The graphs below have the same shape. What is the equation of the red
graph?

Triangle DEF is an isosceles triangle, with two sides of length 8 and one side of length 10.

We can use Heron's Formula to calculate the area of the triangle. Heron's Formula is A = √(s(s-a)(s-b)(s-c)), where s is the semiperimeter, or half of the perimeter, and a, b, and c are the lengths of the sides of the triangle.

The semiperimeter of triangle DEF is (8+8+10)/2 = 16. Substituting these values into Heron's formula yields A = √(16(16-8)(16-8)(16-10)) = √(256(8)(8)(6)) = √11520 = 107.3.

Therefore, the area of triangle DEF is 107.3 square units.

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2 3 as an exponent is written as 2^3 and it represents 2 multiplied by itself 3 times. 2^3 = 2 * 2 * 2 = 8

In the notation 2^3, the number 2 is the base and the number 3 is the exponent. The exponent tells you how many times the base is being multiplied by itself. In this case, 2 is multiplied by itself 3 times.

It's important to note that the exponent is also known as the power, so 2^3 is also read as 2 to the power of 3.

In summary, 2 3 as an exponent is written as 2^3 and it represents 2 multiplied by itself 3 times, or 2 to the power of 3 which is equal to 8. Understanding this concept is important for solving mathematical problems, especially in algebra and calculus.

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An equation that can be used to determine the number of hours, h, that Moira needs to read to finish the book is h + 178 = 214.

In order to write an equation that model this situation, we would assign a variable to the number of hours that is needed to read to finish the book and the total number of hours respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into an algebraic equation based on the fact that she read for 178 hours yesterday as follows;

h + 178 = T

Substituting the given parameters into the algebraic equation, we have the following;

h + 178 = 214

Solving for h, we have the following;

h = 214 - 178

h = 36 hours.

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Answer:

2.4

Step-by-step explanation:

2/5=AB/6

=>AB=2.4

It is "3 pairs" not "3 pair", because a pair is a set of two things, so if you have 3 of them it would be 3 sets of two things or 3 pairs.

Answer:

75 meters long 55 meters wide

Step-by-step explanation:

80*50= 4000

75*55=4125

4125<4000

75+55= 130

80+50=130

Answer: Would it just be 2/3? It says 2/3 are alley cats.

Step-by-step explanation:

Answer:

1/3 of them are alley cats

Step-by-step explanation:

The balance on the credit card after three years would be $20,111.25.

What is continuous compound interest?

Continuous compounding means that there is no limit to how often interest can compound. Compounding continuously can occur an infinite number of times, meaning a balance is earning interest at all times.

The balance on the credit card after three years can be calculated using the formula for continuous compound interest:

A = P * e^(rt)

where A is the final balance, P is the initial principle (the amount of the loan), r is the annual interest rate as a decimal, and t is the number of years.

In this case, P = $12,500, r = 0.1599 (15.99% as a decimal), and t = 3.

Plugging these values into the formula:

A = $12,500 * e^(0.1599 * 3)

A = $12,500 * e^0.4797

A = $12,500 * 1.6089

A = $20,111.25

Rounded to the nearest penny: $20,111.25

Hence, the balance on the credit card after three years would be $20,111.25.

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The value of the liquid assets of the salesperson is; D: $613,570

Liquid assets are defined as a set of property or investment that can be converted easily into cash. These liquid assets include raw cash, fast selling and marketable securities that can be traded and converted into cash within a short time.

Hence the liquid assets of the person, along with their values, are listed as follows:

The returns from someone's retirement portfolio will supplement your Social Security benefits, and it can even prevent you from having to live squarely on a fixed income. Due to the fact that a retirement portfolio is diversified, it can protect you from market volatility by balancing different income classes. Retirement Portfolio in this question is given as  $473,906 (It is called the Retirement fund)

Investments = $139,664

The total value of the person's liquid assets is given by the sum of the values of each of these two assets, hence:

473,906 + 139664 = $613,570

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Answer:

x = 5 ft

Step-by-step explanation:

Volume of a right square pyramid = V = x²h/3

66.7 = x²(8/3)

x² = 66.7(3/8) = 25

x = √25 = 5

The slope and the y-intercept of the line are 3 and 5 respectively.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is the equation of a straight line → y = 3x + 5

The equation of the straight line given is -

y = 3x + 5

We can compare and conclude that -

m = 3

c = 5

Therefore, the slope and the y-intercept of the line are 3 and 5 respectively.

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Answer:

An exponent refers to the number of times a number is multiplied by itself.

Step-by-step explanation:

For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.

The coordinates of V’ in the image of TUV under a dilation centered at the origin with scale 5 followed by a translation 3 units right and 2 units down can be found by following the transformation sequence.

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The domain of f(x) = 4x + 1 is all real numbers.

The domain of a function is the set of all input values for which the function is defined. As the expression f(x) = 4x + 1 does not contain any restrictions on the values of x, the domain of this function is all real numbers.

The domain of a function is the set of all possible input values for which the function is defined. In this case, the function is f(x) = 4x + 1, which does not have any restrictions on the values of x, thus the domain of this function is all real numbers. This means that all real numbers are valid input values, including negative numbers, positive numbers, fractions, irrational numbers, and all other real numbers. This means that regardless of the input value, the output will always be a real number. Thus, the domain of this function is all real numbers.

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The value of x in the rectangle is 7 metres.

A rectangle is a quadrilateral with opposite sides equal to each other and also parallel to each other.

The rectangle has dimension 12 meters and 5 times x metres, with diagonal length of 37 metres.

Hence, the length x can be found using Pythagoras's theorem.

Therefore,

c² = a² + b²

where

Therefore,

37² = 12² + (5x)²

1369 = 144 + 25x²

1369 - 144 = 25x²

1225 = 25x²

divide both sides by 25

x² = 1225 / 25

x² = 49

square both sides

x = √49

x = 7 metres

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in the form ax²+bx+c, in which a, b, and c are constants, the value of given quadratic equation a+b+c is 0.

Simplification is the process of making an expression or equation simpler, while still maintaining its meaning or function. This can be done by combining like terms, combining or removing unnecessary elements, or applying mathematical rules or identities.

For example, in algebra, simplifying an expression might involve combining the coefficients of similar terms (such as 2x + 3x = 5x), or factoring out a common factor from multiple terms (such as [tex]2x^2 + 4x = 2x(x+2).[/tex]

The goal of simplification is to make the expression or equation easier to understand, manipulate, or solve.

The expression given is already in the form ax^(2) + bx + c, so we can simply add the coefficients of the x^(2), x and constant terms to find the value of a+b+c:

[tex](2x^{(2)} -3x+1)-(-2x^{(2)}-3x+2) = 2x^{(2)} - (-2x^{(2)}) + (-3x) - (-3x) + 1 - 2[/tex]

a+b+c = 2 - (-2) + (-3) - (-3) + 1 - 2 = 2 + 2 - 3 - 3 + 1 - 2 = 0

Therefore, the value of a+b+c is 0.

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Answer:

a = 2

b = 7

Step-by-step explanation:

The given rectangle is a parallelogram.

10b + 1 = 9b + 8

10b - 9b = 8 - 1

b = 7

2. WX = ZY

6a + 4 = a + 14

6a - a = 14 - 4

5a = 10

a = 2

Answer:

0.28

Step-by-step explanation:5 (numerator) ÷ 18 (denominator) = 0.28

Answer: 0.28

Step-by-step explanation:

You look it up

Answer:

x=14

Step-by-step explanation:

The angles inside a triangle add up to 180 degress all the time, therefore

58+80+3x=180

simplify

138+3x=180

subtract 138 from both sides of the equation

3x=42

divide both sides by 3

x=14

Inequality formula:

The inequality formula is a mathematical statement that compares two values using the less than (<) or greater than (>) symbols.

The inequality formula is used to determine if one value is greater than, less than, or equal to another value. It can be written in the form of A < B or A > B, with A and B representing any two values. This is useful for solving problems that involve comparison, such as determining whether a number is greater than another or if a certain value is within a certain range. The inequality formula can also be used to graph inequalities on a number line, which is useful for visualizing the relationships between two values.

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The proper way to enter the piece-wise function into Desmos is given as follows:

A piecewise function is a function that has different definitions, based on the input of the function.

The definitions for this problem are given as follows:

The correct command to enter an interval in Desmos is between {}, hence the intervals are given as follows:

The definitions of f(x) are entered using y = f(x), hence the correct option is given by the second option.

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For the given line segment, the value of HJ is 32 and hence option a is the correct answer.

Two unique points on a line define the boundaries of a line segment. A line segment is sometimes referred to as a section of a line that links two places.

Given that:

GJ = 56

[tex]\frac{GH}{HJ} =\frac{3}{4}[/tex]

The line segment GHJ = GJ can be written as follows:

GJ= GH +HJ

From the given ratio we know that:

GH = 3x and

HJ = 4x

Thus, the value of GJ = 3x + 4x

GJ = 7x

56 = 7x

x = 8

Substitute the value of x = 8 in GH = 3x and HJ = 4x.

GH= (3)(8) = 24

HJ = (4)(8) = 32

Hence the value of HJ = 32 and option a is the correct answer.

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An image may be defined as that point, where the light rays coming from an object meet or appears to meet after reflection or refraction.

In this definition, the word 'object' may be defined as anything from which light rays are coming.

A function f from a set A to a set B is a special relation in

which, every element of set A has unique image in set B.

The function f from A to B is denoted by f : A →

If, f(a) = b, then ‘b’ is called the image of ‘a’ under f and ‘a’

is called the pre image of ‘b’ under f.

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Answer:

y = 2x + 5

Figure 505

Step-by-step explanation:

(3,11) ( 4,13)

Find the slope

Change in y over the change in x

[tex]\frac{13-11}{4-3}[/tex] = [tex]\frac{2}{1}[/tex] = 2

slope (m) is 2.

Part A

Find the y -intercept

m = 2

x = 3     from the point (3,11)

y = 11    from the point (3,11)

y = mx + b  Substitute what I know and solve for b

11 = (2)(3) + b

11 = 6 + b  Subtract 6 from both sides

11 - 6 = 6 -6 + b

5 = b

The y intercept (b) is 5

y = mx + b

y = 2x + 5

Part B

y =  2x + 5

1015 = 2x + 5  Subtract 5 from both sides

1015 - 5 = 2x + 5 - 5                                                    

1010 = 2x  Divide both sides by 2

505  

Yuna wam 1.9 miles in the open ocean in two hours, starting off with an average speed of 1.4 mph but decreasing to 0.8 mph. This resulted in a total distance of 2.8 miles.

To calculate Yuna's total distance wimmed, we need to calculate the total time it took her to wim. She wam 1.9 miles in 2 hours, so her average peed for the entire wim wa 1.4 mph.

1.4 mph x 2 hours = 2.8 miles

Therefore, Yuna wam a total of 2.8 miles.

Yuna trained for a triathlon and wam 1.9 miles in the open ocean, which took her two hours. She started off with an average speed of 1.4 mph, but as she got tired and wam against the current her average speed decreased to 0.8 mph. In order to calculate the total distance wimmed, we need to calculate the total time it took her which can be done by multiplying her average speed of 1.4 mph by the two hours. This gives us a total distance of 2.8 miles, which means that Yuna wam a total of 2.8 miles.

Yuna wam 1.9 miles in the open ocean in two hours, starting off with an average speed of 1.4 mph but decreasing to 0.8 mph. This resulted in a total distance of 2.8 miles.

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The equation in slope intercept form is

y = 5/2x + 5

One of the most popular ways to describe a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula may be used to get the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfills.

The slope intercept form is a technique for figuring out a straight line's equation in the coordinate plane. Any point's coordinates on a straight line must fulfill a certain relation, which is known as the equation of a straight line.

Any location that is not on the line will not fulfill the coordinates.

This equation's solution is simple to find. A straight line's slope, or angle of inclination from the x-axis, and the intercept it makes with the y-axis are both necessary to determine the slope intercept form of the line.

Two points on the line are (-2,0) and (0,5)

The slope intercept form is

y = mx + c

so when y = 0 and x = -2

0 = -2(m) + c

or,  2m -c = 0 ..(i)

again when x= 0 y = 5

5 = 0*m + c

c = 5

so putting c= 5 in equation (i) we get

m = 5/2

so the equation in slope intercept form is

y = 5/2x + 5

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Therefore , the solution of the given problem of equation comes out to be  x = 73/19 , y = 5/19 and z = 18/19.

In a mathematical formula, the equal symbol (=) is used to denote that the statements are equivalent. It is demonstrated that many numerical variables are comparable using mathematical equations, which are statements of reality. The equal sign, for instance, separates the numbers 12 or b + 6 split separate halves of the equation y + 6 = 12. It is possible to calculate how many words each sides of a symbol represents. The meaning of a symbol usually contradicts itself.

Here,

Given :

=> x-3y+z=4.......   (1)

=>2x-8y+8z=-2 ........ (2)

=> -6x+3y-15z=9 ......... (3)

Multiply eq (1) by 2 and subtract from eq (2)

=>  2x - 6y + 2z -2x +8y +8z = 8 +2

=>  2y +10z =10

=> y + 5z =5 ..... (4)

and

Multiply eq (2) by 3 and add to eq (3)

=> 6x - 24y +24z  -6x + 3y -15z =-6 +9

=> -21y + 9z = 3

=> -7y + 3z =1 ..... (5)

So ,

from eq (4) and (5)

=> y = 5 -5z

=> -7(5-5z) + 3z = 1

=> -35 + 35z + 3z =1

=> 38z = 36

=> z = 36/38

=> z = 18/19

and

=> y = 5 - 5 (18/19)

=> y = 95 -90/19

=> y = 5/19

and

=> x = 4 -z +3y

=> x = 4 - 18/19 +15/19

=> x = 76 -3 /19

=>  x = 73/19

Therefore , the solution of the given problem of equation comes out to be  x = 73/19 , y = 5/19 and z = 18/19.

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The first packet by the second packet is the better size packet because the first packet is more expensive than the first packet.

The unit technique is a method of problem-solving that entails calculating the value of a single unit, multiplying that value, and then calculating the required value. To put it simply, the unit method is used to extract a single unit value from a specified multiple. One pen costs 400 rupees, thus 40 pens would cost 400 rupees. There might be a regular procedure for doing this out. merely one nation. anything containing a distinctive component. Mathematics of matrices or operators, linear algebra, mathematical analysis, and its adjoint and reciprocal are all equivalent.

given

The price of a 500 g packet of Healthy Flakes is €3.20.

Healthy Flakes come in packets of 750 g for €4.50.

A better size packet of 500 g costs €3.20. A two-pack of 750 g costs €166.66.

The first packet by the second packet is the better size packet because the first packet is more expensive than the first packet.

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The function's value at x = 1, y = - 1 Or f(1) = -1.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

The x-coordinate represents the input and the y-coordinate represents the output.

From the given points in the graph, we can conclude that when x = 1, y = -1.

Therefore, The value of the function f(1) = -1.

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The linear function to model this problem is y = 2.50x + 5

A linear function is a type of mathematical function that describes a straight line. A linear function is defined by an equation of the form:

y = mx + c

Where y is the dependent variable (the variable being measured or predicted), x is the independent variable (the variable being used to make the prediction or explanation), m is the slope of the line (the rate of change of y with respect to x), and c is the y-intercept (the value of y when x is zero).

The linear function to model this problem is given as;

y = 2.50x + 5

We can use a graphing calculator to represent this.

Kindly find the attached graph below

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