Isabel will rent a car for a day. The rental company offers two pricing options: Option A and Option B. For each pricing option, cost (in dollars) depends on miles driven, as shown below.

According to the problem,

• Jennifer is 20 miles North.

• The rate is 55 miles per hour.

Remember that rate of change refers to the slope.

Therefore, the slope is 55.

On the other hand, the y-intercept is the initial condition of the problem since Jennifer started 20 miles North, then the y-intercept is (0,20).

The inequality to represent the situation for Janie will be 3 + 1.2c > 13.50.

From the information, it was illustrated that Janie has $3 and that she earns $1.20 for every chore.

Let the total number of chores that she can do be represented as c.

It should be noted that she also wants about $13.50 to buy her CD. Therefore, the inequality can be represented as:

3 + (1.2 × c) > 13.50

3 + 1.2c > 13.50

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a. We start by noting the number of hours Mark worked, given that h is the number of hours Chris worked.

To get this, we look for the relationship between the number of hours Mark worked and the number of hours Chris worked

From the question, we are told that they worked the same umber of hours, so the number of hours Mark worked is also h hours since they worked equal number of hours.

b. We shll now use the relationship with Kari for both Chris annd Mark to write two equations.

For Chris, we rae told that Kari worked twicw as many hours as he worked.

So if Chris worked h hoirs, then Kari worked 2 * h = 2h hours

For Mark, we are told that Kari worked 10 less than 3 times the number of hours Mark worked

The number of hours Mark worked was h hours, 3 times this is 3 * h = 3h

10 less than this would be (3h - 10) hours

c. An equation describing the expression above;

Since each expressin represents the number o hours Kari worked, then the two expressions must be equal.

Thus;

2h = 3h - 10

1. The z scores in the question are - 2.92 and 1.615

2. The probability that he is the father = 0.054905

The z score for the 242 days

= 242 - 280 / 13

= -2.92

The z score for the 30 days

= 301 - 280 / 13

= 1.615

Next we have to solve for The probability that he is not the father

this is written as

p(242 < x < 301)

p value of -2.92 = 0.00175

p value of 1.615 = 0.946845

Then we would have 0.946845 - 0.00175

= 0.945095

The probability that he is the father is given as 1 - probaility that he is not the father of the child

= 1 - .945095

= 0.054905

The probability that he is the father is 0.054905

This is the term that is used in Statistics and also in the field of mathematics to explain the chances and the likelihood of an event occurring.

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Part A

replace (0,3) on (x,y)

the equivalence is correct so (0,3) is a solution of the first equation

Part B.

replace (0,-3) on (x,y)

the equivalence is incorrect so (0,-3) isnt a solution of the second equation

Part C

To find the slope we need to solve each expresion and take the coefficient of x

first equation

the slope is 2

second equation

the slope is -3

Part D

the y-intercept is the constant without variable on each equation

first equation

the y-intercept is 3

second equation

the y-intercep is 3 too

The Graph

we need two points of the line and join by a right infinite line

first equation

the points (0,3) and (-3/2,0) belong to the line 1

second equation

the points (0,3) and (1,0) belong to the line 2

Solution of the system

we can note the two lines trought the point (3,0) so this is the solution and we can check matching the equations and solving x

and replace x=0 on any equation to solve y I will use the first equation

so the solution point is (0,3)

Answer:

P = 7

Step-by-step explanation:

[tex]{ \tt{ {2}^{p} = {2}^{2p - 7} }} \\ [/tex]

- From the law of indices; If an index has same base, then the powers are equal.

[tex]{ \boxed{ \rm{ \blue{ ({x}^{a} = {x}^{b}) \rightarrow{ \red{a = b}} }}}}[/tex]

[tex]{ \tt{p = 2p - 7}} \\ { \tt{p -2 p = - 7}} \\ { \tt{p = 7}}[/tex]

OR:

Applying logarithms can also be borrowed;

[tex]{ \tt{ log( {2}^{p} ) = log( {2}^{2p - 7} ) }} \\ \\ { \tt{p log(2) = (2p - 7) log(2) }} \\ \\ { \tt{ \frac{p log(2) }{ log(2) } = \frac{(2p - 7) log(2) }{ log(2) } }} \\ \\ { \tt{p = 2p - 7}} \\ \\ { \tt{p - 2p = - 7}} \\ \\ { \tt{p = 7}}[/tex]

Solution

For this case we have the following angle:

30 1/6 º

and then we need to convert to degrees and minutes so we can do this:

1 º= 60 min

then 1/6º* (60min/ 1º)= 10 min

Then the answer is:

30º 60'

Answer:

Infinite solutions or some courses say all real numbers

Step-by-step explanation:

-6x + 2(3x + 4) = 8  substitute 3x + 4 for y

-6x + 6x + 8 = 8  Distribute the 2

8=8  The x's cancel out leaving a true statement.  This means that there are infinite solutions.

Using conversion factors we can conclude that Janet needs 336 yards of string.

So, yards of string are needed:

We know that:

Therefore, using conversion factors we can conclude that Janet needs 336 yards of string.

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The grand total is given by

so, the probability of Caffeinated is

the probability of mint is

and the probability of the intersection is

Then, the probabilty of the union is given by

The rate of change of the line or the slope of the line that contains the two points (1, 4) and (5, -4) is m = 2

As per the question statement, we are supposed to find the  rate of change of the line or the slope of the line that contains the two points (1, 4) and (5, -4).

We know slope [tex]m = \frac{y_{2}-y_{1}}{x_{2} -x_{1}}[/tex] for the line passing though the points (x1,y1) and (x2, y2)

Using the same formula and finding out the rate of change of the line or the slope of the line that contains the two points (1, 4) and (5, -4).

slope m = (-4-4)/(5-1)

m=-8/4

m = -2

Hence the rate of change of the line or the slope of the line that contains the two points (1, 4) and (5, -4) is m = 2

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[tex]m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{ - 3 - ( - 1)}{ - 2 - 12} \\ m = \frac{ - 3 + 1}{ - 14} \\ m = \frac{ - 2}{ - 14} \\ m = \frac{1}{7} [/tex]

ATTACHED IS THE SOLUTION..I also provided you with the formula used to get the gradient.

Answer: 0.1429.

Step-by-step explanation: To double-check our work, multiply 0.1429 by 7 to see that it equals 1.

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

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Answer:

x < 0

Step-by-step explanation:

4(x + 2) < 8

4x + 8 < 8

4x < 0

x < 0

◀━━━━━|──>

                      0

Answer:

-2

I did the math and it came out -2

Answer:

C. (3, -2)

Explanation:

First, we need to reflect the point (2, 3) across the line y = x. To reflect this point, we need to find another point that is at the same distance but on the opposite side of the line, so the reflection is

Therefore, the reflection is the point (3, 2)

Then, reflect (3, 2) across the y-axis, to get:

So, the answer is

C. (3, -2)

First, the parent function is translated 5 units to the left, then it is reflected over the x-axis, and finally, it is translated 6 units down.

Answer:

Reflection: reflect in the x-axis.

Stretch: No stretch nor compression.

Horizontal Translation: Shift 5 units left.

Vertical Translation: Shift 6 units down.

The equation of a proportional relationship between two variables x and y with a constant of proportionality k, is:

If y represents the number of toys and x represents the number of hours, substitute the corresponding values of x and y to find the constant of proportionality k. Use, for instance, the fact that Nicholas made 40 toys in 10 hours:

Divide both sides of the equation by 10:

Since Nicholas's toy-making rate is 4 toys per hour, half that rate would be 2 toys per hour. Then, out equation would become:

Using the letter "t" for toys instead of y and "h" for hours instead of x, then:

The equation of the line that passes through the point (-5,7) with slope -5 in the point-slope form is 5x + y = -18 .

