Polynomials & Factoring
(4m+n)(m-2n)

(2a-4b)(7a-2b)
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The trend line is a strong fit for the data on yellow-spotted salamanders.

A graph can be described as a pictorial representation of data. A trend line is used to show the direction of the data plotted. The trend line shown is positive. This means that as the number of spots increases, the weight of the salamander increases. The trendline is strong because most of the dots lie along the trendline.

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Answer:

x = 9

Step-by-step explanation:

using the rule of logarithms

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

given

[tex]log_{x}[/tex] 729 = 3 then

729 = x³

note 729 = 9³ , so

9³ = x³ ( equating the bases) , gives

x = 9

Answer:

    x = 9

Step-by-step explanation:

Sum of all angles of a triangle = 180

                63 + 7x + 6x  = 180

                  63  +  13x    =180

                             13x   = 180 - 63

                              13x  = 117

                                 x  = 117/13

x = 9

Answer:

X= 9

Step-by-step explanation:

The angles in a triangle all add up to 180°

Hence we can form this equation :

63 + 7x + 6x = 180°

Subtracting 63 from both sides:

7x + 6x = 117°

Adding together to find the total X:

13x = 117°

Finally, diving by 13 on both sides:

X = 9

Answer:

(x-4)² -11 where a = 4, b = 11

Step-by-step explanation:

The final form (x-a)² - b evaluates to x² - 2ax + a² -b

Matching

x² - 8x    +  5    

x² - 2ax  +  a² -b

This gives us -2ax = -8x or -2a = -8 or a = 4

and a² - b = 11 ==> 16 - b = 11 or b =5

Rewritten form is

(x-4)² -11

Answer:

H=4.243

Step-by-step explanation:

Formula: A^2+B^2=C^2

(3)^2+(3)^2=C^2

9+9=C^2

sqrt18=C

C=4.242640....

Answer: 1.9

Step-by-step explanation:

Question 11

9.88 rounds to 10

5.2 rounds to 5

10/5 = 2

Answer:

Negative number Addition and Subtraction.

Step-by-step explanation:

Ok so, 1-(-4)+ to 5

and 2-(-3) also = to 5 so you can kinda see a pattern if you get this 1 has to subtract by 5 bc 1-5=-4 and the same for the others so I hope I get this right and it helps.

y=x+-5

Answer:

New area is 1/9th the original area

Step-by-step explanation:

Original area   =   L x W

now reduce the side lengths

   1/3 L   x    1/3 W

   1/3 * 1/3   * L x W

       1/9   L x W       <===== the new area is 1/9th the original area

Answer:

Option 2

Step-by-step explanation:

Checking whether P(A) × P(B) = P(A∩B) :

Since this does not obey the Multiplication rule of probability, these events are not independent.

So, the answer is :

No, they are dependent because P(A) ⋅ P(B) ≠ P(A ∩ B)

Answer:

Option B

Step-by-step explanation:

Option A should be true if they are independent

So

They are dependant

Answer:

[tex]\frac{3}{20}[/tex]

Step-by-step explanation:

slope/gradient=[tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]

                        =[tex]\frac{-9.75+9}{-1-4}[/tex]

                        =[tex]\frac{3}{20}[/tex]

The completely factored expression of 12x⁴ + 39x³ + 9x² is 3x²(4x + 1)(x + 3)

The polynomial expression is given as;

12x⁴ + 39x³ + 9x²

Factor out 3x² from the expression

3x²(4x² + 13x + 3)

Expand

3x²(4x² + 12x + x + 3)

Factorize the expression

3x² * 4x(x + 3) + 1(x + 3)

Factor out x + 3

3x²(4x + 1)(x + 3)

Hence, the completely factored expression of 12x⁴ + 39x³ + 9x² is 3x²(4x + 1)(x + 3)

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Answer:

28 grapes in total

Step-by-step explanation:

grapes are shared in the ratio 2 : 5 = 2x : 5x ( x is a multiplier )

Eva gets 12 more grapes than Dora , then

5x = 2x + 12 ( subtract 2x from both sides )

3x = 12 ( divide both sides by 3 )

x = 4

total grapes = 2x + 5x = 7x = 7 × 4 = 28

Eva gets 5x = 5 × 4 = 20

Dora gets 2x = 2 × 4 = 8

that is Eva gets 12 more than Dora

Answer:

C) [tex]3\cdot10^{-6}[/tex]

Step-by-step explanation:

Divide the two numbers:

[tex]\displaystyle \frac{6\cdot10^{-2}}{2\cdot10^{-8}}=\frac{6}{2}*\frac{10^{-2}}{10^{-8}}=3\cdot10^{-2-(-8)}=3\cdot10^{-2+8}=3\cdot10^{6}[/tex]

Thus, C is the correct choice.

Answer:

is A

Step-by-step explanation:

Answer: The final price is less than the original

Step-by-step explanation:

    Let us break this down a bit.

The original price is $500

-> At the beginning, the price was marked up by 20%

-> At the end, the price at the beginning of the season is marked down by 20%

    We are solving for: "How does the final price compare with the original price of $500​"

        First, we will find the price at the beginning.

-> Please note a percent divided by 100 becomes a decimal

20% / 100 = 0.2

$500 * 0.2 = $100

$500 + $100 = $600

     Now, we will find the price at the end.

$600 * 0.2 = $120

$600 - $120 = $480

     The final price is less than the original price of $500.

Answer:

Step-by-step explanation:

price marked up by 20%= 500+ [tex]\frac{20}{100}[/tex]×500

                                        =$600

price marked down by 20%= 600- [tex]\frac{20}{100}[/tex]×600

                                             =$480

the final price is less than the original price

Answer: 5/12

Step-by-step explanation: basically divide each number (10 &24) by 2

Answer:

y = mx + b

y = 1/3x + b

Use (2,4) to find b

4 = 1/3(2) + b

b = 4 - 2/3

b = 12 - 2

3

b = 10/3

The equation will be:

The equation will be: y = 1/3x + 10/3

Step-by-step explanation:

[tex] {x}^{2} + 6x - 2 = {x}^{2} + 2px + {p}^{2} + q[/tex]

[tex]2p = 6[/tex]

[tex] {p}^{2} + q = - 2[/tex]

[tex]p = 3[/tex]

[tex] {3}^{2} + q = - 2[/tex]

[tex]q = - 11[/tex]

p=3, q=-11

Answer:

2.8

Step-by-step explanation:

Just substract 7.2 from 10

You get: 2.8

Answer:

2.8

Step-by-step explanation:

because 7.2 plus 2.8 equals

Answer:

13

Step-by-step explanation:

Volume to find radius: [tex](3\frac{V}{4\pi})^1^/^3[/tex]

Substitute: [tex](3\frac{9198.1}{4\pi})^1^/^3[/tex]

Solve: [tex](3(732.3))^1^/^3[/tex]

[tex]2196.9^1^/^3[/tex]

13≈r

Answer:

b=20

Step-by-step explanation:

[tex] {b}^{2} = {c}^{2} - {a}^{2} \\ b = \sqrt{ {25}^{2} - {15}^{2} } \\ b = 20[/tex]

Answer:

$1320

Step-by-step explanation:

4%=0.04

Intrest = 0.04x8

Intrest = 0.32

Intrest = 1000x0.32

Intrest = 320

Then add 1000+320=1320

Answer:

(10-4)/2 , (2-8)/2

6/2 , -6/2

Midpoint = (3,-3)

Answer:

145 is the outlier

Step-by-step explanation:

When compared to the other values, 145 is an exceeding highly value. Hence, it can be considered an outlier in the data set.

[tex]xy \\\\=\left(\log_{5\sqrt 5} ~125 \right)\left(\log_{2\sqrt 2} ~64 \right)\\\\=\left(\log_{5\sqrt 5} ~5^3 \right)\left(\log_{2\sqrt 2}~2^6 \right)\\\\=\left(3\log_{5\sqrt 5} ~5 \right)\left(6\log_{2\sqrt 2} ~2 \right)\\\\=\left( 18 \cdot \dfrac{\ln5}{\ln\left(5\sqrt 5\right)} \cdot \dfrac{\ln 2}{ \ln \left( 2 \sqrt 2 \right)}\right)\\\\[/tex]

[tex]=\left( 18 \cdot \dfrac{\ln5}{\ln\left(5^{\tfrac 32}\right)} \cdot \dfrac{\ln 2}{ \ln \left( 2^{\tfrac 32} \right)}\right)~~~~~~~~~~~;\left[\sqrt a = a^{\tfrac 12}~~ \right]\\\\=\left( 18 \cdot \dfrac{\ln5}{\tfrac 32\ln5^} \cdot \dfrac{\ln 2}{\tfrac 32 \ln 2 }\right)\\\\\\=18 \cdot \dfrac 23 \cdot \dfrac 23 \\\\=\dfrac{72}9\\\\=8[/tex]

Step-by-step explanation:

(x - h)² + (y - k)² = r²

with (h, k) being the center and r the radius.

in our case the center is (1, 3), the radius is 3.

so, the right answer is the third answer option

(x - 1)² + (y - 3)² = 9

Answer:

The median number of shoes for the girls is greater than the median number of shoes for the boys.

Answer:

2)   10.01 year

Step-by-step explanation:

1) already answered elsewhere in your posts

2)    9000 = 6500 e^(.0325 * t)          where t = years

      9000/6500 = e^(.0325*t)          take ln (natural log) of both sides

      .3254224 = .0325t

        t = 10.01      10.01 year

Answer:

The formula to get the circumference of a circle is [tex]C=2*\pi * r[/tex] but in this case we see that a diameter is being used therefore we can get rid of the 2 and the r because that is what the diameter and just replace d into there like this [tex]C=d*\pi[/tex].

We can then input the value and we get that [tex]C=5*\pi[/tex] which then just narrows down to [tex]C=15.708[/tex].

Hope this helps!  Let me know if you have any questions

Answer:

(6.5,-6)

Step-by-step explanation:

(7+6)÷2= 6.5

(-5+-7)÷2=-6

To answer this item, note that what needs to be done is to substitute -4 to all x's in the equation. That is,

                    F(x) = 2^x

will become,

                    F(-4) = 2^(-4) = 1/16 or 0.0625