The length of a rectangle can be found by dividing the area of the rectangle by its height if the area is known. Without the area, additional information is necessary to calculate the length.
To find the length of a rectangle when given the height, we typically need additional information such as the area or the aspect ratio of the rectangle. However, without that information, directly calculating the length is not possible. Let's explore a scenario where we have the area of the rectangle. In such a case, if we are given the area (A) of the rectangle and the height (h), we can use the formula for the area of a rectangle which is A = length times height. Solving for the length (l), we rearrange the formula to get l = A/h. For instance, if the area of the rectangle is 150 square centimetres and the height is 10 centimetres, the length would be 150 cm2 / 10 cm = 15 cm. It's also important to consider proportions when scaling shapes.
If (x + 1)(x - 3) = 12, then which of the following statements is true?
A and B share the cost in a ratio of 3:2. A pays £125 how much does b pay?
To solve this problem, we can set up proportion, which is two equivalent ratios. In this case, we are using the ratio of A to B to figure out the amount that B pays using our value for A. We are allowing x to represent the unknown value for the B payment. This is modeled below:
3/2 = £125/x
To simplify, we can perform cross-multiplication. This means multiplying the numerator of one fraction by the denominator of the other and setting it equal to the product of the other numerator and denominator. This is modeled below:
(125)(2) = (3)(x)
Next, we can simplify the equation by performing the multiplication on both sides of the equation.
250 = 3x
Finally, we should divide both sides by 3 to get our unknown variable x alone on the right side of the equation.
x = 83.33
Therefore, B costs £83.33.
Hope this helps!
The ratio of the areas of two similar polygons is 400:25. what is the ratio of their corresponding sides
Answer: 16:1
simplify 400:25 by dividing 400 by 25, which is 16.
The negative sign can be read as "the opposite of." true or false
Answer:
true
Step-by-step explanation:
Convert \dfrac{23}{50} 50 23 start fraction, 23, divided by, 50, end fraction to a percent.
If using the method of completing the square to solve the quadratic equation x^2+13x-35=0x 2 +13x−35=0, which number would have to be added to "complete the square"?
Answer:
42.25 or 169/4 on delta math
Step-by-step explanation:
Find the margin of error for each sample. Then find an interval likely to contain the true population proportion.
a. 15% of 457 teachers
b. 56% of 87 musicians
Full answers please
Use the x-intercept method to find all real solutions of the equation. x^3-9x^2+11x+21=0
Answer:
c: x=-1,3,7
Step-by-step explanation:
The scores on a final exam were approximately normally distributed with a mean of 82 and a standard deviation of 11. If 85 students took the exam, and above a 60 is a passing grade, how many students failed the exam?
A. 2
B. 12
C. 13
D. 1
A twelve inch candle and an 18 inch candle are lit at 6pm. The 12-in. candle burns 0.5 inches every hour. The 18 inch candle burns two inches every hour. At what time will the two candles be the same height? Let h represent the number of hours.
Answer:
At 10 PM both candles will be same height.
Step-by-step explanation:
Let h represent the number of hours.
We have twelve inch candle and an 18 inch candle are lit at 6pm and the 12-in. candle burns 0.5 inches every hour. The 18 inch candle burns 2 inch every hour.
Height 18 inch candle after h hours, = 18 - 2h
Height 12 inch candle after h hours, = 12 - 0.5h
At same height we have
18 - 2h = 12 - 0.5h
1.5 h = 18 - 12
h = 4 hours.
Time = 6 PM + 4 hours = 10 PM
At 10 PM both candles will be same height.
Answer:
At 10 PM, both the candles will be of same height.
Step-by-step explanation:
Two candles are lit at 6 PM.
The length of candles is 12 inch and 18 inch.
The rate of burning of 12 inch candle is 0.5 inch per hour.
The rate of burning of 18 inch candle is 2 inch per hour.
Let [tex]h[/tex] represents the number of hours of burning.
In [tex]h[/tex] hours, the remaining length of the 12 inch candle will be,
[tex]l_1=12-0.5\times h[/tex]
In [tex]h[/tex] hours, the remaining length of the 18 inch candle will be,
[tex]l_2=18-2\times h[/tex]
Now, it is required to find the time at which the length of both the candles will be same.
So, the time [tex]h[/tex] in hours will be,
[tex]l_1=l_2\\12-0.5h=18-2h\\1.5h=6\\h=4\rm hour[/tex]
So, after 4 hours, both the candles will be of same length.
Therefore, the time will be [tex]6+4=10[/tex] PM. At 10 PM, both the candles will be of same height.
