Answers
\( {x}^{2} - x + 5 = ({x - a})^{2} + b\)
\( {x}^{2} - x + 5 = {x}^{2} + 2ax + {a}^{2} + b \)
This is the equation which mean all the terms must be equalls to the like terms over the " = " peer to peer , look :
\( {x}^{2} = {x}^{2} \)
And
\( - x = 2ax\)
And
\( {a}^{2} + b = 5\)
_____________________________________________
Now it's time to find the a and b values ;
\( - x = 2ax\)
Divide both sides by x
\( \frac{ - x}{x} = \frac{2ax}{x} \\ \)
\( - 1 = 2a\)
Divide both sides by 2
\( \frac{ - 1}{2} = \frac{2a}{2} \\ \)
\(a = - \frac{1}{2} \\ \)
♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡
\( {a}^{2} + b = 5\)
\(( { - \frac{ 1}{2} })^{2} + b = 5 \\ \)
\( \frac{1}{4} + b = 5 \\ \)
Subtract both sides ¼
\( \frac{1}{4} - \frac{1}{4} + b = 5 - \frac{1}{4} \\ \)
\(b = \frac{20}{4} - \frac{1}{4} \\ \)
\(b = \frac{19}{4} \\ \)
_____________________________________________
Thus :
\(a = - \frac{1}{2} \\ \)
\(b = \frac{19}{4} = 4.75 \\ \)
There you go...
Have a great day ❤
Related Questions
For an apartment complex, the association collects $158,000 from all of its 211 residents. What is the average rent per capita for this apartment complex?
Answers
Volunteers for a human performance study were randomly divided into two groups. The first group had their flexibility measured in the morning after a short meditation session while the second group had their flexibility measured in the afternoon with no previous meditation session. The flexibility scores of the two groups were compared. This experiment was not double-blind because:
a. some of the volunteers stretched before they went to the study location.
b. volunteers were allowed to keep their eyes open while having their flexibility measured.
c. volunteers were randomized into the two groups.
d. the volunteers knew whether they had meditated before having their flexibility measured.
Answers
Answer:
C
Have a wonderful day!
The experiment was not double-blind because volunteers were randomized into the two groups. The correct option is c.
What is a double-blind experiment?A type of clinical experiment where neither the research team nor the subjects are aware of the treatment or intervention they are receiving until the trial is complete. As a result, the study's findings are less likely to be skewed.
Because neither the participant nor the clinician is aware of who has received what treatment, double-blind studies are regarded as the most trustworthy sort of research. This is done in an effort to lessen bias and the placebo effect.
Both the researchers and the test subjects must be uninformed of who is receiving the treatment and who is receiving a placebo in a double-blind trial.
Therefore, the correct option is c. volunteers were randomized into the two groups.
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Which ordered pairs are solutions to the equation x+6y=4?
Answers
Answer:
(10 , -1)
Step-by-step explanation:
(10)+6(-1)=4
10-6=4
m.
x-intercept =
1/2
and y-intercept = 3
Write an equation for the line in point-slope form and in slope-intercept form
Answers
Answer:
slope intercept form: y= -6x+3
point slope form: y-0= -6(x -1/2)
Step-by-step explanation:
point slope form: y - y1 = m(x - x1)
substitute the values y-0=-6(x-1/2)
slope intercept form:
find the slope using two given points
m = (y2 - y1) / (x2 - x1)
= (3 - 0) / (0 - 1/2)
= 3 / (-1/2)
= -6
substitute into equation
y= -6x+3
Thomas spends 37of his money on rent and 49of his money on food. Does he spend more money on food or rent?
Answers
Answer:
He spends more money on food
Step-by-step explanation:
Looking in the tens place, we have a 4 and a 3. 4 is greater than three and the 4 belongs to 49. Overall 49>37 so he spent more money on food.
Bob and Laquisha have volunteered to serve on the Junior Prom Committee. The names of twenty volunteers,
including Bob and Laquisha, are put into a bowl. If two names are randomly drawn from the bowl without
replacement, what is the probability that Bob's name will be drawn first and Laquisha's name will be drawn
second?
Answers
Answer:
1/380
Step-by-step explanation:
Probability of Bob's name drawn first is:
1/20 as there are 20 people with equal chanceAnd probability of Laquisha's name drawn second is:
1/19 as there are 19 people left with equal chanceProbability of the two events happening is:
1/20*1/19 = 1/380 product of individual probabilitiesAnswer:
Hey there!
1/19 (1/20)=1/380, so the probability is 1/380
Let me know if this helps :)
Please helppp meeee for brainliest!! ❤️❤️
Answers
Answer:
I'm sorry but I couldn't see the hole question
Which statement best describes a strategy for estimating the perimeter of the figure below if the grid squares have
side lengths 1 cm?
Add the lengths of the horizontal and vertical segments, and then subtract 5 because the diagonal side is 4 units
wide and 2 units tall.
O Add the lengths of the horizontal and vertical segments, and then subtract 3 because the diagonal side is 4 units
wide but only 2 units tall.
O Add the lengths of the horizontal and vertical segments, and then add 3 because the diagonal side is 4 units wide
but only 2 units tall.
O Add the lengths of the horizontal and vertical segments, and then add 5 because the diagonal side is 4 units wide
and 2 units tall.
Answers
The best statement that describes the strategy for estimating the perimeter of the figure (please see the attached diagram) is the option;
Ad the lengths of the horizontal and vertical segments, and then add 5 because the diagonal side is 4 units wide and 2 units tall
What is an estimate of an amount?An estimate is an approximation of a true value, which is a value that is close to the actual value of the measured quantity.
Please find attached a diagram of the possible figure created with MS Word
The length of the side of the sides of the possible figure in the figure, obtained from a similar question on the internet are;
Base length = 5 units
Height = 4 units
The figure has a diagonal side which is 4 units wide and 2 units tall.
The length of the slant side, found using Pythagorean theorem can be obtained as follows; Length = √(4² + 2²) = 2·√5 ≈ 5
The correct option is therefore to add the lengths of the horizontal and vertical segments, and then add 5 because the diagonal side is 4 units wide and 2 units tall
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Find the missing length indicated
Please help, no links
Answers
Answer:
x = 48
Step-by-step explanation:
36/x = x/64
x² = 36 x 64 = 2304
x = √2304 = 48
Let z denote a variable that has a standard normal distribution. Determine the value z* to satisfy the following conditions. (Round your answers to two decimal places.)
a. P(z < z*) = 0.0244
z* =
b. P(z < z*) = 0.0098
z* =
c. P(z < z*) = 0.0496
z* =
d. P(z > z*) = 0.0204
z* =
e. P(z > z*) = 0.0098
z* =
(f) P(z > z* or z < -z*) = 0.201
z* =
Answers
Answer:
a) z* = -1.97
b) z* = -2.33
c) z* = -1.65
d) z* = 2.04
e) z* = 2.33
f) z* = -1.25.
Step-by-step explanation:
Z-score:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
a. P(z < z*) = 0.0244
We have to look at the ztable, and find z which has a pvalue of 0.0244. So it is z* = -1.97
b. P(z < z*) = 0.0098
We have to look at the ztable, and find z which has a pvalue of 0.0098. So it is z* = -2.33
c. P(z < z*) = 0.0496
We have to look at the ztable, and find z which has a pvalue of 0.0496. So it is z* = -1.65
d. P(z > z*) = 0.0204
We have to look at the ztable, and find z which has a pvalue of 1 - 0.0204 = 0.9796. So z* = 2.04
e. P(z > z*) = 0.0098
We have to look at the ztable, and find z which has a pvalue of 1 - 0.0098 = 0.9902. So z* = 2.33
(f) P(z > z* or z < -z*) = 0.201
This is z which has a pvalue of 0.201/2 = 0.1055. So it is z* = -1.25.
them: Simplify: (3x^2 + 5x – 6) – (4x^2 + 7x - 3)
Answers
Answer: -7x^2 - 2x - 3
Step-by-step explanation:
(3x^2 + 5x – 6) – (4x^2 + 7x - 3)
first, solve the exponents
9x^2 + 5x - 6 - 16x^2 - 7x + 3
then combine like terms
-7x^2 - 2x - 3
Simplify (4x5y³)(-3x³y²).
O-12x³y5
Ox³y5
O-12x³y6
O-12x¹56
***
Answers
Answer:
-12x^4y^5
Step-by-step explanation:
When multiplying equal bases, add the exponents.
Remember that in a simple expression such as x, the exponent is 1.
(4x5y³)(-3x³y²) = -12x^4y^5
Here's a graph of a linear function. Write the
equation that describes that function.
8
Express it in slope-intercept form.
Enter the correct answer
000
DONE
Call
?
-8
-6
-4
-4
-6
-8
Answers
Answer:
y = 3/2x + 1
Step-by-step explanation:
I hope this helps
The equation of the linear function in slope intercept form is y = 3/2 x + 1.
What is the Equation of line in Slope Intercept form?Equation of a line in slope intercept form is y = mx + b, where m is the slope of the line and b is the y intercept, which is the y coordinate of the point where it touches the Y axis.
Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
Slope = Change in y coordinates / Change in x coordinates
The line passes through (0, 1) and (-2, -2).
Slope = (-2 - 1) / (-2 - 0)
= -3 / -2
= 3/2
The line touches the Y axis at (0, 1).
So the y intercept is 1.
So the equation in slope intercept form is,
y = 3/2 x + 1.
Hence the equation is y = 3/2 x + 1.
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7. A floor is covered by 800 tiles measuring 10 squared cm. How many square tiles of side 8 cm would be needed to cover the same floor?
Answers
Answer:
1000 tiles
Step-by-step explanation:
Determine total floor space
800 x 10 = 8000 squared cm total floor space.
Divide floor space by size of tile
8000 / 8 = 1000 tiles now required to cover the floor.
The following are ages of 17 of the signers of the Declaration of Independence.
49, 34, 42, 43, 39, 36, 50, 44, 45, 33, 34, 27, 33, 69, 46, 50, 41
Send data to calculator
Find 25th and 80th percentiles for these ages.
(If necessary, consult a list of formulas.)
(a) The 25th percentile:
The 80th
percentile:
Answers
Answer:
Step-by-step explanation:
The problem specifies that you may use a calculator. The formula, as reference, is:
You can use a regular calculator or an online spreadsheet to solve. In sheets, arrange your data and use the =PERCENTILE( ) function. In the parentheses, write the range of your data and the requested percentile as a decimal. So if I type the data (the ages of the signers for this example) in cells A:4 through A:23, I'd write =percentile(A7:A23,0.25).
So the answers:
25th percentile is 34.
80th percentile is 48.4.
Using only addition and multiplication, combine the single -digit numbers 1,2,3,4,5,6,7,8,9. So they total 100. the number must stay in the same order (Parentheses are not needed)
Answers
It is not possible to find a combination using addition and multiplication of the given single-digit numbers that totals exactly 100 while keeping the same order.
To combine the single-digit numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 using only addition and multiplication so that they total 100 while keeping the same order, we can form the following expression:
1 + 2 + 3 + 4 + 5 + 6 + 78 + 9
In this expression, we group the numbers 7 and 8 together to form 78. Then, we add all the other numbers from 1 to 6 and the number 9. Adding them up, we get:
1 + 2 + 3 + 4 + 5 + 6 + 78 + 9 = 108
Unfortunately, the sum obtained from this expression is 108, not 100 as required.
It is not possible to obtain a sum of exactly 100 by combining the single-digit numbers 1 to 9 in the given order using only addition and multiplication. This is because the largest single-digit number, 9, is relatively small compared to the desired total of 100.
Adding all the single-digit numbers in order without any multiplication would result in a sum of 45, which is significantly lower than 100. Multiplication can only further decrease the sum, making it even more difficult to reach 100.
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Could u please help
Answers
Answer:
The answer is C,(x^2+2)(x+7)
Step-by-step explanation:
x3 + 7x2 − 2x − 14.
We will group the terms.
Make pairs of the terms:
(x3 + 7x2 ) - (2x + 14.)
Now find the common factor of each pair
x^2(x+7)-2(x+7)
(x^2-2)(x+7)
Thus the factors of x3 + 7x2 − 2x − 14. are (x^2-2)(x+7)
A can is 7 inches high and has a radius of 2 inches.
P2 in
7 in
Enter the volume, in cubic inches, of the can. Round your answer to the nearest hundredth.
Answers
9514 1404 393
Answer:
87.96 in³
Step-by-step explanation:
The volume is given by the formula ...
V = πr²h
Using the given numbers, we find the volume to be ...
V = π(2 in)²(7 in) = 28π in³ ≈ 87.96 in³
Magic Realm, Inc., has developed a new fantasy board game. The company sold 15,000 games last year at a selling price of $20 per game. Fixed costs associated with the game total $182,000 per year, and variable costs are $6 per game. Production of the game is entrusted to a printing contractor. Variable costs consist mostly of payments to this contractor.
Required:
1) Prepare a contribution format income statement for the game last year and compute the degree of operating leverage.
2) Management is confident that the company can sell 18,000 games next year (an increase of 3,000 games, or 20%, over last year).
Compute:
a) The expected percentage increase in net operating income for next year.
b) The expected total dollar net operating income for next year.
Answers
The expected total dollar net operating Income for next year = $70,000
1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:
Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000
Variable expenses (15,000 × $6) = $90,000
Contribution margin = $210,000
Fixed expenses = $182,000Net operating income = $28,000
Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)
The expected percentage increase in net operating income for next year:
The expected sales in next year = 18,000
games selling price per game = $20
Therefore, Total sales revenue = 18,000 × $20 = $360,000
Variable expenses = 18,000 × $6 = $108,000
Fixed expenses = $182,000
Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses
= $360,000 – $108,000 – $182,000= $70,000
The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%
The expected total dollar net operating income for next year = $70,000
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Solve:
Three less than the product of eight thirds and nine.
Pls HELP ME
Answers
Answer:
21Step-by-step explanation:
Product of eight thirds and nine:
8/3×9 = 24Three less than the product of eight thirds and nine:
24 - 3 = 2110.8.8 Check Your Understanding
Allison went on a business trip and stayed at a hotel for three nights. She paid a total of $782.07 for the room and to
park her car. Each night, the hotel charged d dollars and $17.20 for parking. Which equation represents the total
amount, in dollars, Allison paid for the three nights?
A) d+3(17.20) = 782.07
(B) 3d+17.20 = 782.07
C) 3(d-17.20) = 782.07
D) 3(d+17.20) = 782.07
Answers
We can see that the correct equation that can depict the problem is 3(d+17.20) = 782.07. Option D
Which equation shows the total charge?We have to look at the problem that we have here. In the case of the question that we have been asked, we can see that for the problem that has been given here, it is clear that; Allison went on a business trip and stayed at a hotel for three nights. She paid a total of $782.07 for the room and to park her car.
If it is known that Each night, the hotel charged d dollars and $17.20 for parking. We can say that let the amount that is charged for the lodging be d and we have the equation as; 3(d+17.20) = 782.07.
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Find the rank of the matrix [
2 − 1 − 3 − 1
1 2 3 − 1
1 0 1 1
0 1 1 − 1
]
Answers
The rank of the matrix is 3, since there are three linearly independent rows.
The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. It is denoted by the symbol "rank(A)" for a matrix A.
To find the rank of the matrix:
[-2, -1, -3, -1] [ 1, 2, -3, -1] [ 1, 0, 1, 1] [ 0, 1, 1, -1]
We can perform row operations to reduce the matrix to row echelon form, which will help us determine the rank.
\(R_2 = R_2 + 2R_1 R_3 = R_3 + 2R_1 R_4 = R_4 + R_2\)
This gives us the following matrix:
[-2, -1, -3, -1] [ 0, 0, -9, -3] [ 0, -1, -1, 1] [ 0, 0, -4, -4]
We can see that the third row is not a linear combination of the first two rows, and the fourth row is not a linear combination of the first three rows. Therefore, the rank of the matrix is 3, since there are three linearly independent rows.
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Hi I need help with dis answer
Answers
Answer:
the second answer
juzt find the scale factors of the two numbers given (120 and 96).
Step-by-step explanation:
120/15=8 But 96/15≠6
A patient is prescribed Coreg 12.5 mg by mouth twice a day. How many tablets should the patient
receive for one dose if the medication available is 6.25 mg/tablet?
Answers
Answer:
yes...
Step-by-step explanation:
k
PLASE HELP !
Which of the following could be the lenghts of the sides for a triangle that is similarto the one shown ? 4 left 9 right 12 down ( no picture) .
A. 12,18, and 26
B. 2,4.5, and 6
C. 10,18, and 24
D. 6,12.5, and 18
Answers
The triangle having lengths 2,4.5, and 6 is similar to the given triangles.
What are similar triangles?Similar triangles are the triangles that look similar to each other but their sizes might not be exactly the same.
Given that, a triangle have side lengths 4 left 9 right 12 down, we need to find the lengths of the similar triangle to it from the given options,
We know that, two triangles to be similar, they should have equal ratios of the corresponding sides,
Therefore,
1) 12,18, and 26
Checking for the ratio,
4 / 12 = 1 /3, 9 / 18 = 1 / 2
Therefore,
The sides are not in equal ratios.
2) 2,4.5, and 6
Checking for the ratio,
4 / 2 = 2, 9 / 4.5 = 2 and 12 / 6 = 2
Since, the sides are in equal ratios.
Therefore, the triangle having lengths 2,4.5, and 6 is similar to the given triangles.
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Line j is perpendicular ( T inverse) to like k and passes through the point (2, 6).
What is the slope of line j?
Answers
Answer:
y = (1/5)x + 8
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals of each other, so the slope of line J is ...
-1/(-5) = 1/5
We can use this with the given point in the point-slope form of the equation of a line:
y = m(x -h) +k . . . . . . . line with slope m through point (h, k)
y = (1/5)(x -5) +9
y = 1/5x +8 . . . . . simplified
Katherine el día lunes utiliza 3 horas en las redes sociales, el día martes utiliza 4.30 cuantos minutos utiliza Katherine en los 2 días
Answers
Answer: 450 minutes
Step-by-step explanation:
4 hours and 30 minutes equals 4.5 hours.
3+4.5=
7.5 hours
1 hour equals 60 minutes
Hence,
7.5*60=
450 minutes
This is due in like a hour please help!
Answers
Answer:
i think the fourth one is equvilent ratio
Step-by-step explanation:
Find the distance between the point (5,12) and the line y = 5x + 12 (rounded to the nearest hundredth).
A. 1.36 units
B. 2.19 units
C. 4.81 units
D. 4.90 units
Answers
The distance between the point (5,12) and the line y = 5x + 12 is 4.90 units
How to find the distance between a point and a line?
If a point P with the coordinates (x₁, y₁), and we need to know its distance from the line represented by ax + by + c = 0
Then the distance of a point from the line is given by the formula:
d = (ax₁ + by₁ + c) / √(a² + b²)
Given: the point (5,12) and the line y = 5x + 12. The line can be written as
5x-y+12 = 0. Thus:
x₁ = 5, y₁ = 12, a = 5, b = -1, c = 12. Substitute these into the formula:
d = (ax₁ + by₁ + c) / √(a² + b²)
d = (5×5 + (-1×12) + 12) / √(5² + (-1)²)
d = 25/√26 = 4.90 units
Therefore, the distance between the point and the line is 4.90 units. Option D is the answer
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Which angle is a central angle in circle A? A) Angle 1, B) Angle 2, C) Angle 3, D) Angle 4.
