Answers
3. First you should identify which line corresponds to which equation.
x + 2y = -8 ⇒ y = -x/2 - 4
is the line with slope -1/2 and intercept (0, -4), so the first inequality refers to the lower line in the graph.
For the inequality itself, the solution set that satisfies it is either the region above or below it. To decide which, pick any point in the plane and plug its coordinates into the inequality. The origin is a natural choice, since it's not on the line and working with 0s is easy.
In the first inequality, we have
x = 0 and y = 0 ⇒ 0 + 2•0 = 0 < -8
which is not true. So (0, 0) is not in the solution set, and it stands to reason that any point in the same region will not be a solution. In other words, the region above the line x + 2y = -8 does not satisfy the inequality, while the one below it does.
In the second inequality,
x = 0 and y = 0 ⇒ 2•0 + 0 = 0 ≥ -1
which is true. This means the region containing (0, 0) above the upper line solves the second inequality.
The solution to the system of inequalities is then the intersection of these two regions. (See attached; I've labeled the solution to the first inequality in blue, the solution to the second one in red, and the solution to both in green.)
All this work is kind of overkill for this particular question, though. All you really need to do is check if the given point satisfies the inequalities:
• (-5, 5) :
x = -5 and y = 5 ⇒ -5 + 2•5 = 5 < -8 ⇒ NO
• (2, -5) :
x = 2 and y = -5 ⇒ -2 + 2•5 = 8 < -8 ⇒ NO
• (-4, -6) :
x = -4 and y = -6 ⇒ -4 + 2•(-6) = -16 < -8 ⇒ MAYBE
x = -4 and y = -6 ⇒ 2•(-4) + (-6) = -14 < -8 ⇒ YES
• (5, -7) :
x = 5 and y = -7 ⇒ 5 + 2•(-7) = -9 < -8 ⇒ MAYBE
x = 5 and y = -7 ⇒ 2•5 + (-7) = 3 < -8 ⇒ NO
4. x is the number of candy boxes with chocolates and y is the number of boxes without chocolates. Each of the x boxes cost $27.50, so if you have x boxes, their total cost is $27.5x. Each of the y boxes cost $25.00, so y boxes cost $25y. The sponsor doesn't want to order more than 100 boxes total, so
x + y < 100
but wants to raise at least $2000, so
27.5x + 25y ≤ 2000
Now do the same thing as before; plug in the listed x- and y-coordinates and pick the point that satisfies both inequalities. You will find that (50, 30) is the correct choice.
5. Consult the "overkill" part of problem 3. The line y = -3x + 6 has a negative slope, so it's the downward sloping one. Check if the origin satisfies the inequality:
x = 0 and y = 0 ⇒ 0 ≤ -3•0 + 6 ⇒ 0 ≤ 6 ⇒ YES
This means Regions II and III solve the first inequality.
Do the same with the other inequality:
x = 0 and y = 0 ⇒ 0 ≥ 1/2•0 + 1 ⇒ 0 ≥ 1 ⇒ NO
This tells us that Regions I and II solve the second inequality.
The intersection of these regions is of course Region II.
6. One of the plotted lines is apparently y = x + 4, which has a positive slope, so this must be the upper line. The shaded region below it corresponds to the solution of either y < x + 4 or y ≤ x + 4 and we eliminate B.
The other line has negative slope, which eliminates A and D since
3x - 4y = 20 ⇒ y = 3/4x - 5
has positive slope. This leaves D.
Related Questions
Tony was on the bumper cars at the amusement park. He turned his steering wheel 25 degrees to bump his friend. How many one-degree turns is this?
100 one-degree turns
50 one-degree turns
2.5 one-degree turns
25 one-degree turns
Answers
Answer:
25 one degree turns
Step-by-step explanation:
if one degree is one degree than 25 degrees are 25 one degree turns since 25 divided by 1 equals 25
Answer:
25
Step-by-step explanation:
A bird drops a stick to the ground from a height of 90 ft. The function h=16ft^2+90 gives the sticks approximate height h above the ground, in feet, after t seconds. At about what time does the stick hit the ground? How many seconds does it hit the ground?
Answers
Answer:
The stick hits the ground 2.37 seconds after it is dropped.
Step-by-step explanation:
Your function is incorrect.
I will assume that the correct function is
h = -16t² + 90
When the stick hits the ground, its height is 0.
We are looking for the value of t, time, when h = 0.
Set h = 0, and solve for t.
h = -16t² + 90
-16t² + 90 = 0
-16t² = -90
t² = 5.625
t = 2.37
The stick hits the ground 2.37 seconds after it is dropped.
