What is the explicit formula for this geometric sequence

Answer:

16.2

Step-by-step explanation:

A trick to remember for right triangles is SOH-CAH-TOA:

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent

Here, we have the side adjacent to the angle and the hypotenuse.  So we should use cosine.

cos 22° = 15 / x

x = 15 / cos 22°

x ≈ 16.2

Answer:

Step-by-step explanation:

multiply the top and bottom of the fraction by 15x

2*15x

=======

5*15x

30x

====

75x

Volume of a sphere is defined:

[tex]V=\frac{4\pi r}{3}[/tex]

Solve for radius.

[tex]3V=4\pi r\Longrightarrow r=\frac{3V}{4\pi}[/tex]

Now put in the data.

[tex]

r=\frac{3\cdot2143.572}{4\cdot3.14} \\ \\

r=\frac{6430.716}{12.56}\approx\boxed{30010}

[/tex]

The radius of the sphere is 30010ft.

Hope this helps.

r3t40

Answer:

Final answer is [tex]\frac{5}{(x+1)}[/tex].

Step-by-step explanation:

Given expression is [tex]\frac{5\left(x-1\right)}{(x+1)(x-1)}[/tex] where x doesn’t equal 1 or -1. Now we need to find about which of the given choices is equal to the given rational expression. Choices are missing but we can still solve this problem.

[tex]\frac{5\left(x-1\right)}{(x+1)(x-1)}[/tex]

cancel out common factors from top and bottom.

[tex]=\frac{5}{(x+1)}[/tex]

Hence final answer is [tex]\frac{5}{(x+1)}[/tex].

Answer:

5/x+1

Step-by-step explanation:

ANSWER

[tex]log( \frac{14}{3} ) + log( \frac{11}{5} ) - log( \frac{22}{15} ) =\log 7[/tex]

EXPLANATION

The given logarithmic expression is:

[tex] log( \frac{14}{3} ) + log( \frac{11}{5} ) - log( \frac{22}{15} ) [/tex]

We apply the product rule to the first two terms to get:

[tex]log( \frac{14}{3} \times \frac{11}{5} ) - log( \frac{22}{15} ) [/tex]

We the apply the quotient rule:

[tex]log( \frac{14}{3} \times \frac{11}{5} \div \frac{22}{15} ) [/tex]

[tex]log( \frac{14}{3} \times \frac{11}{5} \times \frac{15}{22} ) [/tex]

We cancel out the common factors and simplify to obtain:

[tex]log( 7 ) [/tex]

Required Knowledge.

log(ab) =log(a) + log(b)

log(a/b) = log(a) -log(b)

SOLUTION

log(14/3) +log(11/5) -log(22/15)

=log((14/3)×(11/5)) -log(22/15)

=log(154/15) -log(22/15

=log( (154/15) ÷ (22/15) )

=log( (154/15) × (15/22) )

=log(154/22)

=log(77/11)

=log(7)

Hence 7 is your answer...

Hope it helps...

Regards;

Leukonov/Olegion.

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]x^{2} +y=7[/tex]

[tex]y=-x^{2}+7[/tex] ----> equation A

This is the equation of a vertical parabola open downward

The vertex is the point (0,7)

[tex]x^{2} +y^{2}=49[/tex]

[tex]x^{2} +y^{2}=7^{2}[/tex] ----> equation B

This is the equation of a circle with center at (0,0) and radius equal to 7 units

The y-intercepts of the circle are the points (0,7) and (0,-7)

therefore

The graph in the attached figure

Answer:

B

Step-by-step explanation:

The van needs 21 gallons of gas. Take 16/(320/420)

The van will need 21 gallons of gas to travel 420 miles, based on its fuel efficiency of 20 miles per gallon.

The student is asking how many gallons of gas a van needs to travel 420 miles, given that it travels 320 miles on 16 gallons of gas.

First, we calculate the van's fuel efficiency which is found by diving the miles traveled by the gallons of gas used. For the van in the question:

Fuel efficiency: 320 miles / 16 gallons = 20 miles per gallon (MPG)

Next, we can use this fuel efficiency to find out how many gallons will be needed for 420 miles. We divide the total miles by the MPG:

Gallons needed: 420 miles / 20 MPG = 21 gallons

Therefore, the van will need 21 gallons of gas to travel 420 miles.

Answer:

8800 yards

Step-by-step explanation:

1760 feet * 5  = 8800 yards

Answer:

8800

Step-by-step explanation:

I googled it

Answer:

its 42%

Step-by-step explanation:

the answer above is wrong

The inflation rate in the car is 42%.

Inflation Rate (CPI, annual variation in %) Inflation refers to an overall increase in the Consumer Price Index (CPI), which is a weighted average of prices for different goods.

Sarah bought a car last year to drive back and forth to work after she spent $1,098 on gas this year she spent $1,562.

Based on the above information, the calculation is as follows:

[tex]\rm Inflation \ rate=\dfrac{1562-1098}{1098}\\\\ Inflation \ rate=\dfrac{464}{1098}\\\\ Inflation \ rate=0.42\\\\ Inflation \ rate=0.42 \times 100\\\\ Inflation \ rate= 42 \ percent[/tex]

Hence, the inflation rate of the car is 42%.

Learn more about the inflation rate here;

https://brainly.com/question/25892558

#SPJ2

Answer:

a. By Pythagorean Theorem: [tex]ET=\sqrt{113}[/tex]

b. By Distance Formula: [tex]ET=\sqrt{113}[/tex]

Step-by-step explanation:

The given rectangle has vertices R(-3,-4), E(-3, 4), C(4,4), and T(4-4).

The points have been plotted on the coordinate plane as shown in the attachment.

a. Using the Pythagoras Theorem;

[tex]ET^2=EC^2+CT^2[/tex]

We substitute the side lengths to obtain:

[tex]ET^2=7^2+8^2[/tex]

[tex]ET^2=49+64[/tex]

[tex]ET^2=113[/tex]

Take positive square root to obtain:

[tex]ET=\sqrt{113}[/tex]

b. The distance formula is given by:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The endpoints of ET are at E(-3,4) and T(4,-4).

Using the distance formula;

[tex]ET=\sqrt{(4--3)^2+(-4-4)^2}[/tex]

[tex]ET=\sqrt{(7)^2+(-8)^2}[/tex]

[tex]ET=\sqrt{49+64}[/tex]

[tex]ET=\sqrt{113}[/tex]

(3,6) I think is the answer

Answer:

I believe it's (19,10)

Answer:

See below

Step-by-step explanation:

In order to solve for the length of a cube, you must already know its width, depth, and volume. Then, arrange the problem as an equation:

Length x width x depth = volume

Next, solve the equation for the length. For example, If I have a cube with a width of 5ft, a depth of 5ft, and a volume of 50ft^3, I will solve for the length by arranging the values to fit the formula shown above:

L x 5 x 5 = 50

Then I'll multiply the values on the left:

25L = 50

And, finally, I will divide either side by 25, which leaves the answer:

L = 2ft

Hope this helps! Feel free to ask questions!

Answer:

Rotated about an axis

Step-by-step explanation:

APEX

Reflectional symmetry is the quality a design has if it maintains all characteristics when it is (blank) lying in its plane Option: A) rotated about an axis.

Consider a plane. Consider a design or shape on that plane. Now consider an axis.

If we think of that axis as a mirror, and on the opposite side of that axis create the image of the considered shape, then if the shape's image looks exactly as the shape itself, then that shape is called to have a reflectional symmetry.

Instead of that mirror intuition, we can also think that we sort of rotated that image about that considered axis, and after half rotation, the figure is again onto its plane. If that rotated figure looks alike to the initial figure, then that figure has rotational symmetry.

Thus, reflectional symmetry is the quality a design has if it maintains all characteristics when it is (blank) lying in its plane Option: A) rotated about an axis.

Learn more about symmetry here:

https://brainly.com/question/7783612

Answer:

4.4 miles is the height

Step-by-step explanation:

Area = base x height

22= 5 x 4.4

Answer:22=5*4.4

Step-by-step explanation:

the base is 5 miles so you do 22 / 5 and it gives you 4.4 for the height

Answer:

Step-by-step explanation:

[tex]1.\\\bold{YES}\\A.\ (x+5)^2=49\iff x+5=\pm\sqrt{49}\\\\x+5=\pm7\qquad\text{subtract 5 from both sides}\\\\x=-13\in\mathbb{Q}\ or\ x=2\in\mathbb{Q}\\\\C.\ x^2=81\iff x=\pm\sqrt{81}\\\\x=\pm9\in\mathbb{Q}\\\\\bold{NOT}\\B.\ x^2=12\to x=\pm\sqrt{12}\notin\mathbb{Q}\\D.\ (x-1)^2=20\to x-1=\pm\sqrt{20}\notin\mathbb{Q}[/tex]

