Problem 1
Answers:
Domain: [tex]-3 \le x < 5[/tex]
Range: [tex]-4 < y \le 3[/tex]
--------------------
Explanation:
The domain is the set of allowed x inputs of a function. The smallest x value we can use is x = -3 (note the very left-most point of the graph). The right-most point involves x = 5, but we can't actually use this x value due to the open hole. So that's why we don't have "or equal to" attached to the 5.
The range is the set of possible y outputs. The lowest we can go is y = -4, but we don't include this as part of the range. The largest y can get is y = 3. So the range is [tex]-4 < y \le 3[/tex]
===========================================
Problem 2
Answers:
Domain: [tex]-2 < x < 4[/tex]
Range: [tex]-2 < y < 5[/tex]
--------------------
Explanation:
We use the same idea as in problem 1. Both endpoints are open holes, so we don't include them as part of the domain and range. For instance, we can't include x = 4 but we can get closer and closer to it. The same idea applies to the range as well.
===========================================
Problem 3
Answers:
Domain: [tex]1 \le x \le 4[/tex]
Range: [tex]-4 \le y \le -1[/tex]
--------------------
Explanation:
The same idea applies as used earlier. This time we include both endpoints, so we have "or equal to" as part of each inequality sign.
The function m is given in three equivalent forms.
Which form most quickly reveals the vertex?
the answer to your question. is c
Answer:
Here you go
Step-by-step explanation:
5 of the 25 players on the soccer team are 7th graders. Find the Percent of 7th graders
Lin's job pays $8.25 an hour plus $10 of transportation allowance each week. She has to work at least 5 hours a week to keep the job, and can earn up to $175 per week (including the allowance). 1. Represent this situation mathematically. If you use variables, specify what each one means and how many hours per week can Lin work? explain or show reasoning
Enter the sum in simplest form. pls answer I give brainliest
11/12 -5/12 would equal 7/12. 7/12 can not be simplified, because seven and twelve can not be divided by the same number to get smaller numbers. 7/12 is the simpliest form
Answer:
1/2
the 1 goes on top and the 2 goes at the bottom
Which equation represents a line that passes through (2, ) and has a slope of 3?
O y-2= 3(x +)
O y-3=2(x +)
Oy+= 3(x-2)
O y+=2(x–3)
Answer:
y - 3 = 2 (x + 1/2)
Step-by-step explanation:
y= mx + b
M is your slope and B is your y-intecept.
Hope this helped!! <3
1/6x + 3/2 slope of line
Answer: m=1/6
Step-by-step explanation:
in an 7th grade class with 80 people, seven tenths of the students wore shorts, how many students wore shorts
Answer:
56
Step-by-step explanation:
80 x (7 / 10) = 56
Alex stayed up 20 a week How many hours did Alex stay up in 12 weeks?
Answer:
240 hours
Step-by-step explanation:
1 week = 20 hours
12 weeks = 20 × 12
= 240 hours
A company wishes to manufacture a box with a volume of 20 cubic feet that is open on top and is twice as long as it is wide. Find the width of the box that can be produced using the minimum amount of material.
Answer:
2.47 feet
Step-by-step explanation:
Let l, b, and h be the length, width, and height of the box.
As the length is twice the width, so l=2b ...(i)
The volume of the box is 20 cubic feet, so
lbh=20
(2b)bh=20 [by using (i)]
[tex]h=\frac {20}{2b^2} \\\\h= \frac {10}{b^2} ...(ii)[/tex]
The material required= surface area, S, of the open box
S= lb+2bh+2lh
By using equation (i) and (ii), we have
[tex]S= 2b(b)+2b\times \frac {10}{b^2} +2(2b)\times \frac {10}{b^2}[/tex]
[tex]S= 2b^2+ \frac {20}{b} + \frac {40}{b} \\\\S= 2b^2+ \frac {60}{b} \cdots(i)[/tex]
Now, we have the surface area, S, as the function of width, b.
Differentiate S with respect to b then equate it to zero to get the extremum values, as
[tex]\frac {dS}{db}=0 \\\\\frac {d}{db}(2b^2 +60/b)=0 \\\\4b-\frac{-60}{b^2}=0 \\\\4b=\frac{60}{b^2} \\\\b^3=\frac{60}{4} \\\\b=(15)^{1/3}[/tex]
b=2.47 feet.
Now, by second differentiation, checking the nature of extremum value.
[tex]\frac {d^2S}{db^2}=4+\frac {120}{b^3}[/tex]
For [tex]b>0, \frac {d^2S}{db^2} >0[/tex]
So, the width of the box, b=2.47, is the minima for the area, S(b).
Hence, the width of the box that can be produced using the minimum amount of material is 2.47 feet.
In the diagram FEL ~ JOS
Which ratios are equivalent to tan F? Select all that apply. (Don’t just choose one)
9514 1404 393
Answer:
EL/EF and OS/OJ
Step-by-step explanation:
In the similar triangles, angle F and angle J have the same measure, so will have the same tangent. The tangent is the ratio of the opposite side to the adjacent one.
In ΔFEL, the desired ratio is ...
tan(F) = EL/EF . . . . . 2nd choice
In ΔJOS, the equivalent ratio is ...
tan(J) = tan(F) = OS/OJ . . . . . 7th choice
I have no clue what to put in all of these boxes help me
i dont think it right i only could do the first one i dint know the last one cuz ...
what is the solution to the equation below?
The answer is B. x=-7
Explanation:
I just substituted x for all of the answer choices until I found the right one.
Please mark Brainliest!
Roman created the following table to represent the balance of his loan, y, over a period of months, x. The equation for the line of best fit of Roman's table of dadt is y= -200.22x + 5,014.20.
Answer: extrapolation, and 25 months
Step-by-step explanation:
I took the Plato test and got it right, but if you want to know. Interpolation means based on the numbers given you could see the answer, extrapolation means you have to go farther than the last plot point given to get your answer. Which you do since it does not go past 12 months.
The second answer you can roughly get by pluging in each of the choices in the equation for x
For example: y=-200.22(25)+5015.20
That should give you an answer pretty close to zero so there is your answer
Answer:
extrapolation, and 25 months
Step-by-step explanation:
A line with a slope of 5 passes through the point (2, 5). What is its equation in
slope-intercept form?
Answer:
y = 5x - 5Step-by-step explanation:
slope-intercept form of equation: y = mx + b
where m is slope and b is y-intercept
If line y=ax+b passes through point (x₀,y₀) that means
that the equation y₀=ax₀+b is true
(2, 5) ⇒ x=2, y=5
m = 5
So:
5 = 5×2 + b
5 = 10 + b
b = -5
Therefore equation in slope-intercept form:
y = 5x + (-5)
y = 5x - 5
The equation of the line in slope-intercept form is y = 5x - 5.
Given that the slope of the line is 5 and it passes through the point (2, 5), we can use the point-slope form of a linear equation to find the equation of the line.
The point-slope form is given by:
y - y1 = m(x - x1),
where (x1, y1) is the given point and m is the slope.
Substituting the values, we have:
y - 5 = 5(x - 2).
Now, let's simplify this equation:
y - 5 = 5x - 10.
Next, let's isolate y:
y = 5x - 10 + 5.
Simplifying further:
y = 5x - 5.
So, the equation of the line in slope-intercept form is y = 5x - 5.
Learn more about slope-intercept form here:
https://brainly.com/question/29146348
#SPJ2
Here is a picture of a circle. Each square represents 1 square unit.
Explain why the area of the circle is less than 4 square units.
Answer:
No picture?
Step-by-step explanation:
i need a picture to anwser
The function B gives the depth of the water, in inches, t minutes after Tyler began to fill the bathtub. What does B(9)=11 mean?
Answer:
B(9) = 11 means the depth of the water in the bathtub, 9 minutes after Tyler began to fill the bathtub is 11 inches
Step-by-step explanation:
Whereby the function is expressed as B(t) = d,
Where;
d = The depth of the water
Therefore, when we have B(9) = 11, by comparing with the general form of the function, B(t) = d, we have;
t = 9 = The time in minutes after Tyler began to fill the bathtub = 9 minutes
d = The depth of the water = 11 inches
Which gives the meaning of the equation, B(9) = 11 as the depth of the water in the bathtub, 9 minutes after Tyler began to fill the bathtub is 11 inches.
Solve for W: P=2L + 2W
A. W=P-L
B. W= 1/2P - L
C. W= 1/2 P + L
D. W= 2P - L
Answer:
B
Step-by-step explanation:
[tex]P=2L+2W[/tex]
[tex]P-2L=2W[/tex] (Subtract 2L from both sides of the equation)
[tex]2W=P-2L[/tex] (Symmetric Property of Equality)
[tex]W=\frac{P-2L}{2}[/tex] (Divide both sides of the equation by 2)
[tex]W=\frac{P}{2} -\frac{2L}{2}[/tex] ("Split" the fractions)
[tex]W=\frac{1}{2}P-L[/tex] (Simplify)
Hope this helps!
A students cost for last semester at her community college was 2100 she spent 231 of that on books what percent of last semesters college costs was spent on books
Work Shown:
Divide the two amounts, smaller over bigger, to get
231/2100 = 0.11
Then move the decimal point over two spots to the right to get to 11%
Note how 11% of 2100 = 0.11*2100 = 231.
A 5 pound tub of cottage cheese at n dollars per pound costs $10.25 .
Write an equation for the following word problem
Answer:
5n = $10.25
Step-by-step explanation:
We know that the tub is 5 pounds, and costs $10.25. We also know that n is in dollars per pound. Dollars per pound can be written as the product of dollars, divided by pounds, so we can plug that in being n = $10.25/5, next we want to make the equation contain an integer on both sides and not contain any fractions, so we multiply both sides by 5, resulting in 5n = $10.25
What is 1+1 * the square root of 199 and 198
Answer:2.14.07
Step-by-step explanation:
Triangle ABC has coordinates A(2, -5), B(1, -3), and C(6, 1). If the triangle is rotated 90° counterclockwise about the origin, what are the coordinates of A'?
Answer:
A(5,2)
Step-by-step explanation:
A 90 degree rotation counterclockwise is
(x , y) -> (-y , x)
Therefore the coordinates of A changes from
A(2 , -5) to A(-(-5) , 2)
A(5,2)
Esther deposited $5,000 into an account that grows at a rate of 8% per year. To the nearest cent, how much will be in the
account after 5 years?
Answer:
The total amount after five years = $7,000
Step-by-step explanation:
Step(i):-
Given Esther deposited $5,000 into an account
Principal amount 'P' = 5000
Given rate of interest (R) = 8%
r = R / 100 = 0.08 per year
Step(ii):-
The total amount after 5 years
[tex]A = P( 1 + r t )[/tex]
[tex]A = 5000(1+ (0.08 X 5) = 7000[/tex]
Final answer:-
The total amount after five years = $7,000
You deposit $2000 in an account that earns 5% annual interest compounded quarterly. Find the account balance after 10 years
Answer:
You deposit $2000 in an account that earns 5% annual interest compounded quarterly. Find the account balance after 10 years
On every three hamburgers that McDonalds makes, they use 9 pickles. How many pickles would they use on 100 burgers?
Answer:
300 pickles
Step-by-step explanation:
9/3=3, 3*100=300
Answer:
11.1 repeating
Step-by-step explain
You would figure out that they have 3 pickles on each burger so do 100/9 and 11.1 repeating.
Someone help me with this question please! I'm having a hard time answering it!
Step-by-step explanation:
2 * 2 for potatoes = £4
3 * 3 for carrots = £9
90p * 3 for turnips = 270p = £2.70
total price = 9+4+2.70=15.70
change = 20 - 15.70 = £4.30
The chef at LaBerge started the week with 50 pounds of cheese and used 15 4/5 pounds. How much cheese
remains in inventory?
Answer: 34.2 pounds
Step-by-step explanation:
First, convert 15 4/5 into an improper fraction. You should get 79/5. Then, convert 50 into a fraction that has a denominator of 5. Right now, 50= 50/1 so just multiply the top and bottom by 5 to make it 250/5. Then, subtract 79/5 from 250/5. You should get 171/5. Lastly, simplify. You should get 34.2 pounds as your final answer. Hope this helps!
7. A shirt marked at $600 is sold at 30% off.
(a) Find the selling price of the shirt.
(b) If the shirt is sold at a profit of 5%, find the cost pric
Answer:
a) $420 b) $399
Step-by-step explanation:
a) $600 = 100%
$60 = 10%
$60 times 3 gives 30% = $180
$600 - $180 = $420
b) $420 = 100%
$42 = 10%
$21 = 5%
this means, they profitted by $21.
so $420 - $21 = $399
therefore, $399 is the cost price
PLEASE HELP ASSP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!111
Answer:
2.3
Step-by-step explanation:
Your beginning equation is 5 (t + 3) = -3.5. You start by dividing by 5. This leaves you with t + 3 = 0.7. If you add 3 you get 2.3
What is the solution of....
[tex]\huge \mathscr{\blue {\underline {\red{\underline{Answer :-}}}}} [/tex]
[tex] \bf \frac{5}{2} x - 7 = \frac{3}{4} x + 14[/tex]
[tex] \bf \implies \: \frac{5}{2} x - \frac{3}{4} x = 14 + 7[/tex]
[tex] \bf \implies \: \frac{10x - 3x}{4} = 14 + 7[/tex]
[tex] \bf \implies \: \frac{7}{4} x = 21[/tex]
[tex] \bf \implies \: 7x = 21 \times 4[/tex]
[tex] \bf \implies \: x = \frac{21 \times 4}{7} [/tex]
[tex] \bf \implies \: x = 3 \times 4[/tex]
[tex] \bf \implies \: x = 12[/tex]
ᴏᴘᴛɪᴏɴ (ᴅ) x = 12 ɪs ʏᴏᴜʀ ᴄᴏʀʀᴇᴄᴛ ᴀɴsᴡᴇʀ
[tex]{\huge{\underline{\small{\mathbb{\blue{HOPE\:HELPS\:UH :)}}}}}}[/tex]
Pls tell me the answer
Answer:
1/4
Step-by-step explanation: