If 10^x=5. What is x?

AnswerAnwser key

Step-by-step explanation:

Answer:

1) -6

2) -8

3) 125185623/1000000000 ( i didn't really understand this one but i hope i got it right)

4) 1

5) 0.94736842

6) 4/5 = 5/4

I can only do up to there for now .... sorry

but i can do the second part in a few mins.

Step-by-step explanation:

i really hope this is right....

Answer:

The coordinates of the midpoint M are (-3,4.5)

Step-by-step explanation:

Here, we are interested in calculating the coordinates of the midpoint.

To do this, we make use of the midpoint formula;

Mathematically;

(x , y) = (x2 + x1)/2 , (y2 + y1)/2

Substituting the values;

(x , y) = (1+(-7))/2, (6 + 3)/2

(x , y) = (1-7)/2, 9/2

(x ,y) = -6/2,9/2

(x,y) = -3, 4.5

The meaning of Dilation is changing the size of an object without changing its shape. The size of the object may be decreased or increased based on the scale factor.

One example of dilation math is a square of side 5 units can be dilated to a square of side 25 units, but the shape of the square remains the same.

Dilation is the method of resizing or transforming an object. It is a transformation that makes the objects larger or smaller with the help of the given scale factor.

The new figure get after dilation is called the image and the real image is called the pre-image. Dilation can be of two types:

1. Expansion - It happens when the size of an object is increased.

2. Contraction - it happens when the size of an object is decreased.

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The price of a 1940 movie ticket in today's dollars, which was option (e) $4.64.

To determine the price of a 1940 movie ticket in today's dollars, we need to adjust the price using the CPI. The CPI in 1940 was 14, while the CPI today is 260. The formula for adjusting the price for inflation is:

Adjusted Price = Price in Year T1 x CPI in Year T2 / CPI in Year T1

Where T1 is the base year and T2 is the target year.

In this case, the base year is 1940, and the target year is today. Therefore, we can calculate the adjusted price of the 1940 movie ticket as follows:

Adjusted Price = $0.25 x 260 / 14

Adjusted Price = $4.64

Therefore, the price of a 1940 movie ticket in today's dollars is $4.64.

Then the correct option is (e).

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Answer:

The angles are supplementary.

x = 31

Step-by-step explanation:

The way the two angles lay together and make a straight line shows that they are supplementary. Supplementary means that they add up to 180°

Use this idea to write an equation.

2x + 3x + 25 = 180

combine like terms

5x + 25 = 180

subtract 25

5x = 155

divide by 5

x = 31

Answer:

x = 31

Step-by-step explanation:

(3x + 25) and 2x are a linear pair and are supplementary, that is

3x + 25 + 2x = 180

5x + 25 = 180 ( subtract 25 from both sides )

5x = 155 ( divide both sides by 5 )

x = 31

Answer:

Step-by-step explanation:

2(x-5)+3(4+6) distibrute 2 through the parenthesis(uwu)

2x-10+3x10 multiply the numbers :) basta multiply mo

2x-10+30 calculate the sum :- kayo na sumalat nan uwu

2x+20

ito sulotion

2x+20

Answer:

2x + 20 OR 2(x + 10)

Step-by-step explanation:

2(x - 5) + 3(4 + 6) =>

2x - 10 + 12 + 18   =>

2x + 20 OR 2(x + 10)

The missing number so that the equation has no solution is -3 5/6.

A linear equation is an equation that has a single variable that is raised to the power of one. When shown on a graph, a linear equation is a straight line that slopes either upwards or downwards.

If the equation has no solution, it means that the value of the left hand equation and the value of the right hand equation are equal.

In order to determine the solution, take the following steps:

x + 19 = 2x - 4 - 7x

Combine similar terms together: 19 + 4 = 2x - 7x - x

Add similar terms together: 23 = -6x

Divide both sides of the equation by -6: x = 23 / - 6

x = -3 5/6

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Answer:

K is the midpoint of JL.

