If f(x)= 2x2 + x - 7 and g(x)= x + 5, then evaluate g(f(3)).

There are 11649 solutions for the given binomial series x¹ + x² + x³ + x⁴ + x⁵ = 21.

x¹ + x² + x³ + x⁴ + x⁵ = 21, where xi, i = 1, 2, 3, 4, 5, is a non-negative integer such that: 0≤ x1 ≤10 and x², x³, x⁴, x⁵ can range in between 0 to 21.

Now we have to choose the coefficient of x²¹ in the following expression

(1 + x + x² + x³.....+ x¹⁰) (1 + x + x² + x³.......+x²¹)(1 + x + x² + x³.....+ x²¹)(1 + x + x² + x³.....+ x²¹)(1 + x + x² + x³.....+ x²¹)

also we can extend term of x², x³, x⁴, x⁵ from x²¹ upto infinty because it didn't  change the value of x²¹ coefficient . 

(1 + x + x² + x³.....+ x¹⁰) (1 + x + x² + x³.......∞)(1+ x + x² + x³.....+ ∞)(1 + x + x² + x³.....+ ∞)(1 + x + x² + x³.....+ ∞)

(1 - x¹¹)/(1 - x)[1/(1 - x)⁴]

(1 - x¹¹) [1/(1 - x)⁵]

now we have to find only the coefficient of x²¹ for which we consider the coefficient of x²¹ and x¹⁰ in [tex]1-x^{-5}[/tex]

general term of the binomial coefficient is [tex]\binom{n+r-1}{r}[/tex]

[tex]\binom{5+21-1}{21}-\binom{5+10-1}{10}[/tex] = 12650-1001 = 11649

--The given question is incomplete; the complete question is

"How many solutions are there to the equation x¹ + x² + x³ + x⁴ + x⁵ = 21,

where xi, i = 1, 2, 3, 4, 5, is a nonnegative integer such that: 0≤ x¹≤ 10?"--

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Answer:

6.4166

Step-by-step explanation:

77/12 = 6.41666666667

An expression equivalent to (5k-3) (2k-1) is k (10 k - 11) + 3.

simplify | (5 k - 3) (2 k - 1)

Results:

1\/40 (20 k - 11)^2 - 1\/40

k (10 k - 11) + 3.

An expression equivalent to (5k-3) (2k-1) is k (10 k - 11) + 3.

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Answer:

∠ BAS = 122° , ∠ N = 89°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

(2)

∠ BAS is an exterior angle of the triangle, then

19x + 8 = 6x + 11 + 75

19x + 8 = 6x + 86 ( subtract 6x from both sides )

13x + 8 = 86 ( subtract 8 from both sides )

13x = 78 ( divide both sides by 13 )

x = 6

Then

∠ BAS = 19x + 8 = 19(6) + 8 = 114 + 8 = 122°

--------------------------------------------------------------

(4)

11x + 31 is an exterior angle of the triangle , so

11x + 31 = 5x - 4 + 10x - 1

11x + 31 = 15x - 5 ( subtract 15x from both sides )

- 4x + 31 = - 5 ( subtract 31 from both sides )

- 4x = - 36 ( divide both sides by - 4 )

x = 9

Then

∠ N = 10x - 1 = 10(9) - 1 = 90 - 1 = 89°

Answer:

either the exponent is "negative" or else the base is between 0 and 1.

Step-by-step explanation:

Answer: Yes, but it's also exponential decay if the base if between 0 and 1.

Step-by-step explanation: I hope this helps!

The relative frequency table shows the distribution of the data with respect to all 140 people.

Frequency refers to how often something occurs over a given period of time. It can be used to describe the rate of oscillations of a wave, the number of occurrences of a given event, or the rate at which a signal is processed. Frequency is typically measured in hertz (Hz), which is the number of occurrences per second. Frequency can also be expressed in terms of cycles per second (cps), revolutions per minute (rpm), or vibrations per second (vps). Frequency is an important concept in many fields such as physics, engineering, and mathematics.

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Table is attached below:

Answer: The smallest critical value is -5

Step-by-step explanation:

Critical values occur at critical points(they give you important information).

In all rational functions, x-intercepts(zeros) and discontinuities need to be considered. So the critical values here are -5, -3, and -2.

[tex]\textit{Logarithm Change of Base Rule} \\\\ \log_a b\implies \cfrac{\log_c b}{\log_c a}\qquad \qquad c= \begin{array}{llll} \textit{common base for }\\ \textit{numerator and}\\ denominator \end{array} \\\\\\\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\log_2(x-3)+\log_4(x) \\\\[-0.35em] ~\dotfill\\\\ \log_4(x)\implies \stackrel{\textit{change of base rule}}{\cfrac{\log_2(x)}{\log_2(4)}}\implies \cfrac{\log_2(x)}{\log_2(2^2)}\implies \cfrac{\log_2(x)}{2}\implies \cfrac{1}{2}\log_2(x) \\\\[-0.35em] ~\dotfill\\\\ \log_2(x-3)+\log_4(x)\implies \log_2(x-3)+\cfrac{1}{2}\log_2(x)\implies \log_2(x-3)+\log_2(x^{\frac{1}{2}}) \\\\\\ \log_2(x-3)+\log(\sqrt{x})\implies {\Large \begin{array}{llll} \log_2( ~~ \sqrt{x}(x-3) ~~ ) \end{array}}[/tex]

So, the slope of the given line is 2.

The slope of a line is a measure of the steepness of the line and is represented by the letter "m" in the equation of a line: y = mx + b. The slope is calculated by the ratio of the change in y to the change in x.

The equation of a line y = 2x - 10 is already in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

In this case, the slope of the line is m = 2.

This means that for every unit increase in x, y will increase by 2 units. If we graph this line, we can see that it has a steepness of 2, which means it has a positive slope. A positive slope indicates that the line increases as we move to the right and a negative slope indicates that the line decreases as we move to the right.

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The required True options for the give equation are 2 and 3.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

We have,

y = [tex]\frac{2x+5}{x-1}[/tex]

1) The function is undefined foe x= -5/2

It is false because at  x= -5/2 function is defined equal to 0.

2) The point (0, -5) lie on its graph,

To check it, Value of x in equation

y = 2(0)+5/0-1 = -5

So, this option is true.

3) The line x = 1 is asymptote

For  asymptote, denominator of function must be zero.

x - 1 = 0

x = 1

It is true

4) The function is undefined foe x=  -1

It is false because at  x= -1 function is defined equal to -3/2

Thus, True options are 2 and 3.

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A parallelogram and a semicircle both have an area of 264 and 628 square metres, respectively. A = 892 is the total area.

We have a half-circle and a parallelogram.The parallelogram's area is A=basis*height. [tex]A = r^2[/tex], where r is the radius, is the formula for a circle's area (half of diameter). As a result, the half circle's area is equal to

[tex]$A=\frac{\pi r^2}{2}$[/tex]

parallelogram:

b=12

h=22

A=12 × 22

A=264

Half circle:

r=20

A=(3.14 × 20²)/2

A=628

Total Surface Area of the Figure:

A=264 + 628

A=892 .

Half of a circle's surface area makes up a semicircle. As a circle's area is [tex]r^{2}[/tex], Therefore, a semicircle's area is equal to 1/2([tex]r^{2}[/tex]), where r is its radius. 3.14, or 22/7, is the value of.

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Answer: 20.15

Step-by-step explanation:

First, make the percentage into an actual number. So divide 65 by 100 (because percent is based off of 100) which gives you 0.65. Then multiply 0.65 by 31 which gives you 20.15. Have a good day ;)

Step-by-step explanation:

1. Draw the diagonal BD of length 6 cm as base.

2. Draw perpendicular bisector of DB which intersects DB at O.

3. Take O as centre and draw an arc of 3 cm above and below the line segment BD.

4. Join A, B, C and D.

square.

see attachment....

Answer:

[tex]\left(x+5\right)^2- 33=0[/tex]

See explanation below for steps

Step-by-step explanation:

We are given the quadratic equation

[tex]x^2+10x-8 = 0[/tex]

and asked to rewrite it in the form
[tex]\left(x+a\right)^2=b[/tex]

Move 8 to the right side:
[tex]x^2+10x=8[/tex]

[tex]\mathrm{Rewrite\:in\:the\:form}\:x^2+2ax+a^2[/tex]
[tex]\mathrm{Solve\:for\:}a,\:2ax=10x:\quad a=5[/tex]

[tex]\mathrm{Add\:}a^2=5^2\mathrm{\:to\:both\:sides}[/tex]

[tex]x^2+10x+5^2=8+5^2[/tex]

So we get the original equation as:
[tex]\left(x+5\right)^2=33[/tex]

which can be rewritten as
[tex]\left(x+5\right)^2- 33=0[/tex]

Here a = 5, b = -33

The side with length 5 cm is the hypotenuse.

The given lengths of the sides are 3 cm,4 cm and 5 cm

3²=3×3=9;

4² =4×4=16;

5² =5×5=25;

We found that

9+16=25

3²+4²+5²

Therefore, the triangle is a right-angled triangle.

Note : In any right-angled, triangle the hypotenuse happens to be the longest side.

In this example the side with length 5 cm is the hypotenuse.

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When a line L is perpendicular to two lines on the plane that intersects line L , then line L is perpendicular to the plane.

We know that two lines are perpendicular to each other if they intersects and these two lines are inclined at angle 90° (right angle)

Perpendicular lines are intersecting lines.

Mathematically, the perpendicular lines are represented by the symbol, ‘⊥‘.

When a line is perpendicular to two lines on the plane then it is perpendicular to the plane.

We can say that when the line L is perpendicular to every line in the plane that intersects line L, then we can say that a line and a plane are perpendicular.

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The average  rate of change on the interval - 1≤ x ≤ 4 for the given equation is 7.4

What is Quadratic equation ?

Quadratic equation can be defined as the equation which is in the form of ax^2+bx+c = 0 .

Given to find the average rate of change on the interval -1<= x <= 4

for the equation y = x^2+4x+1

put x = -1 in the equation  y = x^2+4x+1

y(-1) = -1*-1 + 4(-1) + 1

= -1-4+1

= -4.

y(4) = 4*4 + 4*4 + 1

= 16 + 16 + 1

=33

average rate = y(-1) - y(4) / -1-4

= -4-33 / -5

= 37 / 5

= 7 . 4

Hence, The average  rate of change on the interval - 1≤ x ≤ 4 for the given equation is 7.4

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The principal of interest 3415 naira, rate = 5% and time 4 yrs and 3 months​ is 4017.64 naira.

In the context of borrowing, principal refers to the initial sum of a loan; it can also refer to the balance still owed on a loan. For instance, the principal of a $50,000 mortgage is $50,000. If you pay off $30,000, the remaining $20,000 constitutes the principal balance.

The principal of a loan determines how much interest you will pay. When you pay a loan off each month, the amount first goes to pay off the interest that has accumulated; only then is the remaining amount applied to the principal. The only way to lower the monthly interest payment is to reduce the loan's principal.

given

I=3415

r=5%

time=4yrs 3 months

=4.25 yrs

we know,

p=Ix100/tr

= 3415x100/4.25x0.05

=4017.64 naira

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Answer: The total clockwise moment of the weight of the diving board and the weight of the girl at about Point A can be calculated using the equation:

moment = force x distance

In this case, the force is the weight of the diving board (800 N) and the weight of the girl (600 N) and the distance is the distance from Point A to the support (2.5m).

So the total clockwise moment is:

moment = (800 N + 600 N) x 2.5 m = 1400 N x 2.5 m = 3500 Nm

The unit for moment is Newton-meter (Nm).

It's worth noting that in this problem, the clockwise moment is calculated by considering the force and the distance in the same direction, and the moment is positive, if the force is acting in a clockwise direction.

Step-by-step explanation:

Answer:

x = 2

y = 5

Step-by-step explanation:

Brainly doesn't provide online graphing tools, so I will try to walk you through what to do.

First put both equations in slope-intercept form:

y + x = 7  →  y = -x + 7

3y - 6x = 3   →   3y = 6x + 3  →  y = 2x + 1

These are easy to graph now.  

For equation (1), place a point on the y-intercept (0,7), then draw a line with a slope of -1  (down one, over one, down one, over one, etc.).  The x-intercept is (7,0).

For equation (2), the y-intercept is point (0,1).  Draw a line with a slope of 2 (up 2, over 1, up 2, over 1, etc.)  The x-intercept is (-1/2, 0).

Where the 2 lines intersect is the solution.  They should intersect at point (2,5).

y = -2(x - 8)(x - 2)

y = -2(x² -2x -8x +16)

y = -2(x² - 10x + 16)

y = -2x² + 20x - 32

Answer:

y= −2x^2+20x−32

Step-by-step explanation:

y = −2(x−8)(x−2)

= - 2(x^2 - 10x +16)

= - 2x^2 - (-10x)-2. 16

= - 2x^2 +20x - 32

Mike is correct as to make 30 batches of Raisin Nut energy bars, the bakery will use 84 cups of granola and to make 15 batches of Honey Almond energy bars, the bakery will use 63 cups of granola.

