A cafeteria is in the shape of a rectangle. The length of the rectangle is four times its width. The area of the cafeteria is 14,800 square feet. What is the length of the cafeteria? Round to the nearest foot.

The values of the coefficients and constant are 1, -8 and -5

Standard quadratic equation

The standard quadratic expression is given as:

y = ax^2 + bx + c

where a, b and c are the constant

Given the quadratic function f(p) = p2 – 8p – 5, on comparing:

a = 1

b = -8

c = -5

Hence the values of the coefficients and constant are 1, -8 and -5

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The quotient of (x^5 – 3x^3 – 3x^2 – 10x + 15) and (x^2 – 5) is a  (x^5-3x -3 - 24x/(x²-5)) polynomial.

Quotients are the number that is obtained by dividing one number by another number.

The quotient of (x^5 – 3x^3 – 3x^2 – 10x + 15) and (x^2 – 5) is a polynomial.

(x^5 - 3x³ - 3x² - 10x + 15) / p = x² - 5

p = (x^5 -3x³ - 3x² - 10x + 15)/(x² - 5)

= x^5 -3x - 3 - 24x/(x² - 5)

x^5 3x³ + 15x

x^5 - 3x² - 24x + 15

x^5 - 3x² + 15

0 - 24x + 0

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Answer: C

Step-by-step explanation:

Answer:

308 minutes or 5 hours and 8 minutes

Step-by-step explanation:

First, let's add the bicycles of both boys and girls together:

6 + 8 = 14

Now, let's multiply that number by 22 since she will have to assemble all of those bicycles and it will take 22 minutes for each:

22 x 14 = 308

It will take a total of 308 minutes or 5 hours and 8 minutes to assemble all of those bicycles.

Answer:

210

Step-by-step explanation

One yard is equal to 3 feet so the simplest way is to divide the number of feet by 3 and that will give you your answer.

Answer:

210

Step-by-step explanation:

Answer:

61-33...

Step-by-step explanation:

If he gave away 61 from his 33 then its 61-33

Step-by-step explanation:

remember. the radius is always half the diameter.

volume of a cylinder

pi × r² × height

pi×7.5²×48 = pi×56.25×48 = 8,482.300165... in³

volume of a sphere

4/3 × pi × r³

and that volume should be the same as the cylinder. so,

4/3 × pi × r³ = pi×56.25×48

4/3 × r³ = 56.25 × 48

1/3 × r³ = 56.25 × 12

r³ = 56.25 × 36 = 7.5² × 6² = (7.5×6)² = 45² = 2025

[tex]r = \sqrt[3]{2025} [/tex]

which would be 12.65148998... in.

Answer:

4

Step-by-step explanation:

Answer:

[tex]\color{indigo}\rule{1pt}{1000000pt}[/tex]

The solution of the given quadratic equation are,

[tex]x=\frac{-5-\sqrt{57} }{2}[/tex],[tex]x=\frac{-5+\sqrt{57} }{2}[/tex]

The equation to solve is given as

[tex]x^2=-5x+8[/tex]

Rearrange the given equation in standard form, [tex]ax^2+bx+c=0[/tex]

where,  a,b and c are constants.

Therefore, we add 5x-8 on both sides to get,

[tex]x^2+5x-8=0[/tex]

Here, a=1,b=5 and c=-8

The solution to the above equation is

[tex]x=\frac{-b\±\sqrt{b^2-4ac} }{2a}[/tex]

Use the value of a,b,c in the quadratic formula and solve for x

[tex]x=\frac{-5\±\sqrt{5^2-4(1)(-5)} }{2(1)}[/tex]

[tex]x=\frac{-5\±\sqrt{25+35} }{2(1)}[/tex]

[tex]x=\frac{-5\±\sqrt{57} }{2(1)}[/tex]

Therefore, the solutions are

[tex]x=\frac{-5-\sqrt{57} }{2},x=\frac{-5+\sqrt{57} }{2}[/tex]

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Answer:

answer is b

Step-by-step explanation:

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. The account which is earning compount interest will earn $41.19 more on interest.

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,

[tex]\text{Simple Interest}= \dfrac{P \times R \times T}{100}[/tex]

where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.

The interest on account S which earns simple interest at rate of 4.5% can be written as,

[tex]\text{Interest in Account S}= \dfrac{P \times R \times T}{100} = \dfrac{\$400 \times 4.5 \times 10}{100} = $180[/tex]

The interest on accout C which earns compound interest at a rate of 4.5% can be written as,

[tex]\text{Interest in Account C}=P(1+r\%)^n - P\\[/tex]

[tex]\text{Interest in Account C}=\$400(1+4.5\%)^{10} - $400 = $221.19[/tex]

The difference in the amount earned by the two account will be,

[tex]\rm Difference = (Interest\ in\ Account\ C) -(Interest\ in\ Account\ S)[/tex]

                [tex]=\$221.19 - \$180\\\\=\$ 41.19[/tex]

Hence, the account which is earning compount interest will earn $41.19 more on interest.

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Answer:

answer a

Step-by-step explanation:

thats rlly the only one that makes sense to me, i really hope this will help <3

The expression that Yuri should write will be t < -3. Then the correct option is C.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The temperature on a winter day was less than –3 degrees Fahrenheit.

Yuri wants to write an inequality for the temperature on the winter day.

Yuri uses the variable t to represent the temperature.

The sign used for less than is " < ".

t < -3

The expression that Yuri should write will be t < -3.

Then the correct option is C.

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Answer:

30ft³

Step-by-step explanation:

asuming it has the shape of a rectangular prism

formula would be

V=whl

step 1 swap the numbers

V= (2)(5)(3)

step 2 multiply

V= 30

step 3 add the labels

V=30ft³

Considering the dilation, the surface area of the rectangular prism is of 0.432 units².

The surface area of a rectangular prism of dimensions l, w and h is given by:

Sa = lwh.

In this problem, the dilation means that all dimensions are divided by 5, hence they will be considered as:

w = h = 0.6, l = 1.2.

Hence the surface area of the prism will be of:

Sa = lwh = 1.2 x 0.6 x 0.6 = 0.432 units².

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The surface area of the solid created upon dilation by a factor of 5 is 2250 unit²

An equation is an expression that shows the relationship between two or more variables and numbers.

The solid below is dilated by a scale factor of 5. Hence:

New length = 6 * 5 = 30, new width = 3 * 5 = 15, new height = 3 * 5 = 15

Surface area = 2(30 * 15 + 30 * 15 + 15 * 15) = 2250 unit²

The surface area of the solid created upon dilation by a factor of 5 is 2250 unit²

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Answer:

4 hours.

Step-by-step explanation:

2/3 * 6

= 12/3

= 4 hours.

Answer:

4

Step-by-step explanation:

Hope this helps <3

try to stay out of trouble lol

Answer:

The number of times people got cheese and wheat is 1200

Step-by-step explanation:

Hope this helps! Have a good day! :)

Answer:

[tex]\sf \dfrac{12}{19}[/tex]

Step-by-step explanation:

To begin, add the column and row totals to the table (see attachment).

Let W = Wheat

Let C = With cheese

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

[tex]\implies \sf P(W)=\dfrac{1900}{3125}=\dfrac{76}{125}[/tex]

[tex]\implies \sf P(C)=\dfrac{2000}{3125}=\dfrac{16}{25}[/tex]

[tex]\implies \sf P(W \cap C)=\dfrac{1200}{3125}=\dfrac{48}{125}[/tex]

As the events W and C are not independent, we can use the formula:

[tex]\sf P(C\: | \:W)=\dfrac{P(W \cap C)}{P(W)}[/tex]

Substituting the values into the formula:

[tex]\sf P(C\: | \:W)=\dfrac{\frac{48}{125}}{\frac{76}{125}}=\dfrac{48}{76}=\dfrac{12}{19}[/tex]

Answer:

four spaces to the left, and 6 spaces up.

