Please help I don't know how to do this

The two points with an x-coordinate of 2 and a distance of 5 from (-2, -4) are: (2, -4 + 2√13) and (2, -4 - 2√13)

What is distance formula?

Distance is a measurement of how far away two things or locations are, either numerically or occasionally qualitatively.

Distance formula: \(distance = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)}\)

We can solve this problem using the distance formula, which gives us the distance between two points in a plane:

\(distance = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)}\)

Let (x, y) be a point with an x-coordinate of 2. Then we can write the distance from (-2, -4) to (x, y) as:

\(distance = \sqrt{((x - (-2))^2 + (y - (-4))^2)}\)

Simplifying this expression, we get:

\(distance = \sqrt{((x + 2)^2 + (y + 4)^2)}\)

We know that the distance between (-2, -4) and (x, y) is 5. Therefore, we can write:

\(\sqrt{((x + 2)^2 + (y + 4)^2)} = 5\)

Squaring both sides, we get:

\((x + 2)^2 + (y + 4)^2 = 25\)

Expanding the left side, we get:

\(x^2 + 4x + 4 + y^2 + 8y + 16 = 25\)

Simplifying this expression, we get:

\(x^2 + 4x + y^2 + 8y - 5 = 0\)

To find all points with an x-coordinate of 2 that satisfy this equation, we can substitute x = 2 and simplify the resulting equation:

\(2^2 + 4(2) + y^2 + 8y - 5 = 0\)

Simplifying this equation, we get:

\(y^2 + 8y + 3 = 0\)

We can solve this quadratic equation using the quadratic formula:

y = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 8, and c = 3.

Plugging in these values, we get:

y = (-8 ± sqrt(8^2 - 4(1)(3))) / 2(1)

Simplifying this expression, we get:

y = (-8 ± √52) / 2

y = (-8 ± 2√13) / 2

y = -4 ± √13

Therefore, the two points with an x-coordinate of 2 and a distance of 5 from (-2, -4) are: (2, -4 + 2√13) and (2, -4 - 2√13)

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Answer:

A-true

Step-by-step explanation:

The answer is K^2 = 711.6Y on solving the given equation.

Given that, 1 = 711.6Y/K^2 and we have to solve it for the value of K^2. For this we simply have to solve the given equation steps wise. So, let's proceed to solve the equation.

1 = 711.6Y/K^2

Now, multiply K^2 with 1, we get

K^2 = 711.6Y

So, the value of k^2 will be equal to Y times 711.6 and further we can solve it for the various value of Y.

Let us suppose, we have to solve the above equation for the specific value of Y.

So, put Y = 1

On solving, we get

K^2 = 711.6x1

K^2 = 711.6

K = (711.6)^(1/2)

K = 26.67

∴ K^2 = 711.6Y is the equation we will get on solving the equation given to us in the question.

Hence, K^2 = 711.6Y is the required answer.

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Answer:

6

Step-by-step explanation:

Answer:

all of them

Step-by-step explanation:

A rational number is any integer, fraction, terminating decimal, or repeating decimal

Derrick will receive total of $340 from all of his deductions

To create a histogram for these values using four classes, we must first determine the class width, which is determined as the data range divided by the number of classes. The data range is 151 - 58 = 93, which is the difference between the biggest and smallest numbers. The breadth of the class is 93/4 = 23.25. We'll round it up to 24 because we can't have a fractional class width.

Then, for each of the four classes, we'll start with the smallest number (58) and add the class width (24) again until we reach the maximum value (151). The lowest class boundaries for the four classes are as follows:

Class 1: 58

Class 2: 82

Class 3: 106

Class 4: 130

We'll determine the upper class limit for each lower class limit by adding the class width (24) - 1. The upper class restrictions are as follows:

Class 1: 81

Class 2: 105

Class 3: 129

Class 4: 153

Finally, we'll tally the amount of deductions made in each class and utilise that data to create the histogram. Each class has the following number of deductions:

Class 1: 1 (58)

Class 2: 3 (97, 98, 101)

Class 3: 3 (103, 127, 144)

Class 4: 3 (144, 151, 65)

We can compute the total amount Derrick will earn from all of his deductions now that we know the number of deductions in each class. He will earn $25 for each deduction of less than $130, and $45 for each deduction of $130 or more.

Derrick will receive the following total from all of his deductions:

$25 * 1 (for the single deduction of less than $130) + $45 * 7 (for the seven deductions of $130 or over) = $25 + $315 = $340

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Answer:

1

Step-by-step explanation:

The number of Jim's model car is 48

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

Ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6

This means that

Jim : Terrence = 8 : 6

Also from the question, we have

Terrence owns 36 models cars

This means that

Terrence = 36

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

Jim : 36 = 8 : 6

Multiply by 6

Jim : 36 = 48 : 36

So, we have

Jim = 48

Hence, the number of car is 48

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Answer:

8x - 2

Step-by-step explanation:

2x + 3 - (5 - 6x) ← distribute parenthesis by - 1

= 2x + 3 - 5 + 6x ← collect like terms

= (2x + 6x) + (3 - 5)

= 8x + (- 2)

= 8x - 2

Answer:

51x² + 8x

Step-by-step explanation:

Step 1: Write expression

6x² + 10x - 1 + 45x² - 2x + 1

Step 2: Combine like terms (x²)

51x² + 10x - 1 - 2x + 1

Step 3: Combine like terms 9x)

51x² + 8x - 1 + 1

Step 4: Combine like terms (constants)

51x² + 8x

Answer:

60 numbers

Step-by-step explanation:

3 4 5 6 7

for everything starting with 3

345

346

347

354

356

357

364

365

367

376

375

374

we know the results will be the same

there was 12 numbers in that sequence

theres 4 other numbers it could start with

12 + (12x4) = 12x5

60

Answer:

4 x’s for 1/4

2 x’s for 2/4

1 x for 3/4

2 x’s for 1

Step-by-step explanation:

The probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%

It is a branch of mathematics that deals with the occurrence of a random event.

Given,

Amounts of weight that male college students gain during their freshman year are normally distributed

mean of μ = 1.1 kg and

Standard deviation of o= 4.6 kg.

Z score=x-μ/o

=25-1.1/4.6

=23.9/4.6

=5.196

Z score=x-μ/o

=25-1.1/0

=0

Z score=25-1.1/3

=23.9/3

=7.966

By observing the z table the probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%

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Answer:

1. x  =  − 7  +  2 y

2. x  =  1  −  2 y /3

Step-by-step explanation:

Answer:   [1]    x + 2y = 7

  [2]    3x - 2y = -3

Answer:

See below in bold.

Step-by-step explanation:

P = {2, 4, 6, 8, 10}

Q = {3, 6, 9}

R = {1, 3, 5, 7, 9}

PUQUR is the union of the 3 sets and is:

{1, 2, 3,4, 5, 6, 7, 8, 9, 10}

P∩Q∩R is the intersection of the 3 sets and is:

∅.

- that is the empty set . There are no common elements in the 3 sets.

Answer:

\(\displaystyle \sin(\theta)= \frac{\sqrt{17}}{17}\)

\(\displaystyle \cos(\theta)= \frac{4 \sqrt {17} }{ 17 }\)

Step-by-step explanation:

We want to find sin(θ) and cos(θ) given that tan(θ) = 1/4 and sin(θ) > 0.

First, since tan(θ) and sin(θ) are both positive, cos(θ) must be positive as well.

Recall that tangent is the ratio of the opposite side to the adjacent side.

Therefore, the hypotenuse is:

\(h=\sqrt{4^2+1^2}=\sqrt{16+1}=\sqrt{17}\)

So, with respect to θ, the opposite side is 1, the adjacent is 4, and the hypotenuse is √17.

Then it follows that:

\(\displaystyle \sin(\theta)=\frac{1}{\sqrt{17}} = \frac{\sqrt{17}}{17}\)

And that:

\(\displaystyle \cos(\theta)= \frac{4}{\sqrt{17}} = \frac{4 \sqrt {17} }{ 17 }\)

Answer:

the answer might be (-4,0) for x coordinates

Answer:

\( 2^{2x + 2} = 2^{4x - 4} \)

Step-by-step explanation:

\( 4^{x + 1} = 16^{x - 1} \)

\( 2^{2(x + 1)} = 2^{4(x - 1)} \)

\( 2^{2x + 2} = 2^{4x - 4} \)

The correct answer is John's weekly salary is $240 based on his hourly pay rate and the number of hours worked.

Let's choose the function "Weekly salary is a function of the hourly pay rate and the number of hours worked."Example: John works as a part-time employee at a grocery store. His hourly pay rate is $12, and he worked for 20 hours in a week. We can evaluate the function to find his weekly salary.

Weekly salary = Hourly pay rate * Number of hours worked

Weekly salary = $12/hour * 20 hours

Weekly salary = $240

So, John's weekly salary is $240 based on his hourly pay rate and the number of hours worked.

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The average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.

To determine the average rate of change of the school's enrollment during the given time period, we can use the formula:

Average rate of change = (Change in enrollment) / (Change in time)

The change in enrollment is calculated by subtracting the initial enrollment from the final enrollment, while the change in time is calculated by subtracting the initial year from the final year.

Given that in 2004 there were 975 students enrolled and in 2009 there were 730 students enrolled, we can calculate the change in enrollment:

Change in enrollment = 730 - 975 = -245 students

The change in time can be calculated as:

Change in time = 2009 - 2004 = 5 years

Now we can calculate the average rate of change:

Average rate of change = (-245 students) / (5 years) = -49 students per year

Therefore, the average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.