If tan (x) = 24/19 (in Quadrant 1), find
Give exact answers.
sin (x/2) =
cos(x/2) =
tan (x/2) =
Answers
If x is in quadrant I, then both sin(x) and cos(x) are positive. The angle x/2 also belongs to quadrant I, and hence each of sin(x/2), cos(x/2), and tan(x/2) are positive.
Recall that for all x,
cos²(x) + sin²(x) = 1
and multiplying through both sides by 1/cos²(x) = sec²(x) gives another flavor of this identity,
1 + tan²(x) = sec²(x)
It follows that
sec(x) = √(1 + tan²(x)) = √937/19
which immediately gives us
cos(x) = 19/√937
and from the identity above we find
sin(x) = √(1 - cos²(x)) = 24/√937
Recall the half angle identity for cos :
cos²(x) = (1 + cos(2x))/2
which means
cos(x/2) = + √[(1 + cos(x))/2] = √[1/2 + 19/(2√937)]
Then
sin(x/2) = + √(1 - cos²(x/2)) = √[1/2 - 19/(2 √937)]
and by definition of tan,
tan(x/2) = sin(x/2) / cos(x/2) = 1/12 √[649/2 - 19 √937/2]
Just to be clear, the solutions are
[tex]\cos\left(\dfrac x2\right) = \sqrt{\dfrac12 + \dfrac{19}{2\sqrt{937}}}[/tex]
[tex]\sin\left(\dfrac x2\right) = \sqrt{\dfrac12 - \dfrac{19}{2\sqrt{937}}}[/tex]
[tex]\tan\left(\dfrac x2\right) = \dfrac1{12} \sqrt{\dfrac{649 - 19\sqrt{937}}2}[/tex]
Find all angles, 0º < 0 < 360°, that satisfy the equation below, to the nearest 10th
of a degree.
2 tan^2(theta)+ tan(theta)= 0
Answers
[tex]2tan^2(\theta )+tan(\theta )=0\implies tan(\theta )[2tan(\theta )+1)]=0 \\\\[-0.35em] ~\dotfill\\\\ tan(\theta)=0\implies \theta=tan^{-1}(0)\implies \theta= \begin{cases} 0\\ 360^o \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 2tan(\theta)+1=0\implies 2tan(\theta)=-1\implies tan(\theta)=-\cfrac{1}{2} \\\\\\ \theta=tan^{-1}\left( -\cfrac{1}{2} \right)\implies \theta \approx \begin{cases} \stackrel{180^o~~ - ~~26.57}{153.43^o}\\ \stackrel{360~~ - ~~26.57}{333.43^o} \end{cases}[/tex]
for the second pair of angles, the angle of reference is really about 26.57°. Now, the tangent is only negative in two quadrants, the II and IV Quadrants, using the angle of reference, it'd give us those angles.
Make sure your calculator is in Degree mode.
Is this right? Please help me!!
Answers
Answer:
Yes
Step-by-step explanation:
There are two green regions and two red regions which makes four regions in total. If there is an equal probability to land on each region, it means that the probability to land on a green region is 2/4 because there are two green regions out of the four total regions. You could also simplify it to 1/2.
Solve the equation. Write the answer in terms of the natural logarithm.
e^(8x+9)=14
The Solution set is { }.
Type exact answer in simplified form.
Answers
Step-by-step explanation:
Take the natural logarithm of both sides;
8x+9 = ln (14)
Transposition;
8x= ln(14)-ln(e⁹)
[tex]x = \frac{ ln(14) - ln( {e}^{9} ) }{8} [/tex]
[tex]x = \frac{1}{8} ( ln(14) - 9)[/tex]
Fractions of a revolution
It starts at 12 and turns through 1/3 of a revolution
Answers
Answer:
1/3 of twelve is 4 so four must be the answer
Step-by-step explanation:
Which is an equation of the line that passes through
the points (5, 2) and (10, -3)?
Answers
Answer:
y = -x + 7
Step-by-step explanation:
Hi there!
We are given the following points:
(5,2) and (10,-3)
We want to find the equation of the line that passes through these 2 points
There are 3 ways to write the equation of the line, yet the most common way is slope-intercept form, which is y=mx+b (m is the slope and b is the y intercept).
First, let's find the slope of the line.
The slope can be calculated from 2 points using the equation [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points
We have everything we need to find the slope, but let's label the values of the points to avoid confusion and mistakes.
[tex]x_1=5\\y_1=2\\x_2=10\\y_2=-3[/tex]
Now substitute these values into the formula to find the slope
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{-3-2}{10-5}[/tex]
Simplify
m=[tex]\frac{-5}{5}[/tex]
Divide
m=-1
The slope of the line is -1
We can substitute this value as m in y=mx+b.
Here's the equation of our line so far:
y=-x+b
Now we need to find b
As the equation passes through the points (5,2) and (10,-3), we can use either point to find the value of b
Taking (5,2) for example:
Substitute 5 as x and 2 as y
2=-5+b
Add 5 to both sides
7=b
Substitute 7 as b in the equation
y = -x + 7
Hope this helps!
See more on this topic here: https://brainly.com/question/27166723
I need help on this ASAP.
Answers
The seattle great wheel is an illustration of sectors, arcs, circumference and area of circles
The circumference of the wheelThe diameter is given as:
d = 175 feet
The circumference (C) is calculated as:
C = πd
This gives
C = 3.14 * 175
C = 549.5 feet
Hence, the circumference of the wheel is 549.5 feet
The area of the wheelThis is calculated as:
A = π(d/2)^2
This gives
A = 3.14 * (175/2)^2
A = 24040.625
Hence, the area of the wheel is 24040.625 square feet
The central angle (degrees)This is calculated as:
θ = 360/n
Where n is the number of capsules
So, we have:
θ = 360/42
This gives
θ = 8.57 degrees
Hence, the central angle of the wheel in degrees is 8.57
The central angle (radians)This is calculated as:
Radians = Degrees × π/180
So, we have:
θ = 360/42 * π/180
This gives
θ = π/21 rad
Hence, the central angle of the wheel in radians is π/21 rad
Arc length between two capsulesThis is calculated as:
L = θ * d/2
So, we have:
L = π/21 * 175/2
This gives
L = 175π/42
Hence, the arc length between two capsules is 175π/42
Area of sector between two capsulesThis is calculated as:
A = 0.5 * (d/2)^2 * θ
So, we have:
A = 0.5 * (175/2)^2 * π/21
This gives
A = 168π
Hence, the area of sector between two capsules is 168π
Read more about sector areas and arc lengths at:
https://brainly.com/question/4115882
HELP PLS 50 PTS! Molly made a scaled copy of the following square. She used a scale factor greater than 1.
What could be the length of the scaled copy of the square?
Question 2 options:
18 units
10 units
27 units
20 units
Answers
Answer:
D. 27 units
Step-by-step explanation:
27 is greater than 20. The scale factor is more than 1, so the answer(s) have to be more than 1.
The graph shows the location of point P and point R. Point R is on the y-axis and has the same y-coordinate as point P. P (n, 3). Point Q is graphed at (n, 2). The distance from point P to point Q is equal to the distance from point P to point R. What is the distance from point P to point Q? What is the value of n? Explain how you determined the distance from point P to point Q, and the value of n. Enter your answers and your explanations in the space provided.
Answers
Answer:
1
Step-by-step explanation:
have you smiled today? its very important:)
easy question for bonus ;)
Answers
Answer:
970,060
Step-by-step explanation:
i think this is correct-
Edit: i just realised the number was 907,060 ._.
976
Step-by-step explanation:
Read the paragraph below. Which would be the most helpful peer review comment to make about the writer’s style?
Wolves are a familiar animal in stories and movies. They are usually the bad animal. Some people think wolves are dangerous to people. But is this the truth? Wolves eat sheep and people don’t like that because they’re raising the sheep for themselves and some wolves can even take down cattle. Wolves make scary howls that can frighten people. But a sound can’t hurt you!
“You use the word “wolf” a lot. Can you find a more interesting way to say “wolf”?”
“I think wolves are scary, too. You’ll have to do more to convince me that they’re not!”
“I like your sentences about wolves, especially the ones where you describe how scary they are.”
“It would help me follow your ideas more easily if you broke up some of the longer sentences.”
Answers
Answer:
“I think wolves are scary, too. You’ll have to do more to convince me that they’re not!”
Step-by-step explanation:
There are two taxi cab companies in Redwood. Their charges are listed below.
Redwood Taxi
$2.00 for the first mile
plus
$1.00 for each additional mile
Max's Taxi Service
$5.00 for the first mile
plus
$0.50 for each additional mile
According to the graph below, for how many miles will the charges from both taxi cab companies be equal?
1. 8
2. 1
3. 7
4. 4
Answers
Help I know that I have to move 3x to 4x with will be -3x and then I will subtract it then I will be left with -x and then I'll be with -x -3 what do I do after ?
4x -3 = 3x
Answers
Answer:
[tex]\sf \boxed{\bold{x = 3}}[/tex]
Explanation:
4x -3 = 3xsubtract both sides by 4x
4x - 3 -4x = 3x - 4xgroup similar terms
4x - 4x - 3 = -xsimplify
-3 = -xdivide both sides by -1 or cancel out the negatives
x = 3Check:
4(3) -3 = 3(3)12 - 3 = 99 = 9L.H.S = R.H.S Thus x = 3 confirmed
Answer:
x = 3
Step-by-step explanation:
We are trying to move all terms that have x on one side of the equal sign and terms that do not have an x on the other side of equal sign.
terms with x = terms without x
4x -3 = 3x , subtract 3x from both side of the equation
4x -3x -3 = 3x -3x
4x -3x -3 = 0 , add 3 to both sides of the equation
4x -3x -3 + 3 = 0 + 3
4x -3x = 3 , combine like terms
x = 3
Or
We can think we move each term where we want it, yet keep in mind that once we cross the equal sign we change the sign of the term if addition or subtraction are the only operations involved.
4x -3 = 3x , 3x is positive so will become negative on the other side of the equal sign and -3 is negative so will become positive on the other side.
4x -3x = 3
x = 3
5. Which of the following is a function?
A. (1,7), (2,14), (3, 21), (1, 28)
B. (0, A), (5, B), (10, C), (15, D), (5, E)
C. (-5,1),(-10,1),(-15, 1), (-20,1),(-15,1)
D. (1, 1), (2, 2), (3, 3), (4,4), (5,5)
Answers
Answer:
D. (1, 1), (2, 2), (3, 3), (4,4), (5,5)
Hope this helps!
A car can be rented for $75 per week plus $0.15 per mile. How many miles can be driven if you have at most $180 to spend for weekly transportation
Answers
Answer:
60+0.5x <= 180
0.5x <= 120
x <= 240 miles
Step-by-step explanation:
Find the volume of the cone. Round your answer to the nearest tenth. 7 ft, 4ft
Answers
Answer:
117.29 cubic feet
Step-by-step explanation:
* means multiplied by
V=π*r^2*(h/3)
V=π*4^2*(7/3)
V=3.14*16*(7/3)
V≈117.29
Last week, Pauline worked 35 hours and made $280.
How much money did Pauline make per hour?
Answers
Answer:
Pauline made $8 per hour last week.
Step-by-step explanation:
$280÷35=$8
90 POINTS!! IM STUCK!!
2. Alicia is writing the program for a video game. For one part of the game she uses the rule to move points on the screen.
(a) What output does the rule give when the input is -6,0 ? Show your work.
(b) What output does the rule give when the input is 3, -4 ? Show your work.
(c) Is the rule a function? Explain why it is or why it is not
Answers
Answer:
(x-3,y+4) is the rule
a. -6, 0 input. This would equal (-6)-3 for x and (0)+4 for y. Answer: -9, 4
b. 3, -4 input. This would equal (3)-4 for x and (-4)+4 for y. Answer: -1, 0
c. The rule is a function because each input only has one output
Answer:
QuestionAlicia is writing the program for a video game. For one part of the game she uses the rule (x, y) → (x - 3,y + 4) to move points on the screen.
(a) What output does the rule give when the input is (-6, 0)?
Show your work.
(b) What output does the rule give when the input is (3, -4)?
Show your work.
(c) Is the rule a function? Explain why it is or why it is not.
Solution(a) Input (-6, 0) → Output (-6 - 3, 0 + 4) = (-9, 4)
(b) Input (3, -4) → Output (3 - 3, -4 + 4) = (0, 0)
(c) The rule is a one-to-one function as each value in the range (y-values) corresponds to exactly one value in the domain (x-values).
Robbie factored the following expression incorrectly. Identify his mistake, then write a few sentences
explaining to him how to fix it.
Answers
Answer:
3(3r - 4)(3r + 4)
Step-by-step explanation:
I can't see the writing very clearly.
This is the correct solution:
27r^2 - 48 Divide through by 3:
= 3(9r^2 - 16) 9r^2- 16 is the difference of 2 squares so:
= 3(3r - 4)(3r + 4)
The Perimeter of Rhombus WXYZ is 240 cm and XY = 5k + 10
What is the value of'k?
w
х
A +
(B) 9
(С 10
[7 7
(D2
E 16
Z
Answers
Hope this helps
Have a good day!
a trader buys 200 oranges for 60 kobo and sells them at 8 for 12 kobo.what is his gain
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
Cost price for each Orange :
[tex]\qquad \tt \dashrightarrow \: \dfrac{60}{200} [/tex]
[tex]\qquad \tt \dashrightarrow \:0.3 \: \: kobo[/tex]
Now, Cost price for 8 oranges :
[tex]\qquad \tt \dashrightarrow \:0.3 \times 8[/tex]
[tex]\qquad \tt \dashrightarrow \:2.4 \: \: kobo[/tex]
And we have been given that selling price for 8 oranges is 12 kobo.
