Give the following number
in Base 10.
F16 = [? ]10

The equation of the perpendicular line will be x + y - 5 = 0. Then the correct option is B.

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation of the line passing through (-5, 6) and (-6, 5) will be given as,

(y - 6) = [(5 - 6) / (- 6 + 5)](x + 5)

y - 6 = (x + 5)

y = x + 1

The equation of the line that is perpendicular to the above line is given as,

y = - x + c

The equation of the line is passing through (3, 2)

3 = - 2 + c

c = 5

Then the equation of the perpendicular line will be given as,

y = -x + 5

x + y - 5 = 0

The equation of the perpendicular line will be x + y - 5 = 0. Then the correct option is B.

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The complete question is given below.

Answer:

(a) The next tide will occur at 6:55pm

(b) [tex]y = 3.12 \cos(\frac{24\pi}{149}(x - 6.5)) + 2.74[/tex]

(c) The height is: 2.904ft

Step-by-step explanation:

Given

[tex]T_1 = 12hr:25min[/tex] --- difference between high tides'

Solving (a): The next time a high tide will occur

From the question, we have that:

[tex]High =6:30am[/tex] --- The time a high tide occur

The next time it will occur is the sum of High and T1

i.e.

[tex]Next = High + T_1[/tex]

[tex]Next = 6:30am + 12hr : 25min[/tex]

Add the minutes

[tex]Next = 6:55am + 12hr[/tex]

Add the hours

[tex]Next = 6:55pm[/tex]

Solving (b): The sinusoidal function

Given

[tex]High\ Tide = 5.86[/tex]

[tex]Low\ Tide = -0.38[/tex]

[tex]T = 12hr:25min[/tex] -- difference between consecutive tides

[tex]Shift = 6.5hr[/tex]

The sinusoidal function is represented as:

[tex]y = A\cos(w(x - C)) + B[/tex]

Where

[tex]A = Amplitude[/tex]

[tex]A = \frac{1}{2}(High\ Tide - Low\ Tide)[/tex]

[tex]A = \frac{1}{2}(5.86 - -0.38)[/tex]

[tex]A = \frac{1}{2}(6.24)[/tex]

[tex]A = 3.12[/tex]

[tex]B = Mean[/tex]

[tex]B = \frac{1}{2}(High\ Tide + Low\ Tide)[/tex]

[tex]B = \frac{1}{2}(5.86 - 0.38)[/tex]

[tex]B = \frac{1}{2}(5.48)[/tex]

[tex]B = 2.74[/tex]

[tex]w = Period[/tex]

[tex]w = \frac{2\pi}{T}[/tex]

[tex]w = \frac{2\pi}{12:25}[/tex]

Convert to hours

[tex]w = \frac{2\pi}{12\frac{25}{60}}[/tex]

Simplify

[tex]w = \frac{2\pi}{12\frac{5}{12}}[/tex]

As improper fraction

[tex]w = \frac{2\pi}{\frac{149}{12}}[/tex]

Rewrite as:

[tex]w = \frac{2\pi*12}{149}[/tex]

[tex]w = \frac{24\pi}{149}[/tex]

[tex]C = shift[/tex]

[tex]C=6.5[/tex]

So, we have:

[tex]y = A\cos(w(x - C)) + B[/tex]

[tex]y = 3.12 \cos(\frac{24\pi}{149}(x - 6.5)) + 2.74[/tex]

Solving (c): The height at 3pm

At 3pm, the value of x is:

[tex]x=3:00pm - 6:30am[/tex]

[tex]x=9.5hrs[/tex]

So, we have:

[tex]y = 3.12 \cos(\frac{24\pi}{149}(x - 6.5)) + 2.74[/tex]

[tex]y = 3.12 \cos(\frac{24\pi}{149}(9.5 - 6.5)) + 2.74[/tex]

[tex]y = 3.12 \cos(\frac{24\pi}{149}(3)) + 2.74[/tex]

[tex]y = 3.12 \cos(\frac{72\pi}{149}) + 2.74[/tex]

[tex]y = 3.12 *0.0527 + 2.74[/tex]

[tex]y = 2.904ft[/tex]

Answer:

Rate of the current: 19 kilometers per hour

Rate of the boat in still water: 80 kilometers per hour

Answer:

y = 2x + 7

Step-by-step explanation:

y + 1 = 2 ( x + 4 )

y = 2x + 8 - 1

y = 2x + 7

So we know that we need to add 15 to the double of this number. We know we need to add 15 since it says "15 more than" and we know we need to double/multiply the number by two since it says "twice a number"! We also know that this mystery number equals 5.

Therefore, we can set up our equation and solve! The variable x is used to represent the number we're looking for!

2x + 15 = 5

2x = -10

x = -5

So, your answer should be -5!

Answer:

10+12x

Step-by-step explanation:

9−4x+2x+8x+1+6x

(9+1)+(−4x+2x+8x+6x)

10+12x

Answer:

D. 1.89 sq. m

Step-by-step explanation:

Plz mark brainliest

Answer:

1: 1 1/5!

2: 1 4/7!

3: 5 1/4!

4: 4 4/7!

5: 2 6/9!

6: 4 1/6!

Answer:ANSWER would either be 120π or about 376.8

Step-by-step explanation:

A=2πrh+2πr2

A=2π*6*8+2π*6*2

A=96π+24π

A= 120π

or

A≈376.8

ANSWER would either be 120π or about 376.8

Answer: the real answer is 527.788 the top answer is wrong I did it and it said it was wrong

Step-by-step explanation:

Answer:

M<C = 37 degrees

M<D = 86 degrees

M<DEC = 111 degrees

Step-by-step explanation:

The exterior angle theorem can be measured by the hypotenuse of a 90 degree angle. Since there is no hypotenuse in the matrix, you don't need to make it positive :)

Therefore, after using this theorem, I came to the conclusion that m/C would be 37 degrees, since I calculated the measure of the angle. I used the same tactic on m/D and m/DEC.

I hope this helps :)

The values of A and B are 2 and 4 respectively.

Given is the equation as -

(x + A)² - 3 = x² + 4x + B

We can write the given equation as -

(x + A)² - 3 = x² + 4x + B

x² + A² + 2Ax = x² + 4x + B

A² + 2Ax = 4x + B

A² + 2Ax = B + 4x

Equating both sides, we get -

A² = B

and

2A = 4

A = 2

Then B will be equivalent to 4.

B = 4

Therefore, the values of A and B are 2 and 4 respectively.

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Answer:

[tex]\small\mathfrak\green{here \: is \: your \: answer...} \\ \\ \small\mathfrak\pink{exponential \: decay...} \\ \\ \small\mathfrak\green{hope \: it \: helps...}[/tex]

To translate the point P(x,y) , a units left and b units down, use P'(x−a,y−b) .

y=|x-10|-3

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Answer:

[tex]h \geq 2[/tex]

Step-by-step explanation:

h has to be 2 or more since there is at least 2 hours.

Answer:

s = 2 cm

Step-by-step explanation:

Given the following data;

Area of equilateral triangle = √3 cm

Mathematically, the area of an equilateral triangle is given by the formula;

A = √3 * s²/4

Where, s represents the sides of length.

Substituting into the formula, we have;

√3 = √3 * s²/4

Dividing both sides by √3, we have;

1 = s²/4

Cross-multiplying, we have;

4 = s²

Taking the square root of both sides, we have;

s = √4

s = 2 cm

Answer:

Triangle, rectangle

Step-by-step explanation:

I solved it visually

Answer:

Triangle and rectangle

Answer:

Step-by-step explanation:

Answer:

2 x v

Step-by-step explanation:

Two books per shelf would mean 2+ per shelf.

So if she took out 5 shelves it would be 2+2+2+2+2 in other words. 5*2.

So the equation would be 2 x v

Answer:

17

Step-by-step explanation:

First of all we find the total number of students:

4+6+2+2+3+4+6+3=30

Then we find the amount of seniors:

2+3=5

Now to find the probability we find the percentage of students which are seniors:

[tex]\frac{5}{30}[/tex] Which is also [tex]\frac{1}{6}[/tex] and when you put that into your calculator you get:

0.16666... which is a decimal, we need a percentage, so we multiply by 100 to convert it:

0.16666...×100=16.666...

which is equal to 17 once rounded as the third digit (6) rounds up

The width of the two gardens will be equal to 5 feet.

A rectangle is a quadrilateral having four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

Given that a rectangular garden has a length twice as great as it’s width. a second rectangular garden has the same width as the first garden and a length that is 4 meters greater than the length of the first garden. the second garden has an area of 70 square meters.

For the first rectangle, the  dimensions will be,

L = 2w

For second rectangle width is same then the area is,

L x w = 70

( 2w +4 ) x w = 70

2w² + 4w - 70 = 0

w² + 2w -35 = 0

w² + 7w - 5w -35 = 0

w(w + 7 ) -5(w+7) = 0

w =-7 and  w = 5

Hence, the width is w = 5 ft.

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Decomposition of the fraction [tex]1\frac{3}{4}[/tex] =7/4 = 17/4 - 10/4

Here, the numerator, or top number, 7, indicates how many pieces we will examine.

Please look at figure a and pay attention to the three coloured components. The bottom number, our denominator, provides the total number of components. As a result, pay close attention to figure a. There are a total of four parts, numbered 1, 2, 3, and 4. However, since we are working with 7/4, we will just examine the three shaded parts.

7/4 = 17/4 - 10/4

7/4 = 11/4 - 4/4

Unit fraction decomposition will be used. Unit fraction - what is it? What would we focus on if we just looked at one element? It is one in four, or 1/4. Because this is the first of a series that includes 1, 2, 3, and 4. The third component would also be 1/4, and the second piece would be 1/4.

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Answer:

To solve this problem, we can set up the following equation:

2L + 2W = 64

We are told that the length of the rectangle is two more than double the width, so we can write the following equation:

L = 2W + 2

Substituting this equation into the first equation, we get:

2(2W + 2) + 2W = 64

Simplifying this equation, we get:

6W + 4 = 64

Subtracting 4 from both sides, we get:

6W = 60

Dividing both sides by 6, we get:

W = 10

The width of the rectangle is 10 feet.

To find the length of the rectangle, we can substitute this value back into the equation L = 2W + 2 to get:

L = 2(10) + 2

= 20 + 2

= 22

The length of the rectangle is 22 feet.

Therefore, the dimensions of the rectangle are 10 feet by 22 feet.

Step-by-step explanation:

The slope of the table shown in the image attached below is equal to: D. 1/3.

Mathematically, the slope of the given table can be calculated by using the following mathematical expression;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

From the information provided in the table, we have the following data points:

Points on x-axis = (-2, 2).

Points on y-axis = (-4, -2).

Substituting the given points into the slope formula, we have;

Slope, m = (12 - 8)/(15 - 3)

Slope, m = 4/12

Slope, m = 1/3

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Answer:

steps below (C)

Step-by-step explanation:

1. x³ -> (x+1)³   ... horizontal translation left 1 unit

2. (x+1)³ -> -(x+1)³  .... reflection over x axis

3. -(x+1)³ -> -(x+1)³ + 1  ... vertical translation up 1 unit

Answer:

To graph an arithmetic sequence, you can start by plotting the first few terms of the sequence on the coordinate plane. The x-axis represents the term number, and the y-axis represents the value of the term.

In this case, we are given that the fourth term is 20 and the common difference is -1/5 times the first term. Let's say the first term is x. Then, the second term is x - (1/5)x = 4/5x, the third term is 4/5x - (1/5)x = 3/5x, and the fourth term is 3/5x - (1/5)x = 2/5x.

Therefore, the first four terms of the sequence are x, 4/5x, 3/5x, and 2/5x. If we plot these terms on the coordinate plane, we get the following graph:

(0, x)

(1, 4/5x)

(2, 3/5x)

(3, 2/5x)

This graph represents the first four terms of the arithmetic sequence. To find the fifth term, we can use the formula for the nth term of an arithmetic sequence: a_n = a_1 + (n - 1)d, where a_1 is the first term, d is the common difference, and n is the term number.

For this sequence, the fifth term is x + (-1/5)x = 4/5x. To find the sixth term, we can use the same formula: a_6 = x + (-1/5)x = 3/5x.

By continuing this process, we can plot the rest of the terms of the arithmetic sequence on the coordinate plane.

Step-by-step explanation:

The area of the parallelogram is 72 square units. Option B

The formula for calculating the area of a parallelogram is expressed as;

A = bh

Given that;

From the information given, we have that;

Now, substitute the values

x + y = 8 + 4

add the values

x + y = base = 12 units

h = 6 units

Now, substitute the values into the formula, we get;

Area, A = 12(6)

multiply the values

Area, A = 72 square units

Hence, the value is 72 square units

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