Rewrite the quadratic function in vertex form. Then, determine the maximum or minimum and the axis of symmetry.

y = -3x 2 + 18x - 2

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:

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:

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

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:

42-24n

Step-by-step explanation:

(7 - 4n) . 6

= (7)(6) - (4n)(6) ...........using distributive property, multiply each term by (6)

= 42 -24n (answer)

The probability she will choose a pair of white socks is [tex]\frac{2}{5}[/tex]

Given that,

Total number of outcomes [tex]=4+3+1+2=10[/tex]

We have to find the probability she will choose a pair of white socks.

Number of favourable outcomes[tex]=4[/tex]

the probability she will choose a pair of white socks is,

                  [tex]P=\frac{4}{10} =\frac{2}{5}[/tex]

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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:

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:

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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To find the number of 3-digit multiples of both 4 and 6, we find the least common multiple (LCM) of 4 and 6, which is 12. Then, we count the number of 3-digit multiples of 12.

To find the number of 3-digit multiples of both 4 and 6, we need to find the least common multiple (LCM) of 4 and 6. The LCM of 4 and 6 is 12. Since 12 is a multiple of both 4 and 6, any multiple of 12 will be a multiple of both 4 and 6.

Now, we need to find the number of 3-digit multiples of 12. The smallest 3-digit multiple of 12 is 108, and the largest is 996. So, we need to find how many numbers from 108 to 996 are divisible by 12.

We can divide 996 by 12 to find that the quotient is 83 and the remainder is 0. So, there are 83 3-digit multiples of 12. Therefore, there are 83 3-digit multiples of both 4 and 6.

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!

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:

(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:

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:

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 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:

segment bisector

Step-by-step explanation:

Too cut in half, think bisect.

So we are talking about a segment, so segment bisector

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:

The answer is the first one. Inside the absolute value symbols it is negative but absolute value answers are always positive. Instead of -30 the answer is 30.

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

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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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: 401.33 inches

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:

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

For this case we have to:

[tex]1 \frac {3} {8} = \frac {8 + 3} {8} = \frac {11} {8}[/tex]

We must divide:

[tex]\frac {\frac {11} {8}} {\frac {1} {6}} =[/tex]

Applying double C we have:

[tex]\frac {11 * 6} {8 * 1} = \frac {66} {8} = \frac {33} {4}[/tex]

Converting to a mixed number we have:

[tex]8 \frac {1} {4}[/tex]

Answer:

[tex]8 \frac {1} {4}[/tex]

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

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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