A line passes through the point (2, 7) and has a slope of 5. Write an equation in slope-intercept form for this line.​

The solution to the initial value problem in this problem is given as follows:

[tex]y = 0.0022e^{5x} - 0.8853e^{-x}[/tex]

The initial value problem is given as follows:

y''-4y'-5y = 0.

The first step is finding the roots of the characteristic equation, which is given as follows:

r² - 4r - 5.

The equation can be factored as follows:

r² - 4r - 5 = (r - 5)(r + 1).

Applying the inverse Factor Theorem, the roots are given as follows:

These roots are real, hence the format of the solution is given as follows:

[tex]y = Ae^{5x} + Be^{-x}[/tex]

Considering the initial condition at x = 1, we have that:

Ae^(5) + Be^(-1) = 0

Considering the initial condition of the derivative at x = 1, we have that:

5Ae^(5) - Be^(-1) = 2.

Adding the two equations, the condition A is obtained as follows:

6Ae^(5) = 2.

A = 2/(6e^5)

A = 0.0022.

Hence the condition B is:

B = -0.0022e^(5)/e^(-1)

B = -0.8853.

Hence the solution is:

[tex]y = 0.0022e^{5x} - 0.8853e^{-x}[/tex]

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Answer:

  c.

Step-by-step explanation:

You want a linear combination of the given 3×3 matrices.

We observe that the answer choices are different in most corresponding terms, so we only need to find the value of one term in order to choose the correct answer.

The expression applied to the matrices is applied to corresponding terms of the matrices. That is, for ...

  [tex]C = -2A +7B[/tex]

you will have ...

  [tex]c_{11}=-2a_{11}+7b_{11}\\\\c_{11}=-2(4)+7(7)=-8+49\\\\c_{11}=41[/tex]

This matches choice c.

__

Additional comment

Many graphing calculators and all spreadsheets can do the necessary calculations to help you find the desired result matrix.

Answer:

190 cm²

Step-by-step explanation:

     Area of one regular hexagon is given. Multiply 23 *2 and it will give the area of two regular hexagons.

There are 6 rectangles. Find the area of one rectangle and multiply it by 6.

 Area of regular hexagon = 23 cm²

Area of rectangle = length * width

                             = 8 * 3

                             = 24 cm²

      Area of the regular hexagon prism = 2* area of regular hexagon + 6*area of rectangle.

                                                                 = 2*23 + 6*24

                                                                 = 46 + 144

                                                                 = 190 cm²

Answer:

First we convert the sentence to an equation so:

[tex] \frac{3}{4} x = 24[/tex]

Now to isolate x divide by the recuprical of 3 over 4 which is 4/3

[tex] \frac{3}{4} \times \frac{4}{3} = 24 \times \frac{4}{3} [/tex]

24x4= 96 and 3 remains.

[tex]x = \frac{96}{3} [/tex]

Now we can simplify by 3 and we will get the final answer which is

[tex]x = 32[/tex]

The slope-intercept definition of the linear function is given as follows:

y = x + 2.

The slope-intercept representation of a linear function is obtained by the rule presented as follows:

y = mx + b.

The coefficients of the function, along with their meaning, are shown as follows:

For this problem, the values of these coefficients are given as follows:

Hence the slope-intercept rule for the function is:

y = x + 2.

The graph of the linear function is given by the image shown at the end of the answer.

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The number of chocolate bars, c, the sports club must sell in order to reach their goal is 80

An inequality refers to a statement that has two quantities in which one is specifically less than (or greater than) another. Symbols of inequality includes:

Let

The inequality that represent the situation is given by

3c ≥ 240

c ≥ 240/3

c ≥ 80

Therefore, all real whole numbers greater than or equal to 80 is the number of chocolate bars, c, the sports club must sell in order to reach their goal.

The shaded area to the right of the solid line c = 80 is the graph which represent the inequality.

Complete question:

A sports club needs to raise at least $240 by selling chocolate bars for $3.00 each. Sebastian wants to know how many chocolate bars, c, the sports club must sell in order to reach their goal. He represented this situation as 3c > 240. Which graph represents this inequality?

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Answer:

Equation:

50t + 100 = P

Table:

T             P

0          100

1           150

2           200

3           250

4            300

Step-by-step explanation:

$100 - starting value because it is the initial studio use fee

50t - since 50 dollars is the hourly fee, you have to multiply it by t (time)

Answer:

21.5

Step-by-step explanation:

geometric progression formula: [tex]A_{n}[/tex]=A*[tex]r^{n-1}[/tex]

where An is nth term

A is first term

r is common ratio

given [tex]A_{99}[/tex] = 48

A=12

we find r

48=12 *[tex]r^{99-1}[/tex]

48/12=[tex]r^{98}[/tex]

[tex]\sqrt[98]{4}[/tex]=r

r=1.014

so to find 50th term

[tex]A_{50}[/tex]=12*[tex]1.012^{50-1}[/tex]

[tex]A_{50}[/tex]=21.53

Answer:

Step-by-step explanation:

Find the equation of p(x) using table.

We see it is a proportional relationship, therefore:

Conveyor belt2: p(x) = 62.8x

As we see 157.1 > 62.8 which means conveyor 1 belt is faster.

Answer:

The conveyor belt 1 is faster.

Step-by-step explanation:

Speed of conveyor belt 1,

→ m(x) = 157.1x

Now the speed of conveyor belt 2,

→ p(x) = x

→ p(125.6) = 2x || p(188.4) = 3x

→ x = 125.6/2 || x = 188.4/3

→ [ p(x) = 62.8 ] || [ p(x) = 62.8 ]

Then the fastest conveyor is,

→ m(x) = 157.1x > p(x) = 62.8

→ 157.1x > 62.8

→ Conveyor 1 > Conveyor 2

Hence, the conveyor belt 1 is faster.

The slope is -5/3

From the question, we have

slope, m = change in y/change in x

= (-6+1)/(8-5)

=-5/3

The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.

Slope of a Line :

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

As a result, m = change in y/change in x = y/x is the formula for the change in y-coordinate with respect to the change in x-coordinate.

where "m" represents a line's slope.

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

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Considering a discrete distribution modeling the situation, it is found that:

a) The expected value of each $1 bet in roulette is of: -$0.988.

b) The interpretation is given as follows: Over time, you should expect to lose about 999 cents for every dollar you bet.

The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability.

The total number of outcomes for the three-number bet is of:

10 x 10 x 10 = 1000.

As three numbers are taken, and for each number, there are 10 possible outcomes.

Hence the probability of winning is of:

p = 1/1000.

As there is only one correct sequence.

The probability of losing is of:

p = 1 - 1/1000 = 999/1000.

Considering a payout of $11 for a $1 bet, the distribution of earnings is presented as follows:

Hence the expected value of a $1 bet is calculated as follows:

E(X) = 11/1000 - 999/1000 = -$0.988.

Which means that you are expected to lose approximately 99 cents for every dollar that you bet.

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The annual percentage growth rate is 5.9%

The doubling time of an investment of $10000 is 12 years

The compound interest caluclated annually can be given by

A=P(1 + r/n)^nt

where A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

20000 = 10000(1 + r)¹²

2⁻¹² = 1 + r

r = 1.059 - 1

r = 0.059

Rate of inetrest = 5.9%

Therefore, the annual percentage growth rate is 5.9%

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The probability that the spinner would land on a number that is not between 16 and 25 as required in the task content is; 13 / 15.

It follows from the task content that the probability that the spinner would land on a number that is not between 16 and 25, inclusive be determined.

Since the spinner contains 1 through 75, the number of event in the sample space is; 75 events.

Also, the number of events between 16 and 25, inclusive is; 10.

Therefore, the number of events outside 16 through 25 is; 75 - 10 = 65.

Therefore, the required probability that the spinner would land on a number that is not between 16 and 25 is;

= 65 / 75

= 13 / 15.

Therefore, the required probability is; 13 / 15.

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Answer:

Step-by-step explanation:

Answer:

+8 or -8

Step-by-step explanation:

Both can be the qrt of 64 because   -8 * -8 = + 64

The recursive equation for the nth term is aₙ = -4aₙ₋₁

The definition of the functions is given as

a₂ = 2

a₅ = -384

Sequence type = Geometric sequence

The nth term of a geometric sequence is represented as

aₙ = arⁿ⁻¹

So, we have

a₂ = ar = 6

a₅ = ar⁴ = -384

Divide the equations

r³ = -384/6

Evaluate

r³ = -64

Take the cube roots

r = -4

The recursive equation for the nth term is represented as

aₙ = aₙ₋₁ * r

So, we have

aₙ = -4aₙ₋₁

Hence, the equation is aₙ = -4aₙ₋₁

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Answer:

t=1.33333 seconds

Step-by-step explanation:

1. We are give the the position function, s(t). We must differentiate s(t) twice in order to find the acceleration function, a(t).

s(t) = t⁶-2t⁵

Taking the power rule to differentiate s(t), we find the velocity function, v(t).

v(t) = d/dt (t⁶-2t⁵)

v(t) = 6t⁵-10t⁴

Differentiate v(t) using the power rule again to find the acceleration function, a(t).

a(t) = d/dt (6t⁵-10t⁴)

a(t) = 30t⁴-40t³

2. To find the other t value where acceleration is equal to zero, we must set a(t) to zero.

a(t) = 30t⁴-40t³ = 0

3. Algebraically solve for t. Factoring out 10t³ from a(t), we have:

10t³(3t-4)=0

Our solutions are t=0 and t=4/3.

The other value of t when acceleration is equal to zero is 4/3, or 1.33333 seconds.

The probabilities in this problem are given as follows:

The probabilities for each strike are given as follows:

The probabilities are independent, meaning that for each trial they are the same.

Thus the probability that your first strike was a critical hit but not your second strike is obtained as follows:

P = 0.33 x 0.67 = 0.2211 = 22%. (rounded).

Damage is caused with two consecutive critical hits, hence:

p = 0.33 x 0.33 = 0.11 = 11%.

The final probability, that your strike was not critical but your next 2 attacks were, is obtained as follows:

p = 0.67 x 0.33 x 0.33 = 0.07 = 7%.

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The sample size will be needed to estimate the mean time to spoilage with an accuracy of one day is 166

The formula for the margin of error is given as

[tex]E = Z*\frac{sd}{\sqrt{n} }[/tex]

The standard deviation is given as sd = 5 days

We have to find the critical value of Z at the confidence level of 99 %

This value is given as 2.576

E = 1 day because the accuracy has been said to be within one day.

We have to insert the values in the formula that we have here

[tex]1 = 2.576*\frac{5}{\sqrt{n} }[/tex]

√n = 12.88

square both sides to get rid of the square root sign

n = 12.88²

n = 165.89

n ~ 166

The sample size would be 166

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The mean of the number of plants (d) increases by 5.5

From the question, we have the table of values that can be used in our computation:

In the table, we have the following rows

Plants and Number of tomatoes

The mean of the number of plants is calculated as

Mean plant = Total number of tomatoes/Total number of plants

For the four plants, we have

Total number of tomatoes = 31 + 25 + 6 + 28 =  90

Total number of plants = 4

Substitute the known values in the above equation So, we have the following equation

Mean plant = 90/4

Mean plant = 22.5

For the three plants, we have

Total number of tomatoes = 31 + 25 + 28 =  84

Total number of plants = 3

Substitute the known values in the above equation So, we have the following equation

Mean plant = 84/3

Mean plant = 28

See that the difference is an increment of

Increment = 28 - 22.5

Evaluate

Increment = 5.5

Hence, the mean increases by 5.5

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Answer:

a = 108°

b = 72°

c = 48°

d = 48°

Step-by-step explanation:

• ∠a and the 72° angle are on a straight line. Therefore they add up to 180°:

∠a + 72° = 180°

⇒ ∠a = 180 - 72°

⇒ ∠a = 108°

• ∠b and the 72° angle are corresponding angles (the angles make an F-shape). Therefore, they are equal:

∠b = 72°

• ∠d and the 48° angle are alternate angles (the angles make a z-shape). Therefore they are equal:

∠d = 48°

• ∠c and ∠d are vertically opposite angles. Therefore, they are equal:

∠c = ∠d

⇒ ∠c = 48°

Answer:

  B. The graph of K has a greater y-intercept

  D. The graph of J has a greater slope.

Step-by-step explanation:

Given a table for function J and an equation for function K, you want to know which has the greater slope, and which has the greater y-intercept.

The y-intercept is the value of the function when x=0. We see from the table that y=2 corresponds to x=0 for function J.

We see from the equation for function K that the constant is 8. This is the value of y when x=0.

Function K has the greater y-intercept (8 vs. 2).

The slope is the change in y-value when x increases by 1 unit. We see from the table that y=7 when x=1, so the change in y from x=0 to x=1 is 7-2 = 5. The slope of function J is 5.

The equation for function K has an x-coefficient of 3. This means a change in x of 1 unit will result in a change in y of 3 units. The slope of function K is 3.

Function J has the greater slope (5 vs. 3).

Additional comment

Both functions are graphed in the attachment. The y-intercepts have their points labeled. The graph with the steeper slope is the blue line, function J.

Answer:

Nepali=17 English=18

Step-by-step explanation:

first in Nepali,

Answer:

[tex] \huge{ \bold{y = 45x + 94}}[/tex]

Step-by-step explanation:

Equation of a line in slope-intercept form is represented by

[tex]y = mx + c[/tex]

where

m is the slope

c is the y intercept

From the question

m = 45

In order to find c we substitute the point (0,94) into the equation y = mx + c

That's

[tex]94 = 45(0) + c \\ 94 = 0 + c \\ c = 94[/tex]

We now substitute m and c into the equation

We have the final answer as

[tex] \bold{y = 45x + 94}[/tex]

Hope this helps you

Suppose that the equations of line [tex]C[/tex] and [tex]D[/tex] are as follows;

If these two lines are parallel to each other, the following equality must be satisfied.

In summary, the slope of the two lines must be equal to each other.

We know the equation of line [tex]C[/tex]. Then let us form the equation of line [tex]D[/tex].

We must find the variable [tex]c_{1}[/tex] by placing the given point [tex](-3,-1).[/tex]

If we write it in slope-intercept form, the correct answer will be as follows;

Answer:

<ABC is bisected by ray BD, 2m<DBC = m<ABC, BC = 1/2AC

Step-by-step explanation:

The y-intercept is (0, 400), which represents the amount of money the radio station originally had. The x-intercept is (8, 0), which represents the number of weeks it will take for the radio station to have $0 left.

In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Similarly, the x-intercept can be defined as the point at which the graph of any function crosses the x-coordinate and the value of "y" is equal to zero (0).

For the y-intercept, x = 0 and we have the following:

y = 400 - 50x

y = 400 - 50(0)

y = 400.

For the x-intercept, y = 0 and we have the following:

y = 400 - 50x

0 = 400 - 50x

50x = 400

x = 400/50

x = 8.

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86.135 is the IQ score separating the bottom 25% from the top 75%.

The number between a data set's lowest and median is known as the first quartile. We would utilize a Z table to locate it.

As we are looking on the left side of distribution, value of z-score will be negative.

z-score equation for x : [tex]z = \frac{x-M}{S}[/tex]

                                       [tex]x = zS+M[/tex]

where x = value we're looking for

M = Mean

   = 99.2

S = Standard deviation

  = 19.5

z = z-score

  = -0.67

Putting the value in equation,

x = -0.67*19.5 + 99.2

  = -13.065 + 99.2

  = 86.135

Hence, 86.135 is the IQ score separating the bottom 25% from the top 75%.

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Assuming Pod wrote that N could be equal to -18, Pod is correct.

A quadratic equation is an equation with a variable to the second power as its highest power term.

The Standard Form of a Quadratic Equation:

ax² + bx + c = 0

where:

x² + 7x - 18 = (x + 9)(x - 2) . . . . . g = 9, h = -2

There are no integer factors of 13 that add to give 7. 13 is prime, so the sum of its integer factors is 1+13 = 14.

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