Based on the domain, the equation of the function f(x) is F(x - h) = x^2 - 2xh + h^2 + 2
What is the domain of a function?The domain of the function is the set of input values of the graph
How to determine the solution of the function f(x)?The equation of the function is given as
F(x) = x^2 + 2
The required function is given as
F(x - h)
The above means that the value of x in the function F(x) = x^2 + 2 is x - h
i.e.
x = x - h
So, we substitute x - h for x in the equation F(x) = x^2 + 2
This gives
F(x - h) = (x - h)^2 + 2
Evaluate the exponent
So, we have
F(x - h) = x^2 - 2xh + h^2 + 2
The above equation cannot be further simplified
Hence, the solution of the function f(x) at the given domain is F(x - h) = x^2 - 2xh + h^2 + 2
Read more about domain at
https://brainly.com/question/2264373
#SPJ1
what is the slope of this line?
SOLUTION
From the question,
We have that the equation of the line is 5x + 2y = 9.
2y = - 5 x + 9
Divide both sides by 2, we have :
y = 1/ 2 ( -5x + 9 )
The slope of this line = -5 / 2
7. Let A=(8,9,10,11,12,13).
n=
a. How many subsets does A have?
b. How many proper subsets does A have?
subsets.
a. A has
(Type a whole number.)
b. A has
(Type a whole number.)
proper subsets.
a. A has 64 subsets.
b. A has 63 proper subsets.
What are subsets and proper subsets?If all of the items of Set A are also present in Set B, Set A is said to be a subset of Set B. Set A is, in other words, contained within Set B.
If Set B has at least one element that is not present in Set A, Set A is considered a proper subset of Set B.
If a set has "n" members, the number of subsets of that set is 2ⁿ, and the number of proper subsets of that subset is 2ⁿ-1.
Given:
Set A=(8,9,10,11,12,13)
Number of elements in the given set,n = 6
a. Number of subsets of A = 2ⁿ = 2⁶ = 64
b. Number of proper subsets of A = 2ⁿ-1 = 2⁶-1 =63
To know more about sets visit:
https://brainly.com/question/23454979
#SPJ13
A triangle has side lengths of,x, x+1, and 11. Find each side length when the perimeter is 30 inches
The sides of the triangle whose perimeter is 30 are given by-
[a] = 9 , [b] = 10 , [c] = 11.
What is the perimeter of triangle?
The perimeter of triangle is the sum of its sides. Mathematically -
Perimeter [P] = a + b + c
Given is a triangle whose side measurements are x, x + 1, and 11. The perimeter of triangle is 30 inches.
From the definition of the perimeter of a triangle -
Perimeter = sum of its sides
x + (x + 1) + 11 = 30
x + x + 1 + 11 = 30
2x + 12 = 30
2x = 18
x = 9
Now -
Length of side 1 = [a] = 9
Length of side 2 = [b] = 10
Length of side 3 = [c] = 11
Therefore, the sides of the triangle whose perimeter is 30 are given by-
[a] = 9 , [b] = 10 , [c] = 11.
To solve more questions on triangle's, visit the link below-
https://brainly.com/question/15034576
#SPJ1
Determine the solution for 45= 3(4b - 1).
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{45 = 3(4b - 1)}[/tex]
[tex]\mathsf{3(4b - 1) = 45}[/tex]
[tex]\mathsf{3(4b) + 3(-1) = 45}[/tex]
[tex]\mathsf{12b - 3 = 45}[/tex]
[tex]\large\textsf{ADD 3 to BOTH SIDES}[/tex]
[tex]\mathsf{12b - 3 + 3 = 45 + 3}[/tex]
[tex]\large\textsf{Simplify it}[/tex]
[tex]\mathsf{12b = 45 + 3}[/tex]
[tex]\mathsf{12b = 48}[/tex]
[tex]\large\textsf{DIVIDE 12 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{12b}{12} = \dfrac{48}{12}}[/tex]
[tex]\large\textsf{Simplify it}[/tex]
[tex]\mathsf{b = \dfrac{48}{12}}[/tex]
[tex]\mathsf{b = 4}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{b = 4}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
Find the indicated complement.
A certain group of women has a 0.04% rate of red/green color blindness. If a woman is randomly selected, what is the
probability that she does not have red/green color blindness?
Brian is driving on a highway. He uses one gallon of gas every 40 miles he drives. The distance, D (in miles), he travels on g gallons of gas is given by the following function.
D (g) = 40g
How far does Brian drive if he uses 4 gallons of gas?
Help with this question
When solving for the lengths of the sides of a right triangle, we can make use of the acronym SOH-CAH-TOA. In this problem, because x is adjacent to the 52-degree angle and we are also given the length of the hypotenuse, we can use the "CAH" part, which stands for cosine x = adjacent/hypotenuse.
[tex]\begin{gathered} \cos\theta=\frac{adjacent}{hypotenuse} \\ \\ \cos52=\frac{x}{18} \\ \\ 18\cos52=x \\ \\ 11.08=x \end{gathered}[/tex]So the answer is x = 11.08.
7. Isaiah has a summer internship at a technology company and is paid $3,000. After Federal and state taxes, Social Security, and Medicare are deducted, his take-home pay is $2,500. Which of the statements below is correct?
The correct statement regarding Isaiah is that A. His gross pay is $3,000 and net pay is $2,500
How to illustrate the information?Before taxes, benefits, and other payroll deductions are taken out of an employee's paycheck, that amount is known as their gross pay. Net pay, often known as take-home pay, is the amount that is left after all withholdings have been taken into account. Determining the number of pay periods you have throughout the year is the first step in calculating the gross compensation for a salaried employee.
The time range for which you pay your employee is known as a pay period. You must first determine your employee's gross compensation before you can determine their net pay. This is where you should start. The next thing you need to know is what payroll deductions your employee receives.
Since the take-home pay is $2,500, this is the net pay.
In conclusion, the correct option is A.
Learn more about tax on:
https://brainly.com/question/24248628
#SPJ1
Isaiah works at a technology company in the summer and earns
$3000. After federal, state, and Social Security/Medicare taxes are
deducted, his take-home pay is $2,500. Which of the statements
below is CORRECT? *
His gross pay is $3,000 and net pay is $2,500
His gross and net pay are $3,000
His gross and net pay are $2,500
His gross pay is $2,500 and net pay is $3,000
fourteen less than three fourth of a number is negative eight. find the number . translate each sentence into an equation and solve
Answer: n = 8
Step-by-step explanation:
Let the number be n:
The equation is:
[tex]\frac{3}{4}[/tex]n - 14 = -8
Now to solve:
[tex]\frac{3}{4}[/tex]n - 14 + 14 = -8 + 14
[tex]\frac{3}{4}[/tex]n = 6
[tex]\frac{4}{3}[/tex]×[tex]\frac{3}{4}[/tex]n = 6×[tex]\frac{4}{3}[/tex]
n = 8
A 1nch candle burns in 4hours at what rate does the candle burn in inches per hour
Answer:
4 1x4=4 so 4 is ur answer
Step-by-step explanation:
mrs green wants to use wood to make a fence around her circular garden. Her garden has a radius of 16 feet How much wood will she need to enclose her garden?.
ANSWER
100.5 feet
EXPLANATION
The radius of the circular garden is 16 feet.
To find how much wood she would need to make a fence around the garden, we need to find the circumference of the garden.
Circumference can be found using the formula:
[tex]C\text{ = 2}\pi r[/tex]where r = radius
Therefore:
[tex]\begin{gathered} C\text{ = 2 }\cdot\text{ }\pi\cdot\text{ 16} \\ C\text{ = 100.5 ft} \end{gathered}[/tex]She would need 100.5 ft length of wood to enclose the garden.
-4x^2-5x=-9 please show a step by step answer
We can solve the quadratic equation using factorization method.
First, let's re-write the equation:
[tex]\begin{gathered} -4x^2\text{ - 5x = -9} \\ \text{divide through by -1 } \\ 4x^2\text{ + 5x = 9} \\ Re-\text{arranging, we have} \\ 4x^2\text{ + 5x - 9 = 0} \end{gathered}[/tex]Next, we try to factorize the expression by the left:
[tex]\begin{gathered} 4x^2\text{ - 4x + 9x - 9 = 0} \\ (4x^2\text{ - 4x) + (9x - 9) = 0} \\ 4x\text{ (x - 1) + 9(x -1)}=0 \\ (4x\text{ + 9)(x - 1)}=0 \end{gathered}[/tex]Next, we equate each factor to zero to find the value of x
[tex]\begin{gathered} 4x\text{ + 9 = 0} \\ 4x\text{ = -9} \\ \text{x = }\frac{-9}{4} \\ x\text{ - 1 = 0} \\ x\text{ = 1} \end{gathered}[/tex]We can conclude that :
[tex]x\text{ = 1 or }\frac{-9}{4}[/tex]We can also do a check by substituting the value of x back into the equation:
[tex]undefined[/tex]66 is 75% of what number?
Answer:
88
Explanation:
Let us call the number NUMBER, then we know that
[tex]\frac{75}{100}\times\text{NUMBER =66}[/tex]The above says that 75% of the number is 66.
Then how do we find the value of NUMBER?
Multiplying both sides by 100/75 gives
[tex]undefined[/tex]A car rental agency charges $150 per week plus $0.30 per mile to rent a car. Express the weekly cost to rent the car, f, as a function of the number of miles driven during the week, x.
If the number of miles driven is 'x', then the weekly cost to rent a car f(x) is:
[tex]f(x)=0.3x+150[/tex]One week a student exercise 2 hours at school in another 1/4 of an hour at home if 16 of the students total exercise came from plain soccer how much time did the students spend plane soccer that week enter your answer in hours do not include units in your answer
In a week, a student exercise 2 hours at school and another 1/4 of an hour at home.
The total exercise of the students came plain soccer
The total hour a student exercise both home and school is
2 + 1/4
Our LCM is 4
4x2/1 + 4*1/4 /4
8 + 1 / 4
9/4 hours
A student exercise a total of 9/4 hours in a week
If one student exercise a total of 9/4 hours in a week then how many hours will 16 students exercise in a week
Mthematically,
1 student ========= 9/4 hours
16 students ======= x hours
Introduce cross multiplication
1 * x = 16 x 9/4
x = 16 x 9/4
x = 144/4
x = 36 hours
Therefore, 16 students exercise a total of 36 hours in a week
The answer is 36 hours
x = 144 / 4 hours
A toy costs 35 000 lndonesian rupiah (Rp).
The conversion rate is Rp 1000 = 5$0.145 598.
Without using a calculator, estimate the price of
the toy in S$.
The price of the toy on dollars is 5.22.
Here, we are given that a toy costs 35,000 lndonesian rupiah (Rp).
Further, the conversion rate is-
Rp 1000 = $0.145
Now, if 1000 Rp = $0.145 then 1Rp will be = $0.145/1000
= $0.000145
Thus, we get 1Rp = $0.000145
Now, we need to find how much 36,000 Rp is in dollars.
Since, 1Rp = $0.000145, 36,000 Rp will be = $(0.000145 × 36,000)
= 0.145 × 36
= 145/1000 × 36
36 can be written as- (40 - 4)
= 145 (40-4)/ 1000
= {(145 × 40) - (145 × 4)} / 1000
= (5,800 - 580)/1000
= 5,220/1000
= 5.22
Thus, the price of the toy on dollars is 5.22.
Learn more about the unitary method here-
https://brainly.com/question/24587372
#SPJ1
25×10 to the power of -3 to standard form
The standard form of the expression 25×10 to the power of -3 is 2.5×10⁻⁴
What exactly is meant by "scientific notation"?Scientific notation can be employed to reduce exceptionally large figures to positive exponential values, as well as very small figures to negative exponential values.When writing a number in m10n scientific notation, you can use decimal numbers and positive exponents to transform a long number to a shorter one.The Index Power Rule:
According to this formula, when the power of a number is raised to another power, this same indices are multiplied.This is the fourth index law, and it's the Index Law for Powers.For the given expression;
25×10 to the power of -3
This can be written as follows;
= 25×10⁻³
To write the expression in standard form, shift the decimal to the left of the number and add one more power to base 10.
= 2.5×10⁻⁴
Thus, the expression in the standard form becomes 2.5×10⁻⁴.
To know more about the scientific notation, here∧
brainly.com/question/1767229
#SPJ10
Find the polynomial function f with real coefficients that has the given degree, zeros, and solution point.
Degree
Solution Point
f(0) = -8
4
Zeros
-4, 1, 1
Polynomial function f with real coefficients that has the given degree, zeros, and solution point is f(x) =2(x⁴ +3x³ -3x²+3x-4).
As given,
Polynomial function f with real coefficients for the given degree, zeros, and solution point is:
Degree 4
Solution Point f(0) = -8
Zeros -4, 1, i
f(x)=k(x +4)(x -1)(x -i)(x +i)
=k (x² + 3x -4) (x² -i²)
=k(x² + 3x -4) (x² +1) ___(1)
Solution point f(0) =-8
-8 =k(0² +3(0) -4)(0² +1)
⇒ k=2
Substitute k=2 in (1)
f(x) =2(x² + 3x -4) (x² +1)
=2(x⁴ +3x³ -3x²+3x-4)
Therefore, polynomial function f with real coefficients that has the given degree, zeros, and solution point is f(x) =2(x⁴ +3x³ -3x²+3x-4).
The complete question is:
Find the polynomial function f with real coefficients that has the given degree, zeros, and solution point.
Degree 4
Solution Point f(0) = -8
Zeros -4, 1, i
Learn more about polynomial function here
brainly.com/question/12976257
#SPJ1
which system is represented by the graph?
Answer: (A)
Step-by-step explanation:
By elimination, none of the other answers choices fit the lines; B, C, and D all have at least one positive slope. Both lines shown in the graph have negative slopes, so both equations have to have a negative x value when simplified, so it's A.
What is the scale factor of the dilation?
The scale factor for the square LMNO to L'M'N'O' is k = 1/2.
What is the scale factor of the dilation?Remember that for any length L, a dilation of scale factor k gives a new length L' such that:
L' = k*L
Look at line LM, it has a length:
L = √(6^2 + 2^2) = √40
Now line L'M' has a length:
L' = √(1^2 + 3^2) = √10
Then we can see that:
L' = k*L
√10 = k*√40
√10/√40 = k
√(1/4) = k
1/2 = k
The scale factor is 1/2.
Learn more about dilations:
https://brainly.com/question/3457976
#SPJ1
Find the value of x so that f ll g. 18x-44 8x-10
Answer:
x = 3.4
Step-by-step explanation:
18x - 44 = 8x - 10
+10
18x - 34 = 8x
-18x
-34 = -10x
/ 10
x = 3.4
Proof:
18 x 3.4 = 61.2 - ( 44 ) = 17.2
8 x 3.4 = 27.2 - ( 10 ) = 17.2
HELP ALGEBRA 2!
One side of a square is increased by 2 inches, while adjacent side is decreased by 2 inches. The area of the resulting rectangle is 32 square inches. What were the dimensions of the original square?
Answer:
(x+2)(x-2)=32(x+2)(x-2)=32x^2+2x-2x-4=32(x+2)(x-2)=32x^2+2x-2x-4=32x^2-4-32=0(x+2)(x-2)=32x^2+2x-2x-4=32x^2-4-32=0x^2-36=0(x+2)(x-2)=32x^2+2x-2x-4=32x^2-4-32=0x^2-36=0(x+6)(x-6)=0(x+2)(x-2)=32x^2+2x-2x-4=32x^2-4-32=0x^2-36=0(x+6)(x-6)=0x-6=0x=6 the length of the original side of the square.(6+2)(6-2)=32(6+2)(6-2)=328*4=32(6+2)(6-2)=328*4=3232=32Scientists determined that Alaska's average winter was -30.2C. The difference between this temperature and Alaska's highest recorded temperature was 50.33 degrees. What was Alaska’s highest recorded temperature?
*
Answer: -82.2
Step-by-step explanation:
What is the length of XY
SolutionSoltuion:
From the question, the given value id
[tex]\begin{gathered} XQ=3 \\ XR=RW \\ XR+RW=XW \\ XQ=QY \\ XQ+QY=XY \end{gathered}[/tex]By applying the theorem above, we will have the value of XY be
[tex]\begin{gathered} XQ+QY=XY \\ XQ=3 \\ QY=3 \\ XY=3+3 \\ XY=6 \end{gathered}[/tex]Hence,
The final answer = 6
How to Calculate the missing value: P = 1000 W, E = ____, I = 20 A.
The voltage E of the electrical appliance using a power of 1000 watts is 50 Volts.
How to calculate voltage using the power formula?Power is simply the quantity of energy transferred per unit time. It can be expressed as;
P = E × I
Where E is voltage and I is current.
Given the data in the question;
Power P = 1000WCurrent I =20AVoltage E = ?To determine the voltage of the appliance, plug in the given values into the formula above and solve for E.
P = E × I
1000W = E × 20A
E = 1000 / 20
E = 50V
Therefore, the missing value voltage E is 50 volts.
Learn more about Ohm's law here: brainly.com/question/12948166
#SPJ1
find the area of a circle with a radius of 6 centimeters use 3.14 for [tex]\pi[/tex]
Radius = 6 cm
The area of circle is given by:
[tex]\begin{gathered} A=\pi r^2\text{ } \\ \pi\text{ = 3.14} \\ A\text{ = 3.14 }\cdot6^2 \end{gathered}[/tex][tex]A=113.04cm^2[/tex]A = 113.04 cm^2
GUYSSSSS HELP ME PL,S PSP[JOWQHIFUEFIDoisd[jofbwkeqi
ITS SO HARDDD TO SOLVE
if you dig a 6 feet hole how deep is it?
PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS HELPPPPPPPPPPPPPPPPPPP
Answer:
You're question is incomplete.Please try to make it more clear
PLEASE HELP I WILL GIVE BRAINLYEST! ALGEBRA 1 HW
The average rate of change of helicopters height when it starts descending is : - 630.01 ft/min
Solution:Rate of change between two points,
We calculate the average rate of change by dividing the change in y (output) by the change in x. (input). And all we're doing visually is calculating the slope of the secant line that connects two points.Follow these steps to calculate the rate of change on a graph when given two points on the graph:
Determine the coordinates of the given points.Determine the difference in the output values.Determine the difference in the input values.Determine the ratio of the change in y to the change in x: ΔyΔx.Here in the question ,
Given two points (0 , 8400) and (13.333 , 0)
to find the average rate of change ,
Average rate of change = y2 - y1/ x2 - x1
by substituting values,
Average rate of change = 0 - 8400/ 13.333 - 0
= - 8400 / 13.333
= - 630.01 ft/min
since the helicopter is descending the rate of change will be negative
so the rate of change of helicopters height is - 630.015 ft/min
To learn more about rate of change refer to :
https://brainly.com/question/25184007
#SPJ13
David buys last year's best-selling novel, in hardcover, for $13.30. This is with a 30% discount from the original price. What was theoriginal price of the novel?
Since the price paid got 30% discount from the original price, so this price represents 70% of the original price.
Using the variable x to represent the original price, we can write the following equation and solve it for x:
[tex]\begin{gathered} 13.3=70\text{\% of x} \\ 13.3=\frac{70}{100}\cdot x \\ 13.3=0.7\cdot x \\ x=\frac{13.3}{0.7} \\ x=19 \end{gathered}[/tex]Therefore the original price is $19.
Please expand (3x+4)(5x-2)(4x-3) and simplify fully.
The complete expansion of the expression would give; 60x^3 - 11x^2 - 74x + 24
How can the expression be expanded?To expand an expression means that we should be able to obtain the original long expression that was factorized in order to get it. In this case, the expression that we have is (3x+4)(5x-2)(4x-3). We would now have to carry out the expansion in stages.
1) (3x+4)(5x-2)
15x^2 - 6x + 20x - 8
2) We can now carry out the next step in the expansion as we multiply the bracket with the last term in the expression;
15x^2 - 6x + 20x - 8(4x-3)
60x^3 - 45x^2 - 24x^2 + 18x + 80x^2 - 60x -32x + 24
We can now collect the like terms;
60x^3 - 45x^2 - 24x^2 + 80x^2 + 18x - 60x - 32x + 24
60x^3 - 11x^2 - 74x + 24
Learn more about expansion:https://brainly.com/question/2165968
#SPJ1