The transformation of f (x) exists g (x) = f (x) - 4.
What is meant by exponential functions?A mathematical function using the following formula is an exponential function: f (x) = an x. where x is a variable and an is a fixed amount known as the function's base. The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.
A function that has a positive constant increased to a variable exponent, other than 1, is referred to as an exponential function. By solving at a certain input value, a function is assessed. When the beginning value and growth rate are known, an exponential model can be discovered.
We observed that:
f (0) = 2
For the function g (x) we have:
g (0) = -2
Therefore,
g (x) = f (x) - 4
Looking for intersection with axis and we have:
g (0) = f (0) - 4
g (0) = 2 - 4
g (0) = -2 (correct demonstration)
The transformation of f (x) is: A. g (x) = f (x) - 4
Therefore, the correct answer is option A. g (x) = f (x) - 4.
The complete question is;
Two exponential functions, f and g, are shown in the figure below, where g is a transformation of f.
Which of the rules given below shows the transformation of f?
A. g(x) = f(x) - 4
B. g(x) = f(x - 4)
C. g(x) = f(x) + 4
D. g(x) = f(x + 4)
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Complex mathematical
A) [tex]$x+y=(1+2 \sqrt{3})+(1-\sqrt{3}) i$[/tex]
B) [tex]$y+z=(\sqrt{3}+1)-(2+\sqrt{3}) i$[/tex]
c) [tex]$y-z=(\sqrt{3}-1)-\sqrt{3} i$[/tex]
are the value of given algebraic expression.
What is Complex Number?The numbers which can be expressed in the form of [tex]$x+iy[/tex] where, [tex]$x, y$[/tex] are real numbers and 'i' is an imaginary number called "iota".
here [tex]$\mathrm{i}$[/tex] is iota whose value is: [tex]$\mathrm{i}=\sqrt{-1}[/tex]
Given .
[tex]$$\begin{aligned}& x=1+\sqrt{3}+2 i \\& y=\sqrt{3}-(1+\sqrt{3}) i \\& z=1-i\end{aligned}$$[/tex]
upon solving two complex number we solve coefficient of iota together and real number together.
A) to find [tex]$(x+y)$[/tex]
[tex]$$\begin{aligned}& x+y=(1+\sqrt{3}+2 i)+(\sqrt{3}-i-\sqrt{3} i) \\& x+y=(1+2 \sqrt{3})+(2-1-\sqrt{3}) i \\& x+y=(1+2 \sqrt{3})+(1-\sqrt{3}) i\end{aligned}[/tex]
B) [tex]$\mathbf{y}+\mathbf{z}$[/tex]
[tex]$$\begin{aligned}& y+z=(\sqrt{3}-i-\sqrt{3} i)+(1-i) \\& y+z=(\sqrt{3}+1)-(2+\sqrt{3}) i\end{aligned}[/tex]
c) [tex]$\mathbf{y}-\mathbf{z}$[/tex]
[tex]$$\begin{aligned}& y-z=(\sqrt{3}-i-\sqrt{3} i)-(1-i) \\& y-z=(\sqrt{3}-1)-\sqrt{3} i\end{aligned}[/tex]
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how many positive 10 digit numbers can you make using seven ones and three zeros
The number of positive 10 digit numbers that can be made using seven ones and three zeros is; 28
How to solve probability combinations?We want to find the number of positive 10 digit numbers that can be made using seven ones and three zeros.
Now, the leftmost position digit cannot be 0 and as such it is 1, due to the fact that there are no other possibilities.
The rightmost position therefore must be 0 in order to fill the need for an even number.
Thus, we have 8 remaining positions that we need to fill with six ones and two zeros using an arbitrary manner.
This means that we can place two digits of zero among 8 positions by using combination formula as;
⁸C₂ = 8!/(2! * 6*)
= 28 different ways
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Please help will mark Brainly
Answer:
x=-1 and y=4
Step-by-step explanation:
When you draw a graph you will see point of intersection which is solution
can you simplify 2/6?
Answer:
1/3
Step-by-step explanation:
2÷2=1
6÷2=3
Solution: 1/3
find angle D thank you so much need help. geomtry
The angle m∠D of the triangle is 78 degrees.
How to find the angles of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
The ΔKDT and ΔKPQ are isosceles triangle.
Isosceles triangle is a triangle that has two sides and angles equal to each other.
