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2 years ago

Find the value of x in each case:

Mathematics

2 answers:

iogann1982 [59]2 years ago

8 0

Answer: How’s that 2021 going for u?

Step-by-step explanation:

Yakvenalex [24]2 years ago

5 0

Nice... you might have put the wrong picture lol

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Alex is 12 years older than George. Carl is Three times older than Alex The sum of their ages is 68 Find the ratio of George’s a

earnstyle [38]

Ratio of George’s age to Carl’s age to Alex’s age is 1 : 12 : 4

Solution:

Let "a" be the age of Alex

Let "g" be the age of George

Let "c" be the age of Carl

Alex is 12 years older than George

Therefore,

Age of Alex = 12 + Age of George

a = 12 + g

g = a - 12 ---- eqn 1

Carl is Three times older than Alex

Age of Carl = 3 x Age of Alex

c = 3a -------- eqn 2

The sum of their ages is 68

age of Alex + age of George + age of Carl = 68

a + g + c = 68 ----------- eqn 3

Substitute eqn 1 and eqn 2 in eqn 3

a + a - 12 + 3a = 68

5a - 12 = 68

5a = 12 + 68

5a = 80

a = 16

Substitute a = 16 in eqn 2

c = 3(16) = 48

c = 48

Substitute a = 16 in eqn 1

g = 16 - 12 = 4

g = 4

Find the ratio of George’s age to Carl’s age to Alex’s age

Ratio of George’s age to Carl’s age to Alex’s age = g : c : a

g : c : a = 4 : 48 : 16

Divide the above ratio by 4 to reduce to lowest terms

g : c : a - 1 : 12 : 4

Thus ratio of George’s age to Carl’s age to Alex’s age is 1 : 12 : 4

6 0

3 years ago

The fish tank has side lengths 20in, 10in and height 15in. The water level is two inches below the top of the tank. A glass sphe

Kitty [74]

Answer:

Part 1) The new distance from the water to the top of the tank is $1.979\ in$

Part 2) The maximum number of balls that can be put into the tank with the tank not overflowing is 95

Step-by-step explanation:

step 1

Find the total volume of the tank

$V=20*10*15=3,000\ in^{3}$

step 2

Find the volume of the tank if the water level is two inches below the top of the tank

$V=20*10*(15-2)=2,600\ in^{3}$

step 3

Find the volume of the glass sphere

The volume of the glass sphere is equal to

$V=\frac{4}{3}\pi r^{3}$

we have

$r=1\ in$

assume

$\pi=3.14$

substitute

$V=\frac{4}{3}(3.14)(1)^{3}$

$V=4.2\ in^{3}$

step 4

What is the new distance from the water to the top of the tank?

we know that

$2 in -----> represent (3,000-2,600)=400\ in^{3}$

using proportion

Find how many inches correspond a volume of $4.2\ in^{3}$

$\frac{2}{400}\frac{in}{in^{3}}=\frac{x}{4.2}\frac{in}{in^{3}}\\ \\x=4.2*2/400\\ \\x=0.021\ in$

The new distance from the water to the top of the tank is

$2-0.021=1.979\ in$

step 5

Find how many of these balls can be put into the tank with the tank not overflowing

we know that

The volume of one ball is equal to $4.2\ in^{3}$

using proportion

$\frac{1}{4.2}=\frac{x}{400}\\ \\x=400/4.2\\ \\x=95.23\ balls$

therefore

The maximum number of balls that can be put into the tank with the tank not overflowing is 95

4 0

3 years ago

Find the point, M, that is two-sevenths of the distance from A(-9, 2) to B(-2, -12).

Softa [21]

(2B +5A)/7 = (2(-2, -12) +5(-9, 2))/7 = (-4-45, -24+10)/7 = (-7, -2)

Selection B is appropriate.

3 0

3 years ago

How do you get 40y from the difference of 2 squares with the problem (5y+4+3x)(5y+4-3x)? I understand distribution method. I don

otez555 [7]

Answer:

Step-by-step explanation:

(5y+4+3x)(5y+4-3x) = (5y+4)² - (3x)²......(from the difference of 2 squares )

by identity : (a+b)(a-b) = a² - b²

in this exercice ; a = 5y+4 and b = 3x

3 0

2 years ago

The first time a census was taken in Esinville, the population was 12,621. Each year after that, the population was about 6% hig

Sedbober [7]

Step-by-step
Population was 12.621 when it was measured

Next year it rose by 6%, so add that 6% to 100% and multiply with population measured

12.621 × (100%+6%) = 12.621 × 106% = 13.379,24

Since a man cant be 0,24, we count that as +1

13.379,24 = 13.379 + 1 = 13.380

That was for a year after measurement, now let's calculate for another year
Now, add those 6% to a new population number

13.380 × (100%+6%) = 13.380 × 106% = 14.182,8

since 0,8 isn't a man, instead we add again +1

14.182,8 = 14.182 + 1 = 14.183

now let's do it for another year after last, by adding those 6% to a newest population number

14.183 × (100%+6%) = 14.183 × 106% = 15.033,98

round it again to +1, since 0.98 isn't a man

15.033,98 = 15.033 + 1 = 15.034

that is it, now graph is in the picture.

8 0

2 years ago