Megan is going on a long distance road trip. She drives for 13 miles before being able to travel at a constant speed using cruise control. The equation used to find her total distance traveled is shown below.

y = 59x + 13


If y is the total number of miles driven, and x is the number of hours driven after reaching 13 miles, which statement best describes the rate of change in the distance traveled?

A. For every 13 hours, she will drive 72 miles.
B. For every two hours, she will drive 59 miles.
C. For every hour, she will drive 59 miles.
D. For every hour, she will drive 72 miles.

Answer:

The distance between these two is 3 3/5

Step-by-step explanation:

In order to find the distance between two points, we subtract one from the other. Then if the result is negative, we take the absolute value.

2 3/5 - -1

2 3/5 + 1

3 3/5

Let's solve your equation step-by-step.

4−x=11−8

Step 1: Simplify both sides of the equation.

4−x=11−8

4+−x=11+−8

−x+4=(11+−8)(Combine Like Terms)

−x+4=3

−x+4=3

Step 2: Subtract 4 from both sides.

−x+4−4=3−4

−x=−1

Step 3: Divide both sides by -1.

−x /-1=-1/-1

x=1

Answer:

x=1

y = 4

first note that the right side simplifies to 12, equation can be written

[tex]\frac{2y+1.6}{0.8}[/tex] = 12 ( multiply both sides by 0.8 )

2y + 1.6 = 9.6 ( subtract 1.6 from both sides )

2y = 8 ( divide both sides by 2 )

y = 4

Hey there!!

We have:

... (2y+1.6)/0.8 = 30/2.5

... (2y+1.6)/0.8 = 12

Multiplying 0.8 on both sides.

... (2y+1.6) = 12×0.8

... 2y+1.6 = 9.6

Subtracting 1.6 on both sides:

... 2y = 9.6-1.6

... 2y = 8

Dividing by 2 on both sides:

... y = 8/2

... y = 4

Hence, the required answer is 4.

Hope my answer helps

Answer: The number of pages in the U.S. tax code x=20000 and the number of pages in the King James Bible y = 1472

Step-by-step explanation:

Let the number of pages in the U.S. tax code be x and the number of pages in the King James Bible be y.

According to the given problem , we have the following system

x - y = 18528    ..............(1)

x + y = 21472     ..............(2)

Adding (1) and (2) , we get

2x = 18528 +21472 = 40000

⇒ 2x =40000

⇒ x =20000

Putting value of x = 20000 in (2) ,we get

20000 + y =21472

⇒ y = 1472

Ans  the number of pages in the U.S. tax code x=20000 and the number of pages in the King James Bible y = 1472

Final answer:

By setting up an equation and solving for B, which represents the number of pages in the Bible, it is determined that the King James Bible has 1,472 pages.

Explanation:

To determine how many pages are in the King James Bible, we need to set up an equation based on the information given in the problem. We know that the number of pages in the U.S. tax code exceeds the number of pages in the King James Bible by 18,528 and the combined total of pages in both the tax code and the Bible is 21,472.

Let's let B represent the number of pages in the Bible. Then the number of pages in the U.S. tax code would be B + 18,528. The total number of pages in both is given to be 21,472, so we can write the following equation:

B + (B + 18,528) = 21,472

Simplifying the equation, we get:

2B + 18,528 = 21,472

Subtract 18,528 from both sides to get the number of pages in the Bible:

2B = 2,944

Divide by 2 to solve for B:

B = 1,472

Therefore, the King James Bible has 1,472 pages.

Dana wants to find the sum

  3 4 6

  4 2 1

+1 5 2

________

We will not regroup this ones place because the sum of the digits in the ones place is not up to. It's just 6+1+2 = 9.

Therefore, 13a) No.

There is no regrouped tens to add, so we would not able to regroup the ones place.

Therefore, 13b) No.

We regroup the tens place because the sum of the digits in the ones place is upto to 10.

And 13c) Yes.

We add the regrouped hundred as we regrouped the ones place.

Therefore,

13 D) Yes.

Answer:

a

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

i did it and got it right

the picture is my evidence.

