The domain of this function is { - 4, - 1, 0, 3 } and range of the function is
{ - 4 }.
What is the domain and range of a function?Suppose we have an ordered pair (x, y) then the domain of the function is the set of values of x and the range is the set of values of y for which x is defined.
The domain of the function f(x) is the set of x values that are
{ - 4, - 1, 0, 3 }
and the range of the function f(x) is { - 4 }.
As for every input, the output of the function remains the same so it is a constant function.
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What is the simplified form of (x – 2)(2x +3)? Use the Distributive Property.
2x2 – x – 6
2x2 – 6
2x2 – 7x – 6
2x2 + x – 6
2. What is the simplified form of (3x + 2)(4x – 3)? Use a table.
12x2 + 18x + 6
12x2 + x – 6
12x2 + 18x – 6
12x2 – x – 6
3. What is the simplified form of (4p – 2)(p – 4)?
4p2 + 6p – 16
4p2 – 18p + 8
4p2 – 14p – 6
4p2 – 6p + 16
4. The radius of a cylinder is 3x – 2 cm. The height of the cylinder is x + 3 cm. What is the surface area of the cylinder? Use the formula A = 2r2 + 2rh.
Answer:
Step-by-step explanation:
A. The given equation is:
[tex](x-2)(2x+3)[/tex]
simplifying this,
[tex]2x^{2}-4x+3x-6[/tex]
[tex]2x^{2}-x-6[/tex]
Option A is correct
B. The given equation is:
[tex](3x+2)(4x-3)[/tex]
simplifying this,
[tex]12x^{2}+8x-9x-6[/tex]
[tex]12x^{2}-x-6[/tex]
Option D is correct.
C. The given equation is:
[tex](4p-2)(p-4)[/tex]
simplifying this,
[tex]4p^2-2p-16p+8[/tex]
[tex]4p^2-18p+8[/tex]
Option B is correct.
D. The radius of a cylinder is 3x – 2 cm. The height of the cylinder is x + 3 cm. Then,
Surface area of cylinder=[tex]2r^{2}+2rh[/tex]
=[tex]2r(r+h)[/tex]
=[tex]2(3x-2)(3x-2+x+3)[/tex]
=[tex]2(3x-2)(4x+1)[/tex]
=[tex]2(12x^{2}-8x+3x-2)[/tex]
=[tex]24x^{2}-10x-4[/tex]
Therefore, Surface area of cylinder=[tex]24x^{2}-10x-4[/tex] sq units
Which expression is equal to 5/(sqrt)11?
a) 5(sqrt)11/11
b) (sqrt)5/11
c) (sqrt)55/11
d) 25/11
please help, I'm confused.
Answer:
Option A is correct
the expression is equal to [tex]\frac{5}{ \sqrt{11}}[/tex] is [tex]\frac{5\sqrt{11}} {11}[/tex]
Explanation:
Given expression is, [tex]\frac{5}{ \sqrt{11}}[/tex]
Multiply and divide by the denominator by [tex]\sqrt{11}[/tex] in the given expression, we have,
[tex]\frac{5}{\sqrt{11}} \times \frac{\sqrt{11}} { \sqrt{11}}[/tex]
or
[tex]\frac{5 \cdot \sqrt{11}} {\sqrt{11} \cdot \sqrt{11}}[/tex]
use : [tex]\sqrt{a}\cdot\sqrt{a}=(\sqrt{a} )^2 = a[/tex]
then;
[tex]\frac{5\sqrt{11}} { (\sqrt{11})^2} =\frac{5\sqrt{11}} {11}[/tex]
Therefore, the expression is equal to [tex]\frac{5}{ \sqrt{11}}[/tex] is, [tex]\frac{5\sqrt{11}} {11}[/tex]
A refrigerator is priced at $1,250. There are two options offered to reduce the price: either a 25% discount off the price or a rebate of $300. Which is the better choice, and what is the extra amount saved?
A.The 25% discount is better; it saves $12.50.
B.The rebate is better; it saves $12.50.
C.The 25% discount is better; it saves $75.
D.The rebate is better; it saves $75.
Answer:
A.The 25% discount is better; it saves $12.50.
Step-by-step explanation:
Here, the given marked price of the refrigerator = $ 1250,
In first option,
Discount percentage = 25 %,
Thus, total discount = 25 % of the marked price
= 0.25 × 1250
= 312.5
Thus, the selling price = 1250 - 312.5 = $ 937.5,
In second option,
Discount = $ 300,
Thus, the selling price = 1250 - 300 = $ 950,
Since, 937.5 < 950
Hence, First option is better than that of second.
Also, total saving = 950 - 937.5 = $ 12.5
⇒ The 25% discount is better; it saves $12.50
suppose you went to a carnival. the price in was $6, and you paid $0.50 to get on each ride. if you went to the carnival and rodeo 11 rides, how much did you spend?
suppose you went to a carnival. the price in was $6, and you paid $0.50 to get on each ride. if you went to the carnival and rodeo 11 rides, how much did you spend?
Answer: 11.50
Step-by-step explanation:
6$ to get in+ rides=$
11(rides)*.50(price of rides)=5.50
5.50+6=$11.50
Work out the area of a triangle with a height of 6m and a base length of 14m
What is the common difference in the sequence 5, 10, 15, 20, 25,...?
A. -5
B. 1/2
C. 2
D. 5
what does it mean for an equation to be balanced and why must you keep an equation in balance?
A(n) ______ is a letter or symbol that represents some unknown value.
A. term
B. equation
C. variable
D. expression
what divided by 6 equals 4
The correct answer is 1.5.
What is the formula of divide?The formula of divide is Dividend ÷ Divisor = Quotient + Remainder.
What is Remainder?Remainder is the left over number in the division.
Given:
6 ÷ ? = 4......(1)
Here we assume x is divided by 6 equals 4.
Then put x in given equation (1).
6 ÷ x = 4
x = 6 ÷ 4.
x = 6/4 = 1.5
Here 6 is dividend, 4 is divisor and 1.5 is quotient.
Therefore, 1.5 divided by 6 equals 4.
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One year there was a total of 73 commercial and noncommercial orbital launches worldwide. In addition, the number of noncommercial orbital launches was one more than three times the number of commercial orbital launches. Determine the number of commercial and noncommercial orbital launches.
Final answer:
The number of commercial orbital launches is 18, and the number of noncommercial orbital launches is 55.
Explanation:
Let's assume that the number of commercial orbital launches is represented by x. According to the problem statement, the number of noncommercial orbital launches is more than three times the number of commercial orbital launches. So, the number of noncommercial orbital launches would be 3x + 1.
Given that the total number of commercial and noncommercial orbital launches is 73, we can set up the equation:
x + (3x + 1) = 73
Combining like terms, we get:
4x + 1 = 73
Subtracting 1 from both sides, we get:
4x = 72
Dividing both sides by 4, we get:
x = 18
Therefore, there were 18 commercial orbital launches and 55 noncommercial orbital launches.
The number of commercial orbital launches is 24, and the number of noncommercial orbital launches is 49.
Explanation:Let's assume that the number of commercial orbital launches is represented by 'x'. According to the question, the number of noncommercial orbital launches is one more than three times the number of commercial orbital launches. So, the number of noncommercial orbital launches can be represented by '3x + 1'.
Given that the total number of commercial and noncommercial orbital launches is 73, we can set up the equation 'x + (3x + 1) = 73' to represent the total launches. Solving this equation will give us the values of 'x' and '3x + 1', which represent the number of commercial and noncommercial orbital launches, respectively.
By solving the equation, we find that 'x = 24' and '3x + 1 = 73 - 24 = 49'.
lim x tanx/ 1-cosx
x―>0
please help... ...?
You want to put $2,500 in a simple interest account. It has a 4% annual interest rate. How long will it take you to earn $200 in interest? 2nd question of the day. See if you can answer it.
Which expression gives the distance between the points (2, 5) and (-4, 8)?
The expression for the distance between the points (2, 5) and (-4, 8) is the square root of 45 or 3√5, which is approximately 6.708.
Explanation:The expression that gives the distance between the points (2, 5) and (-4, 8) is found using the distance formula which is derived from the Pythagorean theorem. The formula is √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are coordinates of the two points.
To find the distance between (2, 5) and (-4, 8), substitute x1=2, y1=5, x2=-4, and y2=8 into the formula:
√((-4 - 2)² + (8 - 5)²) = √((-6)² + (3)²) = √(36 + 9) = √45
The distance is therefore the square root of 45, which can be simplified to 3√5 (approximately 6.708).
Final answer:
The distance between the points (2, 5) and (-4, 8) is calculated using the distance formula, resulting in 3√(5) units.
Explanation:
The distance between the points (2, 5) and (-4, 8) can be calculated using the distance formula, which is derived from the Pythagorean theorem. The distance formula is √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the given values, the distance d can be calculated as follows:
√((-4 - 2)² + (8 - 5)²) = √((-6)² + (3)²) = √(36 + 9) = √(45) = 3√(5)
Therefore, the distance between the points (2, 5) and (-4, 8) is 3√(5) units.
For any given rational function, differentiate between a function’s vertical and horizontal asymptotes. In two or more complete sentences, make a connection between the asymptotes and the function’s domain and range.
Consider the function
f(x) = [tex]\frac{x-3}{x-4}[/tex]
Domain of the function = All real numbers except , x≠4 .
[tex]y=\frac{x-3}{x-4} \\\\ xy - 4y = x-3 \\\\ x y -x= 4 y-3\\\\ x=\frac{4 y-3}{y-1}[/tex]
Range = All real numbers except , y≠1 .
Horizontal Asymptote= Since the degree of numerator and denominator of rational function is same , So Divide coefficient of x in numerator by divide coefficient of x in denominator.
So Horizontal Asymptote , is : y=1
To get vertical asymptote, put
Denominator =0
x-4=0
x=4 , is vertical asymptote.
Domain = All real numbers except vertical Asymptote
Range = All real numbers except Horizontal Asymptote
Final answer:
The vertical asymptotes of a rational function can be found by determining the roots of the polynomial in the denominator, while the horizontal asymptotes can be determined by analyzing the behavior of the function as x approaches infinity. The asymptotes are closely related to the function's domain and range.
Explanation:
Vertical asymptotes of a rational function can be determined by finding the roots of the polynomial in the denominator. Each root corresponds to a vertical asymptote. For example, if the polynomial has a factor of (x - 2), then there is a vertical asymptote at x = 2.
On the other hand, horizontal asymptotes of a rational function can be found by analyzing the behavior of the function as x approaches positive or negative infinity. If the leading terms of the numerator and denominator have the same degree, then the function will have a horizontal asymptote. For instance, if the leading terms are both x^2, then the horizontal asymptote will be y = 0.
The domain of the function is the set of all valid inputs, while the range is the set of possible outputs. The vertical asymptotes and the behavior of the function as x approaches infinity are closely related to the domain, while the horizontal asymptotes are related to the range.
Write 0.000045 in scientific notation.
The options are:
A. 4.5 · 10-4
B. 4.5 · 10-6
C. 4.5 · 10-5
D. 4.5 · 105
What is one half plus one fifth?
A shopper purchased 8 T-shirts and 5 pairs of pants for $220. The next day he purchased 5 T-shirts and 1 pair of pants for $112. How much does each T-shirt and each pair of pants cost?
By setting up a system of linear equations based on the shopper's purchases and solving it, we found that the cost of each T-shirt is $20, and the cost of each pair of pants is $12.
Explanation:To find out how much each T-shirt and each pair of pants cost based on the shopper's purchases, we can set up a system of linear equations. Let's denote the cost of a T-shirt as T and the cost of a pair of pants as P.
The two purchases give us these equations:
8T + 5P = $220
5T + 1P = $112
Next, we use a method such as substitution or elimination to solve these simultaneous equations. If we multiply the second equation by 5, we get:
5(5T + 1P) = 5($112)
25T + 5P = $560
Now subtract the first equation from this result:
25T + 5P - (8T + 5P) = $560 - $220
17T = $340
T = $20
Now that we know the cost of a T-shirt, we can substitute T in one of the original equations to find P:
5T + P = $112
5($20) + P = $112
$100 + P = $112
P = $12
So, a T-shirt costs $20 and a pair of pants costs $12.
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Liam has purchased a fee-for-service health insurance plan from Leroux Health Insurance. Plan A includes a $248.00 monthly premium and an annual deductible of $5,500.00 (not including co-pays).
Liam is a fairly healthy young man. He visits his primary care physician three times a year on scheduled visits. He sees a chiropractic specialist every week to help with lower back pain. He has no current prescriptions that need refilling regularly.
Assuming Liam maintains his regular visits with his primary care physician and his chiropractor, and avoids any trips to the emergency room or urgent care, how much will Liam pay in health care related fees this year?
