Answer:
L = 12ft
W = 13ft
Step-by-step explanation:
Let's use the two pieces of information to make 2 equations (we need 2 eqns to solve for 2 variables: Length and Width).
The length and width are consecutive integers
L+1=W
The area of the rectangle is 156 square feet.
L*W=156
We know that W=L+1 from our first equation, so substituting that information into our second equation we get
L*(L+1)=156
Let's distribute that L
L^2 + L = 156
and subtract 156 from both sides
L^2 + L - 156 = 0
Now we can use the quadratic formula to find L. L cannot be negative, so
L = 12
using our very first equation we know L, so we can solve for W.
L+1=W
12+1=W
W = 13
The formula in Ohm's Law is E = IR, where E represents voltage measured in volts, I represents current measured in amperes, and R represents resistance measure in ohms. Solve for R.
To solve for R in Ohm's Law, you can rearrange the formula to isolate R on one side of the equation. To solve for R, you can divide both sides of the equation by I:
R = E/I
This rearranged formula shows that the resistance R is equal to the voltage E divided by the current I. For example, if you have a voltage of 10 volts and a current of 2 amperes, the resistance would be 5 ohms:
R = 10 volts / 2 amperes = 5 ohms
Let's prep ourselves before attempting to answer the question. What do we need to know?
We'll need to know a couple of basic concepts before we tackle the problem. Namely, we'll need these ones:
Equality PropertiesWhat are equality properties? These are the equality properties:
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityDefineFrom the problem, we are given Ohm's Law, which is E = IR. The problem states that it wants to solve this equation for R.
WorkIn order to solve Ohm's Law for R, we can use the Division Property of Equality. What does this property state? It states that if you divide something (number, variable, etc.) on one side, you must do the same for the other.
Now, let's apply this property to find our answer. We divide by I on both sides to isolate R:
[tex]\displaystyle\begin{aligned}E & = IR \\IR & = E \\\frac{IR}{I} & = \frac{E}{I} \\R & = \boxed{ \frac{E}{I} } \\\end{aligned}[/tex]
Answer[tex]\displaystyle \boxed{ R = \frac{E}{I} }[/tex]
Hope this helped!
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How much power is needed to get up the stairs, if I can do this with 30 Joules of work in 3 seconds?
Answer:
10 Joules/second
Step-by-step explanation:
To find the power needed to get up the stairs, we need to divide the amount of work done (30 Joules) by the time it took to do the work (3 seconds):
Power = Work / Time
Power = 30 Joules / 3 seconds
Power = 10 Joules/second
Therefore, it takes 10 Joules/second of power to get up the stairs.
please help me solve this
Answer:
8+5x
Step-by-step explanation:
Perimeter = sum of the all sides of triangle
= 6+3x-4+2x + 6
= 8+5x
Answer:
5x + 8
Step-by-step explanation:
To find the perimeter, add up all the sides
6 + 3x-4 + 2x +6
Combine like terms
5x + 8
a road running north to south crosses a road going east to west at the point pp. car a is driving north along the first road, and car b is driving east along the second road. at a particular time car a is 1010 kilometers to the north of pp and traveling at 80 km/hr, while car b is 15 kilometers to the east of pp and traveling at 100 km/hr. how fast is the distance between the two cars changing?
The speed at which the gap between the two vehicles is narrowing is 154.4 km/h.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. what kinds of values and units
Let's say you go to the store to buy six apples.
You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when using the unitary technique to a problem.
Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.
We are aware of the quantity of apples and the amount of money in the aforesaid problem.
According to our question-
D^2 = (x^2 + y^2) + z^2
2*D*dD/dt = 2*x*dx/dt + 2*y*dy/dt + 0 (since z is constant)
D^2 = c^2 + z^2 = (x^2 + y^2) + z^2 = 10^2 + 15^2 + 2^2 = 100 + 225 + 4 = 329
= 2800/sqrt(329) = 154.4 km/hr
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Write the following as an algebraic expression. Then simplify
The sum of three consecutive even integers is
330. Find the integers.
Answer:
108, 110, 112
Step-by-step explanation:
You want three consecutive even integers whose sum is 330.
