Which of the following is the graph of the piecewise function f of x is equal to the piecewise function of the quantity square root of negative x minus 1 if x is less than or equal to negative 1 and the function negative x over the quantity x squared minus x minus 2 end quantity if negative 1 is less than x is less than 2 and the function log in base 2 of the quantity x minus 1 end quantity if x is greater than or equal to 2 question mark

The exact value of cos(5π/12), using the cosine summation identity, is (√6 - √2)/4.

The exact value of cos(5π/12) can be found using the cosine sum identity, which is:

cos(a + b) = cosa · cosb - sina · sin b

In this case, we can rewrite 5π/12 as (π/4) + (π/6) and use the identity:

cos(5π/12) = cos[(π/4) + (π/6)] = cos(π/4) · cos (π/6) - sin(π/4) · sin (π/6)

Using the values of cos(π/4) = √2/2, cos(π/6) = √3/2, sin(π/4) = √2/2, and sin(π/6) = 1/2, we can plug them into the equation:

cos(5π/12) = (√2/2) · (√3/2) - (√2/2) · (1/2) = √6/4 - √2/4 = (√6 - √2)/4

Therefore, the exact value of cos(5π/12) is (√6 - √2)/4.

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The amount of cost for the fabric is given by A = $ 13

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It displays the similarity of the connections between the phrases on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.

Given data ,

Let the total cost of red fabric be represented as A

Now , the amount of red fabric be = 6 1/2 yards

And , the cost of red fabric per yard = $ 2

So , the total cost of red fabric A = amount of red fabric x cost of red fabric per yard

On simplifying the equation , we get

The total cost of red fabric A = ( 6 1/2 ) x 2

The total cost of red fabric A = ( 13/2 ) x 2

The total cost of red fabric A = $ 13

Therefore , the value of A is $ 13

Hence , the total cost of red fabric is $ 13

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Answer: +-root15/2

To find the x-intercepts, set the function equal to 0 and solve for x.

0.8x^2 - 3 = 0

0.8x^2 = 3

x^2 = 15/4

x = +- root15/2

The value of x is 9 and the sides are 28,8

what is a triangle ?

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always is 180 degrees.

From the given figure ,

we can say that the two triangles are similar ,

21 / 3x+1  =  6 / x-1

21 ( x-1) = 6 (3x+1)

21x - 21 = 18x + 6

21x - 18x = 21 + 6

3x = 27

x = 9

3x + 1 = 3* 9 + 1 = 28

x-1 = 9-1 = 8

Therefore, The value of x is 9 and the sides are 28,8

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The correct answer is B. 25/3.

We can use the equation of a parabola with a focus at (h, k) and a directrix at y = k + p to find the depth of the reflector. The equation is:
(y - k)² = 4p(x - h)

Since the focus is at the light center, we can set h = 0 and k = 0. The distance of the focus from the vertex is 3/4 cm, so p = 3/4. The diameter of the reflector is 10 cm, so the x-coordinate of the vertex is 5 cm. We can plug in these values to find the depth of the reflector:
(y - 0)² = 4(3/4)(x - 0)
y² = 3x
y = √(3x)

When x = 5, we can find the depth of the reflector:

y = √(3*5)
y = √15
y = 3.87 cm
The depth of the reflector is 3.87 cm, or 25/3 cm.

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When a car headlight reflector is cut by a plane along its axis, the section obtained is a parabola. This parabola is such that the light center is at the focus. The distance of focus from the vertex is 3/4 cm and the diameter of the reflector is 10 cm. The depth of the reflector comes out to be CD = VC - VF = (10/3) - (3/4) = 27/4 cm

The vertex of the parabola is the midpoint of the diameter of the reflector. Let V be the vertex of the parabola and let F be the focus. The distance between V and F is given as 3/4 cm.The reflector is such that light rays from the source (headlamp) placed at the focus of the parabola are reflected by the parabola in such a way that the rays are parallel to the axis of the parabola. This is known as the reflecting property of the parabola.

