Explain the first steps to factoring when the leading coefficient is 1.

a) List the factors of a that add up to b.
b) Split the c term to factor by grouping.
c) Find the factors of c that add up to b.
d) Multiply b and c, then find the factors.

The linear equation for a line made of points  (r,5) and (6,r) has slope = 5/8 so r=5.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

As slope (m)=(y2-y1)/(x2-x1)

and m=5/8, (x1,y1) and (x2,y2) are (r,5) and (6,r)

Therefore, 5/8=(r-5)/(6-r) --> 5(6-r)=8(r-5)--->13r=70-->r=5

Hence,

         r=5

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The expression for the perimeter of the gardening area is 10x+16

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

The perimeter of the garden will be the sum of all the sides of the garden.

left side = x+3+x = 2x+3

right side = x+3x+x =2x+3

top side = x+3+x+3+x = 3x+6

bottom side = 3x+6

therefore this shot the garden as a rectangular shape.

The perimeter of a rectangle = 2(L+B)

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

= 2( 5x+8)

therefore the expression that best represents the perimeter of the garden is 10x+16

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The value of side AB is 6 units for parallelogram ABCD with perimeter is 22 units.

An equation is an expression that shows how two or more numbers and variables are related to each other. Types of equations can either be linear, quadratic or cubic

Parallelogram is a quadrilateral (four angles and sides) in which opposite sides are equal and parallel.

From the diagram:

AB = DC  (opposite sides are equal)

2y + 1 = 4 - 4w

2y + 4w = 3    (1)

AD = BC  (opposite sides are equal)

3x - 2 = x - w + 1

2x + w = 3    (2)

The perimeter of ABCD is 22:

2(AB + AD) = Perimeter

2(2y + 1 + 3 - 4w) = 22

2(2y - 4w + 4) = 22

4y - 8w + 8 = 22

4y - 8w = 14    (3)

From the three equations:

w = -0.5, x = 1.75, y = 2.5

AB = 2y + 1 = 2(2.5) + 1 = 6 units

The value of side AB is 6 units

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For loop is a type of looping structure that is used in programming to repeat a sequence of codes until a certain condition is met.

In mathematics, a function is a relation between a set of inputs and a set of outputs, such that each input is related to exactly one output. Functions are often represented as mathematical expressions, or as a graph or table. The input to a function is known as the argument, while the output is known as the value. Functions are used to describe physical phenomena, and to model relationships between different variables.

It is commonly used to go through each element in an array or a list without having to write the same code multiple times. For example:

// Initialize array
int arr[] = {1, 2, 3, 4, 5};

// For loop to print out each element in the array
for (int i = 0; i < 5; i++) {
 System.out.println(arr[i]);
}
In this example, the for loop will print out each element of the array until it reaches the condition that i is less than 5, which is the length of the array.

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The equation of the circle center, C(2, -3), with the point on the circle, P(-4, 5), is the option;

The standard form of the equation of a circle is presented as follows;

(x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The length of the radius of the circle

The location of the specified center of the circle, C = (2, -3)

The location of the point P = (-4, 5)

The radius of the circle found using the distance formula used for finding the distance between two points is therefore;

r = √((-4 - 2)² + (5 - (-3))²) = √((-6)² + (8)²) = 10

The radius of the circle, r = 10

Therefore;

The center of the circle, (h, k) = (2, -3)

The equation of the circle = (x - 2)² + (y - (-3))² = 10²

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The equations which are equivalent to -1/4(x) + 3/4 = 12 are -1(x/4) + 3/4 = 12 and -x/4 +3/4 = 12. Choose the 2nd and 5th options

Equivalent equations are equations that work the same way even though they look different

The given equation is -1/4(x) + 3/4 = 12 which can simplified as:

-1/4(x) + 3/4 = 12

(-x + 3)/4 = 12

Compare with options:

