Given:
The given equation is
[tex]x^2-8x+16=0[/tex]
To find:
The correct statement for the given equation.
Solution:
We have,
[tex]x^2-8x+16=0[/tex]
It can be written as
[tex]x^2-2(x)(4)+(4)^2=0[/tex]
Using the identity of perfect square trinomial, we get
[tex](x-4)^2=0[/tex] [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]
[tex](x-4)=0[/tex]
[tex]x=4[/tex]
Here, x=4 has multiplicity two because the power of factor (x-4) is 2.
x=4 is a double root and the equation is a perfect trinomial.
Therefore, the correct options are C and E.
Answer:
B) Factor to solve.
C) x = 4 is a double root.
E) The equation is a perfect square trinomial.
Step-by-step explanation:
Factor to solve.<
By inspection, the equation is a perfect square trinomial.
x = 4 is a double root
By inspection, the middle term's coefficient 8 is twice the square root of 16, the constant; therefore, it is a perfect square trinomial.
x2 − 8x + 16 = 0 → (x − 4)(x − 4) = 0 → x = 4 is a double root.
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you bought 12 red apples and 15 green apples to make a pie?
what is the ratio of the number of red apples to the total number of apples simplified?
Answer:
4:9
Step-by-step explanation:
12 red apples and 27 apples in total so it would be 12:27. Just divided it by 3
I think that's what the question is asking...
104
5
-10
-6
10
N
-10*
Given the graphs of f(x) = 3x - 3 and g(x) = -x + 5, which statements are true?
A)
The system has two solutions.
B)
The system has infinitely many solutions.
C)
Point (2, 3) is the only solution.
D)
Any point on either line is a solution.
E)
The point of intersection is the solution.
Answer:
C
Step-by-step explanation:
7. The prime factorization of which number is 2^5 x 5?
A) 50
B) 125
C) 160
D) 500
I need help fast like i apericiate the help i just dont get this
Answer:
30
Step-by-step explanation:
Since this is a right angle, we can use trig functions
Cos theta = adjacent side/ hypotenuse
cos ? = 20/23
Take the inverse cos of each side
cos ^-1 (cos ?) = cos ^-1(20/23)
? =29.59184579
To the nearest degree
? = 30
1. A ball is launched upward at 14 m/s from a platform that is 30 m high.
a. Find the maximum height the ball reaches.
Step-by-step explanation:
Initial velocity ,u= 14 m/s
a =_g
= 9.8 m/s
velocity at highest point,v=30 m/ s
=2as=v sqare _u square
=s= 35.99 m
A k out of n system is one in which there is a group of n components, and the system will function if at least k of the components function. For a certain 4 out of 6 system, assume that on a rainy day each component has probability 0.7 of functioning, and that on a non rainy day each component has probability 0.9 of functioning.Assume that the probability of rain tomorrow is 0.20. What is the probability that the system will function tomorrow
Using the law of total probability, the probability that the system will function is 0.86.
Let,
the probability of rainy day is= p(r),
probability of non-rainy day = p(nr),
probability that system will function = p(f),
probability that system will function if it is a rainy day = p(f|r)
probability that system will function in non-rainy day = p(f|nr)
Then the following information is given in the question:
p(r) = 0.20
then, p(nr) = 1-0.20 = 0.80
p(f|r) = 0.7 (4 out of 6 components function with 0.7 probability each)
p(f|nr) = 0.9 (4 out of 6 components function with 0.9 probability each)
We have to find the probability that the system will function tomorrow.
According to the total probability law:
Probability that function will function tomorrow = p(r)p(f|r) + p(nr)p(f|nr)
Substitute the given probabilities:
P(f) = 0.20 x 0.7 + 0.80 x 0.9
P(f) = 0.14 + .72
P(f) = 0.86
Hence, the probability that the system will function tomorrow is 0.86.
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Then determine the domain and range.
{(4,0), (3, 2), (3,0), (-3,-2), (4,-1)}
Can sb plz help ♂️
Answer:iscusses the domain and range of a function, and how to find the domain ... {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)} ... If you find any duplicate x-values, then the different y-values mean that you do not have a function. ... I'll just list the x-values for the domain and the y-values for the range: domain: {–3, –2, –1, 0, 1, 2}. range: {5}.
Step-by-step explanation:
Harriet wants to buy items worth $248.50. She is using a store coupon for 25 percent off her purchases. She has to pay 5 percent sales tax. Calculate the total cost of the items.
A.
$195.70
B.
$186.38
C.
$177.06
question:
-12 = 24 + 4b
Answer:
b = -9
Step-by-step explanation:
Answer:
-9
Step-by-step explanation:
-12 = 24 + 4b
-12 -24 = 4b
-36 / 4 = b
b = -9
The sum of fifteen times a number and thirty is less than the difference of ten times a number and forty-five
Answer:
15x+30<10x-45
Step-by-step explanation:
Find the approximate circumference, in terms of π, of chicken pie that had a radius of 3.25 inches.
A) 3.25 πin.
B) 6.5 πin.
C) 20 πin.
D) 1.625 πin.
Answer:
B
Step-by-step explanation:
I Had this
321.5 miles in 5 hours
Answer:
i think its 64.3
What is the volume of the following rectangular prism?
Step-by-step explanation:
To find the volume of a rectangular prism, we multiply the length of the prism by the width of the prism by the height of the prism.
Apply Theorem 22-B to solve for "b" State the proportion, and then the answer 27 12
Step-by-step explanation:
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zbajaibaaujabajaja
buwsusbvajz
The sum of three consecutive even integers is
312. Find the Integers.
Answer:
104, 105, 106
Step-by-step explanation:
Consider three consecutive integers. If the first is x then the second is 1 more than x (or x+1) and the third is x+2
The sum of these three integers is x + x+1 + x+2 and is known to be 312, so
x + x+1 + x+2 = 312, gather like terms
3x + 3 = 312, subtract 3 from both sides
3x = 309, divide both sides by 3
x = 104, so the integers are
104, 105, 106
the square root of the sum of twice a number and 3 is 6. find the number
Answer in fraction form = 33/2
Answer in decimal form = 16.5
===========================================================
Work Shown:
n = some number
2n = twice that number
2n+3 = "sum of twice a number and 3"
[tex]\sqrt{2n+3}[/tex] = square root of the previous expression
The equation we need to solve is [tex]\sqrt{2n+3} = 6[/tex]
We'll follow PEMDAS in reverse, undoing each operation, to isolate n
[tex]\sqrt{2n+3} = 6\\\\\left(\sqrt{2n+3}\right)^2 = 6^2 \ \ \text{ ... square both sides}\\\\2n+3 = 36\\\\2n+3-3 = 36-3 \ \ \text{ ... subtract 3 from both sides}\\\\2n = 33\\\\\frac{2n}{2}=\frac{33}{2} \ \ \text{ ... divide both sides by 2}\\\\n = \frac{33}{2}\\\\n = 16.5[/tex]
Answer:
[tex]\frac{33}{2}[/tex]
Step-by-step explanation:
In the problem, "The square root of the sum of twice a number and 3 is 6" can be converted to an equation that looks like this:
Let x be the number:
[tex]\sqrt{2x+3 = 6 }[/tex]
In order to solve the problem:
[tex]\sqrt{2x+3}^2=6^2[/tex]
By squaring both sides to remove the exponent:
[tex]{2x + 3 = 36}[/tex]
Simplify:
[tex]{2x+3-3=36-3}[/tex]
Subtract 3 from both sides:
[tex]{2x = 33 }[/tex]
Then Simplifying further:
[tex]\frac{2x}{2} = \frac{33}{2}[/tex]
Divide both sides by 2 to remove 2 from the x.
[tex]{x = \frac{33}{2} }[/tex]
Thus, meaning the answer is [tex]\frac{33}{2}[/tex]
Hope this helps you.
4 (k - 6) = 6 (-4 - 5k)
a) 10
b) 0
c) -2
d) 8
Step-by-step explanation:
step 1. what is the question? solve for k? okay.
step 2. 4(k - 6) = 6(-4 - 5k)
step 3. 4k - 24 = -24 - 30k
step 4. 34k = 0
step 5. k = 0.
A recent study of the hourly wages of maintenance crew members for major airlines showed that the mean hourly salary was $20.50, with a standard deviation of $3.50. Assume the distribution of hourly wages follows the normal probability dis- tribution. If we select a crew member at random, what is the probability the crew member earns: a. Between $20.50 and $24.00 per hour
Answer:
0.3413 = 34.13% probability that the crew member earns between $20.50 and $24.00 per hour
Step-by-step explanation:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 recent study of the hourly wages of maintenance crew members for major airlines showed that the mean hourly salary was $20.50, with a standard deviation of $3.50.
This means that [tex]\mu = 20.5, \sigma = 3.5[/tex]
a. Between $20.50 and $24.00 per hour
This is the pvalue of Z when X = 24 subtracted by the pvalue of Z when X = 20.5. So
X = 24
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{24 - 20.5}{3.5}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
X = 20.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20.5 - 20.5}{3.5}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.5
0.8413 - 0.5 = 0.3413
0.3413 = 34.13% probability that the crew member earns between $20.50 and $24.00 per hour
The area of a parallelogram is 513cm² and the height is 19cm. Calculate the base length.
Evaluate the expression of Pg +12 when p=7 and g =-3
Answer:
-9
Step-by-step explanation:
(7)(-3)+12
-21+12
-9
Answer:
-9
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
pg + 12
p = 7
g = -3
Step 2: Evaluate
Substitute in variables: 7(-3) + 12Multiply: -21 + 12Add: -9Jake ran 6.8 miles yesterday and 10.4 miles today. How many more miles did he run today?
Answer:
3.6 more miles
Step-by-step explanation:
10.4 - 6.8 = 3.6
How did the Great Depression impact European nations?
- Peter's bike bill is automatically
deducting $78 from his bank
account every month. If his bank
account balance is at $234, how
many months will it take for Pete to
run out of money?
PLEASE
how to find (a) and (b)?
Answer:
A) Gradient = -3
B) 3y - x = 7
Step-by-step explanation:
The curve has the equation;
y = x³ - 6x² + 9x + 1
We are given the pints it passes through as;
A(2,3) and P(3, 1)
A) to find the gradient, we will find the derivative of the given equation.
Thus;
Gradient = y' = 3x² - 12x + 9
At point A, x = 2. Thus;
Gradient = 3(2²) - 12(2) + 9
Gradient = 12 - 24 + 9
Gradient = -3
B) since the gradient of the tangent = -3, it means the gradient of the normal will be; -1/-3 = 1/3
Thus, equation of the normal to the curve at point A will be;
(y - 3) = ⅓(x - 2)
Multiply both sides by 3 to get;
3y - 9 = x - 2
3y - x = 9 - 2
3y - x = 7
what is the horizontal cross section of the figure shown helpppp ill give brainliest answer
Answer:
Square
Step-by-step explanation:
Probably square
Elena is selling tickets for an amusement park.
• She sells triple the number of student tickets as adult tickets.
• She sells 8 fewer senior tickets than adult tickets. If Elena sells 15 adult tickets, does she sell at least 100 total tickets?
Answer:
Adult Tickets 3a
Student Tickets = a
Senior Tickets a+8
Step-by-step explanation:
Answer:
a=students
3a=adults
3a+8=senior
Step-by-step explanation:
The sun is 93,000,000 miles from Earth. What is the value of the 3 in the number 93,000,000
Answer:
three million
Step-by-step explanation:
Put the items least to greatest based on the importance
Answer:
Hi
Step-by-step explanation:
the enrollment at Middle School drop by 168 cents from 2015 to 2019 find the average change in the number of students each year
Answer:
42
Step-by-step explanation:
It changes 42 cents each year
A line has a slope of 7. One of the points on the line is (3,5). Which of the following could be
another point on the line?
A. (-1, -24)
B. (-2, -30)
C. (6, 24)
D. (10,55)
Answer:
c
Step-by-step explanation:
I think
The points that could be on the line
y = 7x - 16 are (-2, -30)
-30 = 7 X -2 - 16
-30 = -14 - 16
-30 = -30
Option B is the correct answer.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
A line has a slope = 7 and passes through the point (3, 5).
Now,
The equation of a line can be written as,
y = mx + c
m = 7
y = 3x + c
Now,
(3, 5) = (x, y)
5 = 7 x 3 + c
5 = 21 + x
5 - 21 = c
c = -16
The equation of the line.
y = 7x - 16
The points that could be on the line have to satisfy the equation.
y = 7x - 16
A.
(-1, -24)
y = 7 x -1 - 16 = -7 - 16 = -23
This is not true
B.
(-2, -30)
y = 7 x -2 - 16 = -14 - 16 = -30
This is true.
C.
(6, 24)
y = 7 x 6 - 16 = 42 - 16 = 26
This is not true.
D.
(10,55)
y = 7 x 10 - 16 = 70 - 16 = 54
This is not true.
Thus,
The points that could be on the line
y = 7x - 16 are (-2, -30)
-30 = 7 X -2 - 16
-30 = -14 - 16
-30 = -30
Option B is the correct answer.
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