What is the solution to the system of equations?
A. (-2,-1)
B. (-1,-2)
C. (1,-2)
D. (-2,1)

To calculate Nathan's net worth, we need to determine his total liabilities (debt) and subtract that from his total assets. The debt ratio tells us that Nathan's liabilities are 80% of his total net worth.

Total liabilities = Car loan + Mortgage + Student loans = $2,000 + $150,000 + $15,000 = $167,000

Nathan's net worth = Total assets = Total liabilities / Debt ratio = $167,000 / 0.8 = $208,750

So, Nathan's net worth is $208,750.

Answer:

Step-by-step explanation:

Hi, Emily. The average rate of change can be calculated by adding all the profits together and dividing by the different profits (4 profits all together A to D) so 10,600+21,600+-21,600+-10,600= 0

0/4= 0

So we can best describe this as 0 or nothing at all as it hasnt changed from year 2 to 4.

Many Regards,

                          Abdelmumen Nakoa

A fellow 8th grader.

One candy costs approximately 1.22 dollars.

Let's assume the cost of one candy is x dollars.

The information provided indicates that nine candies cost eleven dollars, which is stated as nine times eleven.

Similar to how 13 sweets cost 15 dollars, 13x = 15 can be used to illustrate this.

To find the cost of one candy, we need to solve for x in either of the equations. Let's solve the first equation:

9x = 11

Dividing both sides of the equation by 9:

x = 11/9

Therefore, one candy costs approximately 1.22 dollars (rounded to two decimal places).

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Answer:

(-2,-7)

alternatively

x: -2

y: -7

To find ,we can break down each vector into its horizontal and vertical components. The horizontal component represents the vector's magnitude in the x-axis , and the vertical component the magnitude in the y-axis direction.

To verify the sum of vectors using the components method, we can add the horizontal components together and the vertical components together. If the resultant sum of the horizontal components equals the horizontal component of the resultant vector, and the sum of the vertical components equals the vertical component of the resultant vector, then the components method is verified.

To find the vector components, we typically use trigonometry. Given a vector with magnitude (r) and an angle (θ) measured counterclockwise from the positive x-axis, we can find the horizontal component (x-component) and the vertical component (y-component) using the following equations:

x-component = r * cos(θ)

y-component = r * sin(θ)

To verify the sum of vectors using the components method, we add the horizontal components together and the vertical components together. Let's say we have two vectors A and B. The components of vector A are (A₁, A₂), and the components of vector B are (B₁, B₂). The components of the resultant vector R would be (A₁ + B₁, A₂ + B₂).

To verify the sum, we check if the sum of the horizontal components (A₁ + B₁) equals the horizontal component of the resultant vector R, and the sum of the vertical components (A₂ + B₂) equals the vertical component of the resultant vector R. If these conditions are satisfied, the sum of vectors using the components method is verified.

In summary, vector components can be found by breaking down vectors into their horizontal and vertical components. To verify the sum of vectors using the components method, we add the horizontal and  vertical components separately and check if they match the components of the resultant vector.

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Answer:

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain. In plain English, the definition means: The range is the resulting y-values we get after substituting all the possible x-values.

Answer:

  8.5 years

Step-by-step explanation:

You want to know the number of years until 18500 depreciates to 9100 at the rate of 8% per year.

The depreciation rate given as a percentage of current value tells you the depreciation is exponential. The formula will be ...

  value = (initial value) × (1 - (depreciation rate))^t

where the rate is "per year" and t is in years.

  value = 18500·(1 -0.08)^t

  9100 = 18500·0.92^t . . . . fill in the value of interest

  9100/18500 = 0.92^t . . . . divide by 18500

  log(91/185) = t·log(0.92) . . . . take logarithms

  t = log(91/185)/log(0.92) ≈ -0.3081/-0.03621 ≈ 8.509

It will be about 8.5 years until the value is $9100.

__

Additional comment

The graph shows the solution to ...

  18500·0.92^t -9100 = 0

We find it fairly easy to locate an x-intercept, so we wrote the equation in the forms that makes the x-intercept the solution.

Answer:

y < 45

Step-by-step explanation:

Pittsburgh Steelers scored 45 points.

The Miami Dolphins will be represented by a variable y.

y scored less than 45 points.

y is less than 45

y < 45

Answer: The point estimate for this population proportion is 0.2

Step-by-step explanation:

The point estimate for this population proportion is also referred to as the sample proportion. This is also known as the probability of success, p. The formula for determining p is expressed as

p = x/n

Where

n represents the number of samples

x represents the number of success

From the information given,

n = 200

x = 40

p = 40/200 = 0.2

The maximum amount you can earn is $540

a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.

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the correct choice is {0, 18}. These elements are unique to set C and do not appear in set A.

To find the set difference C - A, we need to remove all elements from A that are also present in C. Let's examine the sets:

C = {0, 6, 12, 18}

A = {2, 4, 6, 8, 10, 12}

We compare each element of A with the elements of C. If an element from A is found in C, we exclude it from the result. After the comparison, we find that the elements 2, 4, 8, 10 are not present in C.

Thus, the set difference C - A is {0, 18}, as these are the elements that remain in C after removing the common elements with A.

Therefore, the correct choice is {0, 18}. These elements are unique to set C and do not appear in set A.

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Answer:

By adding equation we get:

2x-y=3

x +y=9

______

3x=12

x=6

Step-by-step explanation:

cut the positive and negative (y)

To find the probability that a randomly selected worker has a retirement plan or health insurance, we need to add the probabilities of having a retirement plan and having health insurance and then subtract the probability of having both,

Since we don't want to count those workers twice. P(retirement plan or health insurance) = P(retirement plan) + P(health insurance) - P(both), P(retirement plan or health insurance) = 0.56 + 0.68 - 0.49, P(retirement plan or health insurance) = 0.75.

Therefore, the probability that a randomly selected worker has a retirement plan or health insurance is 0.75. we'll use the formula: P(A or B) = P(A) + P(B) - P(A and B), where A represents having a retirement plan, B represents having health insurance, and P(A and B) represents having both.

Given:
P(A) = 56% (retirement plan)
P(B) = 68% (health insurance)
P(A and B) = 49% (both)

Now we can plug these values into the formula: P(A or B) = 0.56 + 0.68 - 0.49 = 0.75, The probability that a randomly selected worker has a retirement plan or health insurance is 75%.

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A cyclic quadrilateral is a quadrilateral inscribed in a circle

The measure of angle A is 106

From the question, we have:

<C= 74

Opposite angles of a cyclic quadrilateral add up to 180.

So, we have:

<A + <C = 180

This gives

<A + 74 =180

Subtract 74 from both sides

<A =106

Hence, the measure of angle A is 106

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Answer:

For 1 cup of  pineapple 1 .5  cups of strawberries are used.

Step-by-step explanation:

This question can be solved by using ratios

Strawberry       :      Pineapple

1     cup              :          2/3 cup

x cup                  ;            1 cup

Using the cross product rule

2/3 * x= 1*1

x= 1*1 ÷ 2/3

x= 1*3/2= 1 1/2= 1.5

For 2 cups of pineapple 3 cups of strawberries are used.

For 1 cup of  pineapple 1 .5  cups of strawberries are used.

For 3 cups of pineapple 4.5 cups of strawberries are used.

Answer:

-5

Step-by-step explanation:

You divide 80 by -16

Step-by-step explanation:

since 36% is 576 seats, 100% would be 576/36 x 100 = 1600seats

Topic: Percentage

If you like to venture further, feel free to check out my insta (learntionary). It would be best if you could give it a follow. I'll be constantly posting math tips and notes! Thanks!

Using the Binomial probability distribution,

the probability that sheer guesswork will yield exactly 18 correct answers is ²⁷C₁₈(0.2)¹⁸(0.8)⁹

We have given that,

total number of multiple choice questions= 27

each question has number of possible answer

= 5

but only one is correct .

we have to find out the probability that sheer guesswork will yield 18 correct answer.

P(C) = probability of answering any question correctly = (1 / 5) = 0.2

P(W) = probability of answering any question wrongly = (4/ 5) = 0.8

Using the Binomial probability distribution,

P(X= x) = ⁿCₓ(p)ˣ(q)⁽ⁿ⁻ˣ⁾

Probability of answering exactly 18 questions correctly = P(X=18) = ²⁷C₁₈(0.2)²⁸(0.8)⁹

Hence, the probability value is ²⁷C₁₈(0.2)²⁸(0.8)⁹

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The area of the square is changing at 12√2 + 2√2t square inches/minute when the circle is increasing at 1 in/min.

Let us find the relationship between r and s using the Pythagorean theorem. Since the square is inscribed in the circle, the diameter of the circle is equal to the diagonal of the square.

2r = s√2
Squaring both sides, we get:
4r² = 2s²or s² = 2r²
Dividing by 2 on both sides, we get:
s²/2 = r²
Differentiating both sides with respect to t, we get:
ds²/dt = 2r (dr/dt)
Dividing both sides by 2s, we get:
ds/dt = r (dr/dt) / s

Substituting r² = s²/2,

\(ds/dt = r (dr/dt) / √2s2s ds/dt = r (dr/dt)s ds/dt = (r/2) (dr/dt)2s ds/dt = r (dr/dt) or dA/dt = 2s ds/dt = 2r (dr/dt)\)

Now, substituting r² = s²/2,

dA/dt = 2s ds/dt = 2(√2 s) (dr/dt) = 2(√2) r (dr/dt)

Now, substituting dr/dt = 1 in/min and r = 6 in (since the circle is increasing at 1 in/min, the radius after t minutes is 6 + t),

dA/dt = 2(√2) (6 + t) (1) = 12√2 + 2√2t square inches/minute

Therefore, the area of the square is changing at a rate of 12√2 + 2√2t square inches/minute.

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What type of sequence does this scenario represent, and why?

✔ arithmetic; the sequence has a common difference

If the pattern of the sequence continues, how many guests will the restaurant have on its 14th night?  

✔ 360

This example doesn't accurately depict arithmetic because the succession has a common difference. The restaurant will host 360 customers on its fourteenth night if the pattern of the series holds.

Arithmetic sequences always add or subtract the same amount to go from one term to the next. Finding the difference between any AP phrase and its predecessor will reveal the common difference, indicated by the letter "d."

An arithmetic sequence's nth term is determined by, Formula an = a1 + (n - 1)d. The common difference, or d, is the difference between any two consecutive terms in an arithmetic series; it can be calculated by deducting any pair of terms starting with a and an+1.

an = 100 + (14 - 1)20.

an = 360

The restaurant will host 360 customers on its fourteenth night if the pattern of the series holds.  

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Answer:

maybe its a and e

Step-by-step explanation:

Answer: A and E

Explanation:

A has a triangle to show the slope. If you count the boxes along the triangle the vertical side is 10 boxes and the horizontal side is 4. This means the slope is 10/4 which simplifies to 5/2.

E doesn’t have a triangle to show the slope but if you count in the triangle pattern from one point to the next point the slope equals 5/2.

Answer:

h(t) = 40,000 - 1,500t

Step-by-step explanation:

Let h(t) be the height of the airplane after t minutes.

h(t) = 40,000 - 1,500t

Answer:

Option a :- 2x+32 = 60

Step-by-step explanation:

Formula to calculate perimeter:-- P=2(l+w)

2(l+w) = P

2l + 2w = P

2x + 2(16) = 60

2x + 32 = 60

\( \therefore \) The equation that represents this problem = 2x+32 = 60

Answer:

The correct answer is C. Statement: m∠3 + m∠5 = 180° and m∠4 + m∠6 = 180° Reason: definition of supplementary angles.

This statement uses the definition of supplementary angles, which states that two angles are supplementary if their measures add up to 180 degrees. Since ∠3 and ∠6 are corresponding angles, and ∠4 and ∠5 are also corresponding angles, their measures must add up to 180 degrees in order for the parallel lines to be cut by the transversal.

Answer:

Option, D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem

Step-by-step explanation:

In this question that you have put:

7 ≅ ∠6 and ∠8 ≅ ∠5 Reason =

Vertical Angles Theorem ( Or in similar terms VAT )

Make sure that you remember the following:

vertical angles are the angles that are opposite each other when the two line " meet together "

Thus, your answer to your questions is.

D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem

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The expression which is equivalent to (2³)^-5 is; 1/(2)^15.

By the law of indices, it follows that exponents as that given in the task content can be evaluated as follows;

(2³)^-5

= (2) ^(3×-5)

= 2 ^(-15)

Hence, the expression can be rewritten as; 1/(2)^15.

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Answer:

a

Step-by-step explanation:

i did the test

Answer:

a.

Explanation:

In the chart, the average temperature of each month at the beginning of the year gradually rises until August, where it begins to decrease. This trend is displayed in graph a. Additionally, each month on the x-axis is shown correctly because the months should only span numbers 1-12.

Answer: the answer is A

Step-by-step explanation: hope this helps :D can u plz give a brainliest

The dollar amount for the return on stocks is $3375 and the dollar amount for the return on bonds is $1125.

Two equations can be derived from the question:

s + b = $90,000 equation 1

0.1s + 0.02b = $4500 equation two

$4500 = 0.05  x $90,000

The above equation is a simultaneous equation and it would be solved using the elimination method.

The following steps would be take to determine the value of b

Multiply equation 1 by 0.1

0.1s + 0.1b = 9000 equation 3

Subtract equation 2 from 3

0.08b = $4500

b = $56,250

The following step would be taken to determine the value of s

Substitute for b in equation 1

s + $56,250 = $90,000

$90,000 - $56,250 = s

s = $33,750

Dollar amount for the return on stocks = $33,750 x 0.1 = $3375

Dollar amount for the return on bonds = $56,250 x 0,02 = $1125

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Answer:

6

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

|bc|

a = 5

b = -3

c = -2

Step 2: Evaluate