If one of the longer sides is 6.3 centimeters, what is the length of the base

Konichiwa~! My name is Zalgo and I am here to help you out today. The factorization of your equation is 4 (2a+b) (2a-b). If you do not understand this, it means 4 multiplied by 2a+b which is also multiplied 2a-b.

I hope that this helps! :P

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Answer:

4(2a+b)(2a-b)

Step-by-step explanation:

Distributive property: A(B+C)=ab+ac

4²=4*4=16

4*4a²-4b²

Term of 4.

4 (4a²-b²)

Simplify, to find the answer.

4a²-b²= (2a+b)-(2a-b)

(2a+b)-(2a-b) is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

Step-by-step explanation:

METHOD 1:

Calculate what fraction of 1600 is 3100 and convert it to the percent:

[tex]\dfrac{3100}{1600}=\dfrac{31}{16}\\\\\dfrac{31}{16}\cdot100\%=\dfrac{3100}{16}\%=193.75\%[/tex]

METHOD 2:

[tex]\begin{array}{ccc}1600&-&100\%\\\\3100&-&p\%\end{array}\qquad\text{cross multiplu}\\\\\\1600p=310000\qquad\text{divide bpth sides by 1600}\\\\p=193.75\ (\%)[/tex]

For this case we must simplify the following expression:[tex]7 (\sqrt [3] {2x}) - 3 (\sqrt [3] {16x}) - 3 (\sqrt [3] {8x})[/tex]

We rewrite:

[tex]16x = 2 ^ 3 * 2x\\8x = 2 ^ 3 * x[/tex]

We rewrite the expression:

[tex]7 (\sqrt [3] {2x}) - 3 (\sqrt [3] {2 ^ 3 * 2x}) - 3 (\sqrt [3] {2 ^ 3 * x}) =[/tex]

By definition of properties of powers and roots we have:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

Then, taking the terms of the radical:

[tex]7 (\sqrt [3] {2x}) - 3 (2 \sqrt [3] {2x}) - 3 (2 \sqrt [3] {x}) =\\7 \sqrt [3] {2x} -6 \sqrt [3] {2x} -6 \sqrt [3] {x} =[/tex]

We add similar terms:

[tex]\sqrt [3] {2x} -6 \sqrt [3] {x}[/tex]

Answer:

Option C

Answer:

23

Step-by-step explanation:

plug and chug: 5(4)+3=20+3=23

Hello There!

The answer would be "23"

When we have an expression like this, the "x" next to a number means that we multiply the number next to the variable by it.

In this case, if "x" equals 4, then we multiply 5 by 4 and we get a product of 20 and we add 3 to get a sum of 23.

Have A Great Day!

Be Safe!

TheBlueFox

[tex]\bf 40a^2+20a-30=(-1)(15a^3+30)\implies 40a^2+20a~~\begin{matrix} -30 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~=-15a^3~~\begin{matrix} -30 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} \\\\\\ 40a^2+20a=-15a^3\implies 15a^3+40a^2+20a=0\implies 5a(3a^2+8a+4)=0 \\\\\\ 5a(3a+2)(a+2)=0\implies a= \begin{cases} 0\\ -\frac{2}{3}\\ -2 \end{cases}[/tex]

Hello There!

50*50 is 2,500

Answer:

1000

Step-by-step explanation:just multiply

Answer:

x ≈ 50.8

Step-by-step explanation:

Given

sin80° = [tex]\frac{50}{x}[/tex]

Multiply both sides by x

x × sin80° = 50 ( divide both sides by sin80° )

x = [tex]\frac{50}{sin80}[/tex] ≈ 50.8 ( to 1 dec. place )

Answer:

[tex]\large\boxed{x\approx50.77}[/tex]

Step-by-step explanation:

[tex]\text{Look at the picture.}\\\\\sin80^o\approx0.9848\\\\\text{Substitute it the the equation}\ \sin80^o=\dfrac{50}{x}:\\\\0.9848=\dfrac{50}{x}\\\\\dfrac{9848}{10000}=\dfrac{50}{x}\qquad\text{cross multiply}\\\\9848x=(10000)(50)\\\\9848x=500000\qquad\text{divide both sides by 9848}\\\\x\approx50.77[/tex]

Answer:

option B

Step-by-step explanation:

Paul bought 6 pounds of hamburger. He used 3 1/ 2  pounds to make burgers. Paul says he has 2 1/ 2  pounds of hamburger left.

To find out pounds of hamburger left we subtract 3  1/2 from 6 pounds

[tex]3 \frac{1}{2} =\frac{3*2+1}{2}=\frac{7}{2}[/tex]

Now we subtract the fraction from 6

[tex]6 - \frac{7}{2} = \frac{12}{2} - \frac{7}{2} =\frac{5}{2}[/tex]

Now we convert 5/2 into mixed fraction

[tex]\frac{5}{2} = 2\frac{1}{2}[/tex]

Paul's answer is correct. because when we add [tex]3\frac{1}{2} + 2\frac{1}{2}[/tex] we will get 6

Answer:

usually means establishing a series of equal monthly payments that will provide

a principal payment that will cause the unpai principal balance to decrease each month so that the principal balance will be zero at the time of the final payment

Answer:

To amortize a loan refers to equal and periodic payments (monthly in most of the cases), on which the lender runs some interest ratio due to the amortization.

In other words, it means that the total amount of money the lender is going to "give" you is divide in smaller amount of moneys, which he is gonna lend you periodically, monthly. For example, if you need a $60,000 loan, and your lender propose to lend that money with a 4% of annual interest, that means he is gonna give your $1771.4 per month, he won't give you the whole money, instead he amortize the loan and give your a certain quantity based on the interest rate.

Answer:

The answer is option B : $30,000.

Step-by-step explanation:

To avoid Primary Mortgage Insurance or PMI, one need to have the loan balance to be 80% or less of the home value.

Hence, Bella needs to deposit a down payment of at least 20% of $150,000

This value becomes:

[tex]0.20\times150000=30000[/tex] dollars

Therefore, the answer is option B : $30,000.

Answer:

B $30,000

Step-by-step explanation:

PMI then with the given amount is how we find the answer

Answer:

d

Step-by-step explanation:

In an axiomatic system, the definition is 'the accepted meaning of a term'. An axiom is an accepted unproven fact. A fact proven by using logic is a theorem.

In an axiomatic system, the phrase that best describes the 'definition' would be option A - 'the accepted meaning of a term.' An axiomatic system is a sort of framework within mathematics where definitions, axioms, and propositions work together. A definition in this context offers the precise description or meaning of a term used within that mathematical system.

An axiom (option B) would most accurately be described as an accepted fact that is not proven, but instead accepted as truth within an axiomatic system (option C). A fact proven by using logic, on the other hand, would be a theorem (option D).

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Step-by-step answer:

If one is constrained to move to the right, or up, or diagonally upwards (i.e. remain in the first quadrant), then

there are three choices at A.

At the next position, whichever path one has taken, there are also three choices.

At the following position, there are no more choices.

Therefore, there are 3*3 = 9 different paths.

We can notice that 731.8 is the Greatest among all numbers because 731 is always greater than 730

Now consider the remaining numbers : 730.38 , 730.1 , 730.63

★  730.1 can be written as 731.10

As the Number part of remaining numbers is same (730), we need to consider the decimal parts of the numbers in order tell which number is greatest among them

★ Decimal part of 730.38 is 38

★  Decimal part of 730.10 is 10

★  Decimal part of 730.63 is 63

As 63 > 38 > 10 :

We can say that : 730.63 > 730.38 > 730.10

So, Arrangement of given numbers from greatest to least is :

★  731.8 > 730.63 > 730.38 > 730.10

Answer:

B

Step-by-step explanation:

Answer:

The answer should be: B. (9,3)

Answer:  B. (9,3)

Step-by-step explanation:

To solve this problem, we start organizing the equation to the Slope intercept form:

[tex]y=5(x-9)+3[/tex]

[tex]y=5x-45+3[/tex]

[tex]y=5x-42[/tex]

Where 5 is the positive slope of the line, and -42 is the y-axis intercept. knowing the y-intercept, we may infer that choices C or D are incorrect, because values must be lower than -42. Thus, we replace the x value of choices A and B to verify which one applies:

Choice A

[tex]y=5(3)-42[/tex]

[tex]y=-27[/tex]

[tex]27\neq 9[/tex]

Choice B

[tex]y=5(9)-42[/tex]

[tex]y=3[/tex]  Correct!