For raising, we have = 28(3) = 84 cups

For honey almond, we have = 4.2(1.5) = 63 cups

To make 30 batches of Raisin Nut energy bars, the bakery will use 84 cups of granola and to make 15 batches of Honey Almond energy bars, the bakery will use 63 cups of granola which is why Mike is considered to be correct.

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The full question is:

The table shows the number of cups of granola that a bakery uses for every 10 batches of energy bars.

Type of Energy Bar Amount of Granola (cups)

Raisin Nut 28

Honey Almond 42

Cranberry Walnut 36

Mike says that the bakery uses more granola to make 30 batches of Raisin Nut energy bars than to make 15 batches of Honey Almond energy bars.

Is Mike correct? Use the drop-down menus to explain.

Mike is Correct/Incorrect . To make 30 batches of Raisin Nut energy bars, the bakery will use 84/28/42/56 cups of granola. To make 15 batches of Honey Almond energy bars, the bakery will use 126/84/63/42 cups of granola.

The multiplicative inverse of 'a' is assure by a-1 or 1/a. on other side, the multiplicative inverse of a number is present as 1 divided by the number.

The multiplication inverse of 3/7 is 7/3.

hence, the multiplicative inverse of -3/7 is -7/3 power 9.

The multiplicative inverse is defined as the reciprocal of a given number. It is used to define mathematical expressions.

The word 'inverse' concludes something contrary/opposite in effect, order, position. or direction. A number when multiplied by its multiplicative inverse results in 1.

The multiplicative inverse approach is called that the multiply of a number and its reciprocal is 1.

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The factors or multiples of the algebraic expression, x² - 36 are (x-6) and (x+6) .

Factorization of algebraic expressions is defined as the process of finding the factors of an expression which refers to finding two or more expressions whose product is equals to that expression. Some Identities which are used to Factorize Algebraic Expressions,

(a+b)² = a² + b² + 2ab

(a - b)² = a² + b² - 2ab

a² - b² = (a+b)(a -b) etc.

We need to factorise, p(x) = x² − 36.

The algebraic expression, p(x) can be factorised by using property, a² - b² = (a+b)(a-b). So, it can be written as x² - 6², comparing it with a² - b² , here a = x,

b = 6. Hence, (x² − 36) = (x+6)(x−6). Therefore, the required factors are (x+6)(x−6).

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Answer:

The number 25 is not a prime number

Using the percentage, the amount raised in the first three months is $840

How can I calculate the money raised in three months?

By the conclusion of the academic year, the Helping Hands Student Club hoped to have raised $3,000 for a project.

It has attained 28 percent of its objective after three months.

The following formula can be used to determine how much was raised within the first three months:

amount raised = 28% × 3000

amount raised = 28 / 100 × 3000

amount raised = 84000 / 100

Therefore,

the amount raised in the first three months = $840

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Answer:

10.224 hours

Step-by-step explanation:

1 day on Earth = 24 hours

1 day on Saturn = 42.6% of 24 hours

42.6% = 0.426

24 x 0.426 = 10.224 hours

So, there are 10.224 hours on Saturn.

Answer:

Step-by-step explanation: Using data from NASA's Cassini spacecraft, researchers believe they solved a longstanding mystery of solar system science: the length of a day on Saturn. It's 10 hours, 33 minutes, and 38 seconds. i hope this helps

To simplify a complex fraction, we use the following steps:

1- Use various rules of fractions to simplify both the numerator and denominator into a simple fraction. Divide the numerator by the denominator by multiplying the numerator by the reciprocal of the denominator.

2- Use the following rule to evaluate the result.

3- If needed, simplify the rational expression.

A complex fraction in mathematics is one that has another fraction in either the numerator, the denominator, or both. Simplifying difficult fractions is frequently helpful when working with them. This may be accomplished by utilizing a few straightforward procedures and different fractional rules.

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Fairfax is 15.94 miles more in distance to Manchester than to Hillsboro

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the distance between Manchester and Newton be = 10.94 miles

Let the distance between Newton and Fairfax be = 13.57 miles

Let the distance between Fairfax and Hillsboro be = 8.57 miles

Now , the distance between Manchester and Fairfax = distance between Manchester and Newton + distance between Newton and Fairfax

Substituting the values in the equation , we get

The distance between Manchester and Fairfax = 10.94 + 13.57

The distance between Manchester and Fairfax = 24.51 miles

So , the difference between the distances A = distance between Manchester and Fairfax - distance between Fairfax and Hillsboro

Substituting the values in the equation , we get

The difference between the distances A = 24.51 - 8.57

The difference between the distances A = 15.94 miles

Hence , the distance is 15.94 miles

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