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The equation log₂(x - 1) = x³ - 4x has one solution at x = 2.

To determine the solutions to the equation log₂(x - 1) = x³ - 4x, we can set the two expressions equal to each other:

log₂(x - 1) = x³ - 4x

Since we know that the graphs of the two functions intersect at the points (2, 0) and (1.1187, -3.075), we can substitute these values into the equation to find the solutions.

For the point (2, 0):

log₂(2 - 1) = 2³ - 4(2)

log₂(1) = 8 - 8

0 = 0

The equation holds true for the point (2, 0), so (2, 0) is one solution.

For the point (1.1187, -3.075):

log₂(1.1187 - 1) = (1.1187)³ - 4(1.1187)

log₂(0.1187) = 1.4013 - 4.4748

-3.075 = -3.0735 (approx.)

The equation is not satisfied for the point (1.1187, -3.075), so (1.1187, -3.075) is not a solution.

Therefore, the equation log₂(x - 1) = x³ - 4x has one solution at x = 2.

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Answer:

The tangent of the angle is 1

Step-by-step explanation:

The solution is in the image

Answer:

5

Step-by-step explanation:

Answer:

The answer would be 6.

Step-by-step explanation:

First, we need to make equations for these electricians fee's.

Electrician one: Y=25x+50, 50 is the upfront cost and 25 is the cost per hour for work.

Electrician two: Y=27.50x+35, It is the same thing for these numbers.

Then you need to incert numbers into the X place. Y will be your answer.

Y=25(6)+50, Y=150+50, Y=200

Y=27.50(6)=35, Y=165+35, Y=200

The answer would be 6. If both the electricians worked for 6 hours each, their prices would be equal.

Answer:

Step-by-step explanation:

3. In particular, the set of solutions to 2x - 3y = 7 is a straight line. (This is why it's called a linear equation.)

The radius of circle F is equal to: C. 12.

In Mathematics and Geometry, Pythagorean's theorem is modeled or represented by the following mathematical equation (formula):

a² + b² = c²

Where:

a, b, and c represents the length of sides or side lengths of any right-angled triangle.

By substituting the given side lengths into the formula for Pythagorean's theorem, we have the following;

a² + b² = c²

a² + 9² = 15²

a² = 225 - 81

a = √144

a = 12 units.

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ANSWER:

The value of x is equal to -8.49

STEP-BY-STEP EXPLANATION:

We have the following equation:

We solve for x:

The value of x is equal to -8.49

minutes of long-distance calls in a month make plan A the better deal= 300.

you are choosing between two long-distance telephone plans. Plan A has a monthly fee of $15 with a charge of $0.08 per minute for all long-distance calls. Plan B has a monthly fee of $3 with a charge of $0.12 per minute for all long-distance calls.

f(x)=15+0.08x

g(x)=3+0.12x

The costs for the two planes be the same when f(x)=g(x),

15+0.08x=3+0.12x

12=0.04x

x=300 minut.

f(x)=15+0.08*300=15+24=39.

g(x)=3+0.12*300=3+36=39.

 minutes of long-distance calls in a month make plan A the better deal= 300.

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Answer:

x=31

Step-by-step explanation:

x=180-149

x=31

Answer:

height of the cuboid=480/(12×8)

=480/96

=5 cm

The correct value of the inequality as solves is x > 14 , and the error made by the student was that he directly divided the RHS by 7.

To simplify the equation we will multiply 7 on both the sides.

Then we will get the result as 7x > 98

Thus, we can say that the new inequality will be x > 14 ,

Hence , the mistake made by the student was that he didn't divided both the sides by 7 but only one side.

So a result, he obtained the incorrect result x>2.

Inequality is a concept in mathematics and uses symbols such as > , < , <= , >= etc.

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The measure of the third angle, C, is 30 degrees. So, the correct answer is (c) 30.

Let's assume the three angles of the triangle are A, B, and C, where A, B, and C are measured in degrees.

We know that the sum of the angles in a triangle is 180 degrees. Therefore, we can write the equation:

A + B + C = 180

The obtain of two angles is 150 degrees, we can set up another equation:

A + B = 150

To obtain the measure of the third angle, which we'll call C, we can subtract the sum of the other two angles from 180:

C = 180 - (A + B)

Substituting the value of the sum of two angles (150 degrees), we have:

C = 180 - 150

C = 30

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There are 900000000 nine-digits numbers and exactly half of them have an even sum of digits (because every number can be paired with another of the opposite parity by changing the last digit).

Answer:  200,000,000.

we have 9 spaces we need to fill in

There are 10 total numbers(0–9)

There are 5 even numbers(0,2,4,6,8)

fill from left to right

u cannot start with 0 so pick another number 2,4,6,8 any of those

4*10^7*5= 20*10^7 = 2*10^8

200,000,000.

Answer:

50 percent

Step-by-step explanation:

because sally was tried yesterday and went 25 percent faster today.

Answer:

1419.23

Step-by-step explanation:

I used go0gle ......hopenit helped

Answer:

1419.23

Step-by-step explanation:

Step-by-step explanation:

Given

Area of rectangle (A) = 243.9 m²

Length (L) = 15 m

first calculating the breadth (b)

We know

L * b = A

15 * b = 243.9

b = 243.9/ 15

b = 16.26 m

Now

Perimeter (p)

= 2 ( L + b)

= 2 ( 15 + 16.29)

= 62.58 m

Hope it will help

If area of a rectangle is 243.9 m2. If the length is 15 m, then  perimeter of the rectangle is 62.58 m.

The area of Rectangle is length times of width.

Given,

Area of rectangle (A) = 243.9 m²

Length (L) = 15 m

To find the  perimeter we need to know the breadth

Calculate the breadth (b)

Area=Length×Breatdth

243.9=15 × b

Divide both sides by 15

b = 243.9/ 15

b = 16.26 m

Perimeter= 2 ( Length + breadth)

= 2 ( 15 + 16.29)

= 62.58 m

Hence  the perimeter of the rectangle is 62.58 m.

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The ratio for the number of egg in three boxes to the total number of egg is 1 : 10

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio.

We use the ratio formula while comparing the relationship between two numbers or quantities. The general form of representing a ratio of between two quantities say 'a' and 'b' is a: b, which is read as 'a is to b'.

According to the question,

Total boxes of  eggs a farmer have = 30 boxes of egg

Number of eggs in each box = 6

Total number of eggs in 3 boxes = 6 × 3

=> 18 eggs

Total number of eggs in 30 boxes = 30 × 6

=> 180 eggs

Ratio of number of egg in three boxes to the total number of egg = 18 : 180

=> 1 : 10 is the ratio

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Answer: sin=7/13,cos=2.sqrt30/13

Step-by-step explanation:

SOH COH TOA  

sin=opp/hyp,cos=adj/hyp

Use pyth. theorem to find the adjacent of C.

13^2 =7^ + b^2

169 = 49 + b^2

120 = b^2

sqrt120 = sqrtb

2.sqrt30 = b is the missing side.

Answer:

46%

Step-by-step explanation:

100% is equal to the total earnings in a month which is $4000.So 33% is the rent so you say:

If 100%=4000

33%=?

[(33×4000)÷100]=$ 1320

Answer:

It is not.

Step-by-step explanation:

The formula of a right triangle is "\(a^{2}+b^{2} =c^{2}\)" where c is the hypothenuse (the longest side of the triangle) if we replace the formula with the values we will get

  "\(30^{2} +122^{2} =125^{2} \\900 + 14884 = 15625\\15784\neq 15625\)

The value of x is 11.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

From the figure,

5x + 3x + 2 = 90

Solve for x.

8x + 2 = 90

8x = 90 - 2

8x = 88

x = 11

Thus,

x is 11.

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The simulation that could be used to fairly represent the situation is A. Use a computer to randomly generate 4 numbers from 1 to 3. Each time 1 appears, it represents a strawberry taffy.

The probability of each taffy being strawberry is 0.25, so the probability of all 3 taffies being strawberry is:

0.25 * 0.25 * 0.25 = 0.015625 or approximately 1.56%

Therefore, the likelihood of all taffies being strawberry is very low.

The simulation that could be used to fairly represent the situation is to use a computer to randomly generate 4 numbers from 1 to 3. Each time 1 appears, it represents a strawberry taffy. This simulates the probability of each taffy being strawberry being 0.25 or 25%.

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After using proportion the enlarged photo length is C)15 inches.

What is proportion?

A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.

Here According to the question before enlargement the width is 4 inches and length is 6 inches. Taking proportion between before and after enlargement of the measurements then,

=> \(\frac{ width}{length}\)

=> \(\frac{4}{6}=\frac{10}{x}\)

=> x = \(\frac{10\times 6}{4}\)

=> x = 5 × 3 = 15

Hence after enlargement the photo length is 15 inches.

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The type of solution set in the system of equation is no solution

From the question, we have the following parameters that can be used in our computation:

x=-71+34 x+71=32

This equation can be properly expressed as

x = -71y + 34

x + 71y = 32

Make x the subject in the second equation

x = -71y + 32

Substitute x = -71y + 32 in x = -71y + 34

-71y + 32 = -71y + 34

An equation that has no solution is represented as:

ay + b = ay + c

The above means that the variable term of both sides of the equations are the same, while the constant terms are different

The equation -71y + 32 = -71y + 34 conform to the statement above

Hence, the equation has no solution

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Complete question :

The line plot shows the weights of packages of meat that members of a club bought. The meat will be mixed with vegetables to make stew for a club dinner. Each serving of the stew contains 1/4 pound of meat. How many servings of the stew can the club make?

Answer:

36 servings

Step-by-step explanation:

From the plot ; we take the sum of total weight of meat packages :

(5/8 * 2) + 6/8 + 1 + (9/8 * 3) + 10/8 + 11/8

10/8 + 6/8 + 8/8 + 27/8 + 10/8 + 11/8 = 72 / 8 = 9 meat packages

Each serving of meat = 1/4

Number of servings the club can make :

Total meat package / pound of meat per serving

(9 ÷ 1/4)

9 * 4/1

= 36 servings

Answer:

36 hope this help

Step-by-step explanation:

Answer:

24 5/2!   That's the answe becayse 6 times 4 is 20 add the 2 by two times / multiply the 2 and get 4 add four to 20 now you have your answer

Step-by-step explanation:

The new dimensions are 10 inch by 15 inch.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

Estebe enlarged a 4-inch by 6-inch.

scale Factor = 5/2.

So, the Dimensions after enlarging

4 inch = 4 x 5/2 = 10

and, 6 inch = 6x 5/2 = 15

Hence, the new dimensions are 10 inch by 15 inch.

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False. In statistical process control (SPC), the mean and the standard deviation serve different purposes and are not interchangeable.

The mean, often denoted as μ, represents the central tendency or average of a set of data points. It provides information about the typical or expected value of the process under consideration.

The mean is commonly used as a reference point in SPC to monitor and control the process performance. Control charts, which are a fundamental tool in SPC, typically plot the mean of the process data over time to detect any shifts or trends.

On the other hand, the standard deviation, often denoted as σ, is a measure of the dispersion or variability of the data points around the mean. It provides insights into the spread or consistency of the process. The standard deviation is not used as a substitute for the mean in SPC; rather, it is used to calculate control limits on control charts.

Control limits help identify when the process is exhibiting unusual variation that may indicate a special cause or a deviation from the desired performance.

In summary, the mean and the standard deviation are distinct statistical measures, each with its own role in SPC. They provide complementary information and should not be used interchangeably.

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