1. Name the congruent segments in this figure.

The number 49 has exactly three factors. Since 98 is a multiple of 49, which must be true of 98? It must have only two factors.

Mumz [18]

Answer:

Step-by-step explanation:

⇒49=7×7 =1 × 49

Factors of 49 = 1,7,49

⇒It is given that ,98 is a Multiple of 49.

98 = 49 × 2

So, apart from factors of 49, number 2, and 98 are also included in the set of factors of 98.

→Factors of 98 are =1,2,7,49,98

3 0

3 years ago

Two dice are thrown simultaneously. Given that sum of the numbers is NOT more than 5, what is the probability that sum is more t

defon

A method to know the probability is to list down all of the possible combinations that would present an outcome of not more than 5. This is listed below:

1 + 4
4 + 1
2 + 3
3 + 2
1 + 1
2 + 2
1 + 2
2 + 1
1 + 3
3 + 1

There are 10 possible outcomes. But among these, the only ones that can have a sum more than 3 are:

1 + 4
4 + 1
2 + 3
3 + 2
2 + 2
1 + 3
3 + 1

There are only 7 possible outcomes that meet both requirements. Given that there are 7 outcomes within the total of 10, the probability would be 7/10, or 0.7.

3 0

3 years ago

A cone has a surface area of 200 pi square inches. If the radius of the

Helen [10]

Answer:

$20\:\mathrm{in}$

Step-by-step explanation:

The lateral surface area of a cone is given by $A=\pi r\ell$ , where $r$ is the radius of the base of the cone and $\ell$ is the cone's slant height.

Solving for $\ell$ :

$200\pi=10\pi\ell,\\\ell=\frac{200\pi}{100\pi}=\boxed{20\:\mathrm{in}}$

*Note: It is implied that the surface area of 200 pi square inches is lateral surface area and not total surface area, because it is impossible to obtain a total surface area of 200 pi with a radius of 10 inches.

5 0

3 years ago

What is the smallest number with three different prime factors which is not a multiple of 3 or 5?

weeeeeb [17]

Primes are
2,3,5,7,11,13...
ok, so it must be multiplule of 2,7 and 11
2*7*11=154

answer is 154

4 0

3 years ago

Helpppp pleaseeeeeeeeeeeeeee

Vesna [10]

Answer:

Find below the calculations of the two areas, each with two methods. The results are:

Upper triangle:

$Area=5000\sqrt{3}units^2$

Lower triangle:

$Area=14,530m^2$

Explanation:

A) Method 1

When you are not given the height, but you are given two sides and the included angle between the two sides, you can use this formula:

$Area=side_1\times side_2\times sin(\alpha)$

Where, $\alpha$ is the measure of the included angle.

1. Upper triangle:

$side_1=200units\\ \\ side_2=100units\\ \\ \alpha =60\º\\ \\ Area=200units\times 100units\times sin(60\º)/2\\ \\ Area=5000\sqrt{3}units^2$

2. Lower triangle:

$side_1=231m\\ \\ side_2=150m\\ \\ \alpha =123\º\\ \\ Area=231m\times 150m\times sin(123\º)/2\\ \\ Area=14,529.96m^2\approx14,530m^2$

B) Method 2

You can find the height of the triangle using trigonometric properties, and then use the very well known formula:

$Area=(1/2)\times base\times height$

Use it for both triangles.

3. Upper triangle:

The trigonometric ratio that you can use is:

$sine(\alpha)=opposite\text{ }leg/hypotenuse$

Notice the height is the opposite leg to the angle of 60º, and the side that measures 100 units is the hypotenuse of that right triangle. Then:

$sin(60\º)=height/100units\\ \\ height=sin(60\º)\times100units\\ \\ height=50\sqrt{3}units$

$Area=(1/2)\times base\times height=(1/2)\times 200units\times 50\sqrt{3}units=5,000\sqrt{3}units^2$

3. Lower triangle:

$sin(180\º-123\º)=height/231m\\ \\ height=sin(57\º)\times 231m\\ \\ height=193.7329m^2$

$Area=(1/2)\times base\times height=(1/2)\times 150m\times 193.7329m^2\\\\ Area=14,529.96m^2\approx 14,530m^2$

5 0

3 years ago