Which table shows a proportional relationship?

Answer: 24480

Step-by-step explanation:

just multiply the two numbers since 24 is distributing to 1020...24 times 1020

Answer:

the answer is 24480

Step-by-step explanation:

Answer:

4(x +3)(x +4)

Step-by-step explanation:

First of all, recognize that each coefficient is a multiple of 4.

Factoring that out makes it easier to see that you need factors of 12 that add to give 7. Those are not hard to find as being 3 and 4. These numbers go into the binomial factors to give ...

... 4x^2 +28x +48 = 4(x^2 +7x +12) = 4(x +3)(x +4)

Answer:

[tex]4x^2 + 28x +48 = 4(x+4)(x+3)[/tex]

Step-by-step explanation:

We are given the following information in the equation:

[tex]4x^2 + 28x +48[/tex]

We have to factorize the given expression.

We will use the technique of splitting the middle term to factorize.

Factorization can be done in the following manner:

[tex]4x^2 + 28x +48\\\Rightarrow 4(x^2 + 7x + 12)\\\Rightarrow 4(x^2 + 4x + 3x + 12)\\\Rightarrow 4[x(x+4)+3(x+4)]\\\Rightarrow 4(x+3)(x+4)[/tex]

Hence, the given expression can be factorized as:

[tex]4x^2 + 28x +48 = 4(x+4)(x+3)[/tex]

Answer:

5feet per year

Step-by-step explanation:

We need to find the distance it grew in that 7 1/2 years:

63 - 25 1/2 = 37 1/2

Now to find the average yearly growth we can divide this by 7 1/2:

37.5 ÷ 7.5 = 5

So the yearly rate of growth of the tree is 5f/y

The given expression is simplified as x² + 3x - 4.

What is an Algebraic expression?

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is as below,

((4x²+ 12x - 16) / (2x + 10)) / ((6x + 24) / (x ²+ 9x + 20))

It can be simplified as,

((4x²+ 12x - 16) (x ²+ 9x + 20)) / (2x + 10) (6x + 24)

Now, (4x²+ 12x - 16)  and  (x ²+ 9x + 20) can be factorised as,

4x²+ 12x - 16 = 4x²+ 16x - 4x - 16

                   = 4x(x + 4) - 4(x + 4)

                   = (4x - 4) (x + 4)

And, x ²+ 9x + 20 = x ²+ 5x + 4x + 20

                           = x(x + 5) +4(x + 5)                            = (x + 4) (x + 5)

Substitute the factors to get the expression as,

(4x - 4) (x + 4) (x + 4) (x + 5) /  (2x + 10) (6x + 24)

= (4x - 4) (x + 4) (x + 4) (x + 5) /  2 × 2(x + 5) (x + 4)

=  (4x - 4) (x + 4) / 4

= 4(x - 1) (x + 4) / 4

= (x - 1) (x + 4)

= x² + 3x - 4

Hence, the given expression can be simplified as  x² + 3x - 4.

Answer:

Step-by-step explanation:

7-9x=56

Answer:

D. -1,1,-2i, 2i

Step-by-step explanation:

We should have 4 roots since this is a 4th degree polynomial.  We just have to watch since some of them may be multiple roots.

x^4+3x^2-4 = 0

Factoring this equation

(x^2 - 1) (x^2+4) = 0

We can factor the first term

(x-1) (x+1) (x^2+4) =0

Using the zero product property

x-1 =0  x+1 = 0  x^2+4 =0

x=1        x=-1        x^2 = -4

                            Taking the square root of each side

                           sqrt(x^2) =± sqrt(-4)

                                     x =± sqrt(-1) sqrt(4)

                                       x =±i *2

                                       x = ±2i

So firstly, I will be factoring by grouping. Firstly, what two terms have a product of -4x⁴ and a sum of 3x²? That would be -x² and 4x². Replace 3x² with -x² + 4x²:

[tex]0=x^4-x^2+4x^2-4[/tex]

Next, factor x⁴ - x² and 4x² - 4 separately. Make sure that they have the same quantity on the inside:

[tex]0=x^2(x^2-1)+4(x^2-1)[/tex]

Now you can rewrite it as:

[tex]0=(x^2+4)(x^2-1)[/tex]

However, we can simplify it even further. With the second factor, apply the difference of squares rule (x² - y² = (x + y)(x - y)):

[tex]x^2-1=(x+1)(x-1)\\\\0=(x^2+4)(x+1)(x-1)[/tex]

Now it's fully factored. With this, apply the zero product property and solve:

[tex]x^2+4=0\\x^2=-4\\x=\pm \sqrt{-4}=\pm \sqrt{4}i\\x=\pm\ 2i\\x=2i,-2i\\\\x+1=0\\x=-1\\\\x-1=0\\x=1[/tex]

In short, your answer is D. -1, 1, -2i, 2i

Final answer:

To find 3/4 of 12, you multiply 12 by the fraction 3/4. Multiplying 0.75 (the decimal equivalent of 3/4) by 12 results in 9. Hence, 3/4 of 12 is 9.