This is equal to CD.Let P be the point on the parabola, as shown in the diagram below, such that PF is equal to the diameter of the reflector. Then, by the definition of the parabola, the distance from P to the vertex C is the same as the distance from the focus F to P, i.e., PF = PC. Since PF is equal to the diameter of the reflector, it is given that PF = 10 cm.Therefore, PC = 10 cm. It is also given that VF = 3/4 cm. Therefore, VC = PC - PV = 10 - 20/3 = 10/3 cm.

Hence, the depth of the reflector is CD = VC - VF = (10/3) - (3/4) = 27/4 cm. Therefore, the depth of the reflector is 27/4 cm, which is the correct option among the given choices.

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Simplifying x^7/x^3 we get x^4.

We have the numerator of the given fraction x^7/x^3 as x^7, that is x raised to the power 7. We can rewrite x^7 equals to (x^4)(x^3) , that is x raised to the power 4 multiplied by x raised to the power 3 (by exponential method).

Similary, the denominator of the given fraction x^7/x^3 is x^3, that is x raised to the power 3.

Rewritting the fraction x^7/x^3 as,

(x^4)(x^3) / x^3  { using division rule}

= x^4  (that is, x raised to the power 4)

Thus after simplifying x^7/x^3 (using division rule) we get x^4.

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The area of the yellow part of the pattern is found as: 72 cm²

The dimension of the square: 12 x 12

Area of yellow part = Area of triangle with base height equals side of square.

Then,

Area of yellow part = 1/2 * B * H

Area of yellow part = 1/2 *12 *12

Area of yellow part = 72 cm²

Thus, the area of the yellow part of the pattern is found as: 72 cm².

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The correct question is-

Work out the area of the yellow part of the pattern. This is a pattern that is being used to make a patch quilt. The pattern is a square, measuring 12cm

by 12cm square.

The approximate solution using the three-point formula with step size h = 1/2 is y(t) = 0 for all t.

The boundary value problem given is y′′ − y = 0 with boundary conditions y(0) = 0 and y(2) = e2 − e−2.

(a) To find the exact solution y(t), we can use the characteristic equation r^2 - 1 = 0. This gives us r = 1 and r = -1. The general solution is therefore y(t) = c1e^t + c2e^-t.

Using the boundary conditions, we can find the constants c1 and c2.

For y(0) = 0, we have 0 = c1 + c2, which gives us c2 = -c1.

For y(2) = e2 − e−2, we have e2 − e−2 = c1e^2 + c2e^-2. Substituting c2 = -c1, we get e2 − e−2 = c1e^2 - c1e^-2.

Solving for c1, we get c1 = (e2 − e−2)/(e^2 - e^-2) = 1/2. Therefore, c2 = -1/2.

The exact solution is y(t) = (1/2)e^t - (1/2)e^-t.

(b) To use the three-point formula with step size h = 1/2, we can set up a table with tn and yn values.

tn | yn
---|---
0  | 0
1/2| y1
1  | y2
3/2| y3
2  | e2 - e-2

The three-point formula is yn+1 = yn-1 + 2h(y′n). We can use this formula to find the values of y1, y2, and y3.

For y1, we have y1 = 0 + 2(1/2)(y′0) = y′0. Since y′0 = y′(0) = (1/2)e^0 - (1/2)e^0 = 0, we have y1 = 0.

For y2, we have y2 = y0 + 2(1/2)(y′1) = 0 + 2(1/2)(0) = 0.

For y3, we have y3 = y1 + 2(1/2)(y′2) = 0 + 2(1/2)(0) = 0.

Therefore, the approximate solution using the three-point formula with step size h = 1/2 is y(t) = 0 for all t.

It is important to note that the three-point formula is not accurate for this particular boundary value problem due to the size of the step and the nature of the differential equation. A smaller step size or a different numerical method may yield a more accurate approximation.

