The graph of a quadratic function is represented by the table.
Х
f(x)
6
-2
7
4
8
6
9
4
10
-2
What is the equation of the function in vertex form?
Substitute numerical values for a, h, and k.

Step-by-step explanation:

if each the bonus is shared equally each will get 420

if 40% is shared by managers each manager will get 560

if 7 sales persons share 60% each will get 360

therefore Peter salesperson will get 360

but he thinks he will get 336 because if 420 is 125% that is including his extra 25% then hundred percent of the 420 is 336 which is not what he will get there for Janet is correct

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Explanation:

Parallel lines have equal slopes, but different y intercepts. The given line y = -2x+4 has a slope of -2. Any line parallel to this will also have a slope of -2.

So m = -2

The unknown line goes through the point (x,y) = (2,4). Which means x = 2 and y = 4 pair up together.

Plug m = -2, x = 2, y = 4 into y = mx+b and solve for b

y = mx+b

4 = -2(2)+b

4 = -4+b

4+4 = b ... adding 4 to both sides

8 = b

b = 8

Since m = -2 and b = 8, we go from y = mx+b to y = -2x+8

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

Side note: the y intercept of the original equation is 4 while the y intercept of the new equation is 8

Answer:

y=-2x+8

Step-by-step explanation:

y= -2x + 4 and passes through point A(2, 4)

if a line is parallel then the two lines have the same slope

since the line passes through A(2,4) then

y=-2x+b find b

4=-2(2)+b

b=4+4=8

b=8

y=-2x+8

Answer:

y ≤ -1/5x +1

Step-by-step explanation:

The line had an incline of -1/5 and the intersect with the y-axis is 1, so the line is given by

y = -1/5x +1

The indicated area in graph is below the line, so now you have enough to get the right inequality:

y ≤ -1/5x +1

Answer:

Probability of blue or red = 3/10

Step-by-step explanation:

4 are black 10 are blue, 3 are red, 6 are green , 6 are blue and red and 1 .

Total = 30

Probability of having a blue = 6/30

Probability of having a blue= 1/5

Probability of a red = 3/30

Probability of a red= 1/10

Probability of a blue or a red=

Probability of blue + probability of red

= 6/30 + 3/30

= 9/30

= 3/10

Answer:

x=0 , y=4

Step-by-step explanation:

3x - 3y = -12        - eq1

4x + 3y = 12        - eq 2

Add eq 1 and 2

3x - 3y + 4x +3y = -12 + 12

7x = 0

x = 0

By substituting the value of x in  eq 2

4x + 3y = 12

4(0) + 3y = 12

3y = 12

y = 12 / 3

y = 4

Answer:

(x,y)=(24,-28)

Step-by-step explanation:

1. Multiply both sides by -1

3x+3y=-12

-4x-3y-=-12

2. Elimnate one variable by adding the equations

-x=-24

3. Change the signs

x=24

4. Susbstitue the value of x in the equation 3x+3y=-12

3 x 24 + 3 y = -12

y=-28

5. Check the solution by plugging in the values.

(x,y)=(24,-28)

How many magazines are there?

12 magazine.

Step by step explanation:

The ratio of stories to magazines is 4 to 3, if there are 28 stories, how many magazines are there?

Story: c

Magazine: r

C / R

C = 4K

R = 3k

4K + 3k = 28

7k = 28

K = 7/28

K = 4

Substituting:

C = 4X4 = 16

R = 3x4 = 12

Ratio of stories to magazines: 4:3

There are 28 stories, so that would mean we would have to divide 28 by 4 to get the common rate.

28/4 = 7

So, now we can substitute it to solve the amount of magazines.

4 x 7 = 28

3 x 7 = 21

Thus, there are 21 magazine and the non-simplified ration of stories to magazines is 28:21.

Answer:

16

Step-by-step explanation:

Apply PEMDAS:

Solve the exponent, multiply from left to right, and then subtract and add from left to right.

[tex]3-2^2+4*3+5\\\\3-4+4*3+5\\\\3-4+12+5\\\\-1+12+5\\\\11+5\\\\\boxed{16}[/tex]

Answer: 16

Step-by-step explanation:

The important thing to remember here is the Order of Operations

The Order of Operations states that first solve Parentheses, then Exponents, then Multiplication and Division, then Addition and Subtraction.

There are no parentheses.

Exponents: 3 - 4+4*3+5

Multiplication and Division: 3 - 4 + 12 + 5

Addition and Subtraction:

-1+12+5

11+5

16

Hope it helps <3

Answer:

x=80

Step-by-step explanation:

the figure depicts a pentagon.

we can use linear pair method to find x

we should find interior angles

angle E= 180-90= 90

angle D=180-60= 120

angle C=180-x

angle A= 90 given

angle B= 180-40= 140

angle sum of a pentagon = 540

by formula (n-2)180. n is the number of sides

equation= 90+120+180-x+90+140= 540

620-x= 540

620-540=x

80=x

Answer:

≈ 10.7 ft

Step-by-step explanation:

We have 2 secants to a circle from an external point.

The product of the measure of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant.

let the internal part of the right secant be x , then

6(6 + x) = 4(4 + 12) = 4 × 16 = 64 ( divide both sides by 6 )

6 + x ≈ 10.7 ( subtract 6 from both sides )

x ≈ 4.7

length of pass = 6 + 4.7 = 10.7

Answer:

solution,

[tex]a. \: x(x + 2) \\ \: \: = x \times x + 2 \times x \\ \: \: = {x}^{2} + 2x[/tex]

[tex]b . \: x(2x - 5) \\ \: = x \times 2x - x \times 5 \\ \: \: = 2 {x}^{2} - 5x[/tex]

[tex]c. \: 2x(3x + 4) \\ \: = 2x \times 3x + 2x \times 4 \\ \: \: = 6 {x}^{2} + 8x[/tex]

[tex]d. \: 6x(x - 2) \\ \: \: = 6x \times x - 6x \times 2 \\ \: \: = 6 {x}^{2} - 12x[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

16

Step-by-step explanation:

64 = 4x

64/4 = 4x/4

16 = x

Answer:

48 miles per hour.

Step-by-step explanation:

The definition of a sample statistic is "any function of observed data, such as the sample mean, sample variance, etc.".

We are given both the sample mean and the sample variance. But samples exist to be compared to the population.

Since we are given the data that "the mean speed of vehicles is greater than 45 miles per hour", we are told what is happening to the mean, not the standard deviation. So, we will use the mean of the sample of 25 vehicles to state the sample statistic: mean speed of 48 miles per hour.

Hope this helps!

Answer:

730 trains would be needed  to seat 350,000 passengers , 10950 carriages would be needed and 350400 seats would be required

Step-by-step explanation:

Number of carriages in 1 train = 15

Number of seats in 1 carriage = 32

Number of seats in 15 carriages =[tex]32 \times 15 =480[/tex]

So, Number of seats in 1 train = 480

Number of trains needed  to seat 350,000 passengers=[tex]\frac{350000}{480}=730[/tex]

Number of carriage in 1 train = 15

Number of carriage in 730 trains = [tex]15 \times 730=10950[/tex]

Number of seats in 1 carriage = 32

Number of seats in 10950 carriage =[tex]32 \times 10950=350400[/tex]

Hence 730 trains would be needed  to seat 350,000 passengers , 10950 carriages would be needed and 350400 seats would be required

Answer:

Correct answer is

[tex]\text{Quotient of }\dfrac{a-3}{7}\div\dfrac{3-a}{21} = -3[/tex]

Step-by-step explanation:

Let us rephrase the given statement mathematically.

We are given the fractions as:

[tex]\dfrac{a-3}{7}[/tex]

to be divided by:

[tex]\dfrac{3-a}{21}[/tex]

To find:

[tex]\dfrac{a-3}{7}\div\dfrac{3-a}{21}[/tex]

Now, let us have a look at the division rule in fractions:

[tex]\dfrac{a}{b} \div \dfrac{c}{d}[/tex]

is equivalent to

[tex]\dfrac{a}{b} \times \dfrac{d}{c}[/tex]

In other words, we say that the second fraction [tex]\frac{c}{d}[/tex] is changed to [tex]\frac{d}{c}[/tex] and [tex]\div[/tex] is changed to [tex]\times.[/tex]

Now solving the given fraction by applying above rules:

[tex]\dfrac{a-3}{3}\div\dfrac{3-a}{21}[/tex]

[tex]\Rightarrow \dfrac{a-3}{7}\times \dfrac{21}{3-a}\\\Rightarrow \dfrac{a-3}{7}\times \dfrac{21}{-(a-3)}\\\Rightarrow \dfrac{1}{1}\times \dfrac{3}{-1}\\\Rightarrow -3[/tex]

So, correct answer is:

[tex]\text{Quotient of }\dfrac{a-3}{7}\div\dfrac{3-a}{21} = -3[/tex]

Answer:

d on edg

Step-by-step explanation:

taking test rn

Answer:

64

Step-by-step explanation:

Answer:

D) n(c) = c/15 - 2.

Step-by-step explanation:

c(n) = 15n + 30

c = 15n + 30

15n + 30 = c

15n = c - 30

n = c/15 - 2

D) n(c) = c/15 - 2

Hope this helps!

The correct answer is option D which is n(c) = c/15 - 2.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The inverse function of the given expression will be calculated as follows:-

c(n) = 15n + 30

c  = 15n + 30

15n + 30 = c

15n = c - 30

n = c/15 - 2

Therefore the correct answer is option D which is n(c) = c/15 - 2.

To know more about Expression follow

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Answer:

20 centimeters

Step-by-step explanation:

A square has all sides equal.

6x - 1 = 4x + 6

6x - 4x = 6 + 1

2x = 7

x = 7/2

Plug in x as 7/2 in one of the side lengths.

6(7/2) - 1

42/2 - 1

21 - 1 = 20

Answer:

Step-by-step explanation:

Sides of a square are always equal.

6x - 1 = 4x + 6

Move the variable to L.H.S and change its sign

6x - 4x - 1 = 6

Move the constant to RHS and change its sign.

6x - 4x = 6 + 1

Simplify

2x = 7

Divide both sides by 2

2x/2 = 7/2

X = 7/2

Again,

6x - 1

plugging the value of X

= 6 * 7/2 - 1

= 3 * 7 - 1

= 21 - 1

= 20

Hope this helps...

Answer:

perimeter=[tex]2(l+b)[/tex]

2(3b+5+2b-1)=

2(5b+4)=0

5b+4=o

b=-4/5

but be can't be -ve

therefore,b=4/5 or 0.8

Answer:

6) The perimeter of the triangle is 3(3x - 1)

7) The perimeter of the rectangle is 2(5b + 4)

Step-by-step explanation:

The perimeter of a triangle and a rectangle is found by adding up all the sides.

6) Perimeter of triangle = 3x - 3 + 4x - 1 + 2x + 1 = 3x + 4x + 2x - 3 - 1 + 1 = 9x - 3 = 3(3x - 1)

7) Perimeter of rectangle = 2(L + B) = 2(3b +5 + 2b - 1) = 2(5b + 4)

Answer:

Step-by-step explanation:

Q1; 10 units

The dotted lines separate the figure into 3 shapes - 1 square, 2 triangles.

The area of a square is s^2, where s is the side length.

The side length of the square is 2. 2^2 =4

The area of the square is 4 units.

The area of a triangle is bh/2, where b is the base and h is the height.

The base of the triangle on the left is 2 and the height is also 2. 2(2)/2 =2

The area of the left triangle is 2 units.

The triangle on the right has a base of 2 and a height of 4. 4(2) =8 /2 = 4

The area of the right triangle is 4 units.

The area of the composite figure is the area of the 2 triangles and the square added together; 4+2+4 =10

The area of the figure is 10 units.

Q2: The area of the shaded area is 44.2654825 [tex]cm^2[/tex].

The area of a circle is π[tex]r^2[/tex]. The radius of this circle is 4cm.

Therefore, the area of the circle is 16π[tex]cm^2[/tex].  

The formula for area of a rectangle is length times width. The length of this rectangle is 3 and the width is 2.

Therefore, the area of the rectangle is 6 cm^2

We're looking for the area of the shaded region (area of circle- rectangle), so we subtract the area of the rectangle from the area of the circle.

16π simplifies to 50.2654825 cm^2.

50.2654825-6 = 44.2654825 cm^2

The area of the shaded area is 44.2654825 [tex]cm^2[/tex].

Answer:

Below in bold.

Step-by-step explanation:

The surface area of the box

= x^2 + 4hx  where x = a side of the square base and h is the height.

So x^2 + 4hx = 8

The volume of the box

V = x^2h

From the first equation we solve for h

4hx = 8 - x^2

h = (8 - x^2) / 4x

Now we substitute for h in the formula for the volume:

V = x^2 * (8 - x^2) / 4x

V =  8x^2 - x^4 / 4x

V =  2x - 0.25x^3

Finding the derivative:

V' = 2 - 0.75x^2 =  0  for max/mimn values

x^2 = 2/ 0.75 = 2.667

x = 1.633.

So the  length and width of the base is 1.633 m and the height

= ( 8 - 2.667) / (4*1.633)

= 0.816 m

The maximum volume =  0.816 *  2.667 =  2.177 m^2.

The answers are correct to the nearest thousandth.

Answer:

the ratio would be 1:4

Step-by-step explanation:

ratio of those who has nuts:

1/5

ratio of those who dont:

1-1/5=4/5

one against another:

1/5 : 4/5 = 1:4 = with : without

Answer:

Step-by-step explanation:

If you plot those points on a coordinate plane, you'll see that the distance from the origin up the y-axis to the point is greater than is the distance from the origin down the x-axis to the other point. That means 3 things to us: 1. the greater distance is a and the shorter is b; 2. the point (0, 11) is the vertex while the point (4, 0) is the co-vertex; and 3. this is a vertically stretched ellipse. A vertically stretched ellipse has an equation

[tex]\frac{(x-h)^2}{b^2} +\frac{(y-k)^2}{a^2} =1[/tex] where h and k are the coordinates of the center, a is the greater distance (between the center and the vertex), and b is the smaller distance (between the center and the co-vertex).  Here's what we have then thus far:

h = 0

k = 0

a = 11

b = 4

Filling in our equation then looks like this:

[tex]\frac{(x-0)^2}{4^2} +\frac{(y-0)^2}{11^2} =1[/tex] and simplifying:

[tex]\frac{x^2}{16} +\frac{y^2}{121} =1[/tex]. It appears that the last answer is the one you want, although when I teach this to my precalc students, I do not encourage them to move the x and y terms around as that answer appears to have done. But addition is also commutative so I'm sure it's acceptable (I just think it looks strange that way).

The equation of ellipse is [tex]\dfrac{y^2}{121}+\dfrac{x^2}{16}=1[/tex] option D is correct.

Important information:

The standard form of an ellipse is:

[tex]\dfrac{x^2}{b^2}+\dfrac{y^2}{a^2}=1[/tex]

Where, [tex](0,a)[/tex] is vertex and [tex](0,b)[/tex] is vertex.

Substitute [tex]a=11,b=4[/tex] in the above equation.

[tex]\dfrac{x^2}{(4)^2}+\dfrac{y^2}{(11)^2}=1[/tex]

[tex]\dfrac{x^2}{16}+\dfrac{y^2}{121}=1[/tex]

[tex]\dfrac{y^2}{121}+\dfrac{x^2}{16}=1[/tex]

Therefore, the correct option is D.

Find out more about 'Ellipse' here:

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Answer:

I hope it will help you...

Answer:

a . See attachment

b. because we will find the distance from the bottom of the ladder to the base of the building.

c. sin 60 = opposite side / hypotenuse

d.sin 60 = x / 10

e .  8.66 ft =x

f. see attachment

i. cos 60° = adjacent side / hypotenuse

Step-by-step explanation:

a . See attachment

b. because cos 60° = adjacent side / hypotenuse, the hypotenuse is equal to the length of the ladder (10), and the adjacent side that we will find is the distance from the bottom of the ladder to the base of the building. not the height that the ladder reaches .

c. sin 60 = opposite side / hypotenuse

Because we will find the opposite side which is the height that the ladder reaches.

d.sin 60 = x / 10

e .  

