One of the five quadratics below has a repeated root. (The other four have distinct roots.) What is the repeated root?
Answers
The quadratic equation with a repeated root is:
8*x^2 - 32*x +32
And the repeated root is x = 2
What is the repeated root?For a quadratic equation:
0 = a*x^2 + b*x + c
We define the discriminant as:
D = b^2 - 4ac
If D = 0, we have only one real root (or two repeated roots). Then we just need to see which of the given quadratic equations has a discriminant of zero.
1) -x^2 + 18x + 81
The discriminant is:
D = 18^2 - 4*(-1)*81 = 648
2) 3x^2 - 6x + 9
The discriminant is:
D = (-6)^2 - 4*3*9 = -72
3) 8*x^2 - 32*x +32
The discriminant is:
D = (-32)^2 - 4*8*32 = 0
So this is the one with a discriminant of zero.
The roots are given by:
8*x^2 - 32*x +32 = 0
Using Bhaskara's formula we will get:
x = (- (-32) ± √( (-32)^2 - 4*8*32))/(2*8)
x = (32/16) = 2
The repeated root is x = 2
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Related Questions
what polynomial is twice the sum of -2x^(2)+5x-3 and 5x^(2)-4 show your work
Answers
The polynomial is twice the sum of -2x² + 5x - 3 and 5x² - 4 is 6x² + 10x - 14.
What polynomial is twice the sum of the given polynomial?Given the polynomials in the question;
-2x² + 5x - 3 and 5x² - 4
First, we find the sum of the polynomials
(-2x² + 5x - 3) + (5x² - 4)
-2x² + 5x - 3 + 5x² - 4
Collect like terms and simplify
-2x² + 5x² + 5x - 3 - 4
3x² + 5x - 7
Next, multiply the polynomial by 2.
2(3x² + 5x - 7)
Using distributive property,
2×3x² + 2×5x +2×-7
6x² + 10x - 14
Therefore, the polynomial is twice the sum of -2x² + 5x - 3 and 5x² - 4 is 6x² + 10x - 14.
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help me plsssss plssss plsssss i will double kiss you
Answers
Answer:
A
Step-by-step explanation:
Sin A = [tex]\frac{opposite}{hypotenuse}[/tex]
Cos A = [tex]\frac{adjacent}{hypotenuse}[/tex]
Answer:
[tex]\text{a.} \quad \sin A=\dfrac{3}{5}, \quad \cos A=\dfrac{4}{5}[/tex]
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angle.O is the side opposite the angle.A is the side adjacent the angle.H is the hypotenuse (the side opposite the right angle).Therefore:
[tex]\implies \sin A =\dfrac{BC}{AB} = \dfrac{3}{5}[/tex]
[tex]\implies \cos A =\dfrac{AC}{AB} = \dfrac{4}{5}[/tex]
The endpoints of AB are -4 and 6. Find the coordinate of Point P that partitions the segment in a 2:3 ratio.
Answers
Answer: 0
Step-by-step explanation:
Since it is 10 units total from -4 to 6,
4/10 and 6/10 would give a ratio of 2:3
4 units from -4 would be at 0, which is also 6 units away from the 6
4 units to 6 units equals a ratio of 2:3
3) At midnight, the temperature was 15 degrees
Fahrenheit. When we woke up in the morning, the
temperature was -3 degrees. What was the change in
temperature from midnight to the morning?
Answers
Answer:
Step-by-step explanation:
First of all it has to drop 15 degrees to get to 0.
We have another three degrees to go.
15 - - 3 = 18
The temperature change was 18 degrees from midnight to morning.
Gabriella's school is selling tickets to a choral performance. On the first day of ticket sales the
school sold 14 senior citizen tickets and 14 child tickets for a total of $252. The school took in
$154 on the second day by selling 9 senior citizen tickets and 7 child tiekets. Find the price of a
senior citizen ticket and the price of a child ticket.
Answers
The ticket price of
A Senior citizen = $14
A Child = $4
First day of ticket sales :
Senior citizen tickets (s) = 14
Child tickets (c) = 14
Total price of both tickets = $252
14s + 14c = 252 eq. (1)
Second day of ticket sales :
Senior citizen tickets (s) = 9
Child tickets (c) = 7
Total price of both tickets = $154
9s + 7c = 154 eq. (2)
Multiplying equation 2 with 2, we get
18s + 14c = 308 eq. (3)
Now, we will subtract eq. (1) from eq. (3)
18s + 14c = 308 eq. (3)
-14s - 14c = -252 eq. (1)
____________________
4s = 56
s = 56/4
s = 14
We get the ticket price of one senior citizen which is 14 Dollars.
Now, we will put s = 14 in eq. 2,
So, 9s + 7c = 154
(9×14) + 7c = 154
7c = 154 - 126
c = 28 / 7
c = 4
Ticket price of one child is 4 Dollars.
Hence, the ticket price of a senior citizen and a child is $14 and $4, respectively.
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Four dice are rolled sequentially. What is the probability that the first die shows six and the other dice show an odd number? IN FRACTIONS!
Answers
Answer:
1/48
Step-by-step explanation:
The total number of different outcomes when rolling 4 dice is
6 × 6 × 6 × 6 = 1296
The possible number of outcomes of rolling a 6 followed by 3 odd numbers is
1 × 3 × 3 × 3 = 27
p(6 followed by 3 odd numbers) = 27/1296 = 1/48
The radius of a circle measures 16 yd.. What is the circumference of the circle? Use 3.14 for pi , and do not round your answer. Be sure to include the correct unit in your answer.
Answers
C=2πr=2·π·16≈ 100.53096
When the signs are of the integers the same, 1.__________
the integers and copy the 2.) ________ sign. When the signs are
3,) ____________, subtract them and use the sign of the number
with the greater 4) _________. If we add two same numbers with
different signs, then the answer is equal to 5.) ___________.
The sum of two negative integers is a 6. )_________ integer. The
sum of two positive integers is a 7.) ___________ integer.
Answers
The completed statement on the addition and subtraction operations with integers is presented as follows;
When the signs are of the integers of the same sign
1. Add the integers and copy the 2.) integer sign. When the signs are 3) different, subtract them and use the sign of the number with the greater 4) magnitude. If we add two same numbers with different signs, then the answer is equal to 5.) zero. The sum of two negative integer is a 6.) negative integer. The sum of two positive integers is a 7.) positive integer.
How can the operation of adding integers be simplified?The process of adding integers is as follows;
Integers that have the same sign are added together, and the sign of the integers are placed before the result.
The addition of two integers that have different signs involve subtracting the integers and including the sign of the integer with the largest magnitude to the result.
The addition of two the same numbers that have different signs gives the same result as subtracting a number from itself, which is zero.
The sign of the result of the addition or subtraction of two integers of the same is the same as the sign of the integers in the operation.
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ALGAE A scientist has a fish tank in the shape of a rectangular prism. The tank is 18 inches high, 14 inches wide, and 30 inches long. After one month, the scientist found that the sides and bottom of his fish tank were covered with algae. The scientist wants to run tests on the algae to help determine why it started to grow. How much algae is there for the scientist to test?
Answers
the algae that is present with the scientist to research upon covers a surface area of 2004 inches² in the rectangular prism.
The dimensions of the rectangular prism is given by:
Height = h = 18 inches
Width = w = 14 inches
Length = l = 30 inches
Now, we have to calculate the surface area of the tank excluding the top of the tank to find out how much algae has been present there for the scientist to test.
So, the formula for surface area will become:
A = 2(w l + h l + h w) - l w ( as the top has to be excluded)
Now substituting the values of l, w and h, we get that:
A = 2 [ (14) (30) + (18) (30) + (18) (14) ] - (30) (14) inches²
A = 2 [ 420 + 540 + 252 ] - 420 inches²
A = 2 [ 1212 ] - 420 inches²
A = 2424 - 420 inches²
A = 2004 inches²
Therefore, we get that, the algae that is present with the scientist to research upon covers a surface area of 2004 inches² in the rectangular prism.
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Determine whether the following statement is true or false. Explain.
The graph of y = |x-2|- 2 is a translation two units to the right and two units upward of the graph of y = |x|.
Choose the correct answer below.
A. True, because the graph of y = f(x - h) + k is the translation of the graph of y = f(X) |k| units upward if k= 0 or downward if k < 0, and h units to the right if h> 0 or to the
left if h < 0.
B. True, because the graph of y = f(x- h) + k is the translation of the graph of y = f(x) In| units upward if h = 0 or downward if h < 0, and k units to the right if k> O or to the
left if k < O
C. False, because the graph of y = f(x- h) + k is the translation of the graph of y = f(x) |k| units to the right if k>0 or to the left if k < 0, and h units upward if h downward if h < 0.
D. False, because the graph of y = f(x- h) + k is the translation of the graph of y = f(x) h units to the right if h > 0 or to the left if h < 0, and k units upward if k>downward if k < 0.
Answers
Answer:
Determine whether the following statement is true or false. Explain.
The graph of y = |x-2|- 2 is a translation two units to the right and two units upward of the graph of y = |x|.
Choose the correct answer below.
A. True, because the graph of y = f(x - h) + k is the translation of the graph of y = f(X) |k| units upward if k= 0 or downward if k < 0, and h units to the right if h> 0 or to the
left if h < 0.
B. True, because the graph of y = f(x- h) + k is the translation of the graph of y = f(x) In| units upward if h = 0 or downward if h < 0, and k units to the right if k> O or to the
left if k < O
C. False, because the graph of y = f(x- h) + k is the translation of the graph of y = f(x) |k| units to the right if k>0 or to the left
8
k
-2
-1
0
1
b=
2
RETRY✔
f(x) = -x² + x + 6
a
4
b
6
10
Answers
The missing values are a = 0, b= 6 and c=4.
What is Function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
We have function,
f(x) = -x² + x + 6
At x= -2
f(-2) = -(-2)² + (-2) + 6 = -4 -2 + 6= 0
At x = 0
f(0) = -0² + 0 + 6= 6
At x = 2
f(2) = -2² + 2 +6 = -4 + 8= 4
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what is the simplest form of 2/4 divide by 4/9
Answers
Answer:
it 9/ 8
Step-by-step explanation:
2/4× 9/4
18/16
9/8
the midpoint of \overline{\text{ab}} ab is m(0, -3)m(0,−3). if the coordinates of aa are (2, 1)(2,1), what are the coordinates of bb?
Answers
If the coordinates of the point a is (2,1) and midpoint is (0.-3), then the coordinates of b is (-2,-7).
Midpoint:
Midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
The formula for midpoint is,
[tex](x_{m},y_{m})= (\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2} }{2} )[/tex]
Where
(x₁,y₁) is the coordinates of the first point and
(x₂,y₂) is the coordinates of the second point
and
[tex](x_m,y_m)[/tex] is the mid point of the first and second points.
Given,
Mid point = (0,-3)
Point a = (2,1)
Here we need to find the point b.
Let (x,y) be the point of b.
Now,
Apply the values on the formula,
Then we get,
[tex](0,-3)=(\frac{2+x}{2},\frac{1+y}{2})[/tex]
Compare the values in order to solve it,
=> 0 = (2 +x)/ 2
=> 0 = 2 + x
=> x = -2
Similarly,
=> -3 = (1 + y)/2
=> -3 x 2 = 1 + y
=> -6 = 1 + y
=> y = -6 - 1
=> y = -7
Therefore, the coordinates of b is (-2,-7).
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89. Philip solved the following problem incorrectly. Explain his mistake.
1659
x 21
1659
+3318
4977
Answers
Philip's mistake is he did not add zero at ten's place.
When the multiplication is performed with two or more digits in the bottom number, zeroes are added as per the position. We see that in number 21, one is at one's place and 2 is at ten's place. Hence, when multiplying the digit 2 with the number 1659, we will add zero at one's place.
Performing the correct multiplication -
1659
× 21
1659
+33180
The result of multiplication will be the sum of numbers 1659 and 33180.
Result = 34,839
Therefore, the multiplication of the numbers will give result 34,839. Hence, the mistake is not keeping zero at one's place, while performing multiplication.
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a family is comparing different car seats. one car seat is designed for a child up to and including lb. another car seat is designed for a child between lb and lb. a third car seat is designed for a child between lb and lb, inclusive. model those ranges with compound inequalities. which car seats are appropriate for a -lb child?
Answers
According to the given statement the following car seats are adequate for a 32-pound child:
car seat suited for a youngster weighing between 15 and 40 pounds, andcar seat intended for children weighing 30 to 85 poundsWhat is an interval notation?Interval notation tells which part of the number line, from left to right, is included in the solution (i.e., which part of the number line is shaded). Parentheses are written next to endpoints which are NOT included in the solution while brackets are written next to included endpoints.
According to the given statement:The Inequality car seat is intended for children weighing up to 30 pounds.
let the child's weight = x
x ≤ 30
Inequality for a car seat built for a child weighing between 15 and 40 pounds;
15 < x < 40
Inequality for a car built for a youngster weighing between 30 and 85 pounds;
30 < x < 85
According to the given statement the following car seats are adequate for a 32-pound child:
car seat suited for a youngster weighing between 15 and 40 pounds, andcar seat intended for children weighing 30 to 85 poundsTo learn more about interval notation visit:
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The given question is not complete.
A family is comparing different car seats. One car seat is designed for a child up to and including 30 lb. Another car seat is designed for a child between 15 lb and 40 lb. A third car seat is designed for a child between 30 lb and 85 lb, inclusive. Model these ranges on a number line. Represent each range of weight using interval notation. Which car seats are appropriate for a 32-lb child?
what is 3 4 5 6 7 as in mean .
Answers
Answer:
5
Step-by-step explanation:
add the numbers up then divide by how many there are.
3+4+5+6+7=25
25÷5 = 5
23
6. A penny weighs 2.5 grams while a dime weighs about 2.27 grams. How much do a penny and two dimes weigh?
O2.04 g
5.68 g
4.77 g
7.04
Answers
Answer:
7.04
Step-by-step explanation:
2.27
2.27
2.50 equals 7.04
Stacy has a part time job.
She earns 8 pounds an hour.
She wants to buy a new smartphone costing 220 pounds.
How many hours does she need to work to earn enough to buy it.
Answers
220/8 = 27.5
27.5 x 8 = 220
She’ll have to work 27 hours and 30 minutes to get 220 pounds.
a location that is 30 degrees north and 45 degrees west is what of the prime meridian and what of the equator
Answers
A location that is 30 degrees north and 45 degrees west is west of the prime meridian and north of the equator.
A prime meridian refers to an arbitrary meridian which is there in a geographic coordinate system. Here, the longitude is defined as 0°.
A prime meridian and its anti-meridian will together form a great circle in a geographic coordinate system.
The Equator is a circle of latitude, about 40,075 km in circumference, that divides Earth into the Northern and Southern hemispheres.
It is an imaginary line that is located at 0 degrees latitude, and is a halfway between the North and South poles.
Therefore, we get that a location that is 30 degrees north and 45 degrees west is west of the prime meridian and north of the equator.
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Help pls points added
Answers
Answer:
A: (-10, 2)
B: (-5, 2)
C: (-5, 7)
D: (-10, 7)
Step-by-step explanation:
When you reflect over the x axis, you flip the y value, so that what I did.
A cup of cereal has 12 grams of fiber, which is 40% of the amount of fiber jared’s doctor recommends he consume each day. how much fiber does jared’s doctor recommend he consume each day?
Answers
The amount of fiber asked by the doctor to be consumed is 30 grams .
Method to calculate percentages :
Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100 .
Let the amount of fiber asked by the doctor to be consumed be x .
According to question ,
40 % of x = 12
Solving the equation ,
( 40 / 100 ) * x = 12
x = 1200 / 40
x = 30
Hence , the amount of fiber asked by the doctor to be consumed is 30 grams .
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Answer:
30
Step-by-step explanation:
what’s 17x3-11y2-14y3
Answers
Reason:
Subtract 14x^3 from 17x^3
Answer:
3x^3-11y^2
Step-by-step explanation:
17x^3 -11y^2 -14x^3
collect like terms
17x^3 -14x^3 =3x^3
3x^3-11y^2
I hope it helps.
Anyone know this?????
Answers
Answer:
Final answer: P=(1,5)
Step-by-step explanation:
The line APB is a line such that AP/PB= 1/3. From the points A and B that we have we can find the distance between those points using the formula d= [(y2-y1)^2=(x2-x1)^2]^1/2
d= 4 (13)^(1/2)
Now the ratio is 1:3. AP= sq rt(13) and PB= 3 sq rt(13)
Using mid point formula the mid point of AB (say Q) = [(-1+7)/2,(2+14)/2]= (3,8).
Hence the mid point of AQ is P which can found out again using the mid point formula
P= [(-1+3)/2,(2+8)/2]= (1,5)
Please help me find ABCD!!
Answers
A= 1/2(a+b)h
So in this instance, a and b are 10 and 15 cm, and the height is 9 so just substitute it like this:
A= 1/2(9+10)9
A= 85.5
if \mathbf{x}x is an optimal solution to a linear program pp, then \mathbf{x}x is a vertex of pp's feasible region.
Answers
Yes, it is true that if "x" is an optimal solution to a linear programming problem, then it is a vertex of the feasible region.
Linear programming (LP) is one of the most basic methods of optimization. By making a few simplifying assumptions, it can assist you in solving some highly complicated optimization issues.Linear programming is a basic approach that uses linear functions to represent complicated connections and then finds the optimum spots.Linear programming is used to find the best solution to a problem given certain limitations. In linear programming, we transform a real-world issue into a mathematical model. It consists of an objective function, linear inequalities, and constraints.A graphical technique entails constructing a collection of linear inequalities that are constrained. The disparities are then plotted on an X-Y plane. When we plot all of the inequalities on a graph, the intersecting region provides us with a viable region. The viable region describes all of the values that our model may take. It also provides us with the best solution.At the point of intersection, when the constraints are active, the best viable solution is found. This signifies that the intersection of the equations provides the best answer.
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A stack of Sunday newspapers sits on a skid 3" off the ground.
Each newspaper is 13" thick.
a. How high is the stack if there are n newspapers in it?
b. If the top of the stack is 3' high, about how many newspapers
are in the stack?
Answers
Answer: a. 3+13n
b. About 3 newspapers
Step-by-step explanation:
a. T=total thickness of newspapers on a skid in inches
T=3+13n
b. 3'=3 ft
1 ft=12 inches
3 ft=3*12 inches
3 ft=36 inches
36=3+13n
13n=33
n=2.54 ==> About 3 newspapers
In your own words, describe what transformations are possible in a linear function and what in the equation causes these movements.
Answers
The transformations that is possible in a linear function is: g(x) = (x - 3)².
What in the equation causes these movements?if the function of the g (x) is known to be the original function, then one can say that:
g(x) = (x - 3)²
= g(x) = x²
This is one that is shifted by 3 unit to the right because in the above, one need to substitute x for x - 3.
Hence , it functional graph can be said to be a parabola with a vertices that is known to be opening at (3,0)
Therefore, based on the above, the example of the transformations that is possible in a linear function is: g(x) = (x - 3)².
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help pls no clue where to start
Answers
Answer:
[tex]P_{rofit}=13x-50\\C_{ost}(70)=960\\P_{rofit}(70)=860\\C_{ost}(100)=1350\\P_{rofit}(100)=1250\\For\ a\ profit\ of\ \$1100\ one\ must\ sell\ 89\ stuffed\ animals.[/tex]
Step-by-step explanation:
I would suggest starting with 1 and working to 4, as it is set up for you like that.
