Index form of 2m⁴-3m²+7

Answer:

Step-by-step explanation:

a.

a = 1 > 0  ← that means the parabola opens up, so the vertex is minimum of the function

b.

  [tex]f(x)=x^2+10x+20\\\\f(x)=\underline{x^2+10x+25} - 25+20\\\\f(x)=(x+5)^2-5[/tex]

Answer:

[tex]\sqrt{13}[/tex]

Step-by-step explanation:

d = √(7-4)²+(3-1)²

= √3²+2²

= √9+4

= √13

The coefficient of x⁸y⁹ is 81662929920.

A binomial is a two-term algebraic expression. Examples of binomials include a + b, x - y, and more.

The binomial expansion formulae are used to find the powers of the binomials that cannot be extended using the algebraic identities. 

Given expansion (3x + 2y)¹⁷

to find the coefficient of x⁸y⁹

this is found by binomial expansion,

(x + y)ⁿ = ∑ₙˣ⁻⁰ ⁿCₓxⁿ⁻ˣyˣ

here n = 17 and x = 9

(3x + 2y)¹⁷ = ¹⁷C₉ (3x)¹⁷⁻⁹ (2y)⁹

¹⁷C₉ = 24310

(3x + 2y)¹⁷ = 24310 (6561) (x)⁸ (512) (y⁹)

(3x + 2y)¹⁷ = 81662929920x⁸y⁹

Hence the coefficient is 81662929920.

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The solution of the equations are x = √1 = ± 1

Now, According to the question:

The given equation is [tex]9x^4 - 2x^2 - 7 = 0[/tex]

Using the substitution rule we put [tex]x^{2}[/tex] = u .

The given equation now changes to

[tex]9u^2 - 2u - 7 = 0[/tex]--- (1)

Equation(1) is a simple quadratic equation which can be solved by factorization as follows:

[tex]9u^2 - 2u - 7 = 0[/tex]

(9u + 7)(u - 1) = 0

Therefore

9u + 7 = 0 → u = -7/9

u -1 = 0→ u = 1

Since u = [tex]x^{2}[/tex] implies

x = √-7/9 = ± i√7/9

x = √1 = ± 1

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The complete question is this:

What are the solutions of the equation [tex]9x^4 - 2x^2 - 7 = 0[/tex]? use u-substitution to solve.

Binomial is the referred to the polynomial algebraic expression that has two terms.

An expression with two dissimilar terms joined by an addition or subtraction operator is called a binomial in algebra. Since there are two terms, for instance, 2xy + 7y is a binomial. According to the quantity of terms present, algebraic expressions can be divided into different types, such as monomial, binomial, trinomial, etc.

An expression in algebra with two terms is called a binomial. Alternatively stated, a binomial expression is an algebraic expression made up of two terms that are dissimilar and have constants and variables. Using mathematical operators like + (plus) and - (minus), these terms are joined. Depending on how many terms it contains, an algebraic expression is classified as a binomial, monomial, trinomial, quadrinomial, etc.

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Answer:

27.3%

Step-by-step explanation:

300/1100 = 0.2727

to get percentage we multiply ^^ by 100

so = 27.27% or rounded to nearest tenth = 27.3

Answer:

C)

hope this helped

Step-by-step explanation:

Answer:

7:13

Step-by-step explanation:

Answer:

if im thinking correctly ratios can be written in 3 ways

Step-by-step explanation:

so it could be 7/13, 7 to 13, or 7:13

Answer:

x = 8

Step-by-step explanation:

∠ B ≅ ∠ D

∠ A ≅ ∠ C

Then

Δ BAD ≅ Δ DCE ( AA postulate )

Then the ratios of corresponding sides are equal, that is

[tex]\frac{BA}{DC}[/tex] = [tex]\frac{BD}{DE}[/tex] , substitute values

[tex]\frac{x}{4}[/tex] = [tex]\frac{12}{6}[/tex] = 2 ( multiply both sides by 4 to clear the fraction )

x = 8

Answer:

x > -5

( -5, ∞)

Step-by-step explanation:

6 - 11x < 61

Subtract 6 from both sides

-11x < 55

Divided both side by -11. When divided by a negative number the < switch to >

So, the answer is

x > -5

Or

(-5,  ∞)

Answer:

27 L

Step-by-step explanation:

To find 12.5% of 24, move the decimal all the way to the left and multiply 24 by 0.125. You get 3, which is how much was added to the original volume.

24 + 3 = 27, which is the new volume.

Answer:

hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Step-by-step explanation:

Answer:

50 miles.

Step-by-step explanation:

You can visualize this as a triangle. the west route is one leg and the south route is the other. The distance from the starting point is the hypotenuse. 48^2+14^2=c^2, c=50.

Answer:

50

Step-by-step explanation:

[tex]48^{2} + 12^{2} = x^{2} \\X= 50[/tex]

Answer:

B, 6

Step-by-step explanation:

As there are 2 service options and 3 regular options All you do is multiply them:

2×3=6

Heres a different way to show it:

FS = Full service

SS = self service

R = regular

M = Midgrade

P = Premium

FS,R FS,M FS,P

SS,R SS,M SS,P

So it's 6

Answer:

B. 6

Step-by-step explanation:

Full/self service = 2 options

regular/mid/premium = 3 options

2 x 3 = 6

The amount of eroded rock in cubic kilometres is 1 km3.

To calculate the amount of eroded rock in cubic kilometres, we need to find the volume of the area that has been eroded. The volume of a rectangular shape is found by multiplying the length, width, and height (or depth) together.

In this case, the area that has been eroded is 10 km long, 5 km wide, and 20 m deep. However, we need to convert the depth from meters to kilometres to match the units of the other measurements. Since 1 km = 1000 m, we can convert the depth by dividing by 1000:

20 m / 1000 = 0.02 km

Now that all of the measurements are in kilometres, we can find the volume by multiplying them together:

10 km * 5 km * 0.02 km = 1 km3

So the amount of eroded rock in cubic kilometres is 1 km3.

Complete Question:

The amount of eroded rock is measured in cubic kilometres (km3). A cubic kilometre is a cube that measures 1 km on each side. How many km3 of rock were eroded in an area that is 10 km long, 5 km wide, and 20 m deep?

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When subtracted -2a+7b=-5 from the other equation so the b-terms become opposites, we get 2a -7b = 5 as the result.

In mathematics, an equation is an expression or a statement made up of two algebraic expressions with the same value that are separated by the equal sign. It is a mathematically quantified version of an otherwise expressed statement. Equations can take many different forms. Equations are used to compare two expressions.

To Subtract -2a+7b=-5 from the other equation so the b-terms become opposites, we need to make +7b to -7b

This is only possible when the other term has 14,

Lets solve

 2a + 7b = - 5

- 4a + 14b = -10

-2a -7b = 5

Thus, when subtracted -2a+7b=-5 from the other equation so the b-terms become opposites, we get 2a -7b = 5 as the result.

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Answer:

Supplementary angles

Step-by-step explanation:

I took the test and this was the correct answer

Answer:

x=12

Step-by-step explanation:

10x-18+6x+6=180

16x-12=180

16x=180+12

16x=192

x=192/16

x=12

plz mark as brainliest

r = (sin theta + C)^(-1) where C is an arbitrary constant of integration.

Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation. Assuming that a function's rate of change with regard to x is inversely proportional to y, we may write it down as dy/dx = k/y.

r = (cos(theta) - d/d(theta) of sec(theta)) / sec(theta)

The differential equation assists us in presenting a relationship between the changing quantity with respect to the change in another variable. The derivative represents nothing more than a rate of change. Be a function with the form: y=f(x), where x is an independent variable, f is an unknown function.

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Answer:

7 : 1 or 7/1

.........................

Answer:

Step-by-step explanation:

f(x) is quadratic function and g(x) is linear (since AP in the right column).

Find the equation of the function f(x), use the points on the graph:

The function is:

Find the equation of g(x)

Find the slope of g(x):

Use (-4, 7) to find its equation:

The y-intercepts:

Values at x = 3:

Average rate of change in the interval [2,5]:

Max of function in the interval [-5, 5];

Answer:

Step-by-step explanation:

What grade are you in bc I did this

The slope of a logarithmic graph depends on the type of logarithm used.

For a logarithmic function in the form y = log(b,x) where b is the base of the logarithm, the slope of the graph is undefined for x=0 and for x<0 because logarithmic functions are not defined in those cases.

For a natural logarithm, the slope is negative infinity at x=0 and positive for x > 0. As x increases, the slope becomes closer to zero.

For a common logarithm, the slope is negative infinity at x=0 and positive for x > 0. As x increases, the slope becomes closer to zero.

It's important to note that logarithmic functions are not linear functions, and therefore they do not have a constant slope, the slope of a logarithmic graph will change throughout the graph.

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The provided phrase, x3+4x2+ 7x+ â' 2 has four terms. and coefficient are 1 , 4 ,7 for the expression

What does the phrase mean?

Expressions are made up of terms. A term might be either a constant, a variable, or a combination of both.

What kind of phrase would that be?

A single letter, a single positive or negative integer, or a number of variables multiplied but never added or subtracted might be the only variable. A number is placed in front of some nouns that have variables. The number used before a sentence is called a coefficient. single-word illustrations: Three times in one phrase.

The mathematical operator + separates the four components in the equation x3+4x2+ 7x+â' 2.

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Answer:

The correct answer is 0 or choice A on edge

Step-by-step explanation:

right on edge

Therefore, value of r(x) as x approaches Infinity : zero

[tex]\bold{\lim_{x \to \infty} r(x)=0}[/tex]

"A function is a special relationship where for each input and their is single outputs."

"Limit is defined as the value that a function approaches for the given input value."

For given situation,

We have been given a function,

r (x) = Start Fraction a x Superscript b Baseline + 8 Over c x Superscript d Baseline End Fraction

We can rewrite it as,

[tex]r(x)= \frac{ax^b+8}{cx^d}[/tex] , where a, b, c, and d are positive integers and b < d.

We need to find the value of r(x) approach as x approaches Infinity.

This means, we need to find the value of the limit [tex]\lim_{x \to \infty} r(x)[/tex]

Now, we find the value of limit for given function.

[tex]\lim_{x \to \infty} r(x)[/tex]

=  [tex]\lim_{x \to \infty} \frac{ax^b+8}{cx^d}[/tex]

= [tex]\lim_{x \to \infty} (\frac{ax^b}{cx^d} + \frac{8}{cx^d})[/tex]

= [tex]\lim_{x \to \infty} \frac{a}{cx^(d-b)} + \lim_{x \to \infty} \frac{8}{cx^d}[/tex]                          ...............(since d > b)

= [tex]0 + 0[/tex]

= [tex]0[/tex]

Therefore, [tex]\bold{\lim_{x \to \infty} r(x)=0}[/tex]

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The degree of the polynomial [tex]5x^{3} + 4x^{2} + 7x[/tex]  is 3 , that means it is a third degree polynomial called as cubic polynomial  .

What is Degree Of Polynomial ?

The degree of the polynomial is defined as  the highest power of the polynomial expression. But, if the polynomial has multiple variables, the degree of polynomial can be found by adding the powers of the different variables  in the polynomial expression.

For Example : the degree of polynomial ⇒  [tex]9x^{2} + 7x + 2[/tex] is  2 .

The polynomial is given as : [tex]5x^{3} + 4x^{2} + 7x[/tex] , we have to find the degree ,

So , we can see that the the term having the highest power of the given polynomial is [tex]5x^{3}[/tex] , and the degree is 3 .

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For example, if S={1, 2, 3, 4, 5, 6, 7} and T={1, 2, 3, 4, 5, 6}, then x=6>5=y, but if S={1, 2, 3, 4, 5, 6, 7} and T={1, 2, 3, 4, 5, 7}, then x=6=y. not sufficient.

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Complete question is: If the ranges of values = 40 and the number of sets = 10 , then what will be the length of set ?