A frog (with webbed feet for sticking to a vertical surface) falls into a 6 ft deep hole with vertical sides. As the frog tries to escape, it is able to jump up 3 ft on a jump, but then slides back down 2 ft before it can jump again. If this continues, how many jumps will it take the frog to reach the top of the hole?

Answer:

The ratio for the surface areas is equal to 4

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

Let

z -----> the scale factor

In this problem

The scale factor is equal to

[tex]z=\frac{2}{1}[/tex] ----> the ratio of its corresponding radii or its corresponding altitudes

step 2

Find the ratio for the surface areas of the cones

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z -----> the scale factor

x ----> the surface area of the larger cone

y ----> the surface area of the smaller cone

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

we have

[tex]z=\frac{2}{1}[/tex]

substitute

[tex](\frac{2}{1})^{2}=\frac{x}{y}[/tex]

[tex]4=\frac{x}{y}[/tex]

The ratio for the surface areas is equal to 4

That means-----> The surface area of the larger cone is 4 times the surface area of the smaller cone

Answer:

The complex number z = -5 into its rectangular form

Step-by-step explanation:

* Lets revise the complex numbers

- If z = r(cos Ф ± i sin Ф), where r cos Ф is the real part and i r sin Ф is the

 imaginary part in the polar form

- The value of i = √(-1) ⇒ imaginary number

- Then z = a + bi , where a is the real part and bi is the imaginary part

  in the rectangular form

∴ a = r cos Ф and b = r sin Ф

* Lets solve the problem

∵ z = r (cos Ф ± i sin Ф)

∵ z = 5 (cos π + i sin π)

∴ The real part is 5 cos π

∴ The imaginary part is 5 sin π

- Lets find the values of cos π and sin π

∵ The angle of measure π is on the negative part of x axis at the

  point (-1 , 0)

∵ x = cos π and y = sin π

∴ cos π = -1  

∴ sin π = 0

∴ a = 5(-1) = -5

∴ b = 5(0) = 0

∴ z = -5 + i (0)

* The complex number z = -5 into its rectangular form

Answer:

(-5,0)

Step-by-step explanation:

just cuz

Answer:

$508.33

Step-by-step explanation:

If I bet $25 (And I win, of course), I will win:

If I win $61 per every $3 bet, then:

61/3 = x/25 ⇒ Solving for 'x':

61*25/3 = $508.33

Finally, if you bet $25 you will win $508.33.

Answer:

5 ft

Step-by-step explanation:

Let the height of the previous jump be represented by j.  Then 1.1j = 5.5 ft.

Dividing both sides by 1.1, we get j = 5 ft.  This was the height of the previous jump.

Answer:

5 ft

Step-by-step explanation:

The previous jumper jumped p

The new jumper jumped p*1.1 and that was 5.5 ft

1.1p = 5

Divide each side by 1.1

1.1p/1.1 = 5.5/1.1

p = 5

The previous jumper jumped 5 ft

Answer:

b = 2

Step-by-step explanation:

In order to find the value of b, we have to isolate b on one side of equation first

So,

[tex]3b+2(b-1)=8[/tex]

Multiplying 2 with b-1

[tex]3b+2b-2=8\\5b-2=8[/tex]

Adding 2 on both sides

[tex]5b-2+2=8+2\\5b=10[/tex]

Dividing by 5 on both sides

[tex]\frac{5b}{5}=\frac{10}{5} \\b=2[/tex]

So the value of b is 2 ..

ANSWER

The value of b is 2

EXPLANATION

The given linear equation in b is

[tex]3b + 2(b - 1) = 8[/tex]

We expand to get:

[tex]3b + 2b - 2= 8[/tex]

We now group similar terms to obtain:

[tex]3b + 2b = 8 + 2[/tex]

Combine the similar terms now to obtain:

[tex]5b = 10[/tex]

Divide both sides by 5 to get:

[tex]b = \frac{10}{5} [/tex]

This simplifies to:

[tex]b = 2[/tex]

Answer:

A = 3/5

Step-by-step explanation:

At the outset, the question doesn't give us a figure to refer to nor does it tell us if this is a right angled triangle. However we observe that both sin A and tan A have the numbers 3, 4 and 5. We recognize this to be consistent with  3-4-5 standard right angled triangle.

Hence we can guess that it is probably a right angled triangle, but we should do the following to confirm:

Knowning that for a right angled triangle,

sin A = opposite / hypotenuse = 4/5

tan A = opposite / adjacent = 4/3

From this we can surmise that

Opposite = 4

hypotenuse = 5

adjacent = 3

Assemble the triangle to see if this works (see attached). We can futher verify that 3-4-5 works using the Pythagorean theorem.

Now that we have determined that the triangle is a 3-4-5 right angled triangle,

cos A = adjacent / hypotenuse = 3/5

Answer:

A

Step-by-step explanation:

Answer:

[tex] 10\sqrt{5} - 4 \sqrt{10} [/tex]

Step-by-step explanation:

[tex] \sqrt{5} (10 - 4 \sqrt{2} )[/tex]

Multiply

[tex] \sqrt{5} [/tex]

with each term within the bracket

[tex] = \sqrt{5} + \times 10 - \sqrt{5} \times 4 \sqrt{2} [/tex]

[tex] = 10 \sqrt{5} - 4 \sqrt{10} [/tex]

Answer:

C

Step-by-step explanation:

Given 2 secants intersect a circle from a point outside the circle, then

The product of the external part and the entire part of one secant is equal to the product of the external part and the entire part of the other secant, that is

x(x + 10 + x) = 6(6 + 10 + x)

x(2x + 10) = 6(16 + x) ← distribute parenthesis on both sides

2x² + 10x = 96 + 6x ← subtract 96 + 6x from both sides

2x² + 4x - 96 = 0 ← in standard form

Divide through by 2

x² + 2x - 48 = 0 ← factor the left side

(x + 8)(x - 6) = 0

Equate each factor to zero and solve for x

x + 8 = 0 ⇒ x = - 8

x - 6 = 0 ⇒ x = 6

However x > 0 ⇒ x = 6 → C

Answer:

[tex]f(x) = 2 \times 2 + 3 \\ f(3) = 4 + 3 \\ 3f = 7 \\ f = \frac{7}{3} [/tex]

Answer:

The  answer is 15

Step-by-step explanation:

If ƒ (x ) = 2x 2 + 3, find ƒ (3).

2(3)^2 +3

6^2+3

= 15

Answer:

1 square meter = 10000 square centimeters.

Step-by-step explanation:

We know that 1 meter = 100 centimeters.

Then 1 square meter = ( 100 cm)(100 cm) = 10000 square centimeters.

Then:

1 square meter = 10000 square centimeters.

ANSWER

A. 1

D. 8

EXPLANATION

The vertical asymptote occurs at where the denominator of a rational function in its simplest form is equal to zero.

The rational function given is

[tex]p(x) = \frac{9}{(x - 1)(x - 8)} [/tex]

This rational function is in it's simplest form.

The vertical asymptotes occurs at

[tex](x - 1)(x - 8) = 0[/tex]

By the zero product principle, we must have either

[tex](x - 1) = 0 \: \: or \: \: (x - 8) = 0[/tex]

This implies that

[tex]x =1\: \: or \: \: x = 8[/tex]

Options A and D are correct.

Answer:

2x + 1.

Step-by-step explanation:

y=x^2 + x + 1

Using the algebraic derivative rule, if y = ax^n then y' =  anx^(n-1) :

The derivative is 2x^(2 - 1) +  1x^(1-1)

= 2x^1 + x^0

= 2x + 1.

Answer:

y'(x) = 1 + 2 x

Step-by-step explanation:

Find the derivative of the following via implicit differentiation:

d/dx(y) = d/dx(1 + x + x^2)

Using the chain rule, d/dx(y) = ( dy(u))/( du) ( du)/( dx), where u = x and d/( du)(y(u)) = y'(u):

d/dx(x) y'(x) = d/dx(1 + x + x^2)

The derivative of x is 1:

1 y'(x) = d/dx(1 + x + x^2)

Differentiate the sum term by term:

y'(x) = d/dx(1) + d/dx(x) + d/dx(x^2)

The derivative of 1 is zero:

y'(x) = d/dx(x) + d/dx(x^2) + 0

Simplify the expression:

y'(x) = d/dx(x) + d/dx(x^2)

The derivative of x is 1:

y'(x) = d/dx(x^2) + 1

Use the power rule, d/dx(x^n) = n x^(n - 1), where n = 2.

d/dx(x^2) = 2 x:

Answer:  y'(x) = 1 + 2 x

Answer:

The correct answer is : DCQ ( angle) = DCE (angle)

Answer:   DCQ=DCE

Step-by-step explanation:

Answer: FIrst option.

Step-by-step explanation:

We need to remember that a tangent is a line that touches a circle at one point. This point is the "Point of tangency".

We can observe in the figure that the line "s" touches the circle A at a point identified as "J" and it also touches the circle B at a point identified as "K". Therefore, we can make the following conclusion:

The point of tangency of line "s" to circle B is: The point K.

This matches with the first option.

Answer:

6/10 but can be reduced to 3/5

Step-by-step explanation:

take every number exept red add them toget her and theres your answer.

The probability that it is not red is 0.6.

Given: A bag contains 10 marbles.

Number of red marbles = 4

Number of blue marbles = 3

Number of white marbles = 2

Number of yellow marble = 1

A marble is drawn at random.

We have to find the probability that the marble is not red.

Hence, the marble can be blue, white and yellow.

∴ Apart from red marbles there are total of 6 marbles in the bag.

⇒ Total favorable outcomes = 6

⇒ Total number of outcomes = 10

Probability = (Total number of favorable outcomes) / (Total number of outcomes)

⇒ Probability = 6/10

⇒ Probability = 0.6

Therefore, the probability that it is not red is 0.6.

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Answer:

See below.

Step-by-step explanation:

If they were similar corresponding sides would be in the same ratio.

Testing: 5/4 = 1.25

8/6 = 4/3 = 1.333...

They are not in the same ratio so  they are not similar.

Two figures are similar if their corresponding angles are congruent and their corresponding side lengths are proportional. We can determine if two figures are similar by comparing the ratios of their corresponding side lengths.

Determining whether two figures are similar involves a thorough examination of their corresponding angles and side lengths. Two figures are considered similar if their corresponding angles are congruent (equal) and their corresponding sides are in proportion, meaning that the ratios of the lengths of corresponding sides are the same throughout the figures.

First, we examine the angles. If all corresponding angles in the two figures are equal, then it's a strong indication of similarity. Similar figures have the same shape, and equal angles ensure that the shapes are the same when scaled up or down.

Next, we analyze the side lengths. For figures to be similar, the ratios of corresponding side lengths must be constant. This means that if you were to take any two sides from the first figure and divide their lengths, and then do the same for the corresponding sides in the second figure, the ratios should be equal.

In summary, similarity between two figures is established by the equality of corresponding angles and the constancy of ratios between corresponding side lengths. If both conditions are met, the figures are indeed similar, which means they have the same shape, and one can be obtained from the other through uniform scaling (enlarging or shrinking).

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Answer:

its A

Step-by-step explanation:

you do 28 x 66 :)

The golf course can provide water for approximately 89,610 families of four.

To find out how many families of four the golf course can provide water for, we need to compare the average water usage of the golf course with the average water usage of a family of four.

The golf course uses an average of 80 million gallons of water daily for irrigation.

To convert this to gallons per year, we multiply by 365:

80 million gallons/day * 365 days/year = 29.2 billion gallons/year.

Now, we divide the total water usage of the golf course by the water usage of one family of four:

29.2 billion gallons/year / 325,851 gallons/year = approximately 89,610 families of four.

The golf course can therefore provide water for approximately 89,610 families of four.

Answer:

q = ± 5[tex]\sqrt{5}[/tex]

Step-by-step explanation:

Given

q² - 125 = 0 ( add 125 to both sides )

q² = 125 ( take the square root of both sides )

q = ± [tex]\sqrt{125}[/tex]

  = ± [tex]\sqrt{25(5)}[/tex]

  = ± [tex]\sqrt{25}[/tex] × [tex]\sqrt{5}[/tex]

  = ± 5[tex]\sqrt{5}[/tex]

Answer:

Roots are [tex]q=5\sqrt{5},-5\sqrt{5}[/tex]

Step-by-step explanation:

Given : Function [tex]f(q)=q^2-125[/tex]

To find : Which are the roots of the quadratic function ?

Solution :

To find the roots equate the function to zero.

[tex]q^2-125=0[/tex]

Add 125 both side,

[tex]q^2=125[/tex]

Taking root both side,

[tex]q=\pm \sqrt{125}[/tex]

[tex]q=\pm \sqrt{5\times 5\times 5}[/tex]

[tex]q=\pm 5\sqrt{5}[/tex]

Therefore, roots are [tex]q=5\sqrt{5},-5\sqrt{5}[/tex]

Answer:

a = -2 , b = -8

Step-by-step explanation:

* Lets talk about the solution of the linear equations

- There are three types of the solutions of the system of linear equations

# If the two lines intersect each other, then there is one solution

- The equations are ax+ by = c , dx + ey = f

# If the two lines parallel to each other, then there is no solution

- The equations are ax+ by = c , ax + by = d in its simplest form ,

  where a is the coefficient of x , b is the coefficient of y and

  c , d are the numerical terms

# If the two lines coincide (over each other), then there are infinite

   solutions

- The equations are ax+ by = c , ax + by = c in its simplest form, where

  a is the coefficient of x , b is the coefficient of y and c is the

  numerical term

* Lets solve the problem

∵ The system of equation is:

   ax - y = 8 ⇒ (1)

   2x + y = b ⇒ (2)

∵ The system create infinitely many solutions

∴ The lines are coincide

- The equations must be equal, then multiply equation(1) or (2) by -1 to

  make the coefficient of y in the two equations equal

∴ -ax + y = -8

∴ 2x + y = b

∵ Their coefficients of x are equal

∵ Their coefficients of y are equal

∵ Their numerical terms are equal

∵ The coefficient of x in equation (1) is -a and in equation (2) is 2

∴ -a = 2 ⇒ multiply both sides by -1

∴ a = 2

∵ The numerical term in equation (1) is -8 and in equation (2) is b

∴ b = -8

* The values for a and b will create infinitely many solutions are -2 , -8

It's not clear if this is a problem to solve or a problem to prove.  Let's see where it goes.

