the captain of a boat knows that the lighthouse on the coast is 200 feet tall. he measures the angle of elevation to the top of the lighthouse to be 2 degrees. how far is the boat from the coast? round to the nearest hundredth of a foot.

Answer:

8 inches

Step-by-step explanation:

Surface area of a prism is:

S = 2A + Ph

where A is the area of the base, P is the perimeter of the base, and h is the height of the prism.

The base is a square, so A = s² and P = 4s:

S = 2s² + 4sh

Given that S = 512 and h = 12:

512 = 2s² + 4s(12)

512 = 2s² + 48s

256 = s² + 24s

0 = s² + 24s - 256

0 = (s + 32) (s - 8)

s = -32, s = 8

Since s must be positive, s = 8 inches.

Follow below steps;

To find the length of the square base of the right prism:

First, calculate the lateral surface area: 512 in² = 4s * 12 where s is the side length of the square base.

Then, solve for s: 512 = 48s, s = 512 / 48 = 10.67 in.

Therefore, the length of the square base is 10.67 inches.

To convert feet per minute into miles per hour, use the conversion factor of 5280 feet in 1 mile and 60 minutes in 1 hour. Divide the given value by 5280 to get the number of miles, then divide the result by 60 to convert minutes to hours.

To convert feet per minute into miles per hour, you need to use the conversion factor of 5280 feet in 1 mile and 60 minutes in 1 hour. Here's the step-by-step calculation:

For example, if you have a speed of 300 feet per minute:

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ANSWER

The choice is correct.

[tex]y = {(x -1)}^{2} + 2[/tex]

EXPLANATION

The equation of a parabola in vertex form is given by:

[tex]y = a {(x -h)}^{2} + k[/tex]

where (h,k) is vertex of the parabola and 'a' is the leading coefficient of the parabola.

From the given options, the leading coefficient must be a=1.

We also have the vertex of the parabola at (1,2). This implies that h=1 and k=2.

We substitute these values into the formula to get,

[tex]y = {(x -1)}^{2} + 2[/tex]

The second option is correct.

Answer:

-6

Step-by-step explanation:

Let x =1

F(x)=-x^3-2x^2+7x-10

F(1) = - (1)^3 -2(1)^2 +7(1) -10

     = -1 -2 +7-10

    = -3+7-10

   =-6

The output of the given function F(x)=-x^3-2x^2+7x-10 when x equals 1 is -6. We substituted x=1 into each term to calculate this.

The given function is F(x)=-x^3-2x^2+7x-10. To find the output of the function when x equals 1, you substitute '1' in place of 'x' in the equation. So let's calculate:

Now, add all the results together: -1 - 2 + 7 - 10 = -6. Therefore, when x equals 1, the output of the function F(x) is -6.

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Answer:

x = 5

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Given

[tex]log_{2}[/tex](3x - 7) = 3, then

3x - 7 = 2³ = 8 ( add 7 to both sides )

3x = 15 ( divide both sides by 3 )

x = 5

The required solution of logarithmic expression  log2 (3x - 7) = 3 is x = 5. Option B is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
To solve for x in the equation log2 (3x - 7) = 3, we first use the definition of a logarithm to change the logarithmic form to the exponential form.

log2 (3x - 7) = 3

2³ = 3x - 7

Next, we solve for x by adding 7 to both sides of the equation:

8  + 7= 3x - 7 + 7

15 = 3x

Finally, we divide both sides of the equation by 3:

x = 5

So, the solution of log2 (3x - 7) = 3 is x = 5.

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let's firstly convert the mixed fractions to improper fractions and then add them up.

[tex]\bf \stackrel{mixed}{36\frac{4}{9}}\implies \cfrac{36\cdot 9+4}{9}\implies \stackrel{improper}{\cfrac{329}{9}} \\\\\\ \stackrel{mixed}{10\frac{2}{9}}\implies \cfrac{10\cdot 9+2}{9}\implies \stackrel{improper}{\cfrac{92}{9}}~\hfill \stackrel{mixed}{18\frac{2}{9}}\implies \cfrac{18\cdot 9+2}{9}\implies \stackrel{improper}{\cfrac{164}{9}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf -\cfrac{329}{9}-\cfrac{92}{9}-\cfrac{164}{9}\implies \stackrel{\textit{using the LCD of 9}}{\cfrac{-329-92-164}{9}}\implies -\cfrac{585}{9}\implies -65[/tex]

Answer:

f(3) = 9

Step-by-step explanation:

Wherever you see an x on the right, put a 3 in for that x

f(x) = 2x^2 + x - 12

f(3) = 2*(3)^2 + 3 - 12

f(3) = 2*9 + 3 - 12

f(3) = 18 + 3 - 12

f(3) = 9

Answer:

17/13

Step-by-step explanation:

Answer:

Step-by-step explanation:

" / " indicates "division" and should not be used in this context.

If you meant:  -2 square root 13 plus 19 square root 13, the simplest result would be 17 square root 13.

Note that if you click on the "omega" symbol (below), a menu of symbols will appear, including the square root symbol √.

Then:  -2√13 + 19√13 = 17√13.

Answer:

B is le answer

Step-by-step explanation:

To find the values of the variables in each equation, isolate the variable on one side by performing operations. The solutions for the variables are 4, -1, 2, 6, no solution, and 10.8 for the respective equations.

To find the value of the variable in each equation, we need to isolate the variable on one side of the equation. Let's solve each equation step by step:

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Answer:

Solution (-2, 7)

Step-by-step explanation:

2x + 3y = 17      (1)

5x + 6y = 32    (2)

Using elimination method

Multiply (-2) to the equation (1)

-4x - 6y = -34  

Now you have 2 new equations

-4x - 6y = -34

5x + 6y = 32

----------------------------Add

x = -2

Substitute x = -2 into 2x + 3y = 17

2(-2) + 3y = 17

- 4 + 3y = 17

3y = 21

 y = 7

Solution (-2, 7)

Final answer:

The solution to the system of equations 2x + 3y = 17 and 5x + 6y = 32 using the elimination method is x = -2 and y = 7.

Explanation:

To solve the system of equations using the method of elimination, we manipulate the equations to make the coefficients of either x or y the same, and then subtract one equation from the other to eliminate that variable. Let's consider the given equations:

2x + 3y = 17 (Equation 1)

5x + 6y = 32 (Equation 2)

We can see that the coefficients of y are in the ratio of 3:6 or 1:2. To use elimination, we want the coefficients to match, so we can multiply Equation 1 by 2:

(2)(2x) + (2)(3y) = (2)(17)

4x + 6y = 34 (New Equation 1)

Now we can subtract the new Equation 1 from Equation 2:

(5x + 6y) - (4x + 6y) = 32 - 34

5x - 4x + 6y - 6y = -2

x = -2

Now that we have a value for x, we can substitute it back into one of the original equations to solve for y. Let's substitute x into Equation 1:

2(-2) + 3y = 17

-4 + 3y = 17

3y = 17 + 4

3y = 21

y = 7

The solution to the system of equations is x = -2 and y = 7.

Answer:

2x-10

Step-by-step explanation:

original equation: 2(×-5)

distributive property: 2(x) 2(-5) =2x-10

Answer:

2x-10

2(x-5)

2*x=2x

2*5=10

Answer:

The Building's tall and wide ratio is 90 : 45 = 2 : 1

now the wide is 3, let's say that tall is a.

2 / 1 = a / 3

a = 2 x 3

a = 6

So the picture will be 6 feet tall.

ANSWER

Relative minimum occurs at x=0

Relative maximum occurs at x=-2

EXPLANATION

The given function is;

[tex]f(x) = 3 {x}^{3} + 9 {x}^{2} - 1[/tex]

We take the first derivative to get:

[tex]f'(x) = 9 {x}^{2} + 18x[/tex]

At turning point f'(x)=0

[tex] 9 {x}^{2} + 18x = 0[/tex]

[tex] 9x(x + 2) = 0[/tex]

[tex]x = 0 \: or \: x = - 2[/tex]

We take the second derivative to get

[tex]f''(x) = 18x + 18

[/tex]

[tex]f''(0) = 18(0) + 18 = 18 \: > \: 0[/tex]

Relative minimum occurs at x=0

[tex]f''( - 2) = 18( - 2)+ 18 = - 18 \: < \: 0[/tex]

Relative maximum occurs at x=-2

Answer:

Relative minimum occurs at x=0

Relative maximum occurs at x=-2

Step-by-step explanation:

Answer:

The correct answer is first option

512 cubic mm

Step-by-step explanation:

Points to remember

Volume of hexagonal pyramid = Base area * height

To find the volume of hexagonal pyramid

It is given that, base area = 64 square mm and

height = 8 mm

Volume = Base area * Height

 = 64 * 8

 = 512 cubic mm

Therefore the correct answer is first option

512 cubic mm

Answer:

2520

Step-by-step explanation:

7×6×5×4×3 = 2520

Imagine □□□□□

For the 1st □, there are 7 choices

For the 2nd □, there are 6 choices (since 1 out of the 7 numbers is already used)

For the 3rd □, there are 5 choices (since 2 out of the 7 numbers are used)

And so on...

The total number of 5-digit numbers that can be formed with the digits 1 to 7, without repetition, is 2520.

Your question pertains to the concept of permutations - the number of ways items can be arranged without repetition. In this case, you are considering how many 5-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 without repeating any digit.

A helpful way to think about this is to think of the 5 places for our 5-digit number (i.e., _ _ _ _ _). For the first position, you have 7 choices (the digits 1 to 7) to choose from. Once you have chosen a digit, you are left with 6 choices for the second position, 5 for the third position, 4 for the fourth, and finally 3 for the fifth. So, the total number of 5-digit numbers you can form is 7 × 6 × 5 × 4 × 3 = 2520.

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Answer:

Option D is correct.

Step-by-step explanation:

We need to find the pattern in the values as the exponents increase.

First value is 1/3

if we multiply 3 with 1/3 i.e. 1/3*3 we get 1

The next value is 1 in the table.

Now, if we multiply 1 with 3 i.e. 1*3 we get 3

The next value is 3 in the table.

Now, if we multiply 3 with 3 i.e 3*3 we get 9

So, the next value is 9 in the table.

So, if we multiply 3 with the previous value we get the next value in the table.

Hence Option D multiply the previous value by 3 is correct.

ANSWER

[tex]p(x) = 6x - 15[/tex]

EXPLANATION

The revenue from selling x necklaces is

[tex]r(x) = 10x[/tex]

The cost of buying x necklaces is

[tex]c(x) = 4x + 15[/tex]

The profit from selling x necklaces is

[tex]p(x) = r(x) - c(x)[/tex]

We substitute the functions to get;

[tex]p(x) = 10x- (4x + 15)[/tex]

[tex]p(x) = 10x- 4x - 15[/tex]

[tex]p(x) = 6x - 15[/tex]

Therefore the function for the profit is

[tex]p(x) = 6x - 15[/tex]

Answer:

If you're looking for the absolute value, its 1/64

Step-by-step explanation:

The absolute value is the distance a number is from 0.

1/64 is 1/64th away from 0/64

So, the answer would be 1/64

I hope this helped you! :)

Answer:

Answer:

The answer is 14

Step-by-step explanation:

IT IS NOT 82 I JUST TOOK THE TEST AND IT WAS WRONG...THE ANSWER IS 14!

The driver expects to be tipped approximately $14.

Given is that Hector paid $68 for a taxi ride. This driver has a sign above his mirror that recommends a 20% tip.

The amount recieved as a tip is given as -

20% of 68

20/100 x 68

13.6

Therefore, the driver expects to be tipped approximately $14.

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When eggs are delivered, if one notices that B. The shells of the eggs have cracks in them, the eggs should be rejected.

Eggs that have cracks in them can be potentially dangerous to people because microorganisms like bacteria can enter through those cracks and either spoil the egg or make it harmful for consumption.

It is therefore best that an egg that has a crack, be rejected upon delivery.

Other options are incorrect because:

In conclusion, if an egg has a crack in it upon delivery, it should be rejected.

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Answer:

Step-by-step explanation:

The question does say at most 10. That includes 10. So the circle on 10 should indicate it is closed or fully filled in.

The shading should go left. It should indicate less than 10.

[tex]12\dfrac{1}{3}-6\dfrac{9}{10}=12\dfrac{10}{30}-6\dfrac{27}{30}=6+\left(-\dfrac{17}{30}\right)=5\dfrac{13}{30}[/tex]

Let the base = x

Then the height would be 2x ( twice the length of the base.

Now using the given formula you get:

25 = 1/2 * 2x *x

Multiply 2x by 1/2:

1/2 * 2x = 2x/2

25 = 2x/2 * x

2x/2 = 1x, now you have:

25 = x *x

Multiply x by x:

25 = x^2

Take the square root of both sides:

x = √25

x = 5

Answer:

f(x) = x + 13

Step-by-step explanation:

Given f(x) then f(x) + c represents a vertical translation

• If c > 0 then vertical shift up ↑ of c units

• If c < 0 then vertical shift down ↓ of c units

here c = + 13, hence

f(x) = x + 13

Answer:

The length of a leg of the triangle = 59.83 cm

Step-by-step explanation:

Points to remember

If a right angled triangle with angles 45°, 45° and 90° then the sides are in ratio 1 : 1 : √2

It is given a right angled triangle with  45°, 45° and 90° and hypotenuse = 84.6 cm

To find the length of a leg

Let 'x' be the length of each leg,

From the figure we can write,

1: 1 :  √2 = x : x : 84.6

Therefore x = 84.6/√2

 = 59.83 cm

Therefore the length of a leg of the triangle = 59.83 cm

ANSWER

59.82

EXPLANATION

The given right angle is an isosceles right triangle.

Let the length of a leg be x cm.

Then by the Pythagoras Theorem,

[tex] {x}^{2} + {x}^{2} = 84.6 ^{2} [/tex]

[tex]2 {x}^{2} = 7157.16[/tex]

Divide both sides by 2.

[tex]{x}^{2} = \frac{7157.16}{2} [/tex]

[tex]{x}^{2} = 3578.58[/tex]

Take positive square root of both sides to get,

[tex]x = 59.82123369[/tex]

Hence the length of a leg is 59.82 to the nearest hundredth.

Answer: 717,000

Step-by-step explanation:

716,773 rounded to the nearest thousand is 717000 because the 7 is closer to 10 than it is to 0

Hello There!

716,772 rounded to the nearest thousand would be 717,000

772 is closer to 717,000 than 716,000

Answer:

y- intercept = 4

Step-by-step explanation:

The y- intercept is the value of the y- coordinate where the line crosses the y- axis.

Here the y- intercept = 4 or (0, 4) ← coordinates of point

Answer:

( 0 , 4 )

Step-by-step explanation:

The y - intercept of the line is where the line hit's or crosses the y - axis and in the case since the line goes through 4 on the y - axis

For this case we have that by definition, the Greatest Common Factor (GCF) is the largest factor that 2 numbers have in common.

So, we have the following expressions:

[tex]42a ^ 5b ^ 3\\35a ^ 3b ^ 4\\42ab ^ 4[/tex]

We look for the positive integers that divide to 35 and 42 without leaving residue:

42: 1,2,3,6,7,14,21

35: 1,5,7

Thus, the GCF of 42 and 35 is 7

Then, the GCF of the three expressions is:

[tex]7ab ^ 3[/tex]

Answer:

[tex]7ab ^ 3[/tex]

Answer:

A) 7ab^3

Step-by-step explanation:

EDG2021