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2 years ago

If Alex is 14 years old, and Ben is 17 years old, in how many years will the sum of their ages be 169 years?

Mathematics

1 answer:

Citrus2011 [14]2 years ago

6 0

Answer:

69 years

Step-by-step explanation:

Sum of Alex's and Ben's current age

= 14 +17

= 31 years

For every year, Alex and Ben will each be one year older. Thus, 2 years would be added to the sum of their ages with each passing year.

Difference in the sum of their ages

= 169 -31

= 138 years

Number of sets of 2 years

= 138 ÷2

= 69

Thus, the sum of their ages will be 169 in 69 years.

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How much must be added to each of the three numbers 1, 11, and 23 so that together they form a geometric progression?

Sliva [168]

Answer:

Step-by-step explanation:

Let x be unknown number which should be added to numbers 1, 11, 23 to get geometric progression. Then numbers 1 + x, 11 + x, 23 + x are first three terms of geometric progression.

Hence,

$b_1=1+x\\ \\b_2=11+x\\ \\b_3=23+x$

and

$b_2=b_1\cdot q\Rightarrow 11+x=(1+x)q\\ \\b_3=b_2\cdot q\Rightarrow 23+x=(11+x)q$

Express q:

$q=\dfrac{11+x}{1+x}=\dfrac{23+x}{11+x}$

Solve this equation. Cross multiply:

$(11+x)^2=(1+x)(23+x)\\ \\121+22x+x^2=23+x+23x+x^2\\ \\121+22x=23+24x\\ \\22x-24x=23-121\\ \\-2x=-98\\ \\2x=98\\ \\x=49$

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3 years ago

Find the lateral and total surface area for the cone. If necessary, round to the nearest tenth and leave the

bija089 [108]

9514 1404 393

Answer:

262.2π cm²
392.16π cm²

Step-by-step explanation:

The lateral surface area is the product of half the circumference, and the slant height:

LA = πrh = π(11.4 cm)(23 cm) = 262.2π cm²

The total surface area adds the area of the base to that:

A = πr² +LA = π(11.4 cm)² +262.2π cm² = (129.96 +262.2)π cm²

A = 392.16π cm²

3 0

3 years ago

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Ira Lisetskai [31]

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I believe that's the answer!

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3 years ago

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2x + (-3) - 16x

-14x + (-3) is the expression?

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