James wants to build a wooden barrel to hold rain water to use for irrigation. He wants the height of the barrel in feet to be 4 less
than the area of the base in square feet. He also wants the area of the base in square feet to be equal to its perimeter in feet. He
also needs to place a pump inside the barrel to move the collected water. After the pump is put inside the barrel, he needs it to
still hold at least 90 cubic feet of water
The cost for the materials to build the barrel will be 58 per square foot. Since the barrel is meant to catch rain water, he will not
need a top. The cost of the pump is proportional to its volume. For each cubic foot of volume that the pump takes up the cost
will be 550 James can only afford to spend up to $1,100 on this project
If x represents the area of the base of the barrel in square feet and y represents the volume of the pump in cubic feet, then which
of the following systems of inequalities can be used to determine the dimensions of the barrel and the volume of the pump?

Answer:

Felicia is 7 years old

Explanation:

The variable, d, can represent Danny's age.

The variable, f, can represent Felicia's age.

Basically, using the information provided, you can make two equations.

1.) d - f = 21

2.) d + f = 35

This is a system of equations. To solve for this, I'm going to subtract the 2 equations:

    d - f = 21

-   d + f = 35

-------------------------

    -2f = -14

       f = 7

If Felicia is 7, and they're total ages added is 35, subtract 7 form 35

35 - 7 = 28

So, Danny would be 28.

To double check your answers;

28 + 7 = 35

28 - 7 = 21

So Felicia is 7 years old. I hope this helps! :)

Answer:

1. a. 3xy²(7x²y³ + 5x - 4y)

2. a. (3x + 2)(5x + y)

3. d. (2a + b)(5x - 4)

Step-by-step explanation:

For #1, your answer was missing an exponent, which I boldfaced. Every term has a y² in common. Then, in numbers 2 and 3, just factor each group one at a time.

Ex: [10ax + 5bx] - [8ay - 4by]

Answer:

The solution is:

Step-by-step explanation:

We have the following equation

[tex]-4(2x+3)=2x+6-(8x+2)[/tex]

To solve the equation apply the distributive property

[tex]-4(2x+3)=2x+6-(8x+2)[/tex]

[tex]-4*2x+3(-4)=2x+6-(1)*8x+2*(-1)[/tex]

Now simplify the expression

[tex]-8x-12=2x+6-8x-2[/tex]

[tex]-8x-12=-6x+4[/tex]

Add 6x +12 on both sides of the equation

[tex]-8x-12+6x+12=-6x+4+6x+12[/tex]

[tex]-2x=4+12[/tex]

[tex]-2x=16[/tex]

Divide both sides of the equality between -2

[tex]\frac{-2}{2}x=\frac{16}{-2}[/tex]

Answer:

The y-intercept indicates that the phone card started with 850 minutes. The slope indicates that 50 minutes were used per day.

Step-by-step explanation:

The graph cuts the y-axis at 850.This indicates that the phone card started with 850 minutes before it was used.

The slope of the graph is -50.This means that in every increase of one in the input variable (number of days), you get a decrease of 50 in the output variable (number of minutes remaining). This indicates every day, 50 minutes were used, hence 50 minutes reduced from the card per day.

The answer is A. The y-intercept indicates that the phone card started with 850 minutes. The slope indicates that 50 minutes were used per day.

This is because she started with 850 and the graph shows a decrease, so this means that she loses 50 per day or that she uses 50 per day.

Answer:

I know this is way late but its(11)

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Answer:

113

Step-by-step explanation:

Total mass of waffles = 45 x 5 = 225 pounds

No. of people needed = 225 / 2 + 1 = 112 + 1 = 113

You need to add 1 because 112 people can only eat 224 pounds, so the last person eats only 1 pound

Answer:

113 people are necessary to eat all of the waffles.

Step-by-step explanation:

There are 5 stacks of huge waffles that each weigh 45 pounds.

Hence, Total amount of waffles=5×45 pounds

                                                   =225 pounds

A person can eat 2 pounds.

and 225/2=112.5

112 people can only eat 224 pounds, so the last person eats only 1 pound.

⇒ 113 people are necessary to eat all of the waffles.

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y\geq (x-4)^{2}[/tex]

The solution is the shaded area above the vertical parabola

using a graphing tool

see the attached figure

Answer:

x = 7

Step-by-step explanation:

recognize that this is a right triangle with one of the  internal angles = 45°. This means that the other angle not shown is 180 - 90 - 45 = 45°

This makes the triangle an isosceles triangle.

If so, x must be the same length as the other side adjacent to 90°

i.e x = 7

Answer:

The distinct factors of 75 are 1, 3, 5, 15, 25, 75.

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

6

Step-by-step explanation:

1,3,5,15,25,75

Answer:

[tex] (3y^2-5)(y^2+1) [/tex]

Step-by-step explanation:

Let's see if we can think of two numbers that multiply to be 3(-5)=-15

andd add up to be -2

How about -5 and 3? That work's! :)

[tex]3y^4-5y^2+3y^2-5[/tex]

Factor by grouping!

[tex]y^2(3y^2-5)+1(3y^2-5)\\(3y^2-5)(y^2+1)[/tex]

The polynomial 3y^4 - 2y^2 - 5 does not appear to be factorable with integer values. The reference to placing the factors in a particular location on a grid would likely relate to a tool or diagram provided by your instructional material.

To factor the cubic polynomial 3y4 - 2y2 - 5, we first find the common factor which in this case is none. The next step is to try grouping, and if that's not possible, we can solve the polynomial using the quadratic formula or synthetic division. However, this polynomial does not seem to be factorable with integer values.

Unfortunately, without additional context, it's not clear what grid the problem refers to, or where the location you're supposed to place the factors is. It's likely this refers to some sort of tool or diagram provided by your teacher or textbook. In general, you would write down the factors in their proper locations in that tool or diagram, according to the rules or guidelines you were given.

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Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

let [tex]log_{125}[/tex] 5 = n, then

5 = [tex]125^{n}[/tex]

note that 125 = 5³ ⇒ [tex](5^3) ^{n}[/tex] = [tex]5^{3n}[/tex]

Since bases are equal ( both 5) equate the exponents

3n = 1 ( divide both sides by 3 )

n = [tex]\frac{1}{3}[/tex]

The value of the expression log₁₂₅5 is 1/3.

The correct option is A.

The inverse of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.

Given:

A logarithmic expression,

let log₁₂₅5 = x

Then simplifying,

5 = (125)ˣ

That means,

x = 1/3

Therefore, x = 1/3.

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Answer:

Last Option

Step-by-step explanation:

Given expression is:

[tex]\sqrt[4]{\frac{24x^6y}{128x^4y^5}}[/tex]

Simplifying the radicand

[tex]=\sqrt[4]{\frac{8*3*x^6*y}{8*16*x^4*y^5}}\\=\sqrt[4]{\frac{3*x^6*y}{16*x^4*y^5}}\\=\sqrt[4]{\frac{3*x^6*y}{2^4*x^4*y^5}}\\=\sqrt[4]{\frac{3*x^{(6-4)}}{2^4*y^{(5-1)}}}\\=\sqrt[4]{\frac{3*x^{2}}{2^4*y^{4}}}\\Applying\ Radical\\= \frac{\sqrt[4]{3x^2}}{2y}[/tex]

Hence,

Last option is correct ..

Answer:

3.2 miles

Step-by-step explanation:

The "mean" of a set of numbers is the average. To get this, you add up all of the numbers and then divide by however many there are. So, let's lay out the races that Kim ran.

1, 1, 1, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 10

These numbers add up to 45 total miles ran. You can add them up individually or make an equation.

x = (3 × 1) + (6 × 2) + (4 × 5) + (1 × 10)

x = 3 + 12 + 20 + 10

x = 15 + 30

x = 45

Now, divide by the total number of races, 3 + 6 + 4 + 1 = 14

So, the mean will be

45 ÷ 14 = 3.21 or about 3.2

Answer:

Straight to the point : 3.2

Explanation is above me my friends.

