Use the linear combination method to solve the system of equations. Explain each step of your solution.
2x-3y=13
2x+4y=-8

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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Answer:

D(Angle A and Angle F)

Step-by-step explanation:

I marked them as abba and a is A and the other one was F which is D

Answer:

alternate angles are congruent angles. So, from figure it is clear that angle A and F are congruent. Also E and B are congruent. on other hand  C & H also D and G

Step-by-step explanation:

Answer:

1.090909090909091

Step-by-step explanation:

12/11 = 1.090909090909091

W = 1.090909090909091

Answer:

w = \(\frac{12}{11}\)

Step-by-step explanation:

11w = 12 ( isolate w by dividing both sides by 11 )

w = \(\frac{12}{11}\)

Answer:

5.

Step-by-step explanation:

1. the formula of the required distance:

\(d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2} ;\)

2. according to the formula above:

\(d=\sqrt{3^2+4^2}=5.\)

The statement which uses deductive reasoning to draw the conclusion is C. The number 14 is even and therefore is divisible by 2.

If a number is even, then it is divisible by 2. g = 14.

The statement which shows the logical reasoning could be the correct one.

A. The number is divisible by 2, therefore, the number is 14.

Here any even number can be divisible by 2 other than 14.

B. The number 14 is even and is greater than 2. The given conclusion does not mention any number that is greater than 2.

C. The number 14 is even and therefore is divisible by 2. This is the correct statement.

D. The number 14 is a real number.

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The probability that both players show rock in the first round is 1/9 or 0.1111 (rounded to four decimal places).

In rock, paper, scissors there are three possible outcomes for each player: rock, paper, or scissors. Assuming both players choose randomly and independently of each other, each player has a 1/3 chance of showing rock in the first round.

To find the probability that both players show rock in the first round, we can use the multiplication rule of probability for independent events. The multiplication rule states that the probability of the intersection of two independent events is the product of their probabilities.

Therefore, the probability that both players show rock in the first round can be calculated as follows:

P(both show rock) = P(player 1 shows rock) x P(player 2 shows rock) P(both show rock) = 1/3 x 1/3 P(both show rock) = 1/9

So the probability that both players show rock in the first round is 1/9 or approximately 0.111.

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The result of the equation 2(x-4)-9 = 3(2x+1)+4 is x= -6

The equation is

2(x-4)-9 = 3(2x+1)+4

The distributive property states that multiplying the sum of two or more variables by a number will produce the same result as multiplying each variables individually by the number and then adding the products together.

2(x-4)-9 = 3(2x+1)+4

Apply distributive property in the equation

2x-8-9 = 6x+3+4

Add the like terms in the equation

2x-17 = 6x+7

Rearrange the terms and combine the like terms in one terms

2x-6x = 7+17

Combine the like terms

-4x = 24

x = 24/-4

x = -6

Hence, the result of the equation 2(x-4)-9 = 3(2x+1)+4 is x= -6

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Answer:

6(4+5)

Step-by-step explanation:

The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

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Answer:

  f(x) = 3(x +4)² -6

Step-by-step explanation:

You want the equation for the parabola shown in the graph with vertex (-4, -6) and additional point (-5, -3).

The vertex form of the equation for a parabola is ...

  f(x) = a(x -h)² +k

where the vertex is (h, k) and 'a' is the vertical scale factor.

The vertex is shown on the graph as (h, k) = (-4, -6), so the equation will be of the form ...

  f(x) = a(x +4)² -6

The value of 'a' is chosen to make the other given point lie on the graph. Substituting for (x, f(x)), we have ...

  -3 = a(-5 +4)² -6

  a = 3 . . . . . . . . . . . add 6

The equation of the graph is ...

  f(x) = 3(x +4)² -6

__

Additional comment

The point (-5, -3) is 1 unit horizontally and +3 units vertically from the vertex. When the point is 1 horizontal unit away from the vertex, that vertical difference (+3) is the scale factor 'a' in the vertex form equation.

In short, you don't need to solve the equation as we did above, you can read 'a' from the graph.

Answer: 36

Step-by-step explanation:

When handling exponents, we have to remember that we're multiplying a number by itself x amount of times

3^3 + (3^2) Parenthesis first

3^3 + (3 x 3)

3^3 + 9 Next Exponents

3 x 3 x 3 + 9

27 + 9  Add

36

Answer:

The rate of change is 28.

Step-by-step explanation:

The equation is in slope-intercept form,  y = mx + b, where m is the slope, and b is the y-intercept.

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Answer:

The geometric mean growth rate of sales is 1.4422.

Step-by-step explanation:

We have two sales values, one from 6 years ago and the other from now.

We have to calculate the geometric growth rate of sales.

We have:

\(y(-6)=1,000,000\\\\y(0)=9,000,000\)

We can write the relation between these two values as:

\(y(0)=y(-6)k^{0-(-6)}\\\\9,000,000=1,000,000k^6\\\\k^6=9\\\\k=9^{1/6}= 1.4422\)

The geometric mean growth rate of sales is 1.4422.

Answer:

The probability that a car chosen at random is not red is 75%.

Step-by-step explanation:

Given that a used car dealer sells SUVs and cars, and of all the vehicles, 60% are cars, and of all the vehicles, 15% are red cars, to determine what is the probability that a car chosen at random is not red you must perform the following calculation:

60 = 100

15 = X

15 x 100/60 = X

25 = X

100 - 25 = 75

Therefore, the probability that a car chosen at random is not red is 75%.

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$5000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &10 \end{cases} \\\\\\ A = 5000\left(1+\frac{0.04}{4}\right)^{4\cdot 10} \implies A=5000(1.01)^{40}\implies A \approx 7444.32\)

From the given below solution the value of m EF is 25%.

A circle graph, also known as a pie chart, is a type of data visualization that displays data as a circular graph, divided into sectors that represent numerical proportions.

Each sector of the circle represents a percentage or proportion of the total data set, and the size of each sector is proportional to its corresponding value.

To find m EF, we need to add the percentages of participation in sports E and F:

m EF = percentage of participation in sports E + percentage of participation in sports F

m EF = 11% + 14%

m EF = 25%

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Answer:

Explanation:

Given the equation:

The unit rate for points per game is determined by dividing the total points scored by the number of games played. In this case, 62 points  3 games = 20.67 points per game (rounded to two decimal places).

To determine the unit rate for points per game, we need to divide the total number of points scored by the number of games played. In this case, Pedro scored 62 points over the last 3 basketball games.

The unit rate for points per game is found by dividing the total points scored by the number of games played. In this case, Pedro scored 62 points over 3 basketball games, so the unit rate for points per game is:

62 points ÷ 3 games = 20.67 points per game (rounded to two decimal places)

So, none of the given options is correct. The correct answer is 62 over 3 points per game, which is equivalent to 20.67 points per game when rounded to two decimal places.

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Answer:

62.01 i took the test

Step-by-step explanation:

James needs 9/4 slices of pizza

James is having a pizza party

Each person at the party eats 3/8 of a pizza

6 people attends the party

The number of slices of pizza that James need can be calculated as follows

3/8 × 6

= 18/8

= 9/4

Hence James need 9/4 slices of pizza

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The remainder of the polynomial division \(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)}\) is 2y²

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

\(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)}\)

When the numerator is expanded, we have

\(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)} = \frac{(y - 1)(y^3 + 1) + 2y^2}{y^3 + 1}\)

Split the expanded expression

\(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)} = \frac{(y - 1)(y^3 + 1)}{y^3 + 1} + \frac{2y^2}{y^3 + 1}\)

Evaluate

\(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)} = y - 1 + \frac{2y^2}{y^3 + 1}\)

From the above, we have

Quotient = y - 1

Remainder = 2y²

Hence, the remainder of the polynomial division is 2y²

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y = 6x + 2 is the function which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.

The linear function in the form y = mx + b represents the situation where y represents the cost of the babysitting job

x represents the number of hours, "m" represents the hourly rate, and "b" represents the additional fee (bus fare).

y = 3x + 2 represents an hourly rate of 3 and an additional fee of 2.

y = 3x + 1 represents an hourly rate of 3 and an additional fee of 1.

y = 6x + 2 represents an hourly rate of 6 and an additional fee of 2.

y = -6x + 2 represents a negative hourly rate of -6 and an additional fee of 2.

Hence, y = 6x + 2 is the which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.

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Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

To determine the number of months it takes to pay off the credit card and the total amount paid, including interest, we can follow these steps:

Step 1: Calculate the monthly interest rate.

The APR (Annual Percentage Rate) is given as 9.5%. To find the monthly interest rate, we divide this by 12 (the number of months in a year):

Monthly interest rate = 9.5% / 12 = 0.0079167

Step 2: Determine the monthly payment.

The monthly payment is given as $400.

Step 3: Calculate the interest and principal paid each month.

The interest paid each month can be calculated by multiplying the monthly interest rate by the current balance.

Principal paid = Monthly payment - Interest paid

Step 4: Track the remaining balance each month.

Starting with the initial balance of $1,367.90, subtract the principal paid each month to determine the new balance.

Step 5: Repeat Steps 3 and 4 until the balance reaches zero.

Continue calculating the interest and principal paid each month, updating the balance, until the remaining balance becomes zero.

Step 6: Determine the total number of months and the total amount paid.

Count the number of months it takes to reach a balance of zero. Multiply the number of months by the monthly payment ($400) to find the total amount paid.

Let's calculate the number of months and the total amount paid, including interest:

Month 1:

Interest paid = 0.0079167 * $1,367.90 = $10.84

Principal paid = $400 - $10.84 = $389.16

New balance = $1,367.90 - $389.16 = $978.74

Month 2:

Interest paid = 0.0079167 * $978.74 = $7.75

Principal paid = $400 - $7.75 = $392.25

New balance = $978.74 - $392.25 = $586.49

Month 3:

Interest paid = 0.0079167 * $586.49 = $4.64

Principal paid = $400 - $4.64 = $395.36

New balance = $586.49 - $395.36 = $191.13

Month 4:

Interest paid = 0.0079167 * $191.13 = $1.51

Principal paid = $400 - $1.51 = $398.49

New balance = $191.13 - $398.49 = -$207.36 (Paid off)

It takes 4 months to pay off the credit card. Now, let's calculate the total amount paid, including interest:

Total amount paid = 4 * $400 = $1600

Therefore, it takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

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Answer:

24

Step-by-step explanation:

i dont know if its correct

The joint relative frequency for school children who plan to attend camp and have swimming lesson is 44%.

The correct option to the given question is option d.

We are required to find the joint relative frequency for school children who plan to attend camp and have swimming lessons, rounded to the nearest percent.

To find the joint relative frequency, we use the formula as follows:

Joint relative frequency = frequency of interest / total frequency

Joint relative frequency for school children who plan to attend camp and have swimming lessons = 42 / 96

(As we are looking for the students who plan to attend camp and have swimming lessons, we are interested in the first column of the table and the entry at the intersection of the first row and second column.)

Joint relative frequency for school children who plan to attend camp and have swimming lessons = 0.4375

Joint relative frequency for school children who plan to attend camp and have swimming lessons (rounded to the nearest percent) = 44%(option d).

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Answer:

270 miles

Step-by-step explanation:

set up as proportion and cross multiply to solve. additionally, i represented 3 hours as 180 minutes

18 miles/12 minutes = x/180 minutes

x = 270

therefore, he went 270 miles

Answer:

\(y=27/2\text{ or } 13.5\)

Step-by-step explanation:

If y and x have a proportional relationship, then they have the standard form:

\(y=kx\)

Where k is the constant of proportionality.

We know that y=9 when x=2. So, we can solve for our k. Substitute 9 for y and 2 for x. Hence:

\(9=2k\)

Divide both sides by 2:

\(\displaystyle k=\frac{9}{2}=4.5\)

So, our constant of proportionality is 9/2 or 4.5.

Therefore, our equation is:

\(\displaystyle y=\frac{9}{2}x\)

To find y when x=3, substitute 3 for x and evaluate. Hence:

\(\displaystyle y=\frac{9}{2}(3)\)

Evaluate:

\(\displaystyle y=\frac{27}{2}=13.5\)

So, when x=3, y=27/2 or 13.5

The correct answer is D. No because 23 and 25 are not supplementary.

In the given diagram, it is stated that the measures of angles 23 and 27 are 45°, and the measure of angle 25 is 135°. To determine if lines C and D are parallel, we need to analyze the angles formed by these lines.

If the alternate interior angles or corresponding angles are congruent, then the lines are parallel. However, in this case, we don't have enough information about the angles formed by lines C and D to make that determination.

The fact that angle 23 and angle 27 are congruent (both measuring 45°) doesn't provide any information about the relationship between lines C and D. Similarly, the measure of angle 25 being 135° doesn't give us any insight into the parallelism of lines C and D. Therefore, we cannot conclude that lines C and D are parallel based on the given information, and the correct answer is D.

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The area of the triangle is 47.91 units²

When all three sides of the triangle are known we can use Heron's formula. Consider the triangle ABC with sides a, b, and c has shown in the image.

Heron’s formula is:

Area =√s(s−a)(s−b)(s−c)

where,

a, b, c are the side length of the triangle

s is the semi-perimeter. s = (a+b+c)/2

In this case:

Using the knowledge of the radius of a circle. We can say:

a = BC = 3 + 9 = 12 units

b = AC = 5 + 3 = 8 units

c = AB = 5 + 9 = 14 units

s = (a+b+c)/2

s = (12+8+14)/2

s = 34/2

s = 17 units

Area = √s(s−a)(s−b)(s−c)

Area = √17(17−12)(17−8)(17−14)

Area = √17(5)(9)(3)

Area = √2295

Area = 47.91 units²

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