I hope this helps:)

The completed statement based on two-dimensional motion in the x-y plane can be presented as follows;

The two-dimensional motion in the x-y plane, the x part of the motion and the y part of the motion are independent, whether or not there is an acceleration in any direction. The correct option is therefore;

D) Whether or not there is an acceleration in any direction

Two-dimensional motion in the x-y plane can be analyzed by separating them into its horizontal (x) and vertical (y) components, and analyze each component using the one dimensional equations of motion.

The meaning of the motion on the x-y plane is that the x-direction motion of an object exclusive or excludes the effect of the motion of the object in the y-direction, vis a vis, the y-direction motion.

The horizontal and vertical components of the motion can be analyzes individually or by themselves, by making use of the equations of motion for a one-dimensional motion, whether or not there is an acceleration in any direction as the acceleration are also evaluated using one dimensional equations.

The possible options in the question from a similar question on the internet are;

A) When there is no acceleration in any direction

B) When there is no acceleration in one direction

C) Only when an acceleration is present in both directions

D) Whether or not there is an acceleration in either direction

E) Only when the acceleration is in the y-direction

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Answer:

side IG < side HI < side GH

(greatest to least)

Step-by-step explanation:

angle with respect to appropriate side

angle GHI < angle HGI < angle HIG

Answer: 1517.54

Step-by-step explanation:

So we can divide solving this question into two parts: the 2% compound interest and the 5% compound interest.

We know that the compound interest equations is A = P(1+r/n)^nt where:

A is final amount

P is principal (initial) amount

r is interest rate

n is number times interest compounded

t is number of time periods

Given this, in the 2% compound we know:

A = ?

P = 1200

r = 2%

n = 1 (because it didn't say how many times compounded so we assume 1)

t = 2

This becomes:

A = 1200 (1 + (0.02/1))^ 1 * 2

A = 1248.48

Because we switching to 5% from 2%, we can assume that the final amount from the 2% will be the initial amount in the 5%. Thus:

A = ?

P = 1248.48

r = 5%

n = 1

t = 4 (because there were 6 years in total and we used 2 years for 2%)

This becomes:

A = 1248.48 (1 + (0.05/1))^ 1 * 4

A = 1517.54

The solution to the given logarithmic equation is x = 1.

The given logarithmic equation is:

ln(x+31) - ln(4-3x) = 5ln2

We can use the first property of logarithms, which states that ln(a) - ln(b) = ln(a/b), to simplify the left-hand side of the equation:

ln(x+31)/(4-3x) = ln(2^5)

We can further simplify the right-hand side using the second property of logarithms, which states that ln(a^b) = b*ln(a):

ln(x+31)/(4-3x) = ln(32)

Now, we can equate the arguments of the logarithms on both sides:

(x+31)/(4-3x) = 32

Multiplying both sides by (4-3x), we get:

x + 31 = 32(4-3x)

Expanding the right-hand side, we get:

x + 31 = 128 - 96x

Bringing all the x-terms to one side, we get:

x + 96x = 128 - 31

Simplifying, we get:

97x = 97

Finally, dividing both sides by 97, we get:

x = 1

Therefore, the solution to the given logarithmic equation is x = 1.

Note that we must check the solution to make sure it is valid, as the original equation may have restrictions on the domain of x. In this case, we can see that the arguments of the logarithms must be positive, so we must check that x+31 and 4-3x are both positive when x = 1. Indeed, we have:

x+31 = 1+31 = 32 > 0

4-3x = 4-3(1) = 1 > 0

Therefore, the solution x = 1 is valid.

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Answer:

(4n+5)(6n2+5)

Step-by-step explanation:

Add and subtract the second term to the expression and factor by grouping.

I factored it I don't know if that's what you wanted

Proofs and Fundamentals: A First Course in Abstract Mathematics" is a textbook that provides an introduction to the fundamental concepts and techniques of abstract mathematics, with a focus on proof writing and logical reasoning.