We note the cotangent half angle formula is

[tex]\cot x = \dfrac{ 1 + \cos 2x}{\sin 2x}[/tex]

The tangent and cotangent half angle is expressible in terms of the full angle without any ambiguity, so let's set b=a/4 so a=4b.  

It turns out to be true for all a (at least all a that don't make the any of the functions undefined).   So it's a problem to prove.

Here's the proof.  I actually did it from the bottom up, but it's better to present it this way as a proof.  

We start with the cosine double angle formula:

[tex]\cos 2b = 2\cos^2 b- 1[/tex]

Multipy both sides by sin b:

[tex]\sin b \cos 2b = 2 \sin b \cos^2 b - \sin b[/tex]

Sine double angle formula:

[tex]\sin b \cos 2b = \sin 2b \cos b- \sin b[/tex]

Add sin 2b to both sides:

[tex] \sin 2b+ \sin b\cos 2b = \sin 2b + \sin 2b \cos b - \sin b[/tex]

Divide by sin b sin 2b

[tex] \dfrac{1}{\sin b} + \dfrac{\cos 2b}{\sin 2b} = \dfrac{1 + \cos b}{\sin b} - \dfrac{1}{\sin 2b}[/tex]

Turn to cosecants and cotangents.  We use the cotangent half angle formula above.

[tex] \csc b + \cot 2b = \cot \frac b 2 - \csc 2b[/tex]

Substituting b=a/4:

[tex] \csc \frac a 4 + \cot \frac a 2 = \cot \frac a 8 - \csc \frac a 2 \quad\checkmark[/tex]

Answer:

x=-4, x=1

Step-by-step explanation:

[tex]x=\frac{-(-6)+\sqrt{(-6)^{2}-4(-2) 8 } }{2(-2)} : -4\\x=\frac{-(-6)-\sqrt{(-6)^{2} -4(-2) 8} }{2(-2)} : 1\\[/tex]

Answer:

(8,2)

Please make sure I interpreted your system correctly below.

x+2y=12

-x=-y-6

Step-by-step explanation:

I assume the system is

x+2y=12

-x=-y-6

-----------

I'm going to multiply both sides of equation 2 by -1 giving me

x+2y=12

x=y+6

I'm now going to plug equation 2 into equation 1.

(y+6)+2y=12   I replaced x with y+6 in the first equation

y+6+2y=12

3y+6=12

3y=6

y=2

So

x=y+6

x=2+6

x=8

The solution is (8,2)

Answer:

an = 8-3(n-1)

an = 11 - 3n

Step-by-step explanation:

This is an arithmetic sequence which is defined by

an = a1 + d(n-1)

where a1 is the first term of the sequence and d is the common difference

a1 = 8

d = a2-a1

d = 5-8 = -3

an = 8 + -3(n-1)

an = 8-3(n-1)

We can simplify this by distributing the -3

an = 8 -3n +3

an = 11 - 3n

Answer:

The second option.

Step-by-step explanation:

4^2 × 4^8

(4 × 4)(4 × 4 × 4 × 4 × 4 × 4 × 4 × 4)  = 4^10

                    Or

4^2 × 4^8

=4^2+8

4^10

When solve an exponential with the same constant, you ga no problem. Just take one of those and and the exponent, you are good to go.

Please mark as brainliest.

Answer:it’s actually 3(x+2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\text{If}\ f(-x)=f(x)\ \text{then}\ f(x)\ \text{is an even function.}\\\\\text{If}\ f(-x)=-f(x)\ \text{then}\ f(x)\ \text{is an odd function.}[/tex]

======================================================

[tex]f(x)=-3x^4+7x^2\\\\f(-x)=-3(-x)^4+7(-x)^2=-3x^4+7x^2\\\\f(-x)=f(x)[/tex]

The function f(x) = -3x⁴ + 7x² is an even function because f(-x) = f(x) =  -3x⁴ + 7x²

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

f(x) = -3x⁴ + 7x²

To check whether the function is odd or even, plug x → -x in the function:

f(-x) = -3(-x)⁴ + 7(-x)²

f(-x ) = -3x⁴ + 7x²

f(-x) = f(x)

The function is even.

Thus, the function f(x) = -3x⁴ + 7x² is an even function because f(-x) = f(x) =  -3x⁴ + 7x²

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Answer:

$0.25/lb

Step-by-step explanation:

Convert 1 lb to 16 oz mentally.  Then the unit cost of the berries is

$4.00

------------ = $0.25/lb

16 oz