Answer:
To find the y-intercept of a line you need to first put it into the equation y=mx+b
x+3y=14 (minus x from each side)
3y=-x+14 (divide both sides by 3)
y=-1/3x+14/3
Your y-intercept is the b in the formula above, so your y-intercept would be 14/3
Hope this helps ;)
8. Mr. Gardner is contemplating which shullle service to take lo the airport. Fost
Shullle charges a $5 pick-up fee and $0.25 per mile. Steady Shullle cholges a $2
pick-up fee and $0.50 per mile.
Part A: When will the two plans cost the same amount
Part B: If the airport is 20 miles away, which company should Mr. Gardner choose?
Answer:
Frosts second mile and steadys 6th mike
Step-by-step explanation:
Part A: The two plans will cost the same amount when the distance to the airport is 12 miles.
Part B: For a 20-mile distance, Mr. Gardner should choose Fost Shuttle, costing $10 compared to $12 for Steady Shuttle.
Let's solve Part A first:
Part A:
Let's denote the distance to the airport as d miles.
For Fost Shuttle:
Cost = Pick-up fee + Cost per mile × Distance
Cost = $5 + $0.25 × d
For Steady Shuttle:
Cost = Pick-up fee + Cost per mile × Distance
Cost = $2 + $0.50 × d
Now, we'll set up an equation to find when the two plans cost the same amount:
[tex]\[5 + 0.25d = 2 + 0.50d\][/tex]
Solving for d:
[tex]\[0.25d - 0.50d = 2 - 5\]\[-0.25d = -3\]\[d = \frac{-3}{-0.25}\]\[d = 12\][/tex]
So, the two plans will cost the same amount when the distance is 12 miles.
For Part B:
Given the distance is 20 miles, let's calculate the cost for each company:
For Fost Shuttle:
Cost = $5 + $0.25 × 20 = $5 + $5 = $10
For Steady Shuttle:
Cost = $2 + $0.50 × 20 = $2 + $10 = $12
Comparing the costs, Mr. Gardner should choose Fost Shuttle as it costs $10 compared to $12 for Steady Shuttle.
A hemispherical tank is filled with water and has a diameter of 6 feet. If water weighs 62.4 pounds per cubic foot, what is the total weight of the water in a full tank, to the nearest pound?
Answer:
The total weight of the water in a full tank, to the nearest pound is 3527 pounds per cubic foot
Step-by-step explanation:
Given:
Diameter of the hemispherical tank = 6 feet
Weight of water per cubic foot = 62. 4 pounds
To Find:
The total weight of the water in a full tank, to the nearest pound?
Solution:
We know that the volume of a sphere is:
[tex]V =\frac{4}{3}\pi r^3[/tex]
where
r = is the radius
In the question we are given with diameter,
So
[tex]radius = \frac{diameter}{2}[/tex]
radius = [tex]\frac{6}{2}[/tex]
Radius = 3
We need the volume of the hemisphere
So the volume of the hemisphere will be half of the volume of teh sphere
[tex]\frac{V}{2} = \frac{2}{3}\pi r^3[/tex]
Thus the volume of the hemisphere is
[tex]V =\frac{2}{3} \pi r^3[/tex]
Now substituting the values
[tex]V = \frac{2}{3} \pi(3)^3[/tex]
[tex]V = \frac{2}{3}\pi(27)[/tex]
[tex]V = \frac{54 \pi}{3}[/tex]
[tex]V = \frac{169.56}{2}[/tex]
V= 56.52 cubic foot
Now, the total weight of water of:
W = 56.52 x 62.4
W= 3526.848 pounds per cubic foot
To the nearest pounds
W= 3527 pounds per cubic foot
Answer:
3529
Step-by-step explanation:
If you are here from delta math this is the Answer
A baker baker 40 cookies in and hour . What is the repentant and independent variable
Final answer:
The independent variable in the scenario is the time spent baking, and the dependent variable is the number of cookies baked. The size of the oven might be another independent variable if comparing productivity between different bakeries.
Explanation:
In the context of the question where a baker bakes 40 cookies in an hour, we are being asked to identify the dependent and independent variables in this scenario. First, let's define these terms:
The independent variable is the variable that you change or control in an experiment to test the effects on the dependent variable.The dependent variable is what you measure in the experiment and what is affected during the experiment.In this particular case, the independent variable could be the time spent baking, because it is what the baker controls. The dependent variable is the number of cookies baked, which depends on the amount of time the baker spends baking. If, for example, the baker decides to bake for two hours instead of one, we would expect the number of cookies baked to potentially double, assuming productivity remains constant.
In a different scenario, where comparing the productivity of bakers with different oven sizes – such as a Canadian worker with an industrial-size oven versus a U.S. worker with a smaller oven – the size of the oven could be seen as the independent variable affecting the dependent variable of productivity measured by the output of loaves of bread in an hour.
The table below shows the distance a train traveled over time. How can you determine the equation that represents this relationship?
Time (s) Distance (m)
2 25
4 50
6 75
8 100
I don’t understand this
Answer:
see the explanation
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
Let
x ----> the time in seconds
y ---> the distance in meters
In this problem we have a proportional relationship between the variables x and y
Find the constant of proportionality k
[tex]k=\frac{y}{x}[/tex]
For x=2, y=25 ---> [tex]k=\frac{25}{2}=12.5[/tex]
For x=4, y=50 ---> [tex]k=\frac{50}{4}=12.5[/tex]
For x=6, y=75 ---> [tex]k=\frac{75}{6}=12.5[/tex]
For x=8, y=100 ---> [tex]k=\frac{100}{8}=12.5[/tex]
so
The value of k is [tex]12.5\ \frac{m}{sec}[/tex]
In this problem the value of k or slope represent the speed of the train
The linear equation is equal to
[tex]y=12.5x[/tex]
or
[tex]Distance=12.5Time[/tex]
-7p-4>26p-94 solve for p
Answer:
[tex]\large\boxed{p<\dfrac{30}{11}\to p\in\left(-\infty,\ \dfrac{30}{11}\right)}[/tex]
Step-by-step explanation:
[tex]-7p-4>26p-94\qquad\text{add}\ 7p\ \text{to both sides}\\\\-7p+7p-4>26p+7p-94\\\\-4>33p-94\qquad\text{add 94 to both sides}\\\\-4+94>33p-94+94\\\\90>33p\qquad\text{divide both sides by 33}\\\\\dfrac{90}{33}>\dfrac{33p}{33}\\\\\dfrac{30}{11}>p\to p<\dfrac{30}{11}[/tex]
Evaluate –x + (–7.5) for x = 6.3.
Answer:
Step-by-step explanation:
The answer is 1.2, you want to replace the x with the 6.3 and then the -7.5 ends up turning into a positive. You then add the two together -6.3 + 7.5 = 1.2
A grocery store bought milk for $2.70 per half gallon and stored it in two refrigerators. During the night, one refrigerator malfunctioned and ruined 12 half gallons. If the remaining milk is sold for $4.02 per half gallon, how many half gallons did the store buy if they made a profit of $60.00?
The store initially bought 82 half gallons of milk.
To solve the problem, we need to find out how many half gallons of milk the store initially bought. We can set up an equation to represent the situation where the cost of milk is subtracted from the sales to find the profit.
Let's assume the store bought x half gallons of milk. Then, the cost of the x half gallons is x multiplied by $2.70:
Cost = 2.70x dollars
The store ruined 12 half gallons, so they can only sell x - 12 half gallons. The revenue from selling each half gallon is $4.02, so the total revenue from selling x - 12 half gallons is:
Revenue = 4.02(x - 12) dollars
We are told the store made a profit of $60, so the revenue minus the cost equals the profit:
4.02(x - 12) - 2.70x = 60
Now we solve for x:
4.02x - 48.24 - 2.70x = 60
1.32x - 48.24 = 60
1.32x = 108.24
x = 82 half gallons
Therefore, the store initially bought 82 half gallons of milk.
A submarine dives at an angle of 13 degrees to the surface of the water. The submarine travels at a speed of 720 feet per minute. About how deep is the sun after 5 minutes?
The depth of sun after 5 minutes is 809.82 feet
Solution:
A submarine dives at an angle of 13 degrees to the surface of the water
The submarine travels at a speed of 720 feet per minute
The figure is attached below
ACB is a right angled triangle
AB is the distance between surafce of water and submarine
BC is the depth of submarine
Let "x" be the depth of sun after 5 minutes
Therefore, distance between submarine and surface of water is:
[tex]AB = 720 \frac{feet}{minute} \times 5 \text{minute} = 3600 feet[/tex]
Submarine dives at an angle of 13 degrees to the surface of the water
Therefore, angle A = 13 degrees
Now we have to find BC
By definition of sine,
[tex]sin \theta = \frac{opposite}{hypotenuse}[/tex]
Here, opposite = BC = x
hypotenuse = AB = 3600 feet
Thus, we get,
[tex]sin \theta = \frac{BC}{AB}\\\\sin \theta = \frac{x}{3600}\\\\sin 13 = \frac{x}{3600}\\\\0.2249 = \frac{x}{3600}\\\\x = 3600 \times 0.2249\\\\x = 809.82[/tex]
Thus the depth of sun after 5 minutes is 809.82 feet
X=4-2y
3x-2y=4 Substitution
Answer:
The solution is x = 2 and y = 1.Step-by-step explanation:
The given equations are x = 4 - 2y.......(1) and 3x - 2y = 4......(2).
Putting the value of the first equation in the second, we get
3x - 2y = 4
or, 3(4 - 2y) - 2y = 4
or, 12 - 6y - 2y = 4
or, 8y = 8
or, y = 1.
Putting the value of y in the first equation, we get x = 4 - 2 = 2.
Answer:
The answer is [tex]x=2[/tex] and [tex]y=1.[/tex]
Step-by-step explanation:
Given:
X=4-2y
3x-2y=4
Now, to solve it by substitution.
[tex]x=4-2y[/tex] .....(1)
[tex]3x-2y=4[/tex] ......(2)
Now, solving the equation (2) by substitution:
[tex]3x-2y=4[/tex]
Substituting the value of [tex]x[/tex] from equation (1):
[tex]3(4-2y)-2y=4[/tex]
[tex]12-6y-2y=4[/tex]
[tex]12-8y=4[/tex]
Subtracting both sides by 12 we get:
[tex]-8y=-8[/tex]
Dividing both sides by -8 we get:
[tex]y=1.[/tex]
Now, substituting the value of [tex]y[/tex] in equation (1):
[tex]x=4-2y[/tex]
[tex]x=4-2(1)[/tex]
[tex]x=4-2\times1[/tex]
[tex]x=4-2[/tex]
[tex]x=2.[/tex]
Therefore, the answer is [tex]x=2[/tex] and [tex]y=1.[/tex]
Please help me guys with this than you
Answer:theres nothimh here to answer
Step-by-step explanation:
Why is important to use mixed numbers in real life
Answer:
It is important to use mixed numbers in real life, because it can help you find the measurements for when you are buying ingredients or baking something.
Hope this helps ;)
Step-by-step explanation:
Zeeshan has collected 812 autographs. Each autograph is either from a baseball star, a football star, or a rock star. He has an equal number of autographs for each group. How many autographs does he have in each group?
Answer:
270
Step-by-step explanation:
Is 12=24-y and Y equals 12
Answer: Yes.
Step-by-step explanation: if y=12, then 24-12=24 aka 24-y=12
is (4•6)^3 equivalent to 4•6^3
Answer:
No, (4•6)^3 is not equivalent to 4•6^3
Step-by-step explanation:
(4•6)^3
4•6^3
Let's solve each one at a time, starting with (4•6)^3
(4•6)^3
Multiply inside the parenthesis first
24^3
Multiply 24 by itself 3 times (Exponents)
24 * 24 * 24
13,824
Now let's solve 4•6^3
4•6^3
Exponents come before multiplication in the order of operations, so multiply 6 by itself 3 times.
4 * (6x6x6)
4 * 216
864
Now we can compare the solutions
13,824 > 864
No, 13,824 is not equivalent to 864.
Hope this helps :)
xavier and yolanda have been married for 40 years. Yolanda is 4 years older than Xavier. Now the sum of their ages is 126. How old was yolanda when they married
Through algebra, we found that Xavier's current age is 61, which makes Yolanda 65. Subtracting the 40 years of marriage from their current ages, we determined that Yolanda was 25 years old when they got married.
Explanation:The question given by the student is a problem that can be solved with simple algebra. To find out how old Yolanda was when they married, we first need to establish the current ages of Xavier and Yolanda based on the information given.
Let's denote Xavier's current age as x years. Consequently, Yolanda's current age will be x + 4 years (since she is 4 years older than Xavier). According to the problem, the sum of their ages now is 126 years. We can set up the following equation based on this information:
x + (x + 4) = 126
By solving the equation:
Combine like terms: 2x + 4 = 126
Subtract 4 from both sides: 2x = 122
Divide both sides by 2: x = 61
This means that Xavier is now 61 years old, and Yolanda is x + 4, which is 65 years old. Since they have been married for 40 years, we subtract 40 from their current ages to get their ages at the time they got married. So, Yolanda was 25 years old when she got married.
graph the function
y = x ÷ 4
Answer:
Slope is 1/4 y-intercept is 0
Step-by-step explanation:
I uploaded the graph below
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Write down the total and the mean for each of the sets below.
a 4, 6, 8, 10 and 12
Answer:
Total: 40
Mean: 8
Step-by-step explanation:
To find the total, we add the numbers together and get 40. Then, to find the mean, we take the total and divide by the number of numbers, which is 5, to get our answer: 8
-AXZ
Which is the solution to the inequality?
y+15 <3
y<-12
y>-12
y<18
y > 18
y < –12
Solution:
Step 1: Given inequality is y + 15 < 3.
To find the solution to the inequality.
Step 2: Subtract –15 on both sides to equal the expression.
⇒ y + 15 –15 < 3 –15
Step 2: Using addition identity property, any number adding with zero gives the number itself.
⇒ y + 0 < –12
⇒ y < –12
Hence the solution to the inequality is y < –12.
Answer:
Step-by-step explanation:
It’s b
(9x + 25) (13x - 19) (17y + 5)
Answer:
1989xsquared y + 585xsquared+ 2618xy + 770x - 8075y - 2375
Step-by-step explanation:
(9x + 25) x (13x - 19) x (17y + 5)
(117x squared - 171x + 325x - 475) x (17y + 5)
(117x squared + 154x - 475) x (17y + 5)
[tex](9x + 25) (13x - 19) (17y + 5)=1989x^2y + 585x^2+ 2618xy + 770x - 8075y - 2375[/tex]
We have to simplify the expression:
(9x + 25)(13x - 19)(17y + 5)
Multiply the first two expressions as
[tex][9x(13x - 19)+25(13x - 19)](17y + 5)[/tex]
[tex]=(117x^2 - 171x + 325x - 475)(17y + 5)[/tex]
[tex]=(117x^2 + 154x - 475)(17y + 5)[/tex]
[tex]=17y(117x^2 + 154x - 475) + 5(117x^2 + 154x - 475)\\=1989x^2y + 585x^2+ 2618xy + 770x - 8075y - 2375[/tex]
Therefore after simplifying , we get
[tex](9x + 25) (13x - 19) (17y + 5)=1989x^2y + 585x^2+ 2618xy + 770x - 8075y - 2375[/tex]
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How do u solve Y+x=7 step by step
Answer:
just use mathpapa it's a game changer itll change your life
100 POINTS!!! Need answer NOW! only correct answers! don't answer if you don't know how to work the problem!!
1.) Mr. Smith’s class sold wrapping paper for $3.50 each and Mr. Davis’ class sold magazines for $2.75 each. Together, the classes sold 72 items and earned $222 for their school.
