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3 years ago

I am a factor of 120, and a common multiple of 3, 4, and 10. The sum of my digits is 6.

Mathematics

1 answer:

Galina-37 [17]3 years ago

7 0

Answer:

At first find the lowest common multiple of 3, 4, 10

so it is 60

and 60is a factor of 120 and also the sum of the digits of 60 = 6+0 = 6

.°. 60 is the answer

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Distance between (-10,9) and (-5,2)

jonny [76]

Answer:

8.60 units (3 s.f.)

Step-by-step explanation:

The distance between 2 points is given by the formula:

$\sqrt{(y1 - y2)^{2} + {(x1 - x2)}^{2} }$

Thus using the above formula,

Distance between (-10, 9) and (-5, 2)

$= \sqrt{ {(9 - 2)}^{2} + {( - 10 + 5)}^{2} } \\ = \sqrt{ {7}^{2} + ( - 5)^{2} } \\ = \sqrt{74} \\ = 8.60 \: units \: (3 \: s.f.)$

8 0

3 years ago

A sphere is inscribed in a cube with a surface area of 216 square centimeters. What is the volume of the sphere

pentagon [3]

Answer:

$V=298.5cm^3$

Step-by-step explanation:

To find the volume of the sphere we need to know its radius.

And the radius can be found with the information we have about the surface area.

The formula for the surface area is as follows:

$SA=4\pi r^2$

from this formula we clear the radius r:

$r^2=\frac{SA}{4\pi}\\ \\r=\sqrt{\frac{SA}{4\pi} }$

and we substitute the known value of the surface area, and also the value of $\pi$ :

$r=\sqrt{\frac{216cm^2}{4(3.1416)} }\\ \\r=\sqrt{\frac{216cm^2}{12.5664} }\\ \\r=\sqrt{17.1887cm^2}\\ \\r=4.146cm$

and now that we know the radius we find the volume:

$V=\frac{4\pi r^3}{3} \\\\V=\frac{4(3.1416)(4.146cm)^3}{3}\\ \\V=\frac{895.521cm^3}{3}\\ \\V=298.5cm^3$

the volume of the sphere is $298.5cm^3$

7 0

2 years ago

Consider the geometric series S(x)=1+2(x−3)+4(x−3)^2+8(x−3)^3+⋯

sergij07 [2.7K]

Consider the geometric series S(x)=1+2(x−3)+4(x−3)^2+8(x−3)^3+⋯
Giving your answer as an interval, find all values of x for which the series converges.
Now assuming that x is in your interval above, find a simple formula for S(x).

5 0

3 years ago

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the number of girls and boys in math class totals 27. how many girls are there if the of girls is 3 more than twice the number b

leonid [27]

Answer: 15 girls

Step-by-step explanation:

27 - 3 = 24

24/2 = 12

12 boys

12 + 3 = 15

15 girls

15+ 12 = 27

7 0

3 years ago

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PLEASE HELP WITH GRAPH LAST QUESTION I NEED

SVETLANKA909090 [29]

Answer:

$\sf g(x) = -1(x+3)^2 -2$

Explanation:

$\sf original \ graph: \ y=-x^{2}$

the graph is translated 3 units to the left and 2 units down.

vertex: (-3,-2) point: (-1,-6)

$\sf so \ new \ graph :$

$\sf y = a(x-h)^2 +k$

$\sf -6 = a(-1-(-3))^2 -2$

$\sf -6 = 4a -2$

$\sf 4a = -4$

$\sf a = -1$

$\sf equation:$

$\sf y = a(x-h)^2 +k$

$\sf y = -1(x+3)^2 -2$

6 0

2 years ago

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