what is the inverse of f(x)=4x^2-16

Answer:

Step-by-step explanation:

i would say a

We know that the area of a rectangle is the width multiplied by its length, basically

But here, we have the area, which is a polynomial, same for the length, then, to find out the width we must do a division of polynomial, I'll call the unknown polynomial as P, we have

So now we got to solve

There is a lot of ways to solve it, first, I'll factor 3 in the denominator

As well the numerator

Then we can already simplify 3, and get an easier expression

Now I'll factor using the grouping method, I want the numerator to be something like (x+1)*(another polynomial), doing that we can "cut" the (x+1).

One way to do it is to expand it in some simple sums, look at 3x³, we want a 3x² to match with him, but look that 9x² is 3x²+6x², let's write that way

It doesn't seem to help us at all, but look that now we can factor 3x², then

Look, we have our first (x+1) in the numerator. Let's use the same idea but now for the term 6x², we want a 6x to match with him, we have 12x, so let's write it as 6x + 6x.

Similar to what we did before, factor 6x, and again

Now we have one more (x+1).

Now the easiest one, factor 6

As we can see we have (x+1) multiplied by something in all terms in the numerator, then we can factor (x+1) now

Now we can cancel (x+1), and our final expression will be

Therefore, the width is

Answer:

 g(x) = f(5x)

Step-by-step explanation:

We assume that "shrink by a factor of 1/5" means that horizontal distances on the graph of g(x) are 1/5 of those on the graph of f(x).

Dividing x by a dilation factor will cause horizontal dilation of a graph. Here, that factor is 1/5, so the desired function is ...

 g(x) = f(x/(1/5))

 g(x) = f(5x)

Answer:

Step-by-step explanation:

solution = (4 , 5)

y = 5 / x = 4

y = 2x - 13

5 = 2(4)- 3

5 = 8 - 3

5 = 5

the equation does make sense

y = x + 1

5 = 4 + 5

5 = 5

the equation does make sense

However, the questions asks if the solution works for both equations, and the solution does work for the first equation and the second one as well. The answer is yes, the solution does work for this system of equations.

First step

We want to find the cost of each shirt Blair paid. In order to find it we want to find the total price Blair paid for the whole order and then divide it by 150 (total number of shirts).

She chose Company B.

They charge $3.10 per shirt, plus 4% of the total order for shipping.

There are 150 shirts, then the total order for shipping is:

150 · $3.10 = $465

we want to add the 4%. The 4% of $465 is

$465 · 4/100 = $465 · 0.04

= $18.60

If we add it to the total order for shipping:

$465 + $18.60 = $483.60

Second step

Now we divide the total price of 150 into 150: this is the cost for one shirt.

$483.60/150 = $3.224

If we round it to the nearest hundredth:

$3.224 ≅ $3.22

Answer- The total cost Blair paid for one T-shirt is $3.22

We know that she needs to add 75% to the total cost.

Let's remember that every percentage is equivalent to it divided by 100: for example 100% is equivalent to 1. For 75%:

75% = 75/100 = 0.75

Then 75% is equivalent to 0.75.

This means that if we want to find the 75% of something we multiply it by its equivalent: 0.75.

Answer- She can calculate the markup by multiplying her total cost by 0.75

Based on the previous parts, we know that we want to add the 75% (0.75) of the cost of each T-shirt Blair paid ($3.22).

We first find the 75% of $3.22 and then add it to it: it will be the cost of sell.

First step

The 75% of the total cost of each shirt ($3.22) is:

0.75 · $3.224 = $2.418

Second step

Adding the 75% to the total price:

$3.224 + $2.418 = $5.642

If we round it to the nearest hundredth:

$5.642 ≅ $5.64

Answer- Blair will sell each T-shirt at the carnival for $5.64.

Given that points A, B, and C are the midpoints of their respective sides, A)  1/2YZ = AC is true about the figure according to SSS congruent rule.

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and angles have the same measure. Slides, rotations, flips, and turns can be used to make these triangles appear identical. They would be in alignment if they were moved. Congruence is represented by the letter "."

When two figures are similar to one another in terms of their size and shape, this is what mathematicians mean by congruence. It can be demonstrated that two triangles are congruent using four congruence rules in general.

However, all six dimensions must be discovered. In light of this, it is possible to determine the congruence of triangles using just three of the six values. Triangles that are congruent have equal corresponding sides and angles.

YX = 2 × AX (A = midpoint of YX)

ZX = 2 × CX (C = midpoint of ZX)

∠X and ∠X are congruent as the Reflexive property rule.

Therefore, triangle XAC is congruent to triangle XYZ (SAS similarity theorem)

Since 2AX = XY and 2XC = XZ Then 2AC = YZ which SSS congruent rule.

So, the correct option is A)  1/2YZ = AC

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First option is correct. A t - shirt cost $7.50 and a pair of shorts cost $23

First, it's crucial to understand linear equations.

Equation connects the two algebraic expressions with an equal to sign to demonstrate the equality between them.

Linear equations are those with one degree.

Simultaneous linear equations are two or more linear equations that can be solved simultaneously to find a common solution.

Let the price of one t-shirt be $x and price of one pair of shorts be $y

A t-shirt and two pairs of shorts cost $53.50

So, x + 2y = 53.50 .................... (1)

Two t-shirts and three pairs of shorts cost $84.

So, 2x + 3y = 84 ................ (2)

Multiplying (1) by 2,

2x + 4y = 107 .............(3)

Subtracting (2) from (3),

4y - 3y = 107 - 84

y = 23

Putting the value of y in (1)

x + 2[tex]\times[/tex]23 = 53.50

x = 53.50 - 46

x = 7.50

A t shirt cost $7.50 and a pair of shorts cost $23

First option is correct

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Answer:

u hv to do middle terms ig

Answer:$19.575

Solution

135/100of $14.50

=$19.575

or 35/100 of $14.50

=$5.075

$14.50+5.075

=$19.575

In elementary algebra, the binomial expansion defines the algebraic expansion of powers of a binomial. The binomial equation be 27x² - 300 exists 3(3x + 10)(3x - 10).

In elementary algebra, the binomial theorem (or binomial expansion) defines the algebraic expansion of powers of a binomial. According to the theorem, it exists possible to extend the polynomial  [tex]$(x+y)^n$[/tex] into a sum involving terms of the form [tex]$a x^b y^c$[/tex], where the exponents b and c exists nonnegative integers with b + c = n, and the coefficient a of each term exists a specific positive integer depending on n and b.

Let the binomial equation be 27x² - 300

Factor out common term 3:

[tex]$\quad 3\left(9 x^2-100\right)$[/tex] [tex]$=3\left(9 x^2-100\right)$[/tex]

simplifying the above equation, we get

Factor [tex]$9 x^2-100: (3 x+10)(3 x-10)$[/tex]

= 3(3x + 10)(3x - 10)

If 3(3x - b)(3x + b) then we get

= 3(3x + 10)(3x - 10)

b = 10

The value of b = 10.

Therefore, the correct answer is option a. 10.

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The equation for the direct linear variation that models the given information is: C. r = 64.5t.

The equation of a direct linear variation can be modelled as y = kx, where the variables are x and y, while the value of k is the constant of proportionality between the variables, x and y.

Given that:

We are told that r varies directly with t. Where k is the constant of proportionality, the equation of the direct linear variation between r and t can be expressed as r = kt.

Constant of proportionality, k = r/t

Number of shirts Rebecca can fold and restock (r) = 129

Amount of time she would spend (t) = 2

Find the constant of proportionality, k:

k = r/t = 129/2

k = 64.5

To write the equation for the direct linear variation, substitute k = 64.5 into r = kt:

r = 64.5t

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Number of 5 digit numbers can be formed using the digits 8, 9 and 0 is 162

The numbers are 8, 9 and 0

Combination is the one of the method to show the number of arrangements the from collection of objects or numbers

Here we have to form 5 digits numbers using the digits 8,9 and 0

The ten thousand's place can be only filled with 8 or 9, we cant fill the digit 0 on the ten thousands place,

In remaining places we can fill all three digits

Therefore the number of combination = 2 × 3 × 3 × 3 × 3

= 162

Hence, number of 5 digit numbers can be formed using the digits 8, 9 and 0 is 162

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Answer:

5 batches

Step-by-step explanation:

60÷ 12=5 batches

[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=4 \end{cases}\implies S=180(4-2)\implies S=360 \\\\[-0.35em] ~\dotfill\\\\ 360 ~~ = ~~ (7x+19)+(15x-1)+(4x-3)+(12x+3) \\\\\\ 360~~ = ~~38x+18\implies 342=38x\implies \cfrac{342}{38}=x\implies \boxed{9=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\measuredangle C}{15x-1}\implies 15(9)-1\implies 135-1\implies \stackrel{\measuredangle C}{\text{\LARGE 134}}[/tex]

The graph of each equation is attached below each showing the point of intersection to the y-axis.

To solve this question, we have to use a graphing calculator to plot the coordinates as well as show the point of intersection.

A line graph is a graphical representation of information that changes over a period of time. It is a chart made by joining points using line segments.

The graph of equation is attached below.

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Answer:

[tex]5x^{2} +12x-7[/tex]

Step-by-step explanation:

Answer:

x equals four

Step-by-step explanation:

collect like terms

then it will be minus 8 x equals minus 13 minus 19 which gives minus 32. Divide both sides by the coefficient of x i.e minus 8

Then x is less than 4

Because you divided with minus so the sign will change

The complete table when Noah is running a marathon at a constant speed of 6 miles per hour is mentioned below:

Time                 Distance

 1                           6

 1/2                        3

 [tex]1\frac{1}{3}[/tex]                         8

 [tex]1\frac{1}{2}[/tex]                         9

  9                        54

 [tex]4\frac{1}{2}[/tex]                        27

The running speed of Noah is 6 mph.

The formula for distance is given as:

D = v × t

Where D is the distance, v is the speed and t is the time.

Now,

When t = 1 hour,

D = 6 × 1 = 6 miles

When t = 1/2hour,

D = 6 × 1/2 = 3 miles

When t = [tex]1\frac{1}{3}[/tex] hour,

D = 6 × [tex]1\frac{1}{3}[/tex] = 6 × 4/3 = 8 miles

When t = [tex]1\frac{1}{2}[/tex] hour,

D = 6 × [tex]1\frac{1}{2}[/tex] = 6 × 3/2 = 9 miles

When t = 9 hours,

D = 6 × 9 = 54 miles

When t = [tex]4\frac{1}{2}[/tex] hour,

D = 6 × [tex]4\frac{1}{2}[/tex] = 6 × 9/2 = 27 miles

Therefore, the table will be:

Time                 Distance

 1                           6

 1/2                        3

 [tex]1\frac{1}{3}[/tex]                         8

 [tex]1\frac{1}{2}[/tex]                         9

  9                        54

 [tex]4\frac{1}{2}[/tex]                        27

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The percentage of squirrels that have a weight between 3 and 5 pounds is; 95.017%

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The equation of the line that passes through the point (-8,6) is x + 4y = 16.

What is a slope?

A line's slope often indicates the steepness and direction of the line. By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.

Given:

point = (-8,6)

equation : x+4y=20

x+4y=20

=> 4y = -x + 20

=> y = - x/4 + 5

Here the slope  m is -1/4.

Now  as the lines are parallel therefore the slope will be equal.

Therefore from the slope intercept form,

y - y1 = m (x - x1)

=> y - 6 = -1/4 ( x + 8 )

=> y - 6 = -x/4 - 2

=> x/4 + y = 4

=> x + 4y = 16

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We're given : x+y+z = 4
x = -2y
z = -3y

So, we replace x = -2y and z = -3y in the original equation.

-> -2y + y + -3y = 4
-> -4y = 4
-> y = -1

Now we have the value of y, we substitute it into x and z
x = -2y = -2(-1) = 2
z = -3(-1) = 3

The expression which is equivalent to the given expression as in the task content is; 4.5⁶.

It follows from the task content that the expression which is equivalent to the given expression is to be determined.

Since the given expression is;

(4.5)-⁵ • (4.5)¹¹

Hence, it follows from the product of exponents law of indices that we have;

(4.5)^(-5 + 11)

= (4.5)⁶

Therefore, the expression which is equivalent is; 4.5⁶.

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After calculating basic arithmetic we have come to find that, 1523 boxes of crayons are produced in each hour if crayons manufactory produces 36,552 crayons in an hour.

Arithmetic ((arithmós) 'number', 'art, craft') is a fundamental branch of mathematics that focuses on the properties of traditional operations on numbers such as addition, subtraction, multiplication, division, exponentiation, and root extraction.

Giuseppe Peano, an Italian mathematician, formalized arithmetic in the nineteenth century with his Peano axioms,[disputed - discuss], which are still very important in the field of mathematical logic today.

The prehistory of arithmetic is limited to a few artifacts that may indicate the concept of addition and subtraction, the best-known of which is the Ishango bone from central Africa, which dates from somewhere between 20,000 and 18,000 BC, though its interpretation is disputed.

We have given that

crayon manufactory produces 36,552 per hours

Each box contain 24 crayons

No. of boxes manufactured in 1 hour = 36,552/24

                                                              = 1523

Thus, 1523 boxes of crayons are produced in each hour if Crayons manufactory produces 36,552 crayons in an hour.

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Given that the length of one of the sides of the triangle is the radius, the length of the other leg of the triangle is also 6 units.

Therefore, this is an instance of a 45-45-90 triangle. The value of x can now be solve by

Given that the side length of the 45-45-90 triangle is 6 units, the length of the hypotenuse x is

Answer:

1.9

Step-by-step explanation:

A major weakness of the Articles of Confederation is that: B. States could ignore laws passed by the Congress.

The Articles of Confederation can be defined as the first written documents that were regarded as the Constitution of the United States of America, which was agreed upon by the thirteen (13) original states.

Under the Articles of Confederation, the national government was unable to raise revenue due to lack of enforcement powers of the confederate Congress.

In conclusion, we can reasonably infer and logically deduce that one of the limitations of the Articles of Confederation was the inability of Congress to enforce the laws it made because they can be ignored by states.

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Complete Question:

What was one major weakness of the Articles of Confederation?

A. State governments lost most of their political power.

B. States could ignore laws passed by the Congress.

C. The national government could not negotiate treaties.

O D. There was no way for new territories to become states.

The plot of the data in the table is shown below.

And the plot of the answer choices is plotted in the following figure.

As we can clearly see, the exponential function of choice D best fits the data in the table,

Hence, choice D is the correct one.

According to the central limit theorem for sums, if you keep taking sums from bigger and bigger samples, the sums will eventually form their own normal distribution (the sampling distribution), which will become more similar to a normal distribution as the sample size grows.

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Answer: x=3

Step-by-step explanation:

6x-15-4x+8=-1

2x-7=-1

2x=6

x=3