Answer:

[tex]x=2- 3\sqrt{2}[/tex] or [tex]x=2+3\sqrt{2}[/tex]

Step-by-step explanation:

We want to solve for x in the equation;

[tex](x-2)^2-18=0[/tex]

Add 18 to both sides

[tex](x-2)^2=18[/tex]

We solve by the square root method.

[tex]x-2=\pm \sqrt{18}[/tex]

[tex]x-2=\pm 3\sqrt{2}[/tex]

Add 2 to both sides

[tex]x=2\pm 3\sqrt{2}[/tex]

Split the plus or minus sign.

[tex]x=2- 3\sqrt{2}[/tex] or [tex]x=2+3\sqrt{2}[/tex]

Therefore the exact solution is [tex]x=2- 3\sqrt{2}[/tex] or [tex]x=2+3\sqrt{2}[/tex]

3.95(3) + 8.95b = 47.65

11.85 + 8.95b = 47.65

Subtract 11.85 from both sides.

8.95b = 35.8

Divide 8.95 from both sides.

b = 4

Hugh bough 4 books.

Answer: Option C

[tex]y=5[/tex], [tex]x=10[/tex]

Step-by-step explanation:

If the lines m and n are parallel then the large triangle and the small triangle are similar triangles, because they have equal angles.

By definition for similar triangles it is satisfied that if they have sides of length a, b, c and a ', b' and c 'then:

[tex]\frac{a}{a'}=\frac{b}{b'} =\frac{c}{c'}[/tex]

In this case

[tex]a = 12\\a' = 4\\c = 15\\c' = y[/tex]

So:

[tex]\frac{12}{4}=\frac{15}{y}[/tex]

[tex]3=\frac{15}{y}[/tex]

[tex]y=\frac{15}{3}[/tex]

[tex]y=5[/tex]

Therefore

if [tex]x+y=15[/tex] and [tex]y=5[/tex] then [tex]x =10[/tex]

Finally

[tex]y=5[/tex], [tex]x=10[/tex]

In the given equation, x is the amount of merchandise she sold.

Replace x with 1900 and solve.

0.24(1900) + 300 = 456 + 300 = 756

Her salary would be $756

Answer:

Step-by-step explanation:

https://brainly.com/question/2264840 Link to this question, but the answer is:

Carissa receives 17$ for each 100$ of merchandise she sells.This is on top of the traditional rate of 300 dollars a month.She will make 623$ for 1900$ worth of merchandise.

Answer:

Sometimes

Step-by-step explanation:

Note that the word "collinear" means lying on the same line.

The three points can be on the same line, but not always. For example, the three points can form a triangle, a square-u, etc.

~

Answer:

sometimes

Step-by-step explanation:

Three points are sometimes collinear

There are infinite points on a line, so they can be collinear.

But 3 points make a triangle, so they are not on a line, so they are not collinear.

Step-by-step explanation:

You use PEMDAS parenthesis, exponents, multiplication, addition, subtraction.

First you will change the -(-3) into positive

-55+-7x6+3x4

Now change the +-7 into negative 7

-55-7x6+3x4

Now multiply 7 times 6...

-55-42+3x4

Now multiply 3 times 4...

-55-42+12

Now add the two negatives, 55 and 42

-97+12

Now add those...

-85

Answer:

c. 20%

Step-by-step explanation:

60 is 20% of 300

The answer to the question is 25%

The percent of profit can be calculated by using the formula:

Profit Percentage = (Profit / Cost Price) x 100%

Given that Cindy made a profit of $60 by selling her camera for $300, her profit percentage would be:

Profit Percentage = (60 / 240) x 100% = 25%

Answer:

[tex]\large\boxed{\{-7,\ 1\}}[/tex]

Step-by-step explanation:

[tex]x^2+6x=7\\\\x^2+2(x)(3)=7\qquad\text{add}\ 3^2=9\ \text{to both sides}\\\\x^2+2(x)(3)+3^2=7+9\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+3)^2=16\Rightarrow x+3=\pm\sqrt{16}\\\\x+3=-4\ \vee\ x+3=4\qquad\text{subtract 3 from both sides}\\\\x=-7\ \vee\ x=1[/tex]

Answer:

Answer is =2x^3+3x^2-11x-6

Step-by-step explanation:

First of all multiply first and second bracket.

=x(2x+1) -2(2x+1)

=2x^2+x-4x-2

=2x^2-3x-2

Now multiply 2x^2-3x-2 with (x+3)

=x(2x^2-3x-2) +3(2x^2-3x-2)

=2x^3-3x^2-2x+6x^2-9x-6

=2x^3+3x^2-11x-6

The expansion and simplification of the expression (2x + 1)(x - 2)(x + 3) is 2x^3 + 3x^2 - 11x - 6.

To expand and simplify the expression (2x + 1)(x - 2)(x + 3), we use the distributive property (a(b + c) = ab + ac) to distribute each term of one binomial with each term of the others.

We start by expanding the first two brackets : (2x + 1)(x - 2). This gives 2x^2 - 4x + x - 2 or, 2x^2 - 3x - 2.

Now, we expand the above result with (x + 3): (2x^2 - 3x - 2)(x + 3) yielding 2x^3 - 3x^2 - 2x + 6x^2 - 9x - 6.

When we simplify that, we get : 2x^3 + 3x^2 - 11x - 6. So, the expansion and simplification is : (2x + 1)(x - 2)(x + 3) = 2x^3 + 3x^2 - 11x - 6.

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Answer:

x = √y+18

Step-by-step explanation:

Given

[tex]y = x^2-18[/tex]

In order to solve the equation for x, we have to isolate x on one side of the equation

So,

[tex]y+18 = x^2 -18 + 18\\y + 18 = x^2[/tex]

We have to find the value for x, so taking square root on both sides

[tex]\sqrt{x^2} = \sqrt{y+18}[/tex]

Solving the squre root

x = [tex]x = \sqrt{y + 18}[/tex]

Hence,

x = √y+18 is the correct answer ..

Substitute the numbers for xy

(6)(3)

= 18

Answer is 18

The expression xy for x = 6 and y = 3 is 18.

We have to evaluate, the expression xy for x = 6 and y = 3.

According to the question,

To find the expression xy calculation must be done in a single unit following all the steps given below.

The value of x = 6 and y = 3,

Then,

The multiplication of xy is,

[tex]= x\times y \\\\= 6 \times 3\\\\= 18[/tex]

Hence, The expression xy for x = 6 and y = 3 is 18.

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Answer:

[tex]330,\frac{5\pi }{3},\frac{7\pi }{6}, \frac{2\pi }{3} ,\frac{\pi }{2}[/tex]

Step-by-step explanation:

We have to find the alternate angles regarding π

So,

[tex]\frac{\pi }{2} = 90 \\330\\\frac{5\pi }{3} = 300\\\frac{7\pi }{6} = 210\\\frac{2\pi }{3} = 120[/tex]

As we have all the angles in number form, we can sort them in descending order to get the answer

330, 300, 210, 120, 90

Writing using pi form

[tex]330,\frac{5\pi }{3},\frac{7\pi }{6}, \frac{2\pi }{3} ,\frac{\pi }{2}[/tex]

Hence, Option D is correct ..

Answer:

D) 330, [tex]\frac{5\pi }{3}[/tex], [tex]\frac{7\pi }{6}[/tex], [tex]\frac{2\pi }{3}[/tex], [tex]\frac{\pi }{2}[/tex]

Step-by-step explanation:

To find the order from greatest to least, we need to convert all [tex]\pi[/tex] terms to degrees.

We know that π = 180°

[tex]\frac{\pi }{2} = \frac{180}{2} = 90[/tex]

[tex]\frac{5\pi }{3} = \frac{5*180}{3} = \frac{900}{3} = 300[/tex]

[tex]\frac{7\pi }{6} = \frac{7*180}{6} = \frac{1260}{6} = 210[/tex]

[tex]\frac{2\pi }{3} = \frac{2*180}{3} = \frac{360}{3} = 120[/tex]

Now we have converted all in degrees. Let's arrange them from greatest to least.

330, 300, 210, 120, 90

Let's write them using [tex]\pi[/tex] term.

330, [tex]\frac{5\pi }{3}[/tex], [tex]\frac{7\pi }{6}[/tex], [tex]\frac{2\pi }{3}[/tex], [tex]\frac{\pi }{2}[/tex]

Therefore, the answer is D) 330, [tex]\frac{5\pi }{3}[/tex], [tex]\frac{7\pi }{6}[/tex], [tex]\frac{2\pi }{3}[/tex], [tex]\frac{\pi }{2}[/tex]

Answer:

A = (3,-2)  

reflect along the y -axis ; set x=-x  

(-3,-2)  

reflect along the x-axis ; set y=-y  

A' = (-3,2)  

Same for B,C and D  

ABCD is reflected across the y-axis and then the x-axis.

Step-by-step explanation:

Answer:

A )rotate 90 degrees counterclockwise,then shift 2 units up.

Step-by-step explanation:

Given  : graph .

To find : what transformation were applied to ABC to obtain A’B’C.

Solution : We have given graph

Parent ABC triangle with coordinates A(2 ,2) ; B (5 ,6) ; C ( 8 , 2).

Transformed triangle with coordinates  A' (-2 ,4) ; B' (-6 ,7) ; C' ( -2 ,15).

By the rotational of 90° counter clockwise : (x ,y) →→ ( -y , x ).

And it is shifted by 2 unit up

(x ,y) →→ ( -y , x + 2 ).

A(2 ,2) →→ A' (-2 ,4)

B (5 ,6) →→ B' (-6 ,7)

C ( 8 , 2) →→ C' ( -2 ,15).

Therefore, A )rotate 90 degrees counterclockwise,then shift 2 units up.

Answer:

D

Step-by-step explanation:

Since the triangle is right using the cosine ratio to solve for BC

noting that the exact value of cos45° = [tex]\frac{1}{\sqrt{2} }[/tex], so

cos45° = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{BC}{n}[/tex]

Multiply both sides by n

n × cos45° = BC

n × [tex]\frac{1}{\sqrt{2} }[/tex] = BC

[tex]\frac{n}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex] = BC

Hence BC = [tex]\frac{n\sqrt{2} }{2}[/tex] → D

The right-angle triangle is given with one angle of 45 degrees. The length of segment BC is n√2/2.

A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse.

The angle of a right angle is always 90 degrees.

Since the triangle is right angle

by using the cosine ratio to solve for BC

The value of cos45° = 1/√2 ,

So,

cos45° = BC / AC = BC / n

Multiply both sides by n

n × cos45° = BC

n × 1/√2 = BC

n/√2 × √2 /√2 = BC

Hence, BC = n√2/2

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Answer:

Step-by-step explanation:

5 * 5 * 5 * 5 * 5 = 5^5

Written in Latex, which is the best way to show this, the answer is

[tex]5^{5}[/tex]

I think you might mean B. If you do then it is correct, but it must be shown as 5^5

Answer:

6a^4-2a

Step-by-step explanation:

First step: Distributive Property -2a^4-2a+8a^4

Second step: Combine like terms 6a^4-2a

Answer:

x<8

Step-by-step explanation:

We have one equation and one inequation:

8=x+y                      [1]

y>0                          [2]

Solving [1] for 'y' we have:

8=x+y → y = 8-x

If y>0, then 'x' must be less than 0. Given that if 'x' is equal or greater than 8, 'y' will take negative values.

Then: x<8