Over which interval is this function continually decreasing? f(x) = |4(x - 1)| + 2

Answer:

32. 74

Step-by-step explanation:

Round money monetary answers to the nearest cent. ... using the Distributive Property and explain each step. ... Alison has $9.70 in dimes and quarters. ... It takes him 2.4 hours to get to Seattle, driving at 15 miles per hour faster than the.

For the equation log6(x) - 2 - 3, the solution is x ≈ 12.83.

For the equation log2(2-x) = log2(4x), there is no real solution.

log6(x) - 2 - 3:

To solve log6(x) - 2 - 3, we first simplify the equation by combining like terms.

log6(x) - 5 = 0.

Next, we can rewrite the equation in exponential form:

x = 6^5.

Evaluating the expression, we find x ≈ 7776.

Rounding off to two decimal places, the solution is x ≈ 12.83.

log2(2-x) = log2(4x):

For the equation log2(2-x) = log2(4x), we can apply the logarithmic property that states if loga(b) = loga(c), then b = c. Using this property, we have:

2-x = 4x.

Rearranging the equation, we get:

5x = 2.

Dividing both sides by 5, we find x = 0.4.

However, when we substitute this value back into the original equation, we encounter a problem. Both log2(2-x) and log2(4x) are only defined for positive values, and x = 0.4 does not satisfy this condition. Therefore, there is no real solution to the equation log2(2-x) = log2(4x).

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On a demand curve for most goods, as the price of the product decreases, the number of units the customer is willing to buy increases.

The relationship between price and quantity demanded is a fundamental concept in economics and is typically represented by a demand curve. According to the law of demand, as the price of a product decreases, the quantity demanded by customers tends to increase, and vice versa. This inverse relationship between price and quantity demanded can be attributed to various factors.

When the price of a product decreases, it becomes more affordable for consumers, leading to an increase in their willingness to purchase it. Lower prices may also create a perception of greater value or incentivize customers to buy more of the product. Conversely, as the price of a product increases, consumers may find it less affordable or less attractive, resulting in a decrease in their willingness to buy.

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Answer:

Step-by-step explanation:

b

The justification for Step 1 is the subtraction property of equality. Option B

The justification for Step 1 within the arrangement prepare, which changes the condition 15x − 8 = 14x + 13 into 15x = 14x + 21, is the subtraction property of uniformity.

The subtraction property of equality states that in the event that we subtract the same amount from both sides of an condition, the condition remains genuine. In this case, we are subtracting 14x from both sides of the condition to confine the term with x.

To clarify Step 1 utilizing the subtraction property of correspondence:

The condition 15x − 8 = 14x + 13 is given.

We need to disconnect the x term on one side of the condition. To do this, we got to dispose of the 8 on the cleared out side.

By subtracting 14x from both sides of the condition, we evacuate the 14x term from the correct side:

15x − 14x − 8 = 14x − 14x + 13

Simplifying:

x − 8 = 13

Now, the 14x term is dispensed with from the proper side of the condition.

To advance streamline the condition, we are able include 8 to both sides to dispose of the -8 term on the cleared out side:

x − 8 + 8 = 13 + 8

Simplifying:

x = 21

Now, we have effectively isolated the x term on one side of the condition.

Therefore, the justification for Step 1 is the subtraction property of equality  (B).

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Complete question

What is the justification for step 1 in the solution process?

15x − 8 = 14x + 13

Step 1: 15x = 14x + 21

A.

the addition property of equality

B.

the subtraction property of equality

C.

the division property of equality

D.

the multiplication property of equality

In this problem the range is the interval

[$5,000, $5,999]

that means

The minimum value of p is $5,000

The maximum value of p is $5,999

I assume that the total value of the appliances is $5,400

because

$5,000 < $5,400 < $5,999

p is a range

the range is [5,000, 5.999]

the total appliance must be lie to this interval

you will assume a value of p that lie on this interval

i assume a value of p equal to 5,400

do you understand the answer?

Are you there?

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The sum of three consecutive terms of an arithmetic sequence is 27, and the sum of their square is 293. What is the absolute difference between the greatest and the least of these three numbers in the arthritic sequence?

Let

x -----> first consecutive term

so

x+d ----> second consecutive term

x+2d ----> third consecutive term

where

d -----> common factor

we have that

x+(x+d)+(x+2d)=27

3x+3d=27------> simplify -----> x+d=9 -----> equation 1

the sum of their square is 293

so

x^2+(x+d)^2+(x+2d)^2=293

x^2+(x^2+2xd+d^2)+(x^2+4xd+d^2)=293 ---------> equation 2

Solve the system by graphing

see the attached figure

the solution is the point (4,5)

so

x=4

d=5

therefore

the first term is 4

the second term is 4+5=9

the third term is 4+2(5)=14

the difference is 14-4=10

The angle of a body segment with respect to a fixed line of reference is known as a "relative angle."

The angle of a body segment with respect to a fixed line of reference is known as a reference angle. This angle is measured between the segment and the reference line, and is used to determine the position and orientation of the segment relative to other parts of the body or external objects. The segment itself refers to a specific part of the body, such as an arm, leg, or torso, that is bounded by two or more joints or points of attachment. By measuring the reference angle of a segment, it is possible to quantify the degree of movement or displacement of that segment, and to track changes in its position over time.
In this context, the angle represents the measurement of the difference in orientation between the body segment and the reference line, while the segment refers to a specific part of the body, such as an arm or leg. The reference line serves as a fixed point for comparison, allowing you to determine the position or orientation of the body segment in relation to it.

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Answer:The answer will be 35ft

Step-by-step explanation:

One way that you can answer this is by using sin law. You will put the length of a side on top and the corresponding angle that faces towards that side at the bottom of a fraction. So for this one it will be 30/sin(70) = x/sin(90) The 90 comes from the bottom of the building with the ground. And the side the angle faces is the ladder. After that you put 30sin(90)/sin(70) to find x. And you get 34.655 which rounds to 35 ft.

Answer:

3

Step-by-step explanation:

SSS similarity states that all 3 sides must be proportional for the triangles to be similar

Answer: ph+2b

Step-by-step explanation:

Answer:

920 ft²

Step-by-step explanation:

2 triangles + 3 rectangles

2(½×15×8) + 20(17+8+15)

120 + 800

920

The equation of radioactive substance left after t hours m(t) =10²(ln(9/10) / -24) ×1 t),the numerical value the rate at which the substance is decaying after 7 hours (10 ×(ln(9/10) / -24) × e²((ln(9/10) / -24) × 7)).

a) The equation that defines the mass of the radioactive substance left after t hours using base e, the exponential decay formula:

m(t) = m₀ × e²(-kt),

where:

m(t) represents the mass of the substance after t hours,

m₀ is the initial mass of the substance,

k is the decay constant.

The initial mass is 10 grams, and to find the value of k.

Given that the mass decreases from 10 grams to 9 grams in one day (24 hours), the following equation:

9 = 10 × e²(-k × 24).

To find k, the equation as follows:

e²(-k × 24) = 9/10.

Taking the natural logarithm (ln) of both sides:

ln(e²(-k × 24)) = ln(9/10),

which simplifies to:

-24k = ln(9/10).

solve for k:

k = ln(9/10) / -24.

b) To find the rate at which the substance is decaying after 7 hours, we need to find the derivative of the mass function with respect to time (t).

m(t) = 10 × e²((ln(9/10) / -24) ×t).

To find the derivative, the chain rule dm/dt as the derivative of m with respect to t.

Using the chain rule,

dm/dt = (10 × (ln(9/10) / -24) × e²((ln(9/10) / -24) × t)).

To find the rate of decay after 7 hours, we can substitute t = 7 into the derivative:

Rate of decay after 7 hours = dm/dt evaluated at t = 7.

Rate of decay after 7 hours = (10 × (ln(9/10) / -24) × e²((ln(9/10) / -24) × 7)).

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Answer:

8.49 × 10⁻³

Explanation:

Standard form of a number: A. × 10ᵇ

(where 'A' is the number, b is the exponent over 10)

For the number "0.00849​", move the decimal point 3 places right so the exponent of 10 is -3.

Standard form: 8.49 × 10⁻³

Other examples of standard/scientific forms are:   standard forms

i) 0.043, move the decimal point 2 places right = 4.3 × 10⁻²

ii) 4030, move the decimal point 3 places left = 4.03 × 10³

Answer:

when a number is given in that manner you have to take that decimal between two whole numbers.

and that is the main reason why I took that decimal from 0.0 to 8.49 and since it went towards the right my answer is going to be 8.49 *10 raised to negative 3.

Answer:

2m = 10

m^2 = 25

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

5times 2 = 10

Answer:

y--3=5(x--6)=5x-y+27

Step-by-step explanation:

mrk me brainliest plz

Tyler made an error in his analysis by assuming the supplementary angle, m<1 = 72, was the same as the angle opposite it. Tyler's mistake was in assuming that the same-side exterior angles theorem and the definition of supplementary angles were interchangeable.

Tyler assumes that because the theorem states that same-side exterior angles are supplementary, then any supplementary angles must be same-side exterior angles. Therefore, he concludes that m<2 is also 72 degrees, and that m<3 is 180-72 = 108 degrees. However, this assumption is incorrect. Supplementary angles can be any two angles that add up to 180 degrees, and they do not have to be same-side exterior angles. Therefore, Tyler's analysis is incorrect. The correct way to solve this problem would be to recognize that the angle opposite m<1 is m<3, and therefore, m<3 = 72 degrees.

In summary, Tyler's error in his analysis was to assume that the same-side exterior angles theorem and the definition of supplementary angles were interchangeable. This assumption led him to conclude that m<2 and m<3 were both same-side exterior angles and therefore both 72 degrees. However, this assumption is incorrect, and Tyler's analysis is flawed. The correct way to solve the problem is to recognize that m<1 and m<3 are supplementary angles, and therefore, m<3 is 72 degrees. Then, because m<2 and m<3 form a straight line, m<2 is 108 degrees. In conclusion, Tyler's error shows the importance of understanding the definitions of basic geometric concepts and not making assumptions based on incomplete knowledge.

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Answer:

x = 18

Step-by-step explanation:

We Know

(10x - 4) + (x - 14) must equal 180°

Find the value of x.

Let's solve

10x - 4 + x - 14 = 180

11x - 18 = 180

11x = 198

x = 18

So, x = 18 is the answer.

True. Probability of an uncertain outcome is a number between 0 and +1, exclusively.

The probability of an uncertain outcome is a measure of the likelihood that the outcome will occur, and it is always a number between 0 and 1, inclusive. A probability of 0 means that the event is impossible, while a probability of 1 means that the event is certain. Probabilities between 0 and 1 indicate the degree of uncertainty about whether the event will occur or not.

Probabilities cannot be negative or greater than 1, as they represent a proportion of the total possible outcomes. If the probability of an event were negative or greater than 1, it would imply that the event is impossible or certain to occur, respectively, and violate the fundamental laws of probability theory.

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Term life insurance typically costs a lot less than its permanent life counterparts, whole life, and universal life, despite the fact that they offer much of the same coverage. This is mainly due to the policy's length, which can range from 5 to 30 years.

The life insurance provider calculates your premiums based on your age, health, and risk factors over the duration of the policy. This makes the term policy less expensive than permanent life policies that offer lifelong protection.Life insurance firms, on the other hand, can make a profit from term life policies since they are only intended to cover a person for a set period, and if the insured does not pass away during that period, the life insurance provider will not have to pay out a death benefit, allowing them to keep the premium payments as profit. This is in contrast to permanent life policies, which are intended to cover a person for the rest of their life, thus the provider will need to pay out a death benefit at some point, resulting in higher premiums.

Term life insurance is a type of life insurance that covers the policyholder for a certain period. This type of policy is usually cheaper than permanent life insurance policies like whole life and universal life. Term policies are less expensive because they cover you for a fixed period, usually between five and thirty years, so the insurance company knows that they will only have to pay a death benefit if you die during the term period.Term life insurance premiums are determined by your age, health, and the term of the policy. Insurance companies calculate the risk that you will die during the policy period and base your premiums on that risk. Because the policy period is limited, term life policies are less expensive than permanent life insurance policies that offer lifelong protection. An insurance company is willing to offer term life insurance at a lower cost because they know that if you don't die during the term, they get to keep the premiums you paid.

Term life insurance is a cost-effective alternative to permanent life insurance policies. It is less expensive because it is designed to cover you for a specific period, which means that the insurance company only has to pay a death benefit if you die during that period. The insurance company can offer term life insurance at a lower cost because they know that if you don't die during the term, they get to keep the premiums you paid.

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Answer:

x = 6

Step-by-step explanation:

• ∠THX and ∠XHV have a common side HX and a common vertex H

This means they are two adjacent angles.

Then

m∠THX + m∠XHV = m∠THV

Then

53 + 12x−9 = 16x + 20

Solving the equation:

53 + 12x−9 = 16x + 20

⇔ (53 − 9) + 12x = 16x + 20

⇔ 44 = 16x - 12x+ 20

⇔ 44 - 20 = 4x

⇔ 24 = 4x

\(\Longleftrightarrow x = \frac{24}{4} =6\)

To display the terms in the Fibonacci sequence, starting with Fib(0) and continuing as long as the terms are less than 10,000, a program is written with a loop construct. This loop is implemented using a `while` loop with a header line that looks like this: `while term < 10000:`.

Fibonacci sequence is named after the Italian mathematician Leonardo Fibonacci who developed a mathematical sequence in the 13th century to explain the geometric growth of a population of rabbits.

The first two terms in this sequence, Fib(0) and Fib(1), are 0 and 1, and every subsequent term is the sum of the preceding two.

The first several terms in the Fibonacci sequence are:

Fib(0) = 0, Fib(1) = 1, Fib(2) = 1, Fib(3) = 2, Fib(4)= 3, Fib(5)=5.

This program continues as long as the value of the term is less than the maximum

The output is as follows:

```1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765```

The while loop could also be used to achieve the same goal.

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Answer:

2^(3/7)

Step-by-step explanation:

For these types of questions, what is inside the root is the numerator, and what is on top is the denominator.

3 is in the root, so it is the numerator

7 is outside the root, so it is the denominator

Therefore, The answer is 2^(3/7)

Answer:

32

Step-by-step explanation:

f(x) = 7, so:

5 · 7 - 3= 35 - 3 = 32

Answer:

x = 2

Step-by-step explanation:

f(x) = 5x - 3    

7 = 5x - 3

10 = 5x

2 = x

So, x = 2

Answer: 4

Step-by-step explanation:

The probability of rolling one 3 and two 2s, given that the sum of the rolls is 7, is 1/72.

The probability of rolling one 3 and two 2s when rolling a six-sided die three times, with the condition that the sum of the rolls is 7, can be calculated using combinatorial methods. The probability of obtaining a specific outcome, such as one 3 and two 2s, can be determined by dividing the number of favorable outcomes by the total number of possible outcomes.

To find the probability of rolling one 3 and two 2s, we need to consider the different arrangements of these numbers in the three rolls. Let's denote "3" as A and "2" as B. There are three possible arrangements: AAB, ABA, and BAA.

For the arrangement AAB, the probability of obtaining this specific outcome is (1/6) × (1/6) × (1/6) = 1/216. Similarly, for the arrangements ABA and BAA, the probabilities are also 1/216.

Since the order doesn't matter, we need to account for all possible arrangements. There are three different arrangements for the desired outcome. Therefore, the total probability of rolling one 3 and two 2s is (1/216) + (1/216) + (1/216) = 3/216 = 1/72.

Hence, the probability of rolling one 3 and two 2s, given that the sum of the rolls is 7, is 1/72.

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Answer:

t= 41.2 minutes

Step-by-step explanation:

\(16=290(0.5)^{\frac{t}{10} }\)

Divide by 290 to get the exponential expression alone

\(\frac{16}{290} \\\frac{8}{145}=(.0.5)^{t/10}\)

Use Logs to solve

\(x=a^{y}\) is equal to \(y=log_{a} x\)

\(\frac{t}{10} =log_{0.5} \frac{8}{145}\)  (put in calculator)

\(\frac{t}{10} = 4.18\)

t= 41.2 minutes

Selling insurance is not risky for an insurance company that insures many thousands of 21-year-old men due to the principle of large numbers and the concept of risk pooling.

The principle of large numbers states that as the number of individuals in a risk pool increases, the actual outcomes tend to approach the expected outcomes. In the case of life insurance for \(21-year-old\) men, while it is true that there is a high probability that each individual insured will live, the insurance company can rely on the law of large numbers to ensure that the overall outcomes align with their expectations.

When an insurance company insures many thousands of 21-year-old men, the law of large numbers comes into play. While it is true that some individuals may die at a young age, the insurance company can accurately predict the mortality rates and life expectancies for large groups based on actuarial data. This allows them to calculate premiums that are sufficient to cover the expected payouts in the event of death.

By pooling the risk of many individuals together, the insurance company can spread the financial risk across the entire pool. While some individuals may experience unfortunate events and their beneficiaries receive payouts, the premiums paid by the larger group of insured individuals ensure that the insurance company can cover these payouts and still make a profit.

In the case of the 21-year-old men, the insurance company can rely on statistical data, mortality tables, and actuarial calculations to determine the appropriate premiums that will cover the expected payouts and still provide a profit for the company. This allows the insurance company to manage the risk effectively and ensure their long-term financial stability.

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Answer:

third 1 down

Step-by-step explanation

take 1 away from bothof the shaded and nonshaded shaded and you get 1/3

The derivative of the function h(x) = 7^(x^2) + 2^(2x) is h'(x) = (ln 7) * (7^(x^2)) * (2x) + (ln 2) * (2^(2x)) * (2).

To find the derivative of the function h(x) = 7^(x^2) + 2^(2x), we can apply the rules of differentiation.

Let's break it down step by step:

Step 1: Start with the function h(x) = 7^(x^2) + 2^(2x).

Step 2: Recall the exponential function rule that states d/dx(a^x) = (ln a) * (a^x), where ln represents the natural logarithm.

Step 3: Differentiate each term separately using the exponential function rule.

For the first term, 7^(x^2), we have:

d/dx(7^(x^2)) = (ln 7) * (7^(x^2)) * (2x)

For the second term, 2^(2x), we have:

d/dx(2^(2x)) = (ln 2) * (2^(2x)) * (2)

Step 4: Combine the derivatives of each term to find the derivative of the entire function.

h'(x) = (ln 7) * (7^(x^2)) * (2x) + (ln 2) * (2^(2x)) * (2)

This is the derivative of the function h(x) = 7^(x^2) + 2^(2x). It represents the rate of change of the function with respect to x at any given point.

It's important to note that this derivative can be simplified further depending on the specific values of x or if there are any simplification opportunities within the terms.

However, without additional information, the expression provided is the derivative of the function as per the given function form.

In summary, the derivative of the function h(x) = 7^(x^2) + 2^(2x) is h'(x) = (ln 7) * (7^(x^2)) * (2x) + (ln 2) * (2^(2x)) * (2).

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