Which relationship is represented by the graph?
Radius of a circle vs. its diameter
Circumference of a circle vs. its diameter
Area of a circle vs. its diameter
Explain your thinking.
This is because the diameter is independent towards the
unlabeled axis; just like how the circumference is depending on
the diameter.
>
What is the constant of proportionality?

Answer:

X=4

Step-by-step explanation:

1. Simplify the expression

2. Multiply the fractions:

3. Break up the fraction:

4. Find the greatest common factor of the numerator and denominator:

5. Factor out and cancel the greatest common factor:

6. Simplify the fraction:

7. Multiply the fractions:

8.Solve by distributing:

9. Simplify the arithmetic:

10.Break up the fraction:

11. Find the greatest common factor of the numerator and denominator:

12. Factor out and cancel the greatest common factor:

13.Combine the fractions:

14. Combine the numerators

15. Find the greatest common factor of the numerator and denominator:

16. Factor out and cancel the greatest common factor:

17. Simplify the right side:

Answer:

a: [tex]f(t)=(t+2)^2-18[/tex]

b: vertex: (-2, -18)

   minimum

c: x = -2

Step-by-step explanation:

Completing the square is difficult to explain in words. but I'll try my best. Let me know if you need any more information.

Part A ===============

Start with the given function in this form:

[tex]f(x)=ax^2+bx+c\\t^2+4t-14[/tex]

We need an additional number, d, and we'll calculate it like this:

[tex]d=(\frac{b}{2a})^2 \\\\d=(\frac{4}{2(1)} )^2\\d=2^2\\d=4[/tex]

d needs to be added and subtracted at the same time. That way we do not change the value of the expression:

[tex]ax^2+bx+d-d+c\\\\t^2+4t+4-4-14[/tex]

And you can separate them like this to make it easier to read:

[tex](t^2+4t+4) + (-4-14)\\(t^2+4t+4)-18[/tex]

Finally, we need to factor the trinomial in the parenthesis. Because we've completed the square, it's now a perfect square trinomial.  The factored form is just:

[tex](x+e)^2[/tex]

where e is half of b, or the square root of c. That looks like this in our case, and you can also expand it to make sure.

[tex](t+2)^2\\\\(t+2)(t+2)\\t^2+2t+2t+4\\t^2+4t+4[/tex]

Put that all together and you get the answer:

[tex]f(t)=(t+2)^2-18[/tex]

Part B ===============

Vertex form is this:

[tex]f(x)=a(x-h)^2+k[/tex]

where (h, k) is the vertex and a is the scale factor.

In part A, we converted the given function into vertex form. Looking at that, you can see the vertex is at (-2, -18), and the scale factor is 1. When the scale factor is positive, the parabola faces upwards. When it's negative, the parabola faces downwards.

The scale factor is a positive 1 in this case, and if you picture that in your mind, the vertex is at the very lowest point, or the minimum, of the parabola.

Part C ==============

The axis of symmetry is always on the vertex, and that is because the vertex is the exact point where the parabola changes direction from positive to negative, or negative to positive.

The vertex of this parabola is (-2, -18), so the axis of symmetry is at x = -2.

Sorry if that got too long and hard to follow, I can clarify any part of it if needed.

Answer:

  0 and 1

Step-by-step explanation:

The scale of the graph is not marked, so we assume each grid line represents 1 unit. The leftmost crossing of the x-axis is between 0 and 1.

_____

Additional comment

The other real zero is between 2 and 3. If this is a polynomial function, it will have additional complex zeros.

Answer:

(7) 3 2 2x 23 xy y - 10 0 Solution The equation 2x2 23xyy2-100 has A2,B 23, and (1 13) as p3 (Example 2). 13: 271279. 2 m) long and 6 ft Step-by-step explanation:

An equation is a collection of variables and constants. The value of b for the given equation b + 23 = 114 will be 91.

There are many different ways to define an equation.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

More than one variable may be present inside a linear equation.

As per the given equation,

b + 23 = 114

Add -23 both sides

b + 23 - 23 = 114 - 23

b + 0 = 91

b = 91

Hence "An equation is a collection of variables and constants. The value of b for the given equation b + 23 = 114 will be 91".

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Answer:

i think 36???

Step-by-step explanation:

3 x 2 is 6 and 6 x 6 is 36

Im going to be honest, I don't know what I'm doing

Check the picture below.

Answer:

the answer is 33 9/11

Step-by-step explanation:

multiply the fractions

.

.

Answer:

33 9/11

Step-by-step explanation:

22 6/11 x 1 1/2

Convert into improper fractions.

248/11 x 3/2

Reduce the numbers with the greatest common factor 2.

124/11 x 3

Calculate

372/11

=33 9/11

Hope this helps :)

Answer:

  x/12

Step-by-step explanation:

There are 12 inches in a foot.

  feet in x inches = x/12

_____

With units, you have ...

  (x in) × (1 ft)/(12 in) = x/12 ft

The correct answer is C. 58

Hope this helps!

