Answers
Domain = [tex]-\infty < x < +\infty[/tex]
Range = [tex]y \le -4[/tex]
======================================
Explanation:
The arrows on the graph indicate it goes on forever in both left and right directions. So the domain is the set of all real numbers and as an inequality, we write [tex]-\infty < x < +\infty[/tex] which is the same as saying [tex]-\infty < x < \infty[/tex]
This says x is between negative infinity and positive infinity.
In set builder notation, we would say [tex]\{x | x \in \mathbb{R}\}[/tex] and in interval notation, we would write [tex](-\infty, \infty)[/tex]
As you can probably see, the domain is the set of all possible x inputs of a function.
--------------------------
The range is the set of all possible y outputs of a function.
The largest output is y = -4 which is where the vertex is located.
There is no smallest y value as the arrows point down, and the graph goes forever in that direction.
So we say the range is [tex]-\infty < y \le -4[/tex] which shortens to [tex]y \le -4[/tex]
The range in set builder notation is [tex]\{y | y \in \mathbb{R}, \ y \le -4\}[/tex]
The range in interval notation is [tex](-\infty, -4][/tex] The square bracket says to include the endpoint, while the parenthesis excludes the endpoint.
Related Questions
convert 8/3 to a mixed number
Answers
============================================
Work Shown:
8/3 = (6+2)/3
8/3 = 6/3 + 2/3
8/3 = 2 + 2/3
8/3 = 2 & 2/3
The whole part is 2. The fractional part is 2/3.
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Another way you could do the problem is to use long division as shown in the diagram below.
The result of the long division is
8/3 = 2 remainder 2
The quotient 2 forms the whole part and the remainder is the numerator of the fractional part 2/3.
So that's another way to get 2 & 2/3
1) Gracie has a piece of wood that is 5 feet long to use for two projects. She uses 2 feet of the wood on her first project. Which statement describes how a number line can be used to find the length of wood Gracie has remaining for her second project? * Start at 5 and then move left 2 Start at 5 and then move right 2 Start at 2 and then move left 5 Start at 2 and then move right 5
Answers
Answer:
Start at 5 and then move left 2
Step-by-step explanation:
Given:
Length of a piece of wood with Gracie = 5 feets
Length of a piece of wood used on the first project = 2 feets
To find: statement that describes how a number line can be used to find the length of wood Gracie has remaining for her second project
Solution:
The statement that describes how a number line can be used to find the length of wood Gracie has remaining for her second project is
Start at 5 and then move left 2
In this way [tex]5-2=3[/tex]
That is Gracie has now 3 feets of wood available that can be used for her second project.
Using the concept of a number line, the number of wood grace has left would be Start at 5 and then move left 2
Using the concept of a number line :
Positive values are to the right of 0 ; hence, the initial amount of wood grace has is +5 Using two feets from the initial length, then we would Subtract 2 from the the initial value ;To perform subtraction on a number line, we count to the left ;Therefore, the correct statement is Start at 5 and then move left 2
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How do you make comparisons between an equation and a graph?
Answers
Answer:
here is a hint
Step-by-step explanation:
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
Compare slope of an equation and slope of a line on graph and compare y-intercepts.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
For linear equation,
Compare slope of an equation and slope of a line on graph and compare y-intercepts.
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
Therefore, compare slope of an equation and slope of a line on graph and compare y-intercepts.
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If Fernando paid 450 for a notebook that was 75percent of the original price, what was the original price?
Answers
Answer:
$600
Step-by-step explanation:
450➗75✖100= 600. The original price was $600.
Answer:
600
Step-by-step explanation:
450/.75=600 dollars
How does the speed (miles per hour) represented by this relationship compare to that of the Peregrine Falcon?
Answers
and Slope
Which point-slope equation represents a line that passes through (3,-2) with a slope of - 4?
5
Oy-3=-=(x + 2)
Oy-2 = (x-3)
Oy+2=-(-3)
Oy+3 = (x + 2)
Answers
Answer: y+2=-4/5(x-3)
Step-by-step explanation:
The equation of the line passing through the point (3, -2) with a slope of - 4 is y = -4x+10
What is an equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given is a slope of a line and a point passing by it, we need to find the equation of the line,
So, the general equation of the line is :-
y = mx + c
where, m is the slope, and the c is the y-intercept.
Put the value of the slope given, in the equation,
y = -4x+c
Now, for find the value of c, just put the values of the x and y from the point in the equation,
-2 = -4(3) + c
c = -2+12
c = 10
Now, we get the value of the c,
So, the equation is y = -4x+10
Hence, the equation of the line passing through the point (3, -2) with a slope of - 4 is y = -4x+10
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Find 1/20 of 180 dollars
Answers
Hope it helps!
Answer:
9
Step-by-step explanation:
180÷20=9.
Could I please have BRAINLIEST?
Determine the height of the triangle if the area is 24 square inches and the base is 12 inches.
Answers
Answer:
4
Step-by-step explanation:
We use 1/2base times height to find the area and since we already have an area we just do 24= 6h then we divide 6 on both sides and height equals 4
Answer: 6 inches
Step 1: Subtract 12 because 12 iches is the base.
24 - 12 = 2
Step 2: Divide 12 by 2 because triangles have two equal sides.
12 ÷ 2 = 6
Answer = 6
In 1999, Marks & Spencer, a British department store, created the biggest sandwich ever made. The tuna and cucumber sandwich was in the form of a triangular prism. Suppose each slice of bread was 8 inches thick. Find each measure to the nearest tenth. a. The surface area in square feet of the sandwich when filled b. The volume of filling in cubic feet to the nearest tenth
Answers
Answer:
A) 19.2 ft^2
B) 28.9 ft^3
Step-by-step explanation:
Thickness = 8 inches
Assuming the triangular prism is made up of an equilateral triangle hence all sides are equal
lets assume the side = 10 inches
lets assume the thickness as the height of the prism = 8 inches
Assume length of the rectangle(l) = 5 feet
A) The surface area of the sandwich triangular prism
total surface area = bh + 2ls + lb
= 10*8 + 2(5*10) + ( 5 * 10 )
= 80 + 100 + 50 = 230 inches = 19.2 ft^2
B ) The volume of filing in cubic feet to the nearest tenth
V = [tex]\frac{1}{4} h \sqrt{-a^4 +2(ab)^2+2(ac)^2-b^4+2(bc)^2-c^4}[/tex] ------- 1
where : a = b = c = 10 inches
h = 8 inches
input the given values into the equation 1 above
V= 346.41 inches ^3 = 28.9 ft^3
Susan rides her bicycle 5 miles in 1/4 of an hour. At this rate, how many miles could she ride in 2 hours?
Answers
Answer:40 miles
Step-by-step explanation:
5*4=20
20*2=40
Answer:
40 miles
Step by Step Explanation:
Each 1/4 of an hour is 15 minutes. 2 hours is 120 minutes, so you divide 120 by 15, which gives you 8. You multiply 8 times the 5 miles , and you get 40 miles. :)
The volume of a gas V held at a constant temperature in a closed container varies inversely with its pressure P. If the volume of a gas is 600 cubic centimeters (cc) when the pressure is 300 millimeters of mercury (mm hg) , find the volume when the pressure is 400 mm hg
Answers
Answer:
V₂ = 450 cm³
Step-by-step explanation:
The volume of a gas V held at a constant temperature in a closed container varies inversely with its pressure P.
[tex]V\propto \dfrac{1}{P}[/tex]
If V₁ = 600 cm³, P₁ = 300 mm hg, P₂ = 400 mm hg
We need to find a new volume. Using the above concept,
[tex]V_1P_1=V_2P_2\\\\V_2=\dfrac{V_1P_1}{P_2}\\\\V_2=\dfrac{600\times 300}{400}\\\\V_2=450\ cm^3[/tex]
So, when the pressure is 400 mm hg, its volume is 450 cubic centimeters
change 84cm into mm
Answers
Answer:
840mm
Step-by-step explanation:
There are 10mm in 1cm, so all you have to do is multiply 84 by 10, which is 840. 84cm=840mm
Have a great day...I hope this helped you :3
Tanner is cutting a 23-inch board into 2.25-inch sections. How many whole sections will he end up with?
11
12
10
13
Answers
23/2.25 = 10.22 (10 whole sections)
hope this helps :)
A carpenter cuts a circle out of a piece of wood. The radius of the circle is
about 23 inches. The carpenter cuts the circle into two semicircles. What is
the area of one semicircle to the nearest hundredth? Use 3.14 for
Answers
Answer:
830.53 in²
Step-by-step explanation:
To find the area of one semicircle, find the area of the full circle and divide it by 2:
Use the circle area formula, A = [tex]\pi[/tex]r²
Plug in 3.14 as pi, and plug in the radius:
A = [tex]\pi[/tex]r²
A = 3.14(23²)
A = 1661.06
Divide this by 2:
1661.06 / 2
= 830.53
So, the area of one semicircle is 830.53 in²
Answer:
850.53 in² is the answer
1/3 minus 1/6 equals to???
Answers
Answer:
1/6
Step-by-step explanation:
In order to add or subtract fractions you have to have the same denominator for both factions. you do this through finding the Lowest Common Denominator (LCD) In this case it's six because both 3 and 6 (the denominators) can go into 6. So turn 1/3 into a fraction with 6 as the denominator through multiplying both the top and bottom of the fraction by 2
1/3 * 2/2 = 1*2/3*2 = 2/6
Then you can straightforwardly subtract
2/6 - 1/6 = 1/6
Solve.
3(x-4) = -3
How do i slove this
Answers
Answer:
[tex]3(x - 4) = - 3 \\ 3x + 12 = - 3 \\ 3x = - 15 \\ x = - 5[/tex]
Firstly, multiply the number and variable in the perenthesis. Then move the variable on it's own side of the equation. The simplify.
Answer:
You need to do the Distributive Property. This means multiplying the number outside the parenthesis to each number inside.
Step-by-step explanation:
3(x)=3x
3(-4)=-12
3x+-12=-3
then evaluate using inverse operations to get x=3
Seth is trying to pay off his credit card. He plans to pay it off in 24 months. Interest on the card is compounded monthly at a fixed annual rate of 11.6%. Seth currently has a balance of $18,875 on his credit card. Use the formula for the sum of a finite geometric series to determine Seth’s approximate monthly payment.
A.
Seth’s approximate monthly payment will be $753.97.
B.
Seth’s approximate monthly payment will be $834.75.
C.
Seth’s approximate monthly payment will be $884.99.
D.
Seth’s approximate monthly payment will be $868.35.
Answers
Answer:
$884.99
Step-by-step explanation:
Just took the quiz and this was the right answer. :)
Answer:
884.99
Step-by-step explanation:
Pls help question is in the pic. Please give a right answer thx :D
Answers
Answer:
61.2
Step-by-step explanation:
You borrow $2000 for three years at an annual interest rate of 12% what is the total cost of the loan at the end of the three years
Answers
Answer:
2,391 paid altogether. The interest Rate was another 391 dollars.
Step-by-step explanation:
HELP PLEASE!!! Show how you got the answer as well!
Answers
Answer:
2 ans is 7 2x_4+2x_7=17
Please help a girl out!! :(( im really confused and it would mean a lot if someone helped!
Answers
Answer:
$7.69
Step-by-step explanation:
2.48+2.48+2.48= $7.44
then add 0.25 which is
$7.69
Which of the following forms a proportion?
5/9 = 14/18 3/5 = 21/35 6/12 = 18/34 1/8 = 2/24
Answers
Answer:
3/5 = 21/35
Step-by-step explanation:
if you reduce 21/35 it is 3/5 so it is the same thing
Solve for x. 0 = 2x² + 3x + 5
Answers
Answer: No real solutions.
Step-by-step explanation:
In rhombus JKLM, if m
Answers
Write the equation of the line in point-slope form that passes through the
given point with the given slope.
(-4, 3); m = 2
Answers
Answer:
y = 2x + 11
plug the values into y = mx+b:
3 = 2(-4) + b
solve, and you get
3 = -8 + b
b= 3+8 = 11
so, the equation is y = 2x+11
Jayden is driving on a long road trip. He currently has 11 gallons of gas in his car. Each hour that he drives, his car uses up 0.75 gallons of gas. How much gas would be in the tank after driving for 4 hours? How much gas would be left after tt hours?
Answers
Answer:
8 gallons left
Step-by-step explanation:
0.75 times 4=3
11-3=8
hope this helps :)
how to do this question plz
Answers
9) Draw a graph of the linear equation y= -2/-5x +3
Answers
Find the product
(-4)(-9)(-2)
Answers
Answer:
-72
Step-by-step explanation:
(-4)(-9)(-2)=
36(-2)=
-72
You should not schedule _____ tasks for the same day.
yearly
daily
weekly
monthly
Answers
Answer:
B. Daily
Step-by-step explanation:
It makes more sense to put "daily" because of "the same day."
Daily means doing something everyday.
You should not schedule daily tasks for the same day.
Answer:
I just took the test.
It is weekly.