Answer:
When the boat is 6 m from the dock, it is approaching the dock at the rate of √37/6 m/sec.
Step-by-step explanation:
Let x = distance of the boat from the dock at time t
y = length of rope at time t
Draw a right triangle with horizontal leg x, vertical leg 1, and hypotenuse y.
We know that dy/dt = -1 and want to find dx/dt when x = 6.
By the Pythagorean Theorem, x2 + 12 = y2.
2x(dx/dt) = 2y(dy/dt)
dx/dt = y(dy/dt) / x When x = 6, y2 = 36 + 1 = 37
So, y = √37
dx/dt = -√37 / 6
When the boat is 6 m from the dock, it is approaching the dock at the rate of √37/6 m/sec.
2.9 - 4.8n - 3n + 5 simplified
Answer:
-7.8n+7.9
Step-by-step explanation:
Julia meaured a line to be 16. 1 inche long. If the actual length of the line i 17. 1 inche, then what wa the percent error of the meaurement, to the nearet tenth of a percent?
The percent error of the meaurement is 6.21%
Julia meaured a line to be 16. 1 inche long
The actual length of the line i 17. 1 inche
Error in length = actual length - measured length
Error in length = 17.1 - 16.1 = 1 inch
Percent of error is defined as the difference between a measured or experiment value and an accepted or known value, divided by the known value, multiplied by 100
error percent = error/ known value x 100
= 1/16.1 x 100
= 6.21%
Therefore, the percent error of the meaurement is 6.21%
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i need help on this , Thanks
Answer:
∴ x = 90
Step-by-step explanation:
(180 - x)° = x° (vertically opposite angles)
180 - x = x
-2x = -180
2x = 180
∴ x = 90
8-9. If AG = 2, GF = 5, FE = 3, GB = 6, CD = 7 and GB || FC || ED, find the lengths of the missing sides?
AB=?
BC=?
FC=?
ED=?
Answer:
AB = 4 2/3BC = 11 2/3FC = 21ED = 30Step-by-step explanation:
In the given triangle AED, segments GB and FC are parallel to base ED. Points G and F are on segment AE in that order. Lengths AG=2, GF=5, FE=3, GB=6, and CD=7 are given. You want the lengths of AB, BC, FC, and ED.
Proportional segmentsSegments of transversals crossed by parallel lines are proportional:
AG : GF : FE = AB : BC : CD
2 : 5 : 3 = AB : BC : 7
Multiplying the first ratios by 2 1/3 will give the second ratios:
2 : 5 : 3 = 4 2/3 : 11 2/3 : 7
This lets us conclude ...
AB = 4 2/3
BC = 11 2/3
Similar trianglesCorresponding segments of similar triangles are proportional:
AG : GB = FA : FC = AE : ED
2 : 6 = (5+2) : FC = (5+2+3) : ED
We notice the second number in the first ratio is 3 times the first number. That means these ratios are ...
2 : 6 = 7 : 21 = 10 : 30
This lets us conclude ...
FC = 21
ED = 30
The lengths of the missing sides are calculated to be
AB = 5BC = 12FC = 21ED = 30How to find the lengths of the missing sidesThe parallel lines in the figure created similarity between the dimensions, this makes the ratio of the dimensions equal
The given dimensions that is used to find the missing sides
Solving for AB
AB / CD = AG / FE
AB / 7 = 2 / 3
cross multiplying
3 * AB = 7 * 2
AB = 14/3 = 4.667
Using AB, GF is calculated
AB / BC = AG / GF
14/3 / BC = 2 / 5
cross multiplying
BC = (5 * 14/3) / 2
BC = 35/3 = 11.667
Solving for FC
GB / FC = AG / A'F
6 / FC = 2 / (2 + 5)
cross multiplying
2 * FC = 6 * 7
FC = 42/2 = 21
Solving for ED
GB / ED = AG / AE
6 / ED = 2 / (2 + 5 + 3)
cross multiplying
2 * ED = 6 * 10
ED = 60/2 = 30
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A new soup recipe contains 33\%33%33, percent less sodium per serving than the old soup recipe. The old soup recipe contained xxx milligrams of sodium per serving.
Which of the following expressions could represent the amount of sodium per serving, in milligrams, in the new soup recipe?
The expression that could represent the amount of sodium per serving, in milligrams, in the new soup recipe is y = 0.67x
How to get the expression?From the information, the new soup recipe contains 33% less sodium per serving than the old soup recipe.
Let's say Sodium in an old soup recipe per serving = x mg
Let's say Sodium in a new soup recipe per serving = y mg
The new soup recipe contains 33% less sodium per serving than the old soup recipe
y = x - (33/100)x
100y = 100x - 33x
100y = 67x
Divide through by 100
y = 0.67x
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Solve for x with steps. Will mark brainliest.
x = 1.53347526
Take the log of both sides of the equation.
[tex]ln(2^{3x-1} ) = ln(3^{x-2} )[/tex]
Expand [tex]ln(2^{3x-1} )[/tex] by moving 3x-1 outside the logarithm
[tex](3x-1)ln(2)= ln(3^{x-2} )[/tex]
Move x-2 outside the logarithm [tex]ln(3^{x-2} )[/tex]
[tex](3x-1)ln(2) = (x-2)ln(3)[/tex]
Solve the equation for x
[tex]x = -[\frac{{2ln(3)-ln(2)}}{3ln(2)-ln(3)} ][/tex]
The value of x is 1.53347526(After applying the log values)
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Eli loads identical crates onto a truck with a load limit of 2000 pounds. Each crate weighs 125 pounds. A function modeling this situation, where y represents the total weight of the crates in pounds, has a range described by which inequality?.
Using the range idea, the following scenario is represented by the inequality 0 ≤ y ≤ 2000. Here option D is the correct answer.
A function's range is the set that contains all of the output values that the function can take. In the context of this problem, the following input and output are provided:
Input the number of crates that have been loaded into the vehicle. Total weight of the crates loaded into the vehicle as output.
Because the weight of an amount can never be negative, and the greatest weight is 2,000 pounds, as stated in the issue, the range in this context is reflected by the following inequality: 0 ≤ y ≤ 2000.
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What are 3 signs of symptoms of an allergic reaction?.
Hives, itching, and pale or flushed skin are examples of allergies. reduced blood pressure (hypotension) breathing difficulties and wheezing can result from airway constriction and swelling of the tongue or throat.
What causes allergies?
Your body reacts to an allergen when it is generally harmless, such as pollen, mold, animal dander, latex, certain foods, or insect bites. The symptoms of allergies can range in severity from minor (rash or hives, itching, runny nose, watery/red eyes) to life-threatening.Why do allergies occur?
If your immune system overreacts to something that is typically harmless but causes an allergic reaction in someone who is sensitive to it, you will experience allergy symptoms. We call this chemical an allergy.
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NEED HELP FAST
question is in the picture attached
Answer:
x=12.99
h=7.5
Step-by-step explanation:
we us cosine rule first to look for OBthe triangle OCB is an isosceles triangle whereby angleOCB=120,angleCOB=angleCBO=30
thus length of BC is 15
[tex]cosine \: rule \\ a {}^{2} = b {}^{2} + c {}^{2} - 2bc \cos(a) [/tex]
=(15^2+15^2)-(2×15×15×cos 120)
=450-(-225)
a^2 =675
a=25.98=OB
finding xx=15sin 60
=12.99
finding hh=15sin 30
=7.5
c. What is the slope?
Step-by-step explanation:
the slope is the inclination of a line, or of the tangent (also a line) on a point of a bent curve.
it is expressed as ratio (y coordinate change / x coordinate change) when going from one point on the line or curve to another point on the line.
it tells us how many units y changes when x changes a certain number of units (like 1).
it is positive, if the line goes up (when going from left to right). the larger the value, the steeper the line goes up.
it is negative, if the line is going down (again, going from left to right). the lower the value, the steeper the line goes down.
a horizontal line has a slope of 0/x = 0.
a vertical line has a slope of y/0, which is undefined, or sometimes expressed as infinite.
Francis mixes 3/8 gal of white paint, 2 7/8 gal of blue paint, and 5/4 gal of red paint.
How much white paint will Francis need to make 7 gallons of the same color paint?
Francis has made _____ gal of paint when he first mixes the three colors.
The constant of proportionality of white paint to gallons of mixed paint is ______
Francis will need __________ gal of white paint to mix together 7 gals of the same color paint.
PLEASE HELP!!!!!
Blank one the options are: thirteen-fourths, thirty-one eights, or nine-halves.
Blank two the options are: one-seventh, one-twelfth, three twenty-sixths, or thirty-six thirds
Blank three the options are one, eighty-four, seven twelfths, or twenty-one twenty-sixths
Please help me with the problem.
The gal in the first mixes is nine-halves, the constant of proportionality is one-twelfth and the white paint required in 7 gals is seven twelfths
How to determine the quantity in mixes and the constant of proportionality?
Given:
White paint = 3/8 gal
Blue paint = 2 7/8 gal
Red paint = 5/4 gal
Gallons of first mixes = White paint + Blue paint + Red paint
Gallons of first mixes = 3/8 + 2 7/8 + 5/4 = 9/2 gal
The constant of proportionality of white paint to gallons of mixed paint:
constant of proportionality = white paint volume/ mixed paint volume
constant of proportionality = (3/8) / (9/2) = 1/12
The constant of proportionality of white paint to gallons of mixed paint gives the fraction of white color in the total volume
In order to make 7 gallons of the same color paint, the quantity of white paint he will need is:
White paint in 7 gallons = 1/12 x 7 = 7/12
Therefore, blank one is nine-halves, blank two is one-twelfth and blank three is seven twelfths
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Which symbol correctly compares these two fractions?
3/10 ? 1/3
A. =
B. >
C.
Answer:
Step-by-step explanation:
3/10 < 1/3
Delaney would like to make a 5 lb but mixture that i 60% peanut and 40% almond. He ha everal kind of peanut and everal kind of a mixture that i 20% peanut and 80% almond. Let p repreent the number of punt of peanut needed to make the mixture, and let m repreent the number of pound of the 80% almond-20% peanut mixture. What i the ytem that model thi ituation
The system that models the equation is m = 2.5 lb.
This is a mixed-up issue. The combination of
80% almonds and 20% peanuts make up combination A.
Completely peanuts in mixture B
both the
As a combination, use 60% peanuts and 40% almonds.
Since mixture C is created by combining mixtures A and B, we may calculate its combined weight in pounds to be 5 pounds.
Hence, we
Let m be the weight in pounds of mixture A (20% peanuts, 80 % almonds).
and
50-m is the quantity of mixture B in pounds.
Consequently, the set of equations that models this circumstance is:
0.20m + 1(50-m) = 0.60(5) (5)
0.80m + 0(50-m) = 0.40(5)
Equation 2's solution for m gives us
m = 2.5 lb.
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Dr. Potter provides vaccinations against polio and measles. Each polio vaccination consists of 4 44 doses, and each measles vaccination consists of 2 22 doses. Last year, dr. Potter gave a total of 60 6060 vaccinations that consisted of a total of 184 184184 doses. How many polio vaccinations and how many measles vaccinations did dr. Potter give last year?.
The number of polio vaccinations is 32 and measles vaccination is 28
Let p represent the number of polio vaccines and let m represent the number of measles vaccines.
We know that each polio vaccine consists of 4 doses, and each measles vaccine consists of 2 doses.
Dr. Potter gave a total of 60 vaccinations last year. Therefore, the sum of the number of polio vaccines and measles vaccines must total 60. Therefore:
p+m=60
Together, they consisted of 184 doses.
Since each polio vaccine has 4 doses, the amount of doses for p polio vaccines is 4p.
And since each measles vaccine has 2 doses, the amount of doses for m measles vaccines is 2m.
So:
4p+2m=184
We now have a system of equations:
p+m=60
4p+2m=184
We can solve using elimination. Let’s multiply the first equation by -2. So:
-2p-2m=-120
Now, we can add this to the second equation. Hence:
(-2p+4p)+(-2m+2m)=(-120+184)
2p=64
p=32
Therefore, Dr. Potter gave out 32 polio vaccinations
p+m=60
By the first equation:
p+m=60
Substitute 32 for p to get
32+m=60
m=60-32
m=28
So, 28 measles vaccinations were given out.
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madge is six years older than bruce. in five years the sum of their ages will be thirty-six. how old is bruce
Answer:
Bruce is 10 years old.
Step-by-step explanation:
m - Madge age.
b - Bruce age.
Madge is six years older than Bruce.
m=b+6 or m-6=b
In five years the sum of their ages will be 36.
m+5 - Madge age after 5 years.
b+5 - Bruce age after 5 years.
m+5+b+5=36
m=b+6
b+6+5+b+5=36
2b+16=36
2b=36-16
2b=20 /:2
b=10
m=b+6=10+6=16
.
Complete the statement. Round to the nearest hundredth if necessary.
12 cu ft ≈ gal
Answer:6978
Step-by-step explanation:304585
Despeja la variable c del siguiente ejercicio E=mc^2
Answer:
Step-by-step explanation:
m = E / c²
R is inversley propeotional to A When R=12, A=1.5
The answer is 3.6 and 2 respectively.
What is the proportionality constant?
The proportionality constant is the ratio that connects two given values in a proportional relationship. The constant of proportionality is also known as the constant ratio, constant rate, unit rate, constant of variation, and even the rate of change.
We have,
R = k / A
where,
k is the proportionality constant
12 = k / 1.5
k = 12 * 1.5
k = 18
now
a) The value of R is?, when A=5.
R = 18 / 5
= 3.6
b) The value of A is? R=9.
A = 18 / 9
= 2
Hence, the answer is 3.6 and 2 respectively.
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Which of the following graphs represents the solution(s) of the following system?
X^ - y = -2, 4y - 8 = x
The graph that represents the solutions of the given system of equations is attached below.
We are given a system of equations. The first equation is a quadratic polynomial. The second equation is linear in nature. The equations are given below.
x² - y = -2
4y - 8 = x
We need to find the solution to the equations using a graph. The graph of the equations is attached below. The graph of the first equation is represented by an upward parabola. The graph of the second equation is represented by a straight line. The intersection points of the two curves are the solutions to the given system of equations.
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Please help me with both questions. the question one put a, b, c, or d. Like this: 1=a and same for the second question like 2=c. The test is due soon please help!
Step-by-step explanation:
4.
p(-2) = 6×-2 + 2 = -12 + 2 = -10
p(4) = 6×4 + 2 = 24 + 2 = 26
so,
p(-2) is smaller than p(4)
3.
r(-1) = -2×-1 - 5 = 2 - 5 = -3
Nathan ha a $75 budget to rent a car for a day. The daily rental charge i $29. 50 and then he will alo have to pay 0. 55 per mile. How many mile can he drive the car without exceeding hi budget? (All partial mile are counted a full mile. )
Nathan can drive 83 miles without exceeding the budget.
Let us assume the number of miles Nathan can go in $75 budget be x. Now forming the equation based on the mentioned information -
The total budget = daily rental charge + number of miles × cost per mile
Keep the values in formula -
75 = 29.50 + 0.55x
Rewriting the equation according to variable x
0.55x = 75 - 29.50
Performing subtraction on Right Hand Side of the equation
0.55x = 45.5
x = 45.5 ÷ 0.55
Performing division on Right Hand Side of the equation
x = 82.7
As 0.7 will be counted a mile, thus, Nathan can drive 83 miles.
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interval notation for t - 1/3 >= -12/9
Answer: [-1, ∞)
Step-by-step explanation:
First, we will simplify the equation.
Given:
t - 1/3 ≥ -12/9
Add 1/3 to both sides of the equation:
t ≥ -1
Next, we know that a bracket is used when representing greater than or equal to and less than or equal to. Here, it's greater than or equal to so we will use a bracket on the left side.
Then, t can be any value to infinity above -1, so we will use ∞) on the right side.
[-1, ∞)
Katalin drove 300 miles on her vacation. she drove an average of 1.9 times faster on the second 150 miles of her trip than she did on the first 150 miles of her trip. which expression represents the time she spent driving?
The expression represents the time she spent driving is [tex]\frac{228.95}{x}[/tex]
The expression represent the time she spent driving can be calculated as follows:
We know that
Time = [tex]\frac{distance}{ speed}[/tex]
Let x be her speed on the first half of the trip.
Then for first half , the tiime she takes is
T1= [tex]\frac{150}{x}[/tex]
while in a second half the time taken by her is
T2= [tex]\frac{150}{1.9x}[/tex]
T2= [tex]\frac{78.95}{x}[/tex]
the total time she spent on driving is
T1 + T2 = [tex]\frac{150}{x}[/tex] + [tex]\frac{78.95}{x}[/tex] = [tex]\frac{228.95}{x}[/tex]
Hence, the expression represents the time she spent driving is [tex]\frac{228.95}{x}[/tex]
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If the length of a rectangle is increased by 40% and the width is decreased by 40% then the area:.