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Please help! Vectors and angles
A ship is sailing through the water in the English Channel with a velocity of 22 knots along a bearing of 157° (knots being a unit used to measure the speed of aircrafts and boats). The current has a velocity of 5 knots along a bearing of 213°. Find the resultant velocity and direction of the ship. (Remember that bearing is measured clockwise from the north axis).
1) 25 knots at 166.5 degree
2) 27 knots at 350 degree
3) 166.5 knots at 25 degree
4) 350 knots at 27 degree
please help with this vertical asymptote of rational functions problem
A. x= -5
B. x=0
C. x= -2
D. x= 5
Suppose that a jar contains 4 pens: 2 black, 1 blue, and 1 red. three people select a pen at random from the jar, sign a document, and replace the pen in the jar before the next person selects a pen. what is the probability that none of the people use the red pen to sign the document?
The ratio of gold charms to silver charms is 1:3. Which statement does not describe the relationship?
Answer: A
Step-by-step explanation:
Danielle built a ramp with a stopping block at the bottom for her scout troop’s pinewood derby. She wants to paint the top and sides of the ramp. Danielle calculated the area by adding the areas of 2 triangular faces and 3 rectangular faces from the ramp and 6 rectangular faces from the block.
Did Danielle calculate the area correctly? If not, what was her mistake?
A. Yes, Danielle calculated the area correctly.
B. No, Danielle needs to remove 1 rectangle from the ramp and 1 rectangle from the block.
C. No, Danielle needs to add 1 triangle to the ramp and remove 1 rectangle from the block.
D. No, Danielle needs to remove 1 triangle from the ramp and add 1 rectangle to the block.
Answer:
Actually its b).
Step-by-step explanation:
She only wants to paint the top and sides of the ramp therefore you will have to take off the bottom parts of the ramps aka b).
No, Danielle needs to remove 1 rectangle from the ramp and 1 rectangle from the block.
What is Area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area. The space inside the perimeter or limit of a closed shape is referred to as the "area".
Danielle calculated the area by adding the areas of 2 triangular faces and 3 rectangular faces from the ramp and 6 rectangular faces from the block.
Danielle calculated some extra Areas.
As, per the discussion Danielle do not need to calculate the part ramp and block that coincides.
Thus, Danielle needs to remove 1 rectangle from the ramp and 1 rectangle from the block.
Learn more about Area here:
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m 2 = 40°, m 4 = 150°, m 3 =
The answer is 110° Hope this helps!
The velocity of sound in air is given by the equation
please only answer if you're gonna show work
Jack has a collection of new nickels and quarters. He has a total of 50 coins worth $10.30. How many of each coin does he have?
The steepness, or grade, of a highway or railroad is expressed as a percent. In the photo of the cog railway at Pike’s Peak, in Colorado, the grade is 18%. Thus, for every 100 ft of horizontal run, the train rises 18 ft. Find the angle of the inclination of the railway.
C) the function f(x) = −x2 + 16x − 60 models the daily profit, in dollars, a shop makes for selling candles, where x is the number of candles sold, and f(x) is the amount of profit. part
a.determine the vertex. what does this calculation mean in the context of the problem? part
b.determine the x-intercepts. what do these values mean in the context of the problem?
which function is a quadratic function?
Answer:
y = -2x² - x is quadratic function.
Step-by-step explanation:
Given : Function .
To find : Which function is a quadratic function.
Solution : We have given that functions .
Quadratic function: A quadratic function is one of the form f(x) = ax² + bx + c, where a, b, and c are numbers.
We can see from given options
y = -2x² - x in form of f(x) = ax² + bx + c,
Where, a = -2 , b = -1 c = 0
Therefore, y = -2x² - x is quadratic function.
If you want to put a 4x8 piece of plywood through a 3 foot square opening in your ceiling by turning it diagonally is the opening big enough? use a 45-45-90 since its a square
Answer: Yes, the 3 foot 3 foot square opening in your ceiling is big enough to insert a 4x8 piece of plywood.
In a 3x3 foot square, we can form two right triangles with same diagonal side or hypotenuse. .
Using the Pythagorean theorem/formula, we can find the length of the hypotenuse or the longest side of the triangle ( c) given the two sides a and b
Substitute values a=3 and b=3 to formula
a^2^+b^2^=C^2^=
3^2^+3^2^=C^2^=
9+9= C^2^
C= square root of 18
C=4.24
A 4x8 piece of plywood can be inserted in a 4.24 opening diagonally.
Why are jobs at food stands and restaurants good for college students?
Answer:
The reason a university student is looking for work is that he needs an extra salary income.
Step-by-step explanation:
It is a way to get a salary without overloading tasks.
In addition to that many times, they are given the time to study and work because there are very flexible schedules.
The university student gets used to the need to work for a fixed salary.
