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3 years ago

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Graham is folding a piece of paper to make an origami figure. Each time he folds the paper, the thickness of the paper is double

d. The paper starts out flat, with a thickness of 3 millimeters.
A. Write a list of six ordered pairs showing the output as the thickness of the paper when the input is the number of times it is folded. Explain how you came up with your ordered pairs.
B. Is this relation a function? Explain why or why not using the ordered pairs you came up with in Part A.

1 answer:

gregori [183]3 years ago

7 0

Answer:

A. Graph attached

B. It's a function. One input has only one output, it passed the vertical line test.

Step-by-step explanation:

a₀ = 3 a₁ = 6 = 3 x 2¹ a₂ = 6 x 2 = 3 x 2² ..... aₙ = 3 x 2ⁿ

answer graph attached

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How many real solutions exist for this system of equations?

Rom4ik [11]

Answer:

One

Step-by-step explanation:

Set each equations equal to each other

${x}^{2} + 4 = 4x$

${x}^{2} - 4x + 4$

Find the discrimant.

${ - 4 {}^{2} - 4(1)(4) } = 0$

This means there is one real solution. Since the discramnt equal 0.

7 0

2 years ago

How was ABCDEFGH transformed to A'B'C'D'E'F'G'H'?

Yanka [14]

So ur going from a smaller shape to a larger shape....means the scale factor is more then 1. The scale factor is the number that u multiply the original shape by to get the other shape.

so lets look at DE...it is 2.....and D'E' is 6

so 2 * x = 6...with ur scale factor being x
2x = 6
x = 6/2
x = 3.....so the scale factor is 3....because multiplying the original shape by 3, gives u the other shape

7 0

4 years ago

Read 2 more answers

Write an equation for a quadratic function that has x intercepts (-3, 0) and (5, 0)

Blizzard [7]

Answer:

One possible equation is $f(x) = (x + 3)\, (x - 5)$ , which is equivalent to $f(x) = x^{2} - 2\, x - 15$ .

Step-by-step explanation:

The factor theorem states that if $x = x_{0}$ (where $x_{0}$ is a constant) is a root of a function, $(x - x_{0})$ would be a factor of that function.

The question states that $(-3,\, 0)$ and $(5,\, 0)$ are $x$ -intercepts of this function. In other words, $x = -3$ and $x = 5$ would both set the value of this quadratic function to $0$ . Thus, $x = -3\!$ and $x = 5\!$ would be two roots of this function.

By the factor theorem, $(x - (-3))$ and $(x - 5)$ would be two factors of this function.

Because the function in this question is quadratic, $(x - (-3))$ and $(x - 5)$ would be the only two factors of this function. In other words, for some constant $a$ ( $a \ne 0$ ):

$f(x) = a\, (x - (-3))\, (x - 5)$ .

Simplify to obtain:

$f(x) = a\, (x + 3)\, (x - 5)$ .

Expand this expression to obtain:

$f(x) = a\, (x^{2} - 2\, x - 15)$ .

(Quadratic functions are polynomials of degree two. If this function has any factor other than $(x - (-3))$ and $(x - 5)$ , expanding the expression would give a polynomial of degree at least three- not quadratic.)

Every non-zero value of $a$ corresponds to a distinct quadratic function with $x$ -intercepts $(-3,\, 0)$ and $(5,\, 0)$ . For example, with $a = 1$ :

$f(x) = (x + 3)\, (x - 5)$ , or equivalently,

$f(x) = x^{2} - 2\, x - 15$ .

6 0

2 years ago

Jamie kicked a soccer ball that traveled along a path described by the parabola y = -x^2 +8x, where y equals the height of the s

andrey2020 [161]

We have that
<span>y = -x</span>²<span>+8x

we know that
when the ball hint the ground is the x-intercepts of the graph
the x-intercepts is for y=0
so
0=-x</span>²+8x--------> x²-8x=0----> x*(x-8)=0

the solution is
x=0
x=8

the x intercepts are the points (0,0) and (8,0)
the distance between the x intercepts points =[8-0]-----> 8 ft

the answer is
8 ft

see the attached figure

6 0

3 years ago

Read 2 more answers

So I'm currently doing online school due to external circumstances and haven't done this type of problem before. I need help fin

Ann [662]

Answer:

DE ≈ 14.91

Step-by-step explanation:

Make use of the relationships between sides and angles in a right triangle. These are summarized by the mnemonic SOH CAH TOA:

Sin = Opposite/Hypotenuse

Cos = Adjacent/Hypotenuse

Tan = Opposite/Adjacent

__

The side DE is opposite the angle 19°, so the sine or tangent relation will be involved. The sine relation requires you know hypotenuse EF. The tangent relation requires you know adjacent side DF.

The only common side between triangles CDF and DEF is side DF. That side is opposite the given 61° angle. The given side length (CF = 24) is adjacent to the 61° angle.

This means you have enough information to use these relations:

tan(61°) = DF/CF = DF/24

DF = 24·tan(61°)

and

tan(19°) = DE/DF

DE = DF·tan(19°) = (24·tan(61°))·tan(19°) . . . . . use DF from above

DE ≈ 24(1.804048)(0.344328) ≈ 14.908

The length of DE is about 14.91.

8 0

2 years ago