THere are 52 students because there is 19 boys and 14 more girls than guys which means 19 + 19 + 14

There are 14 more girls than the 19 boys in the school orchestra, so there are 33 girls. Adding 33 girls and 19 boys, we find there are 52 students in the orchestra.

This question falls under the category of simple addition in mathematics. We are given there are 19 boys in the school orchestra and there are 14 more girls than the boys. To find out the total number of students, we add the number of boys to the number of girls.

First, understand that if there are 14 more girls than boys, the number of girls will be 19 (boys) + 14 = 33 girls. Next, adding the number of boys and girls together would give you 19 (boys) + 33 (girls) = 52 students. Hence, there are total 52 students in the school orchestra.

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Here we are given the inequality:

[tex]y\geq4x-5[/tex]

Let us check for each ordered pair that satisfies the given inequality.

1. (3,0)

LHS: y

here y is 0.

So LHS is 0.

RHS: 4x-5

plugging x as 3,

4(3)-5 = 7

0≥7

False

So (3,0) does not satisfy the inequality.

2. (1,1)

LHS: y

here y is 1.

So LHS is 1.

RHS: 4x-5

plugging x as 1,

4(1)-5 = -1

1≥-1

True

So (1,1)  satisfy the inequality.

1. (3,4)

LHS: y

here y is 4.

So LHS is 4.

RHS: 4x-5

plugging x as 3,

4(3)-5 = 7

4≥7

False

So (3,4) does not satisfy the inequality.

1. (2,1)

LHS: y

here y is 1.

So LHS is 1.

RHS: 4x-5

plugging x as 2,

4(2)-5 = 3

2≥3

False

So (2,1) does not satisfy the inequality.

Answer: (1,1) is the solution of the given inequality.

If you divide by 8, you can put the equation into intercept form. That form is ...

... x/a + y/b = 1

where a and b are the x- and y-intercepts, respectively.

Here, your equation would be

... x/(-2) + y/(-4) = 0

The graph with those intercepts is not shown with your problem statement here. See the attachment for the graph.

A) The time to travel 45 miles at a speed of 30 mph can be found from ...

... time = distance / speed

... time = (45 mi)/(30 mi/h) = 3/2 h = 1 hr 30 min

B) The gas consumption can be found from ...

... (45 mi)/(54 mi/gal) = 5/6 gal

C) The cost of gas can be found from ...

... ($3.23/gal)×(5/6 gal) ≈ $2.69

For a 45 miles trip at 30 mph, it would take about 1.5 hours in a hybrid car that gets 54 mpg. It would use approximately 0.833 gallons of gas, costing about $2.69.

To solve this, we'll need to employ some basic math concepts. Starting off with the time it will take to get to your grandparents' house, you'll use the formula distance = speed x time. Given the speed is 30 mph and you're traveling 45 miles, that will be 45 miles / 30 mph = 1.5 hours.

Next, for the gallons of gas used on the trip, we'll use the car's mileage i.e., 54 miles per gallon. Hence, for a 45-mile trip, we have 45 miles / 54 mpg = 0.833 gallons of gas.

Finally, for the total cost of the trip, we'll multiply the amount of gas needed by the price per gallon. So, it will be 0.833 gallons x $3.23/gallon = $2.69. Thus the round trip will cost approximately $2.69 in gas.

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Answer: The answer is 17.87. However the answer including all the numbers you put in your question is 17.92. I used only the first 2 numbers after the decimal point.

Step-by-step explanation: Consider how many numbers are behind the decimal points as they will help you know where to put the decimal point in your answer.

Hope this helps!

The equation of the line with slope m and passing through the point [tex](x_0,y_0)[/tex] is

[tex]y-y_0=m(x-x_0).[/tex]

Since m=6 and the coordinates of the point are (8,3), then the equation is

[tex]y-3=6(x-8).[/tex]

Answer: correct choice is B.

It's a 3rd grade problem in addition and subtraction, or number lines. As a college-level problem, it might be described as ...

... a part-whole problem, because the length of the third table is part of the total length of the long table

√61 ≈ 7.8

√101 ≈ 10.05

The integers between these numbers are 8, 9, 10. The product of these is 720.

51° 29' + 32° 46' = (51+32)° (29+46)'

= 83° 75' . . . . . there are 60' in 1°, so 75' = 1° + 15'

= 84° 15'

Since, there are 6 science fiction stories, 4 adventure stories, 3 historical stories and 2 sport stories.

So, total number of stories = 6+4+3+2 = 15 stories

Probability that Artie selects a science fiction story = [tex]\frac{6}{15}[/tex]

Probability that Artie selects an adventure story = [tex]\frac{4}{15}[/tex]

Probability that story selected is either a science fiction or adventure fiction = P(Science) + P(Adventure)

= [tex]\frac{6}{15} + \frac{4}{15}[/tex]

= [tex]\frac{10}{15}[/tex]

= 0.66

=0.67

Therefore, the probability that the story Artie selects is either a science fiction story or an adventure story is 0.67.

Answer:Probability of selecting either A or B P(A∩B)=2/3.

Step-by-step explanation:

Total number of story books=6+4+3+2=15

Let A be the event of selecting science fiction story

then its probability P(A)=number of science stories/total stories=6/15

Now let B be the event of selecting adventure story P(B)=number of adventure stories/total stories

=4/15

thus Probability of selecting either A or B P(A∩B)=P(A)+P(B)=6/15+4/15=10/15=2/3.

The answers are in slope-intercept form, so you can see that the slope (coefficient of x) is only correct for choices b and c.

When you substitute x=3/2 into those equations, you find that b gives y=6 (correct) and c gives y=0 (incorrect).

The appropriate choice is ...

... b.) y = 2x+3

Answer:

Rational

Step-by-step explanation:

Any number you can write out completely, or that has a repeating decimal fraction, is a rational number. 291.7 is the entire number, so is rational.

Answer:

The vertices are (0,0), (3,0), (1.5,2) and (0,2.5)

Step-by-step explanation:

We are given the constraints of the problem as,

[tex]4x+3y\leq 12[/tex]

[tex]2x+6y\leq 15[/tex]

[tex]x\geq 0[/tex]

[tex]y\geq 0[/tex]

Using 'Zero Test', which states 'If after substituting (0,0) in the inequalities the result is true, the solution region is towards the origin and if the result is false, the solution region is away from the origin'

So, after plotting the graph, we see that,

The end-points of the feasible region are given by,

(0,0), (3,0), (1.5,2) and (0,2.5)

Answer:

A (0, 0), (0, 2.5), (1.5, 2), (3, 0)

Step-by-step explanation:

edg 2022

to answer this question, you would need the Least Common Denominator.

6, 12, 18, 24, 30

10, 20, 30

So the LCD, Least Common Denominator, is 30.

How many packs of hot dogs did he buy?

5 packs.

How many packs of buns did he buy?

3 packs.

How many hot dogs did he buy?

30 hot dogs.

Hoped this helped,

-Anime

The correct answer is option B.

Let the basic calendars be = x

Let the deluxe calendars be = y

Total calendars are = 72 , so equation becomes:

[tex]x+y=72[/tex]  .............(1)

Cost of 1 basic calendar = $10

So, cost of all basic calendars will be = 10x

Cost if 1 deluxe calendar = $15

So, cost of all deluxe calendars = 15y

As given, the number of deluxe calendars must be greater than or equal to 3 times the number of basic calendars, the equation becomes

y=3x ...............(2)

Putting the value of y from (2) in (1)

[tex]x+y=72[/tex]

[tex]x+3x=72[/tex]

[tex]4x=72[/tex]

x=18

As, y=3x

y=[tex]3\times18=54[/tex]

So we have 18 basic calendars and 54 deluxe calendars.

Cost of 18 basic calendars will be= [tex]18\times10=180[/tex]

Cost of 54 deluxe calendars will be = [tex]54\times15=810[/tex]

So total amount is = $990

Hence, the maximum revenue is $990.

