Write an expression having only two terms that is
equivalent to 2x - 3. Explain how you wrote the
expression and how you can check that it iS equivalent.

The measure of angle 4 is 90 degrees

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

The rectangle

Also, we have

<5 = 12x -3

<6 = 10x + 9

Angles 5 and 6 add up to 90

So, we have

12x - 3 + 10x + 9 = 90

Evaluate the like terms

22x = 84

So, we have

x = 3.82

The angles in a triangle add up to 180

So, we have

<4 + 12 * 3.82 - 3 + 10 * 3.82 + 9 = 180

Evaluate

<4 = 90

Hence, the measure o this angle is 90 degrees

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The length of the pool can either be 7m or 5m.

Remember that for a rectangle of length L and width W, the area is:

A = L*W

And the perimeter is:

P = 2*(L + W)

Here we know that the area is 35m² and the perimter is 24m, then we can write:

35m² = L*W

24m = 2*(L + W)

We want to solve this for L.

Using the second equation we can rewrite:

24m/2 = L + W

12m = L + W

Isolating W we get:

W = 12m - L

Replacing that on the other equation we will get:

35m² = L*(12m - L)

The two solutions of that equation are:

L = 7m

L = 5m

These are the two dimensions of the pool, we can take the length as any of these.

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Answer:

In Fig. 12.35, if ATB = 82°, then the angles of ABC would be A = 82°, B = 98°, and C = 180°. This can be determined by using the fact that the sum of the angles in a triangle is 180°.

Step-by-step explanation:

The bank teller has 21 five-dollar bills.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let's represent the number of five-dollar bills "x". Then, the number of twenty-dollar bills would be "x + 10".

The total value of the money is $725, so we can write the equation:

5x + 20(x + 10) = 725

Expanding the second term and simplifying, we get:

5x + 20x + 200 = 725

Combining like terms, we get:

25x = 525

Dividing both sides by 25, we get:

x = 21

So, the teller has 21 five-dollar bills.

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Answer:

Rational number

Step-by-step explanation:

because all rational number multiple by0 is 0

this System of equations has an infinite solution.

Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given A system of equation 3x + 5y = 15 and  y = -3/5x +3.

Slope interception form of the first equation:

y = -3/5x + 3

Since these equations are the same,

Thus this System of equations has an infinite solution. and a Graph of this is attached below.

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The value of the functions for the condition is,

1. f(x + h) = 3(x + h)² - (x + h) + 5,

2. (fog)(x) =  27x² -33x + 15,

3. f(g(h(-1))) = 16,060.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

Given f(x) = 3x² - x + 5

g(x) = -3x + 2

h(x) = -5x³

1. Find f(x + h),

so  f(x) = 3x² - x + 5

substitute x = x+ h

f(x + h) = 3(x + h)² - (x + h) + 5

2. (fog)(x),

f(g(x))

g(x) = -3x + 2

f(-3x + 2)  = 3(-3x + 2)² - (-3x + 2) + 5

f(g(x)) = 3(9x² + 4 - 12x) - 2 + 3x + 5

f(g(x)) = 27x² + 12 - 36x - 2 + 3x + 5

f(g(x)) = 27x² -33x + 15

3. Find f(g(h(-1)),

h(x) = -5x³

g(x) = -3x + 2

g(h(x)) = -3(-5x³)² + 2

g(h(x)) = -75x⁶ + 2

f(x) = 3x² - x + 5

f(g(h(x))) = 3(-75x⁶ + 2)² - (-75x⁶ + 2) + 5

f(g(h(x))) = 3(5625x¹² + 4 - 300x⁶) + 75x⁶ - 2 + 5

f(g(h(x))) = 16875x¹² + 12 - 900x⁶ + 75x⁶ -2 + 5

f(g(h(x))) = 16875x¹² - 825x⁶ + 10

substitute x = -1,

f(g(h(-1))) = 16875(-1)¹² - 825(-1)⁶ + 10

f(g(h(-1))) = 16,060

Hence  f(x + h) = 3(x + h)² - (x + h) + 5,

2.f(g(x)) = 27x² -33x + 15,

3. f(g(h(-1))) = 16,060.

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Answer:

12.10 pm

Step-by-step explanation:

just take the 45 minutes she uses to bake and add to the time she starts

11.25 a.m+45

12.10 pm

The time at which Miwa takes both medications together again will be 7:30 p.m. Then the correct option is D.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

She takes one medication every 6 hours. She takes the other medication every 4 hours.

The LCM of 4 and 6 will be 12. Then after 12 hours, she takes both medications.

Then the time is given as,

Time = 7: 30 a.m. + 12 hours

Time = 7: 30 p.m.

The time at which Miwa takes both medications together again will be 7:30 p.m. Then the correct option is D.

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Answer: : Sydney must take 8 goals.

Step-by-step explanation:

Brad took 5 kicks and made 4 goals: 4/5.This means denominator is total kicks and numerator is number of goals.Now for Sydney total shots are 10.so we have to find equivalent fraction of 4/5 with denominator as 10.If we multiply denominator 5 by 2 we get denominator as 10.So that means we have to multiply the fraction 4/5 with 2/2This gives us 8/10 as equivalent fraction of 4/5.Numerator represents goals.

The correct equation for the graph include the following: C. y = 2x/3 - 4.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided above, we have the following slope and data points on the line:

At point (0, -4), a linear equation of this line can be calculated in point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-4) = (0 + 4)/(6 - 0)(x - 0)

y + 4 = 2x/3

y = 2x/3 - 4

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The average rate of change of the function f(x)=-1x^2+5x-7, on the interval x€[-4,3] is 0.857.

Rate of change is a major of house quickly one quantity change in relation to another it is parisu of the changing 122 the changing another quantity over specified time period.

The average rate of change of the function f(x)=-1x^2+5x-7, on the interval x€[-4,3] is calculated by taking the difference of the function's values at the endpoints of the interval, divided by the difference in the corresponding x-values. By plugging in the endpoints of the interval into the equation, we find that f(-4)=-25 and f(3)=6. Thus, the average rate of change of the function f(x)=-1x^2+5x-7 on the interval x€[-4,3] is calculated by taking the difference of -25 and 6, divided by the difference of -4 and 3, which is equal to 6/7 or 0.857. Therefore, the average rate of change of the function f(x)=-1x^2+5x-7, on the interval x€[-4,3] is 0.857.

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The missing entries would be x = 4 and y = 2.

Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.

In this equation, x and y are variables. To determine the values of the missing entries, we need to solve the equation. The equation is a quadratic equation of the form y2 = x. To solve it, we need to take the square root of both sides of the equation. This gives us the solution y = √x. So, the value of the missing entries is √x.

For example, if x = 4, then the value of y would be √4 = 2. Therefore, the missing entries would be x = 4 and y = 2.

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Company A, Company B, & Company C have joined to control prices in the market is an example of an economic trust.

Trust is one of the foundations of the economy. With trust, sellers/buyers can transact and investors can send funds with peace of mind. Without trust, commercial trading and money transfer processes will not be realized as smoothly and globally as they are now.

Over the decades, traditional banking and financial institutions have built their reputation on public trust. Banks build tall buildings with magnificent architecture and employees who wear neat shirts to build public trust.

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28. t = I / (Pr)

29. y = -(3x / 5) + (15 / 5)

30. y = -3/5 x + 3

31. y = -3/5 * -1 + 3 = 3 + 3/5 = 3.6

32. 2 tablespoons per serving

33. $0.92 per slice

34. 5 tablespoons

35. 45% (159 / 350 = 0.45 and 0.45 * 100 = 45)

Simple interest is a method of calculating the interest charge on a loan or deposit based on a constant interest rate and the original principal amount. The formula for simple interest is I = Prt, where P is the principal amount, r is the interest rate as a decimal, t is the time period in years, and I is the interest amount. In simple interest, the interest amount is calculated only on the original principal, not on any accumulated interest from prior periods.

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The area of the circle is 78.5 ft^2.

Given that,

A segment is drawn from one point on the circle to another point on the circle through the center of the circle is 10 feet.

So, the diameter of the circle d = 10 feet

The formula for the area of the circle = Пr^2

where r is the radius of the circle and П is given as 3.14

Radius = diameter/2

r = 10 feet/2

= 5 feet

So, by applying the formula

Area of the circle = П × 5 × 5

= 3.14 × 5 × 5

= 78.5 ft^2

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Answer:

Step-by-step explanation:

One input(x-value) can only have one output(y-value) in order to be a function

The zeros of the function y = -4(x-3)² + 8 are -1 and 7 and the intercept is 13

The zero of a function is any replacement for the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

when y = 0

-4(x-3)² +8 = 0

expanding the equation

-4( x²-6x +9)+8 = 0

-4x² +24x -36 +8 = 0

-4x²+24x -28 = 0

divide through by 4

-x²+6x-7 = 0

-x²+7x -x -7 = 0

(-x²+7x)(-x-7) = 0

-x( x-7) 1(x-7)

1-x = 0 or (x-7 )= 0

x = -1 or 7

therefore the zeros are -1 and 7

to find the intercept:

x= 0

y = -4(0-3)²+8

y =-4+9+8

y = 13

therefore the intercept is 13

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Answer:

Below

Step-by-step explanation:

Points   (-3,5)   and   ( 3,1)

distance d can be found using the distance formula ( modified Pyhtagorean theorem)

d^2 = ( x1-x2)^2 + ( y1-y2)^2

d^2 = ( -3 -3)^2  + ( 5-1)^2

d^2 = 36 + 16

d^2 = 52

d = sqrt(52) = 2 sqrt(13)

Answer:

Square root

Step-by-step explanation:

Something to the 1/2 power means the square root of that number.

