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andrezito [222]
3 years ago
8

Math

Mathematics
1 answer:
SIZIF [17.4K]3 years ago
6 0

Answer:

Susanne is 16

Step-by-step explanation:

Let x be Dakota's age

x + 3 = Susanne's age

4(x+3) = Bob's age

Sum of their age is:

x + x + 3 + 4(x + 3) =

Simplify:

x + x + 3 + 4x + 12

6x + 15 = 93

6x = 78

x =  13

Susanne is 3 more than x (13 +3) which is 16

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The sum of the angle measures in a 50-gon is
KATRIN_1 [288]

Answer:

Interior: 8640°

Exterior: 360° (Every shapes' exterior angle sum is 360°)

Step-by-step explanation:

Formula: 180(Sides - 2)

180(50-2) = 180(48) = 8640

8 0
3 years ago
Consider a sphere of radius R > 0. Take two antipodal points A and B on the sphere, and another point C on the sphere. Check
aleksklad [387]

Answer:

To this question; we want to show that if two antipodal points on a sphere were A and B, for any random point C on the sphere, AC is perpendicular to BC?

Step-by-step explanation:

I would proceed by imagining the sphere in a three dimensional Cartesian coordinate system. For example, use a sphere of diameter 2 and let it sit at the origin. Then (0, 0, 1) and (0, 0, -1) are the vector locations of the “north and south poles” of the sphere.

Now choose the vector location of any point on the surface of the sphere. It will have a vector location - we’ll call it (x, y, z). Now the vectors from your point to the two poles are (-x, -y, 1-z) and (-x, -y, -1-z).

Now just form the dot product of those two vectors:

(-x, -y, 1-z) . (-x, -y, -1-z) = x^2 +y^2 + (1-z)*(-1-z)

Now the truth of your claim will be embodied in that dot product being zero:

x^2 + y^2 - (1+z)(1-z) = 0

x^2 + y^2 - (1-z^2) = 0

x^2 + y^2 + z^2 = 1

But that last line is just the definition of points on the surface of a sphere of radius 1, so the claim is proven.

Since R>0 and AC is perpendicular to BC, the <ACB is at right angle.

Please, find attached a simple image to show antipodal points (Two points that makes a diameter) and a point C on the sphere.

5 0
3 years ago
Sarah has to pay a one-time $300 deposit for her apartment. Each month she pays $700 for rent. How much would Sarah pay for “n”
Alex73 [517]

Answer:

700n + 300

Step-by-step explanation:

We know that no matter what happens, Sarah has to pay a One-Time $300 for her deposit.

Now, we know that for every month she stays in the apartment, it will cost her $700.

So, we can come up with a formula to find out how much she would pay:

700n + 300

Hope this helps!

4 0
3 years ago
corey paid for a dinner and left a 15% or $3.45 in tips. How much was the original bill without counting the tip?
Rudiy27

Answer:

19.55 $

Step-by-step explanation:

3.45$×10=34.5=150% of his money overall

34.5÷3=11.5

11.5×2=23= 100% of his money

23-15%=19.55$

5 0
2 years ago
Read 2 more answers
Is (-3,2)(−3,2)left parenthesis, minus, 3, comma, 2, right parenthesis a solution of -4x -10y &lt; -9−4x−10y&lt;−9minus, 4, x, m
r-ruslan [8.4K]

Answer:

The answer to your question is The point (-3, 2) is not a solution

Step-by-step explanation:

Inequality

                                   - 4x - 10y < - 9

-point (-3, 2)

Process

1.- To solve this problem, just substitute the point in the inequality and simplify

a) Substitution

                                    -4(-3) - 10(2) < - 9

b) Simplification

                                    12 - 20 < - 9

c) Result

                                        - 8 < - 9

This is false, -8 > -9

7 0
2 years ago
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