1. 4x/1 + 3/4 = 12

4x/1 + 3/4 = 12

This is not equivalent

2. -1(x/4) + 3/4 = 12

-1(x/4) + 3/4 = 12

-x/4 + 3/4 = 12

(-x + 3)/4 = 12

This is equivalent

3. -(x+3)/4 = 12

-(x+3)/4 = 12

This is not equivalent

4. 1/4(x+3) = 12

1/4(x+3) = 12

This is not equivalent

5. -x/4 +3/4 = 12

-x/4 +3/4 = 12

(-x+3)/4 = 12

This is equivalent

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Answer:it’s b and d

Step-by-step explanation:

The height of the tailgate (from the ground), holding the 8 ft ramp inclined at 35° with the ground, found using trigonometric ratios is about 4.59 ft

A trigonometric ratio (trig ratio) specifies the relationship between an angle in a right triangle and two sides of the right triangle.

The length of the ramp = 8 ft

The angle the ramp forms with the ground = 35°

The ramp leads from the ground to the tailgate of the truck

The height of the tailgate from the ground can therefore be found using trigonometric ratios as follows;

The trigonometric ratio for the sine of an angle, θ, using SOH CAH TOA therefore is; sin(θ) = Opposite side

Where;

θ = 35°

The opposite side to the angle θ = Height of the tailgate from the ground = h

The hypotenuse side of the right triangle formed by the ramp = The length of the ramp = 8 ft. We get;

sin(35°) = (Height of the tailgate from ground, )/(Length of the ramp)

Therefore;

sin(35°) = h/8

h/8 = sin(35°)

h = 8 × sin(35°) ≈ 4.59

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The number that would complete the square is 1.

We know that the method of completing the square would involve a quadratic equation that does have the general form;

ax^2 + bx + c =0

We have to note that the number that is going to complete the square is the number that is going to correspond to 1/2(b).

This implies that we have to look at the b term in the equation and we b = 2.

Thus;

1/2(2) = 1

Hence, we have found that the square can be completed by 1.

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Answer:

There is no such set of two numbers that multiply to get 0 and add to get 7. Since any number multiplied by 0 is 0, it is impossible for two numbers to multiply to 0 and add to 7 as adding two numbers that multiply to 0 will always result in zero.

Answer:

Step-by-step explanation:

the numbers are 0 and 7 itself.

Multiply : 0*7 = 0

Add       : 0+7 = 7

The coefficient of x²y in the product ( 7x²-5y) ( x²+3y) is 16.

The coefficient of x²y in the product (7x²-5y) (x²+3y) is the numerical factor that is multiplied to x²y when the two polynomials (7x²-5y) and (x²+3y) are multiplied together.

To find the coefficient of x²y in the product, you can use the distributive property of multiplication over addition, also called the FOIL method, which states that to multiply two binomials, you must multiply the first term of the first binomial by the first term of the second binomial, the first term of the first binomial by the second term of the second binomial, the second term of the first binomial by the first term of the second binomial, and the second term of the first binomial by the second term of the second binomial.

The product of (7x²-5y) (x²+3y) can be expanded as follows:

(7x²-5y) (x²+3y) = 7x²x² + 7x²3y -5yx² -5y3y

=7x⁴ + 21x²y -5x²y - 15y²

= 7x⁴ + 16x²y - 15y²

So, the coefficient of x²y in the product ( 7x²-5y) ( x²+3y) is 16.

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The area of rectangle is found to be 117 sq. yd.

Let the length of rectangle be L:

The, the width is W + 4 = L

Perimeter = 2(length + width)

P = 2(L + B)

P = 2(W + 4 + W)

P = 2(2W + 4)

40 = 4W + 4

4W =36

W = 9

The, L = 9 + 4 = 13 yd.

Area = length * width

Area = 9*13

Area = 117

Thus, the area of rectangle is found to be 117 sq. yd.

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Answer:

Step-by-step explanation:

The perimeter of a rectangle is the total circumference of the rectangle.

Perimeter=2(Length + breadth)

Perimeter=40yd

Length=x+4 and breadth=x

40=2(x+x+4);

40=4x+8;

4x=32 and x=8yd

So, length=12yd and breadth=8yd.

Area = length*breadth

So Area = 12*8= 96ydsq

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An equation that represents the relationship between n and w is w = 10n + 8.

