What is the domain and range of the graph below? You must use either interval notation or set notation
Answers
Answer:
See below.
Step-by-step explanation:
The domain of a function is simply the span of x-values the graph will encompass.
And the range of a function is simply the span of y-values the graph will encompass.
Since the function is a quadratic, the domain is all real numbers. From the graph, the graph will continue to expand left and right. Therefore, the domain is all real numbers.
In interval notation, this is:
[tex](-\infty,\infty)[/tex]
And in set notation, this is:
[tex]\{x|x\in\mathbb{R}\}[/tex]
For the range, notice that the graph is going downwards. In other words, the graph has a maximum value. From the graph, we can see that this maximum value is at y=-4. The graph never reaches any value above -4. Therefore, our range is all numbers equal to or less than -4.
In interval notation, this is:
[tex](-\infty,-4][/tex]
We use brackets because we include the -4 in the solution set.
Also, note that we write the infinity first because the smallest number should be on the left. [-4, -∞) would not be correct.
And in set notation, this is:
[tex]\{y|y\in\mathbb{R},y\leq 4}\}[/tex]
Related Questions
-6/11 + (-5/11) =? HELP ASAP ps the dash means that there a fraction
Answers
Answer:
-1
Step-by-step explanation:
Since the denominators are the same, then we add the numerators
-6+-5/11
-11/11
-1
Step-by-step explanation:
-6/11 - 5/11 = -11/11
1. The fraction of -5/11 stays negative because -*+ = -. So the fraction stays negative.
2. Then, you can add the two fractions because they are both the same sign and also have the same denomination.
The answer is -1 or -11/11.
Hope this helped,
Kavitha
Without simplifying Select all the expressions that represent a rational number( someone helppppppp)
Answers
Answer:
The correct options are;
[tex]4\dfrac{2}{3} - \dfrac{\sqrt{4} }{8}[/tex]
[tex]4\dfrac{2}{3} \div \dfrac{\sqrt{4} }{8}[/tex]
Step-by-step explanation:
We note that a rational number is one that can be expressed as a ratio of two integers a and b
An irrational number is one that cannot be expressed as a ratio of two integers. Example of an irrational number is √3
Also an irrational number divided by a rational number is an irrational number, therefore, we have, the expressions without irrational numbers, which are;
[tex]4\dfrac{2}{3} - \dfrac{\sqrt{4} }{8}[/tex] = [tex]\dfrac{53}{12}[/tex]
and
[tex]4\dfrac{2}{3} \div \dfrac{\sqrt{4} }{8}[/tex]
Evaluate the following expressions if a = 2, b = -3, c = -1, and d = 4. then solve for
2a + C
Answers
Answer:
3
Step-by-step explanation:
2a + C
Let a = 2 and c = -1
2* 2 + -1
4 -1
3
Answer:
3Step-by-step explanation:
[tex]a = 2\\ b = -3\\c = -1\\ d = 4\\\\2a+c =?\\2(2) +(-1)\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:2\left(2\right)\::\quad 4\\=4+\left(-1\right)\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:4+\left(-1\right)\:\\:\quad 3[/tex]
find the value of f(12) if f(x)=-2x+4
Answers
Answer:
f(12) = - 20
Step-by-step explanation:
To evaluate f(12), substitute x = 12 into f(x), that is
f(12) = - 2(12) + 4 = - 24 + 4 = - 20
The required value of function at x = 12 is f(12) = -20.
Given that,
A function is given,
f(x) = -2x + 4
The solution of the function at x = 12 is to be determined.
Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is the independent variable while Y is the dependent variable.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
the given function is,
f(x) = -2x + 4
At x = 12
put x = 12 in the function
f(12) = -2 * 12 + 4
f(12) = -24 + 4
f(12) = -20
Thus, the required solution of the function at x = 12 is -20.
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How can you tell from the graph of Molly’s garden on the previous slide that it represents a proportional relationship?
Answers
Answer:
The graph of a proportional relationship has the same unit rate, is a straight line, and starts at the origin.
Step-by-step explanation:
this the answer
The graph of a proportional relationship is a straight line.
What is the equation of a straight line? What do you mean by domain and range of a linear function?The general equation of a straight line is -
y = mx + c
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
Other possible equations of lines are -
(y - y₁) = m(x - x₁) {Point - slope form}(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁) {Two point - slope form}x/a + y/b = 1 {intercept form}x cos(β) + y sin(β) = L {Normal form}For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.
We have a graph of Molly’s garden.
Since, the graph is not given, i will write the condition for proportional relationship. The graph of a proportional relationship is a straight line whose equation is given by -
y = mx + c
Therefore, the graph of a proportional relationship is a straight line.
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What is the slope of the line that passes through the points (10, 3)(10,3) and (2, 3) ?(2,3)? Write your answer in simplest form.
Answers
Answer:
0
Step-by-step explanation:
The y's are the same so they do not go up or down so the slope is 0.
The slope of the line passes through points (10, 3) and (2, 3) is 0.
Given that,
The slope of the line that passes through points (10, 3) and (2,3) is to be determined.
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
here,
The slope of the line passes through the point (10, 3) and (2, 3).
Now, put the point in the equation of the slope,
m =(y₂ - y₁) / (x₂ - x₁)
m = 3 - 3 / (2 - 10)
m = 0 / -8
m = 0
Thus, the slope of the line passes through the points (10, 3) and (2, 3) is 0.
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Your sock drawer has two white socks, four brown socks, and two black socks. You randomly pick a sock and put it on your left foot and then pick another sock and put it on your right foot. You leave the house with a white sock on your left foot and a brown sock on your right foot. Find the probability of this occuring.
Answers
Answer:
1/7
Step-by-step explanation:
From the above question, we have the following values:
White socks = 2
Brown socks = 4
Black socks = 2
Total number of socks = 8
We are told in the question that:
You randomly pick a sock and put it on your left foot and then pick another sock and put it on your right foot. You leave the house with a white sock on your left foot and a brown sock on your right foot.
From above question, we can see that this is a probability with dependent events. This means have a white sock on your left foot and brown sock on your right are events that depend on each other, hence, the probability will occur with replacement.
The probability ( having a white sock on your left foot and brown sock on right) =
2/8 × 4/7
= 8/56
= 1/7
Therefore, the probability of this occuring is 1/7
After a baby was born, he began to gain weight at a rate of 2 pounds per month. The weight of the baby at birth was 10 pounds. write an equation for W, in terms of t, representing weight, in pounds, of the newborn baby tt months after birth.
Answers
Answer:
[tex]W(t) = 2t[/tex]
Step-by-step explanation:
Given
Weight = 2 pounds
Rate = monthly
Required
Determine the weight of the baby in t months
When the baby is 1 month old, t = 1;
[tex]Weight = 2\ pounds * 1[/tex]
[tex]Weight = 2\ pounds[/tex]
When the baby is 2 months old, t = 2;
[tex]Weight = 2\ pounds * 2[/tex]
[tex]Weight = 4\ pounds[/tex]
When the baby is t months old;
[tex]Weight = 2\ pounds * t[/tex]
[tex]Weight = 2t\ pounds[/tex]
Represent Weight as a function of t
[tex]W(t) = 2t[/tex]
Hence, the formula is [tex]W(t) = 2t[/tex]
Please hurry simplify the problem a i b 5i c -i
Answers
Answer:
[tex]\frac{90}{5} i[/tex]
Step-by-step explanation:
10 * sqrt(81/25 * -1) = 10 sqrt(81/25) * sqrt(-1) = 10 *9/5 * i
Calculate the perimeter of the trapezium
Answers
Answer:
P = 26
Step-by-step explanation:
see attached
to get the side 5,
sqrt((10-7)² + 4²)
side = 5
P = 4 + 7 + 5 + 10
P = 26
Find the value of x. A. 51 B. 76.25 C. 129 D. 25.25
Answers
Answer:
[tex]\Huge \boxed{\mathrm{C. \ 129 }}[/tex]
Step-by-step explanation:
Apply : Angles of Intersecting Chords Theorem
m∠x is half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
m∠x = 1/2(54+204)
Add numbers in brackets.
m∠x = 1/2(258)
Expand brackets.
m∠x = 129
solve 5u– 5(1–u)=u+8
Answers
Answer:
u= -3
Step-by-step explanation:Solve for
u by simplifying both sides of the equation, then isolating the variable.
Answer : 5u– 5(1–u)=u+8
5u - 5+ 5u = u+ 8
10u -5 = u+ 8
9u = 13
u = 1.44
A restaurant adds a 20% tip to the bills of parties of 6 or more people. Suppose a server waits on five such tables. The bill
without the tip for each party is listed in the table. How much did the server make in tips during this shift?
Distributive Property: a(b + c) = ab + ac and (b + c)a = ba = ca
Party 1
Party 2
Party 3
Party 4
Party 5
$185.45 $205.20 $195.05 $245.80 $262.00
Answers
Answer:
$218.70
Step-by-step explanation:
You need to first convert the percentage to the decimal.
20% = 0.2
Now, you need to find 20% of each bill by multiplying each bill by 0.2.
0.2(185.45) + 0.2(205.20) + 0.2(195.05) + 0.2(245.80) + 0.2(262.00)
Because of the distributive property, you can add up the bills and multiply the sum by 0.2.
0.2(185.45 + 205.20 + 195.05 + 245.80 + 262.00)
0.2(1093.50)
218.7
The waiter made $218.70 in tips.
Your annual salary is $61,061.83 what is your semimonthly salary
Answers
(x²+10x+7)(2x-1) = 2x³+19x²+4x-7 show the steps
Answers
Explanation:
(x^2+10x+7)(2x-1) = 2x^3+19x^2+4x-7
2x^3-x^2+20x^2-10x+14x-7 = 2x^3+19x^2+4x-7
2x^3+19x^2+4x-7 = 2x^3+19x^2+4x-7
What is the product of complex conjugates? The product of complex conjugates is a difference of two squares and is always a real number. The product of complex conjugates is the same as the product of opposites. The product of complex conjugates may be written in standard form as a+bi where neither a nor b is zero. The product of complex conjugates is a sum of two squares and is always a real number.
Answers
Answer:
Last given option is the correct answer:
"The product of complex conjugates is a sum of two squares and is always a real number."
Step-by-step explanation:
The product of two conjugates can be described and solved like this:
[tex](a + b\,i) \,(a - b\,i)= a^2-a\,b\.i+a\,b\,i-b^2\,i^2=a^2+0-b^2\,(-1)= a^2+b^2[/tex]
so, no matter what the values for the real values a and b are, the product is always a real number and the sum of two squares.
Answer:
(a + bi)(a – bi) = a2 – (bi)2 = a2 + b2
The product of a complex number and its complex conjugate is
✔ always
a real number.
Anna is saving to buy some souvenirs on a family vacation. She has already saved $125, and she saves another $2 from her allowance every day. Formulate and then graph the equation that models the total amount Anna saves, y, in terms of the number of days she adds to her savings, X.
Answers
Answer:
125+2x=y (take 125 add 2x for $2 a day and then = y for amount saved)
Points on Graph:
(125,0)
(135,5)
(145,10)
(155,15)
(165,20)
(175,25)
(185,30)
(195,35)
(205,40)
(215,45)
(225,50)
Answer:
Step-by-step explanation:
Dwayne had 136 songs on his phone. He deleted 56 songs. What is the
ratio of songs he kept to songs he deleted (in its simplest form)?
Answers
136 - 56 = 80 songs kept
Ratio of songs kept to songs deleted is:
80:56
Simplify by dividing each number by 8:
The simplest form is: 10/7
Alicia had $-11 in her checking account. She did a few chores and made $44.50. She
decided to pay for her and a friend to go to the movies, and each ticket cost $6.25. How
much money does she have left in her checking account?
Answers
Answer:
she would have 21 dollars left
Step-by-step explanation:
44.50-11
33.50-12.50
Answer:
[tex]\Huge \boxed{\$ \ 21}[/tex]
Step-by-step explanation:
She had $-11 initially and gained $44.50.
-11 + 44.5 = 33.5
She has $33.5 in her account.
She buys two tickets for $6.25 each.
33.5 - (2)6.25 = 21
She has $21 left in her account.
A coordinate axis is drawn with a parabola pointing up that has vertex of 0,3. Determine the intervals on which the function is increasing, decreasing, and constant. Increasing x < 0; Decreasing x > 0 Increasing x > 0; Decreasing x < 0 Increasing x < 3; Decreasing x > 3 Increasing x > 3; Decreasing x < 3
Answers
Answer:
Option (2). Increasing x > 0; decreasing x < 0
Step-by-step explanation:
Equation of the parabola having vertex (0, 3) will be,
y = (x - 0)² + 3
y = x² + 3
To check the function is increasing or decreasing in the given intervals we will find the derivative of the function,
[tex]\frac{dy}{dx}=\frac{d}{dx}(x^{2}+3)[/tex]
y' = 2x
For x < 0 Or x = -1
y' = 2(-1)
= -2 < 0
Therefore, function is decreasing in x < 0
For x > 0 Or x = 1
y' = 2(1) + 3
= 5 > 0
Therefore, function is increasing in x > 0
Option (2) is the answer.
Mr Gupta has some rice of worth RS 3000. He sold 1/3 of it with 10% loss .By how many percent must the selling price be increased for making 10% profit on the outlay?
Answers
Answer:
20% more of cost price, or 30% more of initial selling price
Step-by-step explanation:
Given:
Product CP = Rs. 3000Sold 1/3 at a loss of 10%Target profit = 10%SP for the rest = ?SolutionTotal money to be obtained:
3000 + 10% = 3000*1.1 = Rs. 3300Money already got:
1/3*3000 - 10% = 1000 - 10% = Rs. 900Money left to obtain:
3300 - 900 = Rs. 2400Product left to sell, worth of:
3000*2/3 = Rs. 2000The difference:
2400 -2000 = Rs. 400Required selling price increase:
400/2000* 100% = 20% of CPOr compared to initial price, new SP to be increased by 30%
which is a function? {(8,9),(−2,9),(7,5),(−4,−7)} {(−5,−7),(−5,4),(−2,−8),(3,5)} {(8,0),(−4,−2),(7,1),(0,0)} {(−8,3),(−5,−7),(−4,5),(9,3)}
Answers
Answer:
All but the second {(8,9),(−2,9),(7,5),(−4,−7)} {(8,0),(−4,−2),(7,1),(0,0)} {(−8,3),(−5,−7),(−4,5),(9,3)}Step-by-step explanation:
Function means that for each x we get y, and no no x gives two different y-es
{(−5,−7),(−5,4),(−2,−8),(3,5)} for x = -5 we have two different y-es therefore its not function
If you were in charge of the money, how would you recommend your friends spend it? Explain why you choose the solution you did. Why do you think it's the most fair? (3 points:1 point for stating your recommendation and 2 points for explaining your reasoning)
Answers
Answer:
I would recommend them to go out with their family and spend it because i feel that people always dream about ways to bring their family close again so that can be a good way to bond and do things that often cost a lot of money.
Step-by-step explanation:
Preview: 5 People fit comfortably in a 2 foot by 2 foot area. Use this value to estimate the size of a
crowd that is 4 feet deep on both sides of the street along a 1-mile section of a parade route.
Answers
Answer:
The estimate size of the crowd is 52800 people
Step-by-step explanation:
The given information are;
The number of people that fit comfortably in a 2 by 2 foot area = 5
Therefore, we have;
The area occupied by the 5 people = 2 × 2
The crowd ratio = 5/(2 × 2) = 5/4
The area occupied by the crowd = 4 feet deep, and 1 mile long on both sides of the street
By conversion factors, 1 mile = 5,280 feet
Therefore, the area occupied by the crowd = 4 × 5280 × 2 = 42240 ft²
The number of people in the crowd = Crowd ratio × The area occupied by the crowd
The number of people in the crowd = 5/4 × 42240 = 52800 people
Therefore, The estimated size of the crowd = 52800 people.
Solve F(x) for the given domain. Include all of your work in your final answer. Submit your solution. F(x) = x2 + 2 F(x + h) =
Answers
Answer:
F(x-h) = x² + 2xh +h² +2
Step-by-step explanation:
F(x) = x² + 2, x∈R
F(x + h) = (x + h )² + 2 = x² + 2xh + h² + 2
Answer:
F ( x ) = x^2 + 2
Domain = R
F ( x - h ) = ( x - h )^2 + 2xh + h^2 + 2
How to get the answer
Answers
Answer:
2*x^4*z^3
Step-by-step explanation:
To answer this kind of question, you first start rearranging the terms in the numerator and denominator, so you don't get confused.
