What kind of transformation is illustrated in this figure?
O rotation
O dilation
O translation
O reflection

Answer:

=============================

The given translates as:

Use given x - intercepts to get the equation:

Use the coordinates of P to find the value of a:

The equation of this parabola is:

Answer:

[tex]\textsf{Intercept form}: \quad y=-\dfrac{2}{7}(x+4)(x-7)[/tex]

[tex]\textsf{Standard form}: \quad y=-\dfrac{2}{7}x^2+\dfrac{6}{7}x+8[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

If the x-intercepts are (-4, 0) and (7, 0) then:

Substitute the values of p and q into the formula:

[tex]\implies y=a(x-(-4))(x-7)[/tex]

[tex]\implies y=a(x+4)(x-7)[/tex]

To find a, substitute the given point on the curve P (3, 8) into the equation:

[tex]\implies 8=a(3+4)(3-7)[/tex]

[tex]\implies 8=a(7)(-4)[/tex]

[tex]\implies 8=-28x[/tex]

[tex]\implies a=\dfrac{8}{-28}[/tex]

[tex]\implies a=-\dfrac{2}{7}[/tex]

Substitute the found value of a into the equation:

[tex]\implies y=-\dfrac{2}{7}(x+4)(x-7)[/tex]

Expand to write the equation in standard form:

[tex]\implies y=-\dfrac{2}{7}(x^2-3x-28)[/tex]

[tex]\implies y=-\dfrac{2}{7}x^2+\dfrac{6}{7}x+8[/tex]

Answer:

Step-by-step explanation:

340.56

Answer:

61.92 x 5.50 = 340.56

Answer:

Arithmetic

Step-by-step explanation:

The difference between consecutive terms is 5. Thus, this is an arithmetic sequence with a common difference of 5.

Answer:

Step-by-step explanation:

The average annual rainfall for a town is 43.2 inches.

This is converted to average monthly as:

The difference is:

Answer:

Yeah, they exceeded by 0.4 inches.

Step-by-step explanation:

It is given that,

→ the average monthly rainfall for the previous 9 months was 4 inches.

The monthly rainfall in 12 months,

→ 43.2 inches ÷ 12 months

→ 43.2/12

→ 3.6 inches

Then the difference will be,

→ 4 inches - 3.6 inches

→ 4 - 3.6

→ 0.4 inches

Hence, the difference is 0.4 inches.

The total lifetime of all batteries in a package exceeds that value for only 5% of all packs will be 43.29.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]

σ is the standard deviation

xi is each value from the data set

X is the mean of the data set

n is the number of observations in the data set.

It is given that,

mean,μ=10 hr

standard deviation,σ=1hr

n=4

The lifespan of four batteries combined is,

=4μ

=4×10

=40 hr

z = (x-μ)/σ

1.645=(x-40)/2

x-40=3.29

x=43.29

Thus, the total lifetime of all batteries in a package exceeds that value for only 5% of all packs will be 43.29.

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If the actual length of the pool table is 6 feet , then the length of the pool table in the drawing is 12 inches   .

In the question,

it is given that ,
Barbara drew an scale drawing of the game room.

the scale that she used is 1 feet in the actual length is represented by 2 inches in the drawing ,

which means ,

1 feet = 2 inches

to find the length of 6 feet in the drawing ,

6 feet = 6 × 2 inches

= 12 inches

Therefore , If the actual length of the pool table is 6 feet , then the length of the pool table in the drawing is 12 inches   .

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D set of ordered pairs does not represent a function.

In the given question we have to check which set of ordered pairs does not represent a function.

The given set of ordered pair

(A) (4, 1), (6, 2), (7, 5), (9, 2)

(B) (0, 5), (1, 7), (2, 9), (3, 11)

(C) (-2, 5), (0, 2), (9,-6), (8, 7)

(D) (5, 5), (6, 10), (10, 15), (5, 20)

As we know that in the function a x value always have only one corresponding y value which means for a value of x have only a y value.

But when we see in the ordered pair D. In this pair have pair (5, 5) and (5, 20). This shows different value of y in same value of x.

So, D set of ordered pairs does not represent a function.

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The plant grew by 2 9/40 inches during the week.

A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Initial height of plant = 6 3/8 inches

Final height = 8 3/5 inches

Difference in height = 8 3/5 inches - 6 3/8 inches

converting the mixed fraction to improper fraction

8 3/5 = 43/5

6 3/8 = 51/8

43/5 - 51/8

multiply 43/5 by 8/8 and 51/8 by 5/5 so that both fractions have common denominator, it becomes

344/40 - 255/40

Collect only the numerator we have,

344- 255 = 89 which is no 89/40

divided by 40, we have 2 9/40 inches

In conclusion, the plant grew by 2 9/40 inches

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Answer:

4/7

Step-by-step explanation:

2/7 ÷ 1/2 = 2/7 × 2/1 = 4/7

Answer:

Step-by-step explanation:

1. Write Words into math

2/7/1/2

2. Solve

2/7/1/2=

2/7*2/1=

4/7

Answer: 4/7

Answer:

The equation of the nth term of the sequence is 3n+9.

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=7x is the equation that shows how the total cost of the party favors, y, depends on the number of guests, x

Two or more expressions with an Equal sign is called as Equation.

Given,

Andrew has picked out some party favors.

He calculates that they will cost $7 per guest.

We need to find the equation that shows how the total cost of the party favors, y, depends on the number of guests, x

So y=7x where y is the total cost and x is the number of guests and 7 is the cost per guest.

If there are 2 guests then the total cost will be 14.

Hence y=7x is the equation that shows how the total cost of the party favors, y, depends on the number of guests, x

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The linear equation two variables can be solved by various methods one of the methods to solve the linear equations is the substitution method. The solution of the given equation is x=2 and y=10.

What is  linear equation in two variables ?

A specific point on the graph represents the solution of a linear equation in two variables, ax+by = c, where the total of these two values will equal c when the x-coordinate is multiplied by a and the y-coordinate by b.

Main body:

The given equations are :

10x+3y=50     .... (1)

-5x-y=-20      ....(2)

Multiply equation (2) by 3 and then add the equation (1) to eliminate the variable y.

10x+3y+3(-5x-y)=50+3*-20

-5x=-10

x=2

Now putting the value of x in equation (1), and solve it further.

10*2+3y=50

3y=30

y=10

Hence, the value of x is 2 and the value of y is 10.

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23 tickets are purchased for children and 9 tickets are purchased for adults.

Given,

In the question:

A group entering a zoo purchased 32 admission tickets for a total of $148. Adult tickets cost $7. 50, and tickets for children cost $3. 50.

To find the how many of each type of ticket were purchased?

Now, According to the question:

It is given in the question that 32 tickets are purchased by group which cost total $148.

Let the number of children of the group who are entering the zoo be x. Then the number of adults will be 32- x

Now cost of one ticket for adult = $7.50

Total amount spent on adult tickets = 7.50 × (32-x)

Similarly, cost of one ticket for child= $3.50

Total amount spent on children tickets = 3.50 × x =3.5x

Total amount spent by group on tickets =  $148

⇒ 7.5 × (32-x) + 3.5x = 148

⇒ 240 - 7.5x + 3.5x = 148

⇒ 7.5x - 3.5x = 240 - 148

⇒ 4x = 92

⇒ x = 23

Children = 23

Adults = 32-x = 32-23 = 9

Hence, 23 tickets are purchased for children and 9 tickets are purchased for adults.

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Answer:

p(x)=-2*p*x+4*x+-4=1*-2*p*x+4*x+4=1*-2*p*x+6*x+-6=6*x+4*1*1

Step-by-step explanation:

Answer:

75 cents

Step-by-step explanation:

If 12 bottles cost $9, in order to find the cost of one bottle we must divide the cost by the number of bottles.

[tex] \frac{9}{12} = 0.75[/tex]

therefore the cost of one bottle is 75 cents

1) the speed of Simon per hour is 128 miles/Hr

2) The length of IG is 20 Units.

3) The ratio of SM is 2:1

1) For 1, to obtain the speed of Simon per hour, all you need to do is multiply 32 x 4.
This is because in every hour, 15 minutes occurs four times. That is:

1 hour = 60 minutes

Hence, if 32 miles is done in 15 minutes, then 60 minutes =

32 x 4

= 128 miles

Hence the speed of Simon per hour is 128 Miles/ Hour

2) Given that the two triangles are identical, it means that on the basis on RHS  theorem we have been given all the sides. Note that BG is 6 Units (we are assuming that this is the base) , then AT from the other triangle (see attached) is 20.

We assume this is the Hypotenuse. CT is also given. We assume this is the height. If we have CT and AT, and both triangles are the same, then IG is 20 units.

3) For the quadrilateral, recall that in quadrilaterals opposite sides are equal. If one side is 34u on one, and the other side is 17u on the other quadrilateral, then we already have the measure of the sides for both quadrilaterals.

So the Ratio of AK to WN

34u: 17u - Simplified by dividing by 17u we have

Ratio 2:1

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Plotting the graph of the quadratic function  g(x)=-1/5x^2 + 4x + 1 the range is

The range of the quadratic function is seen at the vertex were the maximum or minimum y value is seen

The graph of the function  g(x)=-1/5x^2 + 4x + 1 is plotted and attached

From the graph the vertex coordinates is v(-10, -16). The y coordinates of the vertex is -19 and this is the minimum values for y

Therefore the range is y ≥ -19

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I will have to reject the offer of the rival company since it's lesser than $40560.

From the information, the person works a basic week of 40 hours and the basic rate is $19.50 per hour. It should be noted that there are 52 weeks in a year. The total amount will be:

= 40 × 19.50 × 52

= $40560

The rival company offers you an annual salary is $36000.

I'll reject the rival company's offer since it's lower.

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Complete question

You work a basic week of 40 hours and your basic rate is $19.50 per hour. A rival company offers you an annual salary is $36.000. Except for the pay, everything is identical between the conpanies. Do you accept or reject the rival company's offer, and why?

Answer:

2.8 pounds per hour

Step-by-step explanation:

[tex] \frac{3.5}{1.25} = \frac{350}{125} = \frac{14}{5} = 2.8[/tex]

Answer:

Take a look at the attachment...

Hope this helps! :)

y = x + 4

Answer:

B

Step-by-step explanation:

given 1 pound = 16 ounces , then

5 pounds = 5 × 16 = 80 ounces

The function f has domain : [-4, 5], range : [0, 9], zero : (3, 0), the function is increasing in intervals at [-4, 0] U [3, 5], decreasing in intervals at (0, 3], the relative minimum values of f : (3, 0), and relative maximum values of f : (5, 9).

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

The function f is given in the graph.

According to the given function, the required solution would be as:

The domain and range of f will be :

domain : [-4, 5]

range : [0, 9]

The zero of f will be :

(x, y) = (3, 0)

The function is increasing in intervals at [-4, 0] U [3, 5]

The function is decreasing in intervals at (0, 3]

The relative minimum values of f : (3, 0)

The relative maximum values of f : (5, 9)

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Length (L) = 42

Width (W) = 18

and the equation which helps to find the width of the garden is

                       L = 6 + 2W

Now, we have to find the length and width of the garden area.

It is given that,

we know that the Length is 6 feet more than twice the width, this in other words, it means that:

                                         L = 6 + 2W       -------------------------(1)

So, let's denote W as X

The perimeter of the garden is 120 and the expression to calculate is:

                                         P = 2W + 2L      ------------------------(2)

Replacing all the values in the above expression we have the following:

                                     120 = 2x + 2(6 + 2x) ---------------------(3)

Solving for x from the above equation (3), we have:

⇒120 = 2x + 12 + 4x

⇒120 - 12 = 6x

⇒108 = 6x

⇒x = 108/6

⇒ x = 18

So the Width is 18, therefore the Length from equation (1):

                L = 6 + 2(18)

             ⇒L = 6 + 36

             ⇒L = 42

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The length of the line YZ is 26 units

The Y is the mid point of the line XZ

The length of the line XY = 20 + 2a

The length of the line YZ = 8 + 6a

When Y is the mid point of the line XZ, then the length of the line XY is equal to the length of the line YZ

The length of the line XY = The length of the line YZ

Substitute the values in the equation and find the value of a

20 + 2a =  8 +6a

Rearrange and group the like term

6a - 2a = 20 - 8

4a = 12

a = 12 / 4

a = 3

The length of the YZ = 8 +6a

= 8 + 6×3

= 8 + 18

= 26 units

Hence, the length of the line YZ is 26 units

The complete question is:

Find the length of YZ when Y is the midpoint of XZ, if XY = 20+2a and YZ = 8+6a.

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If there are 80 cow and 30 buffaloe , the ratio of the cow and the buffaloe is 8:3  .

In the question,

it is given that ,

the number of cows in the farm house = 80

the number of buffaloe in the farm house = 30

we need to find the ratio of cow and the buffaloe .

the ratio can be calculated using the formula .

ratio = (number of cows)/(number of buffaloe)

Substituting the vales , we get

= 80/30

cancelling out the common factor 10 , from both numerator and denominator , we get

= 8/3

So , the ratio is 8:3   .

Therefore ,  If there are 80 cow and 30 buffaloe , the ratio of the cow and the buffaloe is 8:3  .

The given question is incomplete , the complete question is

In a farm house, there are 80 cows and 30 buffaloes . What is the ratio of the cow and the buffaloe ?

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Answer:141

Step-by-step explanation:

angles 4+2= 78

360-78 = 282

282/2 = 141

4,2 equal 6,8

1,3 equal 5,7

Answer:

m7= 141 degrees ; m5 = 141 degrees

Step-by-step explanation:

m3 + m4 = 180

m3 + 39 = 180

m3 = 180 - 39

m3 = 141 degrees

m3 = m5 = 141 degrees

m4 = m8 = 39 degrees

m3 = m7 = 141 degrees

Answer:156

Step-by-step explanation:

(a)The probability that the friend is between 25 and 30 minutes late is 1/2.

(b) It is 10 A.M. There is a 10% probability the friend will arrive within 1 minute.

What is probability?

Uniform distribution

a = 0

b = 10

a) P(friend is between 25 and 30 minutes late) = (30 - 25)/(b - a)

= 5/(10-0)

= 1/2

b) Let the time for arrival be A minutes

(A - 0)/(b-a) = 0.10

A = 0.10 x (10 - 0)

A = 1 minute

Hence, The probability that the friend is between 25 and 30 minutes late is 1/2 and It is 10 A.M. There is a 10% probability the friend will arrive within 1 minute.

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Answer:

which of the following ratios are connected to 5/20?

multiple choice

a 1/5

c 20/100

d 25/100

d is the option 25/100 and

b 1/4