12. When Bruce started bowling, he won
7
of the games he played. Within six months,
he was winning of his games. If he
improves at the same rate, what fraction
16
of his games should he expect to win after
another six months?

The simplified form of the function f(x) = (x² - 4x + 4) / (x² - 4) will be f(x) = (x - 2) / (x + 2).

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function is given below.

f(x) = (x² - 4x + 4) / (x² - 4)

Simplify the equation, then we have

f(x) = (x² - 4x + 4) / (x² - 4)

f(x) = (x - 2)² / [(x - 2)(x + 2)]

f(x) = (x - 2) / (x + 2)

The simplified form of the function f(x) = (x² - 4x + 4) / (x² - 4) will be f(x) = (x - 2) / (x + 2).

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ1

Answer:

[tex]\overline{BC} \cong \overline{EF}[/tex]

Step-by-step explanation:

Corresponding parts of congruent triangles are congruent.

Answer:

(0, 21)

Step-by-step explanation:

Stationary points occur when the gradient of a graph is zero.

Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.

Differentiate the given function:

[tex]\begin{aligned}y & = x^3+ax^2+b\\\implies \dfrac{\text{d}y}{\text{d}x}&=3 \cdot x^{3-1}+2 \cdot ax^{2-1}+0\\\implies \dfrac{\text{d}y}{\text{d}x}& = 3x^2+2ax\end{aligned}[/tex]

Set the differentiated function to zero:

[tex]\begin{aligned} \dfrac{\text{d}y}{\text{d}x}& =0\\ \implies 3x^2+2ax & = 0 \\ \implies x(3x+2a)&=0\end{aligned}[/tex]

Therefore the stationary points occur when:

[tex]\implies x=0[/tex]

[tex]\implies 3x+2a=0 \implies x=-\dfrac{2}{3}a[/tex]

There is a stationary point at (4, -11), therefore substitute x = 4 into the expression for x and solve for a:

[tex]\begin{aligned}x & = 4\\\implies -\dfrac{2}{3}a & = 4\\a & = -\dfrac{3}{2}(4)\\a & = -6\end{aligned}[/tex]

Substitute the found value of a and the point (4, -11) into the function and solve for b:

[tex]\begin{aligned}y & = x^3 + ax^2 + b\\\implies -11 & = (4)^3+(-6)(4)^2+b\\ -11 & = 64-96+b\\b & = -11-64+96\\ b & = 21\end{aligned}[/tex]

Therefore, the function is:

[tex]\boxed{y=x^3-6x^2+21}[/tex]

The other stationary point is when x = 0.  Therefore, to find the coordinates of this point, substitute x = 0 into the function:

[tex]\begin{aligned}y & =x^3-6x^2+21\\x=0\implies y & =(0)^3-6(0)^2+21\\ y & =21 \end{aligned}[/tex]

Therefore, the coordinates of the other stationary point are (0, 21).

To determine if a stationary point is minimum or maximum, differentiate the function again:

[tex]\begin{aligned}y & =x^3-6x^2+21\\\implies \dfrac{\text{d}y}{\text{d}x} & = 3x^2-12x\\\implies \dfrac{\text{d}^2y}{\text{d}x^2} & = 6x-12\\\end{aligned}[/tex]

Substitute the x-coordinate of the stationary point into the second derivative:

[tex]\begin{aligned} \dfrac{\text{d}^2y}{\text{d}x^2} & = 6x-12\\x=0 \implies \dfrac{\text{d}^2y}{\text{d}x^2} & = 6(0)-12= -12 \\\end{aligned}[/tex]

[tex]\textsf{As $\dfrac{\text{d}^2y}{\text{d}x^2} < 0$, stationary point $(0,21)$ is a maximum.}[/tex]

Differentiation Rules

[tex]\boxed{\begin{minipage}{4.8 cm}\underline{Differentiating $ax^n$}\\\\If $y=ax^n$, then $\dfrac{\text{d}y}{\text{d}x}=nax^{n-1}$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{4cm}\underline{Differentiating a constant}\\\\If $y=a$, then $\dfrac{\text{d}y}{\text{d}x}=0$\\\end{minipage}}[/tex]

Answer is x > -5

fid comon demoninator

Answer: x>−5

Step-by-step explanation:

[tex]6(\frac{x}{2} +4) > 9[/tex]

Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.

