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The equation of the vertical parabola in vertex form is written as

Where (h, k) are the coordinates of the vertex and p is the focal distance.

The directrix of a parabola is a line which every point of the parabola is equally distant to this line and the focus of the parabola. The vertex is located between the focus and the directrix, therefore, the distance between the y-coordinate of the vertex and the directrix represents the focal distance.

Using this value for p and (3, 1) as the vertex, we have our equation

Answer:

$4.35

Step-by-step explanation:

8 weeks = $34.80

1 week = x

Cross-multiply

$34.80/8

=$4.35

So, for each week, Paige will pay $4.35

$(4.35 × 8 = 34.8)

STEP - BY - STEP EXPLANATION

What to find?

The power function that the given graph resembles.

Given:

f(x)=(x − 3)³

First, we need to note that;

If f(x) is shifted left q - units, then the new formula of the function becomes f(x+q).

Let q=3

ANSWER

y=x³

Here, we want to use the given information to calculate the lateral and the total surface area

To find the lateral area, we have to calculate the perimeter of the base and multiply this by the height of the triangular prism

Now, we will make the shape lie on its side

This mean the triangles will represent the base

Mathematically, the perimeter of a triangle is the sum of its side

We need the last side of the triangle

We can get this by the use of Pythagoras' theorem

As we can see, the side measure 5 is the hypotenuse as it faces the right angle

The square of the hypotenuse equals the sum of the squares of the two other sides

3,4 and 5 are a Pythagorean triple

This means that, the measure 3 is the last side of the triangle

So the perimeter is;

The height is the measure 8 inches

Thus, the lateral area is;

Now, we want the total surface area, but firstly, we need the area of the base

The area of the base is the area of the triangle

two times this is 12 in^2

The total suface area is thus;

In this problem, we have the transformations

option B (shift the graph of f(x) 4 units up

option C reflect the graph of f(x) over the y-axis

solution

diferent trim levels = 4

different colors = 5

different interior options = 3

then:

answer: 60 different versions of this model

We need to choose 5 members from the general only

The number of general members = 31

As the arrangement is not required

So, the number of committees will be:

so, the answer will be 169,911 committees

To answer this question we need to see it on an axis.

-7> -10 , it is true. -7 it's more near to 0.

If the center of the circle is at O.then the measure of angle ABC is 28 degree

The measure of  angle ABC can be calculated by using central angle theorem

What is central angle theorem

The Central Angle Theorem states that the central angle from two chosen points A and B on the circle is always twice the inscribed angle from those two points ie if the angle inscribes at the circumference is x, then the angle at the center is 2x.

The angle ABC = 1/2 angle AOC

the angle ABC = 1/2 x 56

the angle ABC is 28

Therefore, if the center of the circle is at O.then the measure of angle ABC is 28 degree

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The answer is option B

Given:

/16x^2 + x^2/3 + 3/8x^5

You need to simplfiy the expression given which will give you

6 3/x^5 or the second option

Given data:

The given points are (-2,-1) and (3, -1).

The slope of the line passing through the given points is,

Thus, the slope of the line passing through the given points is 0.

f(x) = x +57

g(x) =7x+15

The solution is (7,64). To rent the cabin for 7 days cost $64

1) Let's examine the graph. We can see two linear equations.

Picking two points for f(t) = (7,64) and (0,57) and for g(t) (0,15) and (7,64) let's find out their respectives slopes:

2) For f(t) , let's plug into the slope-intercept formula, plugging one point:

(0,57)

y=mx+b

57=0x +b

57= b

So the rule for the function is, in terms of f(x) = x +57

(0,15)

y=mx +b

15=0x +b

15 =b

So the rule for the function g(t) , in terms of g(x) is g(x) =7x+15

Interpreting the solution:

The solution to this Linear System of Equations is the common point (7,64).

So filling in the blanks we have:

The solution is (7,64). To rent the cabin for 7 days cost $64

Given: The coordinates of a trapezoid as below

To Determine: The final step on the trapezoid after it is reflected over the x-axis and then reflected over the axis

Solution

Please note that a reflection over the x-axis and reflection over the y-axis is different from the last step, which is a reflection over the y-axis

The reflection over the y-axis could either be a rotation of 90^0 clockwise or anticlockwise.

So get the trapezid onto itself after a reflection over the y-axis from a reflection over teh x-axis requires two steps

We have step 1: Reflection over the x-axis, then

Step 2: Reflection over the y-axis

Hence, the final step is reflection over the y-axis

The given expression is

First, we add x on each side

Then, we subtract 106 from each side

Notice that there are two triangles between the parallel lines.

Also, notice that the angle 160° and y are same-side interior angles, so they sum 180°.

We solve for y.

On the other hand, angles 30 and x are alternate interior angles, which means they are congruent.

Kevin recorded the distances he ran last week. The total number of miles he ran on Monday through Wednesday is the same as the total number of miles he ran on Thursday and Friday. How many miles did Kevin run on Wednesday?​

_______________________

The total number of miles he ran on Monday through Wednesday is the same as the total number of miles he ran on Thursday and Friday.

x + (x + 9) + (x + 4) = 2x + (4x - 2)

_____________________

Can you see the updates?

__________________

x + (x + 9) + (x + 4) = 2x + (4x - 2)

3x + 13 = 6x -2

6x - 3x = 13 + 2

3 x = 15

x = 15/3 miles

x = 5 miles

___________________________

5 + ( 5 + 9) + ( 5 + 4) = 2x + (4x - 2)

28 = 28

________________________

on Wednesday

x=5

x+ 4 = 9

_________________

Answer

On Wednesday he ran 9 miles

_________________

Can you see the updates?

Do you have any questions regarding the solution?

a.

Therefore, your score would be 70% then you will get a C

b.

Your score would be 82.5%, then you will get a B

c.

Your score would be 86.4%, then you will get a B

We can find the horizontal asymptote of this kind of functions using the limit:

Therefore the equation of the horizontal asymptote is:

The equation is,

The equation can be solved if on right side there is only variable with any number in multiplication. So equation can be solved as,

So to eliminate -2/3

A part of a circle is called an arc and an arc is named according to its angle.

The value of b is 11.

From the question, we have

ax² + bx + c

using (0, 9)

substituting the value  we get

9 = a(0)² + b(0) + c

c = 9

Therefore,

-1 = a(-1)² + b(-1) + c

-1  = a - b + 9

-1 - 9 = a - b

a - b = - 10

using (-2, -9)

-9 = a(-2)² + b(-2) + 9

-9 - 9 = 4a - 2b

-18 = 4a - 2b

2a - b = -9

combine the equation

a - b = - 10

2a - b = -9

solving the equations we get

a = 1

Then,

1 - b = -10

b = 1 + 10

b = 11

Hence, the value of b is 11.

Subtraction:

The process of removing items from a collection is represented by subtraction. Subtraction is represented by the minus sign. If, for instance, there are nine oranges stacked together (as shown in the above figure), and four of those oranges are then moved to a basket, the stack will contain nine minus four oranges, or five oranges. As a result, 9 minus 4 equals 5, or the difference between 9 and 4. Incorporating subtraction into other types of numbers is possible in addition to using it with natural numbers.

The symbol for subtraction is the letter "-". The three numerical elements that make up the subtraction operation are the minuend, the subtrahend, and the difference. As the first integer to be subtracted from in a subtraction phrase, a minuend is the first number in the subtraction process.

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Given the function:

to find f(3), we have to make x = 3 and substitute on the function, to get the following:

therefore, f(3)=23

Given the sequence:

1/2, 3/4, 9/8, 27/16, ..........

We are to find the recursive formular

A recursive geometric formular has a pattern:

An = An - 1 * r

Where r is the common ratio. But before we write the formular, we need to look for the value of r.

This r value has to be the same between each consecutive number in the series.

Sinces it's geometric, r is multiplied in. To get from 1/2 to 3/2 we find the r value in this way:

x/2 = 3/4 where x/2 is the same as 1/2 x.

Cross multiply to get 4x = 6 and x = 3/2.

That means that if r is 3/2, then we can multiply every term in that sequence by 3/2 to get the next term in line.

3/4 times 32 is 9/8. So, r = 3/2 and the formulat is:

An = An - 1 * 3/2

Therefore, the crrect optio is B.

From the question we are to determine Britta most likely task in preparing a budget.

First let's know what a budget is.

A budget is an estimation of revenue and expenses over a specified future period of time and is utilized by governments, businesses, and individuals. A budget is basically a financial plan for a defined period, normally a year that is known to greatly enhance the success of any financial undertaking.

So with the above explanation of what a budget is, Britta most likely task is to allot a set amount of money for her expenses.

Therefore the correct option is C, which is She is allotting a set amount of money for her expenses.

A dime has a thickness of 1 7/20 mm and a penny has 1 1/2 mm.

Stacking both coins, we will have :

and we have the inequality :

Note that 1 7/20 is less than 1 1/2, so the inequality symbol is "<"

since 1 1/2 + 1 1/2 is equal to 3mm

Therefore, the thickness of stacking coins is less than 3mm

Hailey's estimate is correct (Yes)

You have the following interval:

(-∞,-2]

the previous interval can be written as follow:

x ≤ -2 as an inequality

and on the number line you have:

The RELATION 1 and 3 represent a function

Rationale

There are no x value with several y values.

For a relation to be a function, there should only one y value fot each x

By the property of congruency of triangles, the following conclusions are taken from the figure

[tex]\angle EAB = \angle ECD[/tex] [Alternate angle]

[tex]\angle EBA = \angle EDC[/tex] [Alternate angle]
AB = CD [Given]

What is congruency of triangles?

Two triangles are said to be congruent if their corrosponding sides and corrosponding angles are same.

There are five axioms of congruency

They are SSS axiom, ASA axiom, AAS axiom, SAS axiom, RHS axiom

Here,

In[tex]\Delta AEB[/tex] and [tex]\Delta DEC[/tex]

[tex]\angle EAB = \angle ECD[/tex] [Alternate angle]

[tex]\angle EBA = \angle EDC[/tex] [Alternate angle]
AB = CD [Given]

So,

[tex]\Delta AEB \cong \Delta DEC[/tex] [ASA axiom]

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We have the distribution;

74, 90, 21, 68, 62, 84, 34, 87,74.

Let's arrange this from ascending to descending order, we obtain;

i. The mean or average of this distribution is

ii. The median is the central value, in this distribution, there are 9 values, so the median value is the 5th value.

iii. The mode is the value with the highest frequency, this is the most occurring value, in this distribution;

iv. The range is the difference between the highest and lowest values, this is;