[tex]\bold{YES}\\C.\\x^2+12x+36=0\\\\x^2+2(x)(6)+6^2=0\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+6)^2=0\iff x+6=0\qquad\text{subtract 6 from both sides}\\\\x=-6\\\\\bold{NOT}\\A.\\3x^2+x-2=0\\3x^2+3x-2x-2=0\\3x(x+1)-2(x+1)=0\\(x+1)(3x-2)=0\iff x+1=0\ \vee\ 3x-2=0\\\text{two different solutions}\\B.\\x^2-15x+36=0\\x^2-12x-3x+36=0\\x(x-12)-3(x-12)=0\\(x-12)(x-3)=0\iff x-12=0\ \vee\ x-3=0\\\text{two different solutions}[/tex]

Answer:

The answer is -9,9 Its funny cuz I just did this problem on Khan academy

Step-by-step explanation:

Can I get brainliest

-9,9 should be the answer

For this case we have to find the inverse of a function, follow the steps below:

Then, it is observed that of option 3:

[tex]f (x) = 4x[/tex]

Replace [tex]f (x)[/tex]with y:

[tex]y = 4x[/tex]

We exchange the variables:

[tex]x = 4y[/tex]

We solve for "y":

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

Finally we change y by [tex]f ^ {- 1} (x):[/tex]

[tex]f ^ {- 1} (x) = \frac {x} {4}[/tex]

Answer:

The correct option is C

Answer:

It's the third choice.

Step-by-step explanation:

f(x) = y = 4x

x = 1/4 y

Change the y to x:

so the inverse g(x) = 1/4 x.

1400 answer choice B

Answer:

[tex]\frac{\cos\left(2x\right)+\cos\left(4x\right)}{\sin\left(2x\right)-\sin\left(4x\right)}=-\cot\left(x\right)[/tex]

Step-by-step explanation:

[tex]\frac{\cos\left(2x\right)+\cos\left(4x\right)}{\sin\left(2x\right)-\sin\left(4x\right)}[/tex]

Apply formula:

[tex]\cos\left(A\right)+\cos\left(B\right)=2\cdot\cos\left(\frac{A+B}{2}\right)\cdot\cos\left(\frac{A-B}{2}\right)[/tex] and

[tex]\sin\left(A\right)-\sin\left(B\right)=2\cdot\cos\left(\frac{A+B}{2}\right)\cdot\sin\left(\frac{A-B}{2}\right)[/tex]

We get:

[tex]=\frac{2\cdot\cos\left(\frac{2x+4x}{2}\right)\cdot\cos\left(\frac{2x-4x}{2}\right)}{2\cdot\cos\left(\frac{2x+4x}{2}\right)\cdot\sin\left(\frac{2x-4x}{2}\right)}[/tex]

[tex]=\frac{\cos\left(\frac{2x-4x}{2}\right)}{\sin\left(\frac{2x-4x}{2}\right)}[/tex]

[tex]=\frac{\cos\left(\frac{-2x}{2}\right)}{\sin\left(-\frac{2x}{2}\right)}[/tex]

[tex]=\frac{\cos\left(-x\right)}{\sin\left(-x\right)}[/tex]

[tex]=\frac{\cos\left(x\right)}{-\sin\left(x\right)}[/tex]

[tex]=-\cot\left(x\right)[/tex]

Hence final answer is

[tex]\frac{\cos\left(2x\right)+\cos\left(4x\right)}{\sin\left(2x\right)-\sin\left(4x\right)}=-\cot\left(x\right)[/tex]

I’m not sure if it’s right try it

For this case we propose a rule of three:

£ 899 ----------------> 100%

x ----------------------> 20%

Where "x" represents the amount of money corresponding to the VAT.

[tex]x = \frac {20 * 899} {100}\\x = 179.8[/tex]

So, the VAT is £ 179.8

ANswer:

The purchse price of VAT is £ 179.8

I assume one of the four options is the correct answer...

Remember that in order to determine if a function rule is correct, you should be able to plug an x value into the equation and get the corresponding y value as the answer.

The first option, f(x) = x + 1, is correct!

Answer:  The correct option is (A) f(x) = x + 1.

Step-by-step explanation: We are given to write a function rule for the following table :

x              -1           0           1             2

f(x)           0           1            2            3

From the given table, we see that

[tex]f(-1)=0=-1+1,\\\\f(0)=1=0+1,\\\\f(1)=2=1+1,\\\\f(2)=3=2+1.[/tex]

Therefore, the required function rule is given by

[tex]f(x)=x+1.[/tex]

Thus, option (A) is CORRECT.

Answer:

The distance between the Earth's surface and the upper edge of the Earth's atmosphere would be Q - V.

The distance from the Sun to the Earth is Q. The distance from the Sun to the upper edge of the atmosphere is V. If you subtract V from Q, the remaining distance is that of the Earth's atmosphere.  Q - V = the atmosphere

Step-by-step explanation:

Answer:

Choice B

Step-by-step explanation:

I just did the question on khan

Answer:

120 miles

Step-by-step explanation:

we know that

The speed is equal to the distance divided by the time

Let

s------> the speed in mph

d-----> the distance in miles

t -----> the time in hours

s=d/t

solve for the distance

d=s*t

It will take Adam four hours to drive to Disney Park

s=x mph

t=4 h

substitute

d=4x -----> equation A

It will take Adam 2.5 times less time if driving 45 mph faster

so

s=(x+45) mph

t=4/2.5=1.6 h

substitute

d=1.6(x+45) -----> equation B

equate equation A and equation B

4x=1.6(x+45)

Solve for x

4x=1.6x+72

4x-1.6x=72

2.4x=72

x=30 mph

Find the distance d

d=4x -----> d=4(30)=120 miles

Answer:

120 miles

Step-by-step explanation:

The x-intercepts are: (-1,0) and (3,0).

The y-intercept is: (0,-9).

Hope this helps!

Answer:

15/p and -3

Step-by-step explanation:

4(px+1)=64

Distribute 4: 4px + 4=64

Subtract 4 from both sides : 4px+4-4=64-4

Divide by 4p: 4px/4p=60/4p

x=15/p

Answer:

Option B

same-side interior angles

Step-by-step explanation:

Given in the question, two non parallel lines a and b.

The area between lines a and b is called the interior of the two lines.

Angles 4 and 5 are same-side interior angles.

Other options are wrong because:

The area which not between lines a and b is called the exterior

Corresponding angles are on same side of the traversal line.

Example

Angles 1 and 5

Alternate interior angles are in interior region but in opposite side of traversal line.

Example

Angles 3 and 5

The coordinates after the reflection of the given graph are A'(1,-4), B'(2,-1), and C'(3,-3). The correct graph that shows the reflection is D).

Given :

The graph given has points -- (1,4), (2,1), and (3,3).

The following steps can be used in order to determine the correct figure that shows the reflection of the given graph:

Step 1 - According to the given graph. the points are A(1,4), B(2,1), and C(3,3).

Step 2 - According to the given data, take the reflection of the given graph.

Step 3 - So, after reflection about the x-axis, the points become A'(1,-4), B'(2,-1), and C'(3,-3).

Therefore, the correct option is D).

For more information, refer to the link given below:

https://brainly.com/question/1878272

Check the picture below.

make sure your calculator is in Degree mode.

Answer:

See below.

Step-by-step explanation:

If we translate h(x) to the left it will override  line d(x) because  the slope of both lines is the same. H(x) will need to move 4 units to the left to do this (because the slope =  2 = 8/4).

To represent the same function as d(x), the linear function h(x) with a slope of 2 should be translated 4 units to the left, resulting in the function h(x+4). This horizontal shift increases the value of y by 8 units, which equates to the vertical shift applied to create d(x).

To translate the linear function h(x) to result in the same function as d(x), which is h(x) translated 8 units up, we need to consider the properties of linear functions and translations. Since h(x) has a slope of 2, we can denote it as h(x) = 2x + b, where b is the y-intercept. When h(x) is translated 8 units up to become d(x), the new function is d(x) = h(x) + 8 = 2x + b + 8. To counteract this vertical shift with a horizontal translation and maintain the same function as d(x), we must shift h(x) in such a way that every x value for h(x) yields the same y-value for d(x) after the translation.

To achieve this, we would have to shift h(x) to the left by 4 units, resulting in the function h(x+4). This is because for every 1 unit increase in x, the value of h(x) increases by 2 units (the slope), so a shift of 4 units left would increase y by 8 units, which is the same effect as the vertical translation applied to obtain d(x). Thus, h(x+4) = 2(x+4) + b = 2x + 8 + b, which aligns with d(x). This explanation confirms that the properties of linear functions and translation mechanics allow us to equate d(x) with a horizontally translated version of h(x).