Henry is hosting a party at his house, and his guests have requested pizza. He invites four of his best friends and two new friends from his class. If Henry and his friends eat 2/8 slices of pizza, how many pizzas should Henry order? Solve and explain your thinking using mathematical reasoning

The length of side walk is 500 feet

Solution:

Given that, A rectangle park measures 300 ft by 400 ft

Length = 300 feet

Width = 400 feet

A sidewalk runs diagonally from one comer to the opposite corner

We have to find the length of side walk

Which means, we have to find the length of diagonal of rectangle

The diagonal of rectangle is given by formula:

[tex]d = \sqrt{w^2+l^2}[/tex]

Where,

d is the length of diagonal

w is the width and l is the length of rectangle

Substituting the values in formula, we get

[tex]d = \sqrt{400^2+300^2}\\\\d = \sqrt{160000+90000}\\\\d = \sqrt{250000}\\\\d = 500[/tex]

Thus length of side walk is 500 feet

The correct answer is D. (3x2 + 5)(x + 3). Here’s how you can use the grouping method to factor the polynomial completely:

Group the first two terms and the last two terms: (3x3 + 9x2) + (5x + 15)

Factor out the greatest common factor from each group: 3x2(x + 3) + 5(x + 3)

Factor out the common binomial factor: (3x2 + 5)(x + 3)

So, the polynomial 3x3 + 9x2 + 5x + 15 can be factored completely as (3x2 + 5)(x + 3).

Hope it helps.

Answer:

Here, we have used the unit rate i.e. speed of 30 mph to get the distance traveled in 5 number of units i.e. 5 hours.

Step-by-step explanation:

We are asked the way to use a unit rate to solve a rate problem for any number of units.

Let, us assume that a car is moving at a unit rate of 30 miles per hour. And we have to calculate the distance it travels in 5 units of time i.e. 5 hours.

Now, the distance traveled in 5 hours will be given by 30 × 5 = 150 miles.

Since  [tex]\textrm {Speed} = \frac{\textrm {Distance}}{\textrm {Time}}[/tex] and here, speed is 30 miles per hour and the time is 5 hours. (Answer)

Answer:

0.33

Step-by-step explanation:

Aight so all we do is use the formula, as shown here:

[tex]\frac{\Delta x}{\Delta y}[/tex]

[tex]x[/tex] is this amount it changed, which is 0.99. So we plug that for [tex]\Delta x[/tex]:

[tex]\frac{0.99}{\Delta y}[/tex]

Then, we find the amount of times the storm changed, and we plug that for [tex]\Delta y[/tex]:

[tex]\frac{0.99}{3}[/tex]

So, now that we have utilized the formula, we can now solve!

[tex]\frac{0.99}{3} = 0.33[/tex]

Good luck!

Answer:

0.33

Step-by-step explanation:

Answer:

original weight of the box = 15 / 16 pounds

Step-by-step explanation:

The simplified answer is [tex]5\frac{2}{9}[/tex].

Option: C.

Step-by-step explanation:

To simply [tex]-3\frac{1}{9} - (-8\frac{1}{3} )[/tex]:

First convert this improper fraction into normal fraction.

[tex]-3\frac{1}{9}[/tex] = [tex]\frac{-28}{9}[/tex].

[tex]-8\frac{1}{3}[/tex] = [tex]\frac{-25}{3}[/tex].

Now we have to simplify [tex]-\frac{28}{9} - (-\frac{25}{3} )[/tex].

= [tex]-\frac{28}{9} + \frac{25}{3}[/tex].

After applying LCM to the denominators, Multiply the second term with 3 in both numerator and denominator.

= [tex]-\frac{28}{9} + \frac{75}{9}[/tex].

=[tex]\frac{-28+75}{9}[/tex].

=[tex]\frac{47}{9}[/tex].

Convert the answer in improper fraction form.

[tex]\frac{47}{9}[/tex] = [tex]5\frac{2}{9}[/tex].

Thus the simplified answer is [tex]5\frac{2}{9}[/tex].

Answer: 0.126?

Step-by-step explanation:

A decimal number between 0.25 and 0.125 could be 0.2 or 0.15. These numbers sit within the specified range and comply with the principles of decimal number placement.

The task here is to identify a decimal number that lies between 0.25 and 0.125. To achieve this, we can carefully select a decimal value that stands in the middle of these two numbers. An example of a suitable decimal would be 0.2, as it comfortably sits within this specified range. Another example could be 0.15. These are both valid decimal numbers that reside between 0.25 and 0.125, and their selection adheres to the principles of decimal number placement on a number line.

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Answer:

x^3-x^2-17x+12

Step-by-step explanation:

(x+4)(x^2-5x+3)

x^3-5x^2+3x+4x^2-20x+12

x^3-5x^2+4x^2+3x-20x+12

x^3-x^2-17x+12

Answer:

see attached picture please

Answer:

240.3

Step-by-step explanation:

Remember SohCahToa for the trig. ratios. You always divide two sides.

'o' is opposite side. 'a' is adjacent side. 'h' is hypotenuse side.

Using alternating angles you can find the angle I marked blue (see diagram below). Because the 31° is parallel to the bottom side of the triangle, you can use alternating angles (Z pattern), where both 'insides' of the Z have the same measure.

The blue angle will be our angle of reference (angle we are talking about) represented by this symbol θ.

Since we need to find 'y', the opposite side, and we know 400ft is the adjacent side, use the tangent ratio.

tanθ = opposite / adjacent

tan31° = y / 400ft           Substitute what you know.

y = (400ft)tan31°          Isolate 'y'. Multiply 400ft and tan31°.

y = 240.344......ft      Exact answer on calculator

y ≈ 240.3ft      Answer rounded to nearest tenth

The nearest tenth is the first decimal. Since the second decimal is '4 or less', you round down, keeping the digit of the first decimal the same.

If the second digit was '5 or more', then you would round up.

Answer:

1. a ≥ –4 and a ≤ 4

Step-by-step explanation:

Rule : | a | ≤ 4 ⇔ -4 ≤ a ≤ 4

:)

Answer: -3 and +3

Step-by-step explanation:

Answer:

12(3+4)

Step-by-step explanation:

Answer:

Etc: 12 34

Step-by-step explanation:

Answer:

Step-by-step explanation:

108 = 2*2*3*3*3=2² * 3³

120 = 2*2*2*3*5=2³*3*5

LCM = 2³*3³*5 = 8*27*5= 1080

To find the LCM of 108 and 120, first find their prime factorizations and then multiply the highest power of each prime factor.

To find the Lowest Common Multiple (LCM) of 108 and 120, we can first find their prime factorizations. The prime factorization of 108 is 2 × 2 × 3 × 3 × 3, while the prime factorization of 120 is 2 × 2 × 2 × 3 × 5. We can then find the LCM by taking the highest power of each prime factor from both numbers. So, the LCM of 108 and 120 is 2 × 2 × 2 × 3 × 3 × 3 × 5 = 2,160.

The Lowest Common Multiple (LCM) of 108 and 120 is 1080. This is found by finding the prime factors of each number, and then multiplying together the highest power of each factor.

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The corresponding element in the range when 7 is an element  in the domain is f(5)=179/5

Step-by-step explanation:

Given that the 5 is an element in the domain of f(x)

The function f is defined by f(x)=8x-21/5

To find the corresponding element in the range:

That is put x=5 in the given function f(x)

Therefore f(x) becomes

f(5) = 8(5)-21/5

     =40-21/5

     =179/5

Therefore corresponding element in the range when 5 is an element  in the domain is f(5)=179/5

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Quotient = 2

Solution:

Given expression is [tex]22x^2y^2\div11x^2y^2[/tex].

To find the quotient.

