Jenn will use 18 connecting cubes to make a model of a park. The model will be in the shape of a rectangle and will have the height of one cube. In how many ways can Jenn make the model of the park?

Answers

Answer 1

Answer: Given Situation : Jenn used 18 connecting cubes to make a model.
Jenn wants her model to be a rectangle shaped and have the height of 1 cube.
Now, We need to find the numbers of ways will Jenn use her model.
=> First we need to find the factors of 18
=> 18 x 1 equals to 18
=> 9 x 2 equals to 18
=> 6 x 3 equals to 18
As we can see, 18 has 3 possible ways. Therefore, Jenn will have 3 ways to model her triangle depending on the choice she wants.

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Explain how Christy can correct her reasoning

Answers

Incorrect reasoning: she said that 47 is greater than 5. But 5 is a whole number, therefore Alex must've ran 5 miles, which is much greater than Christy's.

How to correct her reasoning: She can correct her reasoning by knowing that 47/100 is not not a whole number. 5 miles is equal to saying 500/100, and that is much larger than 47/100.

47/100 < 5

Which story problems could be solved using the given equation?1\4 x 3\5

Choose exactly two answers that are correct.

A.
There is 3\5 of a box of dog treats in the cupboard. Jill’s dog eats1\4 of a box of treats in a week. How many weeks of treats are left in the box for Jill’s dog?

B.
In Sophie’s doll collection,3\5 of the dolls are in their original boxes. Sophie plans to donate 1\4 of the dolls in these boxes to charity. How much of her doll collection will Sophie donate to charity?

C.
Shawn made a poster that has a width of 1\4 meter and a length of 3\5 meter. What is the area, in square meters, of Shawn’s poster?

D.
Christie hiked 1\4 mile on the trail. Jackie hiked 3\5 mile farther than Christie. How far, in miles, did Jackie hike on the trail?

Answers

Answer: Option 'C' and 'B' are correct.

Step-by-step explanation:

Since we have given that

$(1)/(4)* (3)/(5)$

In Option 'C' ,

Length of a poster is given by

$(1)/(4)$

Width of a poster is given by

$(3)/(5)$

So, Area of poster is given by

$Length* breadth\n\n=(1)/(4)* (3)/(5)$

In option 'B', part of dolls are within the original box is given by

$(3)/(5)$

Part of dolls who has charity is given by

$(1)/(4)$

Total dolls she donate is given by

$(1)/(4)* (3)/(5)$

On the other hand, In option 'A' has "Division operation" and option 'D' has "Subtraction operation".

Hence, Option 'C' and 'B' are correct.

Which story problem could be solve using the given equations.
B & C.

Find slope of the line and the y-intercept of each.y=3×+4

y=-2x+8

y=1/2x

y=-3/4x-1

y=x+5

please show work step by step for each.

Answers

1. 3

2. 2

3. 1/2

4. 3/4

5. 1

The answer to the questions for each slope.

1. The equations in this example are already set equal to "y". Identify the slope and y-intercept in each equation. Remember: y = mx + b, where m = slope and b = y-intercept.

y = 2x + 1

slope = 2

y-intercept = 1

y = -x + 7

slope = -1

y-intercept = 7

2. Graph the lines.

This example used the slope-intercept method of graphing straight lines.

The b-value tells you where the line crosses the y-axis.

The slope, m, tells you the rise over the run.

If you need help graphing lines, see Graphing Linear Equations.

Find the intersection point (where the lines cross).

These lines cross at the point (2,5).

This means the solution to this system is:

Solution: x = 2 and y = 5.

graph1

3. CHECK: Substitute x = 2 and y = 5 into BOTH of the original equations. If your solutions are correct, both equations will be true!

y = 2x + 1

5 = 2(2) + 1

5 = 5 (check)

y = -x + 7

5 = -(2) + 7

5 = 5 (check)

"You and your friend leave your houses at the same time to meet at a restaurant. The distance (in miles) your friend is from the restaurant is given by y=−40x+200, where x is the number of hours since your friend left home. You live 100 miles from the restaurant and arrive at the same time as your friend. Write a linear equation that represents your distance from the restaurant."

Answers

The equation will be:

$y=-20x+100$

Why?

Let's work with your friend equation in order to find the time from his house to the restaurant (is the same as yours).

We are given the following function:

$y=-40x+200$

When: $y=0$ our friend arrived, so, calculating "x", we have:

$0=-40x+200\n\n40x=200\n\nx=(200)/(40)=5h$

We have that it took 5 hours for our friend to arrive at the restaurant, and it's the same time for you. We know that you live 100 miles from the restaurant.

Your equation will have the following form:

$y=-k*x+distance$

Where,

y is the position

k is the rate distance/time

x is the time

Now, again, when $y=0$ , you will have arrived at the restaurant too, so:

$0=-k*x+100$

Using "x" equal to 5 hours, because you will have arrived at that time too, we have:

$0=-k*5+100\n\nk=(100)/(5)=20$

Your equation will be:

$y=-20x+100$

Have a nice day!

How do you write 47 billion

Answers

It's not that hard. If you know that a billion has nine zeros, then you write 47 with 9 zeros after it. Commas are optional, and next time you should try to use your resources, such as the internet to ask how many zeros are in a billion. 47,000,000,000

47,000,000,000 is how to write 47 billion in number form

Three less than one-fourth of the product of eight thirds and nine. Please write equation, then solve.

Answers

Put simply, you have to work backwards in making the equations. Start with the product of 8/3 and 9.
$(8)/(3)$ *9

Next take 1/4 of that. This can be done in two ways, either multiplying by 1/4:
( $(8)/(3)$ *9)* $(1)/(4)$

, or dividing everything by 4.
( $(8)/(3)$ *9)/4

Finally, subtract three.

The final equation would read:
(( $(8)/(3)$ *9)* $(1)/(4)$ )-3

Using PE(M/D)(A/S), we'd start with $(8)/(3)$ *9

3 and 9 cancel out to be 1 and 3, leaving us with $(8)/(1)$ , or 8, and 3 and this part of the equation reading 8*3, which is 24.

The next step is $(24)/(4)$ , which is 6.

Lastly we subtract 3 from six, leaving us 3.

¹/₄ × ( ⁸/₃ × 9 ) - 3 = 3

Further explanation

Order of Operations in Mathematics follow this following rule :

Parentheses

Exponents

Multiplication and Division

Addition and Subtraction

This rule is known as the PEMDAS method.

In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.

Let us tackle the problem!

Product of eight thirds and nine

$(8)/(3) * 9$