What is the intermediate step in the form (x + a)2 = b as a result ofcompleting the square for the following equation?x^2 + 74 = -10x
Answers
Given data:
The given expression is x^2+74=-10x.
The given expression can be written as,
\(\begin{gathered} x^2+74=-10x \\ x^2+10x+74=0 \\ x^2+2(x)(5)+25+49=0 \\ (x+5)^2+49=0 \\ (x+5)^2=-49 \end{gathered}\)Thus, the given expression can be written as (x+5)^2 =-49.
Related Questions
help now i will mark a brainlest
Answers
Answer:
71,576,960
Step-by-step explanation:
I hope that helps
Answer:71,576,960
Step-by-step explanation:
Jenny won a charity raffle. Her prize will be randomly selected from the 9 prizes shown below. The prizes include 4 rings, 3 cameras, and 2 headsets.
Prizes
(a) Find the odds against Jenny winning a headset.
(b) Find the odds in favor of Jenny winning a headset.
Answers
The odds against Jenny winning a headset are 88.89% or 8 out of 9, and the odds in favor of Jenny winning a headset are 11.11% or 1 out of 9.
Since Jenny won a charity raffle, and her prize will be randomly selected from the 9 prizes shown below, and the prizes include 7 rings, 1 camera, and 1 headset, to find the odds against Jenny winning a headset, and find the odds in favor of Jenny winning a headset, the following calculations must be performed:
· 1 headset out of 9 total prizes
· 1/9 = headset
· 1/9 x 100 = 11.11%
· 100 - 11.11 = 88.89%
Therefore, the odds against Jenny winning a headset are 88.89% or 8 out of 9, and the odds in favor of Jenny winning a headset are 11.11% or 1 out of 9.
Which of the numbers is greater than zero? Select all that apply?
A) - 2/3
B)0.75
C) 3/2
D) - 3.5
E) 4 2/3
Answers
Answer:
D)-3.5
is correct
answer
Are the experimental probabilities after 300 trials closer to the theoretical probabilities?
Answers
After 300 trials, the experimental probabilities may not align perfectly with the theoretical probabilities. However, with more trials, the experimental probabilities tend to converge towards the theoretical probabilities for closer alignment.
To examine whether experimental probabilities after 300 trials align closely with theoretical probabilities, let's consider an example of flipping a fair coin.
Theoretical probability: When flipping a fair coin, the theoretical probability of obtaining heads or tails is 0.5 each. This assumes that the coin is unbiased and has an equal chance of landing on either side.
Experimental probability: After conducting 300 trials of flipping the coin, we record the outcomes and calculate the experimental probabilities. Let's assume that heads occurred 160 times and tails occurred 140 times.
Experimental probability of heads: 160/300 = 0.5333
Experimental probability of tails: 140/300 = 0.4667
Comparing the experimental probabilities to the theoretical probabilities, we can observe that the experimental probability of heads is slightly higher than the theoretical probability, while the experimental probability of tails is slightly lower.
In this particular example, the experimental probabilities after 300 trials do not align perfectly with the theoretical probabilities. However, it is important to note that these differences can be attributed to sampling variability, as the experimental outcomes are subject to random fluctuations.
To draw a more definitive conclusion about the alignment between experimental and theoretical probabilities, a larger number of trials would need to be conducted. As the number of trials increases, the experimental probabilities tend to converge towards the theoretical probabilities, providing a closer alignment between the two.
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The question probable may be:
Do experimental probabilities after 300 trials tend to align closely with theoretical probabilities? Consider an example scenario and calculate both the theoretical and experimental probabilities to determine if they are close.
A manufacturer records data on the battery life of a new product and discovers the data is normally distributed. The mean life of the battery is 120 hours and has a standard deviation of 10 hours. The manufacturer commits to replacing all batteries that last less than 100 hours. If 32,200 batteries were produced, how many would they expect to replace?
Answers
The firm expects replacing around 734 batteries out of the 32,200 produced.
How to determine how many batteries many would they expect to replaceusing the normal distribution formula z = (x - )
When z denotes the z-score,
x denotes the battery life of interest, is the mean battery life, and is the standard deviation.
For x = 100, use the z-score: z = (100 - 120) / 10 z = -2
Calculate the area under the normal curve to the left of z = -2.
0.0228 is the approximate value.
The number of batteries expected to be replaced by the manufacturer is equal to the proportion of batteries with a battery life of less than 100 hours multiplied by the total number of batteries produced:
Number of batteries to be replaced = 0.0228 x 32,200
734.16 batteries are expected to be replaced.
As a result, the firm anticipates replacing around 734 batteries out of the 32,200 produced.
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What are the coordinates of the vertices of the rose garden after a translation two yards east and four yards south? Use the terms A, B, C, and D
Answers
Answer:
The coordinates of the vertices of the original rose garden are A(3, 6), B(3, 3), C(4, 3), and D(4, 6).
Because the rose garden is translated 2 yards east (2 units in the positive x-direction) and 4 yards south (4 yards in the negative y-direction), add 2 units to the x-coordinates and -4 units to the y-coordinates of all the original vertices.
A(3, 6) will become A'[(3 + 2), (6 + (-4))], or A′(5, 2).
B(3, 3) will become B'[(3 + 2), (3 + (-4))], or B′(5, -1).
C(4, 3) will become C'[(4 + 2), (3 + (-4))], or C′(6, -1).
D(4, 6) will become D'[(4 + 2), (6 + (-4))], or D′(6, 2).
Factor each polynomial. Look for a GCF first.
2x²-8k-90
O
2 (x-9) (x - 5)
2 (x + 9) (x + 5)
2 (x − 9) (x + 5)
2 (x + 9) (x - 5)
Answers
Answer:
Step-by-step explanation:
First, you could factor 2 out of the whole thing. The result would be 2(x^2-4x-45). Now we find the factors of 45 which are 1, 45, 5, 9, 15, 3. We have to find the pair that adds up to 4, and multiply to get 45. After some guess and check, we can find that 5 and 9 are those numbers. Now we have to get the right signs. Since the result is a negative number for -8k, and -90, the number that is a negative must be less than the other negative. -9<-5, so the answer would be 2(x-9)(x+5)
Find the zeroes of the polynomial
2+2√2x -6 and verify the relationship between its zeroes and
coefficients
Answers
To find the zeroes of the polynomial 2 + 2√2x - 6, we set the polynomial equal to zero and solve for x:
2 + 2√2x - 6 = 0
Rearranging the terms:
2√2x = 4
Dividing both sides by 2√2:
x = 2/√2
To simplify the expression, we rationalize the denominator:
x = (2/√2) * (√2/√2) = 2√2/2 = √2
Therefore, the zero of the polynomial is x = √2.
To verify the relationship between the zeroes and coefficients of the polynomial, we can use Vieta's formulas. For a quadratic polynomial in the form ax^2 + bx + c = 0, the sum of the zeroes is given by -b/a and the product of the zeroes is given by c/a.
In this case, the polynomial 2 + 2√2x - 6 is not a quadratic polynomial, but rather a linear one. However, we can still apply Vieta's formulas:
The sum of the zeroes is -b/a = -(2√2)/1 = -2√2.
The product of the zeroes is c/a = (-6)/1 = -6.
Therefore, the relationship between the zeroes (√2) and the coefficients (2, 2√2, -6) is that the sum of the zeroes (-2√2) is equal to the negation of the coefficient of the linear term, and the product of the zeroes (-6) is equal to the constant term of the polynomial.
IMPORTANT:Kindly Heart and 5 Star this answer, thanks!The set of real numbers is composed of rational and irrational numbers.
A. true
B.false
Answers
Answer:
true..... ............
In art class students are mixing blue and red paint to make purple paint. Isaiah mixes 3 cups of blue paint and 7 cups of red paint. Casho mixes 4 cups of blue paint and 13 cups of red paint. Use Isaiah and Casho's percent of red paint to determine whose purple paint will be redder.
Answers
Based on the percent of red paint, Casho's purple paint will be redder than Isaiah's.
To determine whose purple paint will be redder based on the percent of red paint, we need to compare the ratios of red paint to the total paint used by Isaiah and Casho.
Isaiah's Ratio:
Isaiah mixes 3 cups of blue paint and 7 cups of red paint, making a total of 3 + 7 = 10 cups of paint.