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Answer:

x(7y)x(7y)

Step-by-step explanation:

The given expression: 7(xy)7(xy)

i.e. a product of 7 and xy.

The operation used here: Multiplication.

Commutative property of multiplication :-

a\times b=b\times aa×b=b×a for any numbers a and b.

Associative property of multiplication :-

a\times(b\times c)=(a\times b\times c)a×(b×c)=(a×b×c) for any numbers a , band c.

Now, 7(xy)=(7x)y7(xy)=(7x)y [Associative property of multiplication]

=(x7)y=(x7)y [Commutative property of multiplication]

=x(7y)=x(7y) [Associative property of multiplication]

Answer:

2 or 1/50 as a fraction

Step-by-step explanation:

Answer:

The answer is 2

Step-by-step explanation:

Answer:

king, queen, jack, ace

Step-by-step explanation:

this depends on what game's rules and scoring you're using, but I'd say the face cards

Answer:

\(x=-cos(t)+2sin(t)\)

Step-by-step explanation:

The problem is very simple, since they give us the solution from the start. However I will show you how they came to that solution:

A differential equation of the form:

\(a_n y^n +a_n_-_1y^{n-1}+...+a_1y'+a_oy=0\)

Will have a characteristic equation of the form:

\(a_n r^n +a_n_-_1r^{n-1}+...+a_1r+a_o=0\)

Where solutions \(r_1,r_2...,r_n\) are the roots from which the general solution can be found.

For real roots the solution is given by:

\(y(t)=c_1e^{r_1t} +c_2e^{r_2t}\)

For real repeated roots the solution is given by:

\(y(t)=c_1e^{rt} +c_2te^{rt}\)

For complex roots the solution is given by:

\(y(t)=c_1e^{\lambda t} cos(\mu t)+c_2e^{\lambda t} sin(\mu t)\)

Where:

\(r_1_,_2=\lambda \pm \mu i\)

Let's find the solution for \(x''+x=0\) using the previous information:

The characteristic equation is:

\(r^{2} +1=0\)

So, the roots are given by:

\(r_1_,_2=0\pm \sqrt{-1} =\pm i\)

Therefore, the solution is:

\(x(t)=c_1cos(t)+c_2sin(t)\)

As you can see, is the same solution provided by the problem.

Moving on, let's find the derivative of \(x(t)\) in order to find the constants \(c_1\) and \(c_2\):

\(x'(t)=-c_1sin(t)+c_2cos(t)\)

Evaluating the initial conditions:

\(x(0)=-1\\\\-1=c_1cos(0)+c_2sin(0)\\\\-1=c_1\)

And

\(x'(0)=2\\\\2=-c_1sin(0)+c_2cos(0)\\\\2=c_2\)

Now we have found the value of the constants, the solution of the second-order IVP is:

\(x=-cos(t)+2sin(t)\)

The area formula of a triangle given the coordinates of the vertices :

Using the formula above, the area will be :

The answer is 5.5 square units

Answer: The jellyfish is faster

5,6 and 10 have a common multiple of 30 so make the denominator 30.

JF ->3/5=18/30

1/6=5/30

WR->5/6=25/30

3/10=9/30

9h-> 25 miles

1h->2.8 miles

5h->18 miles

1h->3.6 miles

Answer:0.03125

Step-by-step explanation:

GOO*OOGLE

Step-by-step explanation:

(1/2)^5   = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 =   1/32

The equation of the perpendicular bisector of the line segment with endpoints (-7, 2) and (-1, -6) is y = (3/4)x + 1.

To find the equation of the perpendicular bisector of a line segment, we need to determine the midpoint of the line segment and the slope of the line segment. The perpendicular bisector will have a negative reciprocal slope compared to the line segment and will pass through the midpoint.

Given the endpoints (-7, 2) and (-1, -6), we can find the midpoint using the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Midpoint = ((-7 + (-1))/2, (2 + (-6))/2)

= (-8/2, -4/2)

= (-4, -2)

The midpoint of the line segment is (-4, -2).

Next, we need to find the slope of the line segment using the slope formula:

Slope = (y2 - y1)/(x2 - x1)

Slope = (-6 - 2)/(-1 - (-7))

= (-6 - 2)/(-1 + 7)

= (-8)/(6)

= -4/3

The slope of the line segment is -4/3.

Since the perpendicular bisector has a negative reciprocal slope, the slope of the perpendicular bisector will be 3/4.

Now, we can use the midpoint (-4, -2) and the slope 3/4 in the point-slope form of a line to find the equation of the perpendicular bisector:

y - y1 = m(x - x1)

y - (-2) = (3/4)(x - (-4))

y + 2 = (3/4)(x + 4)

y + 2 = (3/4)x + 3

y = (3/4)x + 1.

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