Solve the following equation. x + 6 = x + x

Answer:  15 + |−6| = 21 steps

Its stated that Joy walked 15 steps forward, meaning it would be a positive value. Shaunte walking backwards would give a negative value.

y = ( x-1)^2 +5

FOIL ( x-1)^2 ( x-1)(x-1)

first x*x = x^2

outer x * -1 = -x

inner -1 *x = -x

last -1 *-1 = 1

Add them together

x^2 -x -x+1 = x^2 -2x+1

Replace (x-1)^2 with x^2 -2x+1

y = x^2 -2x+1 +5

= x^2 -2x +6

The answer

y = x^2 -2x+6

The variable 'c' in the given expression has No Solution.

Given, that

2/3c - 1 = 1 + 2/3c

Now, as we have same coefficient of the variable c i.e. 2/3

So, On subtracting 2/3c from both the sides, we get

2/3c - 2/3c - 1 = 1 +2/3c - 2/3c

-1 ≠ 1

Hence, we got no solutions that can satisfy the given expression.

So, the variable 'c' in the given expression has No Solution.

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Answer: 1

Step-by-step explanation:

Rewrite as (i^4)^6

Rewrite i^4 as 1

Rewrite i^4 as (i^2) ^2

((i^2)) ^2)6

Rewrite i^2 as -1

((-1) ^2) 6

Raise -1 to the power of 2

1^6

One to any power is 1.

Answer:

B) y = -3/7x + 41/7

Step-by-step explanation:

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Answer:

∠ ABC = 49°

Step-by-step explanation:

the chord- tangent angle ABC is half the measure of the intercepted arc AB

∠ ABC = \(\frac{1}{2}\) AB = \(\frac{1}{2}\) × 98° = 49°

No, 34.05 is not greater than 34.59.

When comparing two numbers, we look at their digits from left to right.

In this case, both numbers start with 34, which means they have the same value in the tens place.

However, when we move to the decimal part, 0.05 is smaller than 0.59.

Therefore, 34.05 is smaller than 34.59.

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The value of one of the tangent ratios = 1 because tan(A) = tan(X)

If ΔABC ~ ΔXYZ, then the corresponding angles are congruent, which means that:

∠A ≅ ∠X

∠B ≅ ∠Y

∠C ≅ ∠Z

Therefore, we can write:

tan(A) = tan(X)

This is because tangent is a ratio of two sides, and corresponding sides of similar triangles are proportional.

So, the ratio of two tangent ratios:

tan(A) / tan(X) = 1

So, we know the value of one of the tangent ratios = 1 we can use the above relationships to find the other tangent ratios.

since tan(A) = tan(X), we can say that they are equal. This means that the two triangles have equal angles, and they are similar. It also means that the ratio of the corresponding sides of the two triangles is constant.

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The inequality is given as 8 + 4.5x > 44, and then x > 8 minutes which shows that Mr. Burst needs to eat for more than 8 minutes to beat Mr. Bean's record.

Let x represent the time in minutes Mr. Burst needs to continue eating.

We can write the inequality as: 8 + 4.5x > 44, representing the initial 8 spring rolls eaten, plus the rate of 4.5 rolls per minute, needing to exceed 44 to beat the record.

Solving for x, we subtract 8 from both sides: 4.5x > 36.

Dividing both sides by 4.5, we get: x > 8 minutes.

On a graph, this solution is depicted as a line starting at 8 (excluded) on the x-axis (time in minutes) and extending infinitely to the right, showing that Mr. Burst needs to eat for more than 8 minutes to beat Mr. Bean's record.

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Answer:

Step-by-step explanation:

too much

Answer:

$20 would have been the investment made

Step-by-step explanation:

The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is  y > -2

From the question, we have the following parameters that can be used in our computation:

f(x) = 3ˣ ⁻ ¹ - 2

The above equation is an exponential function

The rule of an exponential function is that

In this case, it is -2

So, the range is y > -2

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Answer:

$2250

Step-by-step explanation:

All you have to do is multiply 125×18= 2250

If Gavin contributes towards a Pension fund (7,5% of his Basic Salary), then his net salary will be reduced by the amount he contributed towards pension fund i.e. R652.5.

1.1 Name of employee is Gavin Pillay. 1.2 UIF stands for Unemployment Insurance Fund. UIF is a benefit to provide short-term relief to workers who lose their jobs, or can't work due to illness, maternity or adoption leave. 1.3 The UIF paid by Gavin is calculated correctly.

Firstly, we need to calculate Gross Salary of Gavin, which is given as: Basic Salary + Overtime + M = R8700 + R1200 + R3201 = R13101Then, calculate total deductions from gross salary.

Total Deductions = PAYE + UIF = R1200 + 87 = R1287Hence, Gavin's net salary = Gross salary - Total Deductions = R13101 - R1287 = R11814Therefore, UIF paid by Gavin is calculated correctly as R87.1.4 This payslip is for the month of May i.e.

31/05/2023.1.5 Basic salary of Gavin = R8700. Deduct 7.5% of his basic salary to calculate his pension fund contribution. Pension Fund Contribution = 7.5/100 x R8700 = R652.5.1.6

Total deductions of Gavin includes PAYE, UIF and pension fund contribution.

Therefore, Total Deductions = PAYE + UIF + Pension Fund Contribution = R1200 + R87 + R652.5 = R1939.5.1.7

Gavin's age can not be determined as his date of birth is not provided.1.8 Address of Gavin's workplace is 21 Halsted Road, Pietermaritzburg?

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Answer:10 Safety razors

Step-by-step explanation:

27-12=15

15/1.50=10

The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

Answer:

a) 2

b) 2x, -13

c) 2, -13

Step-by-step explanation:

Term means mathematical equations that are separated by arithmetic symbols like (+,-,x,/).

For example, there is 2 terms in the following example because there is two values separated by arithmetic symbols: 3x+5.

More examples of terms: 7, 5x, x, \(7x^2\), \(x^2\)

Coefficient means the value that you multiply the variable by. The coefficient in the variable: 5x is 5 because you are multiplying x by 5.

The completed sequence is: 3/k, 3/k, 3/k, 9/2k.To complete the sequence of numbers with a constant difference between adjacent numbers, we can calculate the common difference by subtracting the first term from the second term.

Let's denote the missing terms as A and B.

The given sequence is: 3/k, A, B, 9/2k.

The common difference can be found by subtracting 3/k from A or B. Therefore:

A - 3/k = B - A = 9/2k - B.

To simplify, we can equate the two expressions for the                     common difference:

A - 3/k = 9/2k - B.

Next, we can solve for A and B using this equation.

Adding 3/k to both sides gives:

A = 3/k + 9/2k - B.

Now, we can substitute the value of A into the equation:

3/k + 9/2k - B - 3/k = 9/2k - B.

Simplifying further, we have:

9/2k - 3/k = 9/2k - B.

Cancelling out the common terms, we find:

-3/k = -B.

Multiplying both sides by -1, we get:

3/k = B.

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Answer:

4a - 20b - 3c

Step-by-step explanation:

6a - 5b - 8c - 15b - 2a + 5c

= 4a - 20b - 3c

I HOPE IT WILL HELP YOU.

Thank you.

I HOPE YOUR DAY GOES GREAT.

Answer:

the answer is 4.6

Step-by-step explanation:

the explanation is shown in the following attachment below...

hope this helps...

The Point estimate ± Margin of error =39 ± 3.3

Given, that in a survey, 29 people were asked how much they spent on their child's last birthday gift

n = 29 (sample size)

m = 39 (sample mean)

s = 18 (sample standard deviation)

C = 0.95 = 95% (confidence level)

Now, d = degrees of freedom = n-1 = 29-1 = 28

confidence level = 95%

Alpha value = 1 - (95/100) = 1 - (0.95) = 0.05

Then, the critical value is roughly

t = 1 - (Alpha value / 2)

t = 1 - (0.05/2)

t = 0.975

Then, the point estimate is the sample mean i.e. 39 which estimates the population mean.

And the margin of error (MoE) is

MoE = (t×s)/√n

MoE = (0.975×18)/√29

MoE = (0.975×18)/5.385

MoE = 17.55/5.385

MoE = 3.26

MoE = 3.3

Hence, Point estimate ± Margin of error =39 ± 3.3

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The forecasts for September sales volume using a linear trend equation, a five-month moving average, exponential smoothing with a smoothing constant of 0.40, the naive approach, and a weighted average are 17.86, 18.60, 18.72, 21.00, and 19.60 thousands, respectively.

1. A linear trend equation:

This is a method of extrapolating future values from existing data by fitting a linear line to the data points by calculating the slope and y-intercept of the line. To calculate the trend equation, we use the formula Yt = mXt + b, where Yt is the forecasted value, m is the slope of the line, Xt is the independent variable, and b is the intercept. We can calculate m and b by using the formula m = (n∑XY - (∑X)(∑Y)) / (n∑X2 - (∑X)2) and b = (∑Y - m(∑X)) / n. To calculate the forecast for September, we substitute the September value with the 7th month value and solve the equation. Y7 = mX7 + b. Therefore, the forecast for September is 17.86 thousands.

2. A five-month moving average:

This is a method of smoothing data points by taking the average of the preceding five data points and using this average value as the forecast. To calculate the five-month moving average, we use the formula Yt = (Yt-1 + Yt-2 + Yt-3 + Yt-4 + Yt-5) / 5. Therefore, the forecast for September is 18.60 thousands.

3. Exponential smoothing with a smoothing constant equal to .40, assuming a March forecast of 19(000):

This is a method of forecasting future values by using a weighted average of the past data points and the previous forecast. To calculate the forecast, we use the formula Yt = αYt-1 + (1-α)Ft-1, where Yt is the forecasted value, α is the smoothing constant, Yt-1 is the previous data point, and Ft-1 is the previous forecast. Therefore, the forecast for September is 18.72 thousands.

4. The naive approach:

This is a method of forecasting future values by simply taking the most recent data point as the forecast. Therefore, the forecast for September is 21.00 thousands.

5. A weighted average using .50 for August, .20 for July, and .30 for June:

This is a method of forecasting future values by taking a weighted average of the past data points. To calculate the forecast, we use the formula Yt = (0.5Yt-1 + 0.2Yt-2 + 0.3Yt-3) / (0.5 + 0.2 + 0.3). Therefore, the forecast for September is 19.60 thousands.

The forecasts for September sales volume using a linear trend equation, a five-month moving average, exponential smoothing with a smoothing constant of 0.40, the naive approach, and a weighted average are 17.86, 18.60, 18.72, 21.00, and 19.60 thousands, respectively.

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Answer:

The maximum height that the ball reaches is of 3.96 meters.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

\(f(x) = ax^{2} + bx + c\)

It's vertex is the point \((x_{v}, y_{v})\)

In which

\(x_{v} = -\frac{b}{2a}\)

\(y_{v} = -\frac{\Delta}{4a}\)

Where

\(\Delta = b^2-4ac\)

If a<0, the vertex is a maximum point, that is, the maximum value happens at \(x_{v}\), and it's value is \(y_{v}\).

In this question:

The height after t seconds is given by:

\(h(t) = -51t^2 + 20t + 2\)

Which is a quadratic equation with \(a = -51, b = 20, c = 2\)

What is the maximum height that the ball reaches?

This is \(h_v\).

\(\Delta = b^2-4ac = 20^2 - 4(-51)(2) = 808\)

\(y_{v} = -\frac{\Delta}{4a} = -\frac{808}{4(-51)} = 3.96\)

The maximum height that the ball reaches is of 3.96 meters.

Answer:

1/512 or 1/8^3

Step-by-step explanation:

All the given 24:12, 2:1, and 28:14 ratios equivalent to 4:2.

Therefore, we must multiply the two amounts by the same number in order to discover a ratio that is equivalent to another. The given ratio can also be expressed as a fraction, and the numerator and denominator can then be multiplied by the same amount to produce equivalent fractions.

1) The ratio can be written as

\(= \frac{24}{12} \\Divide numerator and denominator by 6\\= \frac{4}{2}\)

The ratio equivalent to 4:2

2) The ratio can be written as

\(= \frac{2}{1} \\multiply numerator and denominator by 2\\= \frac{4}{2}\)

The ratio equivalent to 2:1

3) The ratio can be written as

\(= \frac{28}{14} \\Divide numerator and denominator by 7\\= \frac{4}{2}\)

The ratio equivalent to 2:1

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Answer:

It already is rounded to the nearest percent, 60.

Step-by-step explanation:

The amount paid for the truck for 300 miles is $333

From the question, we have the following parameters that can be used in our computation:

Amount paid per day = $33

Amount paid per mile = $1

Number of miles driven = 300

The amount paid for the truck is then calculated as

Amount paid for the truck = Amount paid per day + Amount paid per mile x Number of miles driven

Substitute the known values in the above equation, so, we have the following representation

Amount paid for the truck = 33 + 300 * 1

Evaluate the products

Amount paid for the truck = 33 + 300

Evaluate the sum

Amount paid for the truck = 333

Hence, the amount is $333

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Mean = 20; standard deviation = 4;

Let x be the success of receiving the right response.

The total number of trials in this case is 100.

The likelihood of receiving the right response is p = 1/5.

In light of the average number of correct answer;

μₓ = np

μₓ = 100 * (1/5);

μₓ = 20;

The standard deviation is now; σ = √(n)(p)(1 - p)

                                                    σ = √(100)(1/5)(4/5)

                                                   σ  = 4

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