The Area of Rectangle would be Decreased by 16% of the original Area. Now the Area of Rectangle is 84%.
Let the Length of rectangle be ‘x’
And width of rectangle be ‘y’
Area of Rectangle = Length X Width
Original Area of rectangle = x X y = xy square units
As the length is increased by 40% then, the new length would be 1+40% i.e 1.4 and,
The width is decreased by 40% then, the new width would be 1-40% i.e 0.6
New Length = 1.4x
New Width = 0.6y
Now , New Area of Rectangle = 1.4x X 0.6y
= 0.84xy square units
The effect is that the New Area of the rectangle is 84% of the original area. There is a decrease of 16% in the area.
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Solve the equation by graphing on a separate sheet of paper. Check your solution.
2x−3=3
Answer:
See attachment...
Hope this helps! :)
a random sample of 784 10-ounce cans of fruit nectar is drawn from among all cans produced in a run. prior experience has shown that the distribution of the contents has a mean of 10 ounces and a standard deviation of .10 ounce. what is the probability that the mean contents of the 784 sample cans is less than 9.995 ounces? a) 0.131 b) 0.081 c) 0.101 d) 0.111 e) 0.121 f) none of the above
The probability that the mean contents of the 784 sample cans are less than 9.995 ounces is 0.081. The correct option is B
Probability is the ability to happen. The subject of this area of mathematics is the occurrence of random events. From 0 to 1 is used to express the value. Probability has been introduced in mathematics to determine how likely events are to occur.
Given mean = 10
standard deviation = 0.10
sample = 784
The probability that the 784 sample cans' average contents will be less than 9.995 ounces
P ( X < 9.995 ) = x - μ/ σ / √n
= 9.995-10/0.10/√784
= -0.005 / 0.10 /28
= -1.400
P(Z < -1.400) = 0.081
Therefore the probability that the mean contents of the 784 sample cans are less than 9.995 ounces is 0.081
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What is the approximate value of the square root of 8?
Answer:
64
Step-by-step explanation:
Hope this helps!
Answer:
2nd answer is the right one
Step-by-step explanation:
the square root of 9 is 3. The square root of 8 is a little smaller because 8 is smaller than 9.
Substitute 6 for the variable, n, using parentheses. Then simplify by multiplying 8 and 6. 8(6) = 48. So you have 56 = 48, which is not a true statement. 6 is not a solution to the equation.
The numeric value of the expression 8n at n = 6 is different of 56, hence n = 6 is not a solution to the expression 8n = 56.
How to verify if a number is a solution to an expression?A number a is a solution to an expression if the numeric value of the expression at input a generates an identity with the expression.
In this problem, the expression is given as follows:
8n = 56.
We want to verify if the number six is a solution to the presented expression.
The numeric value of the expression at n = 6 is found replacing the lone instance of n by 6, hence it is obtained as follows:
8n = 8 x 6 = 48.
(the product of 8 and 6 is 48).
Then the equality would be of:
48 = 56.
Which is a contradiction, hence n = 6 is not a solution to the expression 8n = 56.
Missing InformationThe problem is:
Explain how to determine if the number is a solution to the equation. 56 = 8n for n = 6
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The mean of 2,3,4,5,6,7,y is 10. then the value of y is.
Answer:
43
Step-by-step explanation:
to find mean we add all the terms together and them divide by the amount of terms so lets add what we know first
2+3+4+5+6+7
27
there are 7 terms including the y so for there to be a mean of 10 the terms will have to equal 70 when added so we just subtract
70-27
43
hopes this helps please mark brainliest
find the product (x+2)(3x+1)(x-3)
(x+2)(3x+1)
x(3x+1)+2(3x+1)
3x²+x+6x+2
3x²+7x+2
(3x²+7x+2)(x-3)
x(3x²+7x+2)-3(3x²+7x+2)
3x³+7x²+2x-9x²-21x-6
3x³+7x²-9x²+2x-21x-6
3x³-2x²-19x-6