Answer:

Step-by-step explanation:

volume of a pyramid is V=(lwh)/3

For this case we have that by definition, the volume of a pyramid is the third part of the volume of a prism that has the same area of the base and equal height.

Thus:

[tex]V = \frac {b * h} {3}[/tex]

Where:

b: It is the area of the base

h: It's the height

Answer:

[tex]V = \frac {b * h} {3}[/tex]

Answer:

Anything you own that has value and can be turned into cash.

Step-by-step explanation:

Unless there is a passage that refers to the word, the second option would be the best answer due to Google's online dictionary.

For this case we must simplify the following expression:

[tex]\sqrt {\frac {2160x ^ 8} {60x ^ 2}}[/tex]

We rewrite the expression:

[tex]\sqrt {\frac {60 * 36 * x ^ 8} {60x ^ 2}} =[/tex]

We eliminate common terms:

[tex]\sqrt {\frac {36 * x ^ 8} {x ^ 2}} =[/tex]

For division of powers of the same base, the same base is placed and the exponents are subtracted:

[tex]\sqrt {36x ^ {8-2}} =\\\sqrt {36x ^ {6}} =[/tex]

By definition of properties of powers and roots we have:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So:

[tex]6x ^ {\frac {6} {2}} =\\6x ^ 3[/tex]

Answer:

Option C

Answer:

16/9

Step-by-step explanation:

Step 1 : {Apply exponent rule}

Step 2: repeat

For this case we must solve the following quadratic equation:

[tex]2x ^ 2 -7x -15 = 0[/tex]

We must apply the following formula:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]

We have to:

[tex]a = 2\\b = -7\\c = -15[/tex]

Substituting we have:

[tex]x = \frac {- (- 7) \pm \sqrt {(- 7) ^ 2-4 (2) (- 15)}} {2 (2)}\\x = \frac {7 \pm \sqrt {49 + 120}} {4}\\x = \frac {7 \pm \sqrt {169}} {4}\\x = \frac {7 \pm13} {4}[/tex]

Thus, the solutions are:

[tex]x_ {1} = \frac {7 + 13} {4} = \frac {20} {4} = 5\\x_ {2} = \frac {7-13} {4} = \frac {-6} {4} = - \frac {3} {2}[/tex]

ANswer:

[tex]x_ {1} = 5\\x_ {2} = - \frac {3} {2}[/tex]

Answer:

{-3/2, 5} would be the right choice

Answer:

The number of child tickets = 39

Step-by-step explanation:

It is given that,child admission is $5.20 and adult admission is $8.60

Total sales = $868.00

To find the number of child tickets

Le 'x' be the number of children then number of adults = 2x

(x * 5.20) + (2x * 8.60) = 868

5.2x + 17.2x = 868

22.4x = 868

x = 868/22.4

 = 38.75 ≈ 39

Therefore the number of child tickets = 39

Answer:

3x²

Step-by-step explanation:

Note that when adding, as long as the variables have the same power, you can combine the numbers together.

The sum of 3x² + 7x² = 10x² is correct.

If you used -3x², then it will be wrong, because -3x² + 7x² = 4x².

~

Answer:

Option B

Step-by-step explanation:

we know that

The volume of a solid is the amount of space occupied by a solid object. The volume of solid is expressed as cubic units.

therefore

It is the amount of three -dimensional space inside the solid

Answer:

B. It is the amount of three-dimensional space inside the solid.

Step-by-step explanation:

Volume is defined as the amount of three-dimensional space enclosed by a close surface. Volume is the product of the three dimensions of a body. The SI unit of volume is m³.

eg. Volume of cube = a³

Volume of cuboid = L×B×H

Volume of sphere = [tex]\frac{4}{3}\pi r^3[/tex]

Volume of cylinder = πr²h

Volume of cone = [tex]\frac{1}{3}\pi r^2h[/tex]

The equation that represents the given situation is 3x - (50 - x) - 0.5(50 - x) = 110. This equation is derived from the fact that Desiree gets 3 points for each correct answer, 1 point deducted for each wrong answer, and 0.5 point deducted for each unanswered question.

The equation that represents the given situation is 3x - (50 - x) - 0.5(50 - x) = 110.

This eqUation is derived from the fact that Desiree gets 3 points for each correct answer, 1 point deducted for each wrong answer, and 0.5 point deducted for each unanswered question.