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The derivative of f(x) = (1 + x4 - 1/x)5/3 using the chain rule is (5/3)(1 + x4 - 1/x)2/3(4x3 + 1/x2).

To find the derivative of f(x) = (1 + x^4 - 1/x)^5/3 using the chain rule, we need to use the following steps:

1. Identify the inner function and the outer function. In this case, the inner function is 1 + x^4 - 1/x and the outer function is ( )^5/3.
2. Find the derivative of the outer function with respect to the inner function. This is done by using the power rule: (5/3)( )^2/3.
3. Find the derivative of the inner function with respect to x. This is done by using the power rule and the quotient rule: 4x^3 + 1/x^2.
4. Multiply the derivative of the outer function and the derivative of the inner function together to get the derivative of the original function: (5/3)(1 + x^4 - 1/x)^2/3(4x^3 + 1/x^2).

Therefore, the derivative of f(x) = (1 + x^4 - 1/x)^5/3 using the chain rule is (5/3)(1 + x^4 - 1/x)^2/3(4x^3 + 1/x^2).

Here is the answer formatted in HTML:

To find the derivative of f(x) = (1 + x4 - 1/x)5/3 using the chain rule, we need to use the following steps:

Therefore, the derivative of f(x) = (1 + x4 - 1/x)5/3 using the chain rule is (5/3)(1 + x4 - 1/x)2/3(4x3 + 1/x2).

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The simplified root of the given root i.e. √(400x¹⁰⁰) is 20x⁵⁰. The solution has been obtained by using the law of indices.

What is the law of indices?

The guidelines for simplifying expressions containing powers of the same base number are known as index laws.

We are given an expression as √(400x¹⁰⁰).

Using law of indices,

⇒ √(400x¹⁰⁰) = √400 * √(x¹⁰⁰)             ( as √ab = √a * √b)

⇒ √(400x¹⁰⁰) = 20 √(x¹⁰⁰)

⇒ √(400x¹⁰⁰) = 20 √(x⁵⁰ * x⁵⁰)             ( as a⁴ = a² + a²)

⇒ √(400x¹⁰⁰) = 20x⁵⁰

Hence, the simplified root of the given root i.e. √(400x¹⁰⁰) is 20x⁵⁰.

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Answer:
To calculate the time at which they flash together we need to find the least common multiple of 3 and 8.

Multiples of 3 =

3 x 1 = 3​

3 x 2 = 6​

3 x 3 = 9​

3 x 4 = 12​

3 x 5 = 15​

3 x 6 = 18​

3 x 7 = 21​

3 x 8 = 24​

3 x 9 =27​

3 x 10 = 30

Multiples of 8 =

8 x 1 = 8​

8 x 2 = 16​

8 x 3 = 24

8 x 4 = 32

8 x 5 = 40​

8 x 6 = 48

8 x 7 = 56​

8 x 8 = 64​

8 x 9 =72​

8 x 10 = 80

So LCM of 3 and 8 = 24

So both the lights will flash next at 7:24

Step-by-step explanation:

-6x+25y+66z=232 is the equation of the plane and distance between the point D and the plane is  157/70.

lets find the equation of the line AB and BC and equations of the lines will be of the form

[tex]  \text{ $\frac{x-a}{l}$ = $\frac{y-b}{m}$ = $\frac{z-c}{n}$ } [/tex]

So, the equation of AB is

[tex]  \text{ $\frac{x}{2}$ = $\frac{y-4}{18}$ = $\frac{z-2}{7}$ } [/tex]

So, the equation of AB is

[tex]  \text{ $\frac{x-3}{-1}$ = $\frac{y+2}{24}$ = $\frac{z}{9}$ } [/tex]

let b1 andb2 are the direction vectors of the two above lines.

b1= 2i + 18j + 7k

b2= -1i + 24j + 9k

now n= Det( i       j       k)

                   2      18     7

                  -1       24    9

or, n= -6i + 25j + 66k

the point (0,4,2) lies on the plane. the equation of the plane passing through (0,4,2) and perpendicular to a line with a direction ratio (-6, 25, 66) is

-6x+25(y-4)+66(z-2)=0

or, -6x+25y+66z=232.

now formula of distance between the point (x0,y0,z0) and the plane is

[tex] \frac{Ax0+By0+Cz0+D}{√A^2+B^2+C^2} [/tex]

so for the point D and the plane is

( -6*0 + 25*1 + 66*2 - 132)/√5017 = 157/70.

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Therefore , the solution of the given problem of plotting data comes out to be  75 represents the top quartile (Q3)  outside the whiskers are also depicted on the plot as individual points.

The most popular method for displaying data in a geographical format is to demonstrate the correlation between two additional factors. Digital or hand-drawn sketches are both acceptable. Starting at the starting the spot, move three separate parts upward and then two or more components in the right. The display of the reference system must show the numerals for positions 2, 3, and 4.

Here,

The following details are displayed by the box-and-whisker plot:

The cutoff is somewhere around 35.

=> Around 55 constitutes the bottom quartile (Q1).

=> At around 65, the median (Q2) is.

=> Around 75 represents the top quartile (Q3).

The top number is somewhere around 95.

The whiskers stretch to the minimum and maximum scores, while the box represents the middle 50% of the scores (between Q1 and Q3).

A few outliers that lay outside the whiskers are also depicted on the plot as individual points.

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To calculate the probability that a randomly selected person has at least 2 TV's, you would first calculate the probability of a person having more than 2 TV's:

Then, you would calculate the probability of a person having less than 2 TV's:

Finally, you would calculate the probability of a person having exactly 2 TV's:

Therefore, the probability that a randomly selected person has at least 2 TV's is:

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A.... Any subset of S must be linearly independent, so the set S is linearly independent.

a) Let V be an inner product space and let S = {v1, v2, ..., vm} be an orthogonal set of nonzero elements of V. If the inner product is positive definite, then for any non-zero vector x in V, the inner product x · x is strictly positive. Therefore, for any subset of S, the inner product of the elements in the subset must be strictly positive.

B....This is a counterexample of a non-zero inner product, where a non-zero set of orthogonal vectors is linearly dependent.
b) Consider the inner product space V with inner product (x, y) = x2y2. Let S = {v1, v2} be an orthogonal set of nonzero elements of V, where v1 = (1, 1) and v2 = (1, -1). Since (v1, v2) = 0, S is an orthogonal set. However, S is linearly dependent since v2 = -v1.

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The simplified expression is  [tex]8x^4y^4[/tex].

Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do. For example, take this expression: 4 + 6 + 5.

Here the given expression is

=> [tex](4x^3y^3)(2x.2y)[/tex]

=> [tex]4\times x^3\times y^3\times2x\times2y[/tex]

=> [tex]4\times2\times2\times x^3\times x \times y^3\times y[/tex]

=> 8[tex]\times x^{3+1}\times y^{3+1}[/tex]

=> [tex]8x^4y^4[/tex]

Hence the simplified expression is  [tex]8x^4y^4[/tex].

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Answer:

Trust me I guarantee you it's correct.

Step-by-step explanation:

D. 8x^5y^4

As seen in the attached picture, the account by Grant and the painting are consistent with each other since they both depict a serious and formal situation.

Ulysses S. Grant was an American general and statesman who served as the 18th President of the United States. He was born in 1822 in Ohio and graduated from the United States Military Academy at West Point in 1843. He served in the Mexican-American War and later became a leading Union general in the American Civil War.

As we compare his account of Lee's rendition and the painting provided, we can conclude that they are indeed consistent. Both show how serious and formal the meeting was. Grant even describes the way Lee was dressed, which is confirmed by the painting.

The picture and the account appear in the attachment below.

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After the multiplication of the given decimal numbers and their power, we got the value as 105,000.

One of the number types in algebra that has a whole integer and a fractional portion separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.

Simply change the decimal place to the right by the number of 0s in the power of 10 when multiplying a decimal by a power of 10. Simply change the decimal place to the left by the number of 0s in the power of 10 when dividing a decimal by a power of 10.

We are asked to solve the question:

      (2.5 X 10⁻²)(4.2 X 10⁶)

Now we have to solve this following the PEDMAS rule.

So we have to solve the parentheses first.

2.5 * 10⁻²

Here the exponent has negative power.

10⁻²  = 1/10² = 1/100

Then,

2.5 * 10⁻²  = 2.5 * 1/100 = 0.0025

This is because when the number is divided by the power of 10, the decimal point moves to the left by the value of the power of 10.

Here the power is 2. So it moved two decimal places to the left.

4.2 * 10⁶

Here the decimal number is multiplied by the power of 10. So the decimal point moves  6 places to the right.

4.2 * 10⁶  = 4200000

Now after solving parentheses, we get

0.0025 * 4200000 = 25 * 10⁻⁴ * 4200000 = 105,000,000 * 10⁻⁴

                                                              = 105,000

Therefore after the multiplication of the given decimal numbers and their power, we got the value as 105,000.

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The requried value of the first quartile is 4.5.

Interquartile range (IQR): The IQR is the range of the middle 50% of values in a data set. To calculate the IQR, we first need to find the quartiles of the data set.

To find the first quartile (Q1), we need to arrange the given values in ascending order and then find the median of the lower half of the values.

The given values arranged in ascending order are:

3, 6, 8, 11

The lower half of the values are:

3, 6

The median of the lower half is:

(Q1) = (3 + 6)/2 = 4.5

Therefore, the value of the first quartile is 4.5.

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Area of circle A is 113.04 in²

Area of circle B is 200.96  in²

Area of circle C is 452.16  in²

Area of circle B is 254.34  in²

The number of times that the area of Circle D greater than Circle A is 2.25

A circle is a bounded figure which points from its center to its circumference is equidistant.

Area of a circle = πr²

Where :

π = pi = 3.14

R = radius

here, we have,

Area of circle A = 3.14 x 6² = 113.04 in²

Area of circle B = 3.14 x (6 + 2)² = 200.96  in²

Area of circle C = 3.14 x (8 + 4)² = 452.16  in²

Area of circle B = 3.14 x (12 - 3)² = 254.34  in²

Number of time that is the area of Circle D greater than Circle A = 254.34  in² / 113.04 in² = 2.25

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Complete question:

The radius of Circle A is 6 in. The radius of Circle B is 2 in. greater than the radius of Circle A. The radius of Circle C is 4 in. greater than the radius of Circle B. The radius of Circle D is 3 in. less than the radius of Circle C. What is the area of each​ circle? How many times greater than the area of Circle A is the area of Circle D​?

As a result, the 15 cartons of creamer will last for 1,350 days, or nearly 3.7  expression years. This implies the consumer drinks one serving of creamer per day at a weight of 5 grammes per serving.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

(Total amount of creamer in grammes) / number of days (Amount of creamer consumed per day in grams)

Let's start by calculating the entire amount of creamer in grammes:

(Number of cartons) x (Total quantity of creamer) (Amount of creamer per box)

15 boxes x 450 grammes each box = total quantity of creamer

Total creamer weight = 6,750 g

(Total amount of creamer in grammes) / number of days (Amount of creamer consumed per day in grams)

The number of days is 6,750 grammes divided by 5 grammes each day.

The number of days is 1,350.

As a result, the 15 cartons of creamer will last for 1,350 days, or nearly 3.7 years. This implies the consumer drinks one serving of creamer per day at a weight of 5 grammes per serving.

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The total amount of interest on the investment if compounded continuously comes out to be $10064.60, rounded off to the nearest dollar and cent.

