Find the equation of the line that passes through the point (3,−5) and is perpendicular to the line y=1/5x-2

Answer:

v=12

Step-by-step explanation:

9/v = 6/8

9 = 6v/8

72= 6v

v= 12

Answer:

v = 12

Step-by-step explanation:

Now we have to,

→ Find the required value of v.

Given proportion,

→ (9/v) = (6/8)

Then the value of v will be,

→ (9/v) = (6/8)

→ 9 × 8 = 6 × v

→ 72 = 6v

→ 6v = 72

→ v = 72/6

→ [ v = 12 ]

Hence, the value of v is 12.

B is a 2 by 2 matrix, and the determinant of B written as |B| is equal to -1.

We can find |B|, the determinant of the matrix B by subtracting the multiple of row column and row 2 column 1 from the multiple of row column 1 and row 2 column 2 as follows:

|B| = (-2 × -2) - (1 × 5)

|B| = 4 - 5

|B| = -1.

Therefore, the determinant of the 2 by 2 matrix B written as |B| is equal to -1.

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Observing the given histogram we know that there are 16 pumpkins that have a mass greater than 6 kilograms.

A histogram is a graph that displays the values of a numeric variable's distribution as a collection of bars.

The height of a bar represents the frequency of data points with values falling within the relevant bin; each bar typically spans a range of numerical values known as a bin or class.

Similar to a bar chart, a histogram is produced with bars of varying widths.

In a histogram, the frequency is revealed by the bar's area rather than its height.

We plot the frequency density rather than frequency on the y-axis. To figure this out, divide a group's frequency by its width.

So, the x-axis of the given histogram represents the mass of the pumpkins.

The y-axis of the histogram represents the number of pumpkins.

Then, the pumpkins with greater mass than 6 kilograms:

= 8 + 6 + 2

= 16

Therefore, observing the given histogram we know that there are 16 pumpkins that have a mass greater than 6 kilograms.

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The bottom end of the pendulum travels 18,115.2 meters/day, which is approximately 18.12 kilometers/day (since 1 kilometer = 1000 meters).

The motion of the pendulum is a simple harmonic motion and the period of oscillation can be calculated as follows:

T = 2π√(l/g)

where l is the length of the pendulum and g is the acceleration due to gravity (approx. 9.81 m/s²).

Substituting l = 1 m, we get

T = 2π√(1/9.81)

T ≈ 2.006 s.

In one day, there are

24 hours x 60 minutes/hour x 60 seconds/minute

= 86,400 seconds.

The pendulum makes half a period (i.e., one back-and-forth swing) in 2/2 = 1 second. Therefore, it makes

86,400/2

= 43,200 back-and-forth swings in one day.

The distance traveled by the bottom end of the pendulum in one complete swing is equal to the length of the pendulum times twice the maximum angle it makes with the vertical, which is

2 x 12 degrees

= 24 degrees

= 0.419 radians.

Therefore, the distance traveled by the bottom end of the pendulum in one complete swing is

1 meter x 0.419

= 0.419 meters.

Multiplying by the number of swings in one day, we get:

0.419 meters/swing x 43,200 swings/day

= 18,115.2 meters/day.

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Using a normal distribution calculator and entering the mean as 300, the standard deviation as 30 and the range (300 to 390), the probability that a given tree has between 300 and 390 apples is 0.4987 or 49.87%.

Probability refers to the chance or likelihood that an expected event occurs out of many possible events.

Probability lies between 0 and 1, depending on the degree of certainty.

Mean = 300

Standard deviation = 30

Range = 300 to 390

Thus, the probability that a given tree has between 300 and 390 apples is 0.4987 or 49.87%.

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The value of x in the function f(x) = (1/3)^x - 2 such that f(x) = 7 is -2

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

f(x) = (1/3)^x - 2

When the value of f(x) is 7, we have

(1/3)^x - 2 = 7

So, we have

(1/3)^x = 9

Take the log of both sides

x = log(9)/log(1/3)

Evaluate

x = -2

Hence, the value of x is -2

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The surface area of the rectangular prism is 210 in²

An equation is an expression that shows the relationship between numbers and variables using mathematical operators.

The surface area of a rectangular prism is the sum of each area for the surface.

Hence:

Surface area = 2(8 in * 5 in) + 2(5 in * 5 in) + 2(8 in * 5 in) = 210 in²

The surface area of the prism is 210 in²

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Answer:

29

Step-by-step explanation:

she spends $75 on the gift cards, which brings the total down to $175 which is how much money she has left. She then spends $123.5 on the 13 movie passes, she is then left with $51.5 to spend. Then you divide 51.5 by 1.75 to get 29.4 and rounds down to 29.

_________________________________

_________________________________

Answer:

$6,840

Step-by-step explanation:

The graphs are:

1) not one-to-one

2) one-to-one

3) not one-to-one

A graph represents an one-to-one function only if.

We can't draw a vertical line that touches the graph twice or more.

We can't draw an horizontal line that touches the graph twice or more.

For example, for the first graph, we can see that there are horizontal lines like y = -5 that touch the graph two times.

Similarly forthe third graph, the line y = 0 touches two points-

So these two are not one-to-one.,

For the remaining graph, the middle one, no line touches the graph more than once, so it is one-to-one.

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The decimals as a power of 10 are given as follows:

A number in scientific notation is given by the notation presented as follows:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1, justifying the open interval at 10.

Hence the numbers are represented as follows:

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The result of adding -3 (row 1) to row 2 is determined as (0  10) |-14.

The resultant of the row multiplication in the Matrice is calculated by applying the following method;

row 1 in the given matrices = [1  -4] | 8

To multiply row1 by -3, we will multiply each entity by 3 as shown below;

= -3(1  -4) | 8

= (-3  12) | -24

To add the result to 3;

(-3  12) | -24  +  (3   -2)|10

= (0  10) |-14

Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 3.

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The constant of variation, k, is defined as the ratio between the two variables' values, multiplied by their respective powers:  [tex]k = y/x^a \times z/x^b,[/tex] where a and b are the powers of x in the expressions for y and z, respectively. when   [tex]x = -3[/tex]  and [tex]y = 4[/tex] , z is equal to -81/16.

In this case, we have x = 8, y = 54, and z = 144, so we need to determine the powers of x in the expressions for y and z:

[tex]y = 54 = (8^a) \times k = > a = 3[/tex]

[tex]z = 144 = (8^b) \times k = > b = 2[/tex]

Substituting these values into the formula for k, we get:

[tex]k = y/x^a \times z/x^b = 54/8^3 \times 144/8^2 = 27/64[/tex]

Therefore, the constant of variation is 27/64.

Using the same formula as above, we can solve for z when x = -3 and y = 4:

[tex]k = y/x^a \times z/x^b[/tex]

We need to determine the powers of x in the expressions for y and z:

[tex]y = 4 = (-3)^a * k = > a = -1[/tex]

[tex]z = ? = (-3)^b * k = >[/tex] we don't know b or z yet

Substituting these values into the formula for k, we get:

[tex]k = y/x^a * z/x^b = 4/(-3)^(-1) * z/(-3)^b = -12z/(-3)^2[/tex]

Simplifying this expression, we get:

[tex]k = -12z/9 = -4z/3[/tex]

Now we can solve for z:

[tex]-4z/3 = 27/64[/tex]

Multiplying both sides by 3/(-4), we get:

[tex]z = -81/16[/tex]

Therefore, when  [tex]x = -3[/tex] and   [tex]y = 4, z[/tex] is equal to   [tex]-81/16.[/tex]

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The equation of the quadratic function g whose graph is shown above is g(x) = -(x + 4)² - 4

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided about the vertex and other points, we can determine the value of a as follows:

g(x) = a(x - h)² + k

-13 = a(-7 + 4)² - 4

-13 = a(-3)² - 4

-13 + 4 = 9a

-9 = 9a

a = -1.

Therefore, the required quadratic function is given by:

g(x) = a(x - h)² + k

g(x) = y = -(x + 4)² - 4

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Exactly one-year later,

(a) Mean of the ages will be 13 years and 3 months.

(b) Range of the ages will be same 2 years and 7 months.

Part (a) : To find the mean of the ages of the same group of students exactly one year later, we add one year to each student's age and find the new mean.

New mean is : 12 years and 3 months + 1 year = 13 years and 3 months;

So the mean of the ages of the same group of students exactly one year later is 13 years and 3 months.

Part (b) : The range of their ages would still be 2 years and 7 months because we are adding the same amount to all of their ages, the difference between the youngest and oldest member of the group would remain the same.

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Answer:

Starting with the equation:

-2x + 6 = -x^2

First, we can rearrange it to put it in standard quadratic form:

x^2 - 2x - 6 = 0

To complete the square, we need to add and subtract a constant term that will make the left-hand side of the equation a perfect square. The constant we need to add is (b/2)^2, where b is the coefficient of x. In this case, b = -2, so:

x^2 - 2x + 1 - 1 - 6 = 0

The first three terms can be written as a perfect square:

(x - 1)^2 - 7 = 0

Add 7 to both sides:

(x - 1)^2 = 7

Now we can take the square root of both sides:

x - 1 = ±√7

Add 1 to both sides:

x = 1 ± √7

So the solutions to the equation are:

x = 1 + √7 or x = 1 - √7

mark me brilliant

The probabilities are given as follows:

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem is given as follows:

[tex]\mu = 957, \sigma = 193[/tex]

The probability is the p-value of Z when X = 1000.1 subtracted by the p-value of Z when X = 964.6, hence:

Z = (1000.1 - 957)/193

Z = 0.22.

Z = 0.22 has a p-value of 0.5871.

Z = (964.6 - 957)/193

Z = 0.04.

Z = 0.04 has a p-value of 0.5160.

Hence:

0.5871 - 0.5160 = 0.0711.

For the sample of 58, the standard error is obtained as follows:

s = 193/sqrt(58) = 25.34.

Hence:

Z = (1000.1 - 957)/25.34

Z = 1.7.

Z = 1.7 has a p-value of 0.9554.

Z = (964.6 - 957)/25.34

Z = 0.3.

Z = 0.3 has a p-value of 0.6179.

Hence:

0.9554 - 0.6179 = 0.338.

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Answer:

Step-by-step explanation:

However many decimals you move to get 1 after the first number that is not 0 is what goes in the exponent.  Negative version because to get to a decimal you move in the negative direction.

.1  =  1.0 x [tex]10^{-1}[/tex]

.01 = 1.0 x [tex]10^{-2}[/tex]

.001 = 1.0 x [tex]10^{-3}[/tex]

.000001  =,1.0 x [tex]10^{-6}[/tex]

Answer:

1/3

Step-by-step explanation:

There are 15 tables and 5 have a purple centerpiece. Divide 15 by 5 to get the probability of a randomly selected table being purple.

5/15 is 5 out of 15. 5/15 simplifies to 1/3.

Answer: y = -4

Step-by-step explanation:

Based on these three given points, we can tell that this line is a horizontal line because there is no slope. All of the points have the same y-value, -4.

This means the equation of the line is:

       y = -4

See attached for a visual representation. I have graphed the given points over the top of the equation we wrote for the line.

Answer:

  (3, 9) and (3, -7)

Step-by-step explanation:

You want the end points of the latus rectum for the parabola defined by ...

 (y -1)² = 16(x +1)

Compare the given equation to the form ...

  (y -k)² = 4p(x -h)

we see that (h, k) = (-1, 1) and p = 16/4 = 4. The ordered pair (h, k) is the vertex of the parabola. The scale factor 'p' gives the distance from the vertex to the focus (and from the directrix to the focus). Larger 'p' values result in a "flatter" parabola.

Since the squared term is a y-term, and the value of 'p' is positive, we know the parabola opens to the right. The end points of the latus rectum are ...

  (h+p, k±2p) = (-1+4, 1±2·4) = (3, 9) and (3, -7)

__

Additional comment

If the roles of x and y are interchanged (the parabola opens up or down), then the end points of the latus rectum are (h±2p, k+p).

On a graph of the parabola, the end points of the latus rectum lie on lines through the vertex with slope ±2 (parabola opens in x-direction), or with slope ±1/2 (parabola opens in y-direction).

According to the information, the dilated rectangle would have the dimensions of 2.66cm on the side and 5cm on the base.

To calculate the dimensions of each side of the dilated figure we must identify the dilation factor. In this case it is 3, so we must divide the length of each side into the number of the expansion factor as shown below:

According to the above, the dilated rectangle would remain with the dimensions of 2.66cm on the side and 5cm on the base.

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Answer:

70.4%

Step-by-step explanation:

Assuming the test is the only graded assignment, and the remaining 80% of her grade is still at 73%, we can calculate Kayla's new overall grade as follows:

New overall grade = (0.80 x 73) + (0.20 x 60)

New overall grade = 58.4 + 12

New overall grade = 70.4

Therefore, Kayla's new overall grade is 70.4%

Answer:

70.4% or a C-.

Step-by-step explanation:

To calculate Kayla's new grade after taking the test, you need to first find out what percentage of her overall grade the test is worth. If the test is worth 20% of her grade, then the remaining 80% of her grade is based on other factors, such as homework, quizzes, and other tests.

To calculate Kayla's new grade, you can use the following formula:

New grade = (Current grade x Weight of current assignments) + (Grade on test x Weight of test)

Plugging in the numbers given in the problem, we get:

New grade = (0.73 x 0.80) + (0.60 x 0.20)

New grade = 0.584 + 0.12

New grade = 0.704

Therefore, Kayla's new grade after taking the test would be approximately 70.4%, or a C-.

The maximum voltage produced by the system is 12 volts.

The function given is:

[tex]v_{inst}(t) = 12 * sin(360 * 60 * 6.3 + 79)[/tex]

To find the maximum voltage produced by the system, we need to determine the maximum value of the sine function within the given range.

Let's focus on the argument of the sine function: 360 * 60 * 6.3 + 79.

First, calculate the value of the argument:

360 * 60 * 6.3 + 79 = 136080 + 79 = 136159

Now, substitute this value back into the sine function:

sin(136159)

The sine function has a periodicity of 360 degrees or [tex]2\pi[/tex] radians. Therefore, we can subtract multiples of 360 degrees from the argument without changing the value of the sine function. Let's find the nearest multiple of 360 degrees to 136159:

136159 ÷ 360 [tex]^\sim_\sim[/tex] 378.22

Since the quotient is not an integer, we can conclude that subtracting multiples of 360 degrees will not bring us closer to a maximum or minimum value of the sine function.

Therefore, to find the maximum voltage, we need to evaluate sin(136159) directly. However, calculating the sine function of such a large number is not practical or necessary. The sine function oscillates between -1 and 1, and the maximum value it can reach is 1.

So, regardless of the specific value of sin(136159), the maximum voltage produced by the system will be:

Maximum voltage = 12 * 1 = 12 volts.

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Answer:

x = 23°

Step-by-step explanation:

We Know

The 67° angle + the x must be equal to 90°

Find the x.

Let's solve

67° + x = 90°

x = 23°

Answer:

X = 6

Y = 17

Step-by-step explanation:

The points GHIJ for a cyclic quadrilateral.

The sum of opposite angles of a cyclic quadrilateral is 180°

So

     ∠J + ∠H = 180°

⇒   6y + 78° = 180°

⇒   6y = 180° - 78°

⇒   6y = 102°

⇒   y = 102°/6

⇒   y = 17°

Similarly for angle x

     ∠I + ∠G = 180°

⇒   16x + 14x = 180°

⇒   30x = 180°

⇒   x = 180°/30

⇒   x = 6°

Answer:

  X

Step-by-step explanation:

You want to identify the graph that represents a function.

A graph represents a function if no vertical line intersects the graph in more than one place.

W – the line x=0 intersects the graph at y = -4 and at y = 4. This graph is not the graph of a function.

X – At points where the graph might overlap, one point is identified as not include, (1, -1) for example, while the other point is identified as included (1, 1) for example. This means there is only one function value at that point, so this is the graph of a function.

Y – The vertical line x=-2 intersects the graph in an infinite number of points. This graph is not the graph of a function.

Z – The vertical line x=0 intersects the graph at y = -2, y = 0, and y = 2. This graph is not the graph of a function.

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