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Umnica [9.8K]
3 years ago
10

Complete the following sentence:Trianlge ACB is similar to __ ____________

Mathematics
1 answer:
svetlana [45]3 years ago
7 0

Answer:

Triangle ACB is similar to Triangle DEF by SAS Similarity Theorem

see the explanation

Step-by-step explanation:

we know that

The <u>SAS Similarity Theorem</u>, states that: If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, then the triangles are similar.

In this problem

Angle B and Angle F are congruent

∠B≅∠F

The corresponding sides are

BC and FE

and

AB and DF

Verify if the ratios are proportional

\frac{BC}{FE}=\frac{AB}{DF}

substitute the given values

\frac{24}{16}=\frac{12}{8}

1.5=1.5 -----> is true

therefore

Triangles ACB and DEF are similar by SAS Similarity Theorem

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Negative. A negative number times a positive number is equal to a negative number. X multiplied by Y is a positive.
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3 people can build a shed in 8 hours how long would it take 5 people
harkovskaia [24]

Answer:

3howers

Step-by-step explanation:

Step-by-step exaplanation

8 0
3 years ago
Joe wants to rent an apartment with an initial monthly rent of $1,400. He has been told that the landlord raises the rent 1.25%
nadya68 [22]

Answer: his pay for the 4th year is $1453.16

Step-by-step explanation:

The landlord raises the rent 1.25% each year. It means that the rent is increasing in geometric progression.

The formula for determining the nth term of a geometric progression is expressed as

Tn = ar^(n - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a = $1,400

r = 1 + 1.25/100 = 1.0125

n = 4 years

The 4th term(year), T4 is

T4 = 1400 × 1.0125^(4 - 1)

T4 = 1400 × 1.0125^3

T4 = $1453.16

8 0
3 years ago
System of Equations <br> Need help<br> Trig
Yanka [14]

Looks like the system is

\begin{cases}-2x+y+6z=1\\3x+2y+5z=16\\7x+3y-4z=11\end{cases}

We can eliminate y by taking

(3x+2y+5z)-2(-2x+y+6z)=16-2(1)

\implies3x+2y+5z+4x-2y-12z=16-2

\implies7x-7z=14

\implies x-z=2

so that z=x-2, and

(7x+3y-4z)-3(-2x+y+6z)=11-3(1)

\implies7x+3y-4z+6x-3y-18z=11-3

\implies13x-22z=8

Substitute z=x-2 into this last equation and solve for x:

13x-22(x-2)=8

\implies13x-22x+44=8

\implies-9x=-36

\implies x=4

Then

z=x-2

\implies z=4-2

\implies z=2

Plug these values into any one of the original equation to solve for y:

-2x+y+6z=1

\implies-2(4)+y+6(2)=1

\implies-8+y+12=1

\implies y=-3

Hence the solution is x = 4, y = -3, and z = 2.

6 0
3 years ago
Write the product of 6x-4 and the multiplicative inverse of 1 over 5
nlexa [21]

Answer:

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Step-by-step explanation:

The multiplicative inverse (reciprocal) of 1/5 is 5/1 = 5. Multiplying that by 6x-4 gives ...

  5 × (6x -4) = 30x -20

6 0
3 years ago
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