Write and solve a system of equations that model the problem. Show all your work.
Which class earned more money?
How much more money did that class earn?
Answer:
Mr. Smith's class earned more money.They earned $2 more than Mr. Davis' class.Step-by-step explanation:
[tex]\text{Let}\\\\x-\text{number of wrapping paper of Mr. Smith's class}\\y-\text{number of magazines of Mr. Davis' class}\\\$3.50x-\text{the amount obtained from the sale of wrapping paper}\\\$2.75y-\text{the amount obtained from the sale of magazines}[/tex]
[tex]\bold{SYSTEM\ of\ EQUATIONS:}\\\\\left\{\begin{array}{ccc}x+y=72&\text{subtract}\ y\ \text{from both sides}\\3.5x+2.75y=222\end{array}\right\\\\\left\{\begin{array}{ccc}x=72-y&(1)\\3.5x+2.75y=222&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\3.5(72-y)+2.75y=222\qquad\text{use the distributive property}\\\\(3.5)(72)+(3.5)(-y)+2.75y=222\\\\252-3.5y+2.75y=222\qquad\text{substract 252 from both sides}\\\\-3.5y+2.75y=222-252\qquad\text{combine like terms}[/tex]
[tex]-0.75y=-30\qquad\text{divide both sides by (-0.75)}\\\\\boxed{y=40}\\\\\text{Put it to (1):}\\\\x=72-40\\\\\boxed{x=32}\\\\\$3.5x=\$3.5\cdot32=\$112\\\\\$2.75\cdot40=\$110\\\\\$112-\$110=\$2[/tex]
which inequality represents the graph below ?
what is the equation of the following line? (7,2) (0,0)
A) y=2/7x
B) y=-2x
C)y=-7x
D)y=2x
E)y=1/7x
F) y=7x
Answer:
Step-by-step explanation:
(7,2) , (0,0)
slope = (y2 - y1) / (x2 - x1) = (0 - 2) / (0 - 7) = -2/-7 = 2/7
y = mx + b
slope(m) = 2/7
(0,0)...x = 0 and y = 0
now sub
0 = 2/7(0) + b
0 = b
ur equation is : y = 2/7x + 0.....same as y = 2/7x <====
The equation of the line is y = ( 2/7 )x where the slope is m = 2/7
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 7 , 2 )
Let the second point be Q ( 0 , 0 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 2 - 0 ) / ( 7 - 0 )
m = 2/7
Now , the equation of line is y - y₁ = m ( x - x₁ )
On simplifying , we get
y - 0 = ( 2/7 ) ( x - 0 )
y = ( 2/7 )x
Hence , the equation of line is y = ( 2/7 )x
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A 50-foot tree casts a shadow 9 feet long. The sine of the angle between the ground and the line that connects the top of the shadow to the top of the tree is approximately
Final answer:
The sine of the angle between the ground and the line connecting the top of the shadow to the top of the tree, given a 50-foot tree and a 9-foot shadow, is approximately 0.984, calculated using the definition of sine in a right triangle and the Pythagorean theorem.
Explanation:
The question involves finding the sine of the angle between the ground and the line connecting the top of the shadow to the top of the tree, given that a 50-foot tree casts a 9-foot long shadow. In this scenario, we can visualize a right triangle where the tree represents the opposite side (height), the shadow represents the adjacent side (base), and the hypotenuse is the line from the top of the tree to the end of the shadow on the ground.
To find the sine of the angle, we use the definition of sine in a right triangle, which is sine(angle) = opposite / hypotenuse. However, before we can do that, we need to determine the length of the hypotenuse using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a² + b² = c²).
Let's calculate:
a (opposite) = 50 feet (Height of the tree)
b (adjacent) = 9 feet (Length of the shadow)
c (hypotenuse) = √(50² + 9²) = √(2500 + 81) = √2581 = 50.8 feet (approximately)
Now, we can calculate the sine of the angle:
sine(angle) = opposite / hypotenuse = 50 / 50.8 ≈ 0.984
Therefore, the sine of the angle between the ground and the line connecting the top of the shadow to the top of the tree is approximately 0.984.
what is 5.12 times 0.3
Answer:
1.536
Step-by-step explanation:
Find the equation of a line with the given points.
(0, -2) (-2, 10)
Oy=-2x + 10
Oy = 4x + 10
Oy=x-2
Oy=-6x - 2
Answer:
y=-6x-2
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(10-(-2))/(-2-0)
m=(10+2)/(-2)
m=12/-2
m=-6
y-y1=m(x-x1)
y-(-2)=-6(x-0)
y+2=-6(x)
y+2=-6x
y=-6x-2
Nicki dashed up the shore and into the forest, not stopping
to think. She could feel the footsteps behind her, the
nameless thugs whose loyalties could be bought and sold
like sacks of sugar. Those men were fast; she hoped she
was faster. For the first time since her journey began, a
sliver of doubt entered Nicki's mind. Why did she start all
this in the first place? The doubt would follow her as the
men continued to chase her around the island. They were
unrelenting hounds. She was their timid prey.
Which statement best describes why the men chasing Nicki are examples of
flat characters?
O
A. The men reveal that they are chasing Nicki because she stole
sugar from them.
O
B. The men are unsure if they are faster than Nicki.
O
C. The men simply keep chasing Nicki, and their motivations are not
revealed
O
D. The men are conflicted about whether they should continue to
chase Nicki
Answer:
C. The men simply keep chasing Nicki, and their motivations are not
revealed
a wave has a wavelength of 5m and a frequency of 68 hertz what is the speed
Answer:
Therefore the Speed of a wave is 340 m/s.
Step-by-step explanation:
Given:
Wave Length = 5 m
Frequency = 68 hertz
To Find:
Speed = ?
Solution:
Wave Speed:
Wave speed is the distance a wave travels in a given amount of time, such as the number of meters it travels per second.
Wave speed is related to wavelength and wave frequency.
The Formula is given by
[tex]Speed = Wavelength\times Frequency[/tex]
Substituting the values we get
[tex]Speed = 5\times 68=340\ m/s[/tex]
Therefore the Speed of a wave is 340 m/s.
the regular shipping fee (in dollars) for an online computer store is given by the expression 0.5w + 4.49 where w is the weight (in pounds) of the item. the fee (in dollars) for rush delivery is given by 0.99w + 6.49. You purchase a 26.5 pound computer. How much do you save by using regular shipping instead of rush delivery?
By calculating the shipping fees for regular and rush delivery for a 26.5 pound computer, we find that regular shipping saves approximately 14.90 dollars.
Explanation:We must first calculate the fee for each method and then subtract the regular "shipping fee" from the rush delivery fee to find the savings.
Using the given expression, the regular shipping fee for a 26.5 pound computer is: 0.5*26.5 + 4.49 = 17.74 dollars. Meanwhile, the rush delivery fee for the same computer, using the other given expression, would be: 0.99*26.5 + 6.49 = 32.635 dollars.
Subtracting the regular fee from the rush fee, we find: 32.635 - 17.74 = 14.895 dollars. Therefore, you save about 14.90 dollars by choosing regular shipping over rush delivery.
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64/9 improper fraction
improper fraction
Answer:
If you want the mixed number,it is 7 1/9
Step-by-step explanation:
Divide using long division. The whole number portion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction.