Triangles ABC and DEF are similar triangles. What are the lengths of the unknown sides?

A) DF = 65 cm; DE = 25 cm
B) DF = 39 cm; DE = 15 cm
C) DF = 52 cm; DE = 48 cm
D) DF = 48 cm; DE = 52 cm

Since hypotenuses and legs have the same length, then both are congruent and thus, triangles ABC and DEF are congruent.

The Hypotenuse-Leg theorem states that two right triangles are congruent if and only if their hypotenuses and any of their corresponding legs are congruent. That is to say:

[tex]\overline {AC} \cong \overline {DF}[/tex], [tex]\overline{BC} \cong \overline {EF}[/tex]

[tex]AC = DF, BC = EF[/tex]

[tex]\sqrt{AB^{2}+BC^{2}} = \sqrt{DE^{2}+EF^{2}}[/tex], [tex]BC = EF[/tex]

If we know that [tex]AB = 10[/tex], [tex]BC = 4[/tex], [tex]DE = 10[/tex] and [tex]EF = 4[/tex], then we have the following outcomes:

[tex]\sqrt{10^{2}+4^{2}} = \sqrt{10^{2}+4^{2}}[/tex]

[tex]4 = 4[/tex]

Since hypotenuses and legs have the same length, then both are congruent and thus, triangles ABC and DEF are congruent.

We kindly invite to check this question on triangles: https://brainly.com/question/21972776

Answer:

-5a+a

= -4a

Step-by-step explanation:

mark me brainlist

Here let's use python to find our median.(Console attached)

Spare way:-

Let's use statistics

[tex]\\ \sf\longmapsto Median=\dfrac{n}{2}+\dfrac{n+1}{2}[/tex]

[tex]\\ \sf\longmapsto Median=\dfrac{10}{2}+\dfrac{10+1}{2}[/tex]

[tex]\\ \sf\longmapsto Median=5th+6th/2[/tex]

Order from largest to smallest

[tex]\\ \sf\longmapsto Median=\dfrac{150+149}{2}[/tex]

[tex]\\ \sf\longmapsto 149.5[/tex]

Answer: A I think

Step-by-step explanation:1/3 ÷ 2/5=1/3×5/2

Answer:

Remainder=190

(13 with a remainder of 190)

Step-by-step explanation:

the remainder is the amount leftover after the division. Usually it is swapped with decimals.

3

[tex] \sf \sqrt{x + 3 = 12} [/tex]

[tex] \sf = \sqrt{x = 12 - 3} [/tex]

[tex] \sf = \sqrt{x = 9} [/tex]

[tex] \sf = \sqrt{9} [/tex]

[tex] \sf = \sqrt{3 \times 3} [/tex]

= 3

The solution of the linear equation [tex]\sqrt{x+3} = 12[/tex]  for the variable, x is 141.

Two algebraic expressions separated by an equal symbol in between them and with the same value of the expression are called equations.

Example = 2x +4 = 12

here, 4 and 12 are constants and x is variable

The solution of the equation can be calculated as:

[tex]\sqrt{x+3} = 12[/tex]

Squaring both side,

[tex]x+3 = (12)^2[/tex]

x+3 = 144

Subtract 3 from both the sides,

x = 141

The solution of the linear equation for the variable x is 141.

Learn more about equations here :

https://brainly.com/question/14686792

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Answer:

Option C.

Step-by-step explanation:

First, simplify the inequality. Add 2 to both sides:

4v - 2 < 10

4v - 2 + 2 < 10 + 2

4x < 12

Divide both sides by 4:

4x ÷ 4 < 12 ÷ 4

x < 3

As 3 will not satisfy the inequality, it is not a solution. The option that shows x being less than 3 but not including is option C.

Hope this helps!

Answer:

The answer is 6.

Step-by-step explanation:

If you divide 2 by 2 you get one so if you divide 12 by 2 you get 6 so the value of h is 6

Answer:

h=6 feet

Step-by-step explanation:

since the smaller figure is a ratio of 1:h and the larger one is 2:12, we can assume that the scale factor (the amount we're multiplying the sides on the smaller figure by to reach the size of the larger figure) is 2. (since 2/1 =2 and 12/2 = 6) :)

Answer:

Question 5 options: (4, 4) (1, 1) (3, 1) (10, 4)

Step-by-step explanation:

Answer:

hope it helps.....................

Answer:

2 times 7 is 14

2,4,6,8,10,12,14

Step-by-step explanation:

hope this helps

Answer:

15/16

Decimal form 0.9375

Step-by-step explanation:

The maximum distance between them is the diameter of the circle, which is of 44 units.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The diameter is twice the radius, and is the maximum distance between two points on the same circle.

They are running on a circular path, modeled by:

[tex]x^2 + y^2 - 10x - 18y = 378[/tex]

Completing the squares, the equation is:

[tex](x - 5)^2 + (y - 9)^2 = 378 + 5^2 + 9^2[/tex]

[tex](x - 5)^2 + (y - 9)^2 = 378 + 25 + 81[/tex]

[tex](x - 5)^2 + (y - 9)^2 = 484[/tex]

Then, the radius is: [tex]\sqrt{484} = 22[/tex], which means that the maximum distance between the runners at any given time is of 44 units.

A similar problem is given at https://brainly.com/question/25008198

Answer:

Simplifying

4x + -6 = 2(2x + 3)

Reorder the terms:

-6 + 4x = 2(2x + 3)

Reorder the terms:

-6 + 4x = 2(3 + 2x)

-6 + 4x = (3 * 2 + 2x * 2)

-6 + 4x = (6 + 4x)

Add '-4x' to each side of the equation.

-6 + 4x + -4x = 6 + 4x + -4x

Combine like terms: 4x + -4x = 0

-6 + 0 = 6 + 4x + -4x

-6 = 6 + 4x + -4x

Combine like terms: 4x + -4x = 0

-6 = 6 + 0

-6 = 6

Solving

-6 = 6

Answer:

Factors of 245: 1, 5, 7, 35, 49 and 245.

Answer:

the factor of 245 is 1 5 7 35 49 and 245

Answer:

n = 5

Step-by-step explanation:

5 + 20 = 25

therefore n = 5

Answer:

1) 350

2) 195.83

Step-by-step explanation:

Tuition fee = $12, 000 per year.

30% of it's being paid off by the scholarship, so she'll have to pay:

[tex] = 12000 - ( \frac{30}{100} \times 12000) [/tex]

[tex] = 12000 - 3600[/tex]

[tex] = 8400[/tex]

She'll have to pay $ 8400 by herself, her savings.

If she's saving $ 8400 for two years, she's actually saving $ 8400 for 24 months!

for one month, it'll be

= 8400/ 24

= $ 350 per month

one year fee = $ 10, 700

uncle pays half of it, I.e., 10700/ 2

= $ 5, 350

he gets a grant for $ 3,000

so, the part of the fee he ain't paying

= 5,350 + 3000

= $ 8,350

So, he'll have to save:

= 10,700 - 8,350

= $ 2,350

that is per year,

for per month = 2350/ 12

= $ 195.83

Answer:

C.

Step-by-step explanation:

The formula to convert C° to F° is C = 5(F-32)

Answer:

The answer is A

Step-by-step explanation:

Hope it helps

Answer:

-1.25

Step-by-step explanation:

-9/7.2 = -1.25 or -5/4

Answer:

The logic is there are six sides to each die, so for each number on one die you can pair with six different numbers on the other die. Therefore, the probability of rolling a prime number on two dice is 15/36, which reduces to 5/12

Answer:

B

Step-by-step explanation:

x = the number of times he does laundry.

Let's say he does the laundry 5 times then x = 5.

Each time costs $7,50.

If you want to know how much money he has spent after 5 times, you have to calculate 5 times $7,50. 7,5 times 5 = 37.5.

M stands for how much money he still has left from the 240 dollars.

If you apply the formula it would be 'M = 240 - 7.50x (7.50 times 5) = 240 - 37.5 = 202.5'

Therefore, the correct answer is B (M = 240 - 7.50x).

Answer:

1.

Step-by-step explanation:

Do cross multiplying, 3 x 2 = 6

6 divided by 6 = 1

n = 1

Answer:

n = 1

Step-by-step explanation:

3/6  = n/2 Find the greatest common factor of the numerator and denominator

1:3/2:3 = n/2 Factor out and cancel the greatest common factor

1/2 = n/2 Swap sides

n/2 = 1/2

Answer: i think it is a

Step-by-step explanation:

Answer:a 750g bag is better.

Step-by-step explanation: 3 bags would be more G the 2kg and less money 0.23/100 grams 700 g would be 1.4$ for that so 750 g is the best.

Answer:

750 grams at $1.39

Step-by-step explanation:

To make it easy to see, determine how much each option costs per gram.

750 grams cost 1.39.  Divide 1.39 by 750 which gives you 0.001853

2 kg is 2000 grams costing 3.99.  Divide 3.99 by 2000 which give you 0.001995

100 grams cost $0.23.  Divide 0.23 by 100 which gives you 0.0023

So the 750 grams is the best price.

Step-by-step explanation:

D meter stick

Answer:

It would be $390 for the 4 hours and the cleaning fees. And the slope would be -13 if you are going from 12 to 7 but would be 13 if you are going from 7 to 12...

Step-by-step explanation:

Answer:(-6,30)

Step-by-step explanation:

x=-6

y=30

Answer: (-6,30)

Step-by-step explanation:

-5x=-x+24

+x=+x

-4x=24

÷-4=÷-4

X=-6

Y=-5x

Y=-5(-6)

Y=30

(-6,30)

Answer:

Step-by-step explanation:

jnj

Answer:

I'm pretty sure it's 5

Step-by-step explanation:

It's 5 if: (please confirm before you answer it--the picture is blurry and it's hard to tell).

The line appears to intersect the origin (0,0) and (2.5,12.5).

Slope is rise over run, so if you take the difference in y value and divide it by the difference in x value, you get the slope.