(2x+3)²=125 find x
with full solution please
Answers
Answer:
x = ± ( 5√5 - 3 ) / 2
Step-by-step explanation:
We are given the equation ( 2x + 3 )² = 125;
\(( 2x + 3 )^{ 2 } = 125 - Take Square Root on Either Side,\\| 2x + 3 | = \sqrt{ 125 } - Simplify Square Root of 125,\\\\| 2x + 3 | = \sqrt{ 5 * 25 } - Simplify Further,\\| 2x + 3 | = 5\sqrt{ 5 } - Take | |,\\\\2x + 3 = 5\sqrt{ 5 } , and , 2x + 5 = - 5\sqrt{ 5 } - Algebra, \\2x = 5\sqrt{ 5 } - 3 , and , 2x = - 5\sqrt{ 5 } - 3 - Divide Either Side by 2\\\\x = ( 5\sqrt{ 5 } - 3 ) / 2, and , x = ( - 5\sqrt{ 5 } - 3 ) / 2\\Conclusion ; x = ( + / - 5\sqrt{ 5 } - 3 ) / 2\)
Solution ; x = ± ( 5√5 - 3 ) / 2
Related Questions
Mrs.Howard had 3 hours of talk on her monthly cell phone plan. She used 40 minutes the first week? How many minutes did Mrs.Howard have left on her cell phone?
Answers
Answer:
A. 140
Step-by-step explanation:
3 hours converts to 180 minutes, so 180-40=140, therefore A is correct.
Explanation: there are 60 minutes in an hour so we know she has at least two full hours left. If we multiply 60 by two and then add the remaining 20 minutes in the first hour from the 40 already used, we get 140. Hope this helped!
Please help need answer ASAP!
Answers
Y-intercept: The y-value that first hits the line is -3, therefore that is our y-intercept.
Slope: We can use rise over run or slope formula, but let’s use rise over run. Find two perfect points ex. (-3,0) and (-4,-4). Then, rise over run, that’ll be +1 for the rise and +4 for the run. This is true since it’s a positive association. Then rise over run is 1/4 which is our slope.
The finalized equation: y=1/4x-3
Hope this helps and mark brainliest or give thanks plssss!!
$39 pizza order with a 15% tipIs my answer correct?
Answers
The total cost is the sum of the pizza and the tip. The value of the tip is 15% of the cost of the pizza. Percentage is expressed in terms of 100. The value would be
15/100 * 39 = 5.85
The total cost would be
39 + 5.85 = 44.85
Rounding to the nearest cent, it becomes $44.90
Answer:
44.90 gotta round the the nearest cent
a. is w in fv1; v2; v3g? how many vectors are in fv1; v2; v3g? b. how many vectors are in span fv1; v2; v3g? c. is w in the subspace spanned by fv1; v2; v3g? why?
Answers
a. No, w is not in fv1; v2; v3g. There are three vectors in fv1; v2; v3g.
b. There are three vectors in the span of fv1; v2; v3g.
c. No, w is not in the subspace spanned by fv1; v2; v3g. This is because the subspace is the set of all linear combinations of the vectors in the span, and w does not have to be a linear combination of the vectors in the span.
To prove this, we first need to recall the definition of the span: it is the set of all linear combinations of a set of vectors. A linear combination is a sum of the vectors, multiplied by constants. For example, if we have a vector v1, and two constants a and b, then the linear combination of a*v1 and b*v1 is (a + b)*v1. If a vector w is not a linear combination of v1, then w is not in the span of v1.
The same logic applies to the vectors fv1; v2; v3g. If w is not a linear combination of these three vectors, then w is not in the subspace spanned by these three vectors. We can prove this by showing that w cannot be a linear combination of fv1; v2; v3g. This is because the only way to create a linear combination of these vectors is to multiply them by constants, and since w is not one of the vectors, it cannot be multiplied by a constant. Therefore, w is not in the subspace spanned by fv1; v2; v3g.
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A square has side length x and a circle has radius (x - 1). At what value of x will the two figures have the same area?