In addition, many university students need income to be able to pay the value of the semester or any project necessary for the university.
A system of equations is shown below:
x + y = 3
2x – y = 6
The x-coordinate of the solution to this system of equations is _____.
The coordinate grid shows the plot of four equations. A coordinate plane is shown with four lines graphed. Line A crosses the x axis at negative 3.2 and has a slope of 4. Line B crosses the x axis at 3 and the y axis at 6. Line C crosses the x axis at 1.5 and the y axis at negative 6. Line D crosses the x axis at negative 3 and the y axis at 3. Which set of equations has (2, 2) as its solution? A and D B and D A and C B and C
A rectangular room has an area of 315 square feet. the length is 6 feet more than the width. find the dimensions of the room.
The room's width is calculated to be 15 feet, and the length, which is 6 feet more than the width, comes to 21 feet. These dimensions satisfy the given area of 315 square feet for the rectangular room.
To find the dimensions of a rectangular room with a known area where one dimension is dependent on the other, we can use algebraic methods to determine the length and width. In this case, the area of the room is given as 315 square feet and it is known that the length is 6 feet more than the width. Let's denote the width of the room as 'w' feet. Therefore, the length will be 'w + 6' feet. The area of a rectangle is calculated by multiplying the length by the width, so we have the following equation:
w imes (w + 6) = 315
Expanding the left side of the equation gives us:
w²+ 6w = 315
To find the value of w, let's move all terms to one side to form a quadratic equation:
w²+6w - 315 = 0
Now we can solve this quadratic equation either by factoring, completing the square, or using the quadratic formula. For this case, factoring is applicable. We look for two numbers that multiply to -315 and add up to 6. The numbers 21 and -15 satisfy this condition. Therefore, we can write the equation as:
(w + 21)(w - 15) = 0
The possible solutions for w are -21 or 15; since a width cannot be negative, we take the positive solution:
w = 15 feet
Having obtained the width, we can now find the length:
Length = w + 6 = 15 feet + 6 feet = 21 feet
Therefore, the dimensions of the room are 15 feet in width and 21 feet in length.
Keisha is investing her money in an IRA. Initially she will be putting in $775. Using C as the additional amount invested each month, translate this problem into an algebraic expression that will show how much Keisha invested for the entire year.
To convert a distance of 1.25 miles to feet, which ratio could you multiply by? Remember that 1 mile = 5280 feet.
The equation sin(40o) =b/20 can be used to determine the length of line segment AC. What is the length of AC? Round to the nearest tenth.
An automobile manufacturer sold 30,000 new cars, one to each of 30,000 customers, in a certain year. The manufacturer was interested in investigating the proportion of the new cars that experienced a mechanical problem within the first 5,000 miles driven. (a)
A list of the names and addresses of all customers who bought the new cars is available. Describe a sampling plan that could be used to obtain a simple random sample of 1,000 customers from the list.
Each customer from a simple random sample of 1,000 customers who bought one of the new cars was asked whether they experienced any mechanical problems within the first 5,000 miles driven. Forty customers from the sample reported a problem. Of the 40 customers who reported a problem, 13 customers, or 32.5%, reported a problem specifically with the power door locks. (b)
Explain why 0.325 should not be used to estimate the population proportion of the 30,000 new cars sold that experienced a problem with the power door locks within the first 5,000 miles driven. (c)
Based on the results of the sample, give a point estimate of the number of new cars sold that experienced a problem with the power door locks within the first 5,000 miles driven.
Analyzing the situation of the automobile industry it will be important that:
A)build a list that attracts buyers to cars, looking for an interested audience, through emails, nearby residents.
B) 0.013
C)390
If it is necessary to analyze how to attract a corresponding public so that a car sale can take place, a list will be created that takes into account:
A) 1) Define the sample population: The costumers who bought a new car on a certain year.
2) Define the size of population: Of the 30000 customers who bought a car, you want to contact 1000 customers.
3) Define the contact options: You have a list of names and addresses, therefore you can send a questionnaire via mail.
4) Form a sampling frame: You will send the questionnaires and you will wait two months for the answer.
5) Define the analysis method: In your case, you want a quantitative research and therefore a probabilistic sampling.
B) The 32.5% probability refers to customers having issues with the power doors locks among the costumers who had problems, it does not consider the customers who did not have any problem or those who had problems after the first 5000 miles.
C) In order to find the probability of a power door lock problem if there have been problems within the first 5000 miles, we need to consider the whole sample:
[tex]P= \frac{13}{1000} = 0.013[/tex]
[tex]N=0.013*30000=390[/tex]
Hence, the number of new cars sold that experienced a problem with the power door locks within the first 5000 miles will be 390.