°

3x = 6°

x = 6°/3°

x = 2°

Answer:

64.93=4.73x+22.36

Step-by-step explanation:

64.93 is how much he paid

22.36 is his constant

4.73 is for 1 call

Answer:

D

Step-by-step explanation:

Because pi never ends.

Hence, D (π) is a irrational number.

Answer:

AC=11.38 cm

Step-by-step explanation:

The Law of Cosines

It relates the length of the sides of a triangle with one of its internal angles.

Let a,b, and c be the length of the sides of a given triangle, and x the included angle between sides a and b, then the following relation applies:

[tex]c^2=a^2+b^2-2ab\cos x[/tex]

The figure shows two triangles and we are required to calculate the length of the side AC, knowing two sides and the angle between them. Thus, applying the formula:

[tex]AC^2=17^2+13^2-2*17*13*\cos42^\circ[/tex]

[tex]AC^2=289+169-442*0.7431[/tex]

[tex]AC^2=129.53[/tex]

[tex]AC=\sqrt{129.53}[/tex]

AC=11.38 cm

Answer: 24 km/h

Step-by-step explanation:

She traveled 18 km in 45 minutes, this could be simplified to .4 km/min or 24 km/h

9514 1404 393

Answer:

  a) $336

  b) $1036

Step-by-step explanation:

a) The interest is computed using the formula ...

  I = Prt

where P is the amount invested at rate r for t years.

  I = $700·0.08·6 = $336

The interest earned is $336.

__

b) The balance of the account is the sum of the original amount and the interest earned:

  balance = $700 +336 = $1036

The balance of the account is $1036.

Given:

[tex]\Delta UVW\sim \Delta USR[/tex]

To find:

The missing length marked with a question mark.

Solution:

Let x be the missing value.

We have,

[tex]\Delta UVW\sim \Delta USR[/tex]

Corresponding sides of similar triangles are proportional, so

[tex]\dfrac{UV}{US}=\dfrac{VW}{SR}=\dfrac{UW}{UR}[/tex]

Using this, we get

[tex]\dfrac{UV}{US}=\dfrac{UW}{UR}[/tex]

On substituting the values, we get

[tex]\dfrac{70}{x}=\dfrac{55}{44}[/tex]

[tex]\dfrac{70}{x}=\dfrac{5}{4}[/tex]

On cross multiplication, we get

[tex]70\times 4=5\times x[/tex]

[tex]280=5x[/tex]

[tex]\dfrac{280}{5}=x[/tex]

[tex]56=x[/tex]

Therefore, the missing length is 56 units.

Answer:

I have no idea what it is sorry

Answer:5

Step-by-step explanation:

because idrk my teacher just answered this question and i thought i would share :)

Answer:

48

Step-by-step explanation:

by dividing 9 by 6 you get 1.5 and by using distribution you also multiply 32 by 1.5 to get 48

Answer:

Step-by-step explanation:

It's clear from the graph that the angles of the given triangles are different.

And for similarity of two triangles, at least two angles of the triangles should be congruent.

Therefore, both the triangles are not similar.

The angles are DIFFERENT.Since similarity transformations preserve angle measures, ΔUVW and ΔGHI ARE NOT similar.

Answer:

x=2.2

Step-by-step explanation:

You know that for triangle ABC, side AB=10, CB=2 and AD=AB+BD=10+1=11. Given that triangles ABC and AED have the same angles, they are similar triangles.

So we can use the following ratios to solve for ED=x:

Answer:

[tex]m\angle CBD=35^{\circ}[/tex]

Step-by-step explanation:

Since there are [tex]180^{\circ}[/tex] on each side of a line and [tex]\angle ABC[/tex] is marked as a right angle, [tex]m\angle CBE=180-90=90^{\circ}[/tex].

[tex]m\angle CBE=m\angle DBE+m\angle CBD[/tex], and [tex]m\angle DBE[/tex] is given as [tex]55^{\circ}[/tex].

