(Note that most of the answers are algebraic expressions involving t) A car starts on a trip and travels at a speed of 55 mph. Two hours later, a second later starts on the same trip and travels at a speed of 55 mph. When the second car has been on the road trip for t hours, the first car has traveled _____ miles and the second car has traveled ______ miles.

Answer:

Step-by-step explanation:

6x-y=-5

-6x+y=5

Adding the 2 equations we have:

0 + 0 = 0

0 = 0

This means there are infinite solutions

- the equations are identical.

System B

x+3y=13

-x+3y=5

Adding:

6y = 18

y = 3.

x = 13 - 3(3) = 4.

The system has a unique solution

(x. y) = (4, 3).

Answer:

32780

Step-by-step explanation:

Answer:

32,780

Step-by-step explanation:

It should be 30,000

Answer:

0.5

Step-by-step explanation:

Answer:

answer is 0.5 just got it right

Step-by-step explanation:

x=4

y=2

z=5

2x2 + 3y3 + 4z

2.4.2 + 3.2.3 + 4.5

16 + 18 + 20

34 + 20

54

Answer:

76

Step-by-step explanation:

2*4^2 +3*2^3 + 4*5=32+24+20=76

Answer:

13

Step-by-step explanation:

g(x) = -3x + 4

g(-3) = -3 × -3+4

g(-3) = 9 + 4

g(-3) = 13 ........

Answer:

200

Step-by-step explanation:

1cm=50m

1*4=50*4

4=200 miles

The correct option is C as it consists exact domain and range that we need.

What is domain and range?

The domain of a function f(x) is that the set of all values that the function is outlined, and also the range of the operate is that the set of all values that f takes.

The set of all attainable values that qualify as inputs to a operate is thought because the domain of the operate, or it also can be outlined because the entire set of values attainable for freelance variables. .

Main body:

the given function :

{(2,3), (7,9), (4,-7), (6,2), (3,-5)}

domain = (2,7,4,6,3)

range = (3,9,-7,2,-5)

Hence the correct option is C.

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Answer:

Line C

Step-by-step explanation:

Given:

Create the equation for the line using the given information:

\(\implies y=\dfrac{1}{2}(x-4)\)

Distribute:

\(\implies y=\dfrac{1}{2}x-2\)

\(\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}\)

Compare the found equation with the slope-intercept formula:

The y-intercept is the y-value of the point at which the line crosses the y-axis.  Therefore, the line crosses the y-axis at y = -2.

The slope tells us how much y increases as x increases.  Given the slope is ¹/₂, the line increases by one y-value for every two x-values.

Therefore, the line that represents the given information is line C.

Answer: 17u

Step-by-step explanation:

(9+9+6-7)u=17u

Answer:

17u

Step-by-step explanation:

9u+6u+9u =24u

24u-7u=17u

Answer:

the sequence is adding 5 the next number would be 22

hope this helps

have a good day :)

Step-by-step explanation:

7, 12, 17, 22, 27 . . .  (5n + 2)

n = 1, => 7

n = 2, => 12

n = 3, => 17

n = 4, => 22

The Taylor series for ln(x) centered at 9 is:

ln(x) = ln(9) + (1/9)(x-9) - (1/281)(x-9)^2 + (2/3729)(x-9)^3 + ...

To find the Taylor series for ln(x) centered at a=9, we first need to find the derivatives of ln(x).

The first derivative of ln(x) is 1/x, the second derivative is -1/x^2, the third derivative is 2/x^3, and so on.

Next, we need to evaluate these derivatives at a=9 to find the coefficients of the Taylor series.

The first coefficient is f(9), which is ln(9).

The second coefficient is f'(9), which is 1/9.

The third coefficient is f''(9), which is -1/81.

The fourth coefficient is f'''(9), which is 2/729.

We can then use the formula for the Taylor series to write the series for ln(x) centered at a=9.

The series will converge to ln(x) for values of x that are close to 9.

f(x) = ln(x), a = 9

f(9) = ln(9)

f'(x) = 1/x

f'(9) = 1/9

f''(x) = -1/x^2

f''(9) = -1/81

f'''(x) = 2/x^3

f'''(9) = 2/729

The Taylor series for ln(x) centered at 9 is:

ln(x) = ln(9) + (1/9)(x-9) - (1/281)(x-9)^2 + (2/3729)(x-9)^3 + ...

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Voluntary sampling is not necessarily unbiased even if the sample size is more than 30 or if it passes a normality check so the correct option is b. sometimes.

Voluntary sampling involves individuals choosing to participate in a study or survey voluntarily, which can introduce self-selection bias. This bias occurs because individuals who choose to participate may have different characteristics or opinions compared to those who choose not to participate. Therefore, the sample may not be representative of the entire population, leading to biased estimates.

To minimize bias, random sampling methods should be used, where each member of the population has an equal chance of being selected for the sample. Additionally, sample size alone does not guarantee unbiasedness, as bias can still exist regardless of the sample size. It is important to consider the sampling method and potential sources of bias when making inferences about the population based on a sample.

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Answer:

Step-by-step explanation:

700.5

The amount of interest is $1,782 and the monthly payment is $187.

To find the amount of interest and monthly payment for the loan, we need to use the add-on interest formula. The add-on interest formula is:

\(Total interest = Principal x Interest Rate x Time\)

Total amount due = Principal + Total interest

Monthly payment = Total amount due ÷ Number of payments

Given:

Principal (P) = $4,950

Interest rate (r) = 12%

Time (t) = 3 years

Number of payments (n) = 36 (12 months × 3 years)

Using the formula:

Total interest = P x r x t = $4,950 x 0.12 x 3 = $1,782

Total amount due = P + Total interest = $4,950 + $1,782 = $6,732

Monthly payment = Total amount due ÷ Number of payments = $6,732 ÷ 36 = $187

Therefore, the amount of interest is $1,782 and the monthly payment is $187.

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Answer:

  (a)  There are asymptotes at x=3/2 and x=-1/3

Step-by-step explanation:

The denominator zeros can be found by factoring:

  f(x) = (x +1)/((2x -3)(3x +1))

Neither of the denominator factors is cancelled by the numerator factor, so each represents a vertical asyptote, not a function hole.

The asymptotes are at the values of x where the denominator is zero:

  2x -3 = 0   ⇒   x = 3/2

  3x +1 = 0   ⇒   x = -1/3

Answer:A There are asymptotes at x=3/2 and x=-1/3

Step-by-step explanation:

Answer:

problem one

x = 3- 5y/3

y = 9/5 - 3x/5

problem 2

x= -12 + 10y/3

y= 18/5 + 3x/10

Step-by-step explanation:

The equation of the inverse function of the function f(x) = x^2 - x - 2 is f'1(x) =  0.5 + √x + 2.25

Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function

The function f(x) is given as

f(x) = x^2 - x - 2

Start by expressing the above function in vertex form

Using a graphing calculator, we have

f(x) = (x - 0.5)^2 - 2.25

As a general rule, we start by writing f(x) as a variable (say f(x) = y).

So, the equation of the function becomes

y = (x - 0.5)^2 - 2.25

The next step is to switch/swap the positions of x and y in the above equation y = (x - 0.5)^2 - 2.25

The equation becomes

x = (y - 0.5)^2 - 2.25

Add 2.25 to both sides

So, we have

(y - 0.5)^2 = x + 2.25

Take the square root of both sides

y - 0.5 = √x + 2.25

Add 0.5 to both sides

So, we have

y = 0.5 + √x + 2.25

Express as an inverse function

f'1(x) =  0.5 + √x + 2.25

Hence, the inverse function of the function f(x) = x^2 - x - 2 is f'1(x) =  0.5 + √x + 2.25

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In this problem, we have a binomial probability distribution

so

n=3

p=0.50

q=0.50

Find out P(X=2)

We apply the formula : a^m : a^n = a^(m-n)

-> 3^4 : 3^9 = 3^(4-9) = 3^-5

Since we need the final answer with a positive exponent, 3^5.

Answer:

answer is B

Step-by-step explanation:

cost is = to the amount of a donut .75 times the amount of donuts that you buy. D is the variable that stands the unknown amount of donuts.

Answer: B

Step-by-step explanation:

you need to find the total cost which is C.

$0.75 is the cost of each donut, D represents donuts

Example if you buy 2 donuts, you would multiply 2 by 0.75 to get 1.5

Multiply D (donuts) by 0.75 (cost of each donut) to get C (total cost)

this equals to choice B

Hope this helps!

The approximate value of cos(theta) is 0.8826

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

sin(theta) = 0.47

Express properly

So, we have

sin(θ) = 0.47

The approximate value of cos(theta) is calculated as

sin²(θ) + cos²(θ) = 1

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

cos²(θ) + (0.47)² = 1

So, we have

cos²(θ) = 1 - (0.47)²

Evaluate

cos²(θ) = 0.7791

Take the positive square root of both sides

cos(θ) = 0.8826

Take the arccos of both sides

θ = 28.03

Hence, the approximate value of cos(theta) is 0.8826

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The measure of angle 4 is equal to the sum of the measures of the two nonadjacent interior angles because the angle 4 is exterior to the given interior angles.

The sum of interior angles is equal to the exterior. From the given figure;

Interior angles are 25 degrees and 52 degrees.

The measure of angle 4 is equal to the sum of the measures of the two nonadjacent interior angles because the angle 4 is exterior to the given interior angles.

2) <4 = 25 + 52

<4 = 77 degrees

Hence the measure of angle 4 is 77 degrees

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Answer:

3

Explanation: 3 times 11 is 33

The value of x that makes the equation true is 3.

An equation is a statement that equates to two expressions.

The given equation is:

\(33=11x\)

\(11x=33\)

Divide both sides by 11

\(\frac{11x}{11} =\frac{33}{11}\)

\(x=3\)

So, the required value of x=3.

Hence, The value of x that makes the equation true is 3.

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Answer:

52 degrees

Step-by-step explanation:

Answer:

-6/29

Step-by-step explanation:

12 = x1 -3 = y1 -17 = x2 3 = y2 3 - -3 = 6 - -17 - 12 = -29 = -6/29

Answer:

D) 263

Step-by-step explanation:

Step 1: Define

10m³ - |n|

m = 3

n = -7

Step 2: Substitute and Evaluate

10(3)³ - |-7|

10(27) - 7

270 - 7

263

Answer:

263

Step-by-step explanation:

10(33)− l 7  I

=(10)(27)− I 7  I

=270− I 7  I

=263

Answer:

2

Step-by-step explanation:

(0,2) is the y-intercept

The eigenvalues of A are λ = 0 (with multiplicity 1) and λ = 5 (with multiplicity 2), and the corresponding eigenvectors are [1, 0, -1], [0, 1, -1], and [1, -1, 1].

The matrix A = [5 5 5; 5 5 5; 5 5 5] is a 3x3 matrix with all entries equal to 5.

First, we can calculate the determinant of A - λI, where I is the identity matrix and λ is an unknown eigenvalue:

A - λI = [5-λ 5 5; 5 5-λ 5; 5 5 5-λ]

det(A - λI) = (5-λ)[(5-λ)(5-λ)-25] - 5[5(5-λ)-25] + 5[5-25]

= (5-λ)(λ^2 - 15λ) = -λ(λ-5)^2

From this equation, we can see that the eigenvalues are λ = 0 and λ = 5 (with multiplicity 2).

To find the eigenvectors, we can substitute each eigenvalue into the equation (A - λI)x = 0 and solve for x.

For λ = 0, we have:

A - 0I = A = [5 5 5; 5 5 5; 5 5 5]

(A - 0I)x = 0x = [0 0 0]

This implies that any vector of the form [a, b, -a-b] is an eigenvector for λ = 0. For example, we can choose [1, 0, -1] and [0, 1, -1] as linearly independent eigenvectors corresponding to λ = 0.

For λ = 5, we have:

A - 5I = [0 5 5; 5 0 5; 5 5 0]

(A - 5I)x = 0

⇒ 5x2 + 5x3 = 0

⇒ 5x1 + 5x3 = 0

⇒ 5x1 + 5x2 = 0

This implies that any vector of the form [1, -1, 1] is an eigenvector for λ = 5. Therefore, we can choose [1, -1, 1] as another linearly independent eigenvector corresponding to λ = 5.

Eigenvectors are a fundamental concept in linear algebra. They are essentially special vectors that remain in the same direction when a linear transformation is applied to them, only changing in magnitude. In other words, an eigenvector of a linear transformation is a vector that when multiplied by the transformation matrix, results in a scalar multiple of itself.

Eigenvectors play a crucial role in diagonalizing matrices, which can simplify calculations involving matrix operations. They are also useful for solving differential equations and understanding the behavior of dynamic systems. In addition, eigenvectors are often used for data analysis, such as in principal component analysis (PCA), which is a technique for reducing the dimensionality of data.

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