A car rental agency charges $250 per week plus $0.10 per mile to rent a car.
a. Write an equation that expresses the weekly cost to rent the car, y, in terms of the number of miles driven during the week, x.
b. How many miles did you drive during the week if the weekly cost to rent the car was $260?

The system of equations is

15x + 10y = 800

x + y = 60

and the solution to these equations is

x = 40

y = 20

Given is that an office manager requests a calculator or calendar for each of the 60 office employees. Each calculator is $15 and each calendar is $10. The total order amounted to $800.

We can write the system of equations as -

15x + 10y = 800

x + y = 60

We can write -

y = 60 - x

So, we can write -

15x + 10(60 - x) = 800

15x - 10x + 600 = 800

5x = 200

x = 40

Then -

y = 20

Therefore, the system of equations is

15x + 10y = 800

x + y = 60

and the solution to these equations is

x = 40

y = 20

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{Question in english is -

An office manager requests a calculator or calendar for each of the 60 office employees. Each calculator is $15 and each calendar is $10. The total order amounted to $800. Part A: Write the system of equations that models this scenario. (5 points) Part B: Use the substitution method or the elimination method to determine the number of calculators and calendars ordered. Show all the necessary steps. (5 points)

}

Answer: 8xw=a

Step-by-step explanation:

w=width

a=area

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 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 graph is the graph of straight lines

The point (2, 3) is not included in the solution area

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

4x+2y = 16

x+y=4

The equations are linear equations

We have

(x, y) = (2, 3)

This gives

4(2) + 2(3) = 16 -- false

2 + 3 = 4 -- false

Hence, it is not in the solution

We have

4x+2y = 16

x+y=4

This gives

4x+2y = 16

4x + 4y=16

So, we have

2y = 0

And:

y = 0

This means that

4x + 2(0) = 16

x = 4

So, the solution set is (4, 0)

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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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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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Answer:

Square root

Step-by-step explanation:

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

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 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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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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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 coordinates of point A'  and B' are A'(-12,8) and B'(20, 0)

A dilation is a transformation that changes the size of a figure but not its shape.

In a dilation with respect to the origin, a point (x, y) is transformed to a point (kx, ky) where k is a scale factor.

In this case, the point A (-3, 2) and B (5, 0) are transformed under a dilation of 4 with respect to the origin.

So the images are

A' = (kx, ky) = (-3*4, 2*4) = (-12, 8)

B' = (kx, ky) = (5*4, 0*4) = (20, 0)

So the image point of A(-3,2) under a dilation of 4 with respect to the origin is A'(-12,8)

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Complete question

The triangle ABC is dilated by a scale factor of 4 with the center of dilation at the origin.

a) What are the coordinates of A?

b) What are the coordinates of B?

if A (-3, 2) and B (5, 0)

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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The solution is given below.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

Remember that the Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

According to this, the correct answer is: given below.

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Answer:

Rational number

Step-by-step explanation:

because all rational number multiple by0 is 0

Answer: It is not possible to convert 3 c to mL without a conversion factor. There are several different units of measurement for volume, including cubic centimeters (cc), milliliters (mL), and cubic meters (m^3). To convert from one unit to another, you need to know the conversion factor.

The conversion factor between cubic centimeters (cc) and milliliters (mL) is 1:1, meaning they are equivalent units of measurement. So, 3 cc is equal to 3 mL.

Step-by-step explanation:

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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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:

Equation is

[tex]\mbox {\large \boxed{g(m) = 4.411 (0.94988)^m}}[/tex]

Step-by-step explanation:

We have to translate the information in the table as an equation of the form

[tex]g(m) = P(1 + r)^m\cdots \cdots(1)[/tex]

Let's take the date from the table

For m = 1, g(m) = 4.19

Substituting these values in equation (1) we get:
[tex]g(1) = P(1 + r)^1[/tex]

[tex]4.19 = P(1 + r)^1[/tex]

[tex]P(1 + r)^1 = 4.19 \; \textrm{ (by switching sides)}[/tex]

[tex]P(1+r) = 4.19\; \cdots \cdots (2)\\\textrm{ (an expression raised to the power 1 is the expression itself)}[/tex]

For the next entry in the table, m = 2, g(m) = 3.98

Plugging into (1)

[tex]3.98 = P(1 + r)^2 \cdots\cdots(3)[/tex]
or

[tex]P(1 + r)^2 = 3.98[/tex]

Divide equation (3) by equation (2)

[tex]\dfrac{P(1+r)^2}{P(1+r} = \dfrac{3.98}{4.19}[/tex]

[tex]\textrm{The P terms cancel and } \dfrac{(1 + r)^2}{(1+r)} = 1 + r[/tex]

==> [tex]1 + r = \dfrac{3.98}{4.19}\\\\1 + r = 0.94988\\\\[/tex]

Plugging this value of 1 + r into equation (2):

[tex]P( 0.94988) = 4.19\\\\P = \dfrac{4.19}{0.94988}\\\\P = 4.411\\\\[/tex]

So the equation is

[tex]g(m) = 4.411 (0.94988)^m[/tex]

We can verify this is correct for m = 2, 3 and 4

[tex]m\quad\quad g(m) = 4.411(0.94988)^m\\\------------------\\2\quad\quad 4.411(0.94988)^2 = 3.97992 \approx 3.98\\\\3\quad\quad 4.411(0.94988)^3 = 3.78044 \approx 3.78\\\\3\quad\quad 4.411(0.94988)^4 = 3.59097 \approx 3.59\\\\[/tex]

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 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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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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Note that it is correct to state that LN ≅ MN and Nk ⊥ LM, so NK is the perpendicular bisector of LM and P is on NK. See attached image.

A perpendicular bisector is a line that cuts another line segment across the junction point at a straight angle. As a result, a perpendicular bisector always cuts a line segment through its midway. The phrase bisect implies dividing evenly or uniformly.

A simple technique to determine a perpendicular bisector is to measure the line segment you need to bisect. Then, divide the measured length by two to determine the midway. Draw a line at a 90-degree angle out from this middle.

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Full Question:

Tell whether the information in the diagram allows you to conclude that point P lies on the perpendicular bisector of LM. Explain your reasoning. See attached image.

A) No. You would need to know that LK ⊥ MK

B) No. You would need to know that KP ⊥ LM
C) Yes, t LN ≅ MN and Nk ⊥ LM, so NK is the perpendicular bisector of LM and P is on NK
D) Yes, NK ⊥ LM, so NK is the perpendicular bisector of LM and P is on NK

Answer:

Step-by-step explanation:

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

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 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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Answer: It is 84 degrees