The equation of a line is given below.
2x + 5y = -5
Find the slope and the y-intercept.
Then use them to graph the line.

Answer:

Step-by-step explanation:

y = -1(x + 2)(x - 3)(x - 3)(x + 0)(x + 0)(x + 1)(x + 1)(x + 1)

The 8 degree polynomial for the given roots can be written as  p(x) =  x⁸ - x⁷- 12x⁶ - 4x⁵ + 30x⁴ + 51x³ + 18x².

The factor theorem states that for a polynomial p(x) if there exists a real number a such that p(a) = 0, then (x - a) is one of the factors of p(x).

The roots of the polynomial are given as follows,

Number of roots at -2 = 1

Number of roots at 3 = 2

Number of roots at 0 = 2

And, number of roots at -1 = 3.

Now, the polynomial can be written using factor theorem as,

p(x) = x²(x + 2)(x - 3)²(x + 1)³

      = x²(x + 2)(x²- 6x + 9)(x³ + 3x² + 3x + 1)

      = x⁸ - x⁷- 12x⁶ - 4x⁵ + 30x⁴ + 51x³ + 18x²

Hence, the polynomial for given roots can be written as p(x) =  x⁸ - x⁷- 12x⁶ - 4x⁵ + 30x⁴ + 51x³ + 18x².

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Recall the binomial theorem:

[tex]\displaystyle (a + b)^n = \sum_{k=0}^n \binom nk a^{n-k} b^k[/tex]

where [tex]\binom nk = \frac{n!}{k!(n-k)!}[/tex] is the binomial coefficient.

Take a = x/3, b = -3, and n = 7. Then we get the x⁵ and x⁴ terms when 7 - k = 5 and 7 - k = 4, respectively; or when k = 2 and k = 3.

[tex]k=2 \implies \dbinom 72 \left(\dfrac x3\right)^{7-2} (-3)^2 = 21 \cdot \dfrac{x^5}{243} \cdot 9 = \dfrac79 x^5[/tex]

[tex]k=3 \implies \dbinom 73 \left(\dfrac x3\right)^{7-3} (-3)^3 = 35 \cdot \dfrac{x^4}{81} \cdot (-27) = -\dfrac{35}3 x^4[/tex]

Then when multiplying this expansion by x - 6, we get an x⁵ terms from the products

[tex]\dfrac79 x^5 \cdot (-6)[/tex]

and

[tex]-\dfrac{35}3 x^4 \cdot x[/tex]

so that the x⁵ term in the overall expansion of (x/3 - 3)⁷ (x -  6) has a coefficient of

[tex]\dfrac79\cdot(-6) + \left(-\dfrac{35}3\right) \cdot 1 = \boxed{-\dfrac{49}3}[/tex]

Answer:

y = 3

x = 2

Step-by-step explanation:

-5x + 4y = 2

9x - 4y = 6

Sum both eq.

-5x + 9x = 4x

+4y - 4y = 0

2 + 6 = 8

then:

4x + 0 = 8

4x = 8

x = 8/4

x = 2

from the first eq.

-5x + 4y = 2

-5*2 + 4y = 2

-10 + 4y = 2

4y = 2 + 10

4y = 12

y = 12/4

y = 3

Check:

from the second eq.

9x - 4y = 6

9*2 - 4*3 = 6

18 - 12 = 6

Answer:

0.4 or 2

Step-by-step explanati

that easy

Step-by-step explanation:

again, a line cutting through 2 parallel lines must have the exact same angles with both of them. otherwise they would not be parallel.

therefore, both angles must be identical

3x + 2 = 2x + 6

x = 4

Answer:

-8

Step-by-step explanation:

Pluck in the values:

P = 3 + (-11)

P = 3 - 11 = -8

Answer:

Step-by-step explanation:

How many Skittles is in a 4 pound bag?

Fun-size packages are perfect for parties, party favors, trick-or-treaters, gift baskets, lunch treats and on-the-go snacks. Approximately 20 individual packs per lb.

...

Skittles Fun-Size Packs, 4-Lb Box.

[tex]\\\\\\x^2 -8x +16 = 0\\\\\implies x^2 - 2(4) + 4^2 =0\\\\\implies (x-4)^2 =0\\\\\implies x -4 =0\\\\\implies x =4\\\\\text{This equation has only one solution.}[/tex]

Answer:

a. 6

b. 21

c. 78

d. 13.5

e. 14

f. 24

Hope that helps!

Answer:

If there was another dog whose weight was greater than or less than 12.

Step-by-step explanation:

12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 4

When we add 4 to the data set we have:

184 ÷ 16 = 11.5

This changed the median.

12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 28

When we add 28 to the data set we have:

208 ÷ 16 = 13

This also changed the median.

By adding dog of  weight other than 12 pounds could change the median.

What is median?

The median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average. The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values.

If we add the dog whose weight is more than 12 pounds, median will increase .

If we add the dog whose weight is less than 12 pounds, then median will decrease.

Hence, adding  dog of  weight other than 12 pounds could change the median.

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The potential gain that could have come with golfing

Step-by-step explanation:

Opportunity cost is the loss of something you could have gotten from the choice you didn't go with. so I'm this case, the opportunity cost of chosing the movies is what you missed out on by not going golfing.

Answer:

B. (0,-1)

Step-by-step explanation:

see.. i'm not rude.... :/

Answer:

WT = 63

Step-by-step explanation:

Given Δ SDE is similar to Δ SWT then the ratio of corresponding sides are in proportion, that is

[tex]\frac{WT}{DE}[/tex] = [tex]\frac{ST}{SE}[/tex] , substitute values

[tex]\frac{5x+3}{56}[/tex] = [tex]\frac{4x-3}{40}[/tex] ( cross- multiply )

56(4x - 3) = 40(5x + 3) ← distribute parenthesis on both sides

224x - 168 = 200x + 120 ( subtract 200x from both sides )

24x - 168 = 120 ( add 168 to both sides )

24x = 288 ( divide both sides by 24 )

x = 12

Then

WT = 5x + 3 = 5(12) + 3 = 60 + 3 = 63

Answer:

2677 mi^2

Step-by-step explanation:

Think the shape as an complete rectangle :

The area of the rectangle is calcluated by multiplying height*width

(24+12+19)*55 = 3025 mi^2 now subtract the area of the missing part using same area calculation method:

12*29 = 348 mi^2 the area of the figure:

3025 - 348 = 2677 mi^2

Answer:

LQ = 54

Median = 69

UQ = 94

Step-by-step explanation:

This list is already sorted for you, so you don't need to worry about that, otherwise you would need to sort the numbers in ascending order. To find the median, we do [tex]\frac{n+1}{2}[/tex], where n is the amount of numbers. This gives us 4, so the median is at position 4, so the median is 69. The lower quartile is simply [tex]\frac{n+1}{4}[/tex], so 2, so the lower quartile is 54. The upper quartile is [tex]\frac{n+1}{2} X 3[/tex], so 6, so the upper quartile is 94.

Answer:

the answer u r looking for is 144

Step-by-step explanation:

if u know who this is i will follow u

hint: its from avatar tla

only the first person that answers!!!

Answer:

b = 14

Step-by-step explanation:

Since both angles are diagonal each other, they are equal to each other.

5b = b + 56

-b      -b           (subtract b from both sides)

4b = 56

4       4            (divide both sides by 4 to solve for b)

 b = 14

The expression which is equivalent to 1/4 (5x + 6) is; Choice A: {5(1/4)x} + {6(1/4)x}.

According to the question:

In a bid to expand the expression; we must multiply each term in the parenthesis by (1/4);

In essence; we have;

Read more on multiplication;

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Evaluate the following division: (3b-6a)÷(30a-15b) is -1/5.

~ Algebraic Forms and their Elements

Algebraic form is a mathematical form whose presentation involves symbols or letters to represent unknown numbers.

Elements of Algebra:

1. Variables, Constants and Coefficients

Pay attention to the algebraic form 3x + 2y + 3

From the algebraic form above, x and y are variables (variables), while the number 3 is a constant. A variable is a substitute symbol for a number whose value is not clearly known. While constants are terms of an algebraic form in the form of numbers and do not contain variables.

And what is meant by the coefficient is the constant factor of a term in algebraic form. The coefficient on the 3x term is 3, on the 2y term it is 2.

2. Terms and Factors

» The term is part of the algebraic form which is limited by the operation of addition (+) or difference (-). The term one is an algebraic form that is not connected by the operation of addition or difference.

Example: 2x, 2a², -4xy, . . .

» Term two is an algebraic form that is connected by an operation of sum or difference.

Example: 2x + 3, a² - 4, 3x² - 4x, . . .

» Similar terms in algebraic form are terms that have the same variable and the same power.

Example:

2a is similar to 3a, 4a, etc.

» Factors are part of the algebraic form that is restricted to multiplication operations.

Example: 5n = 5 × n, 5 and n are factors of 4n, respectively.

Calculation Operations on Algebraic Forms

1. Addition and subtraction of algebraic forms can only be done on similar terms.

2. Multiplication and division of algebraic forms.

Multiply two terms by constants or variables.

Example:

3 (4y + 5)

= (3 × 4y) + (3 × 5)

= 12y + 15

Division of two terms with a variable or constant, for example:

(8y+4)/2 = 8y/2 + 4/2 = 4y + 2

(3b-6a)÷(30a-15b)

= (-6a + 3b) ÷ (-5(-6a+3b))

= (-6a+3b)/(-5(-6a+3b))

= -1/5

So, Evaluate the following division: (3b-6a)÷(30a-15b) is -1/5.

(mampir ke indo:v)

_____________

Class: 7 Middle School

Subject: Math

Material: Chapter 2.1 -Operations of Algebraic Forms

Categorization Code: 7.2.2.1

Keywords: Simple form of algebra

Answer:

-10

Step-by-step explanation:

when a number Inside of parentheses is close to another number (like being near a fireplace trying to say warm) it means to multiply :3 !

Example: (3)2=6           6(6)=36

in our case it is (-5)2        So was ist -5 x 2? -10

hope this helped!

for some extra practice to check your knowledge, what is (-3+-2)2 ?

Answer:

0.68

Step-by-step explanation:

Answer:

Option D

Step-by-step explanation:

Use Factoring Methods

[tex]4x^3-8x^2-9x+18\\[/tex]

put bracket around each 2 terms as such [tex](4x^3-8x^2)+(-9x+18)[/tex]

And then factor each respective bracket. We'll start with the first one

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

Then do the other, and try to get similar brackets as the first

[tex](-9x+18)=-9(x-2)[/tex]

Since they are both simiar, the equation is now: [tex](4x^2-9)(x-2)[/tex]

Now factor the first bracket again for final result

[tex]4x^2-9=(2x-3)(2x+3)[/tex]

Ans when you put it all together, you get: [tex](2x-3)(2x+3)(x-2)[/tex]

Correct answer is option D

Answer:

using the pithagerum therom

a² + b² = c²

this formula is to find the side of your triangle with 2 sides already known

the answer is A) 17.7

Answer:

alr yeah i get it now

Step-by-step explanation:

its A 11/14

Answer:

[tex]\frac{11}{14}[/tex]

Step-by-step explanation:

[tex]\frac{2}{7}[/tex] + [tex]\frac{7}{14}[/tex]

Before adding er require the fractions to have the same denominators.

Multiply the numerator/ denominator of the first fraction by 2

= [tex]\frac{2(2)}{7(2)}[/tex] + [tex]\frac{7}{14}[/tex]

=[tex]\frac{4}{14}[/tex] + [tex]\frac{7}{14}[/tex]  ( now add numerators leaving the common denominator )

= [tex]\frac{4+7}{14}[/tex]

= [tex]\frac{11}{14}[/tex]

Answer:

i think d) -25 is answer

Step-by-step explanation:

good luck

Answer:

d) -25

Step-by-step explanation:

Because -25 is less than -23 . as it is negative integers