Select the correct answer.
What is the solution to this system of equations?
x - 2y = 15
2x + 4y=-18
O A. x= 1, y= -6
B.
x= 1, y=-7
C. x= 3, y=-6
D. x= 3. y=-7
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This equation x + (x + 1) + (x + 2) = negative 21 will be used.

Let the first Number is x.

We have to take 3 consecutive integers.

second Number is x+1

third Number is x+2.

Sum of these 3 consecutive integers is x+(x+1)+(x+2).

Sum of these 3 consecutive integers is given as negative21.

so we can write  x+(x+1)+(x+2)=negative 21.

by using above equation we can find the value of 3 numbers.

So the final equation will be x + (x + 1) + (x + 2) = negative 21.

Given Question is incomplete, Complete Question here:

Three consecutive integers have a sum of –21. Which equation can be used to find the value of the three numbers? x + x + x = negative 21 x + 2 x + 3 x = negative 21 x + (x + 1) + (x + 2) = negative 21 x + (x + 2) + (x + 4) = negative 21

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Answer:

A, B, C

Step-by-step explanation:

12+0.25*12=12(1+0.25)=12*1.25

Answer:

B. 12 + 0.25 ⋅ 12

C. 12(1 + 0.25)

Step-by-step explanation:

It asks you how far she walks all together, so you need to find that answer first to figure out the rest correctly. Now, the total she walked is 15 miles. B. and C. give you 15, however, the rest give you different answer than the total she actually walked.

Considering the asymptotes, the rational function given below is the following:

B. \(f(x) = \frac{1}{x(x + 2)}\)

From the graph, the vertical asymptotes are x = 0 and x = -2, hence the denominator is given by:

x(x + 2).

The function has no x-intercepts, hence the numerator is of 1. So the function is given by:

B. \(f(x) = \frac{1}{x(x + 2)}\)

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Answer:

\(f(x +1) = \sqrt{x +7} -8\)

Step-by-step explanation:

Given:

\(f(x) = \sqrt{x +6} -8\)

Solving for \(f(x +1)\):

\(f(x +1) = \sqrt{(x +1) +6} -8 \\ f(x +1) = \sqrt{x +7} -8\)

Answer:

add it my guy it's not that hard

Answer:

x = 1, y = 6

Step-by-step explanation:

Given the 2 equations

y = x + 5 → (1)

y = 6 → (2)

Since we are given the value of y, that is y = 6 then substituting into (1) gives

6 = x + 5 ( subtract 5 from both sides )

1 = x

Solution is x = 1, y = 6

x = 2, y = 81.

u = g(x) = x^2 – 7x + 9

y = f(u) = u^4.

The inside function and outside function in a composite function can be identified by examining the structure of the function. The inside function is the function that is being acted upon by the outside function. In this case, the inside function is u = g(x) = x^2 – 7x + 9, and the outside function is y = f(u) = u^4.

To find the value of y for a given value of x, we first need to find the value of u by substituting the value of x into the inside function. Then, we can substitute the value of u into the outside function to find the value of y.

For example, if x = 2, then:

u = g(x) = x^2 – 7x + 9 = 2^2 – 7(2) + 9 = -3
y = f(u) = u^4 = (-3)^4 = 81
So, when x = 2, y = 81.

In conclusion, the inside function is u = g(x) = x^2 – 7x + 9, and the outside function is y = f(u) = u^4. To find the value of y for a given value of x, we first need to find the value of u by substituting the value of x into the inside function, and then substitute the value of u into the outside function to find the value of y.

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Answer:

y=mx

because line is passing through origin ,so y intercept is 0.

General equation of a line is given as y=mx+c where m=slope of the line.

Answer:

B

Step-by-step explanation:

13a ^2+14-17a-12a ^2+12a+6a-a^ 2

=14-17a+12a+6a

=14+a    or     a+14

Answer:

Your number must be a multiple of 1, 2, and 3.

Step-by-step explanation:

To determine three numbers that your number must be a multiple of, given that it is a multiple of 6, we need to identify factors that are common to 6.

The factors of 6 are 1, 2, 3, and 6.

Therefore, your number must be a multiple of at least three of these factors.

For example, your number could be a multiple of 6, 2, and 3, or it could be a multiple of 6, 3, and 1.

There are several combinations of three numbers that your number could be a multiple of, as long as they include 6 as a factor.

Answer:

B. 103.73

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=mx+b

m=dy/dx=(0-8)/(4-0)=-8/4=-2

y=-2x+b, using point (4,0)

0=-2(4)+b

b=8

y=-2x+8

An equation of an ellipse in standard form with the center at the origin is x^2/9 + y^2/4 = 1.

The standard form equation of an ellipse with center at the origin is:
(x^2/a^2) + (y^2/b^2) = 1 where a and b are the lengths of the major and minor axes respectively.
Using the given characteristics, we can determine that the major axis of the ellipse is horizontal, and has a length of 6 (from (-3,0) to (3,0)). Similarly, the minor axis is vertical, and has a length of 4 (from (0,2) to (0,-2)).
Therefore, we have:
a = 3
b = 2
Substituting these values into the standard form equation, we get:
(x^2/3^2) + (y^2/2^2) = 1
Simplifying:
(x^2/9) + (y^2/4) = 1

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Answer:

~Senpi boi here~

Step-by-step explanation:

Multiply all terms by x and cancel:

x+2x+1=1x

3x+1=x(Simplify both sides of the equation)

3x+1−x=x−x(Subtract x from both sides)

2x+1=0

2x+1−1=0−1(Subtract 1 from both sides)

2x=−1

2x

2

=

−1

2

(Divide both sides by 2)

x=

−1

2

Check answers. (Plug them in to make sure they work.)

x=

−1

2

(Works in original equation)

Answer:

x= −1/2

(Hope this helps!)

The sum of Peter, Richard, and John's ages is 191.

We know that the ratio of Peter's age to Richard's age is = 5/8 --(i)

The ratio of John's age to Peter's age is = 7/12 --(ii)

Similarly, the ratio of John's age to Richard's age is = (5*7)/(8*12)= 35/96 -(iii)

Using the value of (i),(ii),(iii), we get -

Age of Peter = (5*12)/(8*12) = 60/96

= 60 years of age

Age of John = (7*5)/(12*5) = 35/60

=35 years of age

From the value of (iii), since no one is over 100 years of age, the age of Richard= 96 years of age

Hence the sum of their ages is = 96+35+60

= 191

Therefore, we know that the sum of their ages is 191.

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Distinct arrangements are there of PAPA is 12.

There are four letters in the given word 'PAPA'.Arrangements are different from combinations as the order matters in arrangements. To find the arrangements of PAPA, we can follow these steps-

Step 1: Find the total number of ways to arrange four different letters without repetition. This can be done by using the formula: n!

Here, n = 4. Therefore, the total number of ways to arrange four different letters without repetition is 4! = 24.

Step 2: As there are two 'A's in the word 'PAPA'. We must divide the total number of ways by the number of arrangements of two A's which is 2! (as both A's are identical).

Step 3: After dividing, we get 24/2! = 12 distinct arrangements of PAPA.

Hence, the correct answer is: 12

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Answer:

B. Find the ratio of minutes to miles, 4:1. Multiply 7.5 by 4.

Step-by-step explanation:

Look for a pattern within the table.

10 : 2.5

16 : 4

? : 7.5

48 : 12

10/2.5 = 4

16/4 = 4

14/12 = 4

this means that if we multiply 7.5 by 4 we will be able to find the missing number!

Therefore, the answer is B.

Hope this helps! :)

68 inches tall is Sparky

Step-by-step explanation:

just take of 4 tall of lanky then you will get the tall

Answer:

Is there more to the question?

Answer:

A. and H.

Step-by-step explanation:

Answer:

24/25

Step-by-step explanation:

COS = adjacent/hypotenuse

Answer:

24/25

Step-by-step explanation:

my answer is 24/25

The difference between the best and worst credit score interest rates would be = 6.24%

An interest rate is defined as the particular amount of money an individual receives for a period of time due to an investment made.

The difference between the best and the worst credit score interest rates would be to substrate the best score from the worst score.

The best interest rate score = 3.65

The worst interest rate score = 9.89

Therefore the difference = 9.89 - 3.65 = 6.24 %

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The length of the vector function F(t) over the interval -6 ≤ t ≤ 8 is  D) L = 14√56.

The length of the vector function F(t) = <3 - 4t, 6t, -(9 + 2t)> from -6 ≤ t ≤ 8, we need to calculate the integral of the magnitude of the derivative of F(t) with respect to t over the given interval.

The magnitude of a vector v = <x, y, z> is given by ||v|| = √(x² + y² + z²).

First, let's find the derivative of F(t):

F'(t) = <-4, 6, -2>

Next, let's find the magnitude of F'(t):

||F'(t)|| = √((-4)² + 6² + (-2)²)

= √(16 + 36 + 4)

= √56

Now, we can calculate the length of F(t) over the interval -6 ≤ t ≤ 8 by integrating ||F'(t)|| with respect to t:

L = ∫(√56) dt

= √56 ∫dt

= √56 × t + C

Evaluating the integral over the given interval:

L = √56 × t + C| (-6)⁸

= √56 × (8 - (-6))

= √56 × 14

= 14√56

Therefore, the length of the vector function F(t) over the interval -6 ≤ t ≤ 8 is 14√56.

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A pair of functions that are inverses of each other is: B. f(x) = 4x³ + 5 and g(x) = ∛[(x - 5)/4].

In order to determine the inverse of this function f(x) = -1 - 1/5x, we would interchange both the input value (x) and output value (y) as follows:

f(x) = y = ∛(x + 3) - 5

x = ∛(y + 3) - 5

x + 5 = ∛(y + 3)

Taking the cube of both sides of the function, we have:

(x + 5)³ = y + 3

g(x) = y = (x + 5)³ - 3 (Not inverse).

For the second option:

f(x) = y = 4x³ + 5

x = 4y³ + 5

x - 5 = 4y³

Dividing both sides of the function by 4, we have the following:

y³ = (x - 5)/4

Taking the cube root of both sides of the function, we have:

g(x) = y = ∛[(x - 5)/4] (Inverse)

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The final solution in terms of the inverse Laplace transforms:

\(ƒ(t) = L^{-1}[F(s)]\)

We have,

To solve the given ordinary differential equation (ODE) using Laplace transform, we'll follow these steps:

Step 1: Take the Laplace transform of both sides of the equation.

Step 2: Solve for the Laplace transform of the function ƒ(t).

Step 3: Take the inverse Laplace transform to obtain the solution in the time domain.

Let's go through these steps:

Step 1: Taking the Laplace transform of the ODE, we have:

L[f"(t)] + 6L[f'(t)] + 13L[f(t)] = 48L[t - 5]

Step 2: Applying the Laplace transform properties and using the initial conditions, we get:

\(s^2F(s) - sf(0) - f'(0) + 6(sF(s) - f(0)) + 13F(s) = 48(e^{-5s}/s)\)

Simplifying, we have:

\(s^2F(s) + 6sF(s) + 13F(s) - s(0) - 0 + 6sF(s) - 6(0) + 13F(s) = 48(e^{-5s}/s)\)

Combining like terms, we obtain:

\((s^2 + 6s + 13)F(s) = 48(e^{-5s}/s)\)

Step 3: Solving for F(s), we have:

\(F(s) = 48(e^{-5s}/s) / (s^2 + 6s + 13)\)

To find the inverse Laplace transform of F(s), we can use partial fraction decomposition, but the expression involves complex roots.

Therefore,

The final solution in terms of the inverse Laplace transforms:

\(ƒ(t) = L^{-1}[F(s)]\)

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There is a negative rate of change in the function In the interval (-2,-1) on the x-axis.

The slope of the straight line connecting two points is the average rate of change between those two coordinates.

We can infer from the graph,

the slope of the straight line connecting these points is negative in the range of -2 to -1.

As a result, the function's rate of change over this interval is negative.

Hence, In the interval –2 to –1 there is a negative rate of change in the function.

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According to philosopher John Stuart Mill, moral rules have certain advantages over act-calculus, also known as act utilitarianism.

Mill's ethical theory, known as utilitarianism, focuses on maximizing overall happiness or utility as the basis for determining the morality of actions.

One advantage of moral rules, according to Mill, is that they provide general guidance and stability in moral decision-making.

Moral rules offer clear guidelines that can be followed in different situations, which reduces the need to constantly calculate and weigh the consequences of each individual action.

By having pre-established rules, individuals can rely on them to make decisions without having to engage in complex moral calculations every time.

Another advantage of moral rules, according to Mill, is that they protect individual rights and promote justice. In utilitarianism, the well-being and happiness of individuals are essential.

However, relying solely on act-calculus may lead to situations where the rights and interests of some individuals are sacrificed for the greater happiness of the majority.

Moral rules provide a framework for respecting individual rights, ensuring fairness, and preventing potential abuses that may arise from purely calculating the consequences of each action.

Additionally, Mill argues that moral rules provide a sense of security and predictability in society.

When individuals are aware of the rules and understand the general expectations of behavior, they can trust in the consistency and fairness of the moral framework.

This helps to maintain social order and stability, as people can rely on shared rules and norms to govern their interactions.

However, it is important to note that Mill also acknowledged the limitations of moral rules and recognized that they are not infallible.

He emphasized the importance of critical thinking and flexibility in applying moral rules, particularly in situations where strict adherence to a rule may lead to harmful or unjust outcomes.

Mill's position can be seen as a blend of rule-utilitarianism and act-utilitarianism, acknowledging the value of moral rules while also recognizing the need for flexibility and thoughtful consideration of specific circumstances.
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