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Let ​ x2−12x=61 .​ What values make an equivalent number sentence after completing the square?

The value of x from the given diagram is; 36°

The sum of angles on a straight line is 180°.

In this scenario, the sum of angles on the straight line: AOB is 180°.

Therefore, we have

x = 36°

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The calculated value of the probability of 4

From the question, we have the following parameters that can be used in our computation:

The spinner

Where, we have

Sections = 8

Also, we have

Sections that read 4 = 1

Using the above as a guide, we have the following:

P(4) = 1/8

Hence, the probability of 4 is 1/8

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Emily sold 147 candles for a fundraiser. If she sold 70% of the total number of candles sold for the fundraiser, what is the total number of candles sold for the fundraiser?

Solution:

Candles Emily sold=70% of Total Number of Candles

Emily sold 147 candles.

So, We have,

147=70% of Total Number Of Candles

Let, Total Number Of Candles=x

147=70% of x

147=[tex] \frac{70}{100} [/tex] *x

147=[tex] \frac{70x}{100} [/tex]

Let us multiply by 100 on both sides

147*100=[tex] \frac{70x*100}{100} [/tex]

14700=[tex] \frac{70x*1}{1} [/tex]

14700=70x

To solve for x, Let us divide by 70 on both sides

[tex] \frac{70x}{70}=\frac{14700}{70} [/tex]

x=14700/70

x=210

Total Number of Candles=210

Answer:

The answer is C. 72 miles.

Step-by-step explanation:

The values of x and y in parallelogram DEFG are:

Given:

DH = HF and GH = HE

We have the following equations according to the given condition.

x + 5 = 2y ...(1)

3x - 1 = 5y + 4 ...(2)

From equation (1), we can express x in terms of y:

x = 2y - 5 ...(3)

Substitute this value of x in equation (2):

3(2y - 5) - 1 = 5y + 4

Simplify and solve for y:

6y - 15 - 1 = 5y + 4

6y - 16 = 5y + 4

y = 20

Now substitute y = 20 in equation (3) to find x:

x = 2(20) - 5

x = 40 - 5

x = 35

Therefore, the values of x and y in parallelogram DEFG are:

x = 35

y = 20

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The equation that represents this information will be y = 1.5x + 8.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Mike is going to a ball game on Saturday.

He will pay $8.00 for admission, plus $1.50 per item he buys at the concession stand.

Let x be the number of items and y be the total cost.

Then we have

y = 1.5x + 8

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The equation of the image circle is,

(x + 4)² + (y + 5)² = 9.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Since, We know that;

After reflect a point over the line y = -1, we need to use the formula ;

(x,y) → (x, -y - 2).

Hence, We can apply this formula to each point on the circle and simplify to get the equation of the image circle:

(x + 4)² + (y - 3)²= 9

(x + 4)² + (-y - 2 - 3)² = 9

(x + 4)² + (y + 5)² = 9

So, the equation of the image circle is,

(x + 4)² + (y + 5)² = 9.

Therefore, the correct option is,

(C) (x + 4)² + (y + 5)² = 9.

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We have been given a polynomial [tex]f(x)=2x^{3} +x^{2}-3x+1[/tex] and we are asked to find average rate of  change from x = −1 to x = 1.

First of all we will find f(-1) and f(1).

[tex]f(-1)=2\cdot (-1)^{3} +(-1)^{2}-3(-1)+1[/tex]

[tex]f(-1)=2\cdot (-1) +1+3+1[/tex]

[tex]f(-1)=-2 +5=3[/tex]

Let us find f(1),

[tex]f(1)=2\cdot (1)^{3} +(1)^{2}-3(1)+1[/tex]

[tex]f(1)=2\cdot 1 +1-3+1[/tex]

[tex]f(1)=2+1-3+1[/tex]

[tex]f(1)=4-3=1[/tex]

Now let us find slope for our values.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{f(1)-f(-1)}{1-(-1)}[/tex]

[tex]m=\frac{1-3}{1--1}[/tex]    

[tex]m=\frac{-2}{1+1}[/tex]

[tex]m=\frac{-2}{2}=-1[/tex]

Therefore, average rate of change from our given x values will be -1.

Final answer:

To write a system of equations for the scenario, assign variables to the length and width of the rectangular parking lot. Use the information given to create two equations.

Explanation:

To write a system of equations for this scenario, let's start by assigning variables to the length and width of the rectangular parking lot. Let's say the length is represented by 'L' and the width is represented by 'W'. According to the given information, the width is one fourth the length, so we can write the equation:

W = (1/4)L

The perimeter of a rectangle is equal to the sum of all its sides. In this case, the perimeter is given as 190 meters, so we can write the equation:

2L + 2W = 190

Now we have a system of equations:

W = (1/4)L

2L + 2W = 190

These are the equations that represent the given scenario.

We have been given that L'shanda can choose between 3 sweaters and 4 skirts.

We need to figure out the number of ways in which L'shanda can pick 1 sweater and 1 skirt out of the available items.

We need to use combinations here. First of all, we will figure out the number of ways of choosing 1 sweater out of 3 available sweaters. And then we will determine the number of ways of choosing 1 skirt out of 4 available skirts.

Number of ways of choosing 1 sweater = [tex]_{1}^{3}\textrm{C}=\frac{3!}{2!1!}=\frac{3\cdot 2!}{2!} = 3[/tex]

Number of ways of choosing 1 skirt = [tex]_{1}^{4}\textrm{C}=\frac{4!}{3!1!}=\frac{4\cdot 3!}{3!} = 4[/tex]

Therefore, total number of ways to select 1 sweater and 1 skirt are [tex]3\cdot 4 = 12[/tex]

The equation of the circle is given by (x-h)^2 + (y-k)^2 = r^2 where (h,k) represent the center of the circle and r represents the radius

From the question , we have been given (h,k) = (2,-5) and r =12

(x-2)^2 + (y-(-5))^2 = 12^2

The two minuses in the second term cancel out and give a plus. (-*- = +)

(x-2)^2 + (y+5)^2 = 144

So, the equation of the circle is:

(x-2)^2 + (y+5)^2 = 144 (Option A)