How to solve exponential equations with constant prime numbers or number whos fractors are primes?
Example: 3^x+2+3^x−3=244

\(xy-3x^2+2x\)

Factor by pulling out the x-term.

\(x(y-3x+2)\)

Arrange as we get -

\(x(-3x+y+2)\)       ----------> Answer

Answer:

8000 and 12000 respectively

Step-by-step explanation:

Let the amount invested in first account be x and y be the amount invested in the second account.

ATQ, x+y=20000 and 1280=(7/100)*x+(6/100)*y

x=8000 and y=12000.

Answer:

a

Step-by-step explanation:

it is a because the shape is moving to the side

Answer:

The answer is B!

The angle PMR in the quadrilateral is 32 degrees.

The angle PMR can be found as follows;

The line AP is an angle bisector of angle RPM. Therefore, the following relationships are formed.

∠RPM ≅ ∠WPM

Hence,

∠RPM ≅ ∠WPM = 58 degrees

Therefore,

∠WPM = 58 degrees

∠PWM = 90 degrees

Let's find ∠PMR as follows

∠PMR = 180 - 90 - 58

∠PMR = 90 - 58

∠PMR  = 32 degrees

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Answer:

(y-9)8

Step-by-step explanation:

you first solve 8-9, and then multiply is by 8.

Eight times the difference of y and nine will be 8(y - 9).

It should be noted that eight times the difference of y and nine simply means that one has to subtract 9 from y and then multiply the difference by 8.

Therefore, eight times the difference of y and nine will be 8(y - 9).

In conclusion, the correct option is 8(y - 9).

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Answer:

41 meters

Step-by-step explanation:

\(\frac{31}{64}\) = \(\frac{19.8}{x}\)

31x = (19.8)(64)

31x = 1267.2  Divide both sides by 31 and round

x = 41

Answer:

The answer would be 7

Step-by-step explanation:

The equivalent value of the logarithmic equation is x = 7/3

The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm

The properties of Logarithm are :

log A + log B = log AB

log A − log B = log A/B

log Aⁿ = n log A

Given data ,

Let the logarithmic equation be represented as A

Now , the value of A is

A = log ( 14/3 ) + log ( 11/5 ) - log ( 22/5 )

On simplifying , we get

From the properties of logarithm , we get

log A + log B = log AB

log A − log B = log A/B

So , A = log (14/3) + log (11/5) - log (22/5) = log [(14/3) × (11/5) / (22/5)]

A = log [(14/3) × (11/5) × (5/22)]

A = log ( 14/3 /2 )

A = log ( 7/3 )

Hence , the logarithmic equation is solved

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Answer:

This is because it is easier this way.

You avoid the problem of putting an element in one set and then realizing that the element also belongs to another set, then you must erase something in order to put the element in both sets. Starting with the intersection allows you to know where will be each set in the diagram, and in this way, the diagram should end up being more readable or "clean".

This may seem small, but being "clean" when doing math, will allow you to have an easier time dealing with a lot of problems. And also will be easier for other people when reading your equations and such.

We know that

• African country was about 20 million people, in 2003.

• Which is 2 million more than 4 times the population in 1950.

The option that is extraneous solution of

√-3x-2=x+2 is A. -6.

From the information given, taking square both sides

-3x - 2 = (x + 3)²

On applying identity   = a² + b² + 2ab

Then ,

-3x -2 =  x² + 2² + 2 * 2 *x

-3x -2 =  x² + 4 + 4x.

On adding both sides by 3x

-2 =  x² + 4 + 4x + 3x

-2 =  x² + 4 + 7x

On adding both sides by 2

0 =  x² + 4 + 7x + 2

On switching sides

x² +7x + 6 = 0

On Factoring

x² +6x + x + 6 = 0

x ( x+ 6 ) +1 (x +6 ) = 0

On grouping

( x +1) ( x +6) = 0

x = -1, -6.

An extraneous solution is a root of a transformed equation that is not a root of the original equation. Therefore, -6 is the extraneous solution.

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Complete question

Which of the following is an extraneous solution of sqrt(-3x-2)=x+2 a.-6 b.-1 c.1 d.6

Answer:

A. 3

B. 3/4

C. 1/4

Step-by-step explanation:

1/4 of 12 is 3

3 plus 6 is 9 and 9 is 3/4 of 12

12 minus nine is also three leaving the tank still a 1/4 tank empty

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

Explanation:

Highlight XY in the sequence XYZ. We've highlighted the first two letters.

This means that we'll need to highlight the first two letters of MNL to get MN.

XY pairs with its corresponding part MN.

Due to the congruent triangles, we know that XY = MN.

The diagram shows MN = 8. Due to substitution or the transitive property (they're similar ideas) we know that XY = 8 as well.

As you can see, the order of the letters is important so we can properly align the letters.

The given statement in the question , if a sequence of uniformly bounded functions uniformly converges then its limit function must also be uniformly bounded is true.

It is true that a sequence of uniformly convergent bounded functions must converge to a bounded function. A uniformly convergent series of unbounded functions is difficult to describe.

On the real line, for example, f n (x) = x converges uniformly to f (x) = x.

In mathematics, a family of bounded functions is said to be uniformly bounded if all of its members can have their boundaries defined by the same constant.

This constant is greater than or equal to the absolute value of any of the family's functions.

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From the statement we read the following equation:

We solve the equation for x doing the following steps:

Answer

x = 100

Yes, there is a difference in the shapes of the displacement-time graphs for uniform acceleration towards the positive direction, uniform acceleration towards the negative direction, uniform deceleration towards the positive direction, and uniform deceleration towards the negative direction.

Uniform acceleration towards the positive direction:

In this case, the object's velocity increases in the positive direction over time. The displacement-time graph will have a concave-upward shape, forming a curve that starts with a small slope and gradually becomes steeper as time progresses.

Uniform acceleration towards the negative direction:

Here, the object's velocity increases in the negative direction, meaning it accelerates in the opposite direction to its positive direction.

The displacement-time graph will have a concave-downward shape, forming a curve that starts with a steep slope and gradually becomes less steep as time progresses.

Uniform deceleration towards the positive direction:

In this scenario, the object's velocity decreases in the positive direction, but it still moves towards the positive direction.

The displacement-time graph will show a curve with a decreasing slope, forming a concave-downward shape, indicating that the object is slowing down.

Uniform deceleration towards the negative direction:

Here, the object's velocity decreases in the negative direction, opposing its initial direction.

The displacement-time graph will have a curve with a decreasing slope, forming a concave-upward shape, indicating that the object is slowing down but still moving in the negative direction.

In summary, the shapes of the displacement-time graphs differ based on the direction and type of acceleration (positive or negative) and whether the object is undergoing uniform acceleration or uniform deceleration. These differences can be observed through the concavity and slope of the graphs.

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Answer:

.33

Step-by-step explanation:

If you add the times the dice was rolled and landed on a number greater than four, you would get 108. Then, you would divide that by 330 and you get .327. Round that up and you get .33

Answer:

33? ig

Step-by-step explanation:

Answer:

i think this might be it? but most likely :) <3

Step-by-step explanation:

The Area of the shaded portion is: 72 square inches

The formula for the area of a triangle is given by the formula:

Area = ¹/₂ * base * height

Now, to get the area of the shaded portion, we will get the area of the larger triangle and subtract the area of the smaller one from it.

Thus:

Area of larger triangle = ¹/₂ *  17 * 13 = 110.5 square inches

Area of smaller triangle =  ¹/₂ * 11 * 7 = 38.5 square inches

Thus:

Area of shaded portion = 110.5 square inches - 38.5 square inches

Area of shaded portion = 72 square inches

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the dependent variable, as its name says it depends on the other variable

and the independent variable is the one that we can control or vary

the independent variable is the detergent because it is what we change or vary

and the dependent variable is the effect of the detergent since that is what we get

Answer:

a) (V)  = 904.78 of a sphere = 288pi diameter = 12

(V) = 1728cm^3 of a cube = face diagonal = 16.9cm

b) Difference Volume = 1728-904.78 = 823.22cm^3

Step-by-step explanation:

To find volume of an inscribed sphere within a square cube

We use 4 π/3 * r^3 for the equation

As Radius = 6 = 6cm this is the only thing plugged into the equation to create a division first then a multiplication square of radius and then a multiplication. 4pi /3 * 6^3

r^3 = 216

4pi/3 = 4.18

4.18 * 216 = 904.78

This means the answer is 288 pi cm^3.

Answer:

volume of gemstone = 905 cm^3

volume of empty space = 823 cm^3

Step-by-step explanation:

volume of cube = s^3, where s = length of edge

volume of sphere = (4/3)(pi)r^3, where r = radius of sphere

The cube has a 12-cm edge. The sphere fits tightly inside the cube, so the diameter, d, of the sphere is 12 cm. The radius is half the diameter, so radius = r = diameter/2 = 12 cm/2 = 6 cm.

a)

volume of sphere = (4/3)(pi)r^3

volume of sphere = (4/3)(3.14159)(6 cm)^3

volume of sphere = 905 cm^3

b)

The empty space is the difference between the volume of the cube and the volume of the sphere.

volume of cube = s^3

volume of cube = (12 cm)^3

volume of cube = 1728 cm^3

empty space = volume of cube - volume of sphere

empty space = 1728 cm^3 - 905 cm^3

empty space = 823 cm^3

Answer:

10

Step-by-step explanation:

I think i am not sure

10-6=4

9a^2 - 9

Uejdjeujdksjdndkdkdk

Answer:

See below ~

Step-by-step explanation:

Let's take an example :

I'm driving a car Z for 1,750 km and it has consumed 70 L of fuel.

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

Formula for mileage :

Mileage = Distance / Fuel consumed

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

Solving :

⇒ Mileage = 1,750 km / 70 L

⇒ Mileage = 25 km/L

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

Understanding by this method :

We can solve for the mileage of a car if we know how much distance it has covered in unit time, and the amount of fuel it has consumed, we can calculate mileage.

The area of the given figure is 27.5 square centimeter which has a rectangle and triangles

The given figure has a rectangle and triangles

The area of rectangle is length times width

Area of rectangle =5×4

=20 square centimeter

Area of triangle =1/2×base×height

=1/2×2.5×3

=7.5/2

=3.75 square centimeter

As there are two triangle = 2(3.75)

=7.5 square centimeter

Total area = 7.5+ 20

=27.5 square centimeter

Hence, the area of the given figure is 27.5 square centimeter

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Answer:

Third choice from top to bottom.

Step-by-step explanation:

The total amount of students would be exactly - 220 students. So that means reading would be exactly 20% of the students, as of 40/220 = 0.2 = 20%. That means automaticially the third choice would be correct, but let's do more calculations to make sure- 55/220 = 25%, 66/220 = 30%. That means that our answer is in fact correct.