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dexar [7]
3 years ago
5

A number, y, is equal to twice the sum of a smaller number and 3. The larger number is also equal to 5 more than 3 times the sma

ller number. Which equations represent the situation?

Mathematics
1 answer:
RSB [31]3 years ago
7 0

Answer:

A.

Step-by-step explanation:

<em>NOTE: The "larger number" will be referred to as y, and the "smaller number" will be referred to as x.</em>

"A number, y, is equal to twice the sum of a smaller number and 3."

This tells us that we must add our smaller number (x) to 3 within parantheses and then multiply the entire term (x+3) by 2.

y=2(x+3)

"The larger number is also equal to 5 more than 3 times the smaller number."

This tells us that we must multiply 3 against our smaller number (x) and add 5 to it.

y=3x+5

Now, to find your answer, we can put the equations in the same form as the answer choices so as to find an equivalent equation. Lets start with the first equation.

This form calls for us to have our x term first, then our y term, then our constant.

y=2(x+3)\\y=2x+6\\-2x+y=6

Now that we've gotten the equation in that form, we can see that our answer choices hold that our leading co-efficient must be positive, which we can adjust for by dividing both sides by -1.

-2x+y=6\\2x-y=-6

This makes the only possible answer choices (A) and (C).

Now, lets do our second equation. The recipe calls for the same form, again with a positive leading coefficient.

y=3x+5\\-3x+y=5\\3x-y=-5

This is only represented by choices (A) and (B).

Therefore, answer choice (A) is the only one which represents both equations.

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kompoz [17]

Answer:

The 59th Presidential Inauguration will take place on January 20, 2021. There have been many cold ceremonies, as well as warm ceremonies and even some snowy ceremonies.

Step-by-step explanation:

3 0
3 years ago
Expression is equivalent to 486 – 9 + 6 + 33 × 2
mojhsa [17]

Answer:

  549

Step-by-step explanation:

A calculator can give you an equivalent expression.

I might work from the middle outward:

  = 486 -3 +33×2

  = 483 +66

  = (480 +60) + (3 +6)

  = 540 + 9

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7 0
3 years ago
For the △ACD is shown below, select all the true statements. Lengths are rounded to the nearest tenth.
Nina [5.8K]

Answer:

1. No

2. No

3. Yes

4. Yes

Step-by-step explanation:

The diagram has been attached

The total angle in a triangle is 180°

<CAD=45°

<ACD=90°

Therefore <ADB=45°

1. ∠ADB = 30° no

ADC = 90 - 45 = 45

∠BDC = 90 - 65 = 25

∠ADB = 45 - 25 = 20

2.△ABD ∼ △ACD no going

by law of sines

3.CD = 33.7 centimeters => yes

4.BD = 37.2 centimeters => yes

3 0
3 years ago
A circle with radius 9 has a sector with a central angle of 120°.
Vitek1552 [10]

120º is 1/3 of a complete revolution of 360º. So the area of this sector should be 1/3 the area of the complete circle.

A circle with radius 9 has area 9^2 π = 81π.

So the sector has area 81π/3.

Put another way: The area <em>A</em> of a circular sector and its central angle <em>θ</em> (in degrees) occur in the same ratio as the area of the entire circle with radius <em>r</em> according to

<em>A</em> / <em>θ </em>º = (π <em>r </em>^2) / 360º

==>  <em>A</em> = π/360 <em>θ r</em> ^2

In this case, <em>r</em> = 9 and <em>θ</em> = 120º, so

<em>A</em> = π/360 * 120 * 81 = 81π/3

8 0
3 years ago
A bakery uses 300 pounds of flour to make 120 wedding cakes of the same size. At this rate how many pounds of flour are needed t
ElenaW [278]
The answer is 13 minutes and b
4 0
3 years ago
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