Answer:

The CORRECT answer is $1080

Step-by-step explanation:

Your answer would be choice C

1. a= 60 (vertically opposite angles)

b= 360-(60+60)=240/2= 120 (angles at a point)

c= 120 (vertically opposite angles with b)

2. c= 90-40= 50 (vertically opposite angles)

b=a=360-90-90=180/2=90 (angles at a point)

3. a= 180-52-51= 77 (angles on a straight line)

b=52 (angles at a point)

d=51 (angles at a point)

c=77 (angles at a point)

4. a= 60 (vertically opposite angles)

b= 360-(60+60)=240/2= 120 (angles at a point)

c= 120 (vertically opposite angles with b)

e=65

d=f= 360-65-65=230/2=115

h=55

i=g=360-55-55=250/2=125

5. b=163

a=90

e=70

d=360-70-70=220/2=110

c=360-163-163=34/2=17

Hope this helps!

Answer:

137.4 feet

Step-by-step explanation:

Consider the attached diagram. The given angle of depression from the lighthouse to the boat is the same as the angle of elevation from the boat to the lighthouse. The trig relationship for tangent tells you ...

... tan(20°) = opposite/adjacent = AL/AB = 50'/AB

Solving for AB, we get

... AB = 50'/tan(20°) ≈ 50'/0.36397

... AB ≈ 137.4'

Answer:

137.373871

Rounded to the 10th place

137.4

Rounded to the whole number

137

Step-by-step explanation:

There are a few methods for solving this type of problem. Please view the images I have provided. I gave two methods for solving this problem.

The diameter is a vertical line (x=3) and is of length 9 (= 5-(-4)). The radius is half the diameter (so is 4.5), and the center is 4.5 units above the bottom end of the diameter, so is at (3, 0.5). The square of the radius will be 4.5² = 20.25.

A circle with center (h, k) and radius r has formula

... (x -h)² +(y -k)² = r²

The equation of this circle can be written as

... (x -3)² +(y -0.5)² = 20.25

The distributive property tells you the product is found by multiplying each term inside parentheses by the factor outside.

... 4 -6n = 8n +8·7

... 4 = 14n +56 . . . . . . . add 6n to both sides

... -52 = 14n . . . . . . . . . subtract 56 from both sides

... -52/14 = -26/7 = n . . . divide by 14, reduce the fraction

The solution is ...

... n = -26/7 = -3 5/7

Answer:

$75.19

Step-by-step explanation:

Let 'x' be the cost of remote keyless entry.

And [tex]8x[/tex] be the cost of 4-way power front passenger seat.

Total cost = destination charge + title fee + taxes

So we have the equation:

[tex]20,000 = (17,980+x+8x)+0.072(17,980+x+8x)[/tex]

Now solving for 'x', we get:

[tex]20,000 = (17,980+9x)+0.072(17,980+9x)[/tex]

[tex]20,000=17,980+9x+1294.56+0.648x[/tex]

[tex]20,000=19274.56+9.648x[/tex]

[tex]725.44=9.648x[/tex]

[tex]x=\frac{725.44}{9.648} =75.19[/tex]

Therefore, the cost of remote keyless entry is $75.19.

Answer:

$601.53

Step-by-step explanation:

just do what the person did but all they forgot to do was to multiple for the "8 times" so take 75.19*8 to get 601.53.

Jack drives an 18 wheeler. The truck's gas tank holds 105 gallons of gasoline. The driver begins the trip with a full tank.

Tank holds 105 gallons

65% of gasoline is 0.65 * 105 = 68.25

so 68.25 gallons left in the tank

Tank holds 105 gallons  and left out with 68.25 gallons

So gasoline used = 105 - 68.25= 36.75

36.75 gallons of gasoline used

Answer: option. y=-1.33x; 2.67

Solution:

If y varies directly with x, the relation between y and x is:

y=kx

where k is a constant of proporcionality.

We know y=8 when x=-6. Replacing these values in the equation above:

8=k(-6)

8=-6k

Solving for k: Dividing both sides of the equation by -6:

8/(-6)=-6k/(-6)

-1.33=k

k=-1.33

Then the relation between y and x is:

y=kx→y=-1.33x

What is the value of y when x=-2?

Replacing x by -2 in the formula:

y=-1.33x→y=-1.33(-2)→y=2.66