negative 3 plus negative 5 ​

Answer: 10.5 miles

Step-by-step explanation:

Answer:

Step-by-step explanation:

The factorise form of the trinomial  6x² + 11x - 10 is (3x - 2)(2x + 5).

Trinomials is a polynomial that has three terms. Let's factorise the trinomial by grouping as follows:

6x² + 11x - 10

The grouping method can be used to factor polynomials whenever a common factor exists between the groupings.

Hence, let's find the factor of 6x² + 11x - 10

6x² + 11x - 10

let's find two numbers we can multiply to get -60 and add to get 11.

6x² + 15x - 4x - 10

3x(2x + 5) - 2(2x + 5)

Hence,

(3x - 2)(2x + 5)

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The end-behavior of the polynomial is:

A) f(x) → -∞, as x → -∞

f(x) →∞, as x → ∞

What in mathematics is a polynomial?

The only operations used in a polynomial are addition, subtraction, multiplication, and non-negative integer exponentiation. In mathematics, variables are occasionally referred to as indeterminates. An example of a polynomial with a single variable x is x2 4x + 7.

The leading term of the polynomial is -2x⁴, which is negative for negative x and positive for positive x. As x approaches negative infinity, -2x⁴ approaches negative infinity, so the entire polynomial approaches negative infinity. Similarly, as x approaches positive infinity, -2x⁴ approaches positive infinity, so the entire polynomial approaches positive infinity.

Therefore, the end-behavior of the polynomial is:

f(x) → -∞, as x → -∞

f(x) →∞, as x → ∞

E) None of these

The polynomial is continuous for all real values of x. The only way for a polynomial to not be continuous is if there is a hole or a vertical asymptote in its graph. Since the graph of a polynomial is a smooth curve, there are no holes or vertical asymptotes, so the polynomial is continuous for all real values of x.

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Answer:

Step-by-step explanation:

90 inches

10%=9 inches

5%=4.5 inches

5x5=25

4.5 inches x5=22.5 inches

90-22.5=67.5

the new couch is 67.5 inches long

Answer:

(2x-7)(9x+2)

Step-by-step explanation:

Find The Least Common Multiplier of 9x+2, 2x-7

Answer:

L = -7

Step-by-step explanation:

5L - 6 - 7L = 8

combine like terms

5L - 7L - 6 = 8

-2L - 6 = 8

add 6 to both sides

-2L = 14

divide by -2

L = -7

Answer:

Data analytics. Data analytics is a set of tools which helps in organizing, presenting information, and extracting meaning from raw data.

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The difference in rates between the 2 peoples is 2.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

John y=5x

For sally we have to find the equation

m=28-14/4-2

m=14/2=7

14=7(2)+b

b=0

So for Sally y=7x

Hence, the difference in rates between the 2 peoples is 2.

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Answer: The function that models the relationship between the number of games played (n) and the number of credits remaining on the card (C(n)) is C(n) = 5n.

Step-by-step explanation: This function can be derived by realizing that each game costs 5 credits to play, so as the number of games played (n) increases, the number of credits remaining on the card (C(n)) decreases by 5 for each game played.

For example, if Shivani played 16 games before her card ran out of credits, we can substitute n = 16 into the function to find that C(16) = 5(16) = 80 credits. This means that her card had 80 credits on it before she started playing games.

To plot points on the graph, we can select a few different values of n and substitute them into the function to find the corresponding values of C(n). Here are a few examples:

When n = 0, C(n) = 5(0) = 0. This represents the case when Shivani has not played any games yet and has no remaining credits on her card.

When n = 8, C(n) = 5(8) = 40. This represents the case when Shivani has played 8 games and has 40 credits remaining on her card.

When n = 16, C(n) = 5(16) = 80. This represents the case when Shivani has played 16 games and her card has no remaining credits.

We can plot these points on the graph and label them (0,0), (8,40), (16,0) respectively.

Note that the y-intercept is (0,0) and the x-intercept is (16,0)

Graph:

n C(n)

0 0

8 40

16 0

The graph is a straight line starting from (0,0) and going down till (16,0) with a slope of -5.

The area enclosed by the curve x = t² - 2t, y = √(t), and the y-axis is 0.754 square units.

First, find the value of t at x = 0

x = t² - 2t

⇒ t² - 2t = 0

⇒ t(t - 2) = 0

Therefore, t = 0, t = 2.

Derivative of area, dA/dy

dA/dy = (0 - x)

dA = (0 - x) × dy

Since the curve has a negative x in this region.

y = √t (given)

dy/dt = (1/2)/√t

dA = [0 - (t² - 2t)] [(1/2)/√t]dt

dA = [2t - t²]/[(1/2)/√t]dt

dA = [[tex]t^{1/2}[/tex] - (1/2)[tex]t^{3/2}[/tex]]dt

Integrating to obtain A,

A = (2/3)[tex]t^{3/2}[/tex] - (1/5)[tex]t^{5/2}[/tex]

Now apply the limits t = 0 to t = 2

Area = [(2/3)[tex]2^{3/2}[/tex] - (1/5)[tex]2^{3/2}[/tex]] - [0]

Area = √[2(4/3 - 4/5)]

Area = √[2(8/15)]

Area = √(16/15)

Area = 0.754

Thus, the area enclosed by the given curves is 0.754 square units.

