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3 years ago

If 2x+ 3y = 55 and 4x= y+ 47, ﬁnd x − y. Can you please explain with some details?

1 answer:

8 0

4x=y+47, we can subtract 47 from both sides to get:
4x-47=y, now we know what y equals in terms of x, so we can substitute that in to the other equation:
2x+3y=55 becomes 2x+3*(4x-47)=55 which becomes:
2x+12x-141=55 which becomes 14x-141=55 and we can add 141 to both sides:
14x=196, divide 14 by both sides, we get x=14, which we can substitute back into the y=equation:
4x-47=y becomes 14*4-47=y which becomes y=9
x=14, y=9
x-y=14-9=5

You might be interested in

copy the problems onto your paper, mark the given and prove the statements asked. if PO is congruent to PR and UO is congruent t

WINSTONCH [101]

The two-column proof that proves that ∠O ≅ ∠R using the SSS and CPCTC theorems is shown in the image attached below.

<h3>What is the Side-side-side Congruence Theorem (SSS)?</h3>

The side-side-side congruence theorem (SSS) states that when three sides of a triangle are congruent to the corresponding three sides of another triangle, then both triangles are considered congruent to each other.

<h3>What is the CPCTC Theorem?</h3>

The CPCTC theorem states that when two triangles are proven to be congruent by any triangle congruent theorem, then all the corresponding parts of the congruent triangle are congruent. This implies that the corresponding sides and angles of both triangle are equal or congruent.

We are asked to prove that ∠O ≅ ∠R.

With the given image, we would draw segment UP. Thus, based on the reflexive property, UP ≅ UP (one pair of congruent sides).

We are given two pairs of corresponding sides already, which are: UO ≅ UR and PO ≅ PR.

This means that triangles OUP and RUP have three pairs of corresponding congruent sides. Therefore, ΔOUP ≅ ΔRUP.

Applying the CPCTC theorem, ∠O ≅ ∠R.

The two-column proof is attached in the image below.

Learn more about the Side-side-side Congruence Theorem (SSS) on:

brainly.com/question/4280133

#SPJ1

3 0

2 years ago

Drag the tiles to the correct boxes to complete the pairs. Not all tiles are used.

Sati [7]

Answer:

a) aₙ = 4.(2)^n-1

b) aₙ = 2+3(n-1)

c) aₙ = 3+4(n-1)

d) aₙ = 3.(4)^n-1

Step-by-step explanation:

a) a geometric sequence with first term of 4 and a common ratio of 2

aₙ = ar^n-1

where a is the first term and r is the common ratio

aₙ = 4.(2)^n-1

Comparing with the standard form:

1st term = 4

Common ratio = 2

b) an arithmetic sequence with a first term of 2 and a common difference of 3

The standard form of arithmetic sequence is:

aₙ = a₁ + d(n-1)

where a₁ is the first term and d is the common difference

Given: aₙ = 2+3(n-1)

Comparing with standard equation

First term = 2

Common difference = 3

c) an arithmetic sequence with a first term of 3 and a common difference of 4

The standard form of arithmetic sequence is:

aₙ = a₁ + d(n-1)

where a₁ is the first term and d is the common difference

Given: aₙ = 3+4(n-1)

Comparing with standard equation

First term = 2

Common difference = 3

d) a geometric sequence with first term of 3 and a common ratio of 4

aₙ = ar^n-1

where a is the first term and r is the common ratio

aₙ = 3.(4)^n-1

Comparing with the standard form:

1st term = 3

Common ratio = 4

6 0

4 years ago

Please help me. i’ll give you brainliest

SashulF [63]

Answer:

x= 5

Step-by-step explanation:

pythagorean theorem 3^2+4^2=5^2

And it is a 3-4-5 triangle

4 0

3 years ago

Justin is making cookies, using a recipe in which the ratio

Nikolay [14]

Answer:

Part A - he will need 2 cups of sugar

Part B - 12 : 6 : 3

Step-by-step explanation:

Part A :

8 divided by 4 is 2

Part B :

Multiply all the numbers by 3

Hope this helped! :)

7 0

2 years ago

A girl can sweep the garage in 20 minutes, while her brother needs 30 minutes to do the same job. How many minutes will it take

Scrat [10]

I'm not sure your question has enough information to be answered properly, but I'll try to help:

Assuming each of them are sweeping 1/2 of the garge, we're gonna cut each of their times in half.

Now the girl needs 10 minutes for half the garage and her brother needs 15 minutes.

So, if they work together, the first ten minutes will overlap each other while the girls brother gets left behind to finish up for an extra five minutes.

So, when working together, the boy and the girl need 15 minutes to sweep the garage.

6 0

4 years ago