The side length, s, of a cube is 3x + 2y. If V = s3, what is the volume of the cube? 3x3 + 18x2y + 36xy2 + 8y3 27x3 + 54x2y + 18xy2 + 2y3 27x3 + 18x2y + 12xy2 + 2y3 27x3 + 54x2y + 36xy2 + 8y3

The area of a square is calculated suing the formula x^2, where x is a side length of the square. This is just like length times width because a square has equal side lengths.

Take the left side and add the two lengths together because they form one side length of the square. A side length of the square is x + 4.

To find the area using the side length x + 4, you would square the side length. Your answer is (x + 4)^2.

Answer:

SSS Congruence Postulate ​​

Step-by-step explanation:

we know that

The SSS Congruence Postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

In this problem

PN≅QR

NQ≅RP

PQ≅QP -----> is the same side

so

Three sides of triangle PNQ are congruent with three sides of triangle QRP

therefore

△PNQ and △QRP are congruent by SSS Congruence Postulate ​​

SSS Congruence Postulate or theorem proves that △PNQ and △QRP are congruent

According to the dictionary, congruent (of figures) is identical in form; coinciding exactly when superimposed. Two figures or objects are congruent if they have the same shape and size.

According to the picture attached, the answer is SSS Congruence Postulate ​​Because I have three pairs of congruent sides such as

PR = NQ is one pair, QR = NP is another pair, then PQ = PQ is the third pair

SSS Congruence Postulate or theorem proves that △PNQ and △QRP are congruent

Which postulate or theorem proves that △PNQ and △QRP are congruent?

.

The other example can be seen in the second attachment of picture. The question is still the same: Determine which postulate or theorem can be used to prove that ABC = DCB!

Then AC = DB

AB = DC

BC = BC, This side is equal to itself

Therefore the three sides of one triangle equal to 3 sides of the other. It means that the triangles are congruent. Therefore the answer is SSS

Hope it helps you to learn more about triangle.

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Solution:

This problem is a permutation because the order matters here. This means that choosing A as King, B as Knight, C as Bishop and D as Rook results in a different arrangement from B as King, A as Knight, D as Bishop and C as Rook. We would count them both because in the first case A is King, but in the second case A is Knight.

Therefore, the possible number of ways are given below:

[tex]19P4=\frac{19!}{(19-4)!} =\frac{19 \times 18 \times 17 \times 16 \times 15!}{15!} =19 \times 18 \times 17 \times 16 =93024[/tex]

Hence there will be 93024 ways 19 members of a chess club fill the offices of King, Knight, Bishop, and Rook.

There are 19 members in the chess club, and they can fill the offices of King, Knight, Bishop, and Rook in 38760 ways.

In how many ways can the 19 members of a chess club fill the offices of​ King, Knight,​ Bishop, and​ Rook.

To determine the number of ways to fill the offices, we use the concept of permutations. Since each office must be filled by a different member, the number of ways is calculated as 19P4 = 19! / (19-4)! = 38760 ways.

a. 500 X 12 =

b. 20,000

Answer:

[tex]x < 17.89[/tex] or [tex]x > 18.61[/tex] , since [tex]\left | x-18.25 \right |>0.36[/tex]

Step-by-step explanation:

According to the question the weight is rejected if it is more than 0.36 oz, the weight should not be beyond 0.36 oz that is from the target weight of 18.25.  

We can say that, the difference between the actual weight and the target weight is greater than 0.36 oz.

Lets say the actual weight is 'x'. So,

[tex]x-18.25>0.36[/tex]

But there can be times when the actual weight 'x' could be less than 0.36, So the order will be changed:

[tex]18.25-x>0.36[/tex]

The absolute value will sum up these two into a single inequality:

[tex]|x-18.25|>0.36[/tex]

Simplifying the inequalities, we get:

[tex]x-18.25>0.36[/tex]

[tex]x>18.61[/tex]   (we have added 18.25 on both sides)

 [tex]18.25-x>0.36[/tex]

Subtracting 18.25 from both the sides we get:

[tex]-x>-17.89[/tex]

After sign change it is:

[tex]x<17.89[/tex]

So we can see that only [tex]x < 17.89[/tex] or [tex]x>18.61[/tex] since [tex]\left | x-18.25 \right |>0.36[/tex] is the one that represents the scenario given above.

A) the growth is 56% per week. The 1.56 is multiplying the weight of the pumpkin now by the 56% to get the total weight after the 56% increase.

B) Replace P with 80 and solve for n:

80 = 25(1.56)^n

Divide each side by 25:

80/25 = 1.56^n / 25

3.2 = 1.56^n

Take the natural logarithm of both sides:

ln(3.2) = ln(1.56^n)

Remove the exponent:

ln(3.2) = n(ln(1.56)

Divide both sides by ln(1.56)

n = ln(3.2) / ln(1.56)

n = 2.6 weeks, round to 3 weeks.

C)  Change 1.56 to 1.32 and redo the same calculation from B.

80 = 25(1.32)^n

80/25 = 1.32^n /25

3.2 = 1.32^n

ln(3.2) = ln(1.32^n)

ln(3.2) = n(ln(1.32)

n = ln(3.2) / ln(132)

n = 4.2, round to 4 weeks.

Answer:

Refer answer below

Step-by-step explanation:

Given is a graph in the interval (-infinity, infinity).

From the graph we observe that it is continuous graph.

The curve is decreasing for x <-2 and increases for (-2,1) and again decreases from (1,3) then increases from (3,infinity)

Hence f'(x) >0 for (-2,1) and (3,infinity)

f'(x) <0 for (-infty, -2) and (1,3)

From the above we find that f'(x) =0 for x=-2,1,and 3

Extreme points are -2,1 and 3

Absolute and local minima at x=-2, y=-9.67

Local maxima at (1,6.08) and again

local minima at (3,0.75)

Absolute maxima  lies at infinity

Answer:

 Option 4. overall minimum in (-2.9.67)

Step-by-step explanation:

A global maximum point (x0, f (x0)) is defined as the point at which f (x0) is the maximum value of the function. That is, there is no value in the domain of f (x) other than x0 where f (x) is greater than f (x0)

A global minimum point (x0, f (x0)) is defined as the point at which f (x0) is the smallest value of the function. That is, there is no value in the domain of f (x) other than x0 where f (x) is less than f (x0)

Based on that deficion we must look for the point where f (x) has the lowest value.

That point is (-2.9.67)

Therefore that is the overall minimum of the function.

Although the function has a maximum in (1.6.08), the function keeps growing for x> 4, that means that there is a point where the function is bigger than in x = 1.

Therefore this is not a local maximum.

Answer: [tex]x = \frac{2}{3}i , -\frac{2}{3}i[/tex]

Step-by-step explanation:

9x² + 4 = 0

       -4   -4

9x²       = -4

   [tex]\frac{9x^{2} }{9} = \frac{-4}{9}[/tex]

    x² = [tex]\frac{-4}{9}[/tex]

   [tex]\sqrt{x^{2} } = \sqrt{-\frac{4}{9} }[/tex]

    [tex]x = +/- \frac{2}{3}i[/tex]

I think the answer would be 6?

6x-1=4x+6

subtracting  4x from each side

2x-1=6

adding 1 to each side

2x=7

divide by 2

x=7/2 or 3.5

check:  6(7/2) -1 =4(7/2)+6

           21-1 =14+6

20=20  correct

The length of a side of the square can be found using the Pythagorean theorem. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, we find the length of a side of the square to be the square root of half of the square of the hypotenuse.

To find the length of the side of the square, we are going to use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².

Consider a square with a hypotenuse labeled as 's'. If we bisect this square diagonally, we form two right triangles. Since the sides of the square are equal, we can denote the other two sides of the right triangle as 'D' and 'L'. So, the Pythagorean theorem becomes: D² + D² = s², since D = L. Solving this, we find that s² = 2D².

Therefore, the length of a side of the square 'D'= √(s²/2).

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Answer:

2nd, 3rd and 4th equations are correct.

Step-by-step explanation:

[tex]-4x^2(2x^2+5)=-8x^4-20x^2\\\\[/tex]

is right because each term inside is multiplied by -4x square and we find the answer is right.

[tex]-4b^3(5b^2+3)\\\\\\= -4(5)(b^3)(b^2) =-20b^6-12b^3\\[/tex]

Hence correctly done.

[tex]-5a^4(2a^2+4)=  (-5)(2)(a^4)(a^2)+(-5)(4)(a^4\\-10a^6-20a^4\\[/tex]

Correctly done.

[tex]-6^4(4y^2+2)=-24y^8-12y^4\\= -(6)(6)(6)(6) 4y^2 -(6)(6)(6)(6) (2)[/tex]

should be the right answer.

But instead only 6 is multiplied by inner terms. Hence wrong.

I answer is wrong and others are right.

Answer: A:1

Step-by-step explanation:

Answer:

The cost of one sunflower is $2.25. :psksksksk

Step-by-step explanation:

All you have to do is divide 18 divided by 8. easypeasy. ;psksksksk

Complete solution is given in attachment below.

The order of their time spent from least to greatest is; Ari, Cindy, Bety

Distance covered by ari = 2³/₄ miles

Speed of ari = 2¹/₂ miles per hour

Formula for time is;

time = distance/speed

Thus;

Time spent by ari = 2³/₄/2¹/₂

Time spent by ari = 1.1 hours

Distance covered by beth = 1³/₄ miles

Speed of beth = 1¹/₄ miles per hour

Formula for time is;

time = distance/speed

Thus;

Time spent by beth = 1³/₄/1¹/₄

Time spent by beth = 1.4 hours

Distance covered by cindy = 1 hour 21 minutes = 1⁷/₂₀ miles

Speed of cindy = 1¹/₈ miles per hour

Formula for time is;

time = distance/speed

Thus;

Time spent by cindy = 1⁷/₂₀/1¹/₈

Time spent by cindy = 1.35 hours

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Answer:

A) y - 2 = 3(x+4)

Step-by-step explanation:

Given that the equation is a line with slope =m=3 and

a point on it (x1,y1) = (-4,2)

Any line having slope m and passing through (x1,y1) has equation in point slope form as

y-y1 = m(x-x1)

We are given here x1 =-4, y1 =2 and m =3

y-y1 = y-2 and x-x1 = x-(-4) = x+4

So equation is y-2 = 3(x+4)

Verify:

The line is y = 3x+12+2 = 3x+14

Hence slope =3 is verified

Substitute the point x =-4 and y =2

2 =3(-4)+14 = 2 is true

Thus verified

Answer:

A is correct option. Equation of line: y-2=3(x+4)

Step-by-step explanation:

Slope of line is 3 and passing point (-4,2).

If slope and passing point given then we have an equation of line

[tex]y-y_1=m(x-x_1)[/tex]

where,

[tex](x_1,y_1)\rightarrow (-4,2)[/tex]

Slope (m)=3

Equation of line:

y-2=3(x+4)

This equation match with option A

Thus. option A is correct.

Answer:

Hence average rate of change is greater for f(x) in (0,3).

Yes. f(x) is greater than g(x) in the interval (0,3)

Yes. g(3) <f(3)

Step-by-step explanation:

To find average rate of change of f and g in (0,3)

f(3)-f(0)/3 = (9-0)/3 =3

g(3) = -9-18 = -27

g(0) = 0

Rate of change in(0,3) of g(x) = -27/3 =-9

Hence average rate of change is greater for f(x) in (0,3)

---

Both f and g have intercepts of y as 0

Hence both are equal.

3) Yes. f(x) is greater than g(x) in the interval (0,3)

Because g(x) <0 for all x in (0,3) while f(x) >0

4) g(3)= -9-18=-27 <f(3)

Answer:

1).  g(3) ​​ is less than​ f(3).

​2). The average rate of change of f(x) is greater than ​g(x)​ on the interval [0,3] .

Step-by-step explanation:

g(x) = -x^{2} - 6x

so f(3) = 9

let's solve for g(3)

3^{2} = 9

g(3) = - 9 - 18 = -27

so -27 is less than 9

g(3) < f(3)

So our answer is correct: g(3) ​​ is less than​ f(3).

In second option:

put the value from 0 to 3 in function g(x) = - x^{2} - 6x

g(0) = 0

g(1) = -7

g(2) = -16

g(3) = -27

on the other hand values of f(x) are:

f(0) = 0

f(1) = 1

f(2) = 4

f(3) = 9

So average values of f(x) are greater than g(x) so our option is correct.

The average rate of change of f(x) is greater than ​g(x)​ on the interval [0,3] .

i hope you get the idea.

Answer:

To explain the cartoons and the boxes for table tennis balls are like the digits for numbers in base-10 number system

Here we know that, the number of table tennis balls in one box =10 balls

and the number of table tennis balls in boxes in each cartoon = 10 balls

Therefore, The number of table tennis balls in each cartoon =10×10=100 balls

Hence for the number of balls ,the hundreds place tells the number of cartoons and  tens place tells the number of boxes which left as remainder or without cartoon.

For example if the total tennis balls =540 then its hundreds place i.e 5 tells the number of cartoons and its tens place i.e.4 tells the number of boxes which left as remainder or without cartoon.

Answer:

Base 10 Number System = (0,1,2,3,4,5,6,7,8,9)

In a  Carton of table tennis there are  10 boxes.

And Each Box can Hold 10 Balls.and if i mark boxes from 0 to 9, then

then there are 10 boxes , Total number of Balls=100

So if I represent a single Carton by A, then

A[single carton] ={0,1,2,3,4,5,6,7,8,9}= 10 boxes =100 balls

B [2 carton]= 20 boxes=200 balls

C[ 5 cartons + 3 Boxes] = 5× 100+ 3×10 =530 balls

D[ 12 cartons + 8 Boxes]= 12×100+8×10=1280 balls

Now you can see,

Each carton is holding the balls  in decimal number system.

Boxes = Ten's place in number system,

Number of cartons = either Hundred place or thousand place or more than that

In this way we can represent Carton and Box for table tennis balls in decimal number system having base 10 .

The variable expression represents the phrase '25 decreased by the sum of 6 and a number' is 25-(6+x).

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically.

For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and  methods can be used to convert description to mathematical expressions.

We have to find the variable expression represents the phrase '25 decreased by the sum of 6 and a number'

Let the number be x then decrease mean subtract, sum means add

by means parenthesis;

The expression becomes as;

25 - (6 + x)

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See the attached picture for the steps:

5.51181 in feet. Hope this helps

− x^ 2 + 10 x + 7 so the answer is B.

                                                    hope it helps

Answer:

[tex]-x^2+10x+7[/tex]

Step-by-step explanation:

3x^2+8x+7-(4x^2-2x). find the difference of the polynomials

First remove the parenthesis by multiplying minus inside the parenthesis.

[tex]3x^2+8x+7-4x^2+2x[/tex]

Now we combine like terms. the terms with same variables and same exponents are like terms.

[tex]3x^2-4x^2= -1x^2[/tex]

[tex]8x +2x= 10x[/tex]

[tex]3x^2+8x+7-(4x^2-2x)=-x^2+10x+7[/tex]

We could use the standard form of subtraction.

We put 71.120 on top and we put 2.359 at the bottom.

Then, we subtract the thousandths place. It involves a carry-over.

Then, we subtract and the answer is:

68.761

The subtraction of 71.120 and 2.359 equals 68.761.

This question is asking for the subtraction of two decimal numbers, the first being 71.120 and the second being 2.359. To do this, you would stack the numbers on top of each other, aligning the decimal points, and subtract as you would with whole numbers.

So, your subtraction would look like this:

So, 71.120-2.359 equals 68.761.

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ANSWER

EXPLANATION

We want to solve

[tex]0.5(7d+4)=7-1.5d[/tex]

Let us first multiply through by [tex]10[/tex] to clear the decimal.

[tex]10\times 0.5(7d+4)=7\times 10 -1.5d\times 10[/tex]

This implies that;

[tex]5(7d+4)=70 -15d[/tex]

We now expand to obtain;

[tex]35d+20=70 -15d[/tex]

We group like terms to obtain;

[tex]35d+15d=70 -20[/tex]

[tex]50d=50[/tex]

Dividing through by 50 gives;

[tex]d=1[/tex]

Answer:

The value of the equation for d is 1.

Step-by-step explanation:

Consider the provide equation.

[tex]0.5(7d+4)=7-1.5d[/tex]

We need to solve the equation for d.

Open the parentheses.

[tex]3.5d+2=7-1.5d[/tex]

Add 1.5d both sides.

[tex]3.5d+1.5d+2=7-1.5d+1.5d[/tex]

[tex]5d+2=7[/tex]

Subtract 2 from both sides.

[tex]5d+2-2=7-2[/tex]

[tex]5d=5[/tex]

Divide both the sides by 5.

[tex]d=1[/tex]

Hence, the value of the equation for d is 1.

Answer: The two estimates of quotient is 522 and 523 .

Step-by-step explanation:

Compatible numbers are numbers which are close in value to the given numbers, and  make it easy to calculate the answer for any given arithmetic problem .

To find two estimates that the quotient is between in 1045÷2

We now that 1045 is greater than 1044 and less than 1046 i.e.1044<1045<1046

Dividing 2 from all sides ,we get

1044÷2<1045÷2<1046÷2

⇒522<1045÷2<523

As the quotient of 1045÷2 is lying between 522 and 523.

Therefore, the two estimates of quotient is 522 and 523

To estimate the quotient of 1045 divided by 2 using compatible numbers, one can use 1040 (which gives an estimate of 520) and 1050 (which gives an estimate of 525) as they are easily divisible by 2. Hence, the quotient should fall between 520 and 525.

The student is asked to find two estimates that the quotient 1045 ÷ 2 falls between using compatible numbers. To estimate, we look for numbers that are easy to divide. Compatible numbers to 1045 that are close to it and divisible by 2 could be 1040 and 1050. So our two estimates for 1045 ÷ 2 are:

Therefore, the quotient of 1045 ÷ 2 should be between 520 and 525.