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There are two solutions for equation [tex]3x^2-6x+2=0[/tex] are [tex]1+\frac{1}{\sqrt{3}} , 1-\frac{1}{\sqrt{3}}[/tex].

and solutions are irrational solutions.

Every nth degree equation has a total of 'n' real or hypothetical roots. The polynomial [tex]f (x)[/tex] is exactly divisible by ([tex]x -a[/tex] ), which means that ([tex]x -b[/tex] ) is the factor of the provided polynomial [tex]f(x)[/tex].

The theory of equations in algebra refers to the study of algebraic equations, which are equations defined by polynomials. Any expression with one or more terms is considered to be a polynomial. Knowing when an algebraic problem has an algebraic solution was a major challenge in the theory of equations.

Here solution of equation:

[tex]3x^2-6x+2=0\\3x^2-6x+2+1-1=0\\3x^2-6x+3=1\\3(x^2-2x+1)=1\\3(x-1)^2=1\\x=1+\frac{1}{\sqrt{3}} , 1-\frac{1}{\sqrt{3}}[/tex]

So here two solutions are presented for given equation.

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Answer:

[tex]\boxed{12.7\;inches}[/tex]

Step-by-step explanation:

For a circle of radius r, the circumference is given by the expression

C = 2πr

So for this circle of radius 9", the circumference is 2 x π x9 = 18π

The entire circle covers a total angle of 360°

If there is a sector of the circle that is subtended by an angle Ф, then the length of that arc will be Ф/ 360  x C

Here Ф = 81°

So length of arc is

[tex]\dfrac{81}{360} \times 18 \pi\\\\\\\textrm {Using a calculator this works out to }\\\\[/tex]

[tex]\dfrac{81}{360} \times 18 \pi = 12.72345\\\\[/tex]

Rounded to the nearest tenth of an inch this would be
[tex]\boxed{12.7\;inches}[/tex]      ANSWER

Answer:

In isosceles triangle two sides are equal,

So,

3x-1=2x+2

x=3

Perimeter=sum of all sides

=3x-1+2x+2+2x

=7x+1

Substituting value of x

Perimeter=7(3)+1

=21+1

=22

Thus x=3

:. Perimeter of a triangle=22 square units

T3(x) = x - x^2/2 + x^3/6.

The Taylor polynomial of degree 3 for the function f(x) = x + e^-x centered at a = 0 is given by:

T3(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3

= 1 + (-1 + 1)x + (e^-0 - (-1)(-1)e^-0)x^2/2! + (0 + (-1)(-1)(-1)e^-0)x^3/3!

= x - x^2/2 + x^3/6

So T3(x) = x - x^2/2 + x^3/6.

An infinite sum of words that are expressed in terms of a function's derivatives at a single point is known as the Taylor series or Taylor expansion of a function in mathematics.

The nth Taylor polynomial of the function is a polynomial of degree n that is created by the partial sum of the first n + 1 terms of a Taylor series. Approximations of a function made by Taylor polynomials get generally better as n rises. Quantitative estimates of the mistake brought about by the use of such approximations are provided by Taylor's theorem. If a function's Taylor series is converging, its total is the upper bound of the Taylor polynomials' infinite sequence. A function's Taylor series sum may not match.

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Step-by-step explanation:

Suppose that his age is x.

then the opposite of his age is -x.

from the question above, the equation can be written as

[tex] - x + 43 = 27[/tex]

[tex]then \: \\ x = 16[/tex]

Answer:

5. False.

Look at the graph.

Every one day, the cost jumps $30 instead of $60.

Therefore, it is false.

6. True.

Like I said, Every one day, the cost jumps $30.

So when x increases by 1, y increases by 30.

So, y = 30x is correct.

7. False.

Use the equation in the 6th question.

y = 30x.

Put x = 7.

You get y = 210, not 200.

So. it is false.

8. True

Again, same thing.

Use the equation in the 6th question.

y = 30x.

Put x = 9.

You get y = 270.

So the statement is correct.

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Answer:

The expression a2+a4+a6+a8+......a20 can be written in sigma notation as:

∑ a(2n) where n = 1 to 10

To expand this summation, we can substitute in the values of n and evaluate the series:

a(21) + a(22) + a(23) + ... + a(210) = a2 + a4 + a6 + ... + a20

The expression (-1) + 2 +(-3) + 4 + (-5) ....+(-25) can be written in sigma notation as:

∑ (-1)^n*n where n = 1 to 25

To expand this summation, we can substitute in the values of n and evaluate the series:

(-1)^11 + (-1)^22 + (-1)^33 + ... + (-1)^2525 = -1 + 2 - 3 + 4 - 5 +... - 25

Note that the series (-1)^n*n is an alternating series, where the signs of the terms alternate between positive and negative. This series has no closed form solution, but we can evaluate them by adding and subtracting each term.

Answer:

[tex]\displaystyle \sum_{n=1}^{10} a_{(2n)}[/tex]

[tex]\displaystyle \sum_{n=1}^{25} n (-1)^{n}[/tex]

Step-by-step explanation:

Sigma notation means the sum of the series.

Given series:

Therefore:

So each term is a₂ₙ

Therefore, the expression in sigma notation is:

[tex]\displaystyle \sum_{n=1}^{10}a_{(2n)}[/tex]

Given series:

The absolute value of each term of the series is n.

The signs of each term alternate between negative and positive.

Therefore, the expression in sigma notation is:

[tex]\displaystyle \sum_{n=1}^{25} n (-1)^{n}[/tex]

The expansion of each summation has been given in Part I.

However, the full expansions are:

[tex]\displaystyle \sum_{n=1}^{10} a_{(2n)}=a_2+a_4+a_6+a_8+a_{10}+a_{12}+a_{14}+a_{16}+a_{18}+a_{20}[/tex]

[tex]\displaystyle \sum_{n=1}^{25} n (-1)^{n}=(-1)+2+(-3)+4+(-5)+6+(-7)+8+(-9)+10+(-11)+12+\\\phantom{wwwwwwww}(-13)+14+(-15)+16+(-17)+18+(-19)+20+(-21)+22+\\\\\phantom{wwwwwwww}(-23)+24+(-25)[/tex]

The evaluation of each series is:

[tex]\displaystyle \sum_{n=1}^{10} a_{(2n)}=a_2+a_4+a_6+a_8+a_{10}+a_{12}+a_{14}+a_{16}+a_{18}+a_{20}[/tex]

[tex]\displaystyle \sum_{n=1}^{25} n (-1)^{n}=-13[/tex]

Answer: [tex]\lim_{x \to \infty} (\frac{sinh(x)}{e^x})[/tex][tex]= 0[/tex]

Step-by-step explanation:

[tex]\lim_{x \to \infty} (\frac{sinh(x)}{e^x})[/tex]

[tex]\lim_{n \to \infty} \frac{sinh(\infty)}{e^(\infty)}[/tex]

As x approaches infinity, the exponential term e^x becomes much larger than the hyperbolic sine function sinh(x), so the entire expression sinh(x)/e^x becomes very close to zero.

Therefore, the limit of the expression as x approaches infinity is 0:

On solving the the provided question we can say that -  in the equation we have 12a - 3b = 84 - 30 = 54

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

here, we have

a = 7 and b = 10

so, 12a - 3b

84 - 30 = 54

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Check the picture below.

Answer:

[tex]67^{\circ}[/tex]

Step-by-step explanation:

Angles that form a linear pair add to [tex]180^{\circ}[/tex].

Answer:

Step-by-step explanation:

Since angles x and 113° all lie on a straight line,

x + 113° = 180°   (angles on a straight line add up to 180°)

therefore,  x = 180°-113°

x = 67°

The correct statement regarding the two functions in this problem is given as follows:

f(2) = g(2).

The graphic solution of a system of equations is given by the point of intersection of all the equations that compose the system.

The points through which each function passes in this problem are given as follows:

The point that is common to both function is given as follows:

(2,0).

Meaning that the two functions intersect at x = 2, which is the solution to the system of equations, also meaning that they have the same numeric value at x = 2.

The fact that the two functions have the same numeric value at x = 2 means that the correct statement is given as follows:

f(2) = g(2).

Which is the first statement.

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Answer:

it's the second

Step-by-step explanation:

i did this before and it was the second one

?

my guess would be to pick the THIRD ONE

3

x=9.5 y= -2.0

The number of distinct prime factors are 17

The term prime factors in math is defined as a method to find the prime factors of a given number and it can be said a composite number.

As per the definition of prime factor here we have know that a and b have 7 prime factors in common.

Then it can be written as a*b has 28 prime factors

And here we also know that the number of prime factors of a or b that are not common to both is 21

Here we have also know that a has less prime factors than b so at most 10 of these 21 extra prime factors belong to a

Then the  the most prime factors that  a  can have is calculated as

=> 7 + 10 = 17

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The number of Empire State building‑height stacks of dimes required is 589,008.

The height of the  Empire States Building including the antenna is 1,454 feet.

here, we have,

The height of a stack of 100 dimes is 5.3 inches.

The value of a stack of 100 dimes is 10 dollars.

The 2017 U.S. gross domestic product (GDP) = 19,390,604,000 dollars.

Number of stacks of dimes needed = $19,390,604,000 / $10 = 1,939,060,400 stacks of 100 dimes

Height of 1,939,060,400 stacks of 100 dimes in feet = 1,939,060,400 x 5.3/12

Height of 1,939,060,400 stacks of 100 dimes in feet = 856,418,343.3 feet

Number of Empire State building‑height stacks of dimes = 856,418,343.3 / 1,454

Number of Empire State building‑height stacks of dimes = 589,008

In conclusion, the number of Empire State building‑height stacks of dimes required is obtained from the height of the Empire State building and the height of a stacks of 100 dimes.

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Answer:

30, 75, 105

Step-by-step explanation:

Answer:

$355

Step-by-step explanation:

if each pear is 60c and apples are 5c less...

60×5=300

300+55=355

because 60-5=55