Two runners are racing against each other. Jeri graphs a linear equation for each runner that shows the runner's distance from the starting line over time. The two equations form a system that has infinitely many solutions. Describe the intersection point(s) of the lines and explain what solution means in this situation.

let's firstly convert the mixed fraction to improper fraction and then take it from there, keeping in mind that the whole is "x".

\(\stackrel{mixed}{5\frac{5}{6}}\implies \cfrac{5\cdot 6+5}{6}\implies \stackrel{improper}{\cfrac{35}{6}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{3}x~~ = ~~5\frac{5}{6}\implies \cfrac{7}{3}x~~ = ~~\cfrac{35}{6}\implies 42x=105\implies x=\cfrac{105}{42} \\\\\\ x=\cfrac{21\cdot 5}{21\cdot 2}\implies x=\cfrac{21}{21}\cdot \cfrac{5}{2}\implies x=1\cdot \cfrac{5}{2}\implies x=2\frac{1}{2}\)

\(e^y +19-e^2 = 3x^2 +4y^2\\\\\implies \dfrac{d}{dx}(e^y +19-e^2) = \dfrac{d}{dx}(3x^2 +4y^2)\\\\\implies e^y \dfrac{dy}{dx}+0 = 3\dfrac{d}{dx} x^2 +4\dfrac{d}{dx} y^2\\\\\implies e^y y' = 6x + 8y y'\\\\\implies e^y y' -8yy' = 6x\\\\\implies y'(e^y -8y) = 6x\\\\\implies y' = \dfrac{6x}{e^y -8y}\\\\\text{At point (-1,2)}\\\\y' = \dfrac{6(-1)}{e^2 -8(2)} = - \left(\dfrac{6}{e^2 -16}\right) =-0.25\)

Answer: the graph is incorrect

Step-by-step explanation:

The graph should be headed towards the left (the negative x side) because x is negative

Answer:

The graph is not correct, because it is a positive graph. It answers the equation y= x, and Franco said it was y= -x. His line would be negative, and this graph is positive.

Step-by-step explanation:

Answer:

23, so 1. i know because i added 14+9 and got 23. im sorry if you meant like a definition term, please comment if thats what you meant. because i'll help you then.

Step-by-step explanation:

Answer:

y = -3/2x + 13

Step-by-step explanation:

(6,4) and (2,10)

Slope:

m=(y2-y1)/(x2-x1)

m=(10-4)/(2-6)

m=6/(-4)

m =  -3/2

Point-slope intercept:

y - y1 = m(x - x1)

y - 4 = -3/2(x - 6)

y - 4 = -3/2x + 9

y = -3/2x + 13

There are 900 children and 800 adults in attendance

The given parameters are:

Let the kids be x and the adults be y

So, we have

x + y = 1700

1.5x + 3y = 1750

Make y the subject in x + y = 1700

y = 1700 - x

Substitute y = 1700 - x in 1.5x + 3y = 1750

1.5x + 3(1700 - x) = 3750

So, we have

1.5x + 5100 - 3x = 3750

Evaluate the like terms

1.5x = 1350

Divide

x = 900

Recall that

y = 1700 - x

So, we have

y = 1700 - 900 = 800

Hence, the number of children and adults in attendance are 900 and 800 respectively

Read more about linear equations at

https://brainly.com/question/14323743

#SPJ1

Answer:

A. x= 3, y= -2

Step-by-step explanation:

[2] 2x= 4y+14

[1] 3y+5x=9

Solve equation [2] for the variable  x

 [2]    2x = 4y + 14

 [2]    x = 2y + 7

// Plug this in for variable  x  in equation [1]

  [1]    5•(2y+7) + 3y = 9

  [1]    13y = -26

// Solve equation [1] for the variable  y

  [1]    13y = - 26

  [1]    y = - 2

// By now we know this much :

   x = 2y+7

   y = -2

// Use the  y  value to solve for  x

   x = 2(-2)+7 = 3

good luck, I hope this helps!!!

The probability of getting a black card and a numbered card is 9/26.

To calculate the probability of getting a black card (E1), we need to determine the number of black cards in a standard deck of 52 cards.

There are 26 black cards in total, which consist of 13 spades (black) and 13 clubs (black).

Therefore, the probability of drawing a black card (P(E1)) is:

P(E1) = Number of favorable outcomes / Total number of possible outcomes

P(E1) = 26 / 52

Simplifying this fraction, we get:

P(E1) = 1/2

So the probability of drawing a black card is 1/2.

To calculate the probability of drawing a numbered card (E2), we need to determine the number of numbered cards (2 through 10) in a standard deck.

Each suit (spades, hearts, diamonds, clubs) contains one card for each numbered value from 2 to 10, totaling 9 numbered cards per suit.

Therefore, the probability of drawing a numbered card (P(E2)) is:

P(E2) = Number of favorable outcomes / Total number of possible outcomes

P(E2) = 36 / 52

Simplifying this fraction, we get:

P(E2) = 9/13

So the probability of drawing a numbered card is 9/13.

To calculate the probability of both events occurring together (getting a black card and a numbered card), we multiply the individual probabilities:

P(E1 ∩ E2) = P(E1) × P(E2)

P(E1 ∩ E2) = (1/2) × (9/13)

Simplifying this fraction, we get:

P(E1 ∩ E2) = 9/26

Therefore, the probability of getting a black card and a numbered card is 9/26.

For such more questions on probability

https://brainly.com/question/25839839

#SPJ8

Answer:

Step-by-step explanation:

Tricky i give that to the question that so i think f 4 maybe it doesn't show  the options

The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),

To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:

h = h0 + v0t + 1/2at^2

where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).

In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.

At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:

v = v0 + at

we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:

0 = 108 - 32.2t

t = 108/32.2 ≈ 3.35 s

Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.

Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:

h_hill = h0 + v0t + 1/2at^2 - h_top

where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:

h_top = h0 + v0^2/2a

Plugging in the given values, we get:

h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft

Plugging this into the first equation, we get:

h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78

h_hill ≈ 25.73 ft

If the arrow is launched at t0, the equation describing velocity as a function of time would be:

v(t) = v0 - gt

For such more questions on velocity

https://brainly.com/question/25749514

#SPJ8

Answer:

The answer is c 2580/6

Step-by-step explanation:

The answer is c because the ounces are trying to be separated into the 6 jars so it makes sense that they will divide

Answer:

For acute angles, remember what sine means: opposite over hypotenuse. If we increase the angle, then the opposite side gets larger. That means "opposite/hypotenuse" gets larger or increases.

Step by Step:

Keep this in mind >>

Consider the unit circle > The sine and cosine ratios are the only ratios that have 1 (the radius or hypotenuse) as the denominator. The numerators (sides) vary between 0 and 1, thus determining that the sine and cosine do the same.

All of the other ratios (tangent, cotangent, secant, cosecant) have a side as the denominator, varying between 0 and 1. As any denominator approaches 0, the value of the ratio approaches infinity.

Answer:

Step-by-step explanation:

BAD = 42

x + 103 + 42 = 180

x = 180 - 145

x = 35

The equation of the straight line would be -

y = 4x + 5.

Given is that a line y = mx + 5 that passes through the point (1, 6) and is parallel to y = 4x + 6.

       y = mx + c

Equation of the line is -

y = mx + 5

It is parallel to -

y = 4x + 6

Then -

m = 4  {slopes of || lines are equal)

So, we get the equation as -

y = 4x + 5

Therefore, the equation of the straight line would be -

y = 4x + 5.

To solve more questions on algebraic expressions, visit the link below -

brainly.com/question/1041084

#SPJ1

Answer:

y + 1 = 5/3(x + 8)

or

y - 9 = 5/3(x + 2)

*both work

Step-by-step explanation:

First, we can start by finding the slope of the line, which can be represented as:

\(\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\)

We can substitute in the points (-8, -1) and (-2, 9):

\(\frac{9-(-1)}{-2-(-8)}\)

And we can simplify

\(\frac{9+1}{-2+8}\)

\(\frac{10}{6}=\frac{5}{3}\)

The point-slope equation of a line can be written as:

\(y-y_{1} =m(x-x_{1} )\)

We can either use the point (-8, -1) or (-2, 9). It doesn't matter which one we use.

For the point (-8, -1), you get:

y + 1 = 5/3(x + 8)

For the point (-2, 9) you get:

y - 9 = 5/3(x + 2)

The top left graph represents the weight of the radioactive isotope over time.

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for the function in this problem are given as follows:

a = 96, b = 0.5.

Hence the function is given as follows:

\(y = 96(0.5)^x\)

Two points on the graph of the function are given as follows:

(1,48) and (2, 24).

Hence the top left graph represents the weight of the radioactive isotope over time.

More can be learned about exponential functions at brainly.com/question/2456547

#SPJ1

Answer:

Graph W

Step-by-step explanation:

The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.

Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).

The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.

Initial weight: 96 grams

After 1 hour: 96 / 2 = 48 grams

After 2 hours: 48 / 2 = 24 grams

After 3 hours: 24 / 2 = 12 grams

After 4 hours: 12 / 2 = 6 grams

After 5 hours: 6 / 2 = 3 grams

So, the points on the graph would be:

Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

to know more about unitary method

https://brainly.com/question/28276953

Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer: y = 28.8

Step-by-step explanation:

By using ratios

if the values vary with each other, then they will increase the same amount. 6x8 is 48. So 3.6 x 8 is your answer, 28.8

Based on the information in the image, it can be inferred that the sides of the box measure 5 cm each.

To find the measure of the sides of the box we must carry out the following mathematical procedure:

As we know the volume of a cube is the equivalent to the length of its sides raised to the cube (raised to the 3). In this case, to identify the value of the sides we must find the cube root of the volume and the result is the length of the sides.

So this cube has a volume of 125cm³, so its sides would be the cube root of 125.

\(\sqrt[3]{125} = 5\)

According to the above, the length of the sides is 5 taking into account that all the sides are equal.

Learn more about cubes in: https://brainly.com/question/30962206

#SPJ1

Answer:The graph that represents the same relation as the rule y = 2x for all real numbers x is the graph where the points lie on a straight line with a slope of 2.

Based on the given points, the graph that represents this relation would be the one that includes the points (0, 0), (1, 2), and (2, 4), since they follow the pattern of y = 2x.

Therefore, the correct graph is the one where the points are (0, 0), (1, 2), and (2, 4), forming a straight line with a slope of 2.

Step-by-step explanation:

The points (negative 2, negative 4), (negative 1, negative 2), (0, 0), (1, 2), (2, 4) represent the rule y = 2x, because in each pair, the y-value is twice as much as the x-value. This rule defines a line passing through the origin, consistent with these points.

The graph that represents the same relation as the rule y = 2x, for all real numbers x, is illustrated by the points (negative 2, negative 4), (negative 1, negative 2), (0, 0), (1, 2), (2, 4). This is because for each x value in the given points, the y value is twice as much. The rule y = 2x defines a straight line that passes through the origin (0,0) where the y-value is always twice the x-value. This fits perfectly with the points given. The horizontal line intercepting the y-axis at (0, 2) does not reflect the rule y = 2x, because the y-value here is not changing relative to x.

https://brainly.com/question/31180198

#SPJ2

Answer:

a. d < 11

Step-by-step explanation:

4 + d < 15

d < 15 - 4

d < 11

Answer:

3 / 8

Step-by-step explanation:

7 / 8 - 2 / 4 =

2  x 2                4

---               =     ----

4    x 2                8

7           4              3

-      -     -       =     ----

8           8               8

What I did was find a common denominator first Then do the equation

Can I have a crown please?

Answer:

k(-4) = 12

Step-by-step explanation:

The most simple definition of a function is a set of inputs that have a given set of outputs.

Functions are often written as f(x) = "an expression"

Where "x" is the input and "the expression" results in an output. Whatever the input is you plug into "x" and replace all "x"s with the input

Here, we are given the function k(x) = 8 - x and we want to find k(-4)

This can be rewritten as k(-4) = 8 - x

==> replace all x's with -4

k(-4) = 8 - (-4)

==> remove parenthesis

k(-4) = 8 + 4

==> add 8 and 4

k(-4) = 12

The solution of the given quadratic equation -5 = -36 / m + m is,

 m = - 9 or  m = 4

The given equation is

-5 = -36 / m + m

After re arranging it we get,

m² + 5m - 36 = 0

This is nothing but quadratic equation,

Since we know that,

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:

ax² + bx + c = 0

So now we can write,

⇒ m² + 9m - 4m - 36 = 0

⇒ m(m + 9) - 4(m + 9) = 0

⇒ (m + 9)(m - 4) = 0

Therefore,

⇒ (m + 9) = 0 or (m - 4) = 0

⇒ m = - 9 or  m = 4

Thus,

The solution of the given expression is

m = - 9 or  m = 4

To learn more about quadratic equation visit:

https://brainly.com/question/30098550

#SPJ1

Answer:

D. 3(25) + 2(50+75)

Step-by-step explanation:

3 cars = check brakes = $25. So, 3x25 or 3(25)

2 cars = new brakes = $50 + $75. So, 2(50+75)

Add the two semi-totals together: 3(25) + 2(50+75)

Answer:

distributive

Step-by-step explanation:

6 * x = 6x

6 * 4 = 24

move the plus sign

6x+24

The values of the angles x and y are ∠x = 110 and ∠y = 70

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

The lines (parallel, transversal and others)

The measure of angle 1 is calculated as

∠1 = 180 - 140 -- angle on a straight line

So, we have

∠1 = 40

Next, we have

∠2 = 180 - 40 - 80 --- corresponding angles

So, we have

∠2 = 60

This means that

∠y = 180 - 60 - 50 -- angle on a straight line

So, we have

∠y = 70

This also means that

∠x = 180 - 60 - 10 -- angle in a triangle

So, we have

∠x = 110

Hence, the values of x and y are ∠x = 110 and ∠y = 70

Read more about angles at

https://brainly.com/question/25716982

#SPJ1

If Gavin contributes towards a Pension fund (7,5% of his Basic Salary), then his net salary will be reduced by the amount he contributed towards pension fund i.e. R652.5.

1.1 Name of employee is Gavin Pillay. 1.2 UIF stands for Unemployment Insurance Fund. UIF is a benefit to provide short-term relief to workers who lose their jobs, or can't work due to illness, maternity or adoption leave. 1.3 The UIF paid by Gavin is calculated correctly.

Firstly, we need to calculate Gross Salary of Gavin, which is given as: Basic Salary + Overtime + M = R8700 + R1200 + R3201 = R13101Then, calculate total deductions from gross salary.

Total Deductions = PAYE + UIF = R1200 + 87 = R1287Hence, Gavin's net salary = Gross salary - Total Deductions = R13101 - R1287 = R11814Therefore, UIF paid by Gavin is calculated correctly as R87.1.4 This payslip is for the month of May i.e.

31/05/2023.1.5 Basic salary of Gavin = R8700. Deduct 7.5% of his basic salary to calculate his pension fund contribution. Pension Fund Contribution = 7.5/100 x R8700 = R652.5.1.6

Total deductions of Gavin includes PAYE, UIF and pension fund contribution.

Therefore, Total Deductions = PAYE + UIF + Pension Fund Contribution = R1200 + R87 + R652.5 = R1939.5.1.7

Gavin's age can not be determined as his date of birth is not provided.1.8 Address of Gavin's workplace is 21 Halsted Road, Pietermaritzburg?

To learn more about : pension fund

https://brainly.com/question/31531270

#SPJ8