The point (4, 16) is on the graph of f(x) = 2^x. Determine the coordinates of this point under the following transformations.
f(x) = 2^4x: ____________

Answers

Answer 1

The coordinate of the image after the transformation is (4, 65536)

How to determine the coordinate of the image?

From the question, the coordinate of the point is given as

(4, 16)

From the question, the equation of the function is given as

f(x) = 2^x

When the function is transformed. we have the equation of the transformed function to be given as

f(x) = 2^4x65536

So, we substitute 4 for in the equation f(x) = 2^4x

So, we have

f(4) = 2^(4 x 4)

Evaluate the products

f(4) = 2^16

Evaluate the exponent

f(4) = 65536

So, we have (4, 65536)

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Related Questions

Let be two sets E and F such that:E = {x € R: -4 ≤ x ≤ 4}F = {x € R: | x | = x}What is the Cartesian product of the complement of E × F =?

Answers

Given:

[tex]\begin{gathered} E=\mleft\lbrace x\in\mathfrak{\Re }\colon-4\leq x\leq4\mright\rbrace \\ F=\mleft\lbrace x\in\mathfrak{\Re }\colon\lvert x\rvert=x\mright\rbrace \end{gathered}[/tex]

If |x|=x that mean here x is grater then zero.

E is move -4 to 4 and F is grater then zero that mean multiplication of the function is obtaine all real value:

[tex]E\times F=\mleft\lbrace x\in\mathfrak{\Re }\mright\rbrace[/tex]

Solye for x.7(x - 3) + 3(4 - x) = -8

Answers

[tex]x=\frac{1}{4}[/tex]

Explanation

Step 1

apply the distributive property to eliminate the parenthesis

[tex]\begin{gathered} 7(x-3)+3(4-x)=-8 \\ 7x-21+12-3x=-8 \end{gathered}[/tex]

Step 2

add similar terms

[tex]\begin{gathered} 7x-21+12-3x=-8 \\ 4x-9=-8 \end{gathered}[/tex]

Step 3

add 9 in both sides

[tex]\begin{gathered} 4x-9=-8 \\ 4x-9+9=-8+9 \\ 4x=1 \end{gathered}[/tex]

Step 4

divide each side by 4

[tex]\begin{gathered} 4x=1 \\ \frac{4x}{4}=\frac{1}{4} \\ x=\frac{1}{4} \end{gathered}[/tex]

Austin walks 3.5km every day. How far does he walk in 7 days?Write your answer in meters.

Answers

Answer:

24,500 meters

Step-by-step explanation:


a. During a basketball practice, Mai attempted 40 free throws and was successful on
25% of them. How many successful free throws did she make?
410
0
free throws
25%
Unit 3, Lesson 11
50%
75% 100% 125% 150%

Answers

Answer: 10

1/4 (25%) of 40 is 10, meaning Mai made 10 successful free throws.

-Jun 18 of
Find the domain and the range of the given relation.
{(6,8), (-3,4), (-1,-6), (-6, -1)}

Answers

Domain: [-6, -3, -1, 6]
Range: [-6, -1, 4, 8]

Which expression is equivalent to a + 0.2c?O 1.23O 0.22O 0.2x01.023

Answers

If we have the expression:

This is the same to write:

So the answer is 1.2x.

The schedule for summer classes is available and Calculus and Introduction to Psychology are scheduled at the same time, so it is impossible for a student to schedule for both courses. The probability a student registers for Calculus is 0.05 and the probability a student registers for psychology is 0.62. What is the probability a student registers for Calculus or psychology?

Answers

Explanation

The given is that the probability a student registers for Calculus is 0.05 and the probability a student registers for psychology is 0.62. Since it impossible for a student to schedule for both courses, we will have

[tex]\begin{gathered} Pr(Psychology\text{ or calculus\rparen=Pr\lparen P\rparen+Pr\lparen C\rparen-Pr\lparen P}\cap C) \\ =0.05+0.62-0 \\ =0.67 \end{gathered}[/tex]

Answer: 0.67

9. Madison needs $10 000.00 in 16 years at an interest rate of 3 %/a compounded monthly. How much should she invest?

Answers

SOLUTION:

Case: Compound interest

Method:

The formula is:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

P =?

A= $10 000.00

n = 12

r = 3% or 0.03

t = 16 years

[tex]\begin{gathered} 10000=P(1+\frac{0.03}{12})^{12\times16} \\ 10000=P(1.0025)^{192} \\ 10000=P\times1.6151 \\ P=\frac{10000}{1.6151} \\ P=6191.54 \end{gathered}[/tex]

Final answer: To the nearest cent

She should invest $6191.54

Identify the coffecient of x in the expression below.-5x-4y^2

Answers

A coeffecient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression,

So in the given expression, the value "-5" is placed before x and hence is the coffecient of x .

Answer:

Step-by-step explanation:

3

Given the matrices A and B shown below, find – į A+ B.89A=12 4.-4 -10-6 12B.=-3-19-10

Answers

Given:

[tex]\begin{gathered} A=\begin{bmatrix}{12} & {4} & {} \\ {-4} & {-10} & {} \\ {-6} & {12} & {}\end{bmatrix} \\ B=\begin{bmatrix}{8} & {9} & {} \\ {-3} & {-1} & {} \\ {-9} & {-10} & {}\end{bmatrix} \end{gathered}[/tex]

Now, let's find (-1/2)A.

Each term of the matrix A is multiplied by -1/2.

[tex]\begin{gathered} \frac{-1}{2}A=\frac{-1}{2}\begin{bmatrix}{12} & {4} & {} \\ {-4} & {-10} & {} \\ {-6} & {12} & {}\end{bmatrix} \\ =\begin{bmatrix}{\frac{-12}{2}} & {\frac{-4}{2}} & {} \\ {\frac{4}{2}} & {\frac{10}{2}} & {} \\ {\frac{6}{2}} & {-\frac{12}{2}} & {}\end{bmatrix} \\ =\begin{bmatrix}{-6} & {-2} & {} \\ {2} & {5} & {} \\ {3} & {-6} & {}\end{bmatrix} \end{gathered}[/tex]

Now let's find (-1/2)A+B.

To find (-1/2)A+B, the corresponding terms of the matrices are added together.

[tex]\begin{gathered} \frac{-1}{2}A+B=\begin{bmatrix}{-6} & {-2} & {} \\ {2} & {5} & {} \\ {3} & {-6} & {}\end{bmatrix}+\begin{bmatrix}{8} & {9} & {} \\ {-3} & {-1} & {} \\ {-9} & {-10} & {}\end{bmatrix} \\ =\begin{bmatrix}{-6+8} & {-2+9} & {} \\ {2-3} & {5-1} & {} \\ {3-9} & {-6-10} & {}\end{bmatrix} \\ =\begin{bmatrix}{2} & {7} & {} \\ {-1} & {4} & {} \\ {-6} & {-16} & {}\end{bmatrix} \end{gathered}[/tex]

Therefore,

[tex]undefined[/tex]

FIND THE INDICATED PROBABILITY A magazine did a survey to determine its readers favorite types of shoesFavorite types of shoes worn Sneaker boot Sandal other 54% 16% 20% 10% What is the probability that the sneakers Will NOT be the favorite shoe of the next reader?

Answers

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

table:

favorite types of shoes

Step 02:

probability:

probability (not sneakers) = 100% - 54% = 46%

The answer is:

probability (not sneakers) = 46%

Simplify the expression leave expression in exact form with coefficient a and b so we have a✔️b.

Answers

coefficient of a = 2x

Explanation:[tex]\text{The expression: 2}\sqrt[]{x^2y}[/tex]

Simplifying:

[tex]\begin{gathered} \sqrt[]{x^2}\text{ = x} \\ 2\sqrt[]{x^2\times y}\text{ = 2x}\sqrt[]{y} \end{gathered}[/tex]

Since we are told the coefficient of a can be the product of a number and variable:

[tex]\begin{gathered} 2x\sqrt[]{y}\text{ is in the form a}\sqrt[]{b} \\ a\text{ = 2x},\text{ b = y} \\ 2\text{ = number, x = variable} \\ 2x\text{ = product of number and variable} \\ \text{coefficient of }a\text{ = 2x} \end{gathered}[/tex]

Necesito saber si los ejercicios están correctos o no y la explicación

Answers

None of the operations with radicals are correct, as two radical terms can only be added or subtracted if they have the same radical and the same exponent.

Addition and subtraction with radicals

Terms with radicals can only be added or subtracted if they have the same radical and same exponent, for example:

[tex]3\sqrt{2} + 2\sqrt{2} = 5\sqrt{2}[/tex]

In the above example, they have the same radical, of 2, and same exponent, also of 2.

The first example is given by:

[tex]7\sqrt{3} + 4\sqrt{2} = 11\sqrt{5}[/tex]

The mistake is that the two terms cannot be added, as they have different radicals, of 3 and 2.

The second example is given as follows:

[tex]3\sqrt[3]{k} - 6\sqrt{k} = -3\sqrt{k}[/tex]

The terms have the same radical, of k, but they have different exponents, of 3 and 2, hence they cannot be subtracted.

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Simplify the expression (6^2)^46^?

Answers

The given expression is

[tex](6^2)^4[/tex]

We would apply the rule of indices or exponent which is expressed as

[tex]\begin{gathered} (a^b)^c=a^{bc} \\ \text{Therefore, the expression would be } \\ 6^{2\times4} \\ =6^8 \end{gathered}[/tex]

After knee surgery, your trainer tells you to return to your jogging program slowly. He suggests you start by jogging for 14 minutes each day. Each week after, he suggests that you increase your daily jogging time by 7 minutes. How many weeks before you are up to jogging 70 minutes?

Answers

Given that initial time for jogging is,

[tex]a_{_1}=14[/tex]

After each week the time is increased by

[tex]d=7[/tex]

This gives an arithmetic sequence.

To find n such that,

[tex]a_n=70[/tex]

Therefore,

[tex]\begin{gathered} a_n=a_1+(n-1)d \\ n=\frac{a_n-a_1}{d}+1 \end{gathered}[/tex]

So,

[tex]\begin{gathered} n=\frac{70-14}{7}+1 \\ =\frac{56}{7}+1 \\ =8+1 \\ =9 \end{gathered}[/tex]

Therefore, 9 weeks before you are up to jogging 70 minutes.

Find functions f and g such that (f o g)(x) = [tex] \sqrt{2x} + 19[/tex]

Answers

We have the expression:

[tex](fog)(x)=\sqrt[]{2x}+19[/tex]

So:

[tex]g(x)=2x[/tex][tex]f(x)=\sqrt[]{x}+19[/tex]

***

Since we want to get the function g composed in the function f, and the result of this is:

[tex](fog)(x)=\sqrt[]{2x}+19[/tex]

When we replace g in f, we have to get as answer the previous expression. And by looking at it the only place where we will be able to replace values is where the variable x is located. The function f will have the "skeleton" or shape of the overall function and g will be injected in it.

From this, we can have that f might be x + 19 and g might be sqrt(2x), but the only options that are given such that when we replace g in x of f, are f = sqrt(x) + 19 and g = 2x.

Nikolas bought a Falcon's ticket for $80. The sales tax on the ticket is 7%. How much was the tax?

Answers

ok

100% ---------------------------- $80

7% ---------------------------- x

x = (80 x 7)/100

x = 560/100

x = 5.6

The tax was of $5.6

Line segments, AB,BC,CD,DA create the quadrilateral graphed on the coordinate grid above. The equations for two of the four line segments are given below. Use the equations of the line segments to answer the questions that follow. AB: y = -x + 1 BC: y = -3x + 11

Answers

The equations of the line segments are,

[tex]\begin{gathered} AB\colon y=\frac{1}{3}x+1 \\ BC\colon y=-3x+11 \end{gathered}[/tex]

Calculate the equations of CD and AD.

The equation of line Cd is,

[tex]\begin{gathered} (y-(-3))=\frac{-1+3}{4+2}(x+2) \\ y+3=\frac{1}{3}(x+2) \\ 3y=x-7 \end{gathered}[/tex]

The equation of the line AD is,

[tex]\begin{gathered} y-0=\frac{-3-0}{-2+3}(x+3) \\ y=-3x-9 \end{gathered}[/tex]

1)If two lines are parallel slope will be equal and perpendicular product of slope will be -1.

From the equation, the slope of AB is 1/3

From the equation, the slope of Cd is 1/3.

So, they are parallel.

2)The slope of AB is 1/3.

The slope of BC is -3.

The product of two slopes is -1. Therefore, AB is perpendicular to BC.

3) The slope of AB is 1/3 and slope of AD is -3. Since, the product is -1, they are perpendicular.

Another pair of line segments that are perpendicular to each other is AB and AD.

Colin just travelled across Ontario on a road trip. He bought some skis in Blue Mountain for $879.95 plus tax, a boombox in Muskoka for $145.58 including taxes, a souvenir in Niagara Falls for $99.97 plus tax, and some maple syrup in Toronto for $45.14 including tax. Overall, how much HST did Colin pay on his trip? Answer should be rounded off to whole number.

Answers

The Harmonized Sales Tax that Colin paid on this trip was of $152.18.

What is the Harmonized Sales Tax?

The Harmonized Sales Tax is a rate that a person pays over the values of their purchases.

In the context of this problem, the person traveled on Ontario, where the HST rate is of 13%.

The purchases of the person are given as follows:

Skis in Blue Mountain for $879.95.Boombox in Muskoka for $145.58.Souvenir in Niagara Falls for $99.97.Maple syrup in Toronto for $45.14.

The total value of these purchases is given by:

Total value = 879.95 + 145.58 + 99.97 + 45.14 = $1,170.64.

The HST paid is 13% of this amount, hence it is calculated as follows:

HST = 0.13 x 1170.64 = $152.18.

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What does "equidistant” mean in relation to parallel lines?O The two lines lie in the same plane.The two lines have the same distance between them.The two lines go infinitely.The two lines have an infinite number of points.

Answers

we have that

parallel lines (lines that never intersect) are equidistant in the sense that the distance of any point on one line from the nearest point on the other line is the same for all points.

therefore

the answer is

The two lines have the same distance between them.

Anna's goal is to raise more than $200 for a
charity. Three of her neighbors donated $15 each, and one of her
friends donated $5. Write an inequality to show how much more
money Anna needs to raise. Explain how you found the answer.
Tell why you chose the inequality symbol that you used.

Answers

225 dollars because you have to multiply 45 times 5

Answer: 200 < 50 + x

Step-by-step explanation:

Since three of her neighbors donated 15 dollars each, we can find how much she earned from them by doing 3 x 15 = 45.

Including the 5 dollars earned by her friend, we get 50 dollars by doing 45+5 = 50.

Anna needs more than 200 dollars so 200 has to be less than Anna's total earnings. (x) is how much more Anna will need to earn to make the inequality true.

The circumference of a circle is 18pi meters. What is the radius?Give the exact answer in simplest form. ____ meters. (pi, fraction)

Answers

Given:

The circumference of a circle, C=18π m.

The expression for the circumference of a circle is given by,

[tex]C=2\pi r[/tex]

Put the value of C in the above equation to find the radius.

[tex]\begin{gathered} 18\pi=2\pi r \\ r=\frac{18\pi}{2\pi} \\ r=9\text{ m} \end{gathered}[/tex]

Therefore, the radius of the circle is 9 m.

Divide. −3.52−2.2 What is the quotient

Answers

The quotient of - 3.32 / - 2.2 is 8 ÷5.

What is the quotient?

Given fraction:

-3.32 / -2.2

First step is to re-write the given fraction which is - 3.52 / - 2.2

3.52 / 2.2

Second step is to convert the decimal to fraction

352 ÷ 100 / 22 ÷10

Third step is to reduce the fraction

reducing 352/100

=(2^5 × 11)/(2^2 × 5^2)

= [(2^5 × 11) ÷ 2^2] / [(2^2 × 5^2) ÷ 2^2]

= (2^3 × 11)/5²

= 88/25

Reducing 22/10

Divide the numerator and denominator by the greatest common divisor

= 22 ÷ 2 / 10 ÷ 2

= 11 /5

Now let determine  or find the quotient

88 ÷ 25 × 11 ÷ 5

= 8 ÷ 5

Therefore we can conclude that 8 ÷ 5 is the quotient.

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Find the length of the rectangle pictured above, if the perimeter is 82 units.

Answers

The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(length + width)

From the information given,

width = 16

Perimeter = 82

Thus, we have

82 = 2(length + 16)

By dividing both sides of the equation by 2, we have

82/2 = 2(length + 16)/2

2 cancels out on the right side of the equation. We have

41 = length + 16

length = 41 - 16

length = 25

If an item is discounted 30% then what percent of the original price is the sale price? if the organal price of the item is $500 what is the dollar amount of the discount?how much is the sale price ?

Answers

a.) Discount = 30%

Percent of the original price on sale = 100% - 30% = 70%

b.) Original price = $500

Discount = 30%

Dollar amount of the discount = $500 x (30% / 100%) = $500 x 0.30 = $150

c.) The sale price = $500 - (Discount Amount) = $500 - $150 = $350

Function Notation - TransformationIll send a picture of the question

Answers

Given the vertices of the original quadilateral:

(3, 4), (5, 6), (7, 4), and (5, 3)

Vertices of the transformed quadilateral:

(-5, -6), (-3, -4), (-1, -6), and (-3, -7)

Let's describe the transformation rule used for this transformation.

To find the transformation rule, let's find the number of movements in the x-direction and y-direction that would map the original quadilateral to the transformed quadilateral by subtracting the x and y coordinates of the coresponding sides.

We have:

(x, y) ==> (-5 -3, -6 -4) ==> (-8, -10)

(x, y) ==> (-3 -5, -4, -6) ==> (-8, -10)

(x, y) ==> (-1 -7, -6 -4) ==> (-8, -10)

(x, y) ==> (-3 -5, -7 -3) ==> (-8, -10)

For all corresponding sides, we have: (x, y) ==> (-8, -10)

This means there was a shift 8 units to the left, and 10 units downwards.

Therefore, the rule for the transformation shown here is:

(x, y) ==> (x - 8, y - 10)

ANSWER:

B. f(x, y) = (x - 8, x- 10)

37)You need at least 15 pencils or markers. You want to spend at most $14 onpencils and markers. Pencils p are $0.85 each and markers m are $1.45each. Which system of inequalities models the situation?A) p+m>150.85p+1.45m<14B) p+m>140.85p+1.45m>15C) p+m≥150.85p+1.45m≤14D) p+m≥140.85p+1.45m≤15

Answers

Given:

Minimum number of pencils or markers = 15

Maximum amount to spend on pencils and markers = $14

Cost of a pencil = $0.85

Cost of a marker = $1.45

Required: System of inequalities models the situation

Explanation:

Let p denote the number of pencil and m be the number of markers

Since the minimum number of pencils or markers is 15, it gives the inequality

[tex]p+m\geq15[/tex]

Since the maximum amount to spend on pencils and markers is $14, it gives the inequality

[tex]0.85p+1.45m\leq14[/tex]

Final Answer:

[tex]\begin{gathered} p+m\ge15 \\ 0.85p+1.45m\leqslant14 \end{gathered}[/tex]

all you need is in the photo please answer fast please helpppppp DON'T DO STEP BY STEP PUT ONLY THE ANSWER PLEASEEEEEEEEEEEEEEEEEEEEE

Answers

Notice that since the residuals are varying from -1 to 1 without a pattern, we have that the line is not a good fit for the data.

Also, some residuals (for 0, 2, 4 and 6) are relatively large compared to the actual data values.

See attachment for problem

Answers

The liters in the tank when it is filled to a height of 3.70 is  5,580 liters

The liters that needs to be added to 100% capacity is 480 liters

What is the volume?

A right circular cone is a three dimensional object has a flat circular base that tapers to a vertex. The volume of a right circular cone is the amount of space in the right circular cone.

Volume of a cone = 1/3(πr²h)

Where:

π = pi = 3.14r = radius h = height

Volume of the right circular cone when its filled to a height of 3.70 = 1/3 x 3.14 x 3.70 x 1.20² = 5.58 m³

5.58 x 1000 = 5,580 liters

Volume of the right circular cone when it is full =  1/3 x 3.14 x 4 x 1.20² = 6.03  m³

6.03 x 1000 = 6030 liters

Liters that needs to be added to 100% capacity =  6030 liters - 5,580 liters  = 480 liters

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a) Consider an arithmetic series 4+2+0+(-2)+.....i) What is the first term? And find the common difference d.ii) Find the sum of the first 10 terms S(10).b) Solve [tex] {2}^{x - 3} = 7[/tex]

Answers

Answer:

Explanation:

Here, we want to work with an arithmetic series

a) First term

The first term (a) of the arithmetic is the first number on the left

From the question, we can see that this is 4

Hence, 4 is the first term

To find the common difference, we have this as the difference between twwo subsequent terms, going from left to right

We have this as:

[tex]2-4\text{ = 0-2 = -2-0 = -2}[/tex]

The common difference d is -2

ii) We want to calculate the sum of the first 10 terms

The formula for this is:

[tex]S(n)\text{ = }\frac{n}{2}(2a\text{ + (n-1)d)}[/tex]

Where S(n) is the sum of n terms

n is the number of terms which is 10

a is the first term of the series which is 4

d is the common difference which is -2

Substituting these values, we have it that:

[tex]\begin{gathered} S(10)\text{ = }\frac{10}{2}(2(4)\text{ + (10-1)-2)} \\ \\ S(10)\text{ = 5(8+ (9)(-2))} \\ S(10)\text{ = 5(8-18)} \\ S(10)\text{ = 5(-10)} \\ S(10)\text{ = -50} \end{gathered}[/tex]

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