A geometric sequence has these properties.


What is the 7th term of this sequence?

The inverse of the function is; f⁻¹(x) = - 15 ± √(x + 225)

We have been given a quadratic function f(x) =  x(x + 30) and we need to restrict the domain such that it becomes a one to one function.

Now, the given function can also be written in vertex form as;

f(x) = (x + 15)² - 225

We know that vertex of this quadratic function occurs at (-15, -225).

Further, we know that range of this function is (-225, ∞).

If we restrict the domain of this function to either (-∞, -225) or (-225, ∞) , it will become one to one function.

Let us know find its inverse;

y =  (x + 15)² - 225

Upon interchanging x and y, we get:

x =  (y + 15)² - 225

Solving for y gives;

y = - 15 ± √(x + 225)

Thus, the inverse of the function is;

f⁻¹(x) = - 15 ± √(x + 225)

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Answer is

(a) She can buy 7 packages of plain coffee or 5 packages of coffee.

(b) f = [tex]\frac{T- 5.50 p}{7}[/tex]

(c) she can buy 3 packages of  flavoured coffee

(a) she spent on coffee is $ 40

amount of money she spends on coffee is 5.50

then, packages of plain coffee = [tex]\frac{40}{5.50}[/tex] ≈ 7.2

      so she buy 7 packages of plain coffee.

she spent on coffee is $ 40  and amount spends on flavoured coffee is 7

then , packages of flavoured coffee = [tex]\frac{40}{7}[/tex] ≈ 5.7

so she can buy 5 packages of flavoured coffee.

(b)According to question ,

T = 5.50 + 7f

so 7f = T - 5.50

then , f = [tex]\frac{T - 5.50}{7}[/tex]

(c) we get the value of f = [tex]\frac{T - 5.50}{7}[/tex]

given that , f is equal to 3

then,  f = [tex]\frac{T - 5.50}{7}[/tex]

           =   [tex]\frac{T - 5.50}{7}[/tex]×3

we get   =  [tex]\frac{T - 16.5}{7}[/tex]

when T is equal to 40

then , f = [tex]\frac{40 - 16.5}{7}[/tex] ≈ 3.35

so she can buy 3 packages of flavoured coffee.

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Answer: 14

207+14 = 221

221/17 = 13 (so the sum of 207 and 14 is divisible by 17)

Answer: The height of the tree is 35.4 ft.

Step-by-step explanation:

14.16/1.2 = 11.8

3 * 11.8 = 35.4

Answer:

1. acute

2. right

3. straight

Step-by-step explanation:

Answer:

b = 3

Step-by-step explanation:

We already know that x = 2, so just plug it back into the equation to solve for the variable b.

[tex]b(2(2)+6)=30[/tex]

[tex]b(4+6)=30[/tex]

[tex]10b=30[/tex]

[tex]b=3[/tex]

We can check this by plugging it back in:

[tex]3(2(2)+6)=30[/tex]

[tex]3(10)=30[/tex]

[tex]30=30[/tex]

This is the correct solution :)

The distance of point from the axis of rotation of the second hand is 8.2 cm.

Here,

A point located on the second hand of a large clock has a radial acceleration of 0.09 cm/s2.

We have to find the distance of point from the axis of rotation of the second hand.

What is Rotation?

The circular motion of an object around the circle is called Rotation.

Now,

Let us consider the equation for the centripetal acceleration given by;

[tex]a_{c} = \frac{v^{2} }{r}[/tex]

where, v is the velocity and r is the radius.

Now, the velocity can be expressed as;

[tex]v = wr = \frac{2\pi r}{T}[/tex]

where, ω is the angular velocity and T is the period.

Solving for the radius using these equations given as;

[tex]a_{c} = \frac{v^{2} }{r}\\\\v^{2} = a_{c} r\\\\(\frac{2\pi r}{T} )^2 = a_{c} r\\\\\frac{4\pi ^{2}r^{2} }{T^{2} } = a_{c} r\\\\r = \frac{T^{2} a_{c} }{4\pi ^{2} } \\\\r = \frac{(60s)^2(0.09 cm/s^2)}{4\pi ^{2} } \\\\r = 8.2 cm[/tex]

Hence, The distance of point from the axis of rotation of the second hand is 8.2 cm.

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Quadilateral ABCD is reflected over the x-axis. ---> (2, -4)

ABCD is translated 2 units right and 1 unit down. ---> (4, -5)

ABCD is dilated about the origin by a scale factor of 3. ---> (6, 12)

ABCD is rotated 180° clockwise about the origin. ---> (-2, 4)

Four sides, four vertices, and four angles make up a quadrilateral, which is a two-dimensional shape. Concave and convex are the two most common forms. Additionally, there are numerous subgroups of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombus, and squares.

quadrilaterals come in a variety of forms.

Trapezium.

Parallelogram.

Rectangle.

Rhombus.

Square.

Kite.

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The value of both the interior angles of the triangle is calculated as 70° and 35°.

If a triangle side is formed, the exterior angle made is equal to the sum of a 2 interior opposite angles.

Now, as per the given question;

The exterior angle of a triangle is 105°.

Let one of the interior angle is 'x'.

Then, the other interior angle is 35 degree less; x - 35°.

By the exterior angle property.

Sum of interior angles = exterior angle

x + x - 35° = 105°

2x = 105° + 35°

2x = 140°

x = 70°

The other interior angle is; x - 35°

= 70° - 35°

= 35°

Therefore, the two interior angles of the triangles are estimated as 70° and 35°.

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An example of a systematic random sample will be selecting 4 balls from a bag containing. The correct option is B.

A probability sampling technique called systematic sampling involves picking people from the population at regular intervals, such as every 15th person on a list of the population. This can mimic the advantages of straightforward random sampling if the population is arranged in random order.

Here we have two options a.) selecting all the students in a class of 30.

b.) Select 4 balls from a bag containing 30 balls.

Out of the two options, a systematic random sample will be Select 4 balls from a bag containing 30 balls.

Therefore, the correct option is B.

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The irreversible loss of an island from over 100 acres in size to less than 3 acres is an example of the irreversible nature of human change.

Human activity has lead to the change of Earth's climate in unimaginable ways over the last thousand years. Some of these changes are so significant that they are practically inevitable and irreversible.

Due to global warming, the planet's temperature is increasing gradually every year. This change in climate causes polar ice caps to melt and increases the water level.

Islands, which are pieces of land in between water bodies, are reducing in size due to this. The increased water level submerges some or all parts of an island. This is especially threatening for small islands.

This is not only dangerous for the human and wildlife population of these islands, but also for the general habitability. Due to frequent flooding, soil salinity increases and this makes it difficult to cultivate these islands.

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Testing for within × within and between × within moderation using random intercept cross-lagged panel models "allow measurement decomposition into between- & within components and have thus are becoming famous for testing developmental hypotheses."

Cross lagged panel design is a form of structural equation model in which data is gathered at a number of points in time. It is primarily used to assess causal relationships (which may be bi-directional) in a non-experimental setting, where variables are not controlled but simply recorded.

According to cross-lagged panel design analysis:

If we understand that X and Y are correlated but with us data shows no conclusive correlation (neither rX1Y2 or rX2Y1 are significantly different from zero), it is possible that our time lag was just too short (or too long) to enable causal influences to operate, and we need to redesign our experiment.

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Answer: the type of function is linear.

I hoped this helped!

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The percent of simple interest that the account has will be 7.2%.

From the information, Kehlani invests money in an account paying simple interest. No money is added or removed from the investment. To find the balance after a year, she multiplies her current balance by 1.072.

The percent of simple interest that the account has will be:

= 1.072 - 1

= 0.072

= 7.2%

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Answer:

-18

Step-by-step explanation:

x=???

First, we know that the number we are looking for is divisible by 3. So lets list so numbers that are divisible by 3:

all (+,-) 6,9,12,15,18,........

Second, since we know the answer has to be in the double digits from the list we can have only 3 possibles answers.

12÷3=4
4-4=0

-12÷3=-4
-4-4=-8

So 12 nor -12 cant be the answer

18÷3=6
6-4=2

-18÷3=-6
-6-4=-10

So, the answer to the problem is -18÷3-4=-10

Answer: The equation is true

Step-by-step explanation:

Since x=3 and y= 5

Substitute the values for x and y

y=2x-1

5=2(3)-1

5=6-1

5=5

⇒The equation is true

Answer:

X=3

Step-by-step explanation:

Remember to get all your variables on one side by doing the "Reverse function" etc...

Once youve got your variables on one side (and only 1 is remaining) you should get rid of whats BESIDE the variable by dividing it by *whatever it is thats beside the variable!* AND REMEMBER TO DO THIS ON BOTH SIDES OF THE EQUATION SO THAT THEYRE EQUAL!!

The point closest to -

A plane is a two-dimensional flat surface that can extend indefinitely. A plane would be the two-dimensional equivalent of a point with zero dimensions, a line with one dimension, and three-dimensional space.

         ax+by+cz+d=0,

         where minimum one number out of a, b, and c must be non-zero.