0.866025403 = x/10

10 (0.866025403) =x

8.66 ft =x

f. see attachment

i. cos 60° = adjacent side / hypotenuse

Because we will find the adjacent side which is the distance from the bottom of the ladder to the base of the building.

Answer:

The function for the outside temperature is represented by [tex]T(t) = 85\º + 15\º \cdot \sin \left[\frac{t-6\,h}{24\,h} \right][/tex], where t is measured in hours.

Step-by-step explanation:

Since outside temperature can be modelled as a sinusoidal function, the period is of 24 hours and amplitude of temperature and average temperature are, respectively:

Amplitude

[tex]A = \frac{100\º-70\º}{2}[/tex]

[tex]A = 15\º[/tex]

Mean temperature

[tex]\bar T = \frac{70\º+100\º}{2}[/tex]

[tex]\bar T = 85\º[/tex]

Given that average temperature occurs six hours after the lowest temperature is registered. The temperature function is expressed as:

[tex]T(t) = \bar T + A \cdot \sin \left[2\pi\cdot\frac{t-6\,h}{\tau} \right][/tex]

Where:

[tex]\bar T[/tex] - Mean temperature, measured in degrees.

[tex]A[/tex] - Amplitude, measured in degrees.

[tex]\tau[/tex] - Daily period, measured in hours.

[tex]t[/tex] - Time, measured in hours. (where t = 0 corresponds with 5 AM).

If [tex]\bar T = 85\º[/tex], [tex]A = 15\º[/tex] and [tex]\tau = 24\,h[/tex], the resulting function for the outside temperature is:

[tex]T(t) = 85\º + 15\º \cdot \sin \left[\frac{t-6\,h}{24\,h} \right][/tex]

Answer:

9 cm

Step-by-step explanation:

c^2=81

Take the square root of both sides.

The square root of c^2 is c.

The square root of 81 is 9.

c=9

Answer:

C = 9 centimeters

Step-by-step explanation:

First, look at the area of a square, which formula is c^2 or in standard format - s^2. Thus, we can say, c^2 = 81. Then, we can simplify, and put c = √81. Since 81 is a perfect square, 9 *  9 = 81. Thus the answer is 9 centimeters.

Answer:

( x+1) (x+3) (x+4)

let given points be

(x1,y1)=(-3,-3)

and(x2,y2)=(3,1)

equation of given line ,

(y-y1)= ((y2-y1)/(x2-x1))×(x-x1)

therefore, 2x-3y+3=0.........(i)

comparing (i ) with ax+by+c=0 we get

a=2

b= -3

c=3

then the line parallel to (i) is

ax+by+k=0 where k = -bc

that is, 2x-3y+9=0 is the required equation

Answer:

19. y = 2/3x - 10/3

20. y = -3/2x - 4

Step-by-step explanation:

First off, we need to find the equation of the line shown. There are two coordinates given. The slope of the line is (1 - -3) / (3 - -3) = 4 / 6 = 2/3. The line obviously intersects the y-axis at -1, so the equation of the line is y = 2/3x - 1.

19. If a line were to be parallel to the given line, the line would have to have a slope of 2/3. So, we have y = 2/3x + b.

To solve for b, all you need to do is substitute the coordinates given, (2, -2), and solve.

-2 = (2/3) * 2 + b

b + 4/3 = -2

b = -6/3 - 4/3

b = -10/3.

So, the equation of the line is y = 2/3x - 10/3.

20. If a line were to be perpendicular to the given line, the line would have a slope that is the negative reciprocal of the given line's slope. The slope would be -3/2. So, we have y = -3/2x + b.

To solve for b, once again, put in the given coordinates, (-4, 2), and solve.

2 = (-3/2) * (-4) + b

b + 6 = 2

b = -4

So, the equation of the line is y = -3/2x - 4.

Hope this helps!

Answer:

D

Step-by-step explanation:

Given

[tex]R_{y-axis}[/tex] ￮ [tex]R_{y=x}[/tex] : (2, 3 )

Then the order of reflections is from right to left, that is

Under a reflection in the line y = x

a point (x, y ) → (y, x ) , thus

(2, 3 ) → (3, 2 )

Under a reflection in the y- axis

a point (x, y ) → (- x, y ) , thus

(3, 2 ) → (- 3, 2 ) → D