[tex]\frac{x}{2} +4 > \frac{9}{6}[/tex]

Reduce the fraction    

[tex]\frac{9}{6}[/tex]

 to lowest terms by extracting and canceling out 3.

[tex]\frac{x}{2} +4 > \frac{3}{2}[/tex]

Multiply both sides of the equation by 2. Since 2 is positive, the inequality direction remains the same.

x+8>3

Subtract 8 from both sides.

x>3−8

Subtract 8 from 3 to get −5.

x>−5

Answer:

a-b+8=42
a-b=42-8
a-b=36
espero t sirva

Answer:

b=34

Step-by-step explanation:

Answer:

x = 21°

Step-by-step explanation:

180 - 159 = 21

Alternate angles (see image below) are equal, so x = 21

Using corresponding angles and adjacent angles concept, the value of x from the given parallel lines is 21°.

Given that, straight line m parallel to straight line n and t is the transversal.

The corresponding angles definition tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.

Here, y°=159°

Now, y°+x°=180° (Adjacent angles on straight line)

159°+x°=180°

x°=21°

Therefore, the value of x from the given parallel lines is 21°.

To learn more about the corresponding angles visit:

brainly.com/question/1597341.

#SPJ7

Answer:

Reflect over the x axis and than turn 90 degrees clockwise about the origin.

The polynomial functions for which (x+3) is a factor

A polynomial of degree n is a function of the form

f(x) = anx

n + an−1x

n−1 + . . . + a2x

2 + a1x + a0

where the a is a real number (sometimes called the coefficients of the polynomial). Although

this general formula might look quite complicated, particular examples are much simpler. For

example,

f(x) = 4x

3 − 3x

2 + 2

is a polynomial of degree 3, as 3 is the highest power of x in the formula. This is called a cubic

polynomial, or just cubic.

Theorem Polynomial Division: Suppose d(x) and p(x) are nonzero polynomials were

the degree of p is greater than or equal to the degree of d. There exist two unique polynomials,

q(x) and r(x), such that p(x) = d(x) q(x) + r(x), where either r(x) = 0 or the degree of r is

strictly less than the degree of d.

so, if we put x=-3 then f(x) must be equal to zero

here no function satisfies of none of the option is correct for [x+3] factor

to learn more about polynomial visit: -

brainly.com/question/28746313

#SPJ1

(x +3) is a factor of the function f(x)= x³ +5x²-3x³-10x²+2x-3.

Here, we are given 4 functions. If (x+3) is a factor of any of these equations, then x = -3 and y = 0 must be a solution. Let us check each function one by one-

1. f(x) = x²-12x³ +54x² - 108x+81

putting x = -3, we get-

f(-3) = -3²-12(-3)³ +54(-3)² - 108(-3)+81

= 9+324+486+324+81

= 1,224

Thus, (x +3) is not a factor.

2. f(x)=x²-3x³-x+3

putting x = -3, we get-

f(-3) = -3²-3(-3)³-(-3)+3

= 9+81+9+3

= 102

Thus, (x +3) is not a factor.

3. f(x)=x+2x¹-23x³-60x²

putting x = -3, we get-

f(-3) = -3+2(-3)¹-23(-3)³-60(-3)²

= -3-6+621+540

= 1,152

Thus, (x +3) is not a factor.

4. f(x)= x³ +5x²-3x³-10x²+2x-3

putting x = -3, we get-

f(-3) = -3³ +5(-3)²-3(-3)³-10(-3)²+2(-3)-3

= -27+45+81-90-6-3

= 0

Thus, (x +3) is a factor of the function f(x)= x³ +5x²-3x³-10x²+2x-3.

Learn more about Polynomial functions here-

https://brainly.com/question/7693326

#SPJ1

Answer:11/15

Step-by-step explanation:

you have to change them to common denominators.

i chose 15.

to make the denominator for 1/3 into 15 you have to multiply it by 5 which means you have to multiply the numerator (1) by the same thing which gives you 5/15

to make the denominator for 2/5 into 15 you have to multiply the denominator by 3 so you have to multiply the numerator (2) by the same thing which gives you 6/15

you now have the equation 5/15 + 6/15

to add them together you leave the bottom numbers the same and add the top ones which gives you 11/15

Answer:

0.7333333333333333 = 11/15

Step-by-step explanation:

1/3 = 5/15

2/5 = 6/15


add them, and now you get

(5+6)/15 = 11/15

Answer: I could be wrong but I'm pretty sure it's 12^9 but again I could be wrong

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given an assistant bricklayer laying 50 bricks an hour has worked 2 hours longer than a master bricklayer laying 80 bricks an hour, you want an equation stating they have laid the same number of bricks. You also want to know how long each has worked.

The output of each bricklayer is the product of the rate at which they lay bricks and the time for which they do it. If t is the time spent by the master bricklayer, their output will be 80t. The time spent by the assistant will be (t+2) hours, and their output will be 50(t+2).

Here is the equation that says their output is the same:

  80t = 50(t+2)

Solving the equation for t, we have ...

  80t = 50t +100

  30t = 100 . . . . . . . . . subtract 50t

  t = 3 1/3 . . . . . . . divide by 30

The master bricklayer has worked 3 1/3 hours when they have laid the same number of bricks.

The assistant bricklayer has worked 5 1/3 hours at that time.

__

Additional comment

Each will have laid (80)(3 1/3) = 266 2/3 bricks.

The total price of the pick up truck is $27,241.

What is mathematic expression?

A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Base price = $22,225.

Additional options pricing,

6-speed transmission =  $2,908

cruise control = $240

trailer towing package = $230

power windows =  $738

destination charge = $900

All the other charges will be added to the base price if a person chooses all the options available, therefore,

= 22,225 + 2,908 + 240 + 230 + 738 + 900

= $27241

Therefore, The total price of the pick up truck is $27,241.

Read more about  mathematic expression at :

https://brainly.com/question/10413253

#SPJ1

Answer:

{2401, {-2401

Step-by-step explanation:

Sorry couldnt type the root symbol on my ipad.

The two values that serves as the root of the equation are  -1-√7 and  -1+√7

Given the quadratic equation below;

X² + 2X (-6) = 0

x^2 + 2x - 6 = 0

Using the general formula

x = -2±√2²-4(1)(-6)/2(1)

x = -2±√4+24/2

x = -2±√28/2

x =  -2±2√7/2

x = -1±√7

Hence the two values that serves as the root of the equation are  -1-√7 and  -1+√7

Learn more on quadratic equation here: https://brainly.com/question/25841119

#SPJ1

Answer:

k= -3

Step-by-step explanation:

Since we know the line will go through the point (2,-2), we can plug these values into our x,y variables to solve for k. Our 2 is the x-value and our -2 is the y-value.

y = kx+4

-2 = k(2)+4

To get k by itself, we first have to subtract the 4 from both sides.

-2-4 = k(2)+4-4

-6 = k(2)

Then, we can divide each side by the 2 to get our answer.

-6/2 = k(2)/2

k = -3

Answer:

k=-3

Step-by-step explanation:

Answer: 106

Step-by-step explanation:

because there is 106 headphones 106 people can get and there is 16 blankets 156 people can get so 106 people can get headphones and blankets  

Answer:

Step-by-step explanation:

You want the values of three expenditures, given three relations between them.

(The first thing to realize is that the question isn't about averages at all. It is about values that are described as averages.)

Let f, j, c represent the (average) amounts spent on flowers, jewelry, and gift certificates, respectively. The three given relations are ...

  f + j + c = 53.42

  j = 4.40 + c

  f + c = 15.58 + j

Using the second equation to substitute for j in the third, we have ...

  f +c = 15.58 +(4.40 +c)

  f = 19.98 . . . . . . . . . . . . . . simplify

Using this and the second equation to substitute into the first, we have ...

  19.98 +(4.40 +c) +c = 53.42

  24.38 +2c = 53.42

  2c = 29.04

  c = 14.52

Then ...

  j = 4.40 +c = 4.40 +14.52 = 18.92

The average expenditures are ...

__

Additional comment

This solution is one of many ad hoc methods that could be used. There are also graphing and matrix methods available for solving a set of equations like this. The attachment shows a calculator matrix solution.

The value of the given statement rounding to the nearest thousandth = 0.714.

Dependent occurrences are ones that are dependent on previous events. The outcomes of prior events have an impact on these occurrences. Dependent events are two or more occurrences that are dependent on one another. If one event is altered by chance, another is most likely to differ.

The independent and dependent factors are the two most crucial variables in a research experiment. The experimental has authority over the independent variable. The variable that varies in reaction toward the independent variable is known as the dependent variable.

P(A) = 0.74

P(B) = 0.85

P(A|B) = 0.84

Using  dependent events formula:

P(A∩B) = P(A/B) × P(B)

            = 0.84 X 0.85

            = 0.714

The value of the given statement rounding to the nearest thousandth = 0.714.

To know more about dependent events visit:

https://brainly.com/question/12138721

#SPJ9

Answer: 4/9

Step-by-step explanation:

[tex]\displaystyle\\(\frac{27}{8} )^{-\frac{2}{3}} =\\\\(\frac{3*3*3}{2*2*2})^{-\frac{2}{3}}=\\\\ (\frac{3^3}{2^3} )^{-\frac{2}{3}} =\\\\((\frac{3}{2})^3)^{-\frac{2}{3} } =\\\\(\frac{3}{2})^{-\frac{3*2}{3}} =\\\\(\frac{3}{2})^{-2}=\\\\(\frac{2}{3})^2 \\\\\frac{2^2}{3^2} =\\\\\frac{4}{9}[/tex]

Answer:

x = 4.8

Step-by-step explanation:

since the quadrilaterals are similar then the ratios of corresponding sides are in proportion , that is

[tex]\frac{MJ}{DA}[/tex] = [tex]\frac{LM}{CD}[/tex] ( substitute values )

[tex]\frac{x}{6}[/tex] = [tex]\frac{2.4}{3}[/tex] ( cross- multiply )

3x = 6 × 2.4 = 14.4 ( divide both sides by 3 )

x = 4.8

Answer:57.7

Step-by-step explanation:

Answer: (sidenote, I'm sorry if I answered incorrectly ;-;)

C: 4/5 or D 5/4

Step-by-step explanation:

if you solve the numbers inside the radical symbol you'll get 16807. it's hard for it to be separated into 4 groups since it can only be separated in 5, that being 7*7*7*7*7.

so, by process of elimination i suggest you answer either c or d

Answer:

120

Step-by-step explanation:

call the number x,

then x+1090-450

so x+640=760

x=760-640

x=120

hope this works :)

Answer:

120 is the number u thought of first

Step-by-step explanation:

1090-450=640

if we add 120 into 1090

then it will be 1210

so 1210-450=760

What if the median is zero?

A variable that can in principle be only zero or positive can only have mean zero if all values in practice are zero. On the other hand, such a variable can and will have median zero if more than half of the values are zero.

Can you have a median of one number?

Median of one number = the number itself.

FALSE because they are two different ratios