Unfortunately, as an AI language model, I do not have access to specific solutions or resources like textbooks. However, the book is designed to guide students through various topics such as logic, sets, functions, relations, and basic proof techniques.

It aims to develop students' ability to think critically and construct rigorous mathematical arguments. It is recommended for individuals seeking to enhance their understanding of abstract mathematics and develop foundational skills in proof writing and problem-solving.

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As I swam out to investigate the ruins of the 17th-century cruise line, something terrible happened underwater. The team members were attacked by horrifying sea creatures, and only I managed to escape and be rescued.

In the darkness of the deep sea, the ruins came alive with malevolent energy. Ancient sea creatures, long forgotten by time, emerged from the shadows. Their grotesque forms, a result of centuries of evolution, had adapted to the darkness and had become terrifying predators. With razor-sharp teeth and impenetrable scales, they descended upon my teammates with relentless ferocity. The creatures struck swiftly, their powerful tails and jagged claws tearing through flesh and bone. Panic filled the water as my companions fought valiantly, but their efforts were in vain. I swam with all my might, the adrenaline coursing through my veins, until I broke free from the clutches of that underwater nightmare. Gasping for air on the surface, I was the lone survivor of the team's encounter with the monstrous inhabitants of the deep.

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Answer: Jessica can make 3 cupcakes for her sister.

Step-by-step explanation: since each cupcake takes 2/6 of the flour bag a whole bag would be 6/6. We add 2/6 3 times to make a whole. Which comes with the answer 3. So each full flour bag can make 3 cupcakes.

Answer:

B

Step-by-step explanation:

4 x 5 = 20, and that is the total number of squares in the grid.

10% of 20 is 2.

Therefore 10% of the graph is B.

Non-overlapping intervals:

If the intervals(say interval a & interval b) doesn't overlap then the set of pairs form by [a. end, b. start] is the non-overlapping interval.

In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between. Other examples of intervals are the set of numbers such that 0 < x < 1, the set of all real numbers {\displaystyle \mathbb {R} }\mathbb {R} , the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton (set of one element).

Let's take the below mentioned overlapping intervals example to explain the idea: If both ranges have at least one common point, then we say that they're overlapping. In other words, we say that two ranges and are overlapping if: On the other hand, non-overlapping ranges don't have any points in common.

Given N set of time intervals, the task is to find the intervals which don’t overlap with the given set of intervals.

Examples:

interval (a) = { {1, 3}, {2, 4}, {3, 5}, {7, 9} }

Output:  [5, 7]

The only interval which doesn’t overlaps with the other intervals is [5, 7].

interval (a) = { {1, 3}, {9, 12}, {2, 4}, {6, 8} }

Output: [4, 6]  and [8, 9]

There are two intervals which don’t overlap with other intervals are [4, 6], [8, 9].

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Answer:

The final answer is correct.

Answer:

Answer is D

Just expand

And remember

\( \sqrt{ - a} = \sqrt{a} i\)

Goodluck tomorrow

Answer:

Suppose A and B , both has initial volume, say x

120 ML is poured from B to A, then new volumes of A and B will be:

new volume of A (x-120)

new volume of B  (x+120)

Volume of B is now four times volume of A, then

(x+120)= 4(x-120)

(x+120)=4x-180

3x=600

x=200

So, the initial volume of A and B containers is 200

So, at the end, volume of container A = 200-120=80

Hence the answer is 80   :

Step-by-step explanation:

Answer:

The mean of Trail Middle School wrestling team is greater by 20 pounds as compared to that of Burlington Middle School  wrestling team

Step-by-step explanation:

Since the value of absolute deviation in case of Trail Middle School wrestling team and Burlington Middle School  wrestling team is same. Hence, there will be no impact of it while determining the difference in mean deviation of both the team.

Thus, the difference in mean deviation is \(150-130 = 20\)

The mean of Trail Middle School wrestling team is greater by 20 pounds as compared to that of Burlington Middle School  wrestling team

Answer:

v=-1

Step-by-Step Explanation:

Answer:

\(v=-1\)

Step-by-step explanation:

\(6\left(6v+6\right)-5=1+6v\)

Use the distributive property to multiply 6 by 6v+6:

\(36v+36-5=1+6v\)

Subtract 5 from 36 = 31

\(36v+31=1+6v\)

Subtract 6v from both sides:

\(36v+31-6v=1\)

Combine like terms:

\(36v\) and \(-6v\) \(=30v\)

\(30v+31=1\)

Subtract 31 from both sides:

\(30v=-30\)

Divide both sides by 30:

\(\cfrac{30v}{30}=\cfrac{-30}{30}\)

\(v=-1\)

_________________________

To derive the demand function from the given utility function and endowment, we need to determine the optimal allocation of goods that maximizes utility. The utility function is U(x, y) = -e^(-x) - e^(-y), and the initial endowment is (1, 0).

To derive the demand function, we need to find the optimal allocation of goods x and y that maximizes the given utility function while satisfying the endowment constraint. We can start by setting up the consumer's problem as a utility maximization subject to the budget constraint. In this case, since there is no price information provided, we assume the goods are not priced and the consumer can freely allocate them.

The consumer's problem can be stated as follows:

Maximize U(x, y) = -e^(-x) - e^(-y) subject to x + y = 1.

To solve this problem, we can use the Lagrangian method. We construct the Lagrangian function L(x, y, λ) = -e^(-x) - e^(-y) + λ(1 - x - y), where λ is the Lagrange multiplier.

Taking partial derivatives of L with respect to x, y, and λ, and setting them equal to zero, we can find the values of x, y, and λ that satisfy the optimality conditions. Solving the equations, we find that x = 1/2, y = 1/2, and λ = 1. These values represent the optimal allocation of goods that maximizes utility given the endowment.

Therefore, the demand function derived from the utility function and endowment is x = 1/2 and y = 1/2. This indicates that the consumer will allocate half of the endowment to each good, resulting in an equal distribution.

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Answer:

measure of angle 1: 102 degrees

measure of angle 2: 78 degrees

Step-by-step explanation:

angle 1 + angle 2 = 180 degrees because they are a linear pair.

(x+63)+2x=180              angle1  x+63 or (39)+63                angle2 2x or 2(39)

3x+63=180                                  39+63= 102                          2 x 39 = 78

     -63   -63

3x=177

/3   /3

x=39

Hope this helps :D

Answer:

The measure of angle 1 is: 102

The measure of angle 2 is: 78

Step-by-step explanation:

I hope this helps!!

The 95% confidence interval for the slope of the regression line is T = 5.00.

What is confidence interval?

A confidence interval in frequentist statistics is a range of estimates for an unknown parameter. A confidence interval is calculated at a specified degree of confidence; the most popular level is 95%, but other levels, such 90% or 99%, are occasionally used.

As given,

The relationship between the sales and profits of Fortune 500 companies that evaluate slope,

T = (4178.29 - 209.839) / √{(796.977² + 7011.63²)/79}

T = 3968.451 / 793.9496

T ≈ 5.00

Critical value for alpha = 0.05

Then 1.96 so, we reject (H₀).

There is not significant association between sales and profit.

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x and x⁴-16x²+56 are the resulting composite functions respectively.

Given the following functions below

f(x) = 7/x

g(x) = x² - 8

We need to determine the composite functions (fof)(x) and (gog)(x)

(fof)(x) = f(f(x))

f(f(x)) = f(7/x)

Replace x with 7/x

f(7/x) = 7/(7/x)

f(7/x) = 7 * x/7

f(7/x) = x

Similarly:

(gog)(x) = g(g(x))

g(g(x)) = (x² - 8)² - 8

g(g(x)) = x⁴-16x²+64 - 8

g(g(x)) = = x⁴-16x²+56

Hence the resulting composite functions of f(f(x) and g(g(x)) are x and x⁴-16x²+56

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