(2x+3)²=125 find x
with full solution please​

Answer:

\(6(a - 2) = 6a - 12\)

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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The amount to be paid is more on credit card 2 is more, it must be paid first.

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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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

Answer:

6.48

Step-by-step explanation:

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

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

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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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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Answer:

14 mm squared is the area

Step-by-step explanation:

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

Answer:

34 hours

Step-by-step explanation:

358-35=323

323/9.50= 34

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.

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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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...

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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Answer: ab (7a + b - 2)

tu (3tu + 6uv + 2w)

4abc (5c - 7a + 2b)

2qrs (10p + 35q - 25)

Both the equations are plotted on the graph and they intersect each other on (2, 4).

So, graph the equation as follows:

So plot as:

Therefore, both the equations are plotted on the graph and they intersect each other on (2, 4).

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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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A. The y-intercept is at the point (0, 0).

B.  The zeros are x = 0 or x = ±√5

C.

A) 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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Answer:

d

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

x= -2

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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Answer:

A. 140

Step-by-step explanation:

3 hours converts to 180 minutes, so 180-40=140, therefore A is correct.

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 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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Answer:

b

Step-by-step explanation:

used graphing calculator

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.

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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