By solving the equation, you can find the value of x, which represents the number of questions Desiree answered correctly.

Answer:

A = 3.4 cm

Step-by-step explanation:

The length of line segment AB is 3.4cm.

The area of octagon is given as 2a^2(1+sqrt{2})  

Where a is the side of octagaon. All sides of octagon are same.

As, 2a^2(1+sqrt{2}) = 54cm

Then, a^2 = 54/2(1+sqrt{2})

a^2 = 54/4.828

a^2 = 11.19

a = 3.4 cm

Answer:

Step-by-step explanation:

Solve each equation individually, using substitution or elimination.

A. x + 3y = 3

   2x - y = -2

Substitute:

2(3-3y) - y = -2

6-6y-y = -2

6-7y = -2

y = 8/7

plug it back in to the first equation:

x + 24/7 = 3

x = -0.4285, approximately, and since this rounds to -0.4 and 8/7 approximately equals 1.1,

A is your answer.

The system of equations has a solution of approximately (-0.4,1.1) is x+3y=3 and 2x-y=-2.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

here,
To determine whether (-0.4, 1.1) is the solution of which equation,
So, put the solution in the equation of Option A,
x+3y = 3
-0.4 + 3(1.1) = 3
2.9 ≈ 3

And,
2x-y=-2
2(-0.4) - 1.1 = -2
-0.8 - 1.1 = -2
-1. 9 ≈ -2

Thus, the system of equations has a solution of approximately (-0.4,1.1) is x+3y=3 and 2x-y=-2.

Learn more about simultaneous equations here:

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Answer:

(1,-1)

Step-by-step explanation:

A translation of (x,y) ⟶ (x + 4, y – 2) means that the coordinates of the pre-image have moved four units to the right and two units down.

To get the coordinates of the pre-image rom the image, we must reverse the procedure.

That is, we must go two units up and four units to the left.

The coordinates of Point P' are (5, -3), so those of P must have been (1, -1).

Answer:

(1,-1) is the answer

Step-by-step explanation:

Hope this helps

Answer:

IbI

Step-by-step explanation:

The square root of [tex]\( b^2 \)[/tex] is [tex]\( b \),[/tex] as the square root of any positive number is its positive root.

The square root of [tex]\( b^2 \)[/tex]  can be calculated step by step as follows:

Step 1:

Understand the concept.

The square root of a number is a value that, when multiplied by itself, gives the original number. For any real number [tex]\( b \), \( b^2 \)[/tex]  represents [tex]\( b \)[/tex]multiplied by itself.

Step 2:

Apply the square root property.

The square root of [tex]\( b^2 \)[/tex]  is [tex]\( b \)[/tex] because [tex]\( b \times b = b^2 \).[/tex] The square root of any positive number is its positive root.

Step 3:

Interpret the result.

Since the square root of [tex]\( b^2 \)[/tex] is [tex]\( b \),[/tex]  regardless of the value of \( b \), the square root of [tex]\( b^2 \)[/tex] is simply [tex]\( b \)[/tex] . This property holds true for any real number [tex]\( b \).[/tex]

So, the square root of [tex]\( b^2 \)[/tex] is [tex]\( b \).[/tex]

Answer:

The width of the base = the volume ÷ (length × height)

w = V/lh

Step-by-step explanation:

* Lets take about how to re-arrange any formula

- The formula of the volume of the rectangular prism is:

  V = lwh, where l is the length of the base , w is the width of the

  base and h is the height of the prism

- To find the formula of the width from the formula of the volume,

  we must isolate the width in one side and all other dimensions in

  other side

∵ V = lwh ⇒ divide both sides by l and h

∵ V/(lh) = (lwh)/(lh) ⇒ cancel lh up with lh down

∴ V/(lh) = w

∴ w = V/(lh)

∴ w = V ÷ (lh)

* The width of the base = the volume ÷ (length × height)

Answer:

Width=[tex]\frac{Volume}{(Length)*(height)}[/tex]

Step-by-step explanation:

You only have to clear the start of the formula:

V=L*W*H

Since lenght and height are multiplying the width of the base you have to clear them and take them to the other side of the equation dividing:

[tex]\frac{V}{l*h}[/tex]

So you can calculate the width of the base by dividing the volume between the product of the Height times the length.