We are given that:
a x^2 + b x + c = 0
Divide all terms with c/ a:
x^2 + (b / a) x + (c / a) = 0
Subtract c from both sides:
x^2 + (b / a) x + (c / a) – c / a = 0 – c / a
x^2 + (b / a) x = - c / a
Add a constant k to complete the square:
where k = ((b / a) / 2)^2 = (b /2a)^2
x^2 + (b / a) x + k = - c / a + k
x^2 + (b / a) x + (b/2a)^2 = - c / a + (b /2a)^2
So the perfect square trinomial is:
(x + b/2a)^2 = - c / a + (b /2a)^2
Taking the square root of both sides:
x + b/2a = sqrt [- c / a + (b /2a)^2]
x = sqrt [(-c/a) + (b /2a)^2] – (b/2a)
Answer:
My equation is 3x^2 + 12x + 24 = 0. When I divide all of the terms by 3, the equation becomes x^2 + 4x + 8 = 0. When I subtract both sides by the constant, 8, the equation is x^2 + 4x = -8. When I add a constant to create the perfect square, the equation now becomes x^2 + 12x + 36 = 28. Finally, the equation simplified equals (x + 6)= the square root of 28.
Step-by-step explanation:
Which is equivalent to “12 chairs for every 3 tables”?
Answer:
A 12 chairs per 3 table
Step-by-step explanation:
4/1 is equivalent to 12 chairs for every 3 tables.
What is fraction?Fractions are used to represent smaller pieces (or parts) of a whole.
Given a statement, 12 chairs for every 3 tables.
The statement represents 12 chairs per 3 tables, which means 12/3 = 4/1
Therefore, there are 4 chairs for every table.
Hence, 4/1 is equivalent to 12 chairs for every 3 tables.
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What is the next number in the series? 83 79 75 71 67 ?
Answer:
Given the series : 83 , 79 , 75 , 71 , 67, ?
Difference of two consecutive terms;
79 -83 = -4
75 -79 = -4
71-75 = -4
67-71= -4
Since, you can see that the number is decreases by 4 every time.
Let unknown term be x
then;
x - 67 = -4
x = 67-4
x = 63.
Therefore, the next term in the series is 63.
The next number in the series is 63.
In the given series, each number is decreasing by 4.
We can observe that the first number, 83, is decreased by 4 to get the next number, 79.
Similarly, each subsequent number is obtained by subtracting 4 from the previous number.
Following this pattern, the next number would be obtained by subtracting 4 from the last number in the series, which is 67.
67 - 4 = 63
Therefore, the next number in the series is 63.
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What type of graph would have the title, "Monthly Company Profit for the Year?"
bar graph
line plot
line graph
pictograph
Answer:
line graph
Step-by-step explanation:
In △ABC, m∠A=72°, c=61, and m∠B=16°. Find a to the nearest tenth.
Using the law of sines, the length of side a to the nearest tenth is 58.1 units.
What is law of sines?Law of sines states that When we divide side a by the sine of angle A it is equal to side b divided by the sine of angle B, and also equal to side c divided by the sine of angle C.
In ΔABC,
∠A=72°
∠B=16°
∠A + ∠B + ∠C = 180° (angle sum property)
72° + 16° + ∠C = 180°
∠C = 180° - (72° + 16°) = 92°
Using sine law, (refer to the figure attached)
[tex]\frac{sin\ A}{a} = \frac{sin\ B}{b} =\frac{sin\ C}{c} \\\\\frac{sin72}{a} = \frac{sin16}{b} = \frac{sin92}{61} \\\\\frac{sin72}{a} =\frac{sin92}{61} \\\\a = sin72 * \frac{61}{sin92} \\\\= 0.9511 * \frac{61}{0.9994} \\\\=58.05193116\\\\= 58.1[/tex]
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A bike is bought for $1200 and sold 10 months later for $940.
a) Find the depreciation equation.
b.) Value
Value
Depreciation is defined as the reduction in value of an asset over time. In this case, value reduction is due to wear and tear of an equipment (bicycle).
a. The depreciation value would simply be the difference in initial and salvage value divided by time in years.
Depreciation = (Initial value – Salvage value) / Number of years
b. Substituting the given values into the equation where:
Initial value = $1200
Salvage value = $940
Number of years = 10 months = 10/12 years
Calculating:
Depreciation = ($1200 - $940) / (10/12 years)
Depreciation = $312 / year
or
Depreciation = $26 / month
a mechanic charges 50 am hour plus parts if a bill is 450 including 150 in parts how many hours did it take
total = 450
parts = 150
450-150 = 300
50 per hour
300/50 = 6
it took 6 hours
Could one prove that a shape is a square by finding the slopes of each side?
Yes,
If a quadrilateral has four congruent facets and 4 right angles, then it's a square (reverse of the square definition).
If consecutive aspects of a rectangle are congruent, then it is a square neither the reverse of the definition nor the speak of a assets.
How do you show a form is a rectangle with the usage of the slope?If we can display that the slopes of the alternative sides are identical, then the other facets are parallel. The slopes of the opposites have been the same, so ABCD is a parallelogram. Step three: subsequent, show that the parallelogram is a rectangle.
what's the slope of a side?
The slope is just the upward thrust over the run, which is defined as the change in y over the change in x meaning the distinction of the y coordinate factors divided with the aid of the distinction of the x-factors? So we have the two x-factors, so this is six minus two, divided by the, the x-factors 3 minus one.
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A businessman has 10 employees. His salary is equal to 6 times the average of employees salaries. If the 11 of them receive a total of $64,000 in one year, what was the business mans salary that year ??
x = business man's salary
y = employee's salary
x + 10y = 64000
x = 6y
6y + 10y = 64000
16y = 64000
y = 64000/16 = 4000
x = 6*4000
x = 24000
business man's salary was $24,000
is a kiloliter greater than one liter
Find the value of 4 + (27 - 12·2) ÷ 2.
Answer's are 3.5,5.5 and 19
Which one is it
The value of 4 + (27 - 12·2) ÷ 2 would be 5.5.
What is simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.
A Simplification usually involves making the expression simple and easy to use later.
WE follow the rule PEMDAS parenthesis, exponent, multipy, divide, add, substart.
4 + (27 - 12·2) ÷ 2
4 + (27 - 24 ) ÷ 2
4 + (3) ÷ 2
4+3/2, do 3/2=1.5
then add it
4+1.5 = 5.5.
Therefore, the correct answer is 5.5
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What is the greatest common factor of 28 and 42 and 70
Tessa had $110 in her checking account. She paid her cable/internet bill for $75. She deposited $50 from her part-time job before writing a check for $85 to pay her credit card bill. What is Tessa's account balance?
110-75+50-85 =
110+50=160
75+85 = 160
160-160=0
her balance is 0
Find the area of the shaded region when r = 4 feet and the area of the triangle is: 123√ square feet
Use 1.73 for 3√ and 3.14 for π. Round your answer to two decimal places.
what is the square root of -1?
On a resent business trip it took 7 hours 30 minutes to drive 375 miles how many miles per hour was the average
Answer:
50 miles / hours.
Step-by-step explanation:
Speed may be defined as the distance covered by the object per unit time.
Speed = [tex]\frac{distance}{time}[/tex]
the distance of the business trip = 375 miles.
the time taken by the business trip = 7 hours 30 minutes = 7.5 hrs.
Speed = [tex]\frac{375}{7.5}[/tex]
Speed = 50 miles / hours.
Here, the average of miler per hour is 50 miles / hours.
Cylindrical soup radius 4 centimeters height 12 centimeters what is the volume of the soup to the nearest tenth?
Product A is an 8 oz bottle of cough medication that sells for $1.36. Product B is a 16oz bottle of cough medication that cost $3.20. Which product has the lower unit price
How is a calculation of net worth different from a day-to-day or month-to-month tallying of expenses?
If the total price paid for an item is $20.25 and the cost of the item before sales tax is $18.90, what is the rate of sales tax?
20.25 -18.90 = 1.35
1.35 / 18.90 = 0.071428571
= 7.14%
check:
18.90 x 1.34946 Round to 1.35
18.90 + 1.35 = 20.25
Sales tax = 7.14%
((81x^3 y^(-1/3))^1/4)/(x^2 y)^1/4 simplify
three tables are placed side by side. one table is 6 feet 9 inches, another is 5 feet 11 inches wide, and the third is 2 feet 10 inches wide. how wide are they combined
how do you make a equivalent ratio?
What is the probability of rolling a number less than or equal to 8 with the sum of two dice, given that at least one of the dice must show a 6?
"apply quickselect to find the median of the list of numbers 9, 12, 5, 17, 20, 30, 8."
Final answer:
To find the median using quickselect, choose a pivot value, partition the list, and repeat the process with the appropriate partition until the pivot index matches the desired median index.
Explanation:
The median of a list of numbers is the middle value when the numbers are arranged in ascending order. To apply quickselect to find the median, start by choosing a pivot value from the list. Partition the list and move all values smaller than the pivot to the left and all values larger than the pivot to the right. If the pivot index is equal to the desired median index, then the pivot value is the median. Otherwise, if the pivot index is smaller, repeat the process with the right partition; if the pivot index is larger, repeat with the left partition.
In the given example, let's apply quickselect to find the median:
Choose a pivot value, let's say 17.
Partition the list: 5, 8, 9, 12, 17, 20, 30
The pivot index is 4, which is less than the desired median index.
Repeat the process with the right partition: 17, 20, 30
Choose a new pivot value, let's say 20.
Partition the list: 17, 20, 30
The pivot index is 1, which is equal to the desired median index.
Therefore, the median of the list of numbers 9, 12, 5, 17, 20, 30, 8 is 17.
95 is described as what
A group of ladies meet for an afternoon tea party. They bring all their cats. In all, there are 26 heads and 84 feet. How many ladies and how many cats are in the room
The scores on an exam are normally distributed, with a mean of 74 and a standard deviation of 7. What percent of the scores are less than 81?The scores on an exam are normally distributed, with a mean of 74 and a standard deviation of 7. What percent of the scores are less than 81?
We are given the following variables:
Normal distribution
u = sample mean = 74
s = standard deviation of the samples = 7
x = sample value = 81
Since we are asked to find percent of the scores less than 81, this means we have to find the proportion using the z-score. The formula for z score is:
z = (x – u) / s
Substituting the given values:
z = (81 – 74) / 7
z = 1
Using the standard normal distribution tables for z, we find that:
P = 0.8413 at z = 1
Therefore this means that 84.13% of scores are less than 81.
The Answer is the two small boxes just got it right For Plato
FAR LEFT FAR RIGHT
You deposit $70 in a savings account that pays an annual interest rate of 30%. How much simple interest would you earn in 2.5 years?
If 4 is subtracted from twice a number, the result is 10 less than the number. Write an equation to solve this problem. Use n as the variable to represent the number.
Cos (pi/11)+cos (3pi/11)+cos (5pi/11)+cos (7pi/11)+cos(9pi/11)
Answer:
1/2
Step-by-step explanation: