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Related Questions
Solve these problems using the berry method. Please show me the work! (291-298)
Answers
So, you start with a factorization that looks like
.. (ax + __)*(ax + __)
with the blanks to be filled by the numbers you determine in the second step.
Finally, you divide this product by "a" in an appropriate way. Often, that will mean you factor "a" from one of the binomials.
291) 5c^2 +13c +6
.. form to fill: (5c + __)*(5c + __)
We're looking for factors of 5*6 = 30 that add to 13.
.. 30 = 1*30 = 2*15 = 3*10 = 5*6 . . . . . . sums of factors are 31, 17, 13, 11.
The numbers we want are 3 and 10. Putting these into the form gives
.. (5c +3)*(5c +10)
.. = 5(5c +3)(c +2)
The factorization we want is
.. 5c^2 +13c +6 = (5c +3)(c +2)
294) 4d^2 +8d -21
.. 4*-21 = -84 = 84*-1 = 42*-2 = 28*-3 = 21*-4 = 14*-6 = 12* -7
.. These factor pairs have sums 83, 40, 25, 17, 8, 5, so our numbers are 14, -6.
.. (4d +14)(4d -6) . . . . form with numbers filled in
.. = 2(2d +7)*2(2d -3) . . . . . remove a factor of 4 by removing a factor of 2 from each binomial
.. = 4(2d +7)(2d -3)
The factorization we want is
.. 4d^2 +8d -21 = (2d +7)(2d -3)
297) 3g^2 -16g -12
.. 3*-12 = -36 = -36*1 = -18*2 = -12*3 = -9*4 = -6*6
.. These factor pairs have sums -35, -16, -9, -5, 0, so the numbers we want are -18 and 2.
The Berry Method form now looks like
.. (3g -18)(3g +2)
.. = 3(g -6)(3g +2)
The factorization we want is
.. 3g^2 -16g -12 = (g -6)(3g +2)
Explain the steps you would take to model a desert community in which 77% of the area is covered with houses.
Answers
Answer:
77 out of 100 grids will have some marking to differentiate it from others.
Step-by-step explanation:
To model a desert community in which 77% of the area is covered with houses you may use different options as per your choice. You may put a border to the 77 of the 100 grid. If we choose a 10 by 10 grid then it will be preferable for modeling a desert community if you will mark 77 out of 100 grid.
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A full grain silo empties at a constant rate. write an expression to determine the amount of grain left after s seconds
Rate: 3.5 ft 3/s
I'm asking this question again because this is urgent!
Answers
To calculate the remaining amount of grain in a silo discharging at a constant rate, we subtract the total amount discharged (rate times time) from the initial amount. This can be expressed as 'G = I - 3.5s' where 'G' is the amount of grain left after 's' seconds, 'I' is the initial amount, and '3.5' is the discharge rate in ft3/s.
Explanation:If the silo empties at a constant rate, it can be modeled with linear equations. In this case, the rate of grain being emptied from the silo is 3.5 units of grain every second. Please note that to find the amount of grain left after a certain amount of time, we need to know the initial amount of grain in the silo, let's call it 'I'.
For your problem the general mathematical expression would be: total amount of grain left = initial amount of grain (I) - (rate × time),
If we denote the amount of grain left after 's' seconds as 'G', we can write the equation as: G = I - 3.5s
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A boat travel 312 miles each way downstream and back. The trip downstream took 13 hours. the trip back took 26 hours. What is the speed of the boat in still water. what is the speed of the current.
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Let [tex]S _{b} [/tex] be the speed of the boat in still water and [tex]S_{c} [/tex] the speed of the current.
Now, for the downstream trip the boat is traveling with the current, so:
[tex]S_{b} +S_{c} = \frac{156}{13} [/tex]
[tex]S_{b} +S_{c} =12[/tex] this will be our equation (1)
For the trip back the boat is traveling against the current, so:
[tex]S _{b} -S_{c} = \frac{156}{26} [/tex]
[tex]S_{b} -S_{c} =6[/tex] this will be our equation (2)
Next, lets add equation (1) and equation (2) to get rid of [tex]S _{c} [/tex]:
[tex] \left \{ {{S_{b}+S_{c} =12} \atop {+(S_{b}-S_{c} =6})} \right. [/tex]
[tex]2S_{b} =18[/tex]
[tex]S _{b} = \frac{18}{2} [/tex]
[tex]S _{b} =9[/tex]
Finally, now that we know the speed of the boat in still water, lets replace that value in our equation (1) to find the speed of the current:
[tex]9+S_{c} =12[/tex]
[tex]S_{c} =12-9[/tex]
[tex]S_{c} =3[/tex]
We can conclude that the speed of the boath in still water is 9[tex] \frac{mi}{h} [/tex], and the current of the stream is 3[tex] \frac{mi}{h} [/tex].
WHOEVER HELPS FIRST GETS BRAINLIEST. IM BEING TIMED!!!
Answers
Answer:
Step-by-step explanation:
what 9x11
The family size bottle of sunscreen holds 12 fluid ounces of sunscreen. The regular bottle holds 75% less. How many fewer fluid ounces does the regular bottle of sunscreen hold ?
Answers
12×0.75=9
Answer:
9 ounces
Step-by-step explanation:
The information in the question given
The family size bottle of sunscreen holds 12 fluid ounces of sunscreen.
The regular bottle holds 75% less.
we need to find that how many fewer fluid ounces does the regular bottle of sunscreen hold?
Now given family size bottle holds 12 fluid ounces. But regular bottle has 75% less, therefore it can be measured as below
75/100 x 12 = 9 ounces
So the regular bottle holds 9 ounces of fluid.
A convex pentagon has the following measurements for its interior angles: (x-8), (3x-11), (x+8), (x), and (2x+7). Which of the following could be measurements for interior angles of the pentagon? Select all that apply.
A: 60
B: 68
C: 76
D: 108
E: 193
F: 540
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Answer:
60
Step-by-step explanation:
In the fraction 15⁄7, which of the following is 15?
Answers
In the fraction 15⁄7, 15 is the numerator, indicating the number of parts considered, while 7 is the denominator, indicating the total parts in a whole.
Explanation:In the fraction 15⁄7, 15 is the numerator. This is the part of the fraction that represents the number of equal parts being considered. In contrast, the 7 represents the denominator, which indicates the total number of equal parts that make up a whole.
When you see a fraction, the top number, which is called the numerator, answers the question of 'how many parts you have.' The bottom number, the denominator, answers 'how many parts the whole is divided into.' Therefore, in the given fraction, you have 15 parts out of a total of 7 parts, which suggests that you have more than one whole - this is known as an improper fraction, because the numerator is larger than the denominator.
What is the sum of the following amounts of money: $10.15 + $31.60 + $34.75 + $40 + $69.25 + $54.75?
Answers
To find the sum, add each amount together, starting from the ones place and carrying over any excess to the next place value. The total sum is $256.15.
Explanation:To find the sum of the amounts of money, you will add each amount together. $10.15 + $31.60 + $34.75 + $40 + $69.25 + $54.75. Starting with the ones digit, you have 5 + 0 + 5 + 0 + 5 + 5 = 20. Write down 0 and carry over the 2 to the tens place. Next, add the tens place digits, which gives you 1 + 6 + 7 + 0 + 2 + 4 = 20. Write down 0 again and carry over the 2 to the hundreds place. Finally, add the numbers in the hundreds place, which equals 0 + 3 + 3 + 0 + 6 + 5 + 5 = 22. Write down 2 and add it to the sum. The total sum of the amounts of money is $256.15.
The sum of $10.15, $31.60, $34.75, $40.00, $69.25, and $54.75 is calculated by adding each value together, which results in a total of $242.50.
Explanation:To calculate the sum of the amounts of money $10.15, $31.60, $34.75, $40, $69.25, and $54.75, you simply need to add each of these values together. Adding money involves lining up the decimal points and adding each column from right to left, just as with regular addition. Here's how you do it step by step:
First, write down all the numbers, aligning the decimal points:$10.15$31.60$34.75$40.00 (adding the .00 for consistency)$69.25$54.75Next, add the numbers in the rightmost column (the cent column), carry over if necessary, then move to the next column to the left (the dollar column), and do the same:
15 + 60 + 75 + 00 + 25 + 75 = 250 cents which is $2.50 (50 cents and $2 carried over)Then add the dollar amounts: $10 + $31 + $34 + $40 + $69 + $54 + $2 (carried over) = $240Add both totals together:
$240 (dollars) + $2.50 (cents) = $242.50Therefore, the sum of the amounts of money is $242.50.
How do you find x/2 + x/2 = 8/12
Answers
2x=8/6
6*2x=8/6*6
12x=8
x=8/12
x=0.66667
x/2+x/2=8/12
2x/2=8/12
divide both sides by 2, then multiply both sides by 2
x=8/12=2/3
At a factory, a mechanic earns $17.25 an hour. The president of the company earns 6 2/3 times as much for each hour he works. the janitor at the same company earns 3/5 much as the mechanic. How much does the company pay for all three people employees' wages for one hour of work
Answers
Further explanation
Order of Operations in Mathematics follow this following rule :
ParenthesesExponentsMultiplication and DivisionAddition and SubtractionThis rule is known as the PEMDAS method.
In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.
Let us tackle the problem!
At a factory, a mechanic earns $17.25 an hour
[tex]\texttt{ Mechanic's Wage } = \$17.25[/tex]
The president of the company earns 6 2/3 times as much for each hour the mechanic works
[tex]\texttt{ President's Wage } = 6\frac{2}{3} \times \texttt{ Mechanic's Wage }[/tex]
[tex]\texttt{ President's Wage } = 6\frac{2}{3} \times \$17.25[/tex]
[tex]\texttt{ President's Wage } = \$115[/tex]
The janitor at the same company earns 3/5 much as the mechanic
[tex]\texttt{ Janitor's Wage } = \frac{3}{5} \times \texttt{ Mechanic's Wage }[/tex]
[tex]\texttt{ President's Wage } = \frac{3}{5} \times \$17.25[/tex]
[tex]\texttt{ President's Wage } = \$10.35[/tex]
Total all three people employees' wages for one hour of work
[tex]\texttt{ Total Wages } = \$17.25 + \$115 + \$10.35[/tex]
[tex]\texttt{ Total Wages } = \boxed{\$142.60}[/tex]
Conclusion:The company pays $142.6 for all three people employees' wages for one hour of workLearn morePerimeter of Rectangle : https://brainly.com/question/12826246Elimination Method : https://brainly.com/question/11233927Sum of The Ages : https://brainly.com/question/11240586Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Order Of Operations
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent
What is the GCF of the numerator and denominator in the following fraction? -99/176
3
9
11
They are relatively prime.
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176 = 16*11
Both factorizations have 11 show up. It turns out that 11 is the largest common factor.
Answer: C) 11
Note: if you divide both numerator and denominator by 11, then the fraction reduces to -9/16
the answer is 11 :))
select the measurement that is most reasonable
a. a street has a width of 5 meters
b. a cat has a mass of 5 grams
c. a swimming pool has a capacity of 5 liters
d. a beetle has a mass of 5 kilograms
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Let us try to explain each option one by one.
a) a street has a width of 5 meters
This is quite reasonable as the width of street can be approximately 5 meters.
b. a cat has a mass of 5 grams
The mass of a newborn cat is 99 grams. So no cat can weigh 5 grams, as its too small.
c.a swimming pool has a capacity of 5 liters
5 liters is too small quantity for a small sized swimming pool too.
d. a beetle has a mass of 5 kilograms
A beetle is a small creature measuring mostly in grams.
So answer is option a. a street has a width of 5 meters
Can someone help me please?
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.. walkway area = π*(11 m)^2 -π*(9 m)^2 = π*(121 -81) m^2 = 40π m^2
In terms of the length of the walk and its width:
.. walkway area = 2*π*(10 m)*(2 m) = 40π m^2
b) The approximate area is
.. 40*3.14 m^2 = 125.6 m^2
Thurston wants to retire in Nevada when he is 80 years of age. Thurston, who is now 55, believes he'll need $400,000 to retire comfortably. To date, he has set aside no retirement money. To get an interest rate of 6% compounded annually, he'll have to invest today. Using the tables found in the textbook, determine how much he must invest.
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To have $400,000 for retirement in 25 years with an annual interest rate of 6% compounded annually, Thurston must invest $93,171.77 today.
Explanation:Thurston must calculate how much he needs to invest today to have $400,000 when he is 80 years old, given that he is currently 55 years old and the investment will yield 6% interest compounded annually. To find this amount, we use the formula for the present value of a lump sum, which takes into account the future value desired, the interest rate, and the number of compounding periods. The formula is:
PV = FV / (1+r)n
Where PV is the present value, FV is the future value, r is the annual interest rate, and n is the number of years until retirement.
In Thurston's case:
FV = $400,000 (the amount he needs for retirement)r = 0.06 (6% interest rate)n = 80 - 55 = 25 years (number of years until retirement)Plugging these values into the formula gives us:
PV = $400,000 / (1+0.06)25
PV = $400,000 / (1.06)25
PV = $400,000 / 4.29187072
PV = $93,171.77 (rounded to two decimal places)
Thus, Thurston must invest $93,171.77 today to retire with $400,000 in 25 years at an annual interest rate of 6% compounded annually.
You and your friend covered a total distance of 72 kilometers in a bicycle relay race. The tape diagram shows how the distance was covered in 9 equal parts.
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Answer:
Question 1.. A. Question 2.. C Question 3.. D. Question 4.. D. Question 5.. C.
Question 6.. A. Question 7.. B. Question 8.. B. Question 9.. B.
96470000 in scientific notation
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Answer: The answer is 9.647*10^7
Step-by-step explanation: in scientific notation or in standard form the expression can be written as.
9.647*10^7
This was achieved by counting one decimal place after the first digit and multiplying the the whole number by 10 raised to the power of the number counted from the write to the decimal point
The number 96,470,000 in scientific notation is written as 9.647 × 10⁷.
Given is a number we need to write it into scientific notation,
In scientific notation, a number is expressed as a product of two parts: a coefficient and a power of 10. The coefficient is a number between 1 and 10, and the power of 10 indicates the number of places the decimal point needs to be moved to obtain the original number.
To convert 96,470,000 to scientific notation, we start by moving the decimal point to the left until we have a coefficient between 1 and 10. In this case, we need to move the decimal point 7 places to the left, which gives us 9.647.
The next step is to determine the power of 10. Since we moved the decimal point 7 places to the left, the power of 10 is 7.
Therefore, we can express 96,470,000 in scientific notation as 9.647 × 10⁷.
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In this box-and-whisker plot, what is the maximum value of the data?
53
56
60
68
Answers
D. 68
Good Luck
Hope This Helps!
The answer is 68
Hope I could help you!
(Can I have Brainiest??)
the base of a right rectangular pyramid has a length of 12 centimeters, a width of 6 centimeters, and a height of 14 centimeters. Describe the cross section formed by a horizontal plane that intersects the faces of the pyramid above the base.
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A sugar solution was made by mixing 3 gal. of a 50% sugar solution and 9 gal. of a 30% sugar solution. Find the concentration of the new mixture.
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mix = [tex] \cfrac{\text{concentrate} \times gallons+\text{concentrate} \times gallons}{\text{the total number of gallons}} [/tex]
Input the numbers
mix = [tex] \cfrac{50 \% \times 3+30 \% \times 9}{3+9} [/tex]
simplify the dividend and divisor
mix = [tex] \cfrac{150 \%+270 \%}{12} [/tex]
mix = [tex] \cfrac{420 \%}{12} [/tex]
mix = [tex] \cfrac{420 \%}{12} [/tex]
mix = 35%
The new concentration is 35%
mindy needs 3 1/3 cups of raisins for the trail mix shes making she only has 1 2/3 cups of raisins in her pantry how many more raisins does she need?
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onnie is doing the office coffee run one morning. There are two coffee machines in the building: one from STACO and one from TRUCKBASS. They dispense two types of coffee: black (no milk) and white (with milk). The machines are both rather temperamental. Every fourth coffee dispensed from STACO is black and the rest are white. The coffees dispensed from TRUCKBASS are alternately black and white. Lonnie visited one of the machines and bought some coffees, of which three turned out to be white. He went back to the same machine for the afternoon run and bought the same number of coffees again. What are the possible numbers of white coffees that Lonnie could have received this time?
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He went back to the same machine for the afternoon and take another 3 coffees. Since the machine created 3 white in the morning, it should make 1 black coffee in the first run. The 2nd and 3rd run would give white coffee.
So, Lonnie will have 2 white coffee.
The possible numbers of white coffees that Lonnie could have received in the afternoon are 0 or 3.
Explanation:In this problem, Lonnie visited one of the coffee machines and bought some coffees, of which three turned out to be white. He then went back to the same machine for the afternoon run and bought the same number of coffees again. We need to determine the possible numbers of white coffees that Lonnie could have received this time.
Since every fourth coffee dispensed from STACO is black and the rest are white, we can conclude that every 3 out of 4 coffees from STACO are white. Therefore, if Lonnie received only white coffees in the morning, then it is possible that he could have received all black coffees in the afternoon.
On the other hand, the coffees dispensed from TRUCKBASS are alternately black and white. So, if Lonnie received three white coffees in the morning, it is not possible for him to receive all black coffees in the afternoon from TRUCKBASS.
Therefore, the possible numbers of white coffees that Lonnie could have received in the afternoon are 0 or 3, depending on which machine he visited.
The function y= -16t^2 +24t represents the height y (in feet) of a tennis ball bouncing straight up from the ground t seconds after it bounces. After how many seconds does the tens ball return to the ground?
Answers
Answer:
-16t² + 24t = 0
-8t(2t - 3) = 0
t = 1.5 seconds
The tennis ball returns to the ground in 1.5 seconds.
The tennis ball returns to the ground after [tex]\(\frac{3}{2}\)[/tex] seconds.
To find when the tennis ball returns to the ground, you need to determine when the height y is equal to zero. In the given function [tex]y = -16t^2 + 24t\)[/tex], set y equal to zero and solve for t:
[tex]\[ -16t^2 + 24t = 0 \][/tex]
Factor out 8t from both terms:
[tex]\[ 8t(-2t + 3) = 0 \][/tex]
Now, set each factor equal to zero:
1. 8t = 0: This gives t = 0.
2. -2t + 3 = 0: Solve for t.
[tex]\[ -2t = -3 \][/tex]
Divide both sides by -2:
[tex]\[ t = \frac{3}{2} \][/tex]
So, the two solutions are t = 0 and [tex]\(t = \frac{3}{2}\)[/tex]. However, \(t = 0\) corresponds to the initial bounce, and we are interested in the time it takes for the ball to return to the ground after the first bounce.
Therefore, the tennis ball returns to the ground after [tex]\(\frac{3}{2}\)[/tex] seconds.
Helen earns $1,840 per month, after taxes. Of her monthly pay, 45% is for rent, 1/10 is for utilities, and 1/5th is for food. How much money does Helen have left after all these expenses?
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The first step is to find how much money 45% of $1840 is. When you multiply 0.45 by 1840 I got 825. So 45% of $1840 is $840.
Then I needed to find what 1/10 of $1840 is. 1/10 is equal to 10%, or 0.1. If you multiply 0.1 by 1840 you get 184. So 1/10 of $1840 is $184.
1/5 is equal to 20%, or 0.2. Take 0.2 and multiply it by 1840 and get 368. So, 1/5 of $1840 is $368.
I then added all three numbers, 825, 184, and 368, toghter and got 1377.
So now we know that $1377 is used to pay for Helen's expenses.
The last step is to subtract 1377 from 1840 to get the final answer of 463.
So, Helen has $463 dollars left after all her expenses.
The amount of money that Helen would have left after all these expenses is $460.
What is the amount left?In order to determine the amount that would be left, determine the money value of the expenses, add the expenses together and subtract it from the earnings.
Amount spent on rent = 45% x 1840 = $828Amount spent on utilities 1/10 x 1840 = $184 Amount spent on food = 1/5 x 1840 = $368Total value of expenses = 1380Amount left = 1840 - 1380 = $460
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Which represents the reflection of f(x)= square root x over the x-axis?
Answers
The firs graph attached (picture 1)
ExplanationTo reflect the function over the x-axis, you multiply the whole function by -1. So, is you want to reflect [tex]f(x)[/tex], you just need to multiply [tex]f(x)[/tex] by -1: [tex]f(x)*-1=-f(x)[/tex].
Since our function is [tex]f(x)=\sqrt{x}[/tex], we are going to multiply the whole function by -1 to the get the the graph of its reflection over the x-axis (picture 1)
Reflection of f(x) over the x-axis:
[tex]-f(x)=\sqrt{x}[/tex]
[tex]g(x)=-\sqrt{x}[/tex]
Negate the value of the y-coordinate of each point, but leave the x-value the same. Therefore, option A is the correct answer.
The given function is f(x)=√x.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Here, f(x)=√x
Graph using the end point and a few selected points.
(0,0), (1, 1) and (2, 1.41)
The graph for the obtained coordinate points is given below.
The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same.
Therefore, option A is the correct answer.
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Tom borrowed $35,000 to remodel his house. At the end of 5-year loan, he had repaid a total of $46,375. At what simple interest rate did he borrow the money? How can I find the answer to this?
Answers
11375=35000(r)(5)
11375=35000(5)(r) ----- remember that multiplication is commutative
11375=175000r
Divide both sides by 175000 to cancel it:
11375/175000 = 175000r/175000
0.065 = r
To convert this to a percentage, we multiply by 100:
0.065(100) = 6.5%
there were 629,000 women motorcyclists, up from 447,000 eight years ago. what's the percentage of increase?
Answers
From the set {(-2, -5), (0, 10), (5, 8), (8, -3)}, which ordered pairs are a part of the solution set for 5x + 5y > 45?
Answers
-----------------------------------------------
Plug in (x,y) = (-2,-5)
5x + 5y > 45
5(-2) + 5(-5) > 45 ... replace x with -2; replace y with -5
-10 - 25 > 45
-35 > 45
The last inequality is false, so (-2,-5) is not in the solution set.
-----------------------------------------------
Plug in (x,y) = (0, 10)
5x + 5y > 45
5*0 + 5*10 > 45
0 + 50 > 45
50 > 45
The last inequality is true so (0,10) is in the solution set
-----------------------------------------------
Plug in (x,y) = (5,8)
5x + 5y > 45
5*5 + 5*8 > 45
25+40 > 45
65 > 45
The last inequality is true so (5,8) is in the solution set
-----------------------------------------------
Plug in (x,y) = (8,-3)
5x + 5y > 45
5*8 + 5*(-3) > 45
40 - 15 > 45
25 > 45
The last inequality is false, so (8,-3) is not in the solution set
-----------------------------------------------
Summary: The points (0, 10) and (5,8) are in the solution set
Check out the attached image to see a visual representation of this.
Notice how point B and point C are in the red shaded region.
A cup of water holds about 8 ounces. If a recipe calls for 1/3 cup of water, which is the best estimate of the number of ounces that are needed?
Answers
1/3x8 ounces so answer will be 2.66666...... Or can be rounded to 3
The best estimate for the number of ounces of water needed when a recipe calls for 1/3 cup is approximately 2.67 ounces.
What is the best estimate of the number of ounces that are needed?The best estimate of the number of ounces that are needed is calculated as follows;
To determine the number of ounces needed when a recipe calls for 1/3 cup of water, we can use the fact that there are 8 ounces in a cup.
Since 1/3 is a fraction, we need to divide 8 ounces by 3 to find the amount of water needed for 1/3 cup.
8 ounces ÷ 3 = 2.6667 ounces (rounded to four decimal places)
Rounding it to a reasonable decimal place, the best estimate for the number of ounces of water needed when a recipe calls for 1/3 cup is approximately 2.67 ounces.
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What is the area of this polygon?
42.5 units²
41.5 units²
35.5 units²
29.5 units²