ExpressionLet x represent the middle integer. Then the other two are (x-2) and (x+2). The expression for their sum is ...
(x -2) +x +(x +2) = 330 . . . . . an algebraic expression
3x = 330
x = 110
x -2 = 108
x +2 = 112
The three integers are 108, 110, 112.
__
Additional comment
"Consecutive integer" problems are often worked easily by considering the average value of the integers. For three consecutive integers, their average is the middle one.
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Please help with this….
Answer: i belive its B but im not 100%
Step-by-step explanation:
Wright 4.17 * 10 ^ 3 In scientific notation please help
csc^2 - 2 = 0
the answer key shows four answers and i dont understand why
Answer:
approximately 0.63662 or approximately 5.49541
Step-by-step explanation:
The value of the x variable in the equation csc^2 x - 2 = 0 is approximately 0.63662 or approximately 5.49541.
To solve for the x variable in the equation csc^2 x - 2 = 0, we need to use the properties of the cosecant function. The cosecant function is the reciprocal of the sine function, and it is defined as csc x = 1/sin x.
We can rewrite the given equation as csc^2 x = 2, and then use the definition of the cosecant function to get 1/sin^2 x = 2. We can then solve for the value of x by using the identity sin^2 x + cos^2 x = 1 and the fact that the sine function has a period of 2π.
The identity sin^2 x + cos^2 x = 1 tells us that the square of the sine function plus the square of the cosine function is always equal to 1. Since the cosecant function is the reciprocal of the sine function, this means that csc^2 x = 1/sin^2 x = 1/(1 - cos^2 x).
We can use this information to rewrite the equation 1/sin^2 x = 2 as 1/(1 - cos^2 x) = 2. We can then solve for the value of x by rearranging the terms in the equation and using the fact that the sine function has a period of 2π.
We can rearrange the terms in the equation as follows: 1 - cos^2 x = 1/2
cos^2 x = 1/2
cos x = ±√(1/2)
Since the sine function has a period of 2π, this means that the value of x will be the same for all angles that are integer multiples of 2π. Therefore, we only need to find the value of x for one angle, and then we can use this value to find the values of x for all other angles.
We can choose the angle 0 as our reference angle, and then use the above equation to find the value of x. We can substitute 0 for x in the equation cos x = ±√(1/2) to get cos 0 = ±√(1/2). Since cos 0 = 1, this means that the value of x is 0.
We can then use the fact that the sine function has a period of 2π to find the values of x for all other angles. For example, if we add 2π to thereference angle 0, we get 2π. If we substitute 2π for x in the equation cos x = ±√(1/2), we get cos 2π = ±√(1/2). Since cos 2π = 1, this means that the value of x is 2π.
We can repeat this process for other integer multiples of 2π, and we will find that the values of x that satisfy the equation csc^2 x - 2 = 0 are 0, 2π, 4π, 6π, and so on.
We can also use a calculator or a table of trigonometric functions to find the values of x that satisfy the equation. For example, if we use a calculator to evaluate csc^2 x at x = 0, we get csc^2 0 = 1. If we evaluate csc^2 x at x = 2π, we get csc^2 2π = 1.
If we use a table of trigonometric functions to find the value of csc^2 x at x = 0.63662, we get csc^2 0.63662 ≈ 2. Similarly, if we use a table of trigonometric functions to find the value of csc^2 x at x = 5.49541, we get csc^2 5.49541 ≈ 2.
Therefore, the values of the x variable in the equation csc^2 x - 2 = 0 are approximately 0.63662 or approximately 5.49541.
As far as there being 4 solutions:
It is possible for the problem "Csc^2 x- 2 = 0" to have 4 solutions. The problem asks us to find the values of x that satisfy the equation csc^2 x- 2 = 0, and it is possible for the equation to have multiple solutions that satisfy this condition.
In the previous answer, we showed that the equation csc^2 x- 2 = 0 has 2 solutions: x = 0.63662 and x = 5.49541. These are the values of x that make the equation true, and they are the solutions to the problem.
However, it is also possible for the problem to have 4 solutions if each solution is repeated twice. In this case, the problem would have 4 solutions because it has 2 solutions (x = 0.63662 and x = 5.49541) and each solution is repeated twice (x = 0.63662 and x = 0.63662, x = 5.49541 and x = 5.49541).
Therefore, it is possible for the problem "Csc^2 x- 2 = 0" to have 4 solutions if each solution is repeated twice. In this case, the problem would have 4 solutions because it has 2 solutions (x = 0.63662 and x = 5.49541) and each solution is repeated twice (x = 0.63662 and x = 0.63662, x = 5.49541 and x = 5.49541).
(1, 3)
(0, 3)
(1,4)
(0, 1)
y= 3x + 1,
y = x + 3
y = 3x + 1
y=x+3
5
Answer:
(1,4)
Step-by-step explanation:
both equations are equal to y so we set them equal
3x+1=x+3
-x. -x
2x+1=3
-1. -1
2x=2
/2. /2
x=1
3(1)+1=y
3+1=y
4=y
hopes this helps
Melanie combines 7.49 liters of red paint with 6.26 liters of blue paint to make purple paint. She
pours the paint equally into 4 containers, and has 0.43 liters of paint left over. How many liters
of paint are in each container?
Hello,
I hope you and your family are doing well!
The total amount of paint that Melanie combines is 7.49 liters + 6.26 liters = 13.75 liters.
If she pours the paint equally into 4 containers, each container will have 13.75 liters / 4 = 3.44 liters of paint.
The amount of paint left over is 0.43 liters, so the total amount of paint in the 4 containers is 3.44 liters/container * 4 containers + 0.43 liters = 13.75 liters.
Therefore, each container has a total of 3.44 liters of paint.
-----
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for how many pairs of consecutive integers in {1000,1001,1002,...,2000} is no carrying required when the two integers are added?
156 pairs of consecutive integers in {1000,1001,1002,...,2000} is no carrying required when the two integers are added
You will need to consider four cases.
when _999 and _000 are the last three digits of consecutive numbers. Just possible cases are 1999, 2000
At the point when the last 2 digits of the continuous numbers are _ _ 9 9 and _ _ 0 0. 5 possible scenarios (corresponding to (0,1), (1,2), (2,3), (3,4), and (4,5) at the hundredth place) exist.
when the last digit of consecutive numbers is in the form ____ 9 and ____ 0. 5*5 = 25 possible scenarios.
when none fall into that category, possible case=. 5*5*5 = 125,
and the answer is 125+25+5+1 = 156.
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Function A is represented by the equation y= 4x+6. Function B is a linear function that goes through the points shown in the table. 6 3 9 12 18 Which statement correctly compares the rates of change of the two functions? O A. The rate of change of function A is 6. The rate of change of function B is 3. OB. The rate of change of function A is 4. The rate of change of function B is 6. C. The rate of change of function A is 4. The rate of change of function B is 3. D. The rate of change of function A is 6. The rate of change of function B is 6.
its D
. . . . . ... . . . . . . . . . . . .. . .
how much water should we add to 20kg of sea water to change its concentration from 2% to 3%
Answer: 10 kg
Step-by-step explanation:
3% = 0.03
First, take 20 times 0.03 = 0.6kg of salt
We know that the 2% solution of seawater
So, we take 100 times 0.6, then divide by 2 = 30kg
Then take 30 - 20 = 10kg
So, to make a solution from 3% to 2%, we have to add 10 kg of water with a 20 kg solution.
a brick staircase has a total of 12 steps. the bottom step requires 100 bricks. each successive step requires 4 less bricks than the prior one. how many bricks are required to build the staircase.
a brick staircase has a total of number of 12 steps. the bottom step requires 100 bricks.A total of 246 bricks are required to build the staircase.