Answer: D | $6,216.00
Step-by-step explanation:
A circular garden has a radius of 12 feet. what is the approximate circumference of the garden?
a. 1808.6 ft
b. 452.2 ft
c. 75.4 ft
d. 37.7 ft
Answer:
37.7
Step-by-step explanation: K12
what are the two types of exponential functions?
The two types of exponential functions are:
Exponential Growth: exponential growth function is [tex]y = a^x[/tex], where "a" is the base and "x" is the exponent.
Exponential Decay: exponential decay function is [tex]y = a^{(-x)[/tex], where "a" is the base and "x" is the exponent.
The two types of exponential functions are:
Exponential Growth: In an exponential growth function, the base (often denoted by "a") is greater than 1.
As the input (x) increases, the output (y) grows at an increasing rate, creating a steep upward curve on the graph.
The general form of an exponential growth function is [tex]y = a^x[/tex], where "a" is the base and "x" is the exponent.
Exponential Decay: In an exponential decay function, the base (often denoted by "a") is between 0 and 1 (exclusive).
As the input (x) increases, the output (y) decreases at an increasing rate, creating a steep downward curve on the graph.
The general form of an exponential decay function is [tex]y = a^{(-x)[/tex], where "a" is the base and "x" is the exponent.
Both types of exponential functions show rapid growth or decay patterns, and their graphs exhibit a characteristic curve that is continuous and smooth.
The difference lies in the behavior of the output (y) concerning the input (x).
In exponential growth, the output increases exponentially with increasing input, while in exponential decay, the output decreases exponentially as the input increases.
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Help Please? Factor Completely: 2x2 − 32
Prime
2(x2 − 16)
2(x + 4)(x + 4)
2(x + 4)(x − 4) ...?
Answer:
Option 4th is correct
[tex]2 \cdot (x-4)(x+4)[/tex]
Step-by-step explanation:
Using difference of square:
[tex]a^2-b^2=(a-b)(a+b)[/tex]
GCF is the largest number that divide the given polynomial or expression.
Given the expression:
[tex]2x^2-32[/tex]
We have to completely factor the expression.
GCF of [tex]2x^2[/tex] and 32 is, 2
then;
[tex]2 \cdot (x^2-16)[/tex]
Using difference of square
[tex]2 \cdot (x-4)(x+4)[/tex]
therefore, the completely factor of [tex]2x^2-32[/tex] is, [tex]2 \cdot (x-4)(x+4)[/tex]
Answer:
D. 2(x + 4)(x − 4)
Step-by-step explanation:
Pleeease help!!
Write an equation in point-slope form of the line that passes through the given point and with the given slope m.
(-2,1);m=7
Given four functions, which one will have the highest y-intercept?
f(x)g(x)h(x)j(x)
Blake is tracking his
savings account with
an interest rate of 5%
and a original deposit
of $6.
xg(x)
16
28
312
the function h of x equals 4 to the x power, plus 3j(x) = 10(2)x
Answer:
The highest Y-intercept would be f(x)
Solve the system using elimination 4x-7y=3
x-7y=-15
Answer: x=6 and y=3
Step-by-step explanation:
4x - 7y = 3 -------(1)
x - 7y = -15 ------(2)
equation(1) - equation (2)
3x = 18
Divide bothside by 3
x = 18/3
x= 6
also, multiply equation (2) by 4
4x - 28y = -60--------------(3)
subtract equation(3) from equation(1)
21y = 63
divide bothside by 21
y = 63/21
y = 3
Solve by factoring.
3q^2+q-14=0
What is the slope intercept of 2x-8y=24?
PLEASE HELP ASAP
A construction crew is lengthening a road. The road started with a length of 57 miles, and the crew is adding 4 miles to the road each day. Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked. Write an equation relating L to D . Then use this equation to find the total length of the road after the crew has worked 38 days.
Equation:
total length of the road after 38 days: Miles
Which property of equality would be used to solve the equation -3x = 252?
addition
subtraction
multipication
division< is it this one
Hey there! Your answer is division! You were right! Because you would divide by -3 to get x. Hope this helped! Your fellow Brainly user, GalaxyGamingKitty.
joe is a waiter at a local pizza parlor. he usually gets a tip from the tables he waits on. the bill for one table comes to $34
write a formula that will help joe determine how much of a tip he'll recieve from that table.
p= percent tip
t=tip left for the waiter
The price of a gallon of milk is 3.75. circle the price of milk rounded to the nearest dollar