Therefore,
∠D + ∠T + ∠k = 180
∠D = 6x + 6
∠T = 6x + 6
∠K = 2x
Therefore,
6x + 6 + 6x + 6 + 2x = 180
14x + 12 = 180
14x = 180 - 12
14x = 168
divide both side by 14
x = 168 / 14
x = 12
Therefore,
m∠D = 6x + 6 = 6(12) + 6 = 72 + 6 = 78 degrees.
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3. At practice the team wants to know how fast Ryan can skate. He skates 10 laps around the
rink in 3 minutes and, later on in practice he skates 5 laps in 1 minute. What was his
average speed in laps per minute?
The average speed in laps per minute of Ryan is 2.5 laps per minute
How to determine the average speed in laps per minute?From the question, we have the following parameters that can be used in our computation:
He skates 10 laps around the rink in 3 minutes In practice he skates 5 laps in 1 minuteThe above can be expressed as
(x, y) = (1, 5) and (3, 10)
The average speed in laps per minute can be calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Rewrite as
Average speed = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (1, 5) and (3, 10)
Substitute the known values in the above equation
So, we have the following equation
Average speed = (10 - 5)/(3 - 1)
Evaluate
Average speed = 2.5
Hence, the average speed is 2.5
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Given m || n , find the value of x.
Answer:
54°
Step-by-step explanation:
Angles corresponding in parallel lines are the same
Solve each equation for both variables help please 15 points
Answer:
x = -5
y = 2
Step-by-step explanation:
1) -5x-4y = 17
2) 3x-4y = -23
subtract equation 2 from equation 1:
-8x + 0 = 40
-8x = 40
x = -5
substitute x = -5 into equation 1 and solve for y:
-5(-5) - 4y = 17
-4y = -8
y = 2
test answers by substituting x and y values into eqation 2:
3(-5) - 4(2) = -23 Answers are correct!
Miss Morgan is a science teacher she found that 30% of her 120 students are athletes and Mr. Gregory is a math teacher he found that 27 or 15% of his students are athletes
Raj was getting a 5% commission, but now he's getting 6.5%. How much more money will he make on $24,000 of sales than on his old commission?
If Raj was getting a 5% commission, he would make 24000 * 5% = $<<240005.01=1200>>1200 on $24,000 of sales.
If he is now getting a 6.5% commission, he will make 24000 * 6.5% = $<<240006.5.01=1560>>1560 on $24,000 of sales.
Thus, Raj will make 1560 - 1200 = $<<1560-1200=360>>360 more on $24,000 of sales with his new commission rate of 6.5% than he did with his old commission rate of 5%.
Suppose that the function h is defined, for all real numbers, as follows.
h(x) = (x+1)²
{
if x ≤-2
if-2
-x-2 ifx>2
h(-2) = 0
h(-1) = 0
h (3) = 0
Find h(-2), h(-1), and h (3).
0/0
믐
X
3
please help 15 points to whoever does
In light of this, 1,0,8 is the value of the function h(x) = (x+1)2 where h is defined for all real integers.
what is function ?The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
h(x) = (x+1)²
h(-2) = 1
h(-1) = 0
h(3) = 8
In light of this, 1,0,8 is the value of the function h(x) = (x+1)2 where h is defined for all real integers.
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A construction worker is making concrete by mixing sand, gravel, and cement in water. For each pound of sand, he uses 1 2/3 pounds of gravel. For each pound of gravel, he uses 2/5 pound of cement. He is making enough concrete that he needs to use 3 pounds of sand. How many pounds of cement does he use? PLEASE HELP DUE NOW !! TYYY
A. 1 pound
B. 1 4/15 pounds
C. 2 pounds
D. 2 1/15 pounds
Using mathematical operations, the construction worker requires C. 2 pounds of cement to mix 3 pounds of sand.
What are the mathematical operations?The basic mathematical operations are subtraction, addition, division, and multiplication.
These mathematical operations combine numbers, variables, mathematical operands, and the equation symbol to solve mathematical problems.
In this situation, we can apply the mathematical operation of multiplication to determine the quantity of cement required for 5 pounds of gravel.
The quantity of gravel per pound of sand = 1²/₃ = 1.667 pounds
For 3 pounds of sand, the quantity of gravel required = 5 pounds (1²/₃ x 3)
The quantity of cement per pound of gravel = ²/₅ pounds or 0.4
For 3 pounds of sand and 5 pounds of gravel, the quantity of cement required = 2 (5 x 0.4) or (5 x ²/₅)
Thus, 2 pounds of cement are needed to mix with 3 pounds of sand and 5 pounds of gravel.