Answer: 12

Step-by-step explanation:

[tex]\mathrm{The\:mode\:is\:the\:term\:in\:the\:data\:set\:that\:appears\:the\:most.}[/tex]

[tex]\mathrm{If\:there\:is\:more\:than\:one\:term\:that\:appears\:the\:most,\:then\:there\:is\:no\:mode.}[/tex]

[tex]\mathrm{Count\:the\:number\:of\:times\:each\:element\:appears\:in\:the\:list}[/tex]

[tex]\begin{pmatrix}11&13&14&12\\ 1&2&2&3\end{pmatrix}[/tex]

[tex]\mathrm{The\:most\:common\:element\:in\:the\:list\:is\:12}[/tex]

Answer:

I'm sure It's 12

Step-by-step explanation:

To find the mode, order the numbers lowest to highest and see which number appears the most often.

11, 12, 12, 12, 13, 13, 14, 14

11=1

12=3 is the most common element

13=2

14=2

Answer:

CE = 6

Step-by-step explanation:

we use the proportion relationship:

[tex]\frac{AB}{BD} = \frac{AC}{CE\\}\\then[/tex]

[tex]\frac{2}{3} = \frac{4}{CE}\\\\then[/tex]

2×CE = 3 ×4 (cross multiply)

then

2×CE = 12

then

CE = 12/2 = 6

Answer:

the answer is (C) DOL

Step-by-step explanation:

Answer:

A

Step-by-step explanation

Dilation: A shape is scaled up or down by a scale factor

Translation: A shape is moved on a coordinate plane to a different spot.

A works because lets you one side (the bottom side). The bottom has a length of 3, and the bigger one has a length of 6, showing a scale factor of 2.

Answer:

B.  The value of [tex]\sqrt{8}[/tex] is between 2.5 and 3.

Step-by-step explanation:

The square root of 8 is 2.83

Answer:

21 and 32 are the numbers

Step-by-step explanation:

Let assume that the the two numbers are X and Y and that X is the large number.

According to the question,

X + Y = 53 .................. Equation 1

then,  X = 11 + Y........... Equation 2

Substitute equation 2 into equation 1.

[11 + Y] + Y = 53

11 + 2Y = 53

2Y = 53 - 11 = 42

2Y = 42

Y = 42 / 2 = 21,

Therefore, Y = 21 [Small number].

According to equation 1,

X +Y = 53

X + 21 = 53

X = 53 - 21 = 32.

Therefore, X = 32 [Big number]

Answer:

2d - 9.

Step-by-step explanation:

That would be

double d = 2d

subtract  9 = -9   to give:

2d - 9.

Answer:

b=2 and c=6

Step-by-step explanation:

According to the question,

a+b=c

Let b=2 and c =6 then, we get,

4+2=6

or, 6=6

proved

Answer:

Volume of Cube = length cube

Total surface area=2(lb+lh+bh)

Volume of Cuboid=l×b×h

I think it will help you.

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

The Correct choice is 4

If we take value of x as 6 in the given function, then we will get the value of y as 4, as shown in the graph.

Answer: d=-2

Step-by-step explanation:

As we know the order of operations are

1) Parenthesis/Brackets

2) Exponents

3) Multiplication/Division

4) Addition/Subtraction

However, when you solve equations you must do the order of operations backwards

So start by adding 1 to both sides because whatever you do to one side of the equation you must do to the other side

[tex]5d-1=-11\\5d-1+1=-11+1\\5d=-10[/tex]

Now divide both sides by 5 to isolate d

[tex]5d=-10\\\frac{5d}{5} =\frac{-10}{5} \\d=-2[/tex]