Now, as per the question;

A point (x, y, zdistance )'s from the yz plane is equal to |x|.

As a result, for small |x|, the point would be closest to the yz plane.

C does have the smallest among A, B, and C that is |x| = 2.

Thus, c point is closest to yz-plane.

If the point is in the xz-plane, after which y equals 0.

Only A has a y value of zero.

As a result, A is in the xz-plane.

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Answer: -8

Step-by-step explanation:

-2(2)-4 -> -4-4 = -8

Answer:23

Step-by-step explanation: take -15 and negate it which will set you at 15 then add 8 will put you at 23degrees

Answer:

[tex]f(x) = 12 + \frac34x[/tex]

Step-by-step explanation:

Hello!

Function notation simply means replacing the term y with f(x).

Given the equation: y = 3/4x + 12

The equation in function notation is [tex]f(x) = \frac34 x + 12[/tex].

The meaning of f is just the name of the function. x is the variable being used in the function. Therefore, it can also be written as g(y), s(d), or e(f), as long as the variable inside the parenthesis exists in the equation.

Suppose you see a number in the spot for the variable. In that case, you are replacing the variable in that equation to evaluate when the x-value is that number.

Interpreting this will tell you the value of y when x is 1. The y-value is 2.

[tex]\displaystyle\\Answer:\ x=\sqrt{2}\ \ \ \ \ x=-\sqrt{2}\ \ \ \ \ x=\frac{ln5}{2}[/tex]

Step-by-step explanation:

[tex]5x^2-x^2e^{2x}+2e^{2x}=10[/tex]

[tex]Let:\ x^2=t \ \ \ \ \ e^{2x}=v\\Hence,\\5t-tv+2v^2=10\\5t-tv+2v^2-10=10-10\\5t-tv-10+2v^2=0\\t(5-v)-2(5-v)=0\\(5-v)(t-2)=0\\5-v=0\\5-v+v=0+v\\5=v\\5=e^{2x}[/tex]

Prologarithmize both parts of the equation:

[tex]ln5=lne^{2x}\\ln5=2x*lne\\ln5=2x*1\\ln5=2x\\[/tex]

Divide both parts of the equation by 2:

[tex]\displaystyle\\x=\frac{ln5}{2}[/tex]

[tex]t-2=0\\t-2+2=0+2\\t=2\\x^2=2\\x=\sqrt{2} \\x=-\sqrt{2}[/tex]

Step-by-step explanation:

= -7ab² + 9a³b

= -7b × ab + 9a² × ab

= ab × (-7b + 9a²)

The Probability that no person is next to their partner is 104/105.

Probability of an event E represented by P(E) can be defined as (The number of favorable outcomes )/(Total number of outcomes).

Permutations is defined as arrangement of elements/objects in a particular way.

According to the question ,

8 people can be arranged in 8! ways = 40320ways

First let us find the probability that person is next to their partner.

4 couples can be arranged in 4! ways

and the couple itself can be arranged in 2! ways

Since there are 4 couples ,

Number of arrangement = [tex]4!(2!)^{4}[/tex]

=24x16

=384 ways

Probability that person is next to their partner = [tex]\frac{384}{40320} =\frac{1}{105}[/tex]

and the probability that no person is next to their partner is [tex]1-\frac{1}{105} =\frac{104}{105}[/tex].

Therefore , the probability that no person is next to their partner is [tex]\frac{104}{105}[/tex].

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Answer:11

Step-by-step explanation:

Answer:

fdsjfgdndgnxhñgjxgjxgjx

Answer:

[tex]49n^2-70n+25[/tex]

Step-by-step explanation:

Since one side of the square is (7n-5), the area of the square must be [tex](7n-5)^2[/tex]. Simplifying we get [tex]49n^2-70n+25[/tex].

Answer:

yo same

Step-by-step explanation:

ur lookin pretty shreksy

one on right is 2,-2 and one on left is -1,1

4 cm  is the height of the parallelogram.

What in mathematics is a parallelogram?

The area is always given by squared units and never by single units!

The area of a parallelogram is given by the equation

A = b * h

             b is the base length of the parallelogram

             h is the height of the parallelogram

And so, plugging in our given values, we get

24cm² = 6 cm . h

h = 24 cm/6cm

h = 4 cm

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The complete question is -

The area of a parallelogram is 24 centimeters and the base of the parallelogram is 6 centimeters. What is the height of the parallelogram?