Answer:
Ground distance = 10396 feet (nearest foot)
Step-by-step explanation:
The horizontal distance given the vertical is governed by the tangent of the angle of depression.
V/H = tan(angle of depression)
Hence
H = V / tan(angle of depression)
= 2400 / tan(13)
= 10395.5 feet
A tank contains 80 kg of salt and 1000 L of water. A solution of a concentration 0.04 kg of salt per liter enters a tank at the rate 8 L/min. The solution is mixed and drains from the tank at the same rate. Let y be the number of kg of salt in the tank after t minutes. Write the differential equation for this situation
Let A(t) denote the amount of salt (in kg) in the tank at time t.
At the start, there are 80 kg of salt in the tank, so A(0) = 80.
Solution flows into the tank at a rate of 8 L/min at a concentration of 0.04 kg/L, so that salt flows in at a rate of
(8 L/min) * (0.04 kg/L) = 0.32 kg/min
Solution flows out at the same rate, but its concentration depends on the amount of salt in the tank. The concentration of the solution is the proportion of salt in the liquid to the total volume of the liquid. Solution flows in and out at 8 L/min, so the volume of liquid (1000 L) stays the same. A(t) is the amount of salt in the tank, so the concentration is A(t)/1000 kg/L. Hence salt flows out at a rate of
(8 L/min) * (A(t)/1000 kg/L) = 0.008 A(t) kg/min
The net rate at which salt flows through the system is then given by the differential equation,
dA(t)/dt = 0.32 - 0.008 A(t)
(Don't forget to include the initial condition)
Get every whole number from 0−10 using exactly five 3's, and any arithmetic operations and parentheses
Answer:
Step-by-step explanation:
(3 +3 - 3 -3) / 3 = 0
3 - 3/3 - 3/3 = 1
3 + 3 - 3 - 3/3 = 2
(3*3*3/(3*3) = 3
(3 + 3+ 3+ 3) / 3 = 4
(3 * 3) - (3 + 3/3) = 5
((3*3*3)/ 3)) - 3 = 6
(3 * 3) - 3 + 3/3 = 7
(3*3*3 - 3) / 3 = 8
(3 + 3+3 + 3) - 3 = 9
3 + 3 + 3 + 3/3 = 10.
A catering company is catering a large wedding reception. The host of the reception has
asked the company to spend a total of $454 on two types of meat: chicken and beef. The
chicken costs $5 per pound, and the beef costs $ 7 per pound. If the catering company
buys 25 pounds of chicken, how many pounds of beef can they buy?
The answer is 47 pounds
Explanation:
1. First, let's calculate the amount of money that was spent on chicken
$5 per pound of chicken x 25 pounds = $125
2. Calculate the amount of money left to buy beef by subtracting the total spend on chicken to the total of the budget.
$454 (total) - $125 (chicken) = $329
3. Calculate how many pounds of beef you can buy with the money left by dividing the money into the price for one pound.
$329 / $7 = 47 pounds
If f(x) = 2x + 6 and g(x) = x^3 ,what is (gºf)(0)?
Answer:
[tex](gof)(0)=216[/tex]
Step-by-step explanation:
If [tex]f(x)=2\,x+6[/tex], and [tex]g(x)=x^3[/tex]
then [tex](gof)(0)[/tex] can be calculated via:
[tex]g(f(0))=g(2\,(0)+6)=g(6)=(6)^3=216[/tex]
he geometric property of any polygon feature that is represented by the ratio of the perimeter of the polygon to the circle with the same perimeter is called
Answer:
"Compactness" is the right answer.
Step-by-step explanation:
In mathematical or geometry, compactness seems to be the characteristic of some mathematical morphology or spaces which have its primary use during the analysis of parameters based upon such spaces.An accessible space protect (or set) is another series of open field sets shielding another space; i.e., every space position is throughout some series member.So that the above would be the correct answer.
A car is being driven, in a straight line and at a uniform speed, towards the base of a vertical tower. The top of the tower is observed from the car and, in the process, it takes 10 min for the angle of elevation to change from 45° to 60°. After how much more time will this car reach the base of the tower? Options: a. 5( √3+ 1 ) b. 6 (√3 +√2) c. 7 (√3- 1) d. 8 (√3-2)
Answer:
The correct answer is option a.
a. 5( √3+ 1 )
Step-by-step explanation:
Given that the angle changes from 45° to 60° in 10 minutes.
This situation can be represented as right angled triangles [tex]\triangle[/tex]ABC (in the starting when angle is 45°)and [tex]\triangle[/tex]ABD (after 10 minutes when the angle is 60°).
AB is the tower (A be its top and B be its base).
Now, we need to find the time to be taken to cover the distance D to B.
First of all, let us consider [tex]\triangle[/tex]ABC.
Using tangent property:
[tex]tan\theta =\dfrac{Perpendicular}{Base}\\\Rightarrow tan 45=\dfrac{AB}{BC}\\\Rightarrow 1=\dfrac{h}{BC}\\\Rightarrow h = BC[/tex]
Using tangent property in [tex]\triangle[/tex]ABD:
[tex]\Rightarrow tan 60=\dfrac{AB}{BD}\\\Rightarrow \sqrt3=\dfrac{h}{BD}\\\Rightarrow BD = \dfrac{h}{ \sqrt3}\ units[/tex]
Now distance traveled in 10 minutes, CD = BC - BD
[tex]\Rightarrow h - \dfrac{h}{\sqrt3}\\\Rightarrow \dfrac{(\sqrt3-1)h}{\sqrt3}[/tex]
[tex]Speed =\dfrac{Distance }{Time}[/tex]
[tex]\Rightarrow \dfrac{(\sqrt3-1)h}{10\sqrt3}[/tex]
Now, we can say that more distance to be traveled to reach the base of tower is BD i.e. '[tex]\bold{\dfrac{h}{\sqrt3}}[/tex]'
So, more time required = Distance left divided by Speed
[tex]\Rightarrow \dfrac{\dfrac{h}{\sqrt3}}{\dfrac{(\sqrt3-1)h}{10\sqrt3}}\\\Rightarrow \dfrac{h\times 10\sqrt3}{\sqrt3(\sqrt3-1)h}\\\Rightarrow \dfrac{10 (\sqrt3+1)}{(\sqrt3-1)(\sqrt3+1)} (\text{Rationalizing the denominator})\\\Rightarrow \dfrac{10 (\sqrt3+1)}{3-1}\\\Rightarrow \dfrac{10 (\sqrt3+1)}{2}\\\Rightarrow 5(\sqrt3+1)}[/tex]
So, The correct answer is option a.
a. 5( √3+ 1 )
Ifx + iy = 1
1+i/
1-i
prove that, x² + y² = 1
HI MATE
which numbers are the extremes of the proption shown below. 3/4 = 6/8
Answer:
3 and 8
Step-by-step explanation:
Given the proportion:
[tex] \frac{3}{4} = \frac{6}{8}[/tex]
Required:
Find the extreme values.
When given an equation like the one we have here, there is always a very easy way to find the extreme value.
First make rewrite to a ratio form:
Example:
a:b = c:d
Just know that extreme values are the values on the outside of the ratio(a & d)
Therefore,
3:4 = 6:8
When it is written this way extreme values are 3 & 8
Extreme values = 3 and 8
Yesterday at 1:00 P.M., Maria’s train was 42 miles north of Gull’s Beach, traveling north at an average speed of 90 mph. At the same time on the adjacent track, Elena’s train was 6 miles north of Gull’s Beach, traveling north at an average speed of 101 mph. To the nearest hundredth of an hour, after how much time will the trains meet up? 0.23 hours 0.31 hours 3.27 hours 4.36 hours
Answer:
3.27 hours
Step-by-step explanation:
Calculate the difference in speed and distance between the trains.
The relative speed:
101 - 90 = 11 mph
Difference in distance:
42 - 6 = 36 miles
[tex]time=\frac{distance}{speed}[/tex]
[tex]t=\frac{36}{11}[/tex]
[tex]t = 3.27[/tex]
Answer:
yeah she is correct
Step-by-step explanation:
Lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50. Ari buys 3 pounds of apples and 2
pounds of bananas for a total of $5.25. This system of equations represents the situation, where x is the cost per
pound of apples, and y is the cost per pound of bananas.
5x + 3y = 8.5
3x + 2y = 5.25
If you multiply the first equation by 2, what number should you multiply the second equation by in order to eliminate
the y terms when making a linear combination?
Complete the multiplication and add the equations. What is the result?
What is the price per pound of apples? $
What is the price per pound of bananas?
Answer:
price per pound of apple = $1.25
price per pound of banana = $0.75
Step-by-step explanation:
Your first question is what value should you multiply the second equation by in order to eliminate the y terms.
The number should be 3. Let us multiply the first equation by 2 and the second equation by 3 and see how y will be eliminated.
10x + 6y = 17...............(i)
9x + 6y = 15.75...........(ii)
10x - 9x = x
6y - 6y = 0
17 - 15.75 = 1.25
x = 1.25
let us find y
10x + 6y = 17...............(i)
10(1.25) + 6y = 17
12.5 + 6y = 17
6y = 17 - 12.5
6y = 4.5
divide both sides by 6
y = 4.5/6
y = 0.75
In order to eliminate y term from the system of equations we multiply equation 2 by -3.
The price per pound of apple is 1.25 dollars and the price per pound of bananas is 0.75 dollars.
Given equations,
[tex]5x + 3y = 8.5[/tex].........(1)
[tex]3x + 2y = 5.25[/tex].......(2)
Here x is the cost per pound of apples, and y is the cost per pound of bananas.
According to the question, multiply the first equation by 2, we get
[tex]10x+6y=17[/tex].....(3)
So, in order to eliminate y term from the system of equations we multiply equation 2 by -3, we get
[tex]-9x-6y=15.75[/tex].....(4)
Now Adding (3) and (4) equation, we get
[tex]x=1.25[/tex]
Putting the above value of x in equation 3 we get,
[tex]10\times1.25+6y=17\\12.5+6y=17\\6y=17-12.5\\6y=4.5\\y=\frac{4.5}{6} \\y=0.75[/tex]
Hence the price per pound of apple is 1.25 dollars and the price per pound of bananas is 0.75 dollars.
For more details follow the link:
https://brainly.com/question/11897796
Using the unit circle, determine the value of cos(945°).
========================================================
Explanation:
The angle 945 degrees is not between 0 and 360. We need to adjust it so that we find a coterminal angle in this range. To do this, subtract off 360 repeatedly until we get into the right range
945 - 360 = 585, not in range, so subtract again
585 - 350 = 225, we're in range now
Since 945 and 225 are coterminal angles, this means cos(945) = cos(225)
From here, we use the unit circle. Your unit circle should show the angle 225 in quadrant 3, which is the lower left quadrant. The terminal point here at this angle is [tex]\left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)[/tex]
The x coordinate of this terminal point is the value of cos(theta). Therefore [tex]\cos(225^{\circ}) = -\frac{\sqrt{2}}{2}[/tex] and this is also the value of cos(945) as well
Using the periodic property of cos function, you can evaluate the value of cos(945°).
The value of cos(945°) is given by:
[tex]cos(945^\circ) = -\dfrac{1}{\sqrt{2}}[/tex]
Given that:To find the value of cos(945°) using the unit circle.What are periodic functions?
A function returning to same value at regular intervals of specific length(called period of that function).
It is [tex]2\pi[/tex]
Thus, we have:
[tex]cos(x) = cos(2\pi +x) \: \forall \: x \in \mathbb R[/tex]
Using the periodic property of cosine:[tex]cos(945^\circ) = cos(2 \times 360^\circ + 225^\circ) = cos(2\pi + 2\pi + 225)\\ cos(945^\circ) = cos(2\pi) + 225) = cos(225^\circ)[/tex]
There is a trigonometric identity that:[tex]cos(\pi + \theta) = -cos(\theta)[/tex]
Thus:
[tex]cos(945^\circ) = cos(225^\circ) = cos(180^\circ + 45^\circ) = -cos(45^\circ) = -\dfrac{1}{\sqrt{2}}\\ cos(945^\circ) = -\dfrac{1}{\sqrt{2}}[/tex]
Note that wherever i have used [tex]\pi[/tex], it refers to [tex]\pi ^ \circ[/tex] (in degrees).
Thus, the value of cos(945°) is given by:
[tex]cos(945^\circ) = -\dfrac{1}{\sqrt{2}}[/tex]
Learn more about periodicity of trigonometric functions here:
https://brainly.com/question/12502943
Eric spends $30 to buy the ingredients for 5 batches of trail mix. Find the cost of the ingredients eric needs for one batch. How much would eric need for 2 batches?
Answer:
12
Step-by-step explanation:
To get the answer the first step, as it says is to find out how much would it cost for one batch, how to do that? easy! you just have to divided 30 by 5, which equals to 6 then you just multiply 6x2 which equals to 12. SO, your answer is 12
Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 22 days and a standard deviation of 6 days. 72% of all of these types of trials are completed within how many days
Answer:
25.5 days
Step-by-step explanation:
Mean number of days (μ) = 22 days
Standard deviation (σ) = 6 days
Z-score for the 72nd percentile (according to tabulated values) = 0.583
The z-score for any number of days, X, is determined by:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
The value of X that is greater than 72% of the trial times is:
[tex]0.583=\frac{X-22}{6}\\ X=25.5\ days[/tex]
Therefore, 72% of all of these types of trials are completed within 25.5 days.
g The weight of a certain type of apple is normally distributed with a mean of 10.56 ounces and standard deviation of 0.9 ounces. What is the first quartile, Q subscript 1, of the weight of this type of apple?
Answer:
First Quartile Q1 = 9.9525
Step-by-step explanation:
For a standard normal distribution,
First quartile Q1 = μ - 0.675 σ
From the question mean μ = 10.56
Standard deviation σ = 0.9
Plugging these values into the first quartile equation, we have;
Q1 = 10.56 -0.675(0.9)
Q1 = 10.56 - 0.6075
Q1 = 9.9525
Help me! Sorry for the other question.... let’s try it again! 1/2 x + 3/5 x = 5/4
Answer:
x = 1 3/22
Step-by-step explanation:
1/2 x + 3/5 x = 5/4
We need to get rid of the fractions by multiplying by 20 on each side
20 (1/2 x + 3/5 x) = 20 * 5/4
Distribute
10x + 12x = 25
Combine like terms
22x = 25
Divide each side by 22
22x/22 = 25/22
x = 22/22 + 3/22
x = 1 3/22
Answer:
[tex]x = 1\frac{3}{22}[/tex]
Step-by-step explanation:
=> [tex]\frac{1}{2} x + \frac{3}{5} x = \frac{5}{4}[/tex]
LCM = 20
So, Multiplying both sides by 20
=> [tex]20 (\frac{x}{2} + \frac{3x}{5}) = 5 * 5[/tex]
[tex]10 * x + 4*3x = 25\\10x+12x = 25\\22x = 25[/tex]
Dividing both sides by 22
[tex]x = \frac{25}{22}[/tex]
[tex]x = 1\frac{3}{22}[/tex]
* *4.8.21
Question Help
After the release of radioactive material into the atmosphere from a nuclear power plant in a country in 1982, the hay in that country was contaminated by a radioactive
isotope (half-life 5 days). If it is safe to feed the hay to cows when 9% of the radioactive isotope remains, how long did the farmers need to wait to use this hay?
The farmers needed to wait approximately
(Round to one decimal place as needed.)
days for it to be safe to feed the hay to the cows.
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Enter your answer in the answer box and then click Check Answer.
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a
Answer:
17.5 days
Step-by-step explanation:
The half life of this element is five days.
For the first five days it will decrease to 100*0.5=50%.
For the second five days it will decrease to 50*0.5= 25%
For the third five days it will decrease to 25*0.5 = 12.25%
It means in each day in the five days it reduce 0.1 of the it's remaining amount.
12.5 - 9 = 3.5 %
0.5 of 12.5 = 6.25%
It's going to be 15 days + 2.5 days= 17.5 days
When a person throws a ball into the air, it follows a parabolic path that opens downward as shown in the figure to the right. Suppose that the ball's height in feet after t seconds is given by h(t)=-16t^2+32t+2. If possible, determine the time(s) when the ball was at a height of 14 feet.
Answer:
0.5 seconds and 1.5 seconds.
Step-by-step explanation:
h(t) = -16t^2 + 32t + 2
14 = -16t^2 + 32t + 2
16t^2 - 32t - 2 + 14 = 0
16t^2 - 32t + 12 = 0
8t^2 - 16t + 6 = 0
4t^2 - 8t + 3 = 0
(2x - 3)(2x - 1) = 0
2x - 3 = 0
2x = 3
x = 3/2
x = 1.5
2x - 1 = 0
2x = 1
x = 1/2
x = 0.5
So, the ball was at 14 feet at 0.5 seconds and 1.5 seconds.
Hope this helps!
Find the area of the figure. Round to the nearest tenth if necessary. 386.3m^2 194.3m^2 193.1m^2 201.9m^2
Add the top and bottom numbers together, divide that by 2 then multiply by the height.
15.3 + 19.5 = 34.8
34.8/2 = 17.4
17.4 x 11.1 = 193.14
Answer is 193.1 m^2
A sample of 4 different calculators is randomly selected from a group containing 42 that are defective and 20 that have no defects. What is the probability that all four of the calculators selected are defective? No replacement. Round to four decimal places.
Answer: = approx 0.2006
Step-by-step explanation:
The probability that first 1 randomly selected calculator is defective is
P(1st defect)= 42/(42+20)=42/62=21/31
If the first calculator is defective the residual number of defective calculators is 42-1=41. The residual total number number of calculators is 62-1=61
So the probability that second calculator is defected
P(2nd defective)=41/61
If both previous calculators are defective the residual number of defective calculators is 42-2=40. Total residual number of calculators is 62-2=60
So the probability that third calculator is defected
P(3rd defective)=40/60=2/3
Finally the probability that also fourth calculator is defective is 39/59
P(4th defective)=39/59
The resulted probability that all 4 calculators are defective is
P(all 4 are defective)= P(1st defect)* P(2nd defect) * P(3rd defect)* P(4th defect)=21*41*2*39/(31*61*3*59)=67158/334707=0.200647... = approx 0.2006
Tres camiones transportan diferentes semillas:el primero lleva 1200 kg de arroz; el segundo 1100 kg de frijol y el tercero 550 kg de trigo. Si estas deben almacenarse en la menor cantidad de costales con la mayor capacidad posible de semillas, y sin que se combinen, determina cuánto se debe pagar por los costales si el precio de cada uno es de $5
Greetings from Brasil...
We need to use just GCD (greatest common divisor)
MDC in Brasil
GCD 1200, 1100 and 550 = 50
So we have to use bags with capacity of 50kg
In total we have (weight):
(1200 + 1100 + 550)kg
2850kg
total of bags:
Total Weight ÷ GDC
2850 ÷ 50
57 bags
1 bag = U$5
57 bag = X
X = 57.5
X = U$285Which of the following is a radical equation?
x+ square root 5 = 12
x² = 16
3+ square root 7 = 13
7 square root x = 14
Answer:
7 square root x = 14
Step-by-step explanation:
A radical equation will have the variable inside the radical
Answer:
D
Step-by-step explanation:
A radical equation persists when a radical includes a variable within it. In this case the x is in the radical, times 7. The rest of the answers do not have a variable in a radical.
HELP ASAP;The tree diagram represents an
experiment consisting of two trials.
Answer:
P(A) = 0.5
Step-by-step explanation:
Look from the tree root (left) and find A.
When you reach the first branch that shows A, the probability is on it's left, so
P(A) = 0.5
Enrique is making a party mix that contains raisins and nuts. For each ounce of nuts, he uses twice the amount of raisins. How many ounces of nuts and how many ounces of raisins does he need to make 24 ounces of party mix?
Answer:
16
Step-by-step explanation:
1x to 2x ratio
total is 24 oz, aka 3x or 1x+2x
24oz=3x
do some math
x=8oz
raisins = 2x = 16 oz
Answer:
Step-by-step explanation: 2x-16 oz
which of the following descriptions represent the transformation shown in the image? Part 1d
Answer:
(C) Translation of 2 units right, 1 up, and a reflection over the y-axis.
Step-by-step explanation:
Ideally, we are looking for a reflection of the red image over the y-axis, and to do that, we can see how we need to move the black image.
In order for points Q and Q' to be a reflection of each other, they need to have the same y value, and be the exact same distance from the y axis, so the point that Q has to be at is (-1,-3).
Q is right now at (-3,-4) so we can translate this.
To get from -3 to -1 in the x-axis, we go right by 2 units.
To get from -4 to -3 in the y-axis, we go up one unit.
Now, if we reflect it, the triangles will be the same.
Hope this helped!
Answer:
C.
Step-by-step explanation:
When you study the images, it is clear that the black triangle has to be reflected over the y-axis to face the same direction as the red triangle. So, choice A is eliminated.
Once you reflect the black triangle across the y-axis, you have points at (-1, -1), (3, -4), and (3, -2). Meanwhile, the red triangle's coordinates are at (-3, 0), (1, -3), and (1, -1). From these points, you can tell that the x-values differ by 2 units and the y-values differ by 1 unit.
All of these conditions match the ones put forth in option C, so that is your answer.
Hope this helps!
Need help with finding the kg
Answer:
3 kg
Step-by-step explanation:
Inverse relation:
y = k/x
In this case, the acceleration is inversely proportional to the mass, so using a for acceleration and m for mass, we have:
a = k/m
We need to find the value of k.
We use the given information to find k.
a = 9 m/s^2 when m = 5 kg
a = k/m
9 = k/5
k = 9 * 5 = 45
Now we can complete our equation:
a = 45/m
For a = 15 m/s^2, m = ?
15 = 45/m
15m = 45
m = 45/15
m = 3
Answer: 3 kg
The amount Q of water emptied by a pipe varies directly as the square of the diameter d. A pipe 5 inches in diameter will empty 50 gal of water over a fixed time period.
Assuming the same kind of flow, how many gallons of water are emptied in the same amount of time by a pipe that is 2 inches in diameter?
gallons are emptied.
Answer:
Q= 8
The amount emptied is 8 gallons of water
Step-by-step explanation:
First we need to create the equation for the above statement.
Q is directly proportional to the square of d
Q= kd²
Q= 50
d= 5
50= k5²
50 = k25
K = 50/25
K = 2
K is the constant of proportionality.
Now our equation is
Q= 2d²
Where Q = volume in gallons
d = pipe diameters in inch
For a pipe of diameter 2 inch
The amount of gallons of water emptied assuming the same kinf of flow is
Q= 2d²
Q= 2(2)²
Q= 2(4)
Q= 8
The amount emptied is 8 gallons of water
How do I find the length of AB
Also can I get explained on how to do it!!
ASAP
Answers
A-211.63
B-9.35
C-207
D-44.98
Answer:
Hello, there!!!
The answer is option D.
but you can also write 45 by rounding off, alright.
Hope it helps...
hello
now we know that this is a vertical triangle.
if C = 90° and B = 12°
90+12 = 102 180-102=78.
so A = 78°
now look at the A. A is looking to the CB.
so we can set up an equal.
A is 44
and
B is ?
if 78 is 44
12 is x 12×44÷78= 6.7692..
right now
AC = 6.7692
BC is = 44
this is a vertical triangle thats why the verticals angle's lookings (AB) square, should be the others lookings squares sum.
6.7692^2 = 45.2875..
44^2 = 1936
1936+45.2875= 1981.2875
now im taking 1981.2875 into the square root to find AB.
✓1981.2875 = 44.5
there were many numbers after the 1981 thats why it will probably 44.9
good luckk
Please help ASAP!!! Thank you so much!!! Just want confirm my answer it is y=150x-50. A concession stand at a football game took in $100 after being open for 1 hour. After 3 hours, the stand had taken in $400. Assuming a linear function, write an equation in the form y=mx+b that shows the revenue earned from being opened for x hours.
Answer: You have the correct answer. It is y = 150x-50
Nice work on getting the correct answer. For anyone curious, the explanation is below.
=============================================
x = number of hours the stand is open
y = amount earned
(1,100) is from the fact the stand is open 1 hour and earns $100
(3,400) is due to the stand earning $400 after 3 hours.
Slope Formula
m = (y2 - y1)/(x2 - x1)
m = (400-100)/(3-1)
m = 300/2
m = 150 is the slope, and it is the amount earned per hour. It is the rate of change.
Use m = 150 and (x,y) = (1,100) to find the value of b as shown below
y = mx+b
100 = 150(1) + b
100 = 150 + b
100-150 = b
-50 = b
b = -50 is the y intercept and it is the starting amount they earn. The negative earning indicates that they spent $50 to set up the stand, which is the cost of buying the food, equipment, etc.
So we have m = 150 as the slope and b = -50 as the y intercept.
Therefore, y = mx+b turns into y = 150x-50.
-------
As a check, plugging in x = 1 should lead to y = 100
y = 150x-50
y = 150(1)-50
y = 150-50
y = 100 and indeed it does
The same should be the case with (3,400). Plug in x = 3 and we should get y = 400
y = 150x-50
y = 150(3)-50
y = 450-50
y = 400, we have confirmed the answer by showing that the line y = 150x-50 goes through the two points (1,100) and (3,400).
The equation for revenue earned from being opened for x hours will be y=150x-50 so it is absolutely correct.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Given,
$100 for 1 hour
So,
x = 1 and y = 100
And,
$400 for 3 hour
So,
x = 3 and y = 400
Now the slope of the linear equation is given by
m = difference in ys coordinate / difference in xs coordinate
m = (400 - 300)/(3-1) = 150
So equation become
y = 150x + b
Now put (3,400) to find out b
400 = 150(3) + b
b = -50
So, equation
y = 150x - 50
Hence " The equation for revenue earned from being opened for x hours will be y=150x-50".
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Which of the following pairs consists of equivalent fractions? 12/18 and 10/15 12/20 and 10/25 8/16 and 3/4 5/3 and 3/5
Answer:
12/18 and 10/15
Step-by-step explanation:
12/18 simplifies into 2/3
10/15 simplifies into 2/3
12/20 simplifies into 3/5
10/25 simplifies into 2/5
8/16 simplifies into 1/2
3/4 simplifies into 3/4
5/3 simplifies into 5/3
3/5 simplifies into 3/5
The pairs consist of equivalent fractions will be 12/20 and 10/25. Then the correct option is A.
What is a fraction number?
A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of a numerator and a denominator.
Let's check all the options, then we have
A) 12/18 and 10/15
12/18 and 10/15
2/3 and 2/3
Yes, they are equivalent fraction numbers.
B) 12/20 and 10/25
12/20 and 10/25
3/5 and 2/5
They are not equivalent fraction numbers.
C) 8/16 and 3/4
8/16 and 3/4
1/2 and 3/4
They are not equivalent fraction numbers.
D) 5/3 and 3/5
5/3 and 3/5
They are not equivalent fraction numbers.
The pairs consist of equivalent fractions will be 12/20 and 10/25. Then the correct option is A.
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For functions f(x)=2x^2−4x+3 and g(x)=x^2−2x−6, find a. (f+g)(x) b. (f+g)(3).
Answer:
a) 3x^2-6x-3
b) 6
Step-by-step explanation:
f(x)=2x^2−4x+3
g(x)=x^2−2x−6
a) (f+g)(x) = (2x^2−4x+3) + (x^2−2x−6)
collect like terms
(f+g)(x) = 2x^2+x^2-4x-2x+3-6
(f+g)(x) = 3x^2-6x-3
b) (f+g)(3). This implies that x=3
recall (f+g)(3) = 3x^2-6x-3
(f+g)(3) = 3(3)^2-6(3)-3 = 27-18-3
(f+g)(3) = 27-21 =6