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A book publisher find production cost associated 30 and fixed cost 25000 if each book is sold for 50 find cost function and profit function
The cost function is a function that describes the total cost of producing x number of books. The fixed cost of 25000 is a constant cost that does not depend on the number of books produced, so it is not included in the cost function. The cost function is therefore:
Cost function: C(x) = 30x
The profit function is a function that describes the profit made from selling x number of books. The profit is equal to the revenue from selling the books minus the cost of producing the books. The revenue from selling x number of books at a price of 50 each is 50x, so the profit function is:
Profit function: P(x) = 50x - 30x = 20x
This profit function tells you that for every book you sell, you will make a profit of 20.
Evaluate the expression
Answer:
39
Step-by-step explanation:
6a - b = 6 x 8 - 9 = 48 - 9 = 39
Answer: 39
Step-by-step explanation:
Given that a=8 and b=9
The expression is 6a-b
That is; we have to find 6 times a and then subtract b from it.
6a = 6*8=48
b=9
6a-b=48-9=39
Therefore the answer to the question is 39.
Beverly Hobbs earns $683 a week she is single and claims 2 allowances what amount is withheld weekly for federal income tax
Therefore, $52.25 is the answer to the inquiry about what percentage of a person's income is withheld each week for federal income tax.
What is percentage?A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction. Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.
Here,
The Federal Insurance Contribution Act is the American legislative framework in use here, and it contains the criteria and guidelines that are utilized to determine payroll taxes on an employee's paychecks. The social security and Medicare programs are funded through taxation, which is paid by both employers and employees.
The amount of federal income tax deducted from the weekly cheque is:
6.2% from Social Security plus 1.45% from Medicare.
= 7.5 percent of the weekly gross salary.
The amount of federal income tax withheld each week from Beverly Hibbs's $683.00 weekly salary is:
= 0.0765 × 683
= $52.25
Therefore, $52.25 is the answer to the inquiry about what proportion of a person's income is withheld each week for federal income tax.
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Simplify the expression
-4|2.5-6|
Answer: -14
Step-by-step explanation:
hello i need help with question 5 please i need help
a) The total cost of buying the car with HST is given as follows: $36,160.
b) The amount of money saved by the customer leasing the car instead of buying is given as follows: $14,760.
c) The customer should lease a new car, as according to the two options in this problem, leasing is more economic than purchasing a new car.
How to obtain the costs?
The costs are obtained applying the proportions in the context of this problem.
The HST tax is the Ontario Sales Tax, which means that an additional 13% of taxes has to be paid when purchasing the car.
Hence the total cost of buying the car, considering the HST tax, is given as follows:
1.13 x 32000 = $36,160.
The costs for leasing the car are given as follows:
$1,000 down payment.48 payments of $425.Hence the total cost for leasing the car is given as follows:
1000 + 48 x 425 = $21,400.
Then the amount saved by the customers when he/she decides to lease the car instead of purchase is given as follows:
36160 - 21400 = $14,760.
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Terryl invests $1500 in two mutual funds. In the first year, one fund grows 3.8% and the other grows 6%. Write a polynomial to represent the value of Terryl’s investment after the first year if he invested x dollars in the fund with the lesser growth rate.
The polynomial that represents the value of Terryl’s investment after the first year if he invested x dollars in the fund with the lesser growth rate is;
p(x) = x(1 + 6/100)
g(x) = (1500 - x)(1 + 3.8/100)
How to find the compound interest?The compound interest is defined as a form of interest whereby the rate of interest is applied on the amount obtained after every given interval of time.
We are given that;
The total amount invested in the two mutual funds = $1500.
The growth rate of the first mutual fund = 6%.
The growth rate of the second mutual fund = 3.8%.
If the amount invested in the first mutual fund is x, then the amount invested in second mutual fund is 1500 - x.
The growth for both mutual funds can then be represented by;
First mutual fund; p(x) = x(1 + 6/100)
The second mutual fund; g(x) = (1500 - x)(1 + 3.8/100)
Thus, the polynomial expression for both the mutual funds are;
p(x) = x(1 + 6/100) and g(x) = (1500 - x)(1 + 3.8/100) respectively.
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What's the equation and solution?
Using the Algebraic tile method we get x=2 solution for equation model
What is Algebraic Tile method?The algebra tile method is a method of solving equations by using visual models, such as tiles with different values on them, to represent the unknowns and constants in the equation. It is often used to help students understand the process of solving equations and to see how the operations of addition and subtraction correspond to the process of combining or separating algebraic expressions.
In the question, we have 3 kinds of tile
X tilesunit positive tilesunit negative tilesEquation will be :
⇒ 3x - 1 - 1 = 1 + 1 + 1 + 1
⇒ 3x - 2 = 4
⇒ 3x = 6
⇒ x = 2
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HELP ASAP! (20 POINT CUZ I NEED DONE ASAP) In baseball, each time a player attempts to hit the ball, it is recorded. The ratio of hits compared to total attempts is their batting average. Each player on the team wants to have the highest batting average to help their team the most. For the season so far, Jana has hit the ball 7 times out of 10 attempts. Tasha has hit the ball 10 times out of 16 attempts. Which player has a ratio that means they have a better batting average?
Tasha, because she has the lowest ratio since 0.7 < 0.625
Tasha, because she has the highest ratio since 56 over 80 is greater than 50 over 80
Jana, because she has the highest ratio since 56 over 80 is greater than 50 over 80
Jana, because she has the lowest ratio since 0.7 < 0.625
Tasha, because she has the lowest ratio since 0.7 < 0.625
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
The ratio of hits compared to total attempts is their batting average
Each player on the team wants to have the highest batting average to help their team the most.
Jana has hit the ball 7 times out of 10 attempts.
Average is 7/10=0.7
Tasha has hit the ball 10 times out of 16 attempts.
Tasha Average is 10/16=0.625
We need to find the player who has better batting average
Tasha, because she has the lowest ratio since 0.7 < 0.625
Hence, Tasha, because she has the lowest ratio since 0.7 < 0.625
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Using the following conversions between the metric and U.S. systems, convert the measurement.
Round your answer to 6 decimal places as needed.
1 meter= 3.28 feet
1 Liter= 0.26 gallons
1 kilogram = 2.20 pounds
26.794 yd = _________km.
By sing the following conversions between metric and US systems 26.794 yard = 0.024500 .
What is the value of 1meter in terms of centimeter ?
1 meter can be equal to 100 centimeters and suppose for x meters , then it could be around 100x centimeters .
Given,
1 meter= 3.28 feet
1 Liter= 0.26 gallons
1 kilogram = 2.20 pounds
we know that ,
1yard = 0.0009144 km
so ,
26.794 yard = 26.794*0.0009144 km
= 0.024500
Hence by sing the following conversions between metric and US systems 26.794 yard = 0.024500 .
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5432
-2
X
Which linear inequality is represented by the graph?
Oy< ²x + 3
Oy> ²x+3
Oy> ²x + 3
Oy< ²x + 3
Help please
The graph of an inequality in two variables is the set of points that represents all solutions to the inequality.
How do you find the linear inequality of a graph?The boundary line that separates the coordinate plane into two halves by a linear inequality represents the solutions to the inequality in one half. For > and, the border line is solid, and for and, it is dashed.
To determine the equation governing the inequality line, enter your slope and a point into the formula y = mx + B, where "m" denotes the slope, "x, y" denotes a point on the line, and "b" is the y-intercept. By inserting (0, 0), you get 0 = 0 + b, which equals 0.
When you rewrite the equation, you get y = x/2. The linear inequality x - 5 > 3x - 10 is an illustration. Due to the greater than symbol being utilised in this inequality, the LHS is clearly greater than the RHS.
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Question 1 of 10
Which choices are equivalent to the expression below? Check all that apply.
√5. √20
☐
A. 100
B. 5.2
C. 10
D. √5 √√5√4
E. √5 20
F. √25
.
SUBMIT
Choices that is equivalent to the expression √5. √20 is 5.2
Define equivalence.In mathematics, the word "equivalent" designates two quantities, numbers, or meanings that are the same. A bar across an equivalent sign or Equivalent Sign shall be used to indicate the equivalence of two such quantities. Additionally, it denotes the logical equivalent of two values or a group of quantities.
Define expression.Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
x= (5)^1/2*(20)^1/2
x= (5)^1/2*(2.2.5)^1/2
x=5.2
So B is the correct option.
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Given f(x)+3f(-x) = 2x+6, find f(x)
The function f(x) = -x-3.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.
Given function:
f(x)+3f(-x) = 2x+6.
Let the function is an even function.
So, f(-x) = f(x)
To solve for f(x):
Substituting the property of an even function,
f(x) - 3f(x) = 2x + 6
-2f(x) = 2x + 6
f(x) = -x-3
Therefore, f(x) = -x-3 is the function.
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Which of the following numbers is one fifth of a given number if one fourth of that same number is 20
Answer:100
Step-by-step explanation:
Find the sum of all solutions to the equation $4x(x-3) = 23$.
I NEED THIS ASAP
The sum of the solutions of the equation 4x(x - 3) = 23 is 3.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, An equation 4x(x - 3) = 23.
Now, Distributing the terms in the LHS we have,
4x² - 12x = 23.
4x² - 12x - 23 = 0.
By applying Sridhar acharya's formula we have,
[tex]x_{1,\:2}=\frac{-\left(-12\right)\pm \sqrt{\left(-12\right)^2-4\cdot \:4\left(-23\right)}}{2\cdot \:4}[/tex].
[tex]x=\frac{3+4\sqrt{2}}{2},\:x=\frac{3-4\sqrt{2}}{2}[/tex].
Therefore, The sum of the solutions of the equation is,
x + x = (3 + 4√2)/2 + (3 - 4√2)/2.
= (3 + 4√2 + 3 - 4√2)/2.
= 6/2.
= 3.
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A stew recipe uses 3 teaspoons of salt for every 4 cups of water.
Complete the table to show the relationship between the amounts of salt and water in the stew recipe. Enter a number in each box.
Can someone please help me quickly!! And also let me know if I got the first 2 correct
The amount of salt in 3/4 tablespoons is four times that of 3 tablespoons.
What is the amount of salt?A stew recipe uses 3 teaspoons of salt for every 4 cups of water.
There is a ratio issue here.
As X is to three, 3 is to 4.
3 : 4 :: X : 3
To eliminate the fractions, multiply each integer in the ratio by 12.
9 : 12 :: 9X : 12
This is a portion of what is
9 / 12 = 9X / 12
to obtain, cross-multiply.
9 / 12 = 3 teaspoons of salt,
Check: 3 cup of flour yields 3 cups, which is a 4x increase.
The amount of salt in 9/12 tablespoons is four times that of 3 tablespoons.
The amount of salt in 3/4 tablespoons is four times that of 3 tablespoons.
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A manager at a shopping mall counts 244 males and n females as they enter the mall. The manager realizes that 25% of all males and 25% of all females are children. She writes the expression 0.25n + 61 to represent the number of children who enter the mall. Is the manager correct? Why or why not?
The manager (blank, choose is or is not) correct because the original expression 0.25(n + 244) (blank, choose is or is not) equivalent to the manager’s expression, 0.25n + 61.
Answer:
The manager is not correct in her calculation.
Step-by-step explanation:
There are 244 males and n females who entered the mall as the manager at the shopping mall counts.
If 25% of all males are children, then the number of male children are .
Again, the 25% of all female are children, then the number of female chilfren are .
Therefore, the total number of children will be (60 + 0.25n).
But the manager gives the number of children to be 0.25n + 61 who entered the mall.
So, the manager is not correct in that calculation. (Answer)
Step-by-step explanation:
Henrie plays baseball. He hits 80% of the time he bats. If he is up to bat 20 times this weekend at his baseball tournament, how many times is he expected to hit
Answer:16
Step-by-step explanation: If henry hits 80% of pitches, then the easiest way is to make 80% of 10, which is half of 20, is 8. So if it is 20 times he is up to bat, then 8*2, 2*8 is 16, so he hits the ball 16 times.
8-2z+3(x+y), when x=4, y=9, Z=3
[tex]8-2z+3(x+y)[/tex] when x is 4, y is 9, and z is 3
Substitute:
[tex]8-2(3)+3(4+9)[/tex]
[tex]8-6+39[/tex]
Solve:
[tex]8-6+39\\=\fbox{23}[/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{8 - 2z + 3(x + y)}[/tex]
[tex]\mathsf{= 8 - 2(3) + 3(4 + 9)}[/tex]
[tex]\mathsf{= 8 - 6 + 3(4) + 3(9)}[/tex]
[tex]\mathsf{= 8 - 6 + 12 + 27}[/tex]
[tex]\mathsf{= 2 + 12 + 27}[/tex]
[tex]\mathsf{= 14 + 27}[/tex]
[tex]\mathsf{= 41}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{41}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]