Solve the system of equations by graphing.
1. y = x - 1
y = 2x - 2
2. y = 4x
y = x + 3
3. y - x = 1
y = x - 2 + 3

Distance traveled after toll payment is 1.2 miles on highway 40.

The distance may be calculated using a curved route. Displacement measurements can only be made along straight lines. Distance is path-dependent, meaning it varies depending on the direction followed. Displacement simply depends on the body's beginning and ending positions; it is independent of the route.

Distance is the sum of an object's movements, regardless of direction. Distance may be defined as the amount of space an item has covered, regardless of its beginning or finishing position.

The size or extent of the displacement between two points is referred to as distance. Keep in mind that the distance between two points and the distance traveled between them are not the same. The entire length of the journey taken between two points is known as the distance traveled. Travel distance is not a vector.

Distance traveled before toll payment =3/5 miles on highway 40

Distance traveled after toll payment =2*3/5  = 6/5 =

1.2 miles on highway 40.

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Answer:

5 more bottles

Step-by-step explanation:

23 x 25 will give us how many ounces Coach Reynolds have already.

23 x 25 is 575

700 - 575 will give us how many ounces he needs to buy.

700 - 575 is 125

125 divided by 25 will give us how many bottles he needs to buy
125 divided by 25 is 5

So 5 more bottles

Hope this helps! :)

Answer: 4/1 is 1/4 but what are the 4 fractions your talking about?

Step-by-step explanation:

The total costs of the 6 notebooks and 4 dry-erase markers that Roselyn buys are $19.70.

The total costs can be determined using mathematical operations.

The first mathematical operation used is the multiplication operation, involving the multiplicand and the multiplier, to determine the total cost of each item.

The second mathematical operation is the addition operation to determine the grand total.

Notebook: 1.95

Dry erase markers: 2.00

Notebook: $11.70 ($1.95 x 6)

Dry erase markers: $8.00 ($2.00 x 4)

Total costs = $19.70

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The price of each item is listed below

notebook: 1.95

dry erase markers: 2.00

What are the total costs?

Answer:

-----------------------------

Given function:

Graph it first (see attached).

Test the graph for symmetry.

We know the odd degree parent function y = x³ has an origin symmetry, whilst even degree functions may have axis symmetry.

The given function is a translation of cubic function 5 units up so the center of symmetry has translated as well. Therefore correct answer is 4.

Answer:

4. no origin symmetry

Step-by-step explanation:

Functions are symmetric with respect to the x-axis if for every point (a, b) on the graph, there is also a point (a, −b) on the graph:

To determine if a graph is symmetric with respect to the x-axis, replace all the y's with (−y).  If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the x-axis.

\(\begin{aligned}&\textsf{Given}: \quad &y &= x^3 + 5\\&\textsf{Replace $y$ for $(-y)$}: \quad &-y &= x^3 + 5\\&\textsf{Simplify}: \quad &y &= -x^3 - 5\end{aligned}\)

Therefore, since the resultant expression is not equivalent to the original expression, it is not symmetric with respect to the x-axis.

--------------------------------------------------------------------------------------------------

Functions are symmetric with respect to the y-axis if for every point (a, b) on the graph, there is also a point (-a, b) on the graph:

To determine if a graph is symmetric with respect to the x-axis, replace all the x's with (−x).  If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the y-axis.

\(\begin{aligned}&\textsf{Given}: \quad &y&=x^3+5\\&\textsf{Replace $x$ for $(-x)$}: \quad &y&=(-x)^3+5\\&\textsf{Simplify}: \quad &y&=-x^3+5\end{aligned}\)

Therefore, since the resultant expression is not equivalent to the original expression, it is not symmetric with respect to the y-axis.

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Functions are symmetric with respect to the origin if for every point (a, b) on the graph, there is also a point (-a, -b) on the graph:

To determine if a graph is symmetric with respect to the origin, replace all the x's with (−x) and all the y's with (-y).  If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the origin.

\(\begin{aligned}&\textsf{Given}: \quad &y&=x^3+5\\&\textsf{Replace $x$ for $(-x)$ and $y$ for $(-y)$}: \quad &(-y)&=(-x)^3+5\\&\textsf{Simplify}: \quad &-y&=-x^3+5\\&&y&=x^3-5\end{aligned}\)

Therefore, since the resultant expression is not equivalent to the original expression, it is not symmetric with respect to the origin.

Answer:

He spent $90.16 in all.

Explanation

9 Gallons of Gasoline = $40.95

0.2 Gallons of Gasoline = $0.91

$40.95 + $0.91 = $41.86

9 Gallons of Oil = $47.25

0.2 Gallons of Oil = $1.05

$47.25 + $1.05 = $48.30

$41.86 + $48.30 = $90.16

Answer:

The location of the point that is 3/4 the distance from \(A(x,y)\) is \(C(x,y) = (24, -2.5)\).

Step-by-step explanation:

Let \(A(x,y) = (-6,-16)\) and \(B(x,y) = (34,2)\) the endpoints of the segment, we can determine the location of the point that is 3/4 the distance from \(A(x,y)\) by the following vector equation:

\(C(x,y) = A(x,y) + \frac{3}{4}\cdot (B(x,y)-A(x,y))\) (1)

If we know that \(A(x,y) = (-6,-16)\) and \(B(x,y) = (34,2)\), the location of \(C(x,y)\) is:

\(C(x,y) = (-6,-16)+\frac{3}{4}\cdot [(34,2)-(-6,-16)]\)

\(C(x,y) = (-6,-16)+\frac{3}{4}\cdot (40,18)\)

\(C(x,y) = (24, -2.5)\)

The location of the point that is 3/4 the distance from \(A(x,y)\) is \(C(x,y) = (24, -2.5)\).

Answer:

31

Step-by-step explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)

a = 1, b = 1 and c = -930

\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)

\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31

Answer:

9 pizzas total were bought for a party. Maya ate 1/3 of a pizza. John ate 4/9 of the same pizza. How much pizza is left?

Answer: 74/9 or 8.2

Step-by-step explanation:

first add 4/9 and 1/3 since it's in parenthesis

4/9+1/3

they need to have the same denominator, use the LCM (which is 9)

multiply 1/3 by 3 to achieve the LCM

4/9+3/9

add together numerators

7/9

subtract 7/9 from 9

9/1-7/9

get 9 to achieve the LCM (which is 9 again)

multiply 9/1 by 9

81/9 minus 7/9= 74/9

Answer:

If this is asking for the set:

Z = {-3, -2, -1, 0, 1, 2, 3}

Step-by-step explanation:

Z is the set of all integers and it appears that you are being asked for the values in the set Z that are within the range:  -3 ≤x ≤ 3

Answer:

the approximate value of m is -0.12, indicating that the value of Ty's computer decreases by 0.12 (or 12%) each year.

Step-by-step explanation:

o express this depreciation rate as a slope in the equation y = mx + b, we need to determine how much the value changes (the "rise") for each year (the "run").

Since the value decreases by 12% per year, the slope (m) would be -12%. However, we need to express the slope as a decimal, so we divide -12% by 100 to convert it to a decimal:

m = -12% / 100 = -0.12

The present value of the annuity is approximately `7032.08. The correct answer is option (d) None of these.

To find the present value of an annuity, we can use the formula:

PV = PMT * (1 - (1 + r)^(-n)) / r

Where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, the periodic payment is `200, the interest rate is 5% (or 0.05) converted quarterly, and the number of periods is 10 years, which equals 40 quarters.

Plugging in these values into the formula, we get:

PV = 200 * (1 - (1 + 0.05)^(-40)) / 0.05

Simplifying the equation, we find:

PV ≈ 200 * (1 - 0.12198) / 0.05

PV ≈ 200 * 0.87802 / 0.05

PV ≈ 35160.4 / 0.05

PV ≈ 7032.08

Therefore, the present value of the annuity is approximately `7032.08.

None of the provided answer options (a), (b), or (c) match this result. The correct answer is (d) None of these.

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The interest rate required to get a total amount of $3,688.86 from compound interest on a principal of $2,000.00 compounded 12 times per year over 5 years is 12.306% per year.

Given,

The total amount (A)= $3688.86

Principal (P) = $2000

time period (t) = 5 years.

compounded monthly (n) = 12

rate of interest per year = ?

we know that r=n[(A/P)¹/ⁿt  -1]

substitute the above values.

r = 12 × [(3688.86/2000)¹/⁽¹²⁾⁽⁵⁾ - 1]

r = 12 × [(1.84443)¹/⁶⁰ - 1]

r = 12 × 0.0102

r = 0.12306

Now convert r to R as a percentage.

R = r × 100

R = 0.12306 × 100

R = 12.306%

Hence the rate of interest compounded monthly is 12.306%

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Answer:

I think A

Step-by-step explanation:

The correct explanation for the number 3 will be;

⇒ the number of seats at each table.

Option A is true.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The mathematical expression is;

⇒ 3t + 15

Where, t represent the individual tables.

And, The expression represents the total number of seats in the restaurant.

Now,

Since, 't' represent the individual tables.

Hence,

3t = Number of tables for 3 seats

Clearly, 3 represent the number of seats at each table.

Therefore,

The correct explanation for the number 3 will be;

⇒ the number of seats at each table.

Option A is true.

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Answer:

the answer is D just did the quiz hope this helps!!!!!

Step-by-step explanation:

Answer:

\( X= v_i t + \frac{1}{2}a t^2 \)

And from this equation we can solve for a like this:

\( 205m = 3.5m/s *(28.7s) +\frac{1}{2}a (28.7s)^2\)

And solving for a we got:

\( 104.55m = \frac{1}{2}a (28.7s)^2\)

\( a = \frac{2*104.55m}{(28.7s)^2)}= 0.254 m/s^2\)

Step-by-step explanation:

For this case we have the velocity , distance and time given:

\( v = 3.5 m/s, d=205m, t =28.7s\)

And we know from kinematics that he velocity can be expressed like this:

\( v_f = v_i +a t\)

We also know that the distance is given by:

\( X= v_i t + \frac{1}{2}a t^2 \)

And from this equation we can solve for a like this:

\( 205m = 3.5m/s *(28.7s) +\frac{1}{2}a (28.7s)^2\)

And solving for a we got:

\( 104.55m = \frac{1}{2}a (28.7s)^2\)

\( a = \frac{2*104.55m}{(28.7s)^2)}= 0.254 m/s^2\)

Answer:

x^4-3x^3+x^2-4

mrk me brainliest plz

Step-by-step explanation:

Given the following functions

R(x) = 2x^4 – 3x^3 + 2x – 1 and

C(x) = x^4 – x^2 + 2x + 3

We are to find the profit function P(x)

P(x) = R(x) - C(x)

P(x) = 2x^4 – 3x^3 + 2x – 1 - ( x^4 – x^2 + 2x + 3)

P(x) = 2x^4 – 3x^3 + 2x – 1 - x^4 + x^2 - 2x - 3

Collect the like terms

P(x) = 2x^4-x^4-3x^3+x^2+2x-2x-1-3

P(x) = x^4-3x^3+x^2+0-4

P(x) = x^4-3x^3+x^2-4

Hence the required profit function P(x) is x^4-3x^3+x^2-4

Answer:

i think its x^4-3x^3+x^2-4

Step-by-step explanation:

The equation y = \(-0.024x^2\) + 0.0791x + 4.873 represents a quadratic function with a downward-opening parabol

The given expression is a quadratic equation in the form y = -0.024x^2 + 0.0791x + 4.873. Let's analyze its components and characteristics.

The equation represents a quadratic function, where x is the independent variable and y is the dependent variable. The coefficients in front of each term determine the shape, position, and direction of the graph.

The term with the highest power of x is -0.024x^2, which indicates a downward-opening parabola. The coefficient -0.024 determines the steepness of the curve. A negative coefficient means the parabola is concave down.

The term 0.0791x is the linear term and determines the slope of the line. A positive coefficient indicates an upward or positive slope. It affects the overall direction and position of the graph.

The constant term 4.873 is the y-intercept. It indicates the point at which the graph intersects the y-axis when x = 0.

To analyze the graph of the quadratic equation further, we can calculate the vertex. The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a and b are the coefficients of x^2 and x, respectively. In this case, a = -0.024 and b = 0.0791. Substituting these values into the formula, we have x = -0.0791 / (2 * -0.024) ≈ 1.643. By substituting this x-coordinate into the equation, we can find the y-coordinate of the vertex.

Overall, the equation y =\(-0.024x^2 + 0.0791x\) + 4.873 represents a quadratic function with a downward-opening parabola. The specific properties, such as the vertex and other key points, can be determined by further calculations and analysis of the equation.

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Answer:

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

4x+9x-12=1

13x=13

x=1

Answer:

18.90

Hope i got it right

Answer:

Step-by-step explanation:

Four quadrants:

Quadrant I (right side, above the x-axis to the right of the y-axis).

Quadrant II (left side, above the x-axis to the to the left of the y-axis).

Quadrant III ( left side , below the x-axis to the left of the y-axis).

Quadrant IV  (right side, below the x-axis to the right of the y-axis

                          Y

                            l                      

           II  (-x, y)    l           I      (x, y)      

    x                      l                        x

             III            l        IV    

         (-x, -y)         l        (x, -y)

                            l

                          Y      

 Now you can answer the questions by locating the point and explain.

Answer:

-11-(-5)= -6

25-(-3)= 28

-7-(-2)= -5

4-15= -11

6-(-9)= 15

y=-x+6 is the perpendicular equasion

the original one is y=x+6

to find a perpendicular slope you basically take the opposite in this case

so the answers should be

x

-x

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Answer:

Vertex: (3, 5)

Axis of symmetry: x=3

Answer:

range: (-5, ∞)

domain: (-∞, ∞)

Step-by-step explanation:

given vertex, absolute minimum: (-3, -5)

Range look at y-value

(minimum, maximum) the -5 will be on the left  of the comma b/c its the min

If this was a max, you would put the y-value on the right side of the comma

Answer:

25.0158730

Step-by-step explanation:

a product is when you multiply two numbers like 2x5 gets you a product of 10 so,

reverse operations,

1576/63 = 25

Answer:

I do not see all the graphs but it would be the reverse of what is shown for A. graph. The tickets sold to total income would have to be a 1:4 ratio where every 4 dollar leap in the y-axis is a one point (1 unit change in x).

Step-by-step explanation: