The Quinn family drove 228 miles in 4 hours at a constant rate. Which equation can be used to determine how far they traveled each hour?

A. d = 228/4

B. d = 228 x 4

C. d = 228 + 4

D. d = 228 - 4

Answers

Answer 1

Answer: A. The distance traveled each hour would be the total distance divided by the number of hours.

Answer 2

Answer: Distance = Time x Rate of travel miles/hr so D/T = rate of travel 228/4 = 57 miles/hr. Answer is A

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Andre received $60 for his birthday and put it in his piggy bank. Each week, he puts 3 more dollars in his bank. The amount of money in dollars D in his bank is given by D = 3w + 60 where w is the number of weeks he has saved 3 dollars. His sister Lana helped him find how much money he will have after 4, 15, 20, and 36 weeks. This table shows her results. What is the rate of change using Lana’s values for D and w? Is this a linear model or non-linear model?W 4 weeks 15 weeks 20 weeks 36 weeks D D= 3w =60 D = 3w + 60 D = 3w + 60 D = 3w + 60= 3*4 +60 = 3 * 15 = 3 * 20 + 60 = 3 * 36 + 60= 12 + 60 = 45 + 60 = 60 + 60 = 108 + 60= 72 = 105 = 120 = 168A.The rate of change varies. It is a linear model.B.The rate of change varies. It is a non-linear model.C.The rate of change is . It is a linear model.D.The rate of change is 3. It is a linear model.
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Two towns are located at points A(2,-2) and B (8,5). A new school is to be built on a straight road with equation -x+7y=-4. Find the location of the school so that it is equaidistant from the two towns

Answers

Final answer:

The problem asks for a location that is equidistant from towns A and B and lies on the given road. Calculating the midpoint of A and B, we get (5, 1.5). However, this point does not lie on the road denoted by -x + 7y = -4. So, we cannot determine the exact location of the school with the given conditions.

Explanation:

In this problem, the location of the school should be the midpoint of the line between towns A and B as it is equidistant from both towns. First, let's calculate the midpoint (M) coordinates. The formulas for finding the x and y coordinates of the midpoint are (x1 + x2) / 2 and (y1 + y2) / 2 respectively. Using these formulas, we get the coordinates of M as (2+8)/2, (-2+5)/2 = (5, 1.5). However, we should ensure that this point lies on the given road, which is denoted by the equation -x + 7y = -4. Substituting the coordinates of M in the equation, we get -5 + 7*1.5 = -5 + 10.5 = 5.5 which is not equal to -4. So, (5, 1.5) is not a valid location for the school. Unfortunately, with the given conditions, we cannot determine the exact location of the school. Additional information or revision of the conditions might be necessary to solve this problem.

Learn more about Coordinate Geometry here:

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Plz helpp FASTTFind the area of triangle ABC with vertices A(2, 3), B(1, -3), and C(-3, 1).
a.
10 units2
c.
14 units2
b.
12 units2
d.
16 units2

Answers

The area of the triangle will be 14 square units. Then the correct option is C.

What is the triangle?

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The triangle ABC with vertices A(2, 3), B(1, -3), and C(-3, 1).

Then the area of the triangle is given as,

A = 1/2 | {[2 x (-3) + 1 x 1 + (-3) x 3] - [3 x 1 + (-3) x (-3) + 2 x 1]} |

A = 1/2 | {[-6 + 1 - 9] - [3 + 9 + 2]} |

A = 1/2 | {-14 - 14} |

A = 1/2 x 28

A = 14 square units

The area of the triangle will be 14 square units. Then the correct option is C.

More about the triangle link is given below.

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Are you sure about your solves??

I think correct answer is 6,

I don't know but the standard way is in the photo:

How would I do this problem. It says to solve and check 5/k? -6?= -3

Answers

You would first move the 6 onto the other side by adding it. Then you would end up doing -3+6 which is 3. Then your equation will look like: 5/k=3. You would then do opposite operation again to the 5 this time. You do the opposite of dividing, so multiplying. You multiply the 5 on both sides which you would end up doing 5 x 3 which is 15. Your equation will then be looking like k=15. To check if you did it right, just simply plug in the 15 as k. So the equation to check should look like this: 5/15-6=3. Solve it, and you should end up as the answer being equal to 3.

HONESTLY help me I don’t understand math

Answers

Answer:

15. 2m

17. 1.5m

Step-by-step explanation:

just square root it

What are the zeros of j(x) in the polynomial equation?

Answers

Answer: x = $(-3)/(2)$ , 0, $(3)/(2)$

Step-by-step explanation:

To find the zeros, we will find the solutions to this equation that make it equal 0. This is a cubic function, so we can assume that there will be three solutions.

Given:

$\displaystyle J(x) = (12x^3)/(5) -(27x)/(5)$

Set the functionequal to 0:

$\displaystyle 0 = (12x^3)/(5) -(27x)/(5)$

Subtract:

$\displaystyle 0 = (12x^3-27x)/(5)$

Multiply both sides of the equation by 5:

$\displaystyle 0 = 12x^3-27x$

Factor the polynomial:

$\displaystyle 0 = (3x)(2x-3)(2x+3)$

Solve with the zero product property:

0 = 3x 0 = 2x - 3 0 = 2x + 3

0 = x 3 = 2x -3 = 2x

x = 0 x = $(3)/(2)$ x = $(-3)/(2)$

You work for a small business that sells bicycles, tricycles, and tandem bicycles (bicycles built for two). Bicycles have one seat, one front-steering handlebars, two pedals , and two wheels. Tricycles have one seat, one front-steering handlebars, two pedals, and three wheels. Tandem Bicycles have two seats, one front-steering handlebars, four pedals, and two wheels. Part A: On Monday, you counted forty-eight tricycle wheels. How many tricycles were in the shop? Write an algebraic equation that shows the relationship between the number of wheels (w) and the number of tricycles (t). Part B: On Wednesday, there were no tandem bicycles in the shop. There were only bicycles and tricycles. There were a total of twenty-four seats and sixty-one wheels in the shop. How many bicycles and how many tricycles were in the shop? Solve algebraically and show all your work. Let a = the number of tricycles Let b = the number of bicycles Part C: A month later, there were a different number of bicycles, tricycles, and tandem bicycles in the shop. There were a total of 144 front-steering handlebars, 378 pedals, and 320 wheels. How many bicycles, tricycles, and tandem bicycles were in the shop? Solve algebraically and show all your work. Let a = the number of tricycles Let b = the number of bicycles Let c = the number of tandem bicycles.

Answers

Part A: each tricycle has three wheels, so with 48 wheels the number of tricycles was a =48/3=16 tricycles.
t=w/3 (the number of tricycles is the number of wheels divided by 3)

Part B:
The number of seats:
24=b+a (so b=24-a)
The number of seats is the sum of one seat per bicycle and one seat per a tricycle

also, 61=2a+3b (the number of wheels)

So we have:
24=b+a
b=24-a
We can substitute this for b:

61=2a+3(24-a)

and solve:
61=2a+3*24-3a
61=72-a
a=72-61
a=11

There were 11 bicycles!!
and there were 24-11 tricycles, so 13 tricycles.

Part C: each of the bikes has only one front-steering handlebar, so there were a total of 144 vehicles:

a+b+c=144

There were 378 pedals. And the number of pedals is:
2a+2b+4c=378 (the numbers 2,2,4 represent the number of pedals per vehicle)

divide by 2:
a+b+2c=189

Now, we have
a+b+2c=189
and

a+b+c=144
and we can subtract them from each other:
a+b+c-(a+b+2c)=144-189
-c=45
c=45, so there were 45 tandem bicycles!
(this also means that a+b=144-45, that is a+b=99)
now the wheels:
3a+2b+2c=320
Let's substitute c:
3a+2b+90=320

which is
3a+2b=240
We also know that a+b=99, so we can substract this from this equation:
3a+2b+-a-b=240-99
2a+b=141

and again:
2a+b-a-b=141-99
a=42 - there were 42 trycicles!!!

And the bicycles were the rest:
99-42=57 bycicles

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