The Point - Slope form of the line passing through (x₁,y₁) with slope m is given by the equation

(y-y₁)= m(x-x₁)

In the question ,

it is given that the required line passes through the point(-5,7) and have the slope = -5 .

the point is (-5,7)

so x₁= -5 and y₁=7 and m =  -5

Substituting the value in the equation of point slope form , we get

(y-y₁)= m(x-x₁)

(y-7)= (-5)(x-(-5))

simplifying further , we get

(y-7)= (-5)(x+5)

y-7 = -5x -25

5x + y = -25 +7

5x + y = -18

Therefore , the equation of the line that passes through the point (-5,7) with slope -5 in the point-slope form is 5x + y = -18 .

The given question is incomplete , the complete question is

Use point-slope form to write the equation of a line that passes through the point (-5,7) with slope -5 .

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Okay, here we have this:

Considering that the area of a rectangle is:

Area=length*width

Replacing we obtain:

300=(5+x)*x

300=5x+x²

0=5x+x²-300

0=(x-15)(x+20)

This mean that:

x-15=0 or x+20=0

x=15 or x=-20

And considering that the distances are positive we are left with the first solution, x=15; this mean that:

Width=15 yd

Length=(15+5) yd=20 yd.

Finally we obtain that the width is 15 yd and length is 20 yd.

Answer:

  21 ft by 27 ft

Step-by-step explanation:

You want the dimensions of a rug with an area of 567 square feet such that it fits in a 25 ft by 31 ft room with a uniform space all around.

We note the room is 31-25=6 ft longer than it is wide. Since the rug has a uniform border around it, the rug dimensions will be 6 ft longer than wide. We want the rug area to be 567 square feet, so for width w we have ...

  w(w+6) = 567

  w² +6w +9 = 576 . . . . . . add 9 to complete the square

  (w +3)² = 24² . . . . . . . . express as squares

  w +3 = 24 . . . . . . . . . positive square root

  w = 21 . . . . . . . . . . subtract 3 to find the width

  w+6 = 27 . . . . . . add 6 to find the length

The rug should have dimensions 21 ft wide by 27 ft long.

__

Additional comment

The uniform strip of floor around the rug will be 2 feet wide.

Given

Answer

Okay, here we have this:

Considering the provided angle, we are going to evaluate the trigonometric functions, so we obtain the following:

Sine:

Cos:

Tan:

Csc:

Sec:

Cot:

to solve ax^2 + bx + c = 0 using completing the square method

divide all terms by a so as to reduce the coefficient of x^2 to 1

x^2 + bx/a + c/a = 0

subtract the constant term from both sides of the equation

x^2 + bx/a = -c/a

to have a square on the left sie the third term (constant) should be

(b/2a)^2

so add that amount to both side

x^2 + bx/a + (b/2a)^2 = (b/2a)^2 - c/a

rewrite the left side as a square

(x + (b/2a))^2 = (b/2a) - c/a

take the square root of both sides

x + (b/2a) = + square root of (b/2a)^2 - c/a

subtract the constant term on the left side from both sides

we have the equation

using a grahing tool

see the attached figure

To solve a, we need to replace x = 0 in the formula of the function:

The y value when x = 0 is 5.

b is asking the same as a but in a different way. The y-intercept of a function is when x = 0, we just calculated that. The point of y-intercept is (0, 5)

Finally, to solve c, we need to find the values of x that gives us a value of f(x) = 46:

Then solve:

Remember that we must that plus-minus the value when we take square root. ± √41 is the answer to c.

The first plane had a head start of 432 minutes.

The speed, time and distance of any entity can be related by the following expression as Distance = Speed × Time. The speed of the first plane is 180 mph and the time given is 12 hours whereas the speed of second plane is 450 mph. Now, the distance travelled by plane A in time 12 hours is given by

Distance = Speed × Time

Distance = 180 × 12

Distance = 2160 miles.

The second also flies 2160 miles to overtake the first plane. It does this at a rate of 450 mph. So, the time taken for it to fly will be

Time = Distance/Speed

Time = 2160/450

Time = 4.8 hours

Since, 1 hour = 60 minutes, Therefore, 4.8 hours = 4.8×60 = 288 minutes. Now, since the first plane flies for 12 hours = 12×60 = 720 minutes. So, the head start = 720 minutes - 288 minutes = 432 minutes.

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we have that:

having this we get that