3x^3 * 4x^3 * z^4 / 2x * x * 3z
Now you multiply like parts in the numerator and denominator to keep it simple.
(3x^3 * 4x^3) * z^4 / (2x * x) * 3z
3x^3 * 4x^3 = 12x^6
2x * x = 2x^2
12x^6 * z^4 / 2x^2 * 3z
Now divide like terms that are in the numerator and denominator so multiplying later will be easier.
12x^6 / 2x ^ 2 * z^4 / 3z
12x^6 / 2x^2 = 6x^4
z^4/3z = z^3 / 3
Now you multiply both terms,
6x^4 * z^3/3
2*x^4*z^3
On three science tests, Olivia has received scores of 89%, 98%, and 96%. What is the lowest score Olivia can get on her fourth and final science test to
achieve an average score of 95%?
Answers
Answer:
97%
Step-by-step explanation:
89%+98%+96%+?=95×4
283+?=380
?=380-283
?=97%
The lowest score Olivia can get on her fourth test is 97%.
The average score can be determined by dividing the sum of the four scores by the total number of tests taken.
The first step is to determine the sum of the three scores Olivia already has.
Sum of scores = 89 + 98 + 96 = 283%
The second step is to multiply 95 x 4. 95% x 4 = 380%
The third step is to subtract 283% by 380%. 380% - 283% = 97%
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Board 1
C
(3x + 16)°
7
(5x - 54)
Board 2
Enter the measure of ZC.
Answers
Answer:
59°
Step-by-step explanation:
From the question given, we obtained the following:
C + (3x + 16) = 180 (sum of angle on a straight line)
5x – 54 = 3x + 16 (Altanate angles are equal)
Next, we shall determine the value of x.
This can be obtained as follow:
5x – 54 = 3x + 16
Collect like terms
5x – 3x = 16 + 54
2x = 70
Divide both side by the coefficient of x i.e 2
x = 70/2
x = 35
Finally, we shall determine the value of C as shown below:
C + 3x + 16 = 180
But, x = 35
C + 3(35) + 16 = 180
C + 105 + 16 = 180
C + 121 = 180
Collect like terms
C = 180 – 121
C = 59°
Therefore, the value of C is 59°
Problem: What values of a and b make this statement false? |a-b|=|a|-|b|
Answers
Answer:
All (a,b) that satisfy a.b < 0 will make that statement false
Step-by-step explanation:
It is only right when:
|a-b| = |a| - |b|
<=> ( |a-b| ) ^ 2 = ( |a| - |b| ) ^ 2
<=> a^2 - 2ab + b^2 = a^2 - 2.|ab| + b^2
<=> ab = |ab|
<=> ab ≥ 0
So, when ab < 0, it's wrong
1.find the sum. (3^3+5x^2+3x-7)+(8x-6x^2+6)
2. Find the Difference: (8x-4x^2+3\)-(x^3+7x^2+3x-8)
Answers
1.
[tex](3^3+5x^2+3x-7)+(8x-6x^2+6)=\\\\=27\ \underline{+\,5x^2}\ \underline{ \underline{+\,3x}}-7\ \underline{\underline{\,+8x}}\ \underline{-\,6x^2}+6=\\\\=-x^2+11x+26[/tex]
or if you mean (3x^3+5x^2+3x-7)+(8x-6x^2+6):
[tex](3x^3+5x^2+3x-7)+(8x-6x^2+6)=\\\\=3x^3\ \underline{+\,5x^2}\ \underline{ \underline{+\,3x}}-7\ \underline{\underline{\,+8x}}\ \underline{-\,6x^2}+6=\\\\=3x^3-x^2+11x-1[/tex]
2.
[tex](8x-4x^2+3)-(x^3+7x^2+3x-8)=\\\\=\underline{8x}\ \underline{\underline{-\ 4x^2}}+3-x^3\ \underline{\underline{-\,7x^2}}\ \underline{-\,3x}+8=\\\\=-x^3-11x^2+5x+10[/tex]