Step-by-step explanation:

the answer is 58 this is the result I hope I've helped

Answer:

I am almost completely sure its 4.

Step-by-step explanation:

I dont mind brainiests by the way

Answer:

1. (x - 1) × (x + 3)

2. x = 3 and y = -2

Step-by-step explanation:

rewrite the equation:

y = 3x - 11; 2x + 3y = 0

solve y = 3x - 11 for the y:

y = 3x - 11

substitute 3x - 11 for y in 2x + 3y = 0;

2x + 3y = 0;

2x + 3y = 0

2x + 3 (3x - 11) = 0

11x - 33 = 0 (simplify both sides of the equation)

11x - 33 + 33 = 0 + 33 (add 33 to both sides)

11x = 33

11x/11 = 33/11 (divide both sides by 11)

x = 3

subtitute 3 for x in y = 3x - 11

y = 3x - 11

y = (3)×(3) - 11

y = -2  

I showed one equation because the other is self explanatory, hope this helps.

The amount invested in each stock, the stock interest rate and the

duration of the investment, determines the interest.

Reasons:

Let X represent the sum of the amount Brian invested, we have;

Amount invested in stock paying 5% dividend = [tex]\dfrac{X}{2}[/tex]

Amount invested in stock paying 9% dividend = [tex]\dfrac{X}{2}[/tex]

Total annual interest = $420

Required:

The amount invested in the stocks

Solution:

The amount invested is found as follows;

[tex]\dfrac{X}{2} \times 5\% + \dfrac{X}{2} \times 9\% = 420[/tex]

0.025·X + 0.045·X = 420

0.07·X = 420

[tex]\displaystyle \mathrm{The \ amount \ invested , \, X} = \frac{420}{0.07} = \mathbf{ 6,000}[/tex]

The amount he invested = $6,000 ($3,000 in each stock)

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Answer:

17.999999999999999

Step-by-step explanation:

Answer:

25 and 1/12

1/3+1/3+2/3+1/2+1/2+3/4 = 4 and 1/12

6+5+4+3+2+1 = 21

Answer:

54

Step-by-step explanation:

6 3/4 = 6*4 + 3 / 4

= 27/4

=> 27/4  /100 * 800

=> 27/400 * 800

=> 27 * 2

=> 54

Answer:

30%

Step-by-step explanation:

Presuming that "survey 3,000" is the total and "900" is the factor who had problems then dividing the total amount by the amount of problems like equal the relative frequency of people that had problems

Math:

Amount of people you had problems / Amount of people who bought the new car.

900 / 3000 = 0.3

Now you need to multiply by 100% (because % in this case is a unit/measurement)

0.3 * 100% = 30%

Answer:

6[tex]\frac{2}{3}[/tex] inches tall

Step-by-step explanation:

4:6 = x:10

We can set it up like this:

[tex]\frac{4}{6}=\frac{x}{10}[/tex]

And then cross multiply & solve:

40 = 6x

6[tex]\frac{2}{3}[/tex] = x

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

I know answer. give me money I will tell everything..

Answer:

Circle

Step-by-step explanation:

The area of a circle is

[tex]\pi r^{2}[/tex]

A. circle

The area of a circle is 2[tex]\pi[/tex]r²

The Circle Formulas are expressed as,

The collection of all points equidistant from a fixed point in a plane is called a circle.

the circle is a closed 2-dimensional figure in which the set of all the points in the plane is equidistant from a given point called the “center”. Every line that passes through the circle forms the line of reflection symmetry.

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Answer:

x=7/10

Step-by-step explanation:

1/5=2/10

9/10-       =2/10

Substitute the blank with X

9/10-  X  =2/10

x=7/10

Answer:

7/10

Step-by-step explanation:

9/10 - _ = 1/5

Let's represent the unknown as x

Therefore,

9/10 - x = 1/5

9/10 - 1/5 = x

x = 9/10 - 1/5 = 7/10

Answer: the answer is 25

Step-by-step explanation:

First do 100/1

Then do 1 x 100/1 x 4

so then divide 100 by 4 =

25/1 =

25

Answer:

[tex]3\dfrac{1}{4} \ \ or \ \ 3,25[/tex]

Step-by-step explanation:

[tex]\displaystyle12 \frac{3}{8} -9\frac{1}{8} =12-9+\frac{3}{8} -\frac{1}{8} =3+\frac{2}{8} =3\frac{1}{4} \ \ or \ \ 3,25[/tex]

Answer:

$76

Step-by-step explanation:

The length of the longest pipe that can be carried horizontally is given by the minimum value of the function of the length of the pipe.

The longest length that the pipe can be is approximately 16.648 feet.

Reasons:

The length of the pipe, L

Width of the first hallway = 8 ft.

The width of the second hallway = 4 ft.

We have;

(L - a)·sin(θ) = 8

a·cos(θ) = 4

Therefore;

L - a = 8·csc(θ)

a = 4·sec(θ)

L(θ) = 8·csc(θ) + 4·sec(θ)

At the minimum length, we have;

L'(θ) = 4·sec(θ)·tan(θ) - 8·csc(θ)·cot(θ) = 0

4·sec(θ)·tan(θ) = 8·csc(θ)·cot(θ)

Therefore;

[tex]\displaystyle \frac{sec(\theta) \cdot tan(\theta)}{csc(\theta) \cdot cot(\theta)} = \frac{sin(\theta) \cdot tan(\theta) \cdot tan(\theta) }{cos(\theta) } =tan^3(\theta) = \frac{8}{4}[/tex]

[tex]\displaystyle tan(\theta) =\sqrt[3]{\frac{8}{4} } ={\sqrt[3]{2} }[/tex]

θ = arctan([tex]\sqrt[3]{2}[/tex]) ≈ 51.56°

a = 4×sec(arctan([tex]\sqrt[3]{2}[/tex]))

a ≈ 6.434

L = 8·csc(θ) + a = 8 × csc(arctan([tex]\sqrt[3]{2}[/tex])) + 4×sec(arctan([tex]\sqrt[3]{2}[/tex])) ≈ 16.648

The longest length that the pipe can be, L ≈ 16.648 ft.

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The longest length of the pipe is an illustration of trigonometry functions

The longest length of the pipe is 16.64 ft

The widths of the hallways are given as:

[tex]\mathbf{w_1 = 8}[/tex]

[tex]\mathbf{w_2 = 4}[/tex]

See attachment for the diagram that represents the scenario

From the diagram, we have:

[tex]\mathbf{sin(\theta) = \frac 4x}[/tex]

[tex]\mathbf{cos(\theta) = \frac 8y}[/tex]

Make x and y the subject

[tex]\mathbf{x = \frac 4{sin(\theta)}}[/tex]

[tex]\mathbf{y = \frac 8{cos(\theta)}}[/tex]

Where, the total length (L) of the pipe is:

[tex]\mathbf{L = x + y}[/tex]

So, we have:

[tex]\mathbf{L = \frac 4{sin(\theta)} + \frac 8{cos(\theta)}}[/tex]

Differentiate

[tex]\mathbf{L' = -\frac{4cos(\theta)}{sin^2(\theta)} + \frac{8sin(\theta)}{cos^2(\theta)}}[/tex]

Set to 0

[tex]\mathbf{-\frac{4cos(\theta)}{sin^2(\theta)} + \frac{8sin(\theta)}{cos^2(\theta)} = 0}[/tex]

Rewrite as:

[tex]\mathbf{\frac{4cos(\theta)}{sin^2(\theta)} = \frac{8sin(\theta)}{cos^2(\theta)}}[/tex]

Divide through by 4

[tex]\mathbf{\frac{cos(\theta)}{sin^2(\theta)} = \frac{2sin(\theta)}{cos^2(\theta)}}[/tex]

Cross multiply

[tex]\mathbf{2sin^3(\theta) = cos^3(\theta)}[/tex]

Divide both sides by [tex]\mathbf{2cos^3(\theta)}[/tex]

[tex]\mathbf{tan^3(\theta) = \frac 12}[/tex]

Take cube roots of both sides

[tex]\mathbf{tan(\theta) = \sqrt[3]{\frac 12}}[/tex]

[tex]\mathbf{tan(\theta) = 0.7937}[/tex]

Take arc tan of both sides

[tex]\mathbf{\theta = tan^{-1}(0.7937)}[/tex]

[tex]\mathbf{\theta = 38.4}[/tex]

Substitute [tex]\mathbf{\theta = 38.4}[/tex] in [tex]\mathbf{L = \frac 4{sin(\theta)} + \frac 8{cos(\theta)}}[/tex]

[tex]\mathbf{L = \frac 4{sin(38.4)} + \frac 8{cos(38.4)}}[/tex]

Evaluate

[tex]\mathbf{L = 6.43+ 10.21}}[/tex]

[tex]\mathbf{L = 16.64}}[/tex]

Hence, the longest length of the pipe is 16.64 ft

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Answer:

3.34

Step-by-step explanation:

First step: 3x44=132, 132+15=147. Then use 147 as numerator and 44 as denominator.

Second step: Divide 147/44= 3.3409090909091, round and get 3.34.

Hope this helps.

Answer:

2

Step-by-step explanation:

The graph clearly shows that when x = -1, y = 2.

Thus, the output of this function is 2.

Answer:

False

Step-by-step explanation:

-45x < 3

-x <  3/45

-x <  1/15                  Multiply by -1 because x is negative and remember to

                                 change all parts to its opposite.

Therefore  x  >  -1/15      

Answer: 3

Step-by-step explanation:

[tex](f \circ f)(2) = f(f(2)) = f(3) = \boxed 3[/tex]

Answer:

[tex]\frac{5a^2b^2}{4}[/tex]

Step-by-step explanation: