completing the square method sucks!!
find the roots of equation by completing the square method
\(4x {}^{2} + 3x + 5 = 0\)
Answers
\(\huge\underline\purple{Answer ☘}\)
\(4x {}^{2} + 3x + 5 = 0 \\ \\ dividing \: by \: 4... \\ \frac{4x {}^{2} }{4} + \frac{3x}{4} + \frac{5}{4} = 0 \\ x {}^{2} + \frac{3x}{4} + \frac{5}{4} = 0 \\ \\ we \: know \: that... \\ \: (a + b) {}^{2} = a {}^{2} + b {}^{2} + 2ab \\ \\ here... \\ 2ab = \frac{3x}{4} \\ = > 2xb = \frac{3x}{4} \: \: \: \: \: \: \: \: \: (a = x) \\ 2b = \frac{3}{4} \\ b = \frac{3}{4} \times \frac{1}{2} = \frac{3}{8} \)
nσw ín σur єquαtíσn...\(x {}^{2} + \frac{3x}{4} + \frac{5}{4} = 0 \\ \\adding \: and \: subtracting \: (\frac{3}{8}){}^{2} \\ \\ x {}^{2} + \frac{3x}{4} + \frac{5}{4} + ( \frac{3}{8} ) {}^{2} { - ( \frac{3}{8} })^{2} = 0 \\ \\ x {}^{2} + \frac{3x}{4} + (\frac{3}{8} ) {}^{2} + \frac{5}{4} - ( \frac{3}{8} ) {}^{2} = 0 \\ \\ (x + \frac{3}{8} ) {}^{2} + \frac{5}{4 } - ( \frac{3}{8} ) {}^{2} = 0 \\ \\ (x + \frac{3}{8} ) {}^{2} = (\frac{3}{8} ) {}^{2} - \frac{5}{4} \\ \\ (x + \frac{3}{8} ) {}^{2} = \frac{9}{64} - \frac{5}{4} \\ \\ (x + \frac{3}{8} ) {}^{2} = \frac{9 - 5(16)}{64} \\ \\ (x + \frac{3}{8} ) {}^{2} = \frac{9 - 80}{64} \\ \\ (x + \frac{3}{8} ) {}^{2} = \frac{ - 71}{64} \)
ѕíncє..ѕquαrє σf αnч numвєr cαn't вє nєgαtívє..
ѕσ.. αnѕwєr dσєѕ nσt єхíѕt~
hσpє hєlpful~
~Be Brainly!The roots of the equation are ±71/64i - 3/8.
What is completing the square?The completing the square method is one of the methods of solving a quadratic equation. Now we have to solve the equation 4x^2 + 3x + 5 = 0 using this method.
First, we must divide through by 4 to have;
x^2 + 3/4x + 5/4 = 0
Next we add half of 3/4 to both sides after taking 5/4 to the RHS
(x + 3/8)^2 = -5/4 + (3/8)^2
(x + 3/8)^2 = -5/4 + 9/64
(x + 3/8)^2 = -80 + 9 /64
(x + 3/8)^2 =-71/64
x = √-71/64 - 3/8
x = ±71/64i - 3/8
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Related Questions
Consider the following geometric solids. A sphere with a ratio of surface area to volume equal to 0. 15 m-1. A right circular cylinder with a ratio of surface area to volume equal to 2. 2 m-1. What results would you expect if these two models were compared in a diffusion test?.
Answers
Rate of diffusion will be more for right circular cylinder.
"Information available from the question"
In the question:
A sphere with a ratio of surface area to volume equal to 0. 15 m-1.
A right circular cylinder with a ratio of surface area to volume equal to 2. 2 m^-1.
Now, According to the question:
Before, answering the question, First we have to understand the effect of ratio of surface area to volume on the rate of diffusion.
The ratio of diffusion for a body having larger surface area as compared to the ratio of surface area to volume will be more than a body having less surface area, Mathematically it can be written as :
V x R {where V is the rate of diffusion and R is the ratio of surface area to volume}.
As per the question, the ratio of surface area volume for a sphere is given 0.15m^-1
The surface area to volume ratio for right circular cylinder is given 2.2m^-1.
Hence, it is obvious that the ratio is more for right circular cylinder. As the rate diffusion is directly proportional to the surface area to volume ratio.
Hence rate of diffusion will be more for right circular cylinder.
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Solve this in Excel
1.2. (PART 02) [TOTAL 5 POINTS] 1.2.1 Select an appropriate probability distribution using probability plotting as a basis for your selection. 1.2.2 If the percent profit has a normal probability dist
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To select an appropriate probability distribution using probability plotting as a basis for your selection and if the percent profit has a normal probability distribution, the steps are as follows:
Step 1: First, create a set of random numbers in Excel that you want to use to generate a probability plot. This can be done by typing \(\("=RAND()"\)\)into the first cell and dragging down to create as many numbers as you want.
Step 2: Next, sort the numbers in ascending order by selecting the range of cells and clicking the "Sort Smallest to Largest" button under the "Data" tab. This step is important for creating a probability plot.
Step 3: To create a probability plot, click on the "Insert" tab and select "Scatter." Then select the "Scatter with Straight Lines and Markers" option. This will create a scatter plot with a straight line fit through the data points.
Step 4: Right-click on the data points and select "Add Trendline." In the "Format Trendline" window, select the "Linear" option and check the box for "Display Equation on chart." This will add a line equation to the chart.
Step 5: To test if the percent profit has a normal probability distribution, compare the line equation to the standard normal distribution equation, which is y = x. If the line equation is close to y = x, then the data follows a normal distribution.
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Find the general indefinite integral. (Use C for the constant of integration.) ∫6√x7dx Evaluate the integral by making the given substitution. (Use C for the constant of integration.) ∫x2√x3+39dx,u=x3+39.
Answers
The general indefinite integral of 6 \(\sqrt{(x^7)}\ is\ 4/15(x^15/2) + C\). By making the substitution u = x^3 + 39, the integral of \(x^2\sqrt{(x^3 + 39)}\) dx becomes 1/9\((u^{2/3})\) + C.
To find the general indefinite integral of 6\(\sqrt{(x^7)}\), we can use the power rule for integration, which states that ∫\(x^n\) dx = \((1/(n+1))x^{n+1} + C\), where C is the constant of integration. Applying this rule, we have ∫6\(\sqrt{(x^7)}\) dx = 6∫\((x^7)^{1/2}\) dx = 6 * (2/9)\((x^{7/2})\) + C = 4/15\((x^{15/2})\) + C.
Now, let's evaluate the integral ∫x^2√(x^3 + 39) dx by making the substitution u = \(x^3\) + 39. Taking the derivative of u with respect to x gives du/dx = \(3x^2\). Rearranging this equation, we have dx = (1/3x^2) du. Substituting this back into the integral, we get ∫\(x^2\sqrt{(x^3 + 39)}\) dx = ∫\((x^2)(u^{1/2}) * (1/3x^2)\) du = (1/3)∫\(u^{1/2}\) du.
Integrating u^(1/2) with respect to u using the power rule, we have (1/3) * \((2/3)(u^{3/2}) + C = 2/9(u^{2/3}) + C\). Substituting back u = x^3 + 39, the final result is \(2/9(x^3 + 39)^{2/3} + C\).
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Need help with this question
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Answer:
where is the question i cant see it
Step-by-step explanation:
which expressions is equivilant too 0.7590.753
Answers
The equivalent expression of the expression given as 0.75/9 * 0.75/3 is 1/48
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the equivalent expression?The expression is given as
0.75/9 * 0.75/3
Evaluate the product of the numerators
So, we have
0.75/9 * 0.75/3 = 0.5625/9 * 1/3
Evaluate the product of the denominators
So, we have
0.75/9 * 0.75/3 = 0.5625/27
Simplify the fraction
So, we have
0.75/9 * 0.75/3 = 0.0625/3
Further simplify
So, we have
0.75/9 * 0.75/3 = 625/30000
Further simplify
So, we have
0.75/9 * 0.75/3 = 1/48
Hence, the equivalent expression of the expression given as 0.75/9 * 0.75/3 is 1/48
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Someone please help????
Answers
Answer:
11.68 m^2
Step-by-step explanation:
area of triangle = 1/2(b)(h)
b = 7.3, h = 3.2
1/2(7.3)(3.2) = 11.68
Answer:
11.68m
firstly remember area of triangle is half multiplied by base multiplied by height
In A ABC. AB = 6 cm, AC = 15 cm, and mA = 48° What is the area of A ABC? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
Answers
Answer:
To find the area of triangle ABC, we can use the formula A = (1/2) * b * h, where b is the base of the triangle and h is its height. We know that AB = 6 cm and AC = 15 cm, so to find the height of triangle ABC, we need to find the length of the altitude from A to BC.
To find the length of the altitude, we can use trigonometry. Since we know the measure of angle A and the length of two sides (AB and AC), we can use the sine function to find the length of the altitude. Specifically, we can use the formula h = AC * sin(A).
Plugging in the values we have, we get:
h = 15 cm * sin(48°) h ≈ 11.32 cm
Now that we have the height, we can find the area of triangle ABC:
A = (1/2) * AB * h A = (1/2) * 6 cm * 11.32 cm A ≈ 33.96 cm²
So the area of triangle ABC is approximately 33.96 cm². Rounded to the nearest hundredth, the answer is 33.96, and since the question instructs us to only round our final answer, we don't need to round it any further.
Step-by-step explanation:
PLS HELP ME ASAP!! I NEED ANSWERS RN!!
Hernando claims that the two rectangles are congruent. Which of the following statements could he use to prove his claim? Select all that apply.
A) The rectangles are congruent since a reflection over the x-axis followed by a translation of 5 units to the right carries Rectangle 1 onto Rectangle 2.
B) The rectangles are congruent since a translation of 6 units down and 7 units to the left carries Rectangle 1 onto Rectangle 2.
C) The rectangles are congruent since a reflection over the x-axis followed by a translation of 7 units to the right carries Rectangle 1 onto Rectangle 2.
D) The rectangles are congruent since a rotation of 180 clockwise about the Origin followed by a translation of 1 unit to the right carries Rectangle 1 onto Rectangle 2.
E) The rectangles are congruent since a reflection over the y-axis followed by a translation of 1 unit to the right and 6 units up carries Rectangle 1 onto Rectangle 2.
Answers
Answer: C D E
Step-by-step explanation: they’re congruent
The correct option is A) The rectangles are congruent since a reflection over the x-axis followed by a translation of 5 units to the right carries Rectangle 1 onto Rectangle 2.
Step-by-step explanation:
Given :
Two Rectangles are Congruent.
Solution :
According to given image -
Rectangle 1 has reflection over x - axis.
Than shifted towards right by 5 units.
Threfore the correct option is A) The rectangles are congruent since a reflection over the x-axis followed by a translation of 5 units to the right carries Rectangle 1 onto Rectangle 2.
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Let xn =u n-2]-u n-9]. Sketch the result of convolving xn] with each of the following
signals:
hin=un-un-41
h2n = 8 n - 8n- 11
Answers
To convolve the signal xn with hin and h2n, we need to compute the following:
yin[n] = sum(xn[k] * hin[n-k], k=0 to 40)
y2n[n] = sum(xn[k] * h2n[n-k], k=0 to 10)
Here, we will only show the steps for computing yin[n], since the steps for computing y2n[n] are similar.
yin[n] = sum(xn[k] * hin[n-k], k=0 to 40)
= sum((u[k-2] - u[k-9]) * (u[n-k] - u[n-k-41]), k=0 to 40)
= sum(u[k-2]*u[n-k] - u[k-2]*u[n-k-41] - u[k-9]*u[n-k] + u[k-9]*u[n-k-41], k=0 to 40)
We can simplify this expression by breaking it up into four terms:
yin[n] = sum(u[k-2]*u[n-k], k=0 to 40) - sum(u[k-2]*u[n-k-41], k=0 to 40)
- sum(u[k-9]*u[n-k], k=0 to 40) + sum(u[k-9]*u[n-k-41], k=0 to 40)
The first term can be simplified as:
sum(u[k-2]*u[n-k], k=0 to 40) = sum(u[j]*u[n-j+2], j=n-40 to n)
The second term can be simplified as:
sum(u[k-2]*u[n-k-41], k=0 to 40) = sum(u[j]*u[n-j-39], j=max(0,n-40) to n-2)
The third term can be simplified as:
sum(u[k-9]*u[n-k], k=0 to 40) = sum(u[j]*u[n-j+9], j=n-40 to n)
The fourth term can be simplified as:
sum(u[k-9]*u[n-k-41], k=0 to 40) = sum(u[j]*u[n-j-32], j=max(0,n-40) to n-9)
We can now use these simplified expressions to compute yin[n] for any given value of n. Similarly, we can compute y2n[n] using the same approach.
Unfortunately, it is not possible to sketch the result of convolving xn with hin and h2n, as the resulting signals are very complex and not easily visualized.
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Certify Completion Icon Tries remaining: 3 A high school has 52 players on the football team. The summary of the players' weights is given in the box plot. What is the median weight of the players?
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Certify Completion Icon Tries remaining: 3 A high school has 52 players on the football team. The summary of the players' weights is given in the box plot. The median weight of the players on the football team is 160 pounds.
The box plot shows that the median weight of the players is the middle value of the distribution. In this case, the median weight is halfway between the 26th and 27th players, which is 160 pounds.
The box plot also shows that the minimum weight of the players is 150 pounds and the maximum weight is 212 pounds. The interquartile range, which is the range of the middle 50% of the data, is 20 pounds.
In conclusion, the median weight of the players on the football team is 160 pounds. This means that half of the players on the team weigh more than 160 pounds and half of the players weigh less than 160 pounds.
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5⅗-2.2 in decimal and in fraction
Answers
Answer:
3.4 and 3 2/5
Step-by-step explanation:
5 3/5 = 5.6
5.6 - 2.2 = 3.4
3.4 = 3 4/10 = 3 2/5
Complete the equation of the line whose slope is -2 and y intercept is (0,-8)
Answers
Answer:
y=-2x-8
Step-by-step explanation:
What is the perimeter of a parallelogram, if it's area is 36 cm^2 and the distances between the point of intersection of the diagonals and the sides are 2 cm and 3 cm? PLEASE HELP QUICK
Answers
Answer:
The perimeter of a parallelogram is 30cm.
Step-by-step explanation:
From the question , the given area of a parallelogram is 36 cm².
But the area of a parallelogram can be calculated using below formula
Area = base * height
From the question the distances that exist between the point of intersection of the diagonals and the sides are 2cm and 3cm respectively
There is the same distance between point of intersection of the diagonals and the opposite sides then,
The base of the side with 4cm can be calculated as
ha= 2+ 2= 4cm
But area can be calculated as A= base × height
36= b1 × h1
36=b1 × 4
b1= 9cm
The base of the other side can be calculated with 6cm height
h2= 3+3=6cm
A= b2× h2
36= b2 ×h2
36= b2× 6
b2= 6cm
Then the perimeter of the parallelogram can be calculated as
P= 2(b1 + b2)
= 2(6+9)
= 30cm
Hence,the perimeter of the parallelogram is 30cm
Solve the equations. Show the solution sets on a number line.
|2/3q-1|=5
Answers
Answer:
q=9 or q=−6
Step-by-step explanation:
Pls help idk what to put and pls explain
Answers
5. water is poured into a right cylindrical tank at a rate of 6 cubic inches per minute. if the radius of the base is 20 inches long; how fast is the height changing when the water level is 12 inches high?
Answers
The height is changing at the rate of 1/20in per minute in the given right cylindrical tank.
What is the right cylindrical tank?A right circular cylinder has parts that are perpendicular to its base and a closed circular surface with two parallel bases on both ends. Another name for it is a right cylinder.The formula V = r²(h) can be used to determine a cylinder's volume (h). Finding the area of the circular base shape and multiplying it by the height is all that is required to calculate a cylinder's volume.So, the changing the rate of the height:
The volume formula: V = r²(h)Where r is 20in and Volume is given 12in.Calculate height as follows:
V = r²(h)20 = 20²(h)20 = 400(h)h = 20/400h = 1/20in per minute
Therefore, the height is changing at the rate of 1/20in per minute in the given right cylindrical tank.
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What percent of 150 is 90? ANS ________ %
Answers
What percent of 150 is 90? ANS ________ %
In this problem
150 represent 100%
so
Applying proportion
Find out what percentage represent 90
so
100/150=x/90
solve for x
x=(100/150)*90
x=60%
answer is 60%A person invests 3500 dollars in a bank. The bank pays 6.75% interest compounded
quarterly. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 8500 dollars?
nt
A = P(1+2) "²
Answers
A person who invests $3,500 in a bank paying 6.75% interest compounded quarterly, must leave it for a period of 53 quarters (13 years) to reach a future value of $8,500.
What is the future value?The future value is the product of the compounded present value at an interest rate for some periods.
Compounding involves charging interest on the accumulated interest and principal, unlike the simple interest system.
When we are given the interest rate, and present and future values, we can determine the period from an online finance calculator as follows:
I/Y (Interest per year) = 6.75%
PV (Present Value) = $3,500
PMT (Periodic Payment) = $0
FV (Future Value) = $8,500
Results:
N (# of periods) = 53.023
Total Interest = $5,000.00
Thus, the investor needs 53 quarters (13 years) to accumulate a future value of $8,500.
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Linda ate lunch at a deli she ordered a turkey sandwich and a salad for $13.60 the tax was six. 5% what was the total amount Linda paid for her lunch
Answers
Write and equation of the line in slope-intercept form. (0,-2) (1,3)
Answers
Answer:
y=5x−2
I hope this helps!
32 more than a number n
Answers
Answer:
32+n
Step-by-step explanation:
32 more than the number n would be 32+n.
Hope this helps!
In a certain triangle, the measure of angle A is three times as big as the measure of angle C and the measure of angle B is 30 degrees bigger than the measure of angle C. What is the degree measure of angle A
Answers
The degree measure of angle A is 90 degrees if the measure of angle A is three times as big as the measure of angle C and the measure of angle B is 30 degrees bigger than the measure of angle C.
Let x be the measure of angle C in degrees.
According to the problem statement, angle A is three times as big as angle C, measuring 3x degrees.
Angle B is 30 degrees bigger than angle C, so its measure is x + 30 degrees.
The sum of the measures of the angles in a triangle is always 180 degrees so that we can write:
A + B + C = 180
Substituting the expressions we found for the angles in terms of x, we get:
3x + (x + 30) + x = 180
Simplifying and solving for x, we get:
5x + 30 = 180
5x = 150
x = 30
Therefore, angle C has a measure of 30 degrees, angle B has an estimate of 30 + 30 = 60 degrees, and angle A has a measure of 3(30) = 90 degrees.
So the degree measure of angle A is 90 degrees.
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a=1/7(b+c-d) solve for b
Answers
Step-by-step explanation:
ax7=7 x 1/7(b+c-d)
7a=b+c-d
7a-c+d=b
b=7a-c+d
If+you+invest+$100+at+an+interest+rate+of+15%,+how+much+will+you+have+at+the+end+of+eight+years?
Answers
Answer:
$305.9022863 or $305.90 (rounded to 2 decimal places)
Step-by-step explanation:
It is a compound interest, meaning an interest accumulates on an initial amount every period. The formula
A= P(1+R)^n
A= the total amount P=Initial amount R= rate n=time period
P=$100 R=15% or 0.15(decimal) n=8 (years)
A= 100 (1.15)^8
A= 100(3.059022863)
A=305.9022863
The amount you will have after 8 years is $220
Calculating simple interestThe formula for calculating simple interest is expressed as:
SI =PRT
P is the principal = $100
T is the time = 8 years
R is the rate. = 15%
SI = 100 * 8 * 0.15
SI = $120
Amount after 8years = $100 + $120
Amount after 8years = $220
Hence the amount you will have after 8 years is $220
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In the laboratory analysis of samples from a chemical process, 5 samples from the process are analyzed daily. In addition, a control sample is analyzed 2 times each day to check the calibration of the laboratory instruments.a) How many different sequences of process and control samples are possible each day? Assume that the five process samples are considered identical and that the two control samples are considered identical.b) How many different sequences of process and control samples are possible if we consider the five process samples to be different and the two control samples to be identical?c) For the same situation as part (b), how many sequences are possible if the first test of each day must be a control sample?
Answers
a) The total number of different sequences of process and control samples each day is 823,543. b) The total number of different sequences of process and control samples each day is 120. c) The total number of different sequences of process and control samples each day, considering the first test as a control sample, is 46656.
a) To calculate the number of different sequences of process and control samples each day, we can consider the samples as distinguishable. We have 5 process samples and 2 control samples.
For each position in the sequence, we have 7 choices (5 process samples or 2 control samples). Since the samples are independent and can be selected in any order, we can use the multiplication principle.
Therefore, the total number of different sequences of process and control samples each day is 7⁷ = 823,543.
b) Now, let's consider the five process samples to be different and the two control samples to be identical.
We have 5! (5 factorial) ways to arrange the process samples among themselves. However, the two control samples are identical, so they remain fixed in their positions.
Therefore, the total number of different sequences of process and control samples each day is 5! = 120.
c) If the first test of each day must be a control sample, we need to consider the control sample fixed in the first position. We have 1 choice for the first position (control sample) and 6 choices for the remaining 6 positions (5 process samples and 1 control sample).
Therefore, the total number of different sequences of process and control samples each day, considering the first test as a control sample, is 1 * 6⁶ = 46656.
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A small business lost $6200 in its first year, lost $2150 in its second year, and earned $4780 in its third year. Overall, in the 3-year period, how much did the business earn or lose?
Is this the correct expression?
[(6200 - 365) + ( 2150 - 730) + (4780 + 1095)]
Answers
Answer:
-6200-2150+4780
-8350+4780
Overall, they lost $3570
Jiro bought 55 oz of flour for his bakery. He used 16.2 oz to make a loaf of bread, and 0.93 oz for each muffin. How many muffins did jiro make if he had 27.64 oz flour left over
Answers
Answer:
Step-by-step explanation:
29
what is 3 644 mod 645
Answers
The answer to 3 644 mod 645 is 3.
To solve this problem, we need to find the remainder when 3644 is divided by 645.
3644 ÷ 645 = 5 with a remainder of 319 This means that 3644 can be written as:
3644 = 645 × 5 + 319
To find the remainder of 3644 mod 645, we just need to take the remainder from this equation, which is 319.
So,
3644 mod 645 = 319 mod 645
Since 319 is less than 645, the remainder is simply 319.
Therefore,
3 644 mod 645 = 319 mod 645 = 3
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The answer to 3 644 mod 645 is 3.
To solve this problem, we need to find the remainder when 3644 is divided by 645.
3644 ÷ 645 = 5 with a remainder of 319 This means that 3644 can be written as:
3644 = 645 × 5 + 319
To find the remainder of 3644 mod 645, we just need to take the remainder from this equation, which is 319.
So,
3644 mod 645 = 319 mod 645
Since 319 is less than 645, the remainder is simply 319.
Therefore,
3 644 mod 645 = 319 mod 645 = 3
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Two restaurants offer customers large pizzas using different measurements for diameter.
Restaurant 1: One large 12-inch pizza for $18.99
Restaurant 2: One large 31.75-centimeter pizza for $18.99
If 1 inch = 2.54 centimeters, what is the length of the crust around the larger pizza, using π = 3.14?
19.63 inches
37.68 inches
39.25 inches
99.70 inches
Answers
In a case whereby Two restaurants offer customers large pizzas using different measurements for diameter, the length of the crust around the larger pizza is 39.25 inches
How can the length of the crustbe determined?Considering Restaurant 1 which make use of One large 12-inch pizza for $18.99
since 1 inch = 2.54 centimeters
So, 12-inch = 30.48 centimeters
Therefore, restaurant 1 can give the one large 30.48 centimeters pizza with token of $18.99
Considering Restaurant 2: we can see that One large 31.75-centimeter pizza can taken with $18.99
Since the 31.75 centimeters > 30.48 centimeters, we can come into conclusion that the restaurant 2 gives larger pizza.
Then we can determine the length of the crust around the larger pizza. where length of the crust = circumference of circle (pizza) which can be expressed as :
l = (2πr) where 2r = d
Then l = (π × d)
l = (3.14 × 31.75)
=
l = 99.695 centimeters
=39.25 inches
Therefore, option C is correct.
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Answer: Its C
Step-by-step explanation:
Find the value of x in the equation below. 1=x -18
Answers
Answer:
x = 19
Step-by-step explanation:
1 = x - 18
1 + 18 = x
x = 19