[tex]22x^2y^2\div11x^2y^2=\frac{22x^2y^2}{11x^2y^2}[/tex]

In numerator 22 can be written as 2 × 11.

[tex]\frac{22x^2y^2}{11x^2y^2}=\frac{2\times11x^2y^2}{11x^2y^2}[/tex]

Take common term out in the numerator and denominator.

[tex]\frac{22x^2y^2}{11x^2y^2}=\frac{(11x^2y^2)(2)}{11x^2y^2}[/tex]

Common terms in the numerator and denominator will be cancelled.

[tex]\frac{22x^2y^2}{11x^2y^2}=2[/tex]

Hence the quotient is 2.

Answer:

The guy up top is right its 2 with no mistake.

Step-by-step explanation:

Answer:

Anything with a numerator (top) greater then the denominater (bottom) here are some examples:

[tex] \frac{11}{2} [/tex]

[tex] \tfrac{8}{5} [/tex]

[tex] \frac{399}{7} [/tex]

[tex] \frac{6}{2} [/tex]

Hope this information helps my friend!

Answer:

The total discounted price is 34.93

Step-by-step explanation:

The items in the cart are:

Total cart = $ 41.10

Discount = 41.10 * 0.15 = $ 6.17

Discounted total price = 41.10 - 6.17

Discounted total price = 34.93

Answer:

34.94.

Step-by-step explanation:

First we must find the total price of all the items: =$6.35+$6.35+$12.50+$13.40+$2.50=$41.10.

Next, we can calculate the discount: =(15/100)×$41.10=$6.165.

Therefore, our discounted price is $41.10−$6.165=$34.935≈$34.94.

Answer:

Pythagorean theorem theorem that states that the sum of the squares of the two legs is equal to the square of the hypotenuse in a right triangle

Answer:

Step-by-step explanation:

the quotient is the result of division

the quotient of 6 and z...

6/z <===

** pay attention to the wording...because if it would have said : the quotient of z and 6, it would have been z/6

Answer:

no

Step-by-step explanation:

bc

15/18 cant be simplified no matter what

Answer:

No

Step-by-step explanation:

15/18 can not be simplified

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

6= -6, -3.4=3.4, 2.25=-2.25, 8 1/5=-81/5

Answer:

5 liters of water.

Step-by-step explanation:

Let [tex]y[/tex] be the liters of water that must be added to 15 liters of 40% sugar syrup.

Initially, we have [tex]0.4(15)=6[/tex] liters of sugar syrup, and since adding water does not add any new syrup, the amount of sugar syrup must be the same after the water has been added. After the water has been added, 30% of the solution is sugar syrup, or

[tex]Sugar\:syrup =0.3(15+y)[/tex]

And since this must equal the amount of syrup we had before:

[tex]0.3(15+y)=0.4(15)[/tex]

[tex]4.5+0.3y=6[/tex]

[tex]0.3y=1.5[/tex]

[tex]\boxed{y=5}[/tex]

Thus, 5 liters of water must be added to obtain 30% sugar syrup.

Answer:

5 liters of water

Answer:

12r+6

Step-by-step explanation:

2(6r+3)

2(6r)+2(3)

12r+6

There are 5 short essay questions on test

Solution:

Let "a" be the number of multiple choice questions

Let "b" be the number of short essay questions

Worth of each multiple choice questions = 3 points

Worth of each short essay questions = 8 points

There are 25 questions in total

number of multiple choice questions + number of short essay questions = 25

a + b = 25

a = 25 - b --------- eqn 1

The test is worth 100 points. Theerefore, we frame a equation as:

number of multiple choice questions x Worth of each multiple choice questions + number of short essay questions x Worth of each short essay questions = 100

[tex]a \times 3 + b \times 8=100[/tex]

3a + 8b = 100 --------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

3(25 - b) + 8b = 100

75 - 3b + 8b = 100

5b = 100 - 75

5b = 25

b = 5

Thus there are 5 short essay questions on test

The number of short essay questions on the test is 5.

The science test is worth 100 points and has 25 questions. Let's represent the number of multiple-choice questions as 'x' and the number of short essay questions as 'y'. Each multiple-choice question is worth three points, so the total number of points for the multiple-choice questions is 3x. Each short essay question is worth eight points, so the total number of points for the short essay questions is 8y. We can write two equations to represent the given information:

x + y = 25 (since there are 25 questions in total)

3x + 8y = 100 (since the total points for the test is 100)

To find the number of short essay questions on the test, we need to solve these two equations. By substituting x = 25 - y into the second equation, we can solve for y.

3(25 - y) + 8y = 100

75 - 3y + 8y = 100

5y = 25

y = 5

Therefore, there are 5 short essay questions on the test.

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Answer:

Therefore NFC won 28 games and AFC won 25 games.

Step-by-step explanation:

i) let the number of Super Bowls won by NFC be x

ii) let number of Super Bowls won by AFC be y

iii) therefore it is given that  x + y = 53

iv) and also it is given that x = y + 3

v) substituting the equation in iv) into the equation in iii) we get

  (y +3) + y  =  53    ⇒  2y = 50   therefore y = 25.

vi) substituting the value of y from v) into the equation iv) we get

    x  = 25 + 3 = 28.

Therefore NFC won 28 games and AFC won 25 games.

To solve this mathematics problem, we formulate an equation based on the information that total Super Bowls were 53 and NFC won 3 more than AFC. By solving the equation, we find that NFC won 28 games and AFC won 25 games.

To solve this problem, let's start with the total number of games, which is 53. If the NFC has won 3 more Super Bowls than the AFC, that means the number of games won by both conferences adds up to 53. Let's denote the number of games won by the AFC as 'x'. So, the equation will be:

By combining like terms, we get:

Subtracting 3 from both sides, we have:

Finally, when we divide by 2, we solve for x:

This means that the AFC has won 25 games, and the NFC, having won 3 more, has won 28 games.

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The  expression is equivalent to 8/9 divided by 3/4 is 32/27.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

We have to divide the fraction 8/9 by 3/4.

As, the fraction does not allow division then we will perform the multiplication.

So, 8/9 x 4/3

= 32 / 27

Thus, the required fraction is 32/27.

Learn more about Fraction here:

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Answer:

Step-by-step explanation:

If the baby repeats this sleep pattern until she is awakened at 6 a.m., what ... We have 10 hours between 8PM and 6AM = 10 * 60 = 600 minutes ... Awake 12:15 - 12:30 ... There are 4 periods of 2 hour sleep and 1 period of 1 hour sleep = 4*2(60) + 1(60) ... So 540/600 = 54/60 = 9/10 = 90% of the time asleep.

Answer:

87.5%

Step-by-step explanation:

I am not sure how to set this up....so I am just gonna try to figure this a different way....without any formula

8 p.m - 10 pm.......awake for 15 minutes

10 pm - 12 am......awake 15 minutes

12 am - 2 am.......awake 15 minutes

2 am to 4 am.....awake 15 minutes

4 am to 6 am....awake 15 minutes

so from 8 pm to 6 am....that is a total of 10 hrs.....and in those 10 hrs, the baby was awake 5(15) = 75 minutes.....change 10 hrs to minutes.....1 hr = 60 min...so 10 hrs = (10 * 60) = 600 minutes

so in 600 minutes, the baby was awake 75 minutes.....that means the baby was asleep (600 - 75) = 525 minutes

525/600 = 0.875 = 87.5% <=== baby was asleep

or maybe this way....for every 2 hrs, the baby was awake 15 minutes....means the baby was asleep (120 - 15) = 105 minutes.

2 / 105 = 10 / x

2x = 1050

x = 1050/2

x = 525 minutes.....so the baby was asleep 525 minutes out of 600 minutes.

525/600 = 0.875 = 87.5%

I am getting the same answer either way