In Ms. K’s class, 75% of the students are the boys. There are 18 boys in the class. How many students are in the class?
factor ax^2−ay−bx^2+cy+by−cx^2
Final answer:
The expression ax²-ay-bx²+cy+by-cx² can be factored by first combining like terms to get (a-b-c)x² + (b+c)y - ay and then refactoring to x²(a-b-c) + y(b+c-a).
Explanation:
The student has given the expression ax²-ay-bx²+cy+by-cx² to factor. To factor this expression, we must first combine like terms and then group the terms in a way that allows us to factor by grouping.
Combining like terms gives us: (a-b-c)x² + (b+c)y - ay. We can then factor out common factors from each group. Notice that x² terms can be grouped together, as well as the y terms.
The refactored expression is x²(a-b-c) + y(b+c-a). Depending on the specific values of a, b, and c, further factoring may be possible, but with the given information, this is the factored form of the expression.
Final answer:
To factor the expression ax² - ay - bx² + cy + by - cx², group the terms based on their factors and factor out the common factors. The factored form of the expression is x²(a - b - c) - y(a - c + b).
Explanation:
To factor the expression ax² - ay - bx² + cy + by - cx², we can group the terms based on their factors. Group ax² - bx² - cx² together, and -ay + cy + by together. Factoring out the common factors from each group, we get:
x²a - b - c) - y(a - c + b)
Thus, the factored form of the expression is x²(a - b - c) - y(a - c + b).
What is the area for carpeting a floor?
a kitchen measures 3.75 meters by 4.2 meters, wha is tye area of the kitchen
Final answer:
The area of a kitchen measuring 3.75 meters by 4.2 meters is calculated by multiplying these dimensions, resulting in an area of 15.75 square meters.
Explanation:
The question asks for the area of a kitchen with dimensions 3.75 meters by 4.2 meters. To find the area of a rectangle, you multiply its length by its width. Therefore, the calculation for the area of the kitchen is as follows:
Area = Length × Width= 3.75 m × 4.2 m
= 15.75 square meters
Thus, the area of the kitchen is 15.75 square meters. This calculation is a basic application of geometry, specifically dealing with areas of rectangles.
Find the vertex and x-intercepts for 39x^2+38x+8.
Find the slope.
1.) (-4, -18), (-2, -10)
2.) (-19, 3), (7, 16)
7. When dy/dx = (x -6)1/2, what does y equal?
This table shows the daily high temperature, in Fahrenheit, for two cities for ten days. City A 90 85 84 85 80 82 83 85 89 82 City B 77 78 98 91 78 76 78 85 84 71 Which conclusion can be drawn from the data? A: The temperature range between the maximum and minimum values for city A is greater than the temperature range between the maximum and minimum values for city B. B: The median and mode are different for city B. C: The median is less for city A than for city B. D: On average, city A was warmer than city B.
I would have to say it would be D. On average, city A was warmer than city B.
Hope this helps ;}
I need a written response, if you could help explain how as well that would be awesome because I'm really confused!!!
Use the slope formula to find the slope of the line passing through the given points,
(–4, 7) and (0, 8).
Triangle ABC has vertices A(5, 3) , B(3, 7) , and C(1, 4) . Triangle ABC is dilated, and the vertices of the image are A′(2.5, 1.5) , B′(1.5, 3.5) , and C′(0.5, 2) . The center of dilation is the origin.
What is the scale factor of the dilation?
0.25
0.5
2
4
I believe the answer would be 0.5
Hope this helps ;}
Answer: The correct answer is (B) 0.5.
Step-by-step explanation: Given that A(5, 3) , B(3, 7) and C(1, 4) are the vertices of ΔABC and A′(2.5, 1.5) , B′(1.5, 3.5) and C′(0.5, 2) are the vertices of ΔA'B'C'.
We are to find the scale factor of the dilation of the centre of dilation is origin.
We know that the scale factor of dilation is given by the following formula:
[tex]S_c=\dfrac{\textup{length of a side of the dilated figure}}{\textup{length of the corresponding side of the original figure}}.[/tex]
We can calculate the lengths of the corresponding sides AB and A'B' of ΔABC and ΔA'B'C' respectively using distance formula as follows:
[tex]AB=\sqrt{(3-5)^2+(7-3)^2}=\sqrt{4+16}=\sqrt{20}=2\sqrt5,\\\\A'B'=\sqrt{(1.5-2.5)^2+(3.5-1.5)^2}=\sqrt{1+4}=\sqrt{5}.[/tex]
Therefore, the scale factor for the dilation is given by
[tex]S_c=\dfrac{A'B'}{AB}=\dfrac{\sqrt5}{2\sqrt5}=\dfrac{1}{2}=0.5.[/tex]
Thus, the required scale factor is (B) 0.5.
The line plots show the results of a survey of 10 boys and 10 girls about how many hours they spent reading for pleasure the previous week.
Select from the drop-down menus to complete each statement.
A dinner platter is in the shape of a regular decagon. The platter has an area of 161 sqaure inches and a side length of 4.6 inches. What is the area of each triangle? What is the height of each triangle?
what is the order from least to greatest for 5.934, 59/10, 5 8/9, 5.94
A flagpole is 4meters tall how many centimeters tall is the flagpole
Suppose your heart is beating 72 times per minute. At this rate, how many times will it beat in 15 minutes?
Camryn practices the trumpet every 11th day and the flute every 3rd day. Camryn practiced both today. How many days until Camryn practices both the flute and trumpet again?
The correct answer is 33 days. The least number of days until Camryn practices both the flute and trumpet again is 33 days.
To determine how many days until Camryn practices both the flute and trumpet again, we need to find the least common multiple (LCM) of the two periods: every 11th day for the trumpet and every 3rd day for the flute.
The LCM of two numbers is the smallest number that is a multiple of both numbers. To find the LCM of 11 and 3, we can list the multiples of each number until we find a common multiple:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, ...
Multiples of 11: 11, 22, 33, ...
The smallest common multiple of 3 and 11 is 33. Therefore, Camryn will practice both instruments again in 33 days.
Alternatively, we can calculate the LCM using the prime factorization of the two numbers. Since 3 is a prime number and 11 is also a prime number, the LCM is simply the product of the two:
LCM(3, 11) = 3*11 = 33
Thus, the least number of days until Camryn practices both the flute and trumpet again is 33 days.
Suppose that 2% of the students in a school have head lice and the test for head lice is accurate 75% of the time. What is the probability that a student in the school has head lice, given that the test came back positive? Round your answer to the nearest tenth of a percent.
Answer: Probability of getting a student in the school has head lice given that the test came back positive is 0.058.
Step-by-step explanation:
Since we have given that
Let E be the event that the student actually having head lice.
Let A be the event that the report shows positive.
Since there are 2% of the students in a school having lead lice.
P(E) = 0.02
P(E')=1-0.02=0.98
Similarly, the probability that the test for head lice is accurate = 75% of the time.
So, [tex]P(A\mid E)=75\%=0.75\\\\Similarly,\\\\P(A\mid E')=1-0.75=0.25[/tex]
We need to find the probability that a student in the school has head lice , given that the test came back positive.
So, By using Bayes Theorem, we get that
[tex]P(E\mid A)=\dfrac{P(A\mid E).P(E)}{P(A\mid E).P(E)+P(A\mid E').P(E')}\\\\P(E\mid A)=\dfrac{0.02\times 0.75}{0.02\times 0.75+0.98\times 0.25}\\\\P(E\mid A)=\dfrac{0.015}{0.015+0.245}\\\\P(E\mid A)=\dfrac{0.015}{0.26}\\\\P(E\mid A)=0.0576\approx 0.058=5.8\%[/tex]
Hence, Probability of getting a student in the school has head lice given that the test came back positive is 0.058.
Substitute the given values of the variables into the equation. Write True or False to indicate whether the values make the open sentence true or false. Show all work for solving the problem. Values: x=7,y=0.2,z=22
2x+0.8/y=z-4
will is 23% taller than wanda so wills height is ___ % of wanda’s height
Since Wanda's height represents 100% and Will is 23% taller, then Will's height is 123% of Wanda's height.
Explanation:The question tells us that Will is 23% taller than Wanda. In terms of understanding this percentage in relation to Wanda's height, it helps to see Wanda's height as 100% because 100% represents a whole, in this case, Wanda's entire height. If Will is 23% taller, then his height is 100% of Wanda's plus an additional 23%. Thus, Will's height is 123% of Wanda's height.
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A candle is 7 in. Tall after burning for 1 h. The same candle is 5 1/2 in. Tall after burning for 4 h. Write a linear equation to model the height y after burning x hours
Must a decimal divisor and a decimal dividend have the same number of decimal places in order to have a whole number quotient? write a division equation using two decimal numbers to support your answer.
Answer:
NO. They do not have to be equal
Step-by-step explanation:
A whole number takes place when two conditions are satisfied:
1. The numerator or the dividend is greater than the divisor.
For example, when you divide 0.1 by 0.002.
The dividend 0.1 is greater than 0.002
2. The divisor is small than the dividend.
This rule is the same as one above.
for example:
the quotient x is given by [tex]\frac{1}{0.25}\\ = 4[/tex]
If the principal on one loan is $1,000 more than another loan, the total cost of the loan is $1,000 more.
Answer:False
Step-by-step explanation:
whoever answers first gets a brainliest . thanks
How can i express this decimal as a fraction? (Explain please!)
write a story problem for 32 divided by 5 so that the question you pose would be answered by 6 2/5
A story problem for the division problem is: 5 friends sharing going on a holiday and the total cost is $32
Writing a story problem for the divisionFrom the question, we have the following parameters that can be used in our computation:
32 divided by 5
Also, we have the result to be
Result = 6 2/5
A story problem for this division is as follows:
Five friends decided to go on a holiday together. After calculating the total cost of $32, they split it evenly, so each friend contributed $6 2/5.
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pleasee ill give you brainliest
Consider this system of equations: y = x2 y = x + k For which value of k does the system have no real number solutions? For which value of k does the system have one real number solution? For which value of k does the system have two real number solutions?
For the given system of equations, the value of k determines the number of real number solutions.
Explanation:In order to determine the number of real number solutions for the system of equations y = x^2 and y = x + k, we need to analyze the discriminant of the quadractic equation x^2 - (x + k) = 0.
If the discriminant is negative (less than zero), the system has no real number solutions.If the discriminant is zero, the system has one real number solution.If the discriminant is positive (greater than zero), the system has two real number solutions.The discriminant of the quadratic equation x^2 - (x + k) = 0 can be calculated as b^2 - 4ac, where a = 1, b = -1, and c = -k.
For no real number solutions: b^2 - 4ac < 0
For one real number solution: b^2 - 4ac = 0
For two real number solutions: b^2 - 4ac > 0
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Help needed please and thank you!
if the temperature at 9:00 pm was 12 degrees farenheit,and after 6 hours the temperature dropped to 6 degrees Fahrenheit below 0,what was the rate of change in temperature per hour?
Bill Gates wants to construct an in ground swimming pool for his dog. he wants it's length to be 8 yards shorter than twice it's width. he then wants to surround it with a concrete walkway 6 yards wide. he can only afford 570 square yards of concrete. what should the dimensions be of the pool ?
Please find the attached file for a better understanding of the solution provided here:
ABCD is the swimming pool and PQRS is the extent of the swimming pool plus the concrete walkway which is 6 yards wide.
Now, we know that the length is 8 yards shorter than twice it's width. Thus,
l=2w-8
Now the area of the region, A'B'QP will be: length x width. Now, the length here is l+6+6=2w-8+12=2w+4 and width is 6.
Thus, area of the region A'B'QP is (2w+4)x6=12w+24
Likewise, the area of the region D'C'RS will similarly be 12w+24 too.
Now, the area of the region BB'C'C will be 6 x w=6w
Similarly, the area of the region AA'D'D will be 6 x w=6w
Therefore, the total area of the walk way will be:
[tex] 2(12w+24)+2\times 6w=570 [/tex]
[tex] 24w+48+12w=570 [/tex]
[tex] 36w+48=570 [/tex]
[tex] \therefore w=14.5 [/tex]
Therefore, length, l will be:
[tex] l=2w-8=2\times 14.5-8=29-8=21 [/tex]
Therefore, the dimensions of the swimming pool are:
Length, l= 21 yards and Width, w=14.5 yards