Therefore, we can plug in our values and solve:

[tex]90=55+m\angle CBD,\\m\angle CBD=\fbox{35^{\circ}$}[/tex].

Answer:

5 feet

Step-by-step explanation:

By triangle inequality, the sum of lengths of any two sides has to be strictly greater than the length of the third side.

Let x feet be the length of the third side.

We have 3+x>7, x+7>3 and 3+7>x.

Solving these, we get x > 4, x > -4 and x < 10.

The solution is therefore 4 < x < 10 and the smallest whole number which satisfies the inequality is 5.

Therefore the answer is 5 feet.

Answer:

a = -2, b = -3, c = 2

Step-by-step explanation:

We have the following three equations.

ab = 6

ac = -4

bc = -6

Multiply equation 2 and 3, we get

abc^2=24

Dividing it by the first equation, we get

c^2=4

c=2 or -2 (rejected since c is a positive integer)

We can then substitute c=2 into the equations, and find out that a = -2 and b = -3.

Answer:

7.  x = 5

8. x = 2, y = 6

9. x = 21, y = 39

Step-by-step explanation:

For a parallelogram, the lengths across intersection are equal.

7. For a parallelogram, the lengths across intersection are equal.

So that,

3x = 4x - 5

4x - 3x = 5

 x = 5

8. For a parallelogram, the lengths across intersection are equal.

So that,

2x = 4

x = [tex]\frac{4}{2}[/tex]

x = 2

and

y - 1 = 2y -7

7 - 1 = 2y - y

y = 6

x = 2, y = 6

9. For a parallelogram, opposite angles have equal value.

Thus,

3x = (4x - 21)

3x = 4x - 21

x = 21

and

3y = (y + 78)

3y = y + 78

3y - y = 78

2y = 78

y = [tex]\frac{78}{2}[/tex]

  = 39

y = 39

x = 21, y = 39

Answer: A:500-300=4n and C:4n+300=500

Step-by-step explanation:

Answer:

9 years ( approximately)

Step-by-step explanation:

900(1.03)^t = 1200

(1.03)^t= 1.33

( 1.03)^t= ( 1.03)^9

So, t= 9

Answer:

C

Step-by-step explanation:

AE = 14.6 I think. If I'm wrong, use whatever number it is.

Sin(x) = 5/14.6

Sin(x) = 0.3425

x = Sin-1 (0.3425)

x =20.03

Now the other larger triangle has an acute angle of 90 -20.03 =  69.97

===================

Cos(69.97) = 13.1/DE

DE = 13.1/cos(69.97)

DE = 38.25

Answer:

I believe its -82

Step-by-step explanation:

5 × -8 + 7 × -3 = -82

Answer:

The answer should be 40

Step-by-step explanation:

85+55=140

180-140=40

Answer:

Step-by-step explanation:

It's a simple question as we know:

y-y1=m(x-x1)

y-20=12(x-3)

y=12x-36+20

y=12x-16

Now, your line is in slope intercept form you can compare it with

y=mx+c

m=12 and c=16. You can also put your point to verify your answer.

did you get ittttt???

please help me out

Answer:

really easy its 180

Step-by-step explanation:

because you multiply 30 times 6 u get 180

Answer:

5.2 ft

Step-by-step explanation:

[tex] \cos 30 \degree = \frac{6}{length \: of \: platform} \\ \\ \frac{ \sqrt{3} }{2} = \frac{6}{length \: of \: platform} \\ \\ length \: of \: platform = \frac{2 \times 6}{ \sqrt{3} } \\ \\ length \: of \: platform = \frac{12\sqrt{3} }{ 3} \\ \\ length \: of \: platform =4 \sqrt{3} \\ \\ length \: of \: platform =4 \times 1.732 \\ \\ length \: of \: platform = 5.228 \\ \\ length \: of \: platform = 5.2 \: ft[/tex]

Answer:

whichever one corresponds with the answers you have will be right.