The graph of a quadratic function with vertex (0, -1) is shown in the figure below.Find the range and the domain in interval notation please include paranthese or brackets within your answer.
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The domain is all the values that the function can take on the x axis, in this case it would be all the real numbers:
[tex]domain\to(-\infty,\infty)[/tex]The range is all the values that the function can take on the y-axis. For this function it will grow from vertex to infinity:
[tex]range\to\lbrack-1,\infty)[/tex]Remember that when intervals are written, parentheses are used for open values and square brackets for exact values.
Related Questions
what do you do after you multiply an equation in the elimination method?2x -3y=-11x+3y = 8
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1) Let's multiply the second equation by -2, to eliminate x
2x -3y=-11
x+3y = 8
2) Now let's add both equations
2x -3y=-11
-2x-6y = -16
--------------------
-9y = -27
3) Divide both by -9
y=3
4) Plug y=3 into the simpler original equation, to make calculations easier:
x +3y=8
x+3(3) =8
x +9 =8 Subtract 9 from both sides
x = 8-9
x=-1
So, after multiplying it we add both equations to eliminate one variable either x or y.
What is the quotient? 7-^1/7^2
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Hello there. To solve this question, we'll have to remember some properties about powers.
We have to determine the following quotient:
[tex]undefined[/tex]Can you please help me out with a question
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Step 1 :
We use the Intersecting Chord Theorem which states that :
When two chords intersect each other inside a circle, the products of their segments are equal.
This theorem states that A×B is always equal to C×D
(no matter where the chords are).
From the question, A = 15, B = 12, C = ? , D = 18
Step 2 :
Using the equation, where AB = CD
[tex]\begin{gathered} 15\text{ x 12 = C x 18} \\ 180\text{ = 18 C} \\ \text{Divide both sides by 18, we have that:} \\ C\text{ = 10 units.} \end{gathered}[/tex]CONCLUSION :
The value of C = 10 units
Rewrite the expression 8m^6/4m^9 using the rules of exponents
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Answer:
Rewrite the expression 8m^6/4m^9 using the rules of exponents
Step-by-step explanation:
8 ÷ 4 = 2
m^6 ÷ m^9
exponent rule in a division problem is you subtract them so...
6 - 9 = -3
you can't have a negative exponent so it would be 2 over m^3
If you have a negative exponent the rule is "flip it" meaning you flip the sign but when you do that it becomes a fraction. so... 2/m^3
The graph of a quadratic function with the vertex 2,3 is shown in the figure below.Find the domain in the range. Write your answers as inequalities, using X or Y as appropriate. Or, you may instead write “empty set” or “all reals” as the answer.domain=range=
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From the graph, we are asked to find the domain and randge./.
First lets know what domain and range.
Domain of a function is the set of values that are allowed is the plug into our function.
The domain and rang of the function written in an inequality form are:
Domain:
-1 < x < 4
Range:
-10 < y < 3
Dylan looked at the function .and said, "This function is always greater than 0, so 0 is the absolute minimum." Explain why Dylan is incorrect.
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Given data:
The given function is f(x)=4(1/2)^x.
The given function always greater than zero, the given function never become equal to zero, the asymptote at y=0.
Thus, zero can't be consider as the absolute minima of the function.
write a polynomial function in standard form with the given zeros. This is not a test nor homework, I am preparing for the ACT and my teacher said these problems would be on there and therefore I need help1. -1, 3, 42. -3, 0, 0, 53. -2 multiplicity 34. (x+3)^2(x+1)
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For question 1
The zeros of the polynomial are -1, 3 , 4, it means x = -1, x=3 and x=4
therefore,
[tex]\begin{gathered} x\text{ + 1, , x-3, and x-4 are factors of the polynomial} \\ \text{ f(x)= (x+1)(x-3)(x-4) } \\ f(x)=(x^2-3x+x-3)(x-4)^{} \\ =(x^2\text{ -2x -3)(x -4)} \\ =x^3-4x^2-2x^2+8x-3x+12 \\ f(x)=\text{ }x^3-6x^2+5x+12 \end{gathered}[/tex]For question 2
The zeros of the polynomial are -3, 0, 0, 5 it means x = -3, x=0, x=0 and x=5
therefore,
[tex]\begin{gathered} (x+3),\text{ (x-0), (x-0), and (x-5) are factors} \\ f(x)=\text{ (x+3) (x) (x) (x-5)} \\ =x^2(x+3)(x-5)=x^2(x^2-5x+3x-15)=x^2(x^2-2x-15) \\ f(x)=x^4-2x^3-15x^2 \end{gathered}[/tex]For question 3
The zeros of the polynomial are -2, -2, -2 it means x = -2, x=-2, , x=-2
therefore,
[tex]\begin{gathered} (x+2),(x+2),(x+2)\text{ are factors of the polynomial} \\ f(x)\text{ = (x+2)(x+2)(x+2)} \\ =(x^2+2x+2x+4)(x+2)=(x^2+4x+4)(x+2) \\ =x^3+2x^2+4x^2+8x+4x+8 \\ f(x)=x^3+6x^2+12x+8 \end{gathered}[/tex]Can someone help me with this? How do I figure this out?
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We are given the following radical expression:
[tex]\sqrt[]{a+b}[/tex]We are asked to determine the equivalent exponential expression. To do that we will use the following relationship:
[tex]\sqrt[]{x}=x^{\frac{1}{2}}[/tex]Applying the relationship we get:
[tex]\sqrt[]{a+b}=(a+b)^{\frac{1}{2}}[/tex]Therefore, the right answer would be B.
(10,-5)(10-9) what is the linear equation
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
point 1 (10 , - 5) x1 = 10 y1 = -5
point 2 (10, - 9) x2 = 10 y2 = -9
linear equation = ?
Step 02:
Slope formula
[tex]m\text{ = }\frac{y2\text{ -y1}}{x2-x1}[/tex][tex]m\text{ = }\frac{-9-(-5)}{10-10}=\frac{-9+5}{0}=\frac{-4}{0}=\infty[/tex]The answer is:
The equation of the line is a vertical line in x = 10, since the slope is infinite.
Simple random sampling uses a sample of size from a population of size to obtain data that can be used to make inferences about the characteristics of a population. Suppose that, from a population of bank accounts, we want to take a random sample of four accounts in order to learn about the population. How many different random samples of four accounts are possible?
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There will be 1,215,450 different random samples of four accounts are possible.
What is combination and permutation?There are two methods to calculate the number of ways a certain event can happen. Both are used in different circumstances, such as, when the order of arrangement does not matter we use the combination and when the order matters we use permutation.
Given,
Population size, N = 75
Sample size, n = 4
We have selected a random sample of 4 accounts in order to learn about the population because these accounts can not be repeated and can be in any order, so we will use combination without repetition. According to this, the number of ways by which n subjects can be chosen from N subjects are given by,
[tex]\frac{N}{n}[/tex] = [tex]\frac{N!}{n!(N-n)!}[/tex]
Therefore, required number of ways are,
= 75!/4!(75-4)!
= 75!/4!*71!
= 75*74*73*72*/4*3*2
= 1,215,450
Hence, There will be 1,215,450 different random samples of four accounts are possible.
For more references on combination and permutation, click;
https://brainly.com/question/13387529
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Whats the vertex of f(x)= 2x^2-8
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5.65 less than a number equals 49
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Let
x ------> the number
the algebraic expression is equal to
x-65=-49
solve for x
adds 65 both sides -------> by addition equality property
x=-49+65
x=16
the number is 16
If an object is shot upward with an initial velocity, vo, in feet per second (fu/s), the velocity, v, in fus is given by the formula v = vo - 321,where ris time in seconds. Find the initial velocity of an object if the velocity after 2 seconds is 38 ft/s.
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The final velocity function is given to be:
[tex]v=v_0-32t[/tex][tex]\begin{gathered} We\text{ are to find the initial velocity;} \\ v_0,\text{ given final velocity v to be 38ft/s and time t to be 2secs} \end{gathered}[/tex]Thus, we have:
[tex]\begin{gathered} v=v_0-32t \\ 38=v_0-32(2) \\ 38=v_0-64 \\ 38+64=v_0 \\ 102=v_0 \\ v_0=102\text{ft/s} \end{gathered}[/tex]Hence, the initial velocity of the object is 102ft/s
The total area of a polygon is 176 sq.ft. Find the value of x in the drawing
Answers
Answer:
x=6 ft
Explanation:
The given polygon is a trapezium in which:
• The parallel sides are a=16 ft and b=(16+2x) ft
,• The height, h = 8 ft
,• Area = 176 sq.ft.
The area of a trapezium is calculated using the formula:
[tex]\begin{gathered} A=\frac{1}{2}(a+b)h \\ a,b\text{ are the parallel sides} \\ h\text{ is the perpendicular height} \end{gathered}[/tex]Substitute all the known values:
[tex]\begin{gathered} 176=\frac{1}{2}\times8(16+16+2x) \\ 176=4(32+2x) \end{gathered}[/tex]Divide both sides by 4.
[tex]\begin{gathered} \frac{176}{4}=32+2x \\ 44=32+2x \end{gathered}[/tex]Subtract 32 from both sides:
[tex]\begin{gathered} 44-32=32-32+2x \\ 12=2x \end{gathered}[/tex]Divide both sides by 2.
[tex]\begin{gathered} \frac{12}{2}=\frac{2x}{2} \\ x=6\text{ feet} \end{gathered}[/tex]The value of x in the drawing is 6 feet.
Answer:
X=6
Step-by-step explanation:
First multiply 8 by 16 to get 128. Then subtract that from 176 to get 48. Then divide by to because there are two triangles to get 24, so each triangle is 24 square feet. Find a number that multiplied by 8 equals 48 (this will be x). The reason that I did this is because of the formula for area of a triangle (B*H/2=A). After you divide by 48 by 2 you will get 24. The number that was multiplied by 8 is x (x=6).
Angle AED is 146 degrees. Ray EC bisects angle AED. What is the measure of angle AEC?
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STEP 1
We draw a diagram to represent the information.
[tex]\begin{gathered} <\text{AEC}=\frac{In conclusion, the answer is 73 degreesHow would I create a logic proof for this question?
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Let us represent the premises given:
[tex]\begin{gathered} \text{Let } \\ A=\text{John is aardvark} \\ C=\text{Charles has a blue eye} \\ B=\text{Bob counts} \\ E=\text{Edna drives a truck} \\ D=\text{Dan edits} \end{gathered}[/tex]Then
We can subdivide the argument into substatement
Statement 1: If John is an aardvark then either Charlene has blue eyes or Bob counts
[tex]A\Rightarrow(C\lor B)[/tex]Statement 2: If Charlene has a blue eye then Edna drives a truck
[tex]C\Rightarrow E[/tex]Statement 3: Either John is an aadvark or Dan edits
[tex]A\lor D[/tex]Statement 4: Moly claims that either Bob counts or Edna drives a truck, but Moly is wrong
[tex]\begin{gathered} (B\lor E),\text{ But} \\ \sim(B\lor E) \end{gathered}[/tex]Therefor D
[tex]\therefore D[/tex]The above hypothesis and conclusion can be summarized below as;
Using a truth table calculator, the validity of the above arguments is shown below
Hence, we can conclude that the above is a valid argument.
Tell whether the following statement is always, sometimes, or never true for numbers greater than zero. Explain. In equivalent ratios, if the numerator of the first ratio is greater than the denominator of the first ratio, then the numerator of the second ratio is greater than the denominator of the second ratio.
Answers
Answer
The statement is always true.
Explanation
Since equivalent ratios reduce to essentially the same fundamental ratios, if the numerator of one of the ratios is greater than its denominator, then the numerator of each of the equivalent ratios must be greater than each of their corresponding denominators too.
So, this statement is always true!
Hope this Helps!!!
Use the table of values for f and g below to find the indicated compositions. (f \circ g)(8) =Answerg(f(3))=Answerf(f(1))=Answer (g \circ g)(6) =Answer
Answers
In order to find the value of a composition of functions at x = a, (f º g)(a), we first find the value of g(a), then find the value of f(x) at x = g(a).
(f º g)(a) = f(g(a))
In this problem, the values of f(x) and g(x) are shown in the table, for integer values of x from 0 to 9.
So, we have:
1. (f º g)(8) = f(g(8))
From the table, we see that
g(8) = 4 (value of g(x) in the line corresponding to x = 8)
Then:
f(g(8)) = f(4) = 4 (value of f(x) in the line corresponding to x = 4)
Thus:
[tex]\mleft(f\circ g\mright)\mleft(8\mright)=4[/tex]2. g(f(3))
f(3) = 8
g(8) = 4
Thus:
[tex]g(f(3))=4[/tex]3. f(f(1))
f(1) = 6
f(6) = 2
Thus:
[tex]f(f(1))=2[/tex]4. (g º g)(6) = g(g(6))
g(6) = 7
g(7) = 3
Thus:
[tex]\mleft(g\circ g\mright)\mleft(6\mright)=3[/tex]
if eddie buy carrots and her discount is 35% and the original price of the carrots is $7.40 how much did she pay
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First, find what is 35% of $7.40 equal to. To do so, multiply 7.40 times 35/100:
[tex]7.4\times\frac{35}{100}=2.59[/tex]Then, the discount is equal to $2.59. To find the final price, substract the discount (2.59) from the original price (7.4):
[tex]7.4-2.59=4.81[/tex]Therefore, the price that she paid was:
[tex]\text{ \$4.81}[/tex]Use the substitution method to solve the system of equations.3x + 2y = 13y = x - 1O A. (2,1)O B. (2,3)O C. (3,2)O D. (1,2)
Answers
3x + 2y = 13
y = x - 1
We want to substitute the second equation into the first equation.
In the first equation, everytime we see "y" substitute x-1
3x +2y = 13
3x + 2( x-1) = 13
Distribute
3x +2x -2 = 13
Combine like terms
5x -2 = 13
Add 2 to each side
5x-2+2 = 13+2
5x = 15
Divide each side by 5
5x/5 = 15/5
x = 3
Noe we can find the value of y by using the second equation
y = x-1
y = 3-1
y =2
The solution is
( 3,2)
Please solve #24 for me.I’m struggling badly with systems of equations and need some help solving problems with it.Please explain the steps of it as best and basic as possible.
Answers
Data
• Small cones (s): $2
,• Large cones (L): $3.50
,• Total sold (T): $163
,• The number of L sold was 12 more than the number of ,s.
Procedure
We have to build a system of equations based on the information given.
• Equation 1:, she sold $163 of small and large cones
[tex]2s+3.50L=163[/tex]• Equation 2: ,the number of L sold was 12 more than the number of ,s.
[tex]L=s+12[/tex]As we have L isolated in the second equation, it is convenient to use this expression in the first equation to have it in terms of one variable:
[tex]2s+3.50\times\left(s+12\right)=163[/tex]Simplifying the parenthesis we get:
[tex]2s+3.50s+42=163[/tex]As we have two terms with an s we can group in each side of the equation the common terms and simplify them as follows:
[tex]2s+3.50s=163-42[/tex][tex]5.50s=121[/tex][tex]s=\frac{121}{5.50}[/tex][tex]s=22[/tex]Now that we have s, we just have to replace this value in equation 2:
[tex]L=22+12=34[/tex]Answer:
• Small snow cones: 22
,• Large snow cones: 34
Lin ran 234 miles in 2/5 of an hour. Noah ran 823 miles in 4/3 of an hour.Who ran faster, Noah or Lin?How far would Lin run in 1 hour?How far did Noah run in 1 hour?How long would it take Lin to run 1 mile at that rate?How long would it take Noah to run 1 mile at that rate?
Answers
Given:
• For Lin:
Distance = 234 miles
Time = 2/5 of an hour
• For Noah:
Distance = 823 miles
Time = 4/3 of an hour
Let's determine who ran faster.
Let's find the time of each runner by multplying by 60.
Where:
60 minutes = 1 hour
To determine the speed of each of them, apply the formula:
[tex]speed=\frac{dis\tan ce}{time}[/tex]• To find Lin's speed, we have:
[tex]\text{ Lin's sp}eed=\frac{dis\tan ce}{\text{time}}=\frac{234}{\frac{2}{5}\ast60}=\frac{234}{24}=9.75\text{ mph}[/tex]Therefore, Lin's speed is 9.75 miles per hour.
• To find Noah's speed, we have:
[tex]undefined[/tex]how many killer whales are there when there are 5 million beluga whales
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We know that the number of og beluga whales varies directly as the number of killer whales, that means that we can write a relation of the form:
[tex]y=kx[/tex]where y is the number of beluga whales, x is the number of killer whales and k is the constant of proportionality.
To answer the question we first need to find k, to do that we plug the values x=23 and y=14 in the equation above and solve for k:
[tex]\begin{gathered} 14=k23 \\ k=\frac{14}{23} \end{gathered}[/tex]Now that we know k the relation is:
[tex]y=\frac{14}{23}x[/tex]Finally to find the number of killer whales if there are 5 millions of beluga whales we plug y=5 in the equation above and solve for x:
[tex]\begin{gathered} 5=\frac{14}{23}x \\ x=\frac{5\cdot23}{14} \\ x=8.21 \end{gathered}[/tex]Therefore when there are 5 millions beluga whales we have 8.21 millions of killer whales.
What’s your question represents our relationship shown in the graph
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Given the graph of a line
As shown the line passes through the point (0, 0)
So, the relation has the form:
[tex]y=kx[/tex]We will find the value of k using one point lying on the line
As shown the line passes through the point (4, 14)
So, when x = 4, y = 14
Substitute with x and y into the equation: y = k * x
so,
[tex]\begin{gathered} 14=k\cdot4 \\ \\ k=\frac{14}{4}=3.5 \end{gathered}[/tex]so, the answer will be option C) y = 3.5x
Find the conditional relative frequency that a student surveyed prefers cats as pets, given that the student is a girl
Answers
To find the relative frequency asked, you have to divide the number of girls who prefer cats by the number of girls:
[tex]\frac{6}{28}\approx0.2143\Rightarrow21.43\text{percent}[/tex]About 21.43% of the girls prefer cats as pets
In your own words, describe the location of each point on a coordinate plane. Be specific. 1. (0,4)2.(2,5) 3.(-3, 6)
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Locations on the coordinate plane are described as ordered pairs. An ordered pair tells you the location of a point by relating the point's location along the x-axis (the first value of the ordered pair) and along the y-axis (the second value of the ordered pair)
1. Point ( 0, 4)
The coordinate of ( 0, 4) is on the y-axis, because x = 0 and y = 4.
The point ( 0, 4) is on the y-axis at y = 4
2. Point ( 2, 5 )
Starting from the origin, go along the x-axis 2 units in a positive direction (right) and along the y-axis 5 units in a positive direction (up).
3. P( -3 , 4 )
Starting from the origin, go along the x-axis 3 units in a negative direction (left) and along the y-axis 4 units in a positive direction (up).
The slope of this regression line is 0.8 .What does this tell you about the relationship between the amount of fertilizer and the height of the seedlings?
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The slope of a line shows the relation between a unitary increment in the x-variable and the corresponding change in the y-variable.
In this case, the x-variable represents the amount of fertilizer, in grams, and the y-variable represents the height of the seedings, in cm.
Then, the slope of 0.8 means that when the x-variable increases in 1 unit, the y-variable increases 0.8 units. Or more specifically, for each additional gram of fertilizer used, the height of the seedings increases by about 0.8 cm on average.
parallelogram pqrs has diagonals PR and SQ that intersect at T find the value of X and Y
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If a parallelogram PQRS has diagonals PR and SQ that intersects at T, then, T is the midpoint of PR and T is the midpoint of SQ
Given
[tex]\begin{gathered} PT=y \\ TR=3x+1 \end{gathered}[/tex][tex]y=3x+1[/tex]Also
[tex]\begin{gathered} QT=3y \\ TS=4x+13 \end{gathered}[/tex][tex]3y=4x+13[/tex]Now we are going to solve the system of equations with two unknowns
[tex]\begin{gathered} y=3x+1 \\ 3y=4x+13 \end{gathered}[/tex]Substitute equation 1 into 2
[tex]\begin{gathered} 3(3x+1)=4x+13 \\ 9x+3=4x+13 \\ 9x-4x=13-3 \\ 5x=10 \\ x=\frac{10}{5} \\ x=2 \\ \end{gathered}[/tex]x = 2
Substitute x = 2 into equation 1
[tex]\begin{gathered} y=3x+1 \\ y=3(2)+1 \\ y=6+1 \\ y=7 \end{gathered}[/tex]y = 7
The answer would be x = 2, y = 7
what percent of $717 is $239?
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what percent of $717 is $239?
we have that
717 represent the 100%
so
Apply proportion
100/717=x/239
solve for x
x=(100/717)*239
x=
Find the slope of the line passing trough the given points point (3 , 2). Point (1, -1)
Answers
For this question we will use the formula for the slope of a line passing through two points:
[tex]s=\frac{y_2-y_1}{x_2-x_1}\text{.}[/tex]Substituting the given points we get:
[tex]s=\frac{-1-2}{1-3}=\frac{-3}{-2}=\frac{3}{2}\text{.}[/tex]Answer:
[tex]\frac{3}{2}\text{.}[/tex]