A line and a point are ________ coplanar. a. always b. sometimes c. never (The answer is not A)

Answer:

Smaller number = 12

Larger number = 24

Step-by-step explanation:

Let's call X the smallest number, while Y is the largest number.

In this case, Y = 2X

The equation that represents the given case is,

X + Y = 36

But being Y = 2X we substitute in the equation, obtaining ...

X + 2X = 36

Now we add the X ...

3X = 36

We isolate the X to know its value ...

X = 12

Now we calculate the value of Y ...

Y = 2X

Y = 2 (12)

Y = 24

Smaller number = 12

Larger number = 24

Both conditions are met:

(1) The largest number is twice the smallest number: 12 * 2 = 24

(2) The sum of the two numbers is 36: 12 + 24 = 36

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Hope this helps!

Answer: 12 friends.

Step-by-step explanation:

the data we have is:

Mei Su had 80 coins.

She gave the coins to her friends, in such a way that every friend got a different number of coins, then we have that:

The maximum number of friends that could have coins is when:

friend 1 got 1 coin

friend 2 got 2 coins

friend 3 got 3 coins

friend N got N coins

in such a way that:

(1 + 2 + 3 + ... + N) ≥ 79

I use 79 because "she gave most of the coins", not all.

We want to find the maximum possible N.

Then let's calculate:

1 + 2 + 3 + 4 + 5 = 15

15 + 6 + 7 + 8 + 9 + 10 = 55

now we are close, lets add by one number:

55 + 11 = 66

66 + 12 = 78

now, we can not add more because we will have a number larger than 80.

Then we have N = 12

This means that the maximum number of friends is 12.

Answer:

12

Step-by-step explanation:

my

Answer:

see explanation

Step-by-step explanation:

given the function

f(x) = x² - 6x + 8

(a)

to find the y- intercept , let x = 0 in f(x)

f(0) = 0² - 6(0) + 8 = 0 - 0 + 8 = 8 ← y- intercept

(b)

to find the x- intercepts , let f(x) = 0 , that is

x² - 6x + 8 = 0 ← in standard form

(x - 2)(x - 4) = 0 ← in factored form

equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x - 4 = 0 ⇒ x = 4

the x- intercepts are x = 2 and x = 4 or (0, 2 ), (0, 4 ) in coordinate form

(c)

given a quadratic in standard form

f(x) = ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the vertex is

= -

f(x) = x² - 6x + 8 ← is in standard form

with a = 1 and b = - 6 , then

= - = - (- 3) = 3

evaluate f(3) for corresponding y- coordinate

f(3) = 3² - 6(3) + 8 = 9 - 18 + 8 = - 9 + 8 = - 1

vertex = (3, - 1 )

(d)

the axis of symmetry is a vertical line , passing through the vertex with equation

x = c ( c is the value of the x- coordinate of the vertex )

equation of axis of symmetry is then x = 3

Scaled figures are zoomed in or zoomed out (or just no zoom) versions of each other. The correct option is D.

What are Scaled figures?

Scaled figures are zoomed in or zoomed out (or just no zoom) versions of each other. They have scaled versions of each other, and by scale, we mean that each of their dimension(like height, width etc linear quantities) are constant multiple of their similar figure.

So, if a side of a figure is of length L units, and that of its similarfigure is of M units, then:

where 'k' will be called a scale factor.

The linear things grow linearly like length, height etc.

The quantities which are squares or multiple linear things twice grow by the square of the scale factor. Thus, we need to multiply or divide by k²

to get each other corresponding quantities from their similar figures' quantities.

So the area of the first figure = k² × the area of the second figure

Similarly, increasing product-derived quantities will need increased power of 'k' to get the corresponding quantity. Thus, for volume, it is k cubed. or

The volume of the first figure = k³ × volume of the second figure.

It is because we will need to multiply 3 linearquantities to get volume, which results in k getting multiplied 3 times, thus, cubed.

Given that the diameter of sphere A is 2 units, it is dilated by a scale factor of 3 to create sphere B. Therefore, the diameter of sphere B is,

Diameter of sphere B = 3 × Diameter of sphere A

                                    = 3 × 2 units

                                    = 6 units

Now, the ratio of diameters of the sphere and the volume of the sphere can be written as,

Hence, the correct option is D.

Learn more about Scale Factors:

brainly.com/question/11178083

#SPJ2

Answer:

1:27

Step-by-step explanation:

I will use solve in terms of pi

Know that Original volume * scale factor cubed = new volume.

The scale factor is 3 and 3^3 is 27,

Therefore the ratio is 1:27

Answer:

18.8 feet, 59.1 feet to the nearest tenth

Step-by-step explanation:

The diameter is the line drawn that divides the circle into two while the circumference is the perimeter of the circle. Both are a measure of the radius of the circle.

The diameter D = 2r where r is the radius of the circle

The circumference = 2Πr = ΠD where Π = 22/7

Given that the circular fountain has a radius of 9.4 feet

Its diameter =  2 × 9.4 feet = 18.8 feet

The circumference = 22/7 × 18.8 feet

=59.09 feet

≈ 59.1 feet to the nearest tenth