The total number of steps in the brick staircase is 12. The bottom step requires 100 bricks. Each successive step requires 4 less bricks than the prior one. Therefore, the number of bricks required to build the staircase can be calculated as follows:
The first step requires 100 bricks.
The second step requires 96 bricks (100 - 4 = 96).
The third step requires 92 bricks (96 - 4 = 92).
This pattern continues until all 12 steps are accounted for.
Adding the number of bricks required for each step gives a total of 246 bricks required to build the entire staircase.
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Jamyia wants to sell bracelets at a
craft fair for $12 each. The
materials for each bracelet cost
$3.50, and the table rental at the
fair costs $34 for the day. How
many bracesets must she sell for
her revenue to equal her expenses?
A 10
B 3
C 4
D 3.5
By solving a linear equation, it can be calculated that
Jamyia wants to sell 4 bracelets.
What is linear equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here, a linear equation needs to be solved
Let the number of bracelets Jamyia wants to sell be x
Cost of each bracelet = $12x
The materials for each bracelet cost $3.50, and the table rental at the
fair costs $34 for the day.
Her expense = $(34 + 3.5x)
By the problem,
The linear equation is
34 + 3.5x = 12x
12x - 3.5x = 34
8.5x = 34
x = [tex]\frac{34}{8.5}[/tex]
x = 4
Jamyia wants to sell 4 bracelets.
Option C is correct
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tomas is thinking of a number. if he triples it and subtracts 13, the result is 305. of what number is tomas thinking of
Answer:
106
Step-by-step explanation:
(305+13)/3=106
Three glasses of milk and 2 snack bars have a total of 53 carbohydrates (carbs), and 2 glasses of milk and 3 snack bars have a total of 52 carbs. Determine how many carbs are in one glass of milk and in one snack bar
Answer:
1 Glass of milk has 11 Carbohydrates
1 snack bar has 10 Carbohydrates
Step-by-step explanation:
Let M represent a glass of milk and S represent a snack bar! So, we have equations that are
3M + 2S = 53 Carbs
2M + 3S = 52 Carbs
We time the first equation by -1.5 and get
-4.5M - 3S = -79.5 Carbs
2M + 3S = 52 Carbs
Now let's find the Milk carbs by adding both equations
-2.5M = -27.5 Carbs
M = 11 Carbs
Now put 11 in for M to find the Carbs for a snack bar.
2(11) + 3S = 52 Carbs
22 + 3S = 52 Carbs
3S = 30 Carbs
S = 10 Carbs
So, 1 Glass of milk has 11 Carbohydrates
1 snack bar has 10 Carbohydrates
Find the measure of each angle indicated.
A. 111 degree
B. 69 degree
Help!!!
Answer: A. 111 degree
Step-by-step explanation:
Because they are Alternate Interior angles! Which means the two angles are congruent and have the same degree!
P43 000.00 at 10% compounded annually for 5 years.
P43 000.00 at 10% compounded annually for 5 years is :$69,251.93.
How to find the compounded amount ?Using formula
A=pP(1+r/n)^nt
Where:
A=Amount =?
P = Principal = 43,000
r = interest rate = .10
t= time = 5
Let plug in the formula
A = 43,000 (1+ .10/1)^1×5
A = 43,000 (1+ .10)^5
A = 43,000 ( 1.10)^5
A = 43,000 (1.61051)
A =$69,251.93
Therefore the compounded amount is $69,251.93.
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Answer:ANSWER
69251.93
EXPLANATION
P = 43000
r = 10%
n = 1
We know that:
t = 5 Formulate and substitute:
F43000 (1+10. .
1
100 Evaluate the equation/expression: 69251.93
Answer: 69251.93
Step-by-step explanation:
How and his friends bought stickers for $1.25 each and will mark them up 180%. What will they sell the tickets for?
Answer:$2.25x
Step-by-step explanation:
Lets use X to denote the amount of stickers How and his friends bought. so he buys them at 1.25x. An easy trick when doing percentages of a number is thinking of the percent as a fraction. So instead of 180, think of 180/100. Think of 1.25 as 125/100
multiply 180/100 by 125/100
you get 22500/10000 which equals 2.25
or 2.25x
a local department store estimates that 10 percent of its customers return the merchandise they purchase. let the random variable r represent the number of returns for a random sample of 40 customers. assume that random variable r follows a binomial distribution. what is described by the value of (408)
The value of (408) is (0.1)8(0.9)32 for a local department store estimates that 10 percent of its customers return the merchandise they purchase.
The value of (408)(0.1)8(0.9)32 represents the probability of getting 8 returns out of a sample of 40 customers, given that the store estimates that 10% of customers return merchandise.
This probability is calculated using the binomial probability formula, which is used to calculate the probability of a specific number of successes (in this case, returns) in a certain number of trials (in this case, customer purchases), given a certain probability of success (in this case, the estimated probability of customers returning merchandise).
The value of (408)(0.1)8(0.9)32 ( 40 8 ) ( 0.1 ) 8 ( 0.9 ) 32 describes the probability of getting 8 returns out of 40 customers when the probability of a customer returning the merchandise they purchase is 0.1.
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The table shows data for orders of cheese. Multiply each number of pounds of cheese in the table below by its frequency.
Drag the tiles to complete the table. The first one is done as an example. Each tile may be used once, more than once, or not at all.
According to the information in the table, the weights in pounds would be: 1. 1 pound, 2. 6 pounds, 3. 6 pounds, 4. 3 pounds.
How to calculate the total pounds of cheese?To calculate the total pounds of cheese we must follow the instruction of the statement. In this case, we must multiply the fractions by the frequency number to find the total weight in pounds of the cheese orders. Here are all the procedures:
A.
1/4 * 4 = 1
b.
3/4 * 8 = 6
c.
1 1/2 * 4 = 6
d.
1 1/2 * 2 = 3
According to the above, we can infer that the numbers that complete the table are: 1, 6, 6, and 3 respectively in each of the blank spaces from top to bottom.
Note: This question is incomplete because there is some information missing. Here is the complete information:
table:
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help with my thing and get 16 point
A rectangle with a length of (x+2) cm and a width of y cm has a perimeter of 37.5 cm. A second rectangle has twice the perimeter, with a length of (2x - 6.5) cm and a width of (x+2y) cm. Find the values of x and y.
Answer
x=10.5 , y=6.25
Step by Step ^
The solution is, the values of x and y is, x=10.5 , y=6.25.
What is perimeter?A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.
Perimeter refers to the total outside length of an object,
here, we have,
we know,
perimeter of rectangle is:
P = 2*( a+ b)
given that,
A rectangle with a length of (x+2) cm and a width of y cm has a perimeter of 37.5 cm.
i.e. we get,
2( x+2 + y ) = 37.5
or, 2x + 2y = 33.5 ........(1)
and, we have,
A second rectangle has twice the perimeter, with a length of (2x - 6.5) cm and a width of (x+2y) cm.
i.e. we have,
2( 2x - 6.5 + x + 2y ) = 75
or, 3x + 2y = 44.5 .....(2)
solving (1) & (2) , we get,
x=10.5 , y=6.25
Hence, The solution is, the values of x and y is, x=10.5 , y=6.25.
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A 3-gallon container of laundry detergent cot $33. 60. What i the price per cup?
As per the unitary method, the price of the cup is $2.958
Unitary method in statistics is defined as in which the value of one article is first obtained to find out the value of any required articles
Here we have given that the 3-gallon container of laundry detergent cost $33. 60.
And we need to find the price per cup.
While we looking into the given question, we have identified the following details that cost of 3 gallon container of laundry detergent is $33.60.
So, the cost for 1 gallon container of laundry detergent cost,
=> 33.60/3
=> 11.20
Let us consider that the cup can hold 1 liter.
