What is the
intermediate step in the form
(x + a)² = b as a result of completing
the square for the following equation?
-5x² 10x = -315

The factored form of the expression x² + 5x+6 is (x + 3)(x + 2)

To factorize the quadratic equation, we need to take the following steps;

Multiply the coefficient of the x squared by the constant value, we have;

6

Now, find the pair factors of the product that would add up to give 5, we have;

2 + 3

Substitute the values into the expression, we have;

x² + 2x + 3x + 6

Now, group the expression in pairs, we have;

(x² + 2x) + (3x + 6)

Factorize the expressions

x(x + 2) + 3(x + 2)

Then, we have;

x + 3

x + 2

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We can deduce here that the experimental probability that the next time Lea rolls the number cubes, they will land with a 1 showing on the top face of one number cube and a 5 showing on the top face of the other number cube is: 1/36.

Probability is a measure for determining the possibility or chance that a specific event will take place. It is typically stated as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

We can see that there is only one roll where one number cube that shows a 1 and the other number cube shows a 5. Therefore, the number of successful outcomes is 1.

The total number of rolls seen are: 36 rolls = 6 possible outcomes on the first number cube × 6 possible outcomes on the second number cube.

We can then see here that the probability will be = 1/36.

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He run on Thursday is 3.75 miles.

Algebra helps in converting a mathematical statement into an equation. We know if we have ‘more’ or ‘sum’ in the given sentence we use addition operation (+) . Similarly If we have ‘less’ or ‘difference’ we use subtraction (−) . If we have a ‘quotient’ we use division operation (÷) . To define more generalized terms; we use algebra. It is a very vast branch of mathematics and is used in all the branches of mathematics like polynomial, linear equations, graphs, etc. and in daily life too.

Now, Gavriel ran 5 miles on Wed

and,  On Thursday, he ran 3/4 as far.

We have to find the how far did he run on Thursday.

On Thursday , The distance will be:

=> 5 × 3/4

=> 15/4

=> 3.75 miles

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Answer:

color cube

Step-by-step explanation:

Answer:

There are 20 R100 notes and 80 R50 notes.

Step-by-step explanation:

Let's call the number of R100 notes "x" and the number of R50 notes "4x" (since there are 4 times as many R50 notes as R100 notes).

We can set up an equation to represent the total value of the notes:

100x + 50(4x) = 6000

Simplifying:

100x + 200x = 6000

300x = 6000

x = 20

So there are 20 R100 notes and 4 times as many R50 notes:

4x = 4(20) = 80

Therefore, there are 20 R100 notes and 80 R50 notes.

x has a value of 9. The correct response is (D).

Since the measures of angles A and B are equal, we can set them equal to each other and solve for x:

m∠A = m∠B

4x - 2 = 6x - 20

Subtracting 4x from both sides, we get:

-2 = 2x - 20

Adding 20 to both sides, we get:

18 = 2x

Dividing both sides by 2, we get:

x = 9

Therefore, the value of x is 9. Answer choice (D) is correct.

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Answer:

hi i can help you if you want just text

The answer of the given question based on the function is ,  the turning point of the function f(x+4)+5 is at the point (-4, -5).

In mathematics, a function is a rule that assigns each input value (or argument) in a set to a unique output value in another set. In other words, it is a relationship between two sets of numbers, where each input value produces exactly one output value. Functions are usually represented using function notation, where the name of the function is followed by the input value in parentheses.

To find the turning point of the function f(x+4)+5, we need to first rewrite the function in vertex form, which is given by:

f(x) = a(x-h)² + k

where (h, k) is vertex of parabola.

To do this, we can start by completing the square:

f(x+4) + 5 = a(x+4-h)² + k

f(x+4) = a(x+4-h)² + k - 5

To complete the square, we need to add and subtract (4-h)²/4a inside the parentheses:

f(x+4) = a(x+4-h)² + k - 5 + (4-h)²/4a - (4-h)²/4a

f(x+4) = a(x+4-h)² + (4-h)²/4a + (4a*k-20a)/4a

Now the function is in vertex form:

f(x+4) = a(x+4-h)² + (4-h)²/4a + (4a*k-20a)/4a

The vertex of the parabola is at (h, k), so in this case, the vertex is at (-4, -5).

Therefore, the turning point of the function f(x+4)+5 is at the point (-4, -5).

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The two solutions that satisfy the equation 3x^2 + 2x = 6 when rounded to two decimal places are x = 1.12 and x = −1.79. So, correct option is A.

To solve for x in the equation 3x^2 + 2x = 6, we need to rearrange the terms and use the quadratic formula:

3x^2 + 2x - 6 = 0 (subtract 6 from both sides)

x = (-b ± √(b^2 - 4ac)) / 2a (quadratic formula)

In this equation, a = 3, b = 2, and c = -6, so we can substitute those values into the quadratic formula:

x = (-2 ± √(2^2 - 4(3)(-6))) / 2(3)

x = (-2 ± √(4 + 72)) / 6

x = (-2 ± √(76)) / 6

Simplifying this expression, we get:

x = (-2 ± 2√(19)) / 6

x = (-1 ± √(19)) / 3

Rounding these solutions to two decimal places, we get:

x = -1.79 or x = 1.12

Therefore, the answer is (a) x = 1.12 and x = -1.79.

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Answer:

x = 1.12 and x = −1.79

Step-by-step explanation:

i got it right on my quiz

Answer:

Step-by-step explanation:

In the fraction , the greatest number of chess sets each of the 4 teachers should get is 15.

What is fraction?

Part of a whole is a fraction. The quantity is written as a quotient in mathematics, where the numerator and denominator are divided. Each is an integer in a simple fraction. Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.

Here the In starting number of chess sets = 18

Ordered number of chess set cases = 3

In each case number of chess sets= 15

Then total number of ordered chess sets = 3*15 = 45.

Now total number of chess set in chess club = 45+18 = 64.

The number of teacher = 4.

Then expression is ,

The number of chess sets each of the 4 teachers should get = 63/4 = 15 [tex]\frac{3}{4}[/tex]

Remaining set = 3.

Hence the greatest number of chess sets each of the 4 teachers should get is 15.

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A computation time expression ~ n, of means that the computation time increases in proportion to the size of the input.

This presents a computational complexity of O(n). Here 'O' stands for 'Big O Notation' and is used to denote an upper bound on the computational complexity of the algorithm.

That's, the algorithm's computational complexity is straightforwardly corresponding to the measure of the input information.

This shows that as the input estimate increments, the computational time will increment at the same rate.

 Linear time complexity is considered to be very efficient, and many algorithms aim to achieve this level of complexity. This is a relatively efficient computational complexity and is common in algorithms that require only one pass through the input data. 

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The solution to the linear equation is determined as 5.

The equation to solve is:

3x - 8 = 7

To solve for x, you can follow these steps:

Step 1: Add 8 to both sides of the equation to isolate the term with x on one side:

3x - 8 + 8 = 7 + 8 (combine constants here)

This simplifies to:

3x = 15

Step 2: Divide both sides of the equation by 3 to solve for x:

3x/3 = 15/3

This simplifies to:

x = 5

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If the diameter of circular-garden is 18 feet, then it will cost Randy an amount of $85.50 to buy edges for his garden.

The "Circumference" of circle is defined as the "total-length" of the boundary or the outer edge of the circle.

The circumference formula is : Circumference = π × Diameter,

The "diameter" of garden is = 18-feet,

So, Circumference = 3.14 × 18 = 56.52 feet,

Since, Randy needs to buy plastic-edging to cover the entire circumference of garden, he needs to buy 56.52 feet of edging.

We know that, Randy can only buy edging in whole-foot amounts,

So, rounding up to the nearest whole foot, we get 57 feet,

The cost of edging is = $1.50 per foot,

So, "total-cost" for Randy to buy edging for his garden is,

⇒ Total Cost = (Cost per foot) × (Number of feet),

⇒ $1.50 × 57,

⇒ $85.50

Therefore, it will cost Randy $85.50 to buy edging for his circular garden.

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The measurement that is closest to the lateral surface area of the cylinder is 132.15 square centimeters.

To determine the lateral surface area of a cylinder, you can use the formula 2πrh, where "r" represents the radius of the circular base of the cylinder, and "h" represents the height of the cylinder. This formula calculates the total area of the curved part of the cylinder, excluding the top and bottom circular bases.

The height of the cylinder is 5.8 cm and the radius of the circular base is 7.6/2 = 3.8 cm.

So, the lateral surface area of the cylinder is approximately:

2π(3.8)(5.8) ≈ 132.15 cm²

The value that is nearest to the lateral surface area of the cylinder is 132.15 square centimeters.

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The mean of the data in the dot plot is approximately 5.33.

By dividing the sum of the numbers by the total number of numbers, the mean, or average, of the given numbers is determined. Mean is equal to (Sum of all Observations / Total Observations).

We must sum up all the values and divide by the total number of values to determine the mean of the data in the dot plot.

The first step is to count the dots for each value:

3 has 3 dots

4 has 5 dots

5 has 6 dots

6 has 8 dots

7 has 5 dots

8 has 3 dots

Then, multiplying each value by the quantity of dots associated with it, we must total up all the products:

(3 x 3) + (4 x 5) + (5 x 6) + (6 x 8) + (7 x 5) + (8 x 3) = 3 + 20 + 30 + 48 + 35 + 24 = 160

Last but not least, we must divide the entire number of values—i.e., dots—by the sum:

160 ÷ (3 + 5 + 6 + 8 + 5 + 3) = 160 ÷ 30 = 5.33

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Answer: 2.2197307e+25

Step-by-step explanation: I just times it

The best approximation for the p-value for the test statistic t0 = 2.155 is 0.032.

To find the best approximation for the p-value for the hypothesis test with null hypothesis H0: μ=8 and alternative hypothesis H1: μ>8, with variance unknown and n=10, and a test statistic t0=2.155, we need to use the t-distribution with degrees of freedom (df) equal to n-1 = 10-1 = 9.

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true. Since this is a one-tailed test with the alternative hypothesis in the form of μ>8, the p-value corresponds to the area in the right tail of the t-distribution.

Using a t-table or calculator with the t-distribution, we can find the probability of obtaining a t-value as large as 2.155 or larger with 9 degrees of freedom. This probability is approximately 0.032. Therefore, the best approximation for the p-value for this hypothesis test is 0.032.

We can interpret this result as follows: if the null hypothesis is true (i.e., if the population mean is 8), the probability of obtaining a sample mean as extreme or more extreme than the observed one (i.e., greater than 8.215) is 0.032. Since this probability is relatively small, we may reject the null hypothesis in favor of the alternative hypothesis at a significance level of 0.05 or smaller.

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The equation of the line that passes through the point (16, -14) with slope 1 is y = x - 30.

What is meant by equation?

An equation is a mathematical statement that shows that two expressions are equal. It contains an equals sign and can include variables, constants, and mathematical operations. Equations are used to represent relationships between quantities and to solve problems in mathematics and science.

What is meant by slope?

Slope refers to the measure of the steepness of a line. It is calculated by dividing the change in the y-coordinate (vertical distance) by the change in the x-coordinate (horizontal distance) between two points on the line.

According to the given information

The point-slope form of the equation of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line.

In this case, the line passes through the point (16, -14) and has a slope of 1. Plugging these values into the point-slope form, we get:

y - (-14) = 1(x - 16) y + 14 = x - 16 y = x - 30

So, the equation of the line that passes through the point (16, -14) with slope 1 is y = x - 30.

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The slope from of (−4, 6) to (2, 2/3) can be written as  -17/18

The slope of line can be represented as =slope whereby (x1, y1) = serves as the coordinates of first point in the line (x2, y2)serve as as the  coordinates of second point in the line

From the question, x1 = -4, y1 = 6 , x2 = 2, y2 =2/3 then we can set up into the formula as  

(y2 - y1) / (x2 - x1)

(y2 - y1) =(2/3 - 6) =-17/3

(x2 - x1) = (2 - (-4))= 6

Hence slope = -17/18

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Answer:

x = 12

Step-by-step explanation:

If you're bored of solving equations the normal way, why not try this fun and easy method? Just follow these simple steps:

Subtract 3/10 x from both sides to eliminate the x term on the right side. This is like getting rid of the annoying person who always sits next to you in class.

4/5 x - 3/10 x + 15 = 21

Simplify the left side by finding the common denominator and combining the fractions. This is like putting all your candy in one bag and eating it faster.

(8/10 - 3/10) x + 15 = 21

5/10 x + 15 = 21

Subtract 15 from both sides to isolate the x term on the left side. This is like taking away your allowance and making you do chores.

5/10 x = 21 - 15

5/10 x = 6

Multiply both sides by 10/5 to solve for x. This is like giving you a magic wand that makes everything easier.

(10/5) (5/10) x = (10/5) (6)

x = 12

This is the solution of the equation. You can check it by plugging it back into the original equation and verifying that both sides are equal. Or you can just trust me

✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧

Carbon 14 has a half-life of 5,600 years, which means that after 5,600 years, half of the initial amount of Carbon 14 will decay. Therefore, we can use the following formula to find the amount of Carbon 14 that was present 11,200 years ago:

A = A0 * (1/2)^(t/T)

where:

A0 = initial amount of Carbon 14

A = amount of Carbon 14 remaining after time t

t = time elapsed since the initial amount was present

T = half-life of Carbon 14

We know that the fossil contains 3 g of Carbon 14, which is the amount remaining after 11,200 years. We want to find the initial amount, A0.

Let's plug in the values we have into the formula and solve for A0:

3 g = A0 * (1/2)^(11,200/5,600)

3 g = A0 * (1/2)^2

3 g = A0 * 1/4

A0 = 4 * 3 g

A0 = 12 g

Therefore, the fossil contained 12 g of Carbon 14 11,200 years ago.

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The following are the correct vertical translation and you can use this information to fill the table in the picture:

A vertical translation refers to a type of transformation that moves a function or graph vertically up or down without changing its shape. Specifically, a vertical translation of distance c is given by the function:

f(x) + c

where f(x) is the original function and c is a constant that determines the amount and direction of the translation. If c is positive, the graph of the function is shifted upwards; if c is negative, the graph is shifted downwards.

For example, the function f(x) = x^2 has a graph that is a parabola opening upwards. If we apply a vertical translation of 2 units, the resulting function is:

f(x) + 2 = x^2 + 2

The graph of this function is also a parabola, but it has been shifted vertically upwards by 2 units. Similarly, a vertical translation of -3 units would give us the function f(x) - 3 = x^2 - 3, which is the same parabola shifted downwards by 3 units.

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Answer:

57

Step-by-step explanation:

2 X 2 = 4

4 X 8 = 32

32 + 25 = 57

The function f(x) = xlnx is decreasing on the open interval (0, e^-1).

To find the interval on which the function f(x) = xlnx is decreasing, we need to find the intervals where the first derivative f'(x) is negative.

Using the product rule of differentiation, we can find the first derivative of f(x) as

f'(x) = x × (1/x) + ln(x) × 1 = 1 + ln(x)

Now, we need to find the values of x where f'(x) < 0

1 + ln(x) < 0

ln(x) < -1

x < e^-1

Therefore, f(x) is decreasing on the interval (0, e^-1).

Note that we exclude x = 0 from the interval because the function is not defined for x ≤ 0.

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The following probabilities are found under the condition that  a certain national survey of heads of households P(woman asked for a promotion) = 24%, P(woman received promotion, given she asked for one) = 45%, P(woman asked for promotion and received raise) = (24% x 45%) = 10.8%

Now,
Regarding  a national survey concerning the head od households,  only 24% of women interviewed had requested for a promotion and of those women who had asked for a promotion, 45% received the raise.

Therefore,

(a) P(woman asked for a promotion) = 24%
(b) P(woman received promotion, given she asked for one) = 45%
(c) P(woman asked for promotion and received raise) = (24% x 45%) = 10.8%

Probability refers to the percentage of an event taking place in a required time frame, in a specified place. It is considered a great aid in the fields of science and mathematics.

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Given the above conditions in the word problem above, x is also equal to 6.5°.

The angle x is the angle between this perpendicular line and the Earth's surface. It is also equal to the angle between the tangent line and the horizontal axis.

Since the reentry angle is 6.5°, we know that the tangent line makes an angle of 6.5° with the horizontal axis. We also know that the tangent line and the perpendicular line form a right angle, so the angle between the perpendicular line and the horizontal axis is 90° - 6.5° = 83.5°.

Finally, we can subtract this angle from 90° to find x:

x = 90° - 83.5° = 6.5°

Therefore, x is also equal to 6.5°.

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The z-score of a car that is 6 years old is  -0.625.

To find the z-score of a car that is 6 years old, we can use the formula:

z = (x - μ) / σ

where x is the value we are interested in (in this case, 6 years old), μ is the mean of the distribution (8 years), and σ is the standard deviation (3.2 years).

Plugging in the values, we get:

z = (6 - 8) / 3.2 = -0.625

Therefore, the z-score of a car that is 6 years old is -0.625. This indicates that the car is 0.625 standard deviations below the mean age of cars driven by employees at the company. Since the distribution is normal, we can use this z-score to find the probability of finding a car with an age of 6 years or less, using a z-table or a calculator.

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The correct alternative hypothesis for the Wilcoxon rank sum test is: ha: one distribution is shifted in a location higher or lower than the other. Option C is the answer.

This means that the test is designed to determine if there is a significant difference between the medians of two independent groups, rather than testing for a difference in means.

The null hypothesis for the test is that there is no significant difference between the two groups, while the alternative hypothesis states that there is a significant difference.

The Wilcoxon rank sum test is a nonparametric test and is used when the assumptions of the t-test are not met, such as non-normality or unequal variances.

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