To calculate the percent of red paint, we divide the amount of red paint (7 cups) by the total amount of paint (10 cups) and multiply by 100 to get the percentage:
Red paint percentage for Isaiah = (7 cups / 10 cups) * 100 = 70%
Casho's Ratio:
Casho mixes 4 cups of blue paint and 13 cups of red paint, making a total of 4 + 13 = 17 cups of paint.
To calculate the percent of red paint, we divide the amount of red paint (13 cups) by the total amount of paint (17 cups) and multiply by 100 to get the percentage:
Red paint percentage for Casho = (13 cups / 17 cups) * 100 = 76.47% (rounded to two decimal places)
Comparing the percentages, we can see that Casho's purple paint will be redder because Casho's paint has a higher percentage of red paint (76.47%) compared to Isaiah's paint (70%).
Therefore, based on the percent of red paint, Casho's purple paint will be redder than Isaiah's.
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if the mean of x,x+3,x-5,2x and 3x then find the value of x
Answers
The Value of x is 2/3.
The value of x, we need to determine the mean of the given values and set it equal to the expression for the mean.
The mean (average) is calculated by adding up all the values and dividing by the number of values. In this case, we have five values: x, x+3, x-5, 2x, and 3x.
Mean = (x + x+3 + x-5 + 2x + 3x) / 5
Next, we simplify the expression:
Mean = (5x - 2 + 3x) / 5
Mean = (8x - 2) / 5
We are given that the mean is also equal to x:
Mean = x
Setting these two expressions equal to each other, we have:
(x) = (8x - 2) / 5
To solve for x, we can cross-multiply:
5x = 8x - 2
Bringing all the x terms to one side of the equation and the constant terms to the other side:
5x - 8x = -2
-3x = -2
Dividing both sides by -3:
x = -2 / -3
Simplifying, we get:
x = 2/3
Therefore, the value of x is 2/3.
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HURRY PLEASE HELP!!!!!!!
Answers
Answer:
\(\sqrt[3]{9x^{4} }\)
Hope this helps!
Answer:
Let's solve\(\qquad\quad {:}\leadsto\sf (3x^2){}^{\dfrac {2}{3}}\)
\(\qquad\quad {:}\leadsto\sf 3x {}^{\dfrac {2×2}{3}}\)
\(\qquad\quad {:}\leadsto\sf 3x {}^{\dfrac {4}{3}}\)
\(\qquad\quad {:}\leadsto\displaystyle\sf \sqrt [3]{3x^4}\)
Hence option b is correct1- Assume X is a Normal random variable with mean 20 and variance 25. Find the following:
(a) P (X < 15)
(b) P (X > 30)
(c) P (18 ≤ X ≤ 25)
2. Assume ∼(0,1). Find the following:
(a) a such that P (X < a) = 0.95
(b) b such that P (X ≤ b) = 0.05
(c) c such that P (X > c) = 0.8485
Answers
1) The value of given random variable having mean 20 and variance 25 is (a) 0.1587, (b) 0.0228 and (c) 0.5328.
2) The z-score corresponding to a probability of a) 0.95 is 1.645, b) 0.05 is -1.645 and c) 0.1515 is -1.04.
What about mean?The mean is a measure of central tendency, which represents the average value of a set of numbers. It is calculated by adding up all the values in the set and then dividing by the total number of values.
According to question:1) (a) We can standardize the random variable X using the formula z = (X - μ) / σ, where μ is the mean and σ is the standard deviation. Therefore,
z = (15 - 20) / 5 = -1
Using a standard normal distribution table or calculator, we can find P(Z < -1) = 0.1587.
(b) Similarly, we have
z = (30 - 20) / 5 = 2
Using the standard normal distribution table or calculator, we can find P(Z > 2) = 0.0228.
(c) To find P(18 ≤ X ≤ 25), we can again standardize the random variable:
z1 = (18 - 20) / 5 = -0.4
z2 = (25 - 20) / 5 = 1
Then we can use the standard normal distribution table or calculator to find P(-0.4 ≤ Z ≤ 1) = 0.5328.
2) (a) Since we are given that X is a standard normal random variable, we can use the standard normal distribution table or calculator to find the value of a such that P(X < a) = 0.95. From the table, we find that the z-score corresponding to a probability of 0.95 is 1.645. Therefore,
a = μ + σ * z = 0 + 1 * 1.645 = 1.645
(b) Similarly, we can find the value of b such that P(X ≤ b) = 0.05 using the standard normal distribution table or calculator. From the table, we find that the z-score corresponding to a probability of 0.05 is -1.645. Therefore,
b = μ + σ * z = 0 + 1 * (-1.645) = -1.645
(c) We want to find the value of c such that P(X > c) = 0.8485. Since the normal distribution is symmetric about the mean, we know that P(X > c) = 1 - P(X < c), so we can find the value of c such that P(X < c) = 1 - 0.8485 = 0.1515. From the standard normal distribution table, we find that the z-score corresponding to a probability of 0.1515 is -1.04. Therefore,
c = μ + σ * z = 0 + 1 * (-1.04) = -1.04.
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If AB = 10 and m_A = 20° , find AC . Round to the nearest tenth.
Answers
Answer: 9.397
Step-by-step explanation: c = a·sin(C)/sin(A) = 9.39693
N
50°
AOMN~ ARPQ
Find 0.
M
Ө
0 = [?]°
<
P
70°
R
![N50AOMN~ ARPQFind 0.M0 = [?]<P70R](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/veKTlRrJcwtcPEhjGPeUEj7WPgDpy10G.png)
Answers
Answer:
60°
Step-by-step explanation:
In similar triangles, the corresponding angles are congruent.
∠O = R
O = 70°
In ΔOMN,
∠O + ∠M + ∠N = 180 {Angle sum property of triangle}
70 + 50 + Ф = 180
120 + Ф = 180
Subtract 120 from both sides,
Ф = 180 - 120
Ф = 60°
Please I need help badly I also have stuff on my account
Answers
Since D is across from 125 on the transversal that should be the answer.
please help!! i’ll mark u brainliest !! <333333333333
Answers
What is the volume of the composite figure
Answers
Answer:
291
Step-by-step explanation:
2*2*2=8*2=16
16+(11*5*5)=291
Answer:
291cm^3
Step-by-step explanation:
11×5×5=275cm^3
2×2×2=8cm^3
8cm^3 + 8cm^3= 16cm^3
275+16=291cm^3
-12(5/6a-7/8)+1/14(3 1/2a-1 2/5)
Answers
First change mixed fractions to be full fractions
-12(5/6 a -7/8) + 1/14 (7/2 a - 7/5)
Now multiply out
-12(5)/6 a -12(-7)/8) + 7/14(2) a -7/14(5)
-60/6 a + 84/8 + 7/28 a -7/70
-10a + 10.5 + 1/4a - 1/10
-10a + 0.25a +10.5 -0.1
-9.75a + 10.4
*if this =0 and you need to solve for a then
9.75a=10.4
a= 10.4/9.75
a=16/15
Write an expression to describe the
situation.
A car travels 50 miles per hour, h. What expression
represents the total distance you've traveled?
Answers
Answer:
m = 50h, where m is the distance traveled in miles
Probability & Statistics: The Quarantine Puzzle D You are stuck at home watching people walk down the street. Assuming half the people are wearing black shoes, 1/3 are wearing white shoes and 1/6 are wearing red shoes. What is the probability that you will see a person wearing black shoes before you see a person wearing white ones? a) 3/5 b) 1/2 c) 2/5 d) 2/3
Answers
Answer:
i think its a
Step-by-step explanation:
its A
Answer:A
Step-by-step explanation:
In a pre algebra class containing 43 students, there are 4 freshman, 35 sophomores, and 4 juniors. what fraction of the class are sophomores
Answers
The fraction of the class that is sophomores is \(35/43\).
The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.
Number of sophomores = 35
Total number of students = 43
Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)
Fraction of sophomores \(= 35 / 43\)
Therefore, the fraction of the class that are sophomores is = \(35/43\).
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write a question in y=a x b^x whose graph passes through the Coordinate points (2,12) and (3,24)
Answers
The graph of y = 3 x 2^x passes through the coordinate points (2,12) and (3,24).
To write a question in the form of y=a x b^x that passes through the coordinate points (2,12) and (3,24), we need to solve for the values of a and b.
First, let's substitute the coordinates (2,12) into the equation:
12 = a x b^2
Next, let's substitute the coordinates (3,24) into the equation:
24 = a x b^3
We now have two equations with two unknowns (a and b), which we can solve using algebra.
From the first equation, we can solve for a:
a = 12 / b^2
We can then substitute this value of a into the second equation:
24 = (12 / b^2) x b^3
Simplifying this equation, we get:
2 = b
We can then substitute this value of b back into the equation for a:
a = 12 / 2^2
a = 3
Therefore, the equation of the graph that passes through the coordinate points (2,12) and (3,24) is:
y = 3 x 2^x
We can check that this equation is correct by plugging in the coordinates:
When x = 2: y = 3 x 2^2 = 12
When x = 3: y = 3 x 2^3 = 24
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She made her fortune by inventing and selling specialized hair products, including an innovative Edge Control product that sold for $0.45 each. Which algebraic expressions describe the total amount of money spent by consumers for any number of Edge Control products sold, e?
Answers
Answer:
no
Step-by-step explanation:
-4p + (-2) +2p + 3 combine like terms
Answers
Answer:
Step-by-step explanation:
-4p+-2= -6p
-6p+2= -4p
-4p+3= -1p
= -1p
Use the image to determine the direction and angle of rotation.
graph of triangle ABC in quadrant 4 and a second polygon A prime B prime C prime in quadrant 2
90° clockwise rotation
90° counterclockwise rotation
180° clockwise rotation
270° counterclockwise rotation
Answers
The angle of rotation for the described transformation is
180° clockwise rotationHow to know the angle of rotationThe movement or transformation described is form quadrant 4 to quadrant 2.
The transformation will require 180 degrees transformation.
In this type of transformation, both clockwise and the counter clockwise have similar effects
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Which angles below are equal to ∠CDB?
Answers
Answer:
(x) ∠CAB
Step-by-step explanation:
In ΔCOD and ΔBOA
\(\frac{OA}{OB} = \frac{OD}{OC} \\\\\implies \frac{OC}{OB} = \frac{OD}{OA}\)
Also,
∠COD = ∠BOA (vertically opposite angles)
⇒ ΔCOD and ΔBOA are similar
⇒ ∠CDO = ∠BAO
⇒ ∠CDB = ∠BAC
⇒ ∠CDB = ∠CAB
Reread the three paragraphs that begin at the top of page 2 and end on page 3. How does the flashback in these paragraphs advance the plot
Answers
The way the flashback in these paragraphs advance the plot is C. It introduces Evan's motivation for working in the garden with Grandfather.
What is Flashback Narrative?The technique of flashback in storytelling involves interrupting the chronological order of events to depict an earlier event or scene. It uses time travel to furnish the audience with necessary backstory, context, or a deeper understanding of the characters.
The technique of flashbacks is frequently employed as a means of divulging previous occurrences, recollections, or incidents that hold significance to the present narrative being conveyed.
Hence, it can be seen from the given text that the use of flashback helps show the motivation which Evans had for working in the garden with Grandfather
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NEED ASAP
Which value is the solution for the equation tanx/2=1
pi/2
pi/4
3pi/4
3pi/2
Answers
Answer:
a ) π/2, 4π/3, 3π/2. 5π/3.
Step-by-step explanation:
2 sin t cos t + √3 cos t = 0
cos t ( 2 sin t + √3 ) = 0
Therefore:
cos t = 0, t 1 = π/2, t 2 = 3 π/2
or:
2 sin t + √3 = 0
2 sin t = - √3
sin t = - √3 / 2
t 3 = 4 π/3, t 4 = 5 π/3
Answer:
I think its the first option
8.5 x 6.5 i need help with this question
Answers
Answer:
55.25
Step-by-step explanation:
So, all you gotta do is get rid of the decimal, times them both, then add the decimal back into it, and how you do that is you see how many numbers are behind a decimal point in the first place, in this case, it's two (8.5, 6.5) and you got your answer!
Hope this helps! <D