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KATRIN_1 [288]
3 years ago
5

RS = 12, ST = 2x, RT = 34

Mathematics
1 answer:
Harrizon [31]3 years ago
6 0

Answer:

x=11

Step-by-step explanation:

34(RT) minus 12(RS)=22. 22 divided by 2 equals 11.

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If zeba were younger by 5 years than what she really is then the square of her age would have been 11 more than five times her a
RSB [31]

Answer:

14 years old

Step-by-step explanation:

<u>Define the variable</u>

Let x be the actual age of Zeba (in years).

<u>Create an equation</u> using the give information and the variable x:

(x - 5)^2=5x+11

To find Zeba's age now, <u>solve the equation for x</u>.

Expand the brackets:

\implies x^2-10x+25=5x+11

Subtract 5x from both sides:

\implies x^2-10x+25-5x=5x+11-5x

\implies x^2-15x+25=11

Subtract 11 from both sides:

\implies x^2-15x+25-11=11-11

\implies x^2-15x+14=0

<u>Factor the found quadratic</u>

To factor a quadratic in the form ax^2+bx+c<em>, </em>find two numbers that multiply to ac and sum to b, then rewrite b as the sum of these two numbers:

\implies x^2-14x-x+14=0

Factor the first two terms and the last two terms separately:

\implies x(x-14)-1(x-14)=0

Factor out the common term (x - 14):

\implies (x-1)(x-14)=0

Apply the <u>zero product property</u>:

\implies (x-1)=0 \implies x=1

\implies (x-14)=0 \implies x=14

Therefore, Zeba's age now is either 1 or 14 years.

As the question states "If Zeba were younger by 5 years" then 1 must be an <u>extraneous solution</u> since 1 - 5 = -4 and Zeba cannot be -4 years old.

Therefore, Zeba's age now is 14 years old.

<u>Check</u>

Given the actual age of Zeba is 14 years old.

Therefore, If Zeba were younger by 5 years, she would be 9 years old as:  14 - 5 = 9

The square of 9 is:  9² = 81.

5 times her actual age:  5 × 14 = 70

81 is 11 more than 70, hence verifying that her <u>actual age is 14 years old</u>.

Learn more about quadratic equations here:

brainly.com/question/27956741

brainly.com/question/27947331

5 0
1 year ago
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Four out of seven spectators at a different game are routing for North Star Academy. If there are 68 people rooting for North st
iragen [17]

68 divided by 4 is 17 and 17 times 7 (the amount of people watching) is 119

7 0
3 years ago
Please help due today
aleksklad [387]
Turn the triangle around, because you have to reflect it, if you need extra help lmk
6 0
3 years ago
A 13 meter long cylinder with a diameter of 8 meters has a square prism with a base length of 3 meters hole going all the way th
BartSMP [9]

The volume of the solid is 626.12m³

<h3>Volume of composite solids.</h3>

The volume of the given composite solid = volume of cylinder - volume of cube

The volume of cylinder Vc = πr²h

Vc = 3.14(8/2)²(13)

Vc = 3.14(16)(13)

Vc = 653.12 m³

Similarly the volume of the cube:

Volume of cube = 3³

Volume of cube = 27 m³

Volume of the solid = 626.12m³

Hence the volume of the solid is 626.12m³

Learn more on volume of composite solid here; brainly.com/question/9076728

3 0
2 years ago
Ian’s monthly allowance is $21. In January he starts saving for a birthday gift in June. Each month he saves 2/3 of his allowanc
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No 2/3 of $21 is $14 so 6x14 is $84 less than $110

8 0
3 years ago
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