Which of the following values is the solution to the equation
-16 + x = -30 ?

-2
-14
-46
-480

(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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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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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:

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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The input variable is "Height," while the output variable is "Weight."

A variable that is independent is precisely what it sounds like. It is a stand-alone variable that is unaffected by the other variables you are attempting to assess. Age, for instance, could be an independent variable.

The cause is the independent variable. Its value is unaffected by the other study variables. Effect is the dependent variable. Changes in the independent variable affect its value.

When doing an experiment, the independent variable is what you alter, and the dependent variable is what changes as a result of that change. This is an easy way to conceive of independent and dependent variables. The independent variable can alternatively be viewed as the cause, and the dependent variable as the result.

The input and output variables are "Height" and "Weight," respectively.

Detailed explanation:

"Weight and height are related"

As we all know, the independent variable in a function of the form y=f(x) is x, and the dependent variable is y.

In other words, after substituting the values of "x," we are getting the values of the quantity "y."

As a result, we can infer from the assertion that,

We are getting the values of "Weight" after substituting the values of "Height."

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By graphing a plot point using the x-intercept form, the function (x + 4)2 is shown to be x2 + 16 + 8x.

The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

(x + 4)²

= x2 + 16 + 8x

By graphing a plot point using the x-intercept form, the function (x + 4)2 is shown to be x2 + 16 + 8x.

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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 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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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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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

Answer:

quartic trinomial : 3x4 – 2x3 + x2 + 8, a4 + 1, and m3n + m2n2 + mn.

quintic polynomial:  x5 – x3 + x, y5 + y4 + y3 + y2 + y + 1, and 42a3b2.

Step-by-step explanation:

Quartic Polynomial

A polynomial of degree 4.

Examples: 3x4 – 2x3 + x2 + 8, a4 + 1, and m3n + m2n2 + mn.

a quintic function is defined by a polynomial of degree five.

Because they have an odd degree, normal quintic functions appear similar to normal cubic functions when graphed, except they may possess one additional local maximum and one additional local minimum.

The quartic trinomial having a degree of 4 and the quintic polynomial having a degree of 5.

Quartic Trinomial:

A quartic trinomial is a polynomial expression of degree four that consists of three terms.

The general form of a quartic trinomial is:

[tex]ax^4 + bx^2 + c[/tex]

Example:

Let's consider the quartic trinomial:

[tex]2x^4 - 5x^2 + 3[/tex]

In this example, the term "[tex]2x^4[/tex]" is the highest degree term (degree 4), the term "-[tex]5x^2[/tex]" is the second highest degree term (degree 2), and the constant term "3" has no variable.

So, the quartic trinomial has three terms.

Quintic Polynomial:

A quintic polynomial is a polynomial expression of degree five that may contain multiple terms.

The general form of a quintic polynomial is:

[tex]ax^5 + bx^4 + cx^3 + dx^2 + ex + f[/tex]

Example:

Let's consider the quintic polynomial:

[tex]3x^5 - 2x^4 + 4x^3 + x^2 - 7x + 2[/tex]

In this example, the term "[tex]3x^5[/tex]" is the highest degree term (degree 5), the term "-[tex]2x^4[/tex]" is the second highest degree term (degree 4), and so on. The quintic polynomial has six terms, including the constant term "2".

Hence the quartic trinomial having a degree of 4 and the quintic polynomial having a degree of 5.

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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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A graph of each of the exponential equation is shown in the image attached below.

In Mathematics, an exponential function can be modeled by using this mathematical expression:

f(x) = ab^x

Where:

Since Amber shared her photo with 3 people who continued to share it, an exponential function that models the situation is given by:

f(x) = 3(4)^x

Similarly, Ben's post was shared with 2 friends and each of them shared it with 3 more every day, tripling the number of shares every day, an exponential function that models the situation is given by:

g(x) = 2(3)^x

Lastly, an exponential function that represents the spread of Carter's social media post is given by:

h(x) = 10(2)^x

In this scenario, we would use an online graphing calculator to graph each function as shown in the image attached below.

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They continued to share it, so the number of shares increases every day, as shown by the function.

Social Media Post Shares f(x) = 3(4)x

Day Number of Shares

0 2

1 6

2 18 Carter shared his post with 10 friends, who each share with only 2 people each day.

Answer:

Step-by-step explanation:

1 you would pour the water in the cup and see what dash it lands on

let's say you pour the water and it lands on the 1/8 mark it would be one 1/8

Hope this help if not sorry

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 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 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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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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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 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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Therefore , the solution of the given problem of trigonometry comes out to be we can find the sides of triangle by trigonometry ratios.

The area of mathematics known as trigonometry explores the correlation between square side length and As a result of the combination of astronomy and geometry studies, the field initially emerged inside the Nineteenth century, most likely there in third century BC. Precise methods of mathematics cover a number of geometric equations and possible applications to calculations.

Here,

To find the all sides of a triangle

By using trigonometry ,

We can:

Apply the law of sines or trigonometry to find the right triangle side lengths: a = c × sin(α) or

a = c × cos(β)

b = c × sin(β) or

b = c × cos(α)

Therefore , the solution of the given problem of trigonometry comes out to be we can find the sides of triangle by trigonometry ratios.

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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

Answer:

See explanation below.

Step-by-step explanation:

2.3p – 10.1 = 6.5p – 4 – 0.01p?

2.3p -6.5p + 0.01p=  – 4 + 10.1

-4.19p = 6.1           [Combine like terms and moved from one side to the other]

p = -1.456

Select two options.

The options seem to run together.  Where does one equation stop and the other begin?

Are these the equation options?

2.3p – 10.1 = 6.4p – 4

2.3p – 10.1 = 6.49p – 4

230p – 1010 = 650p

– 400 – p 23p – 101 = 65p – 40

– p 2.3p – 14.1 = 6.4p – 4

These don't look correct.   Please review the derivation of p=-1.456 and find the option(s) that provide the same result.

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 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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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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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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