A study of the annual population of toads in a county park shows the population, S(t), can be represented by the function S(t)=152(1.045)t, where the t represents the number of years since the study started. Based on the function, what is the growth rate?

Answer:

One

Step-by-step explanation:

y = 3 x - 5.

y = -x + 4.

x=9/4 and y=7/4

1 solution (9/4 , 7/4)

For a system of the equation to be an Independent Consistent System, the system must have one unique solution. The system of the equation has only one solution. Thus, the correct option is A.

Inconsistent System

For a system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.

Given the two equations y=3x -5 and y=-x+4. If the two of the equations are plotted on the graph. Then it can be observed from the graph that there is only one intersection between the two lines.

Hence, the system of the equation has only one solution. Thus, the correct option is A.

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Answer:

8

Step-by-step explanation:

2 x 2 x 2 = 8

you have 2 choices each time, with or without

Answer:

A

Step-by-step explanation:

First, let's label the variables:

[tex]\text{Let }x \text{ represent Kaylee's number of pens,}\\\text{Let }L \text{ represent Lou's number of pens,}\\\text{And let }I \text{ represent Ilene's number of pens.}[/tex]

The first and second sentence, Kaylee at the start has x pens. She gave half to Lou, who started out with two fewer than Kaylee.

In other words, the total Lou now has is:

[tex]L=(\frac{1}{2}x )+(x-2)[/tex]

The first term represents what Kaylee gave to Lou. The second term represents what Lou had originally (two fewer than Kaylee [x]).

Simplifying, we get:

[tex]L=\frac{3}{2}x-2[/tex]

Third sentence. Lou give half of his new total to Ilene, who started out with three fewer pens than Lou. Lou, remember, started with three fewer than Kaylee (x-2). In other words:

[tex]I=(\frac{1}{2}(\frac{3}{2}x-2) )+((x-2)-3)[/tex]

The left represents what is given to Ilene: one-third of Lou's new total. The right represents Ilene's original total: three fewer than Lou: or five fewer than Kaylee. Simplifying gives:

[tex]I=(\frac{3}{4} x-1)+(x-5)\\I=\frac{7}{4}x-6[/tex]

Finally, Ilene gives a third of this new amount to Kaylee, and Kaylee's final amount is 37. Thus:

[tex]37=x-\frac{1}{2}x+\frac{1}{3}(\frac{7}{4}x-6)[/tex]

The first term represents what Kaylee originally started with. The second term represents what she gave to Lou. And the third term represents what Ilene gave to Kaylee. Simplify:

[tex]37=\frac{1}{2}x+\frac{7}{12}x-2\\39=\frac{6}{12}x+\frac{7}{12}x \\39=\frac{13}{12}x\\ 468=13x\\x=36[/tex]

Answer:

24

Step-by-step explanation:

46 - 22 = 24

Answer:

[tex]d = \sqrt{85}[/tex] or d ≈ 9.22

Step-by-step explanation:

Distance formula:

[tex]d = \sqrt{(2 - (-4))^2 + (-3- 4)^2} \\d = \sqrt{36+ 49}\\d = \sqrt{85} \\[/tex]

Answer:

The equation is  y = -x + 4

Step-by-step explanation:

This is a very trivial exercise:

The general equation of a line is given by:

y - y₁ = m(x - x₁)

where m = slope of the linear graph

From the given graph, it can be observed that the coordinate (x₁, y₁) and (x₂, y₂) are (0, 4) and (4, 0)

The slope, m = (y₂ - y₁)/(x₂ - x₁)

m = (0 - 4)/(4 - 0)

m = -4/4

m = -1

Substituting the values of (x₁, y₁) = (0, 4) and m = -1 into the general equation:

y - y₁ = m(x - x₁)

y - 4 = -1 (x - 0)

y - 4 = -x

y = -x + 4

Answer:

18- 14+8=3x

4+8=3x

12=3x

12/3=2x/3

x=4

Answer:

2/3, -8, -1/6, 4.

Step-by-step explanation:

Step-by-step explanation:

The rational root theorem states that if the leading coefficient is taken to be an and the constant coefficient is taken to be a0 the possible roots of the equation can be expressed as :

Now, from the given options, the possible choices can be :

A, B, C and E

D can be there because after taking any pair the rational root can't be 3

F can't be possible because an does't have 4 in its factors so denominator cannot be 4.

Answer: hypotenuse = [tex]c^{2} + b^{2}[/tex]

Step-by-step explanation: Pythagorean theorem states that square of hypotenuse (h) equals the sum of squares of each side ([tex]s_{1},s_{2}[/tex]) of the right triangle, .i.e.:

[tex]h^{2} = s_{1}^{2} + s_{2}^{2}[/tex]

In this question:

[tex]s_{1}[/tex] = [tex]c^{2}-b^{2}[/tex]

[tex]s_{2} =[/tex] 2bc

Substituing and taking square root to find hypotenuse:

[tex]h=\sqrt{(c^{2}-b^{2})^{2}+(2bc)^{2}}[/tex]

Calculating:

[tex]h=\sqrt{c^{4}+b^{4}-2b^{2}c^{2}+(4b^{2}c^{2})}[/tex]

[tex]h=\sqrt{c^{4}+b^{4}+2b^{2}c^{2}}[/tex]

[tex]c^{4}+b^{4}+2b^{2}c^{2}[/tex] = [tex](c^{2}+b^{2})^{2}[/tex], then:

[tex]h=\sqrt{(c^{2}+b^{2})^{2}}[/tex]

[tex]h=(c^{2}+b^{2})[/tex]

Hypotenuse for the right-angled triangle is [tex]h=(c^{2}+b^{2})[/tex] units

The expression for the length of the hypotenuse is [tex]c^2+ b^2 \ units[/tex].

Given that,

A right-angled triangle has shorter side lengths exactly [tex]c^{2} - b^{2}[/tex] and 2bc units respectively,

Where b and c are positive real numbers such that c is greater than b.

We have to determine,

An exact expression for the length of the hypotenuse?

According to the question,

The Pythagoras theorem states that the sum of the hypotenuse in the right-angled triangle is equal to the sum of the square of the other two sides.

A right-angled triangle has shorter side lengths exactly [tex]c^{2} - b^{2}[/tex] and 2bc units respectively,

Where b and c are positive real numbers such that c is greater than b.

Therefore,

The expression for the length of the hypotenuse is,

[tex]\rm (Hypotenuse)^2 = (c^2-b^2)^2+ (2bc)^2\\\\(Hypotenuse)^2 = c^4+ b^4 - 2c^2b^2 + 4c^2b^2\\\\(Hypotenuse)^2 = c^4+ b^4 +2c^2b^2 \\\\Hypotenuse = \sqrt{c^4+ b^4 +2c^2b^2}\\\\\ Hypotenuse = \sqrt{(c^2+ b^2)^2}\\\\ Hypotenuse = c^2+b^2 \ units[/tex]

Hence, The required expression for the length of the hypotenuse is [tex]c^2+ b^2 \ units[/tex].

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Answer:  Perimeter = 6π ≈ 18.84

                         Area = 15π ≈ 47.10

Step-by-step explanation:

This is a composite of a big semicircle with diameter of 10 --> radius (r) = 5

plus a medium semicircle with diameter of 6 --> r = 3

minus a small semicircle with diameter of 4 --> r = 2

Perimeter of a semicircle = [tex]\dfrac{1}{2}(2\pi r)=\pi r[/tex]

[tex]P_{big}=\pi (5)\quad =5\pi\\P_{medium}=\pi (3)\quad =3\pi\\P_{small}=\pi (2)\quad =2\pi\\P_{composite} =5\pi+3\pi -2\pi\\.\qquad \qquad =\large\boxed{6\pi}[/tex]

Area of a semicircle = [tex]\dfrac{1}{2}(\pi r^2)[/tex]

[tex]A_{big}=\dfrac{1}{2}\pi (5)^2\quad =12.5\pi\\\\A_{medium}=\dfrac{1}{2}\pi (3)^2\quad =4.5\pi\\\\A_{small}=\dfrac{1}{2}\pi (2)^2\quad =2\pi\\\\A_{composite} =12.5\pi+4.5\pi -2\pi\\\\.\qquad \qquad =\large\boxed{15\pi}[/tex]

Answer:  Perimeter = 8π  ≈ 25.12

                        Area = 12π ≈ 37.68

Step-by-step explanation:

This is a composite of two figures.

