Which function is equivalent to f(x) = e2x ?

To find the angle of depression, we can use trigonometry. The elevation of the North Rim and the campground, along with the line of sight distance, can be used to calculate the angle using the tangent function.

To find the angle of depression of the man's line of sight to the campground, we can use trigonometry. The angle of depression is the angle between the line of sight and a horizontal line. In this case, the elevation of the North Rim is 5389 ft and the elevation of the campground is 2405 ft. The line of sight distance to the campground is 3044 ft.

We can use the tangent function to find the angle of depression. Tangent(theta) = opposite/adjacent. The opposite side is the difference in elevation between the North Rim and the campground (5389 ft - 2405 ft) and the adjacent side is the line of sight distance (3044 ft). So, tangent(theta) = (5389 ft - 2405 ft) / 3044 ft.

Using a scientific calculator, we can find the value of theta by taking the inverse tangent (or arctan) of the ratio: theta = arctan((5389 ft - 2405 ft) / 3044 ft). The answer is approximately 57.38 degrees.

Answer:

We have 8 cups of orange juice

Step-by-step explanation:

orange juice:  water:  total

1                     : 3         : 4

Multiply everything by x

1x                 3x             4x

We have 32 cups total

4x = 32

Divide each sice by 4

4x/4 = 32/4

x = 8

We have 8 cups of orange juice

3*8 = 24

We have 24 cups of water

The ratio of orange juice to water in the punch is 1:3, which means that for every single cup of orange juice, there are 3 cups of water. To find out how many cups of orange juice were used to make 32 cups of punch, we find out what 1 part out of the total 4 parts is, which is 32 ÷ 4 = 8. Therefore, James used 8 cups of orange juice for the punch.

The subject of the question is Mathematics and it pertains to the concept of ratios in particular. The ratio of orange juice concentrate to water is given as 1:3. This means that for every 1 cup of orange juice, James uses 3 cups of water. So, the total parts in the punch are 1 (for orange juice) + 3 (for water) = 4 parts.

However, James made 32 cups of punch. Hence, to find out how many cups of orange juice he used, we need to find out what 1 part out of the total 4 parts is. To do this, you divide the total punch made (32 cups) by the number of total parts (4).

Therefore, 32 cups divided by 4 equals 8 cups. Hence, James used 8 cups of orange juice to make the punch.

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Answer:

2500

Step-by-step explanation:

Let the first square number be [tex]x^2[/tex] then the next square number is [tex](x+1)^2[/tex].

The difference between these two consecutive numbers is 99.

This implies that:

[tex](x+1)^2-x^2=99[/tex]

We expand to get:

[tex]x^2+2x+1-x^2=99[/tex]

Simplify:

[tex]2x=99-1[/tex]

[tex]2x=98[/tex]

Divide both sides by 2

[tex]x=49[/tex]

Therefore the value of the larger perfect number is

[tex](49+1)^2=50^2=2500[/tex].

Answer:

a)

The equation of variation is;

N = 80000*S

b)

14400000

Step-by-step explanation:

We are informed that the number of instructions N performed per second by a computer varies directly as the speed S of the​ computer's internal processor. This means that N and S are directly proportional;

N∝S

Introducing a constant of proportionality, k;

N=k*S

We shall find the value of k by using the information given;

N = 1600000

S = 20

k = 1600000/20

  = 80000

a)

The equation of variation is thus;

N = 80000*S

b)

We are required to find N when S = 180

Using the equation of variation obtained above;

N = 80000 (180)

   = 14400000

Answer:

d. arc BCE

Step-by-step explanation:

BE is a diameter which means it cuts the circle in half therefore arc BCE is a semicircle

[tex]\bf \textit{exponential form of a logarithm} \\\\ \log_a b=y \implies a^y= b\qquad\qquad a^y= b\implies \log_a b=y \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_{3x+4}(4096)=4\implies \stackrel{\textit{exponential form}}{(3x+4)^4=4096}\implies (3x+4)^4=2^{12} \\\\\\ \stackrel{~\hfill \textit{same exponents, the bases must be the same}}{(3x+4)^4=2^{3\cdot 4}\implies (3x+4)^4=(2^3)^4}\implies 3x+4=2^3\implies 3x+4=8 \\\\\\ 3x=4\implies x=\cfrac{4}{3}[/tex]

Answer:

The length of the lot is [tex]105.6\ ft[/tex]

Step-by-step explanation:

Remember that

[tex]1\ acre=43,560\ ft^{2}[/tex]

In this problem the area of the lot  is equal to

[tex]\frac{2}{3} (43,560)=29,040\ ft^{2}[/tex]

Let

x-----> the length of the lot

y ----> the deep of the lot

The area of the lot is

[tex]A=xy[/tex]

we have

[tex]A=29,040\ ft^{2}[/tex]

[tex]y=275\ ft[/tex]

substitute and solve for x

[tex]29,040=x(275)[/tex]

[tex]x=29,040/(275)=105.6\ ft[/tex]

The area of a triangle is half the multiplication of the base and the height.

So, if the smaller triangle has height 6 cm and base 2 cm, its are is

[tex]\dfrac{6\times 2}{2}=6[/tex]

Similarly, if the height of the larger triangle is 9 cm, and its base is 3 cm, its area is

[tex]\dfrac{9\times 3}{2}=\dfrac{27}{2}[/tex]

So, the total area is

[tex]6+\dfrac{27}{2} = \dfrac{12}{2}+\dfrac{27}{2}=\dfrac{39}{2}[/tex]

The total area of the two triangles that need to be painted is 19.5 cm².

The total area of the two triangles that need to be painted can be found by adding the area of the smaller triangle and the area of the larger triangle. The formula to calculate the area of a triangle is:

Area = (base * height) / 2

For the smaller triangle, the base is 2 cm and the height is 6 cm. Substituting these values into the formula, we get:

Area of smaller triangle = (2 cm * 6 cm) / 2 = 6 cm²

For the larger triangle, the base is 3 cm and the height is 9 cm. Substituting these values into the formula, we get:

Area of larger triangle = (3 cm * 9 cm) / 2 = 13.5 cm²

To find the total area, we add the areas of the two triangles:

Total area = area of smaller triangle + area of larger triangle = 6 cm² + 13.5 cm² = 19.5 cm²

f(-1) means the x value is -1 and you need to find what the Y value is.

Find -1 in the set of parenthesis and see what the Y value is.

When x = -1, y = 3

The answer would be 3.

A statistical question is a question asked with the goal of collecting data. You could rewrite the question so that it says something like, “How old were you when..” That way the responses will vary and you would be able to graph and compare them.

The statistical question of the given statement is How old were you then.

Hence, the statistical question of the given statement is How old were you then.

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look up a video on the internet and it will show you

Answer:

48 people

Step-by-step explanation:

1. 4/50 = x/600  do 4x600 and 50 times x

2.50x=2400

3. divide both sides by 50 to get a result of x=48.

Answer:

  1. predicted attendance: 141.35

  2. residual: 18.65

Step-by-step explanation:

1. Predicted attendance is ...

  y = -5.9·5 +170.85 = 141.35

__

2. As the problem statement tells you, ...

  actual value - predicted value = residual

  160 - 141.35 = 18.65 . . . the residual

Answer:

80

Step-by-step explanation:

let w = the width of the rectangles

then

12w = the area of one rectangle

8w = the area of other

:

12w - 8w = 320

4w = 320

w = 320/4

w = 80 units wide

;

:

Check

12 * 80 = 960

8 * 80 = 640

--------------

difference: 320

We know that both rectangles have the same width, which is 80 units.

We know that both rectangles have the same width, so we can say that both have the width W.

One of the rectangles has a length of 12 units, and the other of 8 units, so the areas are:

A = 12*W

A' = 8*W

And the largest area is 320 square units more than the other area, so we have:

12*W = 8*W + 320

Solving for W we get:

12*W - 8*W = 320

4*W = 320

W = 320/4 = 80

Then the width of each rectangle is 80 units.

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Answer:

12.3

Step-by-step explanation:

cos(35) = y/15

y = 15 * cos(35) = 12.3

Answer:

y = 12.3 cm

Step-by-step explanation:

Since the triangle is right with hypotenuse 15, use the cosine ratio to solve for y, that is

cos35° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{y}{15}[/tex]

Multiply both sides by 15

15 × cos35° = y, hence

y ≈ 12.3

Answer:

the correct answer would be c, g(x)=2^x+2

Step-by-step explanation:

We can eliminate the first and the last option because the line is going upwards, not downwards(it would if it was negative or had the negative sign in front). We can cross out the second option because if it was 2^x+3, then it would be crossing (0,4) on the y-axis. Therefore the correct option is C, since it crosses right at (0,3).

hope this helps :)

Answer:

Step-by-step explanation:

The question is not biased.  It doesn't push the participants to answer one way or another.

However, the sample is biased.  It does not represent the population.

The first and fourth options are correct.

Answer:

The profit will be [tex]\$22.31[/tex]

Step-by-step explanation:

we know that

To find the profit subtract the cost of the case of bottled water from the sell of all the bottles of water  

Let

x-----> the profit

[tex]x=36*0.75-4.69=\$22.31[/tex]

Answer:

(a, 0)

Step-by-step explanation:

As S is on the x-axis, its y-coordinate will be zero.

And since this is a right trapezoid, ∠QPS and ∠PSR are right angles, so S and R will have the same x-coordinate, which is a.

Therefore, the coordinate of Point S is (a, 0)

Answer:

D. (2.4, -1).

Step-by-step explanation:

The midpoint  of the line segment with endpoints (x1,y1) and (x2,y2) is

[(x1+x2) / 2 , (y1+y1)/2 ].

So here we have : [  (3.2+1.6)/ 2 (2.5 - 4.5)/2)

= (2.4, -1) answer.

The midpoint of the line segment with endpoints (3.2, 2.5) and (1.6, -4.5) is (2.4, -1).

To find the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂), you can use the midpoint formula:

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

For the given endpoints (3.2, 2.5) and (1.6, -4.5), we can calculate the midpoint as follows:

Midpoint (M) = ((3.2 + 1.6) / 2, (2.5 + (-4.5)) / 2)

= (4.8 / 2, -2 / 2)

= (2.4, -1)

Therefore, the midpoint of the line segment with endpoints (3.2, 2.5) and (1.6, -4.5) is (2.4, -1).

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Answer:

e). 4

Step-by-step explanation:

45-45-90

x-x-xsquare root of 2

Final answer:

The measure of the leg of a 45-45-90 right triangle with a hypotenuse of 4√2 is 4 units.

Explanation:

The question asks for the measure of the leg of a 45-45-90 right triangle given that the hypotenuse is 4√2. In a 45-45-90 right triangle, both legs are of equal length and the hypotenuse is √2 times the length of a leg. Using the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a2 + b2), we can find the length of a leg when the hypotenuse is known.

Let the length of each leg be 'a'. Since the hypotenuse is 4√2, the equation according to the Pythagorean Theorem would be a2 + a2 = (4√2)2. This simplifies to 2a2 = 32, so a2 = 16, and thus a = √16. Therefore, each leg measures 4 units.

Answer:

D

Explanation:

A is the same thing as the statement, only that it says if the polygon is convex. Same thing for B. C could've worked if it said exterior instead of interior. D is basically the converse of the statement.

A polygon is not convex if and only if a segment connecting any two vertices passes through the exterior of the polygon i.e option D

Each interior angle of a convex polygon is less than 180° while in the case of the concave polygon at least one angle is more than 180°.

In the diagram attached,

We can see in the case of a convex polygon if we join any two vertices, a line segment joining two vertices never passes through the exterior or interior of the polygon.

In the case of a concave polygon, at least a line segment joining two vertices passes through the exterior of a polygon.

Therefore, A polygon is not convex if and only if a segment connecting any two vertices passes through the exterior of the polygon i.e option D

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Answer:

Second choice

Answer:

5*B=C

Step-by-step explanation:

Five cookies times the number of boxes will give you the total number of cookies

Answer:

Let l = length and w = width of the rectangular garden

=> w < 30

and 2(l + w) ≤ 180

=> l + w ≤ 90

=> 0 < w < 30 and 60 ≤ l < 90.

Step-by-step explanation:

Answer:

# The general form of  x²/3² + (y - 2)²/2² = 1 is 4x² - 36y + 9y² = 0

# The general form of (x + 7)²/7² + y²/6² = 1 is 36x² + 504x + 49y² = 0

# The general form of x²/6² + (y + 4)²/4² = 1  is 16x² + 288y + 36y² = 0

# The general form of (x - 3)²/3² + y²/5² = 1  is 25x² - 150x + 9y² = 0

Step-by-step explanation:

* Lets revise the general form and the standard form of the ellipse

- The general form is Ax² + Bxy + Cy² + Dx + Ey + F = 0

- The standard form is (x - h)²/a² + (y - k)²/b² = 1

* Lets solve the problem

# x²/3² + (y - 2)²/2² = 1

∵ x²/9 + (y - 2)²/4 = 1 ⇒ multiply both sides by 9 × 4 (36)

∴ 4x² + 9(y - 2)² = 36 ⇒ open the bracket power 2

∴ 4x² + 9(y² - 4y + 4) = 36 ⇒ multiply the bracket by 9

∴ 4x² + 9y² - 36y + 36 = 36 ⇒ subtract 36 from both sides

∴ 4x² - 36y + 9y² = 0

* The general form of  x²/3² + (y - 2)²/2² = 1 is 4x² + 9y² - 36y = 0

# (x + 7)²/7² + y²/6² = 1

∵ (x + 7)²/49 + y²/36 = 1 ⇒ multiply both sides by 49 × 36 (1764)

∴ 36(x + 7)² + 49y² = 1764 ⇒ open the bracket power 2

∴ 36(x² + 14x + 49) + 49y² = 1764 ⇒ multiply the bracket by 36

∴ 36x² + 504x + 1764 + 49y² = 1764 ⇒ subtract 1764 from both sides

∴ 36x² + 504x + 49y² = 0

* The general form of (x + 7)²/7² + y²/6² = 1 is 36x² + 504x + 49y² = 0

# x²/6² + (y + 4)²/4² = 1

∵ x²/36 + (y + 4)²/16 = 1 ⇒ multiply both sides by 36 × 16 (576)

∴ 16x² + 36(y + 4)² = 576 ⇒ open the bracket power 2

∴ 16x² + 36(y² + 8y + 16) = 576 ⇒ multiply the bracket by 36

∴ 16x² + 36y² + 288y + 576 = 576 ⇒ subtract 576 from both sides

∴ 16x² + 288y + 36y² = 0

* The general form of x²/6² + (y + 4)²/4² = 1  is 16x² + 288y + 36y² = 0

# (x - 3)²/3² + y²/5² = 1

∵ (x - 3)²/9 + y²/25 = 1 ⇒ multiply both sides by 9 × 25 (225)

∴ 25(x - 3)² + 9y² = 225 ⇒ open the bracket power 2

∴ 25(x² - 6x + 9) + 9y² = 225 ⇒ multiply the bracket by 25

∴ 25x² - 150x + 225 + 9y² = 225 ⇒ subtract 225 from both sides

∴ 25x² - 150x + 9y² = 0

* The general form of (x - 3)²/3² + y²/5² = 1  is 25x² - 150x + 9y² = 0

Answer:In Plato this is the correct answer

Step-by-step explanation:

Answer:

The surface area of the sphere is [tex]529\pi\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of a sphere is equal to

[tex]SA=4\pi r^{2}[/tex]

we have

[tex]r=23/2=11.5\ ft[/tex] ----> the radius is half the diameter

substitute

[tex]SA=4\pi (11.5)^{2}[/tex]

[tex]SA=529\pi\ ft^{2}[/tex]

Answer: 120

Step-by-step explanation:

Answer:

12612837.8375

Step-by-step explanation:

first you have to multiply 5.015 x 10 and you get 50.15 the put that to the power of 3 and then multiply the total by 100.

Hello there! Here are your answers:

Does Kerri's dot plot match the data in the tally table? No.

Look at any of the hours on the chart vs dot plot. Let's take 4 for example. In the tally table, there are 6 class mates. In the plot, there are 3. So no, it is not the same.

The answers for the other problems are in this order (since it's the number of circles on the dot plot at the given hour):

5 - classmates spent 3 hours at the park

3 - classmates spent 4 hours at the park

6- classmates spent 5 hours at the park

4 - classmates spent 6 hours at the park

I hope this was helpful and let me know if you need more help! :) Have a great day! :)

Answer:

the other guy is right

Step-by-step explanation:

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