As we know that 1 gallon = 3.78541 liter.
Then the cost of 1 liter is calculated as,
=> 11.20/3.78541
=> 2.958
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What is the average of 129 and 47?
Answer:
the average for 129 is 159 and the average for 47 is 49
Step-by-step explanation:
Oliver bakes 10 cakes. Look at the table below.
Plot a scatter graph to represent the data.
Draw the line of best fit.
What type of correlation is shown? How are mass of a cake and cooking time related?
The graph of scatter point is attached below. The correlation is linear.
The mass of a cake and cooking time are related linearly.
What is scatter points?
A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of connection, if any, between the values of observed quantities or events, scatter plots are crucial in statistics (called variables).
Given points are (20,610), (30, 680), (20, 700), (50, 750), (40, 825), (30, 840), (50, 845), (75, 965), (45, 1000), (85, 1100).
Plot the points on the graph.
The line of best is a straight line.
Thus the correlation is linear type.
Also, the mass of a cake and cooking time are related linearly.
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The graph below represents the distance of a dog from a trainer after a command is given.
A graph titled Dog Obedience School. The horizontal axis shows Time (seconds), numbered 1 to 10, and the vertical axis shows Distance (yards) numbered 4 to 40. The line shows an increase, then decrease, then constant distance.
Which statement could describe the dog’s movement at 5 seconds once the command was given?
The dog stopped to lie down and obey the trainer’s command.
The dog was running towards the trainer to receive a treat.
The dog was running away from the trainer to chase a squirrel.
The dog was stopped but began running towards the trainer.
The statement dog was running towards the trainer to receive a treat.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given that graph represents the distance of a dog from a trainer after a command is given.
A graph titled Dog Obedience School. The horizontal axis shows Time (seconds), numbered 1 to 10,
The vertical axis shows Distance (yards) numbered 4 to 40.
The line shows an increase, then decrease, then constant distance.
At the point on the graph where time is 5 seconds, the slope of the distance vs time curve is negative, indicating the dog is moving toward the trainer.
The motivation of the dog is unknown, so the above answer choice involves speculation that is not supported by the problem statement.
Hence, the statement dog was running towards the trainer to receive a treat.
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fn is the nth Fibonacci number. show that fn+1fn−1 − f 2 n = (−1)n when n is a positive integer.
The [tex]f_{n+1}f_{n-1}-f^2_{n} = (-1)^n[/tex] when n is a positive integer for nth Fibonacci number is true.
What is Fibonacci number?Fibonacci number is sequences of numbers in mathematics where the next sequence is the result of the sum of the two previous numbers. So we can written for Fibonacci number formula as,
[tex]f_{n}[/tex] = [tex]f_{n-1}+f_{n-2}[/tex].
Usually in mathematics the Fibonacci number is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ... with 0 is the 0 order of Fibonacci number.
For the given equation, we can prove that with many ways. But, the easiest way we can use the usual Fibonacci number above to prove that.
We assume n = 3 so the number is 2.
[tex]f_{n+1}f_{n-1}-f^2_{n} = (-1)^n[/tex]
(3)(1) - (2^2) = (-1)^2
3 - 4 = -1
-1 = -1
We also can assume n = 5 so the number is 5.
[tex]f_{n+1}f_{n-1}-f^2_{n} = (-1)^n[/tex]
(8)(3)-(5^2) = (-1)^5
24 - 25 = -1
-1 = -1
Thus, the given equation is true.
You question is incomplete, but most probably your full question was
T/F. [tex]f_n[/tex] is the nth Fibonacci number. show that [tex]f_{n+1}f_{n-1}-f^2_{n} = (-1)^n[/tex] when n is a positive integer.
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Find the measure of each angle indicated.
A. 127 degrees
B. 53 degrees
Help!!!
Answer:
B. 53 degrees
Step-by-step explanation:
Because the ?-angle is equal to the 53-degree angle. So, the answer is B. 53 degrees