Explanation:

To solve the problem: "What is 3/4 of 12," you would multiply. This type of problem is asking for a part of a whole, where 'of' typically signifies multiplication in mathematics. We can think about this conceptually: if half of 12 is 6, then three-quarters would be half of 12 plus half of 6. In mathematical terms, you would calculate 3/4 × 12 to find the answer.

To break it down:

Convert 3/4 to a decimal if needed, which is 0.75.

Multiply 0.75 by 12.

The result is 9, so 3/4 of 12 equals 9.

This is because when you are finding a portion of a number, you are determining how many times that portion fits into the whole. So, you're effectively scaling the number 12 by the fraction 3/4, which is accomplished through multiplication.

(5q2 − r2s)(25q^4+5q^2r^2s+1r^4s^2)

To factor the expression, identify the difference of squares in the first part and the sum of cubes in the second part. Apply the relevant factoring formulas to obtain the fully factored form.

To factor the expression[tex](q^2 - r^2s) (q^4 + q^2r^2s + r^4s^2),[/tex] we must first recognize that the second part is a sum of cubes. The formula for factoring a sum of cubes is [tex]a^3 + b^3 = (a + b)(a^2 - ab +b^2)[/tex]. The first part, [tex]q^2 - r^2s,[/tex] can be recognized as the difference of squares, which factors as (q - rs)(q + rs). Therefore, after applying these patterns the factored form of the expression is:

[tex](q - rs)(q + rs)(q^2 + qrs + r^2s^2)[/tex]

It is given that, Altitude above sea level =Positive Values

                                          =Positive Integer{1,2,3,4,5,6,7,8,.......}

Altitude below sea Level=Negative values

                                     =Negative Integer{-1,-2,-3,-4,-5,-6,.......}

Now, The situation given is

 A hiker in Death Valley stopping at an altitude of 0 feet

Zero(0)= The Point 0, means neither Positive nor Negative, that is additive Identity with respect to Addition of Integers.That is when two integers having Opposite sign, means additive Inverse of each other, are added together it yields Zero.

For example

-2 + 2=0

2 and -2 are Additive Inverse of each other.

Answer:

Out of every 5 rectangles 2 shall be purple.

3 scarves have 3 times 5 rectangles.

Thus they shall be 3 times 2 that are purple.

Answer: 2/3

Step-by-step explanation:

Slope Intercept Form: y = mx + b

m = slope

So, since 2/3 fits the form above, 2/3 is the slope in this equation.

The slope of the given line equation is [tex]m=\frac{2}{3}[/tex]. Since the given equation is in the form of slope-intercept form of a line y=mx+c.

The slope-intercept form of a line is expressed by the equation y=mx +c. where m is the slope and c is the y-intercept of the line.

Give that the equation of the line is y=2/3x+1

Comparing this equation with the standard form, we get

m = 2/3 and c=1

So, the slope of the given equation of the line is 2/3.

Learn more about slope-intercept form here:

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[tex]\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=-5\\ n=10\\ a_{10}=13 \end{cases} \\\\\\ a_{10}=a_1+(10-1)d\implies 13=-5+(10-1)d \\\\\\ 13=-5+9d\implies 18=9d\implies \cfrac{18}{9}=d\implies 2=d[/tex]

Answer:

Common difference = 2

Step-by-step explanation:

[tex]n^{th}[/tex] term of an arithmetic progression is given by a + (n-1)d, where a is the first term and d is the common difference.

Here first term is given as -5

           a = -5

Tenth term is 13

           n = 10

          [tex]n^{th}[/tex] term = 13

We have

       -5 + (10-1)d = 13

         9 d = 13 + 5

            9 d = 18

               d = 2

Common difference = 2

A fraction will be bigger than another if for the same denominator the numerator is bigger therefore fraction 7/8 will be bigger than 13/15.

In such a fraction, the value that appears above the horizontal line is referred to as the numerator.

In another word, if we divide two numbers by each other then the upper word is called the numerator, and the lower word is called the denominator.

As per the given fractions 7/8 and 13/15

Multiply 15 numerators and denominators to 7/8

(7/8) × 15/15 = (7 × 15/8)/15

⇒ 13.125/15

Since 13.125 > 13

Since A fraction will be bigger than another if for the same denominator the numerator is bigger.

So 7/8 > 13/15.

Hence " A fraction will be bigger than another if for the same denominator the numerator is bigger therefore fraction 7/8 will be bigger than 13/15".

For more about fractions,

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Answer:

Jose: 2/3 = 8/12

Jenna: 7/12

Jose has finished more of the race.

Answer:

Since the exponent of the scientific notation is positive  4, move the decimal point  4  places to the right.  

56800

Step-by-step explanation:

5.68(104)

=5.68*104

=5.68*(10*10*10*10)

=56800

Answer:

The standard form of [tex]5.68\times 10^{4}[/tex] is [tex]56800[/tex]

Step-by-step explanation:

We need to write [tex]5.68\times 10^{4}[/tex] in standard form

Re-write [tex]5.68\times 10^{4}[/tex] as,

[tex]5.68\times 10000[/tex]

⇒[tex]56800[/tex]

Therefore, standard form of [tex]5.68\times 10^{4}[/tex] is [tex]56800[/tex]

Answer:

40.5 g

Step-by-step explanation:

Find how much salt is in 450 g of a 9% salt solution.

Note that

450 g - 100%,

x g - 9%,

then

[tex]\dfrac{450}{x}=\dfrac{100}{9},\\ \\x=\dfrac{450\cdot 9}{100}=40.5\ g.[/tex]

If you evaporated all water from this solution, then you would get 40.5 g of salt.

Answer:

40.5g

Step-by-step explanation:

RSM anyone?

Answer:

x = 27976.22021

Step-by-step explanation:

10x + .0085x = 280000

Combine like terms

10.0085x = 280000

Divide by 10.0085 on each side

10.0085x /10.0085= 280000/10.0085

x = 27976.22021

Answer:

trrtrtrtrtrtrtrtrt

Step-by-step explanation:

Answer:1/6

Step-by-step explanation: because there are 6 side to a cube and you can only have a outcome of 1 so therefore, the answer is 1/6

Final answer:

Juan's experience of rolling the number 2 on a six-sided die 4 times deals with the concept of independent events in probability. The probability of getting a 2 on any single roll is 1/6 and to roll a 2 four times consecutively, you multiply the probabilities, resulting in a much smaller overall probability.

Explanation:

The question involves understanding the probability of rolling a certain number on a six-sided die, which is a concept in mathematics. When Juan rolls the six-sided number cube 4 times and gets the result of 2 each time, we are analyzing a sequence of independent events in probability. Since each roll of the die is independent, the outcome of one roll does not affect the outcome of the next roll and the probability of rolling a 2 on each individual roll remains constant at 1/6.

Event X, described as rolling an even number, has a probability of 3/6 or 1/2, since the even numbers on a die are 2, 4, and 6. However, the probability of rolling multiple 2's in sequence would be the product of probabilities for each roll. That is, the probability of rolling a 2 four times in a row would be (1/6) * (1/6) * (1/6) * (1/6), which is a much smaller probability. This reflects the notion that rolling the same number consecutively multiple times is less likely than rolling it once.

Answer:

Hey!

Your answer is £2121.80 in the account!

Step-by-step explanation:

So to do this, you have to first find out how much would be left after 1 year...

=     3 / 100 x 2000 = £60 *we now add this on to the £2000*

=     2000 + 60 = £2060 *this is what is in the account after 1 YEAR*

Then, find out the amount for the second year!

=     3 / 100 x 2060 = £61.80 *we now add this on to the £2060*

=     2060 + 61.80 = £2121.80 *this is what is in the account after 2 YEARS*

SO AFTER 2 YEARS, THERE IS AN AMOUNT OF £2121.80 IN THE BANK ACCOUNT!

HOPE THIS HELPS!!

Answer:

3/2 or 1.5

Step-by-step explanation:To find the perimeter you need to multiply the four sides why the same number like: 3/8in(4)wich equal 3/2in or in decimal point 1.5 hope it helps. :)

Answer:

See below

Step-by-step explanation:

13x + 5 + 17x - 4.5 + x

NOTE: You can only add/subtract LIKE terms . Here we have  variable terms in x  (13x , 17x and x) and 2 constants ( 5 and 4.5).

Sarah's next line is

18x + 17x - 4.5 + x

This is incorrect . It looks like she  added 13x + 5 and got 18x!! Which is of course wrong because they are NOT LIKE terms. 5 is a constant and 13x is a variable term in x.

The third line is correct:-

35x - 4.5 + x.

She has added the 2 variables 17x and 18x.

Fourth line  is  30.5x + x. She's at it again - Trying to subtract 4.5 from 35x .

Last line 31.5x

She has added  the 2 terms in x correctly, but the final answer is wrong of course due to the earlier errors.

Answer:

The answer is 2x^2 - xy^2 - 6y^4

Step-by-step explanation:

2xx + 2x(-2y^2) + 3y^2x + 3y^2(-2y^2)

2xx - 2 · 2xy^2 + 3xy^2 - 3 · 2y^2y^2

= 2x^2 - xy^2 - 6y^4

Hello.

X= −5/14 y

Step 1: Add -15x to both sides.

x−5y+ −15x= 15x+ −15x

−14x−5y=0

Step 2: Add 5y to both sides.

−14x −5y+5y= 0+5y

−14x=5y

Step 3: Divide both sides by -14.

−14x/−14= 5y/−14

x= −5/14 y

Have a nice day

Answer:

1 / 4 US cups = 4 US tablespoons

Step-by-step explanation:

trust me its right

Answer:

The first one

Step-by-step explanation:

Answer:

C. 4x + y = 21

Step-by-step explanation:

(4 x 3) + 9

12 + 9 = 21

Answer:

It's C.

Step-by-step explanation:

It's right on edmentum. Also, just use substitution. Not that hard.