a cuboid with a volume of 924 cm3 has dimensions 4cm (x+1)cm and (x+11)cm. show clearly that x^2 +12x-220=0. show the equation by factorisation. State both values of x. and finally find the dimensions of the cubiod.

The answer is:

[tex](-x^{2}+9)+(3x^2-11x+4)=2x^{2}-11x+13[/tex]

To solve the problem, we must remember how to add/subtract like terms. The like terms are the terms that share the same variable and the same exponent.

For example:

[tex]2x+3x+x^{2}=x^{2}+(2x+3x)=x^{2}+5x[/tex]

We were able to add only the linear terms (terms that contains the variable x") because they were like terms: they share the same variable and the same exponent.

We need to perform the following operation between polynomials:

[tex](-x^{2}+9)+(3x^2-11x+4)[/tex]

So, calculating we have:

[tex](-x^{2}+9)+(3x^2-11x+4)=2x^{2}-11x+13[/tex]

Have a nice day!

Answer:

{1,-1}

Step-by-step explanation:

Let's do both!

Factoring!

x^2-1 is a difference of squares.

The formula for factoring a difference of squares is: u^2-v^2=(u-v)(u+v).

So the factored form of x^2-1 is (x-1)(x+1).

So we want to solve the equation x^2-1=0 which is equivalent to solving

(x-1)(x+1)=0.

If you have A*B=0 then either A=0 or B=0.

So in our case we have x-1=0 or x+1=0.

Now we just solve the equations.

x-1=0 can be solved by adding 1 on both sides giving us x=1.

x+1=0 can be solved by subtracting 1 on both sides giving us x=-1.

Square root!

When you want to use square roots, you have to have a perfect square containing the variables and a constant.  We have that here.

We have x^2-1=0 which is equivalent to x^2=1.  You could get this last equation by adding one on both sides of x^2-1=0.

Anyway, once you have the square part equals the constant, all you have to do is square root both sides to get rid of the square on the variable part.

[tex]x^2-1=0[/tex]

[tex]x^2=1[/tex]

[tex]\sqrt{x^2}=\sqrt{1}[/tex]

[tex]x=\pm \sqrt{1}[/tex]  It leads to two answers because [tex]\sqrt{x^2}=|x|[/tex].

[tex]x=\pm 1[/tex]

The solution to the equation x^2-1=0 is x = 1 or x = -1.

To solve the equation x^2-1=0 by factoring or finding square roots, we can start by rearranging the equation to get x^2=1. This means that the square of x is equal to 1. To find the square root of both sides, we take the square root of 1, which gives us x=±1. So the solution to the equation is x = 1 or x = -1.

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Answer:

Step-by-step explanation:

A Mutual Fund is invested by Managers in a diversity of stocks bonds and other securities.

A mutual fund is a type of investment in which investors pool their money together to buy a portfolio of stocks, bonds or other securities in order to take advantage of diversification and professional portfolio management at a reasonable cost. It is operated by money managers, who invest the fund capital on the investors behalf. Investing in mutual funds enables those investing a modest amount of money to benefit from the same advantages enjoyed by large institutional investors....

Hey there! :)

Find the value of y when x=1 : 9x + 7y = -12

To find the value of y, simply plug in 1 for x in our given equation.

9(1) + 7y = -12

Simplify!

9 + 7y = -12

Subtract 9 from both sides so that we can isolate y.

7y = -12 - 9

Simplify.

7y = -21

Now, divide both sides by 7 to fully isolate y.

7y ÷ 7 = -21 ÷ 7

Simplify!

y = -3

~hope I helped!~

Answer: NUMBER 9 I'm on gradpoint too

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

  Mass of apples = number of containers × mass in each container

                     6 lb = No of containers × ½ lb

No of containers = 6/½  

To divide a whole number by a fraction, invert the fraction and change divide to multiply.

6/½ = 6 × 2/1

Multiply the numerator by the whole number.

6 × 2/1 = 12/1

Simplify the fraction.

12/1 = 12

Elise can make 12 containers of applesauce.

Answer:

(1, 3).

Step-by-step explanation:

The tree tiles coordinates are x = 5-3 = 2 and the y coordinate = 4 - 2 = 2

- that is (2, 2).

So the coordinates of the second sun are (2-1, 2 + 1)

= (1. 3).

Answer:

.75

Step-by-step explanation:

Answer:

Natural numbers = {1,2,3,4,5…} Answer 1: A is the set of Natural numbers between 1 and 5 inclusive. Answer 2: A is the set of Natural numbers less than 6.

Step-by-step explanation:

Answer:

n = 1, 2, 3, 4

Step-by-step explanation:

Natural numbers are any integers (whole numbers) that are positive.

In this case, all natural number (n) is less than (<) 5

n < 5 is your equality, but in reality it looks like: 0 < n < 5

The numbers that can fit into your problem is n = 1 , 2, 3, 4

n = 1, 2, 3, 4 is your answer.

~

Answer:

[tex]2 {x}^{2} + 8x + 6 \\ 2( {x}^{2} + 4x + 3) \\ = 2( {x}^{2} + x + 3x + 3) \\ = 2(x + 1)(x + 3)[/tex]

Answer:

the answer is correct, just backwards. thanks for your help!

Step-by-step explanation:

Answer:

a = 44 degrees

Step-by-step explanation:

angle 0 + angle a + angle b = 180 degrees

angle b = angle a

92 + a + b = 180 degrees

92 + 2a = 180 degrees

a = 44 degrees

!!

Answer:

g(2) = 3

Step-by-step explanation:

g(x) = x² - 1.

Substituting 2 for x in this formula, we get:

g(2) = 2² - 1, or g(2) = 3

Answer:

g(2) =3

Step-by-step explanation:

g(x) = x^2 -1

Let x=2

g(2) = 2^2 -1

       =4-1

        =3

Answer:

Step-by-step explanation:

[tex]\sqrt{\dfrac{896z^{15}}{225z^6}}=\dfrac{xz^4}{15}\sqrt{14z}\\\\\sqrt{\dfrac{896z^{15}}{225z^6}}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\=\sqrt{\dfrac{(64)(14)z^{15-6}}{225}}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b},\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\\\\=\dfrac{\sqrt{64}\cdot\sqrt{14}\cdot\sqrt{z^9}}{\sqrt{225}}=\dfrac{8\cdot\sqrt{14}\cdot\sqrt{z^{8+1}}}{15}\qquad\text{use}\ a^na^m=a^{n+m}\\\\=\dfrac{8\sqrt{14}\cdot\sqrt{z^8z}}{15}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}[/tex]

[tex]=\dfrac{8\sqrt{14}\cdot\sqrt{z^8}\cdot\sqrt{z}}{15}=\dfrac{8\sqrt{14}\cdot\sqrt{z^{4\cdot2}}\cdot\sqrt{z}}{15}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\dfrac{8\sqrt{14}\cdot\sqrt{(z^4)^2}\cdot\sqrt{z}}{15}\qquad\text{use}\ (\sqrt{a})^2=a\\\\=\dfrac{8\sqrt{14}\cdot z^4\cdot\sqrt{z}}{15}=\dfrac{8z^4\sqrt{14}\cdot\sqrt{z}}{15}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\dfrac{8z^4\sqrt{14z}}{15}[/tex]

[tex]\dfrac{8z^4\sqrt{14z}}{15}=\dfrac{xz^4\sqrt{14z}}{15}\iff x=8[/tex]

Answer:

Choice C:

slope = -18x

y-intercept = 850

Step-by-step explanation:

Drew uses 18 ounces of flour

-18x represents the amount of flour used

850 ounces of flour

or (0,850) is the y-intercept and represents the total number of flour

Answer

slope = -18x

y-intercept = 850

Answer:

C

Step-by-step explanation:

C

The answer is 12 points

I have the table so I added the numbers to get 108, and there are 9 numbers, so yu do 108/9 equaling to 12

Answer:

The ratio of their volumes is 27/64

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In this problem

The scale factor is 3/4

step 2

Find the ratio of their volumes

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

so

[tex](\frac{3}{4})^{3}=\frac{27}{64}[/tex]

This image is being reflected over the y-axis.  When reflecting over the y-axis the y-coordinate will stay the same, but the x-coordinate will have the opposite sign. Here is the rule for this reflection:

(-x, y)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

1/30

Step-by-step explanation:

Answer:

Step-by-step explanation:

The absolute value of number a:

|a| = a for a ≥ 0

|a| = -a for a < 0

|9| = 9

|-3| = -(-3) = 3

Answer:

The length of the third side could be all real numbers greater than 2 units and less than 16 units

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.

so

Applying the triangle inequality theorem

Let

x ------> the length of the third side

we have

First case

1) 7+9 > x

16 > x

Rewrite

x< 16 units

Second case

2) 7+x > 9

x > 9-7

x > 2 units

therefore

The solution for the third side is the interval

(2,16)

All real numbers greater than 2 units and less than 16 units

0,1,4,9

0+1= 1

1+3= 4

4+5= 9

Add the numbers by using an odd number each time.

9+7= 16

16+9= 25

Answer is 16, 25 ( first choice):

0, 1, 4, 9, 16, 25

d = sqrt (2-(-6))² + (-3-4)²)

d = sqrt ( 8² + 7² )

d = sqrt ( 64 + 49 )

d = sqrt (113)

Answer: The distance between the two points is roughly  10,63:

B)

The distance between the points (2,-3) and (-6,4) on the coordinate plane is 10.63 units. This can be obtained by using the distance formula.

The distance between two points (x₁,y₁) and (x₂,y₂) is

d = [tex]\sqrt{{(x_{2}-x_{1} )}^{2} + (y_{2}-y_{1} )^{2}[/tex]

In the given question, (x₁,y₁) is (2,-3) and (x₂,y₂) is (-6,4),

the distance d =  [tex]\sqrt{{(x_{2}-x_{1} )}^{2} + (y_{2}-y_{1} )^{2}[/tex]

                        =[tex]\sqrt{{((-6)-2 )}^{2} + (4-(-3) )^{2}[/tex]

                        =[tex]\sqrt{{(-8)}^{2} + (7 )^{2}[/tex]

                        = [tex]\sqrt{{64 + 49[/tex]

                        =√113 =10.63 units

Hence the distance between the points (2,-3) and (-6,4) on the coordinate plane is 10.63 units. Thus option B is correct.

Learn more about distance formula here:

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Answer:

Correct answer is figure D.

Step-by-step explanation:

According to the attached image Figure  D is correct option.

In a reflection transformation, all the points of an object are reflected or flipped. It is a type of transformation where the new image is the mirror image of the original and x-coordinates and y-coordinates changes the place.

Figure A is rotation and translation and Figure B and C are translation

Thus the correct option is Figure D....

The answer addresses the true or false nature of five statements about the properties of coordinate pairs in a two-dimensional graph with respect to their quadrants, and the location of specific points on the coordinate plane.

The coordinates (x, y) indicate the position of a point on a two-dimensional graph in relation to the origin, which is at (0, 0). In a standard coordinate system, Quadrant I has both x and y as positive, Quadrant II has x as negative and y as positive, Quadrant III has both x and y as negative, and Quadrant IV has x as positive and y as negative.

Answer:

0.00083

Step-by-step explanation:

200*300*30=1800000

1500/1800000=0.00083

The cost per cubic foot of the storage space is approximately $0.00083 per cubic foot. Hence the correct option is D.

To find the cost per cubic foot of the storage space, we need to calculate the total cubic footage of the space and then divide the monthly cost by that number. The storage space measures 200 ft x 300 ft x 30 ft, so the total volume is:

Total Volume = length times width times height

= 200 ft x 300 ft x 30 ft

= 1,800,000 cubic feet

Now, we calculate the cost per cubic foot:

Cost Per Cubic Foot = Total Monthly Cost / Total Volume

= $1500 / 1,800,000 cubic feet

= $0.00083 per cubic foot (rounded to five decimal places).

Answer:

Domain is all real numbers also known as [tex](-\infty,\infty)[/tex] in interval notation.

[tex]f(x)=\sqrt[3]{x-1}[/tex]?

Step-by-step explanation:

If your function is [tex]f(x)=\sqrt[3]{x-1}[/tex] then the domain is all real numbers because you can cube root any real number.

If x is a real number, then x-1 is a real number.

So if you cube root (x-1) for any x then you still get a real number back.

Now if it was a square root, that is when we can run into some problems.

Answer: -infinity and positive infinity

Step-by-step explanation: It's either a on your test or two zero's that look twisted :)

Answer:

4.21 and 4.22 (answers will vary)

Step-by-step explanation:

There are a lot of different numbers you can pick. It just has to be between 4.2 and 4.3. This means that 4.200000000000000000000000000001 can be an answer and 4.29999999999999999999999999 can be an answer.

Answer:

D. 10i √(3)

Step-by-step explanation:

√(-300)

We know sqrt (ab) = sqrt(a) sqrt(b)

sqrt(-300) = sqrt(-3) sqrt(100)

                 = sqrt(-1) sqrt(3) sqrt(100)

The sqrt(-1) =the imaginary number 1 and sqrt(100) =10

                  = i * sqrt(3) * 10

                    =10i sqrt(3)