Therefore, the gain is :
[tex]\qquad \tt \dashrightarrow \:12 - 2.4[/tex]
[tex]\qquad \tt \dashrightarrow \:9.6 \: \: kobo[/tex]
Percentage gain is ~
[tex]\qquad \tt \dashrightarrow \: \dfrac{9.6}{2.4} \times 100[/tex]
[tex]\qquad \tt \dashrightarrow \:4 \times 100[/tex]
[tex]\qquad \tt \dashrightarrow \:400 \: \%[/tex]
20. Joshua sold a batch of tickets for carnival rides. The ratio of adult
tickets to child tickets was 2:5. After he sold another 70 adult tickets and
300 child tickets, the ratio changed to 1:3. How many adult tickets did
Joshua sell in total?*
What is the awnser
Answers
Step-by-step explanation:
a = original number of adult tickets
c = original number of child tickets
a/c = 2/5
a = 2c/5
(a+70)/(c+300) = 1/3
(2c/5 + 70)/(c + 300) = 1/3
2c/5 + 70 = (c + 300)/3
2c + 350 = 5(c + 300)/3
6c + 1050 = 5(c + 300) = 5c + 1500
c = 450
a = 2c/5 = 2×450/5 = 2×90 = 180
Joshua sold therefore in total
180 + 70 = 250 adult tickets.
and by the way
450 + 300 = 750 child tickets.
Richie worked the following hours last Thursday and Friday:
Thursday: 8 a.m. 70 11:30 a.m. and 12 p.m. to 3:45 p.m.
Friday: 8:45 a.m. to 11:30 a.m. and 12:30 p.m. to 3:15 p.m.
If Richie is paid $16 an hour, how much did he make total for Thursday and Friday?
Answers
Answer:
$308
Step-by-step explanation:
Hope this helped! :)
If this is wrong please comment below! :)
Thx!
X-2/x+3+10x/x^2-9
Simplify the sum
Answers
Answer:
(x+2)/(x−3)
Step-by-step explanation:
((x-2)/(x+3))+((10x)/(x+3)(x-3))
((x-2)(x-3)+10x)/(x+3)(x+3)
Brainliest if you can please
Which function is the inverse of f(x) = -5x-4?
Answers
Answer:
B
Step-by-step explanation:
Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=x5+45 f - 1 ( x ) = x 5 + 4 5 is the inverse of f(x)=5x−4 f ( x ) = 5 x - 4 .
Answer:
B. [tex]-\frac{1}{5} x+\frac{4}{5}[/tex]
Step-by-step explanation:
1. Rewrite the function as a linear equation:
y = -5x - 4
2. Swap x and y:
x = -5y - 4
3. Solve for y:
x+4 = -5y - 4+4
x + 4/-5 = -5y/-5
[tex]\frac{x+4}{-5}[/tex] = y can be rewritten as [tex]-\frac{1}{5} x+\frac{4}{5}[/tex]
4. Write in inverse notation:
f(x) = [tex]-\frac{1}{5} x+\frac{4}{5}[/tex]
Therefore, B is the answer.
Avery leans a 24-foot ladder against a wall so that it forms an angle of 80° with the
ground. How high up the wall does the ladder reach? Round your answer to the
nearest tenth of a foot if necessary.
Answers
Answer:23.6ft
Step-by-step explanation:
SOHCAHTOA
sin(80)=(o/24)
Multiply both sides by 24 and 24 on the right side will cancel out.
24sin(80)=23.6ft
The height of the wall where the ladder reaches will be 23.64 feet.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
Avery leans a 24-foot ladder against a wall so that it forms an angle of 80° with the ground.
The height of the wall where the ladder reaches is given as,
sin 80° = h / 24
h = 24 x sin80°
h = 23.64 feet
The height of the wall where the ladder reaches will be 23.64 feet.
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
#SPJ2
A right triangle is shown
5
x
9.1
Enter the value of x. Round your answer to the nearest hundredth
Answers
Answer:
10.38
Step-by-step explanation:
What is greater -3 pi or -9
Answers
if pi is a separate answer, then it is pi
hope this helps :)