Answers
The value of a+ b + c + d + e + f is 2.
What is Factored Form?It is referred to as being in factored form when a quadratic expression is represented as the sum of two linear factors plus a constant.
We have to factor x² – y² – z² + 2yz.
Using the general rule that p² – 2pq + q² = (p – q)² .
So we want to rearrange the last three terms.
= x² + (–y² – z² + 2yz)
Now, If we were to factor out a –1 from the last three terms, we have
= x² – (y² + z² – 2yz)
Now put y² + z² – 2yz = (y – z)².
= x² – (y – z)²
This expression is actually a differences of squares.
We know p² – q² as (p – q)(p + q).
=x² – (y – z)²
= (x – (y – z))(x + (y – z))
Now, let's distribute the negative one in the trinomial x – (y – z)
= (x – (y – z))(x + (y – z))
= (x – y + z)(x + y – z)
Now, comparing (x – y + z)(x + y – z) and (ax + by + cz)(dx + ey + fz)
we get a = 1, b = –1, c = 1, d = 1, e = 1, and f = –1.
So, a+ b + c + d + e + f
= 1 - 1 + 1+ 1 +1 - 1
= 2
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Related Questions
if a water bottle contains 375 ml, what is the volume in quarts? group of answer choices 1.21 qt 355,000 qt 0.396 qt 0.826 qt 2.52 qt
Answers
If a water bottle contains 375 ml, So the volume in quarts is 0.396 qt.
The volume of a water bottle containing 375 ml can be converted into a quart using the conversion formula.
One can use the following conversion formula to convert a given volume in ml to quarts.
The conversion formula for ml to quarts is given as;
1 ml = 0.00105669 quarts
Volume in quarts = Volume in ml × 0.00105669
Now, to calculate the volume of 375 ml of the water bottle in quarts,
We will substitute the given volume in the above conversion formula as follows,
Volume in quarts = 375 ml × 0.00105669
= 0.396 qt
Hence, the volume of the water bottle containing 375 ml is 0.396 qt.
Therefore, the correct option is C. 0.396 qt.
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I GIVE BRAINLIST ON ALL MY QUESTIONS !!!!
Which of the
following is an inequality represented by this graph ?
Answers
Answer:
y > - 1/3 x + 1
Step-by-step explanation:
?
Alice carries out an experiment to record how quickly plants grow. One plant increases in height from 12.0 cm to 13.8 cm in one week. A second plant increases by the same percentage to 16.1 cm. What was the original height of the second plant
WILL GIVE BRAINLIEST
Answers
Answer:
14.0cm
Step-by-step explanation:
if 13.8 = 12.0
then 16.1 = ?
\( \frac{16.1}{13.8} \times 12.0cm = 14.0cm \)
Answer:
14 cm
Step-by-step explanation:
1st plant:
13.8 - 12.0 = 1.8
1.8/12 = .15
.15 x 100 = 15% growth
2nd plant:
let x = original height
x + x(.15) = 16.1
1.15x = 16.1
x = 16.1 / 1.15 = 14.0 cm
Workers in an office of 40 staff were asked their favourite type of take-away. Pizza 9 Curry 6 Fish & chips 11 Kebab 10 Other 4 How many degrees represent 1 person?
Answers
Answer:
Hey there!
In total, there are 360 degrees. If there are 40 staff members, then each member has 360/40=9 degrees.
Hope this helps :)
Answer:
9 degrees
Step-by-step explanation:
There are 360 degrees in a circle
There are 40 people
360 / 40 = 9
Each person gets 9 degrees
Simplify the expression:
10 – 2 (8x – 5)
|
Answers
Answer:
\( - 16x + 20\)
Step-by-step explanation:
1. Expand by distributing terms.
\(10 - (16x - 10)\)
2. Remove parentheses.
\(10 - 16x + 10\)
3. collect like terms.
\( - 16x + (10 + 10)\)
4. Simplify.
\( - 16x + 20\)
Therefore, the answer is, -16x + 20.
3. At an exhibition, the ratio of the number of men to the number of women was 10:3. Halfway through the exhibition, 110 men left and the number of men was 5/12 of the total number of people who remained behind. How many women were there at the exhibition?
Answers
Answer:
Step-by-step explanation:
Let's assume the initial number of men at the exhibition is 10x, and the initial number of women is 3x.
After 110 men left, the number of men remaining is 10x - 110.
The total number of people remaining is (10x - 110) + (3x) = 13x - 110.
According to the given information, the number of men remaining (10x - 110) is 5/12 of the total number of people remaining (13x - 110). We can write this as an equation:
10x - 110 = (5/12)(13x - 110)
To solve this equation, we can start by simplifying both sides:
10x - 110 = (65/12)x - (55/6)
To get rid of the fractions, we can multiply both sides of the equation by 12:
12(10x - 110) = 65x - 110(2)
120x - 1320 = 65x - 220
Next, we can bring the x terms to one side and the constant terms to the other side:
120x - 65x = 1320 - 220
55x = 1100
Dividing both sides by 55, we find:
x = 20
Now, we can substitute the value of x back into the initial expressions to find the number of men and women:
Number of men = 10x = 10(20) = 200
Number of women = 3x = 3(20) = 60
Therefore, there were 60 women at the exhibition
Hope this answer your question
Please rate the answer and
mark me ask Brainliest it helps a lot
Nine seconds elapsed from the time Mark saw the lightning until he heard the thunder. The lightning was about how many kilometers from Mark? (Sound travels about 331 meters per second in air.)
Answers
Use the slopes of UQ, UR, US, and UT to estimate the rate of change of y at the specified value of x. 41) x
Answers
The formula is given as slope = (change in y) / (change in x). We can determine the direction and magnitude of the change in y as x varies.
To estimate the rate of change of y at a specific value of x using the slopes of UQ, UR, US, and UT, you can follow these steps:
Identify the points on the graph corresponding to UQ, UR, US, and UT.
Calculate the differences in y-coordinates (vertical changes) and x-coordinates (horizontal changes) between the points.
Use the slope formula (rate of change) to find the slope between each pair of points.
The formula is given as slope = (change in y) / (change in x).
Substitute the values of the differences in y-coordinates and x-coordinates into the slope formula for each pair of points.
Once you have calculated the slopes for UQ, UR, US, and UT, you can use them to estimate the rate of change of y at the specified value of x by finding the slope that corresponds to the value of x.
Finally, draw a conclusion based on the estimated rate of change of y at the specified value of x.
By calculating the slopes of UQ, UR, US, and UT and using them to estimate the rate of change of y at the specified value of x, we can determine the direction and magnitude of the change in y as x varies.
The estimated rate of change provides valuable insight into the relationship between x and y.
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Precipitation for the month of March was 4 3/4 inches less than average. In April, the precipitation was 1 1/2 inches less than
average. How many inches below average was the precipitation for both March and April?
Answers
Step-by-step explanation:
It is given that,
In March, the precipitation was 4 3/4 inches less than average and for April, the precipitation was 1 1/2 inches less than average.
We need to find how many inches below average was the precipitation for both March and April.
To find it add 4 3/4 inches and 1 1/2 inches. So,
\(4\dfrac{3}{4}+1\dfrac{1}{2}\\\\=\dfrac{19}{4}+\dfrac{3}{2}\\\\=\dfrac{19+6}{4}\\\\=\dfrac{25}{4}\\\\=6\dfrac{1}{4}\ \text{inches}\)
So, for both March and April, the precipitation was \(6\dfrac{1}{4}\ \text{inches}\) less than average.
what is x + 2y = 6? help please
!
Answers
Answer:
There are infinitely many solutions to this problem.
Step-by-step explanation:
Since we have two variables in the problem, we cannot solve for either of them unless we are given another equation with those two same variables. Therefore, there are infinitely many solutions.
A sample proportion is calculated from a sample size of 201. How large of a sample would we need in order to decrease the standard error by a factor of 7?
Answers
The new sample size we need in order to decrease the standard error by a factor of 7 is approximately 9849.
In order to calculate the new sample size needed to decrease the standard error by a factor of 7, we need to use the formula:
n2 = n1 x SE1²/SE2²
where n2 is the new sample size, n1 is the old sample size, SE1 is the old standard error, and SE2 is the new standard error.
We are given that the old sample size is 201. We also know that the formula for standard error for a proportion is:
SE = sqrt(p(1-p)/n) where p is the sample proportion.
Since we are not given the value of the sample proportion, we cannot calculate the old standard error. However, we are given that we want to decrease the standard error by a factor of 7.
This means that the new standard error will be 1/7th of the old standard error.
Therefore: SE2 = SE1/7
We can substitute this into the formula for
n2:n2 = n1 x SE1²/SE2²n2
= 201 x SE1²/(SE1/7)²n2
= 201 x SE1²/((SE1²/49))n2
= 201 x 49n2
= 9849
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i need all of the answers THANK UU
Answers
1. C because 3×3=9
9×3=27
27×3=81.....
2. Answer is C explaination in picture number 2
3. D explaination in picture number 1
You play a game in which you flip a fair coin until it comes up heads. You win a payout of 2n dollars, where n is the number of flips you performed. Assuming an initial cost of $0, what is the expected value of this game
Answers
Flip a fair coin until it comes up heads. You win a payout of 2n dollars, where n is the number of flips you performed. The expected value of this game is $2.
The game you're describing involves flipping a fair coin until you get a heads. The payout is 2^n dollars, where n is the number of flips you performed.
To calculate the expected value of this game, we can consider the probability of winning at each stage and the associated payouts.
Since the coin is fair, the probability of getting a heads on the first flip is 1/2, and the payout would be 2^1 = $2. If you don't get a heads on the first flip, you have a 1/2 chance of getting a heads on the second flip, making the probability 1/2 * 1/2 = 1/4. The payout would be 2^2 = $4. We can continue this pattern for all possible outcomes.
The expected value can be calculated as the sum of the product of the probability of each outcome and its respective payout. So, the expected value (EV) would be:
EV = (1/2 * $2) + (1/4 * $4) + (1/8 * $8) + ...
This is an infinite geometric series with a common ratio of 1/2. To find the sum of an infinite geometric series, we can use the formula:
Sum = a / (1 - r),
where "a" is the first term and "r" is the common ratio. In this case, a = (1/2 * $2) = $1, and r = 1/2. Plugging these values into the formula, we get:
Sum = $1 / (1 - 1/2) = $1 / (1/2) = $2
Therefore, the expected value of this game is $2.
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Classify the following triangle Check all that apply
A. Equilateral
B. Scalene
C. Isosceles
D. Acute
E. Right
F. Obtuse
Answers
it is a scalene and a right angled triangle
x^(2)+x-20
splitting the middle term
Answers
Here is a way you may not have been taught....
(x + a)(x + b) = x^2 + (a + b)x + ab
So you need to find two factors of -20 that add up to +1
-4 x 5 = -20 and -4 + 5 = 1. Perfect
x^2 + x - 20 = (x - 4)(x + 5)
Can some one help me with this question its hard :( down below ill give brainliest
Answers
Answer:
The answer is D
Step-by-step explanation:
when you are dividing two numbers with an exponent you want to subtract the exponents.
7-4 =3
What is the value of x in the equation below?1+2e^x+1=9a). x=log4-1b) x=log4c). x=Ln4-1d). x=ln4
Answers
The -1 part is not inside the natural log.
==============================================
Work Shown:
1 + 2*e^(x+1) = 9
2*e^(x+1) = 9-1
2*e^(x+1) = 8
e^(x+1) = 8/2
e^(x+1) = 4
x+1 = Ln(4)
x = Ln(4) - 1
Mitch is buying candy bars for his friends he wants to give 2 bars to each friend and he wants to have 10 spare bars he can afford to buy 24 candy bars
Answers
Answer:
e can treat 7 friends
Step-by-step explanation:
2f+10=24
2f=24-10=14
f=14/2=7
Solve the system of equations using elimination, or write “no solutions” or “infinite solutions” where applicable
4x-y = 7
Answers
Answer:
no solutions
Step-by-step explanation:
i guess im
Calvin evaluated Negative two-thirds times 5 and one-sixth using the steps below.
Answers
Answer:
answer gonna be B :)))
Step-by-step explanation:
PLEASE HELP I will mark brailist
Answers
Answer:
72m^2
Step-by-step explanation:
Conevert the lengths into what they really are
Length of Patio:12
width of patio:6
Soooo.....
multiply
12x6=72
Which is the ratio formed when finding Tan M?
45
24
K
M M
51
15
17
1
15
8
8
15
8
17
Answers
Answer:
tanM = \(\frac{15}{8}\)
Step-by-step explanation:
tanM = \(\frac{opposite}{adjacent}\) = \(\frac{KL}{LM}\) = \(\frac{45}{24}\) = \(\frac{15}{8}\)
Jamila deposits $800 in an account that earns yearly simple interest at a rate of 2.65%. How much is in the account after 3 years and 9 months?
Answers
Answer:First, we need to calculate the total number of years Jamila's money will be in the account.
3 years and 9 months is equivalent to 3 + 9/12 = 3.75 years.
Next, we can use the simple interest formula:
I = Prt
where:
I is the interest earned
P is the principal amount (initial deposit)
r is the interest rate (as a decimal)
t is the time (in years)
In this case, we have:
P = $800
r = 0.0265 (2.65% expressed as a decimal)
t = 3.75 years
So the interest earned is:
I = 8000.02653.75 = $79.50
Finally, we can add the interest earned to the initial deposit to get the final amount:
800 + 79.50 = $879.50
Therefore, after 3 years and 9 months, Jamila will have $879.50 in the accoun
Step-by-step explanation:
anyone know questions 2, 3, 4, 5 and 6?
Answers
A
J
A
H
those are the answers in order
two students were walking to school one day when they saw two teachers each walking with two dogs. Each dog had two ears.How many dog ears where they in all
Answers
Answer:
there were 8 dog ears in all.
Step-by-step explanation:
Since the statement says that they saw two teachers each walking with two dogs, you have to multiply the number of teachers for the number of dogs each one had to find the total number of dogs they had:
2*2=4
Now, as the statement indicates that each dog had two ears you have to multiply the number of dogs for the number of ears each one has:
4*2=8
According to this, the answer is that there were 8 dog ears in all.
Volume can be found by using the formula: volume = lwh.l = 4, w = 8, and h = 5Volume =
Answers
Answer:
160=volume
Step-by-step explanation:
if l*w*h=volume, and l=4, w=8, and h=5. then we can get an equation:
4*8*5=volume
simplify to get your answer
160=volume
Tina wrote the equations 3 x minus y = 9 and 4 x + y = 5. What can Tina conclude about the solution to this system of equations?
Answers
Answer:
(2, –3) is a solution to the system of linear equations.
Step-by-step explanation:
Given: Equations:
3x - y = 9 --------(1),
4x + y = 5 --------(2),
Add Equation (1) + Equation (2),
3x + 4x = 9 + 5
7x = 14 ( Combine like terms )
x = 2 ( Divide both sides by 7 ),
From equation 1:
3(2) - y = 9
6 - y = 9
-y = 9 - 6 ( Subtraction 6 on both sides )
-y = 3
y = - 3 ( Multiplying -1 on both sides )
The following graph describes function 1, and the equation below it describes function 2. Determine which function has a greater maximum value, and provide the ordered pair. (1 point)
Function 1
graph of function f of x equals negative x squared plus 8 multiplied by x minus 15
Function 2
f(x) = −x2 + 2x − 3
Function 1 has the larger maximum at (1, 4).
Function 1 has the larger maximum at (4, 1).
Function 2 has the larger maximum at (1, −2).
Function 2 has the larger maximum at (−2, 1).
Answers
Finding the vertex of the quadratic functions, the correct statement is:
Function 1 has the larger maximum at (4, 1).
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
\(y = ax^2 + bx + c\)
The vertex is given by:
\((x_v, y_v)\)
In which:
\(x_v = -\frac{b}{2a}\)\(y_v = -\frac{b^2 - 4ac}{4a}\)Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.For function 1, we have that:
f(x) = -x² + 8x - 15.
Hence the coefficients are a = -1, b = 8, c = -15, and the vertex is:
\(x_v = -\frac{8}{2(-1)} = 4\)\(y_v = -\frac{8^2 - 4(-1)(-15)}{4(-1)} = 1\)For function 2, we have that:
f(x) = -x² + 2x - 3.
Hence the coefficients are a = -1, b = 2, c = -3, and the vertex is:
\(x_v = -\frac{2}{2(-1)} = 1\)\(y_v = -\frac{2^2 - 4(-1)(-3)}{4(-1)} = -2\)1 > -2, hence the correct statement is:
Function 1 has the larger maximum at (4, 1).
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If B is the midpoint of AC, AB = x + 6, and AC = 5x - 6, then what is BC?
BC =
HELP PLEASE
Answers
Answer:
bc= 12 :)
Step-by-step explanation:
name all the properties of a square
Answers
Answer:
Here :)
Equilateral Polygon,
Convex Polygon,
Cyclic
Isgonal Figure
Istoxal Figure