Mathematically, the slope-intercept form of a line can be represented by using this linear equation:

y = mx + c

Where:

Next, we would determine the slope of the data points in this table (see attachment) as follows;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (78 - 68)/(7 - 6)

Slope, m = 10/1

Slope, m = 10.

At point (6, 68), an equation of this line can be calculated in slope-intercept form as follows:

y - y₁ = m(x - x₁)

y - 68 = 10(x - 6)

y - 68 = 10x - 60

y = 10x - 60 + 68

y = 10x + 8 ≡ w = 10n + 8.

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The number of people visited the zoo from the state is  200

Number deals with quantity of people that came to the zoo from the state over the period.  These people must be from the state.

The given parameters that will help us to solve the question are:

The ratio is approximately 7 to 3.

The number of people = 2000

The sum of the ratios is equal to 7+3 = 10

This is to say that 10% of the people visited the zoo

10/100*2000/1

Therefore about 200 people visited the zoo

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The four types of Sequence are Arithmetic Sequence , Geometric sequence , Harmonic Sequence and Fibonacci Sequence .

What is a Sequence ?

The Sequence is defined as an arrangement of objects or a set of numbers in a particular order which are followed by some rule .

The Four Types of Sequences are :

(i) Arithmetic Sequence : It is defined as a type of sequence in which  every term of the series is created by adding or subtracting a fixed number to preceding number .

(ii) Geometric Sequence : It is defined as a type of sequence in which  every term is obtained by multiplying or dividing a fixed number with the preceding number .

(iii) Harmonic Sequence : It is defined as a type of sequence in which the reciprocals of the terms follows the Arithmetic Progression .

(iv) Fibonacci Sequence : It is defined as a type of sequence in which every element is obtained by adding the two preceding elements and the sequence starts with 0 and 1 .

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Step-by-step explanation:

Today, we are going to be talking about the three-way principle of mathematics. Basically, there are three ways to solve a problem in math: verbally, graphically, or by example. In this lesson, we will discuss each of these principles by solving sample problems using each type.

The equation m = 4w + 3 shows the number of days in January.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

A pattern shown in the image.

Let m is the number of days in a month.

And w represents the number of days in the weeks.

So, algebraic equation,

m = 4w + 3.

Therefore, the equation is m = 4w + 3.

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As per the given statement, the scuba diver's position means the distance he traveled is below 18 feet at the sea level.

Here we have given that a scuba diver starts at sea level and travels to a position that is a little lower than -18 feet.

Now, we need to find the scuba diver's position means the distance he traveled.

While we consider that the scuba driver travelled on -18 feet.

Here the negative term is defined that the the traveler goes on the bottom level.

Therefore, here we said that the person is going to below the sea level.

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The four coordinate plane quadrants don't have names but are simply known as the first quadrant, second quadrant, third quadrant, and fourth quadrant

example of coordinate

Take into account that the midpoint in between the points (x1,y1) and (x,2y,2) is given by:

xo = (x1 + x2)/2

yo = (y1 + y2)/2

in this case you have

(x1,y1) = (4,-4)

(xo,yo) = (6,-1)

by using the expression for xo and yo, you can find the values of the coordinate of point B, as follow:

xo = (x1 + x2)/2

2xo = x1 + x2

x2 = 2xo - x1

x2 = 2(6) - 4

x2 = 8

yo = (y1 + y2)/2

2yo = y1 + y2

y2 = 2yo - y1

y2 = 2(-1) - (-4)

y2 = 2

Hence, the coordinates of point B is

(xo,yo) = (8,2)

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On solving the provided question, we can say that the provided slope is -2/3 equation of line 2x + 3y -7 = 0

A line's slope determines how steep it is. A mathematical equation for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two spots. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is employed to express it. The y-intercept is located at a location where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).

the provided slope is -2/3

let us assume x1 = 2 and y1 = 1

equation of line =>

y-1 = -2/3(x-2)

y-1 = -2x/3 + 4/3

3y-3 = -2x + 4

2x + 3y -7 = 0

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Answer:

Step-by-step explanation:

0.25

Answer: The statement that is true about the function f(x)=4x-4 is:

It is a linear function, as it is a straight line in the form of y=mx+b where m is 4 and b is -4

The y-intercept of this line is -4, which means when x=0, y=-4

The slope of this line is 4, which means for every 1 unit increase in x, y increases by 4 units

The domain of this function is all real numbers and the range is all real numbers except -4

The equation of the line is y = 4x - 4

The graph of this function is a line with a slope of 4 and y-intercept of -4.

Step-by-step explanation:

1. The function f(x) = (x+5)(x-9) in standard form is x²-4x-45.

2. The function f(x) = (x+4)² in standard form is x²+8x+16.

3. The function f(x) = (x+2)²-25 in standard form is x²+4x-21.

4. The function f(x) = 4(x-2)² in standard form is 4x²-16x+16.

5. The function f(x) = 6(2x+1)² in standard form is 24x²+24x+6.

6. The function f(x) = 3(x+4)(x-5) in standard form is 3x²-3x-60.

7. The function f(x) = (x+10)²-100 in standard form is x²+20x.

8. The function f(x) = 9-(x+1)² in standard form is -x²-2x-8.

9. The function f(x) = 2(x+5)²+10 in standard form is 2x²+20x+60.

What is the standard form?

A linear equation can also be written in standard form, slope intercept form, and point slope form.

The formula for standard form is Ax+By=C.

The first function is y = f(x) = (x+5)(x-9).

Simplifying the equation -

f(x) = (x+5)(x-9)

x(x-9)+5(x-9)

x²-9x+5x-45

x²-4x-45

Therefore, the standard form is x²-4x-45.

The second function is y = f(x) = (x+4)².

Simplifying the equation -

f(x) = (x+4)²

Follow the formula - (a+b)² = (a²+2ab+b²)

(x)²+2(x)(4)+(4)²

x²+8x+16

Therefore, the standard form is x²+8x+16.

The third function is y = f(x) = (x+2)²-25.

Simplifying the equation -

f(x) = (x+2)²-25

Follow the formula - (a+b)² = (a²+2ab+b²)

[(x)²+2(x)(2)+(2)²]-25

x²+4x+4-25

x²+4x-21

Therefore, the standard form is x²+4x-21.

The fourth function is y = f(x) = 4(x-2)².

Simplifying the equation -

f(x) = 4(x-2)²

Follow the formula - (a-b)² = (a²-2ab+b²)

4[(x)²-2(x)(2)+(2)²]

4[x²-4x+4]

4x²-16x+16

Therefore, the standard form is 4x²-16x+16.

The fifth function is y = f(x) = 6(2x+1)².

Simplifying the equation -

f(x) = 6(2x+1)²

Follow the formula - (a+b)² = (a²+2ab+b²)

6[(2x)²+2(2x)(1)+(1)²]

6[4x²+4x+1]

24x²+24x+6

Therefore, the standard form is 24x²+24x+6.

The sixth function is y = f(x) = 3(x+4)(x-5).

Simplifying the equation -

f(x) = 3(x+4)(x-5)

3[x(x-5)+4(x-5)]

3[x²-5x+4x-20]

3[x²-x-20]

3x²-3x-60

Therefore, the standard form is 3x²-3x-60.

The seventh function is y = f(x) = (x+10)²-100.

Simplifying the equation -

f(x) = (x+10)²-100

Follow the formula - (a+b)² = (a²+2ab+b²)

[(x)²+2(x)(10)+(10)²]-100

x²+20x+100-100

x²+20x

Therefore, the standard form is x²+20x.

The eighth function is y = f(x) = 9-(x+1)².

Simplifying the equation -

f(x) = 9-(x+1)²

Follow the formula - (a+b)² = (a²+2ab+b²)

9-[(x)²+2(x)(1)+(1)²]

9-x²-2x-1

-x²-2x-8

Therefore, the standard form is -x²-2x-8.

The ninth function is y = f(x) = 2(x+5)²+10.

Simplifying the equation -

f(x) = 2(x+5)²+10

Follow the formula - (a+b)² = (a²+2ab+b²)

2[(x)²+2(x)(5)+(5)²]+10

2[x²+10x+25]+10

2x²+20x+50+10

2x²+20x+60

Therefore, the standard form is 2x²+20x+60.

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(C) x=-5, y=6 is the solution of the equation 2x+3y=8

To find out which among the following options are solutions of the equation 2x+3y=8, we can substitute the values of x and y in the equation and see if it holds true or not.

a) x=0, y=5 : 2(0) + 3(5) = 0 + 15 = 15 != 8

b) x=3, y=2 : 2(3) + 3(2) = 6 + 6 = 12 != 8

c) x=-5, y=6 : 2(-5) + 3(6) = -10 + 18 = 8 = 8

d) x=-1, y=-2 : 2(-1) + 3(-2) = -2 + -6 = -8 != 8

so the value of left hand side and right hand side of a), b) ,d) is not equals to each other and hence they won't be the equation solution .

So the correct answer is (c) x=-5, y=6

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when graphing inequalities, we use an open  point when the sign is greater or less than  when the sign is ,and a closed point when the sign is greater or less than or equal to

Graph following inequalities.

1) x≥3

2) x<-2

3) x< 7

4) x ≤ -4

explanation

To find the equation of a linear function from its graph:

Find the slope by finding the rise and run.

Find the y-intercept (the point where the line crosses the y-axis)

Substitute the value into the function f(x)= mx+b .

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Answer:

Step-by-step explanation:

You want Lisa's and Myra's ages if the sum of their ages is 40 and in 10 years, Lisa will be 3 times as old as Myra.

The current sum of their ages is 40. In 10 years, 10 will be added to each of their ages, so the sum will be 60.

At that time Lisa's age is 3 times Myra's age, so will be 3/(3+1) = 3/4 of the total.

  Lisa's age in 10 years = (3/4)(60) = 45

Lisa is 35 now, and Myra is 5 now.

__

Additional comment

We could write some equations, but we find a mental solution based on ratios to be quick and easy. Here is a solution using equations:

  L + M = 40

  (L +10) = 3(M +10) . . . . . . age relation in 10 years

  (40 -M) +10 = 3M +30 . . . . substitute for L

  20 = 4M . . . . . . . . . add M-30

  M = 5; L = 40-M = 35

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Answer:

A. c = 15.9 + 12(y - 2014)

B. c = 15.9 + 12(2025 - 2014)

C. 147.9 gigabytes

D. Unsure what you meant

Step-by-step explanation:

A. In this equation, 'c' represents the flash storage capacity in year 'y' and '15.9' is the flash storage capacity in year 2014. '12' represents the yearly increase in storage and '(y-2014)' represents how many years have passed from 2014.

B.To find the average flash storage capacity of smartphones in 2025, we can use the equation:

c = 15.9 + 12(y - 2014)

We can substitute 'y' with 2025 in the above equation to find the average flash storage capacity of smartphones in 2025

C.

c = 15.9 + 12(2025 - 2014)

c = 15.9 + 12(11)

c = 15.9 + 132

c = 147.9 gigabytes

The number of pair of sunglasses that the company needs to sell in order to make profit is 80,000.

In economics, business, and especially cost accounting, the break-even point is the point at which total cost and total income are equal, i.e. "even". There is no net loss or gain, and one has "broken even," despite the fact that opportunity costs were incurred and capital got the risk-adjusted, expected return.

In order to make profit the organization needs to be at breakeven. Therefore, firstly they need to make profit that is equal to the refurbish cost.

The Profit on per pair of glass =  Selling price per pair - Labor and material cost per pair - marketing cost per pair

The Profit on per pair of glass =  $99 - $30 - $19

The Profit on per pair of glass =  $50

Now, the breakeven point can be found as,

Break even quantity = Refurbish Cost / Profit on a pair of sunglasses

                                  = $4,000,000 / $50

                                  = 80,000

Hence, the company needs to sell  80,000 pair of sunglasses.

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