Answer:

( 0,1)

Step-by-step explanation:

y-4x=1

We want to find the y-intercept ( where it crosses the y-axis).

Let x = 0

y-4*0=1

y = 1

The coordinates of the y-intercept are ( 0,1).

Step-by-step explanation:

this you solve via the determinant of the matrix.

for a matrix A

a b

c d

the determinant (A) = ad - bc

so, we have here

x² - 5×-4 = 24

x² + 20 = 24

x² = 4

x = ±2

so, as a simple quadratic equation, there are 2 solutions for x.

The phrase "La sexta parte de la diferencia de dos números" in algebraic sentence can be written as [tex] \frac{x}{6} [/tex] where "x" represents the difference between two numbers.

The quantity [tex] \frac{x}{6} [/tex] is a fraction that represents one-sixth of the difference between two numbers. In other words, if you have two numbers "a" and "b", and you subtract them to find their difference "a-b", then [tex] \frac{x}{6} [/tex] would equal [tex] \frac{(a - b)}{6} [/tex].

The fraction [tex] \frac{x}{6} [/tex] gives us a portion or a ratio of the difference between the two numbers, and in this case, it's one-sixth of that difference. So, if you want to find what one-sixth of the difference between two numbers is, you can simply divide that difference by 6.

Let's say that the two numbers you want to find the difference between are 15 and 6. To find their difference, we would subtract the smaller number from the larger one:

15 - 6 = 9

So, the difference between these two numbers is 9. To find one-sixth of this difference, we would divide the difference by 6:

[tex] \frac{9}{6} = 1.5[/tex]

So, one-sixth of the difference between 15 and 6 is 1.5.

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22% of the population more than 25 years of age have bachelors degree.

percentage, a relative value indicating hundredth parts of any quantity.

Given that the total population is 298957

66722 cincinnati residents over the age of 25 have the bachelors degree.

We have to find the percent of the population more than 25 years of age have bachelors degree.

x/100×298657=66722

2986.6x=66722

Divide both sides by 2986.6

x=22.340

Hence, 22% of the population more than 25 years of age have bachelors degree.

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The combined area of the square and rectangle is 3x² + 3x - 3.

The expression 2x² + 6x - 4 represents the area of a square.  The area of a rectangle is represented by x² - 3x + 1.  The combined area of the square and the rectangle is the sum of the area of the square and the area of the rectangle.

Therefore,

area of the square = 2x² + 6x - 4

area of the rectangle = x² - 3x + 1

Let's find the combined area as follows:

combine area of the square and rectangle = 2x² + 6x - 4 + x² - 3x + 1

combine area of the square and rectangle = 2x² + x² + 6x - 3x - 4 + 1

combine area of the square and rectangle = 3x² + 3x - 3

Therefore,

the combined area = 3x² + 3x - 3

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Answer:

The project cost in terms of X can be expressed as 20X + 700. This can be determined by using the information from mathportal.org, which states that the cost of the fence is $20 per meter plus $350 per gate. Since the field is X meters on a side and there are two gates, each 4 meters wide, the total cost of the project can be expressed as 20X + 700.

Step-by-step explanation:

The correct theorem with the correct pair of congruent triangles are given below:

Two triangles are congruent if all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

The theorems for the congruence of triangles is as follows:

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The statement that will not produce a triangle is side lengths of 5.5 ft, 11 ft, and 5.5 ft, the correct option is C.

Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.

Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,

[tex](a+b) > c\\(b+c) > a\\(c+a) > b[/tex]

Given;

A. angle measures of 47o, 58o, 75o

Here,47o+ 58o,+75o=180

B. angle measures of 61o, 61o, 58o

Here, 61o+61o+58o=180

C. side lengths of 5.5 ft, 11 ft, and 5.5 ft

5.5+5.5 is not equal to 11

D. side lengths of 5 in, 7 in, and 8 in

5+7 is greater than 8

Therefore, the triangle with side lengths of 5.5 ft, 11 ft, and 5.5 ft is not the triangle.

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The area of the circle with a radius of 5 feet will be 78.5 square feet. Then the correct option is D.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle. Then the area of the circle will be

A = πr² square units

The diameter of the circle is 10 feet. Then the radius is given as,

r = d / 2

r = 10 / 2

r = 5 feet

Then the area of the circle is given as,

A = πr²

A = 3.14 x 5²

A = 3.14 x 25

A = 78.5 square feet

The area of the circle with a radius of 5 feet will be 78.5 square feet. Then the correct option is D.

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The size of the total economic surplus in this market is $32.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

Welfare and Efficiency-End of Chapter Problem

Consider the national market for in-home childcare, depicted in the accompanying graph

The size of the total economic surplus in this market,

= (1/2)(18 - 10) 8

= 32

Therefore, the surplus is $32.

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