given the inputs in the table, which function rule produces the outputs?

Answer:

A

Step-by-step explanation:

First find the median of the data set.

The median is the middle value of the data set arranged in ascending order

10, 11, 12, 15, 17, 19, 22, 24, 29, 33, 38

The median = 19

The first quartile ( lower) is the middle value of the data to the left of the median.

10, 11, 12, 15, 17

The first quartile is 12 → A

We know that the whole angle of the triangle is 73. Since the known angle is 45 degrees, we need to find out what the other is.

Subtract 45 from 73 to find the angle of the unknown triangle.

73-45=28.

Now that we know the value of the unknown triangle, solve for x

Make an equation.

2x+5=28

Subtract 5 on both sides.

2x=23

Divide 23 by 2 to isolate x.

X=11.5

The answer is C. 11.5

Hope this helps!

Answer:

f(x)=4(3)^2

(2,36)

36=4(3)^2

36=4(9)

36=36

Step-by-step explanation:

Answer: Hi! here you want a function that pases through the point (2,36)

it means, a function f(x) so f(2) = 36.

Also, f(x) must be an exponential function, this means that f(x) = [tex]a^{x}[/tex]

where a is a real number.

then  [tex]a^{2}[/tex] = 36

so a = [tex]\sqrt{36}[/tex] = ± 6.

then your function can be f(x) = [tex]-6^{x}[/tex] or [tex]6^{x}[/tex].

Notice that i used a very simplest example of exponential function. You actually can found lots of exponential functions F(x) that passes through the point (2,36).

Answer:  [tex]y=(x +3)^2 -6[/tex]

Step-by-step explanation:

The equation of a parabola in Vertex form is:

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

Where [tex](h,k)[/tex] is the vertex of the parabola

We can rewrite the function [tex]f(x)= x^2 + 6x + 3[/tex] as:

 [tex]y= x^2 + 6x + 3[/tex]

 In order to convert it into vertex form we need to Complete the square:

Take the coefficient of the x term, divide it by 2 and square it:

[tex](\frac{6}{2})=3^2[/tex]

Add and subtract 3² on the right side:

[tex]y= x^2 + 6x+3^2 + 3-3^2[/tex]

Now we must convert the right side to a squared expression, then we get:

 [tex]y=(x +3)^2 -6[/tex]

Answer:

D

Step-by-step explanation:

[tex]1/3)^{x}[/tex] = [tex]\frac{1}{3^{x} }[/tex] = [tex]3^{-x}[/tex]

and

[tex]27^{x+2}[/tex] = [tex](3^{3})^{x+2}[/tex] = [tex]3^{3(x+2)}[/tex] = [tex]3^{3x+6}[/tex]

Hence expression D is equivalent

Answer:

Step-by-step explanation:

Use the cosine law (look at the picture).

We have:

[tex]a=a\\b=4\\c=3\\\gamma=32^o[/tex]

[tex]a^2=4^2+3^2-2(4)(3)\cos32^o[/tex]

[tex]\cos32^o\approx0.848[/tex] → look at the second picture

[tex]a^2=16+9-24(0.848)\\\\a^2=25-20.352\\\\a^2=4.648\to a=\sqrt{4.648}\\\\a\approx2.2[/tex]

Answer:

3/5

Step-by-step explanation:

5 / -1 = -5  

so  

-3 / -5 = 3/5

To find x when y=-1, substitute y=-1 into the equation y = -173.5 + 4.83x and solve for x.

To find x when y=-1, you can use the equation of the line where y = 5 when x = -3. Based on the given information, the line of best fit is y = -173.5 + 4.83x. By substituting y = -1 into the equation, we can solve for x:

-1 = -173.5 + 4.83x

Adding 173.5 to both sides of the equation:

172.5 = 4.83x

Dividing both sides by 4.83:

x = 35.69

Therefore, when y = -1, x is approximately 35.69.

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I added the graph below for the verified Apex answer :)

The inequality equation will be 6x + 18y ≤ 234.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Michael can spend a maximum of $234 on office supplies.

Each ream of paper costs $6. Each ink cartridge costs $18.

Then the inequality equation will be

Let x be the number of reams of paper and y be the number of the ink cartridge. Then we have

6x + 18y ≤ 234

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Answer:

12

Step-by-step explanation:

2(a+3)

Given a = 3, all you need to do is just plug in a = 3 into the expression

2(3 + 3)

= 2 (6)

= 12

Answer:

2(3+3)

6x2

12

Step-by-step explanation:

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut-off point with the y axis

[tex]m = \frac {y2-y1} {x2-x1}[/tex]

We have the following points:

[tex](x1, y1): (- 7,25)\\(x2, y2): (- 4,13)[/tex]

Substituting the values:[tex]m = \frac {13-25} {- 4 - (- 7)} = \frac {-12} {- 4 + 7} = \frac {-12} {3} = - 4[/tex]

Thus, the line is of the form:

[tex]y = -4x + b[/tex]

We substitute one of the points and find "b":

[tex]13 = -4 (-4) + b\\13 = 16 + b\\b = 13-16 = -3[/tex]

Finally we have to:

[tex]y = -4x-3[/tex]

Answer:

The equation es [tex]y = -4x-3[/tex]

Answer:

She mixed up the slope and y-intercept when she wrote the equation in step 3.

Answer:

h = (10 ft)(4.01) = 40.1 ft

Step-by-step explanation:

The tangent function relates this elevation to the horizontal distance (10 ft) and the angle of elevation (76 degrees):

                               opp           h

tan 76 degrees = --------- = ------------- = 4.01

                                adj         10 ft

Therefore , h = (10 ft)(4.01) = 40.1 ft

Answer: 40 ft

Step-by-step explanation:

You can find the height of the statue by solving the right triangle.

In this case the adjacent side of the triangle is the horizontal distance to the statue (10 ft). The height of the statue is the opposite side to the angle of 76 °.

By definition, the tangent of an angle is:

[tex]tan(\theta) = \frac{opposite}{adjacent}[/tex]

In this case

[tex]\theta=76\°\\\\opposite = h\\\\adjacent = 10\ ft[/tex]

Therefore

[tex]tan(76) = \frac{h}{10}[/tex]

[tex]h=tan(76) * 10\\\\h=40\ ft[/tex]

Answer:

segment bisector

Step-by-step explanation:

Too cut in half, think bisect.

So we are talking about a segment, so segment bisector

Answer:

A= 57 sq units

Step-by-step explanation:

To calculate the are area of a triangle we use the Herons formula:

A=√s(s-a)(s-b)(s-c) where a, b and c are the sides of the triangle.

s=(a+b+c)/2

s=(10+13+12)/2

=17.5

A=√[17.5(17.5-10)(17.5-13)(17.5-12)]

A= 57 sq units

Answer:

60 units ^2

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

Answer:

27 units on edge.

Answer:

(9m-1)(9m+1)

Step-by-step explanation:

This is a difference of squares

(9m)^2-1^2

Use a^2-b^2=(a-b)(a+b)

So the answer is (9m-1)(9m+1)

Answer:

Step-by-step explanation:

[tex]81m^2-1=9^2m^2-1^2=(9m)^2-1^2\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(9m-1)(9m+1)[/tex]

Answer:

Symmetric

Step-by-step explanation:

If you put a line in the middle of the third row and fold it on itself, it would match.

Answer:

i have to say it's symmetric cos technically uniform would kinda mean "with form if u know what i mean, and is kinda like "random" and like, cut the graph in half and it's a perfect fit

Answer with explanation:

Pre image= Coordinates of point X= (3,4)

When point ,(x,y) is rotated by an angle of 180°, then coordinates of image that is point (x,y) after rotation = (-x, -y)

⇒≡Coordinates of point X(3,4) after rotation by an angle of 180°=X'(-3,-4)

The coordinates after a rotation of 180 degrees about the origin is: X'(-3, -4)

There are different types of transformation such as:

Translation

Rotation

Reflection

Dilation

The transformation rule for the rotation about 180 degrees (180°) about the origin is (x,y)→(−x,−y) .

Thus:

X(3, 4) → X'(-3, -4)

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Answer:

y = - [tex]\frac{1}{3}[/tex] x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (3, 2) and (x₂, y₂ ) = (- 9, 6)

m = [tex]\frac{6-2}{-9-3}[/tex] = [tex]\frac{4}{-12}[/tex] = - [tex]\frac{1}{3}[/tex], hence

y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (- 9, 6), then

6 = 3 + c ⇒ c = 6 - 3 = 3

y = - [tex]\frac{1}{3}[/tex] x + 3 ← in slope- intercept form

Answer:

32/7

Step-by-step explanation:

5 1/3=16/3

1 1/6=7/6

----------------

(16/3)/(7/6)

(16/3)(6/7)

(16/1)(2/7)

32/7

Answer:

y = 2x + 2

Step-by-step explanation:

Start at point (2, 6).

Go up 2 units up (rise = 2) and 1 unit right (run = 1). Now you are at point (3, 8) which is on the graph.

slope = rise/run = 2/1 = 2

The slope of the graph is 2. m = 2

Now look at point (0, 2). The y-intercept is 2. b = 2

The equation is

y = mx + b

y = 2x + 2

Answer:

y = 2x + 2

Step-by-step explanation:

Here we're asked to come up with a linear function relating x and y.

First we find the slope of the line.  As we move from (0, 2) to (3, 8), x increases by 3 and y by 6.  Thus, the slope is

m = rise / run = 6 / 3 = 2.  

Plugging givens into the slope-intercept formula y = mx + b, we find b:

2 = 2(0) + b, so that b = 2.

Then the desired relationship between x and y is y = 2x + 2.

Answer:

C. triangles

Step-by-step explanation:

Pythagoras Theorem is a theorem which states you can work out a side of a right - angled triangle using the other 2 sides. Pythagoras will not work on shapes except from a right - angled triangle and square

Answer:

Part 1) [tex]10\°\ C=50\°\ F[/tex]

Part 2) [tex]87\°\ F=30.6\°\ C[/tex]

Part 3) [tex]-5\°\ C=23\°\ F[/tex]

Part 4) [tex]10\°\ F=-12.2\°\ C[/tex]

Step-by-step explanation:

we know that

The formula to convert degrees Celsius to degrees Fahrenheit is equal to

[tex]F=(\frac{9}{5}C)+32[/tex]

The formula to convert degrees Fahrenheit to degrees Celsius is equal to

[tex]C=(F-32)\frac{5}{9}[/tex]

Part 1) we have

10 degrees Celsius

Convert to degrees Fahrenheit

[tex]F=(\frac{9}{5}10)+32[/tex]

[tex]F=50\°[/tex]

Part 2) we have

87 degrees Fahrenheit

Convert to degrees Celsius

[tex]C=(87-32)\frac{5}{9}[/tex]

[tex]C=30.6\°[/tex]

Part 3) we have

-5 degrees Celsius

Convert to degrees Fahrenheit

[tex]F=(\frac{9}{5}(-5))+32[/tex]

[tex]F=23\°[/tex]

Part 4) we have

10 degrees Fahrenheit

Convert to degrees Celsius

[tex]C=(10-32)\frac{5}{9}[/tex]

[tex]C=-12.2\°[/tex]

Answer:

Degree Celsius:        Degree Fahrenheit:

10                                         50

30.6                                     87

-5                                         23

-12.2                                     10

Step-by-step explanation:

Hope this helps!!

Answer:

They have different slopes and different y-intercepts, so they have no solution

Step-by-step explanation:

Answer:

Infinite solutions Answer explained below

Step-by-step explanation:

Let us see the various conditions for intersections of two lines in simplest way.

1. Same slope and same y intercept : Infinite solutions

2. Same slope and different y intercepts : No solution

3. Different slope and same y intercept : unique solution

4. Different slope and different y intercept : Unique solution

Here slope means the tangent of the angle line makes with the positive x axis and y intercept is the y coordinate at which the line intersect the y axis.

In our equations , we our slopes and y intercepts as

y=-3x+6

slope = -3 and y intercept = 6

y=6-3x

slope = -3 and y intercept = 6

Hence same slope and same y intercept , thus have infinite solutions

Answer:

16 36 169 100

Step-by-step explanation:

just square them

16, 36, 169, 100

square of 4

[tex]4^{2}=16[/tex]

square of 6

[tex]6^{2}=36[/tex]

square of 13

[tex]13^{2}=169[/tex]

square of 10

[tex]10^{2} = 100[/tex]

In the mathematics squaring is easy to understand. Squaring the number means multiplying it by itself. Squaring is written on mathematical symbols by putting a two above the number you are squaring to show that it is multiplied two times

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Answer: $16.850

Step-by-step explanation:

Subtract 2x^2+55x+10 - (2x^2 -15x-40)

70x+50

Then put in 240 for x

Answer:

The given expression is equivalent to 3(2^(3/8))x.

Step-by-step explanation:

The given expression (3 root 8^1/4 x) can be written as:

3√(8^(1/4))x

we know that 2^3 = 8

= 3√(2^(3/4))x

We know that √x = (x)^(1/2)

= 3(2^((3/4)(1/2))x

Powers multiply with each other, 3*1/4*2 = 3/8

= 3(2^(3/8))x

Answer:

15

Step-by-step explanation:

This problem is quite simple; that is, if you know the proper formula that must be applied in finding the distance. The formula for finding the distance between two coordinate points is: √(x2-x1)^2+(y2-y1)^2. Now, obviously, (x2-x1)^2 and (y2-y1)^2 are both under the radical, where x2 and y2 represent the xy coordinates of point A (7,4) and x1 and y1 represent the xy coordinates of point B (-8,4). Now, all you must do is plug the points into the distance formula to get the answer, 15.

The distance between the two points is 15 units.

The coordinate points are A (7, 4) and B (-8,4).

The formula to find the distance between two coordinate points is Distance=[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2}-y_{1} )^{2}}[/tex].

Now, the distance between two coordinate points=[tex]\sqrt{(-8-7)^{2} +(4-4)^{2}}[/tex]

=√225

=15 units

Therefore, the distance between the two points is 15 units.

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For one uniform 15/4 m of cloth is needed, since we need 26 uniforms week need 26 time that much cloth. Set up and multiply the equation like so...

[tex]\frac{15}{4}[/tex]*26

or you can write it like so...

[tex]\frac{15}{4} *\frac{26}{1}[/tex]

Multiply numerator by numerator and denominator by denominator...

[tex]\frac{15*26}{4*1}[/tex]

[tex]\frac{390}{4}[/tex]

^^^This can be further simplified to...

[tex]\frac{195}{2}[/tex]m

or

97.5 m

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

95  1/2 m of cloth

Step-by-step explanation:

Multiply:

(15/4 m)

------------ * 26 uniforms = 95.5 m of cloth needed, or 95  1/2 m of cloth

uniform

Answer:

The volume of the sphere is 24 cm³

Step-by-step explanation:

* Lets explain the difference between the cylinder and the sphere

- The cylinder has two circular bases and a curved surface

- The bases of the cylinder have radius r and the curved surface has

 a height h

- The volume of the cylinder = area of its base × its height

∵ The area of the circle is πr²

∴ The volume of the cylinder is V = π r² h

- A sphere is a perfectly round geometrical object in three-dimensional

 space

- It the set of points that are all at the same distance r from a given point

 that means its radius equals its height

- The volume of the sphere = 4/3 π r³

* Now lets solve the problem

∵ The cylinder and the sphere have the same radius and height

∵ The volume of the cylinder is 18 cm³

- Lets equate the rule of the volume of the cylinder by 18

∵ The volume of the cylinder = π r² h

∴ π r² h = 18 ⇒ divide both side by π

∴ r² h = 18/π

- The sphere and the cylinder have the same radius and height

∴ The radius and height of the sphere have the same value of the

   cylinder

∵ The the height of the sphere is its radius

∴ r²h of the cylinder = r³ in the sphere

∴ r³ = 18/π

- Substitute this value in the rule of the volume of the sphere

∵ The volume of the sphere = 4/3 π r³

∴ The volume of the sphere = 4/3 π (18/π) ⇒ cancel π's

∴ The volume of the sphere = 4/3 (18) = 24 cm³

* The volume of the sphere is 24 cm³