The bigger figure is a quarter-circle with radius (r) = 8 cm

The smaller figure is a quarter-circle with diameter = 8 cm --> r = 4

Perimeter of a quarter-circle = [tex]\dfrac{1}{4}(2\pi r)[/tex] = [tex]\dfrac{\pi r}{2}[/tex]

Perimeter of composite figure = bigger - smaller figure

[tex]P_{bigger}=2\pi(8)\quad = 16\pi\\P_{smaller}=2\pi(4)\quad =8\pi\\P_{composite}=16\pi-8\pi \\.\qquad \qquad = \large\boxed{8\pi}[/tex]

Area of a quarter-circle = [tex]\dfrac{1}{4}\pi r^2[/tex]

[tex]A_{bigger}=\dfrac{1}{4}\pi (8)^2\quad =16\pi\\\\A_{smaller}=\dfrac{1}{4}\pi (4)^2\quad =4\pi\\\\A_{composite}=16\pi-4\pi\\.\qquad \qquad = \large\boxed{12\pi}[/tex]

Answer:

[tex] Area = 1,309.0 in^2 [/tex]

Step-by-step explanation:

Given:

∆TUV

m < U = 22°

TV = u = 47 in

m < V = 125°

Required:

Area of ∆TUV

Solution:

Find the length of UV using the Law of Sines

[tex] \frac{t}{sin(T)} = \frac{u}{sin(U)} [/tex]

U = 22°

u = TV = 47 in

T = 180 - (125 + 22) = 33°

t = UV = ?

[tex] \frac{t}{sin(33)} = \frac{47}{sin(22)} [/tex]

Multiply both sides by sin(33)

[tex] \frac{t}{sin(33)}*sin(33) = \frac{47}{sin(22)}*sin(33) [/tex]

[tex] t = \frac{47*sin(33)}{sin(22)} [/tex]

[tex] t = 68 in [/tex] (approximated)

[tex] t = UV = 68 in [/tex]

Find the area of ∆TUV

[tex] area = \frac{1}{2}*t*u*sin(V) [/tex]

[tex] = \frac{1}{2}*68*47*sin(125) [/tex]

[tex] = \frac{68*47*sin(125)}{2} [/tex]

[tex] Area = 1,309.0 in^2 [/tex] (to nearest tenth).

Answer:

152.87 degree/seconds

Step-by-step explanation:

1 rotation = Circumference of a circle = 2πr

r = 15 inches

1 rotation = 2 × 3.14 × 15

94.2 inches.

We are told in the question that it takes 30 seconds to roll 100 feet along the ground

Convert feet to inches

1 feet = 12 inches

100 feet =

100 × 12 = 1200 inches.

Hence, if

94.2 inches = 1 rotation

1200 inches = X

Cross multiply

94.2 × X = 1200 × 1

94.2X = 1200

X = 1200/94.2

X = 12.738853503 rotations

Formula for Angular velocity = Number of rotations × 2π/time in seconds

Time = 30 seconds

12.738853503 × 2 × 3.14/30

= 2.6666666667 rotations per second

Converting Angular velocity to degree per second

= 2.6666666667 × 180/ π

= 2.6666666667 × 180/3.14

= 152.86624204 degree/seconds

Approximately to 2 decimal places

= 152.87 degree/seconds

Answer:

TW = 3.18 yd (Approx)

Step-by-step explanation:

Given:

TV = 6 yd

∠TYW = 32°

∠TWV = 90°

Find:

TW

Computation:

Using trigonometry application.

TW / TV = Sin 32°

TW / 6 = 0.53

TW = 3.18 yd (Approx)

Answer:

Step-by-step explanation:

If the second angle's measure is based on the first angle's measure, and the third angle's measure is also based on the first angle's measure, then the first angle is the main angle. We will call that x.

1st angle: x

2nd angle: x + 20%

3rd angle: x - 20%

By the Triangle Angle-Sum Theorem, all those angles will add up to 180, so:

x + (x + 20%) + (x - 20%) = 180 and

3x = 180 so

x = 60. That means that

2nd angle: 60 + (.2*60) which is

60 + 12 = 72 and

3rd angle: 60 - (.2*60) which is

60 - 12 = 48. Let's check those angles. If

∠1 = 60

∠2 = 72

∠3 = 48,

then ∠1 + ∠2 + ∠3 = 180 and

60 + 72 + 48 does in fact equal 180, so you're done!

[tex] \Delta = \frac 1 2 a b \sin C[/tex]

[tex]\Delta=5, \quad a=5, \quad b=4[/tex]

[tex]\sin C = \dfrac{2 \Delta}{ab} = \dfrac{2 (5)}{5(4) } = \dfrac 1 2[/tex]

[tex]C=30^\circ \textrm{ or } C=150^\circ[/tex]

Answer: two possibilities, θ=30° or 150°

Answer:

The answer is d

Step-by-step explanation:

Answer:

4kg

Step-by-step explanation:

...../...../

2kg + half of its weight

so half of its weight = 2kg

so 2kg + 2kg= 4kg the weight of the fish

Answer:

Step-by-step explanation:

We'll just work on solving both so you can see what's involved in solving an absolute value equation. Because an absolute value is a distance, we can have that distance being both to the right on the number line of the number in question or to the left. For example, from 2 on the number line, the numbers that are 5 units away are 7 and -3. Using that logic, we will simplify the equation down so we can set up the 2 basic equations needed to solve for x.

If  [tex]3-2|.5x+1.5|=2[/tex] then

[tex]-2|.5x+1.5|=-1[/tex]  What you need to remember here is that you cannot distribute into a set of absolute values like you would a set of parenthesis. The -2 needs to be divided away:

[tex]|.5x+1.5|=.5[/tex]

Now we can set up the 2 main equations for this which are

.5x + 1.5 = .5  and .5x + 1.5 = -.5

Knowing that an absolute value will never equal a negative number (because absolute values are distances and distances will NEVER be negative), once we remove the absolute value signs we can in fact state that the expression on the left can be equal to a negative number on the right, like in the second equation above.

Solving the first one:

.5x = -1 so

x = -2

Solving the second one:

.5x = -2 so

x = -4

We want to find the other solution of the given absolute value equation.

The other solution is x = -4

We know that:

3 - 2*|0.5*x + 1.5| = 2

It has one solution given by:

- 2*|0.5*x + 1.5| = 2 - 3 = -1

|0.5*x + 1.5| = 0.5

0.5*x + 1.5 = 0.5

0.5*x = 0.5 - 1.5 = -1

0.5 = -1/x

Then we have x = -2

To get the other solution we need to remember that an absolute value equation can be written as:

|x - a| = b

or:

(x - a) = b

(x - a) = -b

Then the other solution to our equation comes from:

|0.5*x + 1.5| = 0.5

(0.5*x + 1.5) = -0.5

0.5*x = -0.5 - 1.5 = -2

x = -2/0.5 = -4

The other solution is x = -4

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Answer:

The standard form of the equation is y = -x/2 -2

Step-by-step explanation:

The standard form of equation of this line is expressing the line in the form;

y = mx + c

So let’s make a rearrangement to what we have at hand;

y + 7 = -1/2(x-10)

2(y + 7) = -1(x-10)

2y + 14 = -x + 10

2y = -x + 10 -14

2y = -x -4

divide through by 2

y = -x/2 -2

Answer:

here is your answer

Answer:hey guys just saying its 1/52

Step-by-step explanation:

Answer:

The tower is 73.4 m tall

Step-by-step explanation:

The height of the pole = 2.5 m

The shadow cast by the pole = 1.72 m

Shadow cast by tower = 50.5 m

To find the height of the tower, we proceed by finding the angle of elevation, θ, of the light source casting the shadows as follows;

[tex]Tan\theta =\dfrac{Opposite \ side \ to\ angle \ of \ elevation}{Adjacent\ side \ to\ angle \ of \ elevation} = \dfrac{Height \ of \ pole }{Length \ of \ shadow} =\dfrac{2.5 }{1.72}[/tex]

[tex]\theta = tan ^{-1} \left (\dfrac{2.5 }{1.72} \right) = 55.47 ^{\circ}[/tex]

The same tanθ gives;

[tex]Tan\theta = \dfrac{Height \ of \ tower}{Length \ of \ tower \ shadow} =\dfrac{Height \ of \ tower }{50.5} = \dfrac{2.5}{1.72}[/tex]

Which gives;

[tex]{Height \ of \ tower } = {50.5} \times \dfrac{2.5}{1.72} = 73.4 \ m[/tex]

Answer:

A

Step-by-step explanation:

[tex]f(x) = 20 {e}^{x} [/tex]

The function that could have the graph shown is:

f(x) = 20[tex]e^x[/tex]

Option A is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The function:

f(x) = 20[tex]e^x[/tex]

If we graph this function we get a similar graph that is shown.

The coordinates of f(x) = 20 [tex]e^x[/tex] are:

To find the coordinates, we need to plug in different values of x into the function and calculate the corresponding y-values.

For example, when x = 0, we have:

f(0) = 20e^0 = 20(1) = 20

So one coordinate on the graph is (0, 20).

Similarly, when x = 1, we have:

f(1) = 20e^1 = 20e = 20(2.71828) ≈ 54.6

So another coordinate on the graph is (1, 54.6).

We can find more coordinates by plugging in other values of x and calculating the corresponding y-values.

Now,

As x increases, the function f(x) grows exponentially, meaning the y-values will increase very rapidly.

Thus,

The function f(x) = 20[tex]e^x[/tex] could have the graph shown.

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Answer:

8

Step-by-step explanation:

3x^2 - 4

Let x = 2

3 * 2^2 -4

Exponents first

3 *4 -4

Then multiply

12 -4

Now subtract

8

[tex]\text{Plug in and solve:}\\\\3(2)^2-4\\\\3(4)-4\\\\12-4\\\\8\\\\\boxed{\text{D). 8}}[/tex]

Answer:

6√5

Step-by-step explanation:

We have to solve the expression [tex]\sqrt{180}[/tex]

Break 180 into its factors which are in the perfect square form.

Since, 180 = 9 × 4 × 5

                 = 3² × 2² × 5

Therefore, [tex]\sqrt{180}=\sqrt{3^{2}\times 2^{2}\times 5}[/tex]

                           = [tex]\sqrt{3^2}\times \sqrt{2^{2}}\times \sqrt{5}[/tex] [Since [tex]\sqrt{ab}=\sqrt{a}\times \sqrt{b}[/tex]]

                           = 3 × 2 × √5

                           = 6√5

Therefore, solution of the given square root will be 6√5.

Answer:

[tex]z=5\left(\cos \left(\dfrac{3\pi}{2}\right)+i\sin \left(\dfrac{3\pi}{2}\right)\right)[/tex]

Step-by-step explanation:

If a complex number is z=a+ib, then the trigonometric form of complex number is

[tex]z=r(\cos \theta +i\sin \theta)[/tex]

where, [tex]r=\sqrt{a^2+b^2}[/tex] and [tex]\tan \theta=\dfrac{b}{a}[/tex], [tex]\theta[/tex] is called the argument of z, [tex]0\leq \theta\leq 2\pi[/tex].

The given complex number is -5i.

It can be rewritten as

[tex]z=0-5i[/tex]

Here, a=0 and b=-5. [tex]\theta[/tex] lies in 4th quadrant.

[tex]r=\sqrt{0^2+(-5)^2}=5[/tex]

[tex]\tan \theta=\dfrac{-5}{0}[/tex]

[tex]\tan \theta=\infty[/tex]

[tex]\theta=2\pi -\dfrac{\pi}{2}[/tex]    [tex][\because \text{In 4th quadrant }\theta=2\pi-\theta][/tex]

[tex]\theta=\dfrac{3\pi}{2}[/tex]

So, the trigonometric form is

[tex]z=5\left(\cos \left(\dfrac{3\pi}{2}\right)+i\sin \left(\dfrac{3\pi}{2}\right)\right)[/tex]

Answer:

in degrees the answer is 5 (cos 270 + i sin 270)

in radians the answer is 5 (cos (3pi/2) + i sin (3pi/2))

Step-by-step explanation:

Answer:

58.5

Step-by-step explanation:

Distance = rate * time

so if it's 4.5 hours:

Distance = 13 mph* 4.5 hours

= 58.5 miles

Answer:

-3

Step-by-step explanation:

[tex]F(x)=-\,(-x)\\f(-3)=-(-(-3))\\f(-3)=-3[/tex]

Answer: Rs 1820

Step-by-step explanation:

This is profit, thus is it a percentage increase of 4%. Thus, she sold the saree for 104% of what she bought it for, Rs 1750.  Thus, simply do 1.04*1750 to get 1820.

Hope it helps <3

Answer:

Step-by-step explanation:

Any non-parallel lines in the plane must intersect in one place; thus, there is one solution to the system of equations.