I would start by writing down what you know, then what you need as follows:
[tex]Givens:\\ C_{ost}=13x+50;\\ R_{evenue}=36x;\\P_{rofit}=R_{evenue}-C_{ost};\\ x=N_{umber\ of\ animals}\\[/tex]
[tex]Find:\\1.\ Profit\ equation\\2a.\ C_{ost}\ to\ make\ 70\ animals\\2b.\ P_{rofit}\ from\ selling\ 70\ animals\\3a.\ C_{ost}\ to\ make\ 100\ animals\\3b.\ P_{rofit}\ from\ selling\ 100\ animals\\4.\ N_{umber}\ of\ animals\ needed\ to\ produce\ P_{rofit}\ of\ \$1100[/tex]
Now you can read it easier. Given that Profit is Revenue minus Cost, plug the equations for Cost and Revenue into the Profit equation as follows:
[tex]P_{rofit}=36x-(13x+50)\\NOTE:\ Do\ NOT\ forget\ to\ put\ the\ C_{ost}\ equation\ in\ parenthesis\ as\ you\ \\must\ subtract\ the\ entire\ C_{ost}.\\\\Distribute\ the\ negative:\ P_{rofit}=36x-13x-50\\Combine\ like\ terms:\ P_{rofit}=13x-50[/tex]
With the Profit equation, it is now easier to solve 2b, 3b, and 4.
[tex]C_{ost}\ for\ 70: C_{ost}=13(70)+50=(700+210)+50\\NOTE:\ I\ used\ the\ fact\ that\ 13*70=(10+3)*70=10*70+3*70\\C_{ost}=910+50=960\\This\ could\ also\ be\ written\ more\ clearly\ as\ C_{ost}(70)=960\\\\P_{rofit}(70) = 13(70)-50\\P_{rofit}(70)=(700+210)-50\\P_{rofit}(70)=910-50\\P_{rofit}(70)=860\\\\C_{ost}(100)=13(100)+50\\C_{ost}(100)=(1300)+50\\C_{ost}(100)=1350\\\\P_{rofit}(100)=13(100)-50\\P_{rofit}(100)=(1300)-50\\P_{rofit}(100)=1250\\[/tex]
Problem 4 will involve using the (now) known amount for profit, $1100 to find the unknown number of animals. This will involve a little bit more "algebra" compared to the prior questions.
[tex]P_{rofit}(x)=1100=13x-50\\1100=13x-50\\[/tex]
Because 13x - 50 is 1100, 13x will be 1100 + 50, just as
[tex]5*2+10 = 20\\5*2=20-10\\[/tex]
So, add 50 to both sides:
[tex]1100+50=13x-50+50\\1150=13x\\[/tex]
Because 13x is 1150, x will be 1150÷13, just as
[tex]5*2=10\\5=\frac{10}{2}[/tex]
So, divide 13 from both sides:
[tex]\frac{1150}{13}=\frac{13x}{13}\\\\\frac{1150}{13}=x[/tex]
Because 1150/13 is not an integer, use a calculator, or simplify the improper fraction to obtain...
x=88.5 (Approximately)
But, because you cannot sell half an animal, you would have to sell 89 in order to profit $1100, for bonus points, what is the actual profit accrued by selling 89 animals?
What’s the domain and range ??
USE INTERVAL NOTATION.
Only answer if you know!
Answers
Domain: (-∞, ∞)
Range: (-∞, ∞)
Step-by-step explanation:Domain and range help us describe the values a graph covers.
Defining Domain and Range
The domain is defined as all the x-values included in a function.The range is defined as all of the y-values included in a function.Remember that the x-values are along the horizontal axis, and the y-values are on the vertical axis.
The function given to us extends infinitely to the left and right as shown by the arrows. Additionally, the graph extends up and down infinitely; thus the range is also infinite.
Interval Notation
Interval notation should be written as (minimum value, maximum value). If the minimum and maximum values are included within the range or domain, then the parentheses should be replaced with brackets. This looks like [included minimum, included maximum]. Since a function cannot actually include infinity, an infinity symbol should never have brackets.
Eventually, this linear function will reach every single x and y-value in existence. So, both axes have a minimum of -∞ and a maximum of ∞. Thus, both the domain and range are (-∞, ∞).
Hint for future problems: all linear functions will have a domain and range of (-∞, ∞).
2x+14= use distributive property of addition to complete the statement
Answers
Answer:
I think it's 2(x+7).
Step-by-step explanation:
This is distributive function where a number is multiplied from outer value to inner parenthesis values.
I hope this is the right answer.