To find the total amount of money accumulated for an initial investment of $5200 at 6% compounded quarterly after 11 years, we can use the formula A = P(1+r/n)^(nt), where A is the total amount, P is the principal or initial investment, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the given values, we get:

A = 5200(1+0.06/4)^(4*11)
A = 5200(1.015)^44
A = 5200*1.9878
A = $10336.96

Therefore, the total amount of money accumulated after 11 years is $10336.96, rounded off to the nearest dollar and cent.

To compute the total amount of interest on the investment if compounded continuously, we can use the formula A= P e^(rt), where e is the base of the natural logarithm. Plugging in the given values, we get:

A = 5200 e^(0.06*11)
A = 5200 e^0.66
A = 5200*1.9355
A = $10064.60

Therefore, the total amount of interest on the investment if compounded continuously is $10064.60, rounded off to the nearest dollar and cent.

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603 white-tailed deer are expected to live in the rectangular area. To find the total number of white-tailed deer in the rectangular area, we need to find the area of the rectangle first. The area of a rectangle is given by the formula:

Area = length × width

In this case, the length is 2.25 miles and the width is 6.7 miles. So, the area of the rectangle is:

Area = 2.25 × 6.7

Area = 15.075 square miles

According to the given information, there are about 40 white-tailed deer per square mile in each of 35 Texas counties. We need to find how many white-tailed deer are expected to live in a rectangular area that measures 2.25 miles by 6.7 miles.

Now, we can find the total number of white-tailed deer in the rectangular area by multiplying the area by the number of deer per square mile:

Total number of deer = 15.075 × 40

Total number of deer = 603

Therefore, there are expected to be 603 white-tailed deer in the rectangular area.

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Answer:

Step-by-step explanation:

41+x=81

x=40

The rabbits score 40 points in the second half.

Answer:

55

Step-by-step explanation:

Answer:

Step-by-step explanation: point form: (4,1)

x=4 , y=1

The simplest form is (x+4)/(x-5). Restrictions on the variable are that x ≠ 5  and x≠-4.

The given expression is (x^(2)+8x+16)/(x^(2)-x-20). In order to simplify this expression, we need to factor the numerator and denominator and then cancel out any common factors.

The numerator can be factored as (x+4)(x+4) and the denominator can be factored as (x-5)(x+4).

So the expression becomes:

(x+4)(x+4)/(x-5)(x+4)

Now we can cancel out the common factor of (x+4):

(x+4)/(x-5)

Therefore, the simplest form of the expression is (x+4)/(x-5).

The restrictions on the variable are that x cannot be equal to 5 or -4, because these values would make the denominator equal to zero and the expression would be undefined.

So the final answer is (x+4)/(x-5) with restrictions x≠5 and x≠-4.

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The graphs of y = x and y = -1 are related to each other because they intersect at the point (-1, -1)

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

The standard equation of a linear equation is:

y = mx + b

where m is the rate of change and b is the y intercept

Given the graphs of y = x and y = -1.

As we can see from the graphs, they intersect at the point (-1, -1)

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number 8 (i think) is d, 1 in 1,500, and number 9 is c, 1,513 cars :)

The number that must be added to both sides of the equation x2 + 12x = 13 so that the method of completing the square can be used to solve the roots is 36. The correct answer is C. 36.

To complete the square, we need to add the square of half the coefficient of the x term to both sides of the equation. In this case, the coefficient of the x term is 12, so half of it is 6. The square of 6 is 36, so we need to add 36 to both sides of the equation. Hence the correct option is C) 36.

The equation then becomes:
x2 + 12x + 36 = 13 + 36

Simplifying the right side of the equation gives us:
x2 + 12x + 36 = 49

Now we can factor the left side of the equation into a perfect square:
(x + 6)2 = 49

From here, we can use the square root property to solve for x:
x + 6 = ±√49

Solving for x gives us:
x = -6 ± 7

So the roots of the equation are x = 1 and x = -13.

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