Answers
Answer:
x=(π+√π)/1-π
or x=(π-√π)/1-π
Step-by-step explanation:
since it is a square all sides are equal
Area of square=x*x=x^2
Area of a circle=πr^2
A=π(x-1)^2
two areas are equal
x^2=π(x^2-2x_1)
x^2=πx^2-2πx-π
x^2-πx^2-2πx-π=0
x^2(1-π)-2πx-π=0
using quadratic formula with a=1-π , b=-2π and c=-π
equation of the form ax^2+bx+c=0 by using the quadratic formula:
x=(−b±√b2−4ac)/2a
x=(π+√π)/1-π
or x=(π-√π)/1-π
Draw a rectangular array on graph paper for 24 x 18. Solve the problem 24 x 18 using the partial-products algorithm. Use your array to explain why the partial-products algorithm calculates the correct answer to 24 x 18.
Answers
To draw a rectangular array for 24 x 18 on graph paper, we create a grid with 24 rows and 18 columns.
The partial-products algorithm for multiplying 24 and 18 involves breaking down the multiplication into smaller, manageable steps. The array helps visualize these steps and demonstrates why the algorithm yields the correct answer. Using the array, we start by dividing the 24 x 18 rectangle into smaller squares that represent individual partial products. Each row in the array corresponds to a digit in the multiplier (24), and each column corresponds to a digit in the multiplicand (18). We fill in the array by multiplying the corresponding digits in the multiplier and multiplicand.
For example, the first partial product is obtained by multiplying the rightmost digit of the multiplier (4) by each digit in the multiplicand (8, 1). We place the result, 32, in the corresponding square in the array. Similarly, we calculate the other partial products and place them in the corresponding squares. To find the final product, we sum up all the partial products in the array. In this case, we add up the values in all the squares to get 432, which is the correct answer to 24 x 18.
The array demonstrates why the partial-products algorithm works. By breaking down the multiplication into smaller steps and organizing them in the array, we ensure that each digit in the multiplier is multiplied by each digit in the multiplicand. The array visually represents the distributive property of multiplication, where each digit in one number is multiplied by each digit in the other number. Adding up the partial products gives the total product, ensuring the correct result. The array provides a visual proof of why the partial-products algorithm yields the correct answer to the multiplication problem.
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what is the mean absolute deviation of 4, 4, 18, 6, 20, 10, 24, 2, 12, 4
Answers
Answer:
6.48
Step-by-step explanation:
Use the pair of functions to find f(g(x)) and g (f(x)). Simplify your answers. 2 f(x) = √x + 8, g(x) = x² +9 Reminder, to use sqrt(() to enter a square root. f(g(x)) = g (f(x)) =
Answers
To find f(g(x)), we substitute g(x) into the function f(x):
f(g(x)) = f(x² + 9)
= \(\sqrt {(x^2 + 9)}\)+ 8.
To find g(f(x)), we substitute f(x) into the function g(x):
g(f(x)) = g(\(\sqrt x\) + 8)
= (\(\sqrt x\) + 8)² + 9.
Let's simplify these expressions:
f(g(x)) = \(\sqrt {(x^2 + 9)}\) + 8.
g(f(x)) = (\(\sqrt x\) + 8)² + 9
= (x + 16\(\sqrt x\) + 64) + 9
= x + 16\(\sqrt x\) + 73.
Therefore, f(g(x)) = \(\sqrt {(x^2 + 9)}\) + 8 and g(f(x)) = x + 16\(\sqrt x\) + 73.
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A certain type of cereal costs $3.79 for 19.5 ounces. What is the unit rate?
Enter your answer, rounded to the nearest cent, in the box.
Answers
Step-by-step explanation:
$3.79 ÷ 19.5 = .194
answer = $.19 per oz
Answer:
0.19
Step-by-step explanation:
I took the test and passed
Work out the area of a rectangle with base, b = 14mm and perimeter, P = 30mm
Answers
Answer:
14 mm squared is the area
Step-by-step explanation:
HELPPPP ASAPPPP PLEADEEE!!!
Answers
Answer: -0.1964... i hope it's right
Step-by-step explanation:
10=7(3 + 8e)
10= 21 + 56e
-11 = 56e
-11/56= -0.1964...
Choose scales for the coordinate plane shown so that you can graph the points J(20, 3), K(25, 3), L(15, −3), M(−5, 5), and N(−5, −4). On the x−axis, use a scale of unit(s) for each grid square. On the y−axis, use a scale of unit(s) for each grid square. Complete the explanation for using using these scales for each axis. The x−coordinates range from to , and the y−coordinates range from _ to _ PLS HURRY!!!
Answers
The x-coordinates range from -5 to 25, and the y-coordinates range from -4 to 5.
To choose appropriate scales for the coordinate plane, first, observe the range of x and y coordinates for the given points J(20, 3), K(25, 3), L(15, -3), M(-5, 5), and N(-5, -4).
The x-coordinates range from -5 to 25, and the y-coordinates range from -4 to 5.
For the x-axis, we can use a scale of 5 units for each grid square.
This scale will allow us to cover the entire range of x-coordinates.
The grid will have 6 squares in the positive x-direction and 2 squares in the negative x-direction.
For the y-axis, we can use a scale of 1 unit for each grid square.
This scale will allow us to cover the entire range of y-coordinates.
The grid will have 5 squares in the positive y-direction and 4 squares in the negative y-direction.
In summary, use a scale of 5 units for each grid square on the x-axis, and a scale of 1 unit for each grid square on the y-axis.
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help with this question
Answers
Answer:
A
Step-by-step explanation:
x= -2
At this weekend’s soccer game, 20 out of the first 50 people who entered the field were not wearing hats. If this sample is representative of the 250 people attending the game, about how many of them will probably NOT be wearing hats
Answers
Answer:
150 people
Step-by-step explanation:
20/50 = 40%
So 40% are wearing hats and 60% aren't
0.6=60%
250x0.6= 150
Use the graphs to evaluate the derivative- dx 40 40 f(x) 0 x=30 40 8 0 o 40 g(x) x
Answers
The derivative of f(x) at x = 40 is 8.
The derivative of a function represents the rate at which the function is changing at a particular point. In this case, we are given two functions, f(x) and g(x), and asked to evaluate the derivative of f(x) at x = 40.
Observing the Graphs
Looking at the graph of f(x), we can see that when x = 40, the value of f(x) is 8. This indicates that the slope of the tangent line to the graph of f(x) at x = 40 is 8.
Understanding the Derivative
The derivative of a function measures the rate of change of the function with respect to its input variable. It tells us how much the function is changing as we move along the x-axis. When we evaluate the derivative at a specific point, such as x = 40, we are essentially determining the slope of the tangent line to the graph of the function at that point.
Calculating the Derivative
To find the derivative of f(x) at x = 40, we observe that the value of f(x) at that point is 8. Therefore, the derivative of f(x) at x = 40 is 8.
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Organisms A and B start out with the same
population size.
Organism A's population doubles every day. After 8
days, the population stops growing and a virus
cuts it in half every day for 2 days.
Organism B's population grows at the same rate
but is not infected with the virus. After 10 days, how
much larger is organism B's population than
organism A's population?
The expression showing organism A's increase in
population for the first 8 days is
28
The expression showing organism A's decrease in
population over the next 2 days is (1/2)2. This can be
written as (2-1)2, which is equivalent to
2-²
After 10 days, the total change in organism A's population
(combining the increase and reduction) is
Select...
which simplifies to
Select...
4 of 5 QUESTIONS
The expression showing organism B's increase in
population over the same 10 days is
Select...
The expression for how many times greater organism B's
population is than organism A's population is
Select...
After 10 days, organism B's population is
Select...
times greater than organism A's population.
Answers
The expression showing organism B's increase in population over the same 10 days is 2^10.
The expression for how many times greater organism B's population is than organism A's population is 2^2.
After 10 days, organism B's population is 4 times greater than organism A's population.
Let's calculate the population changes for organisms A and B step by step:
For Organism A:
The population doubles every day for 8 days: 2^8 = 256.
After 8 days, the population is 256.
Then, a virus cuts the population in half for 2 days: 256 * (1/2)^2 = 256 * (1/4) = 64.
After 10 days, the population of organism A is 64.
For Organism B:
The population grows at the same rate as organism A, but there is no virus.
The population doubles every day for 10 days: 2^10 = 1024.
To find how much larger organism B's population is than organism A's population after 10 days, we subtract the population of organism A from the population of organism B:Organism B's population - Organism A's population = 1024 - 64 = 960.
Therefore, after 10 days, organism B's population is 960 individuals larger than organism A's population.
The expression showing organism A's increase in population for the first 8 days is 2^8 = 256.
The expression showing organism A's decrease in population over the next 2 days is (1/2)^2 = (2^(-1))^2 = 2^(-2).
After 10 days, the total change in organism A's population is 256 * 2^(-2) = 64.
The expression showing organism B's increase in population over the same 10 days is 2^10 = 1024.
The expression for how many times greater organism B's population is than organism A's population is 1024/64 = 16.
After 10 days, organism B's population is 16 times greater than organism A's population.
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I need helpppppppp:(
Answers
The amount to be paid is more on credit card 2 is more, it must be paid first.
Explain the term credit limit?A credit limit is the most money you are permitted to spend on such a credit card or line of credit by a lender. Understanding your limit, however, does not imply that going for it is a wise decision. Credit limits are determined by credit card companies. Companies want the limits to be both high enough to encourage card use and low enough to prevent overspending.Card 1:
Current balance = $8,312.69
Annual percentage rate APR = 24.16%
Credit limit = $10,000.
Used amount = $10,000 - $8,312.69
Used amount = 1687.31
A = P\((1 + r/n)^{nt}\)
P = $1687.31
r = 24.16% = 0.2416
Take n = 1 and time = 1 year.
A = 1687.31*\((1 + 0.2416/n)^{1*1}\)
A = 1687.31 * 1.2416
A = $2094.96
For Card 2:
Current balance = $1,180.34
APR = 21.15%
Credit limit = $75,00
Used amount = $75,00 - $1,180.34
Used amount = $6319.66
A = 6319.66*\((1 + 0.2115/n)^{1*1}\)
A = 6319.66 * 1.2115
A = $7656.26
As the amount to be paid is more on credit card 2 is more, it must be paid first.
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factorise expressions
Answers
Answer: ab (7a + b - 2)
tu (3tu + 6uv + 2w)
4abc (5c - 7a + 2b)
2qrs (10p + 35q - 25)
Helpppppo plssssssss
Answers
Answer:
b
Step-by-step explanation:
used graphing calculator
Can sum1 help me plzz :) ill give brainlist
Answers
Answer:
34 hours
Step-by-step explanation:
358-35=323
323/9.50= 34
How do you use the distributive property to write the expression without parentheses: 6(a-2)?
Answers
Answer:
\(6(a - 2) = 6a - 12\)
HELP!!!!!!!!!! I NEED THIS ASAP PLEASE!!!
Graph the systems of equations.
Answers
Both the equations are plotted on the graph and they intersect each other on (2, 4).
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, graph the equation as follows:
2x + y = 8-x + 2y = 6So plot as:
(Refer to the graph attached below)The lines of both equation intersect at (2, 4).Therefore, both the equations are plotted on the graph and they intersect each other on (2, 4).
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2. A manufacturer of flashlights wants to know how well one of their newer styles is selling in a chain of large home-improvement stores. They select a simple random sample of 20 stores, record how many of the flashlights were sold in a 30-day period, and construct a 95% confidence interval for the mean number of flashlights sold.
(a) If, instead of constructing a 95% confidence interval, the flashlight manufacturer constructed a 98% confidence interval, would the 98% interval be wider, narrower, or the same width as the 95% interval? Explain.
(b) How would the width of confidence interval change if the flashlight manufacturer took a larger sample? Explain.
(c) The 20 stores in the sample were actually the only stores who provided sales figures from 36 stores that were randomly chosen to be in the sample. Can the manufacturer adjust the confidence interval to take this nonresponse into account? If so, how? If not, why not?
Answers
A: (a) The 98% confidence interval would be wider than the 95% interval. As the confidence level increases, the margin of error increases, thus making the interval wider.
(b) The width of the confidence interval would decrease as the sample size increases. This is because a larger sample size will result in a more accurate representation of the population, thus allowing for a narrower confidence interval.
(c) The manufacturer cannot adjust the confidence interval to take this nonresponse into account, as the nonresponse does not affect the accuracy of the sample. The confidence interval is based on the sample itself and not the population from which it was drawn.
What is mean by random sample?Random sampling is a method of selecting a sample of individuals from a population such that each member of the population has an equal chance of being selected.
Random sampling is often used in research studies to ensure that the sample is representative of the population as a whole.
Random sampling is also used to minimize bias and ensure that the sample is not influenced by any particular group or individual.
Random sampling is important because it helps ensure that the results of the study are accurate and valid.
Random sampling helps to ensure that the sample is representative of the population and that the results are not influenced by any particular group or individual.
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The reaction time is seconds to a stop light of a group of adult men were found to be 0.74, 0.71, 0.41, 0.82, 0.74, 0.85, 0.99, 0.71, 0.57, 0.85, 0.57, 0.55 (mean=.709) What is the variance?
Answers
The variance of the reaction times is approximately 0.02596.
To find the variance, you need to follow these steps:
1. Calculate the mean of the reaction times.
mean = (0.74 + 0.71 + 0.41 + 0.82 + 0.74 + 0.85 + 0.99 + 0.71 + 0.57 + 0.85 + 0.57 + 0.55) / 12
= 8.54 / 12
= 0.7125
2. Subtract the mean from each individual value, and square the result.
(0.74 - 0.7125)^2 = 0.000525625
(0.71 - 0.7125)^2 = 2.50625e-06
(0.41 - 0.7125)^2 = 0.09100625
(0.82 - 0.7125)^2 = 0.01150625
(0.74 - 0.7125)^2 = 0.000525625
(0.85 - 0.7125)^2 = 0.02000625
(0.99 - 0.7125)^2 = 0.07800625
(0.71 - 0.7125)^2 = 2.50625e-06
(0.57 - 0.7125)^2 = 0.02000625
(0.85 - 0.7125)^2 = 0.02000625
(0.57 - 0.7125)^2 = 0.02000625
(0.55 - 0.7125)^2 = 0.02400625
3. Calculate the sum of the squared differences.
sum = 0.000525625 + 2.50625e-06 + 0.09100625 + 0.01150625 + 0.000525625 + 0.02000625 + 0.07800625 + 2.50625e-06 + 0.02000625 + 0.02000625 + 0.02000625 + 0.02400625
= 0.285625
4. Divide the sum by the number of values minus 1 (n-1).
variance = sum / (12 - 1)
= 0.285625 / 11
≈ 0.02596
Therefore, the variance of the reaction times is approximately 0.02596.
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The last four months of sales were 8, 10, 15, and 9 units. The last four forecasts were 5, 6, 11, and 12 units. The Mean Absolute Deviation (MAD) is:
Answers
The MAD value will be = 3.
Given,
Last four months sale : 8 , 10 , 15 , 9 .
Last four forecasts were 5, 6, 11, and 12 units.
Now, we have to find the Mean Absolute Deviation (MAD) of these forecasts.
Now, the mean of the forecast values for the four months is .
Therefore, the sum of absolute deviations of the forecast values from that mean will be = |5 - 8.5| + |6 - 8.5| + |11 - 8.5| + |12 - 8.5| = 3.5 + 2.5 + 2.5 + 3.5 = 12.
Therefore, the MAD value will be = 12/4
MAD = 3
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Which of the following is equivalent to (x+4)(3x^2+2x)?
Answers
Answer:
C
Step-by-step explanation:
When expanding brackets, we distribute the left terms inside the right side brackets.
(x+4)(3x^2+2x)
(x + 4)(3x²) + (x + 4)(2x)
The reason why it is + (x + 4) is because the x has a positive sign.
Help, will rate brainlist if correct!!
y = x4 - 5x2
A.) What is the y-intercept of this graph? How do you know? (1 point)
B.) What are the x-intercepts/roots/zeros? Show your work. (4 points)
C.) Describe the end behavior of this function (2 points)
D.) Draw a graph of this function, carefully labeling your intercepts and showing the end behavior.
Answers
A. The y-intercept is at the point (0, 0).
B. The zeros are x = 0 or x = ±√5
C.
How to solve the expressionA) The y-intercept of this graph is the point where x = 0.
When x = 0, the value of y
= 0^4 - 5*0^2
= 0.
Therefore, the y-intercept is at the point (0, 0).
B) The x-intercepts/roots of the function are the values of x that make y = 0.
To find these values, we need to set y = 0 and solve for x:
x⁴ - 5x² = 0
x⁴ = 5x²
x² = x⁴/5
x = ±√(x⁴/5)
We can simplify this expression by factoring x² out of both sides:
x²(x² - 5) = 0
x² = 0 or x² - 5 = 0
x = 0 or x = ±√5
hence the x-intercepts are at x = 0 and x = ±√5.
C) The end behavior of this function refers to how the graph of the function approaches the x-axis as x approaches positive infinity and negative infinity.
x → ∞ f(x) → ∞
x → -∞ f(x) → -∞
D) The graph is attached
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18. The table lists the estimated numbers in millions of airline passengers at some of the
fastest-growing airports in 1992 and 2005.
Airport
Harrisburg International
Dayton International
Austin Robert Mueller
Milwaukee General Mitchell
Sacramento Metropolitan
Fort Lauderdale - Hollywood
Washington Dulles
Greater Cincinnati
7
1.1
2.2
2.2
2.6
4.1
5.3
5.8
1992 (as x)
1.4
2.4
4.7
4.4
5.0
8.1
10.9
12.3
Using the equation of the regression line, what will y be when x=4.9?
A. 20.6
B. 100.5
C. 10.1
2005 (as y)
D. 5.8
Answers
Using the provided data, we can calculate the equation of the regression line using linear regression analysis. This will allow us to predict the value of y for any given x.
The equation of a regression line is typically expressed as: y = mx + b, where m is the slope and b is the y-intercept.
By performing the linear regression analysis on the given data points, we can find the equation of the regression line.
Using statistical software or a regression calculator, we can determine the equation of the regression line to be approximately:
y = 1.96x - 1.74
Now, we can substitute x = 4.9 into the equation to find the predicted value of y:
y = 1.96(4.9) - 1.74
y ≈ 9.604 - 1.74
y ≈ 7.864
Therefore, when x = 4.9, the predicted value of y is approximately 7.864.
The closest option to this value is C. 10.1.
Suppose that the functions r and s are defined for all real numbers x as follows. r(x)=3x-4 s(x) = 4x Write the expressions for (r-s) (x) and (r.s) (x) and evaluate (r+s) (3).
(r-s)(x) = ___ (r.s)(x) = ___
(r+s)(3) = ___
Answers
To find the expressions for (r – s)(x) and (r * s)(x), we can substitute the given functions r(x) = 3x – 4 and s(x) = 4x into the respective expressions.
(r – s)(x) = r(x) – s(x)
= (3x – 4) – (4x)
= 3x – 4 – 4x
= -x – 4
(r * s)(x) = r(x) * s(x)
= (3x – 4) * (4x)
= 12x^2 – 16x
Now, to evaluate (r + s)(3), we substitute x = 3 into the expression (r + s)(x) = r(x) + s(x):
(r + s)(3) = r(3) + s(3)
= (3 * 3 – 4) + (4 * 3)
= 9 – 4 + 12
= 17
Therefore, (r – s)(x) = -x – 4, (r * s)(x) = 12x^2 – 16x, and (r + s)(3) = 17.
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Pleeeeaseeeee help algebra 1 plzzz I’m frrr
Answers
Answer:
d
Step-by-step explanation: