What is the equation of the line that passes through the point (-8,5) and has a slope
of o?

Answer:

f(x) = - 2x + 4

Step-by-step explanation:

Since we are only trying to move the graph up 3 units, the slope does not change. So, it would be -2.

We also know that the 1 in f(x)= -2x + 1 is the y-intercept (y=mx+b). But again, we are moving the graph 3 units up, so we have to add 3. That makes it 4 (3+1=4).

So, the new equation would be f(x) = -2x + 4

Step-by-step explanation:

it simply means that g(x) is f(x) just shifted 3 units upwards.

that means nothing else changes, only whatever y result f(x) produces is increased by 3.

so,

g(x) = f(x) + 3 = -2x + 1 + 3 = -2x + 4

therefore, as domain and range were the whole set of real numbers, the addition of 3 does not make any difference in relation to infinity. so, they remain unchanged.

the slope stays the same (g(x) is simply a parallel line to f(x)).

the y-intercept (the y-value when x = 0) also increases by 3, and is 4.

the x-intercept (the x-value when y = 0) changes :

0 = -2x + 4

2x = 4

x = 2

the x-intercept is 2.

Answer:

here is 3

Step-by-step explanation:

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We conclude that after 7/4 years the value of the jet ski is $4,784

The value of the jet ski is given by the exponential equation:

f(t) = 8,500*(0.72)^t

Where t is the time in years, to get the value of the jet ski after 7/4 years, we just need to evaluate the above function in t = 7/4, where evaluating means that we need to replace the variable t by the given number, then we will get:

f(7/4) = 8,500*(0.72)^(7/4) = 4,783.55

If now we need to round it to the nearest dollar, then we round upwards to 4,784

In this way, we conclude that after 7/4 years the value of the jet ski is $4,784

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Answer:

OK Please mark me brailiest to follow your channel.

Answer:

152 hundred

Step-by-step explanation:

164 hundred - 12 hundred = 152 hundred

Please rate!

Answer:

1.52

Hope this helps :)

Step-by-step explanation:

step one:

put them as decimals which would be 1.64 and 0.12

step two:

subtract which would be 1.64 - 0.12

step three:

solve your answer would be 1.52 or 152 hundredths

Answer:

1.  n=10

2. n=35

3. n=6

4. n=0 ? not sure for this one. two variables in the proportion

5. n=36

Step-by-step explanation:

set each set of proportion equal to each other and do cross multiplication

hope this helps !

how are you ?

Answer:

Step-by-step explanation:

Please take a look of the attached photo for the solution.

Answer:

342.30

Step-by-step explanation:

342.296 would round up because 6 is higher than five. The 0.09 would round up to 0.10, making the 0.2 become a 0.3.

Answer: To simplify the expression, we can start by rewriting it as the product of the first fraction and the reciprocal of the second fraction. Then, we can factor the denominators of each fraction and simplify as much as possible.

x + 1 / (x^2 + x - 6) ÷ (x^2 + 5x + 4) / (x - 2)

= (x + 1 / (x + 3)(x - 2)) ÷ ((x + 4)(x + 1) / (x + 4)(x - 1))

= (x + 1 / (x + 3)(x - 2)) * ((x + 4)(x - 1) / (x + 4)(x + 1)) (reciprocal of second fraction)

= (x + 1 / (x + 3)(x - 2)) * (x - 1 / (x + 1)) (cancel out (x + 4) and simplify)

= (x + 1) * (x - 1) / (x + 3)(x - 2)(x + 1) (multiply the numerators and simplify)

= (x - 1) / (x + 3)(x - 2) (cancel out (x + 1) in the numerator and denominator)

Therefore, the simplified form of the expression is 1 / ((x + 3)(x - 2) / (x - 1)). This can be further simplified to:

1 / ((x + 3)(x - 2) / (x - 1)) = (x - 1) / ((x + 3)(x - 2)) * (x - 1) / 1 = (x - 1)^2 / ((x + 3)(x - 2))

So the answer is: 1 over the quantity (x + 3) times the quantity (x - 2), all multiplied by the quantity (x - 1) squared.

Step-by-step explanation:

The simplified form of the given expression is 1 over the quantity x plus 3 times the quantity x plus 4.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one maths operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

The given expression is:

\(\frac{x+1}{x^2+x-6} / \frac{x^2+5x+4}{x-2}\)

When a fraction is in the denominator, we take the reciprocal of the fraction and multiply it with the numerator.

So the expression becomes,

\(\frac{x+1}{x^2+x-6} * \frac{x-2}{x^2+5x+4}\)

We can factorize the expression x² + x - 6

x² + 3x - 2x - 6

= x(x+3) -2 ( x+3)

= (x-2) (x+3)

We can also factorize the expression x² +5 x +4

x² + 4x + x +4

= x(x+4) +1 ( x+4)

= (x+1) (x+4)

Substituting these values, the expression becomes as follows:

\(\frac{x+1}{(x-2)*(x+3)} * \frac{x-2}{(x+1)(x+4)} = \frac{1}{(x+3)(x+4)}\)

Therefore the simplified form of the given expression is 1 over the quantity x plus 3 times the quantity x plus 4.

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Answer:

40

Step-by-step explanation:

AREA=LW

L₁W₁=40

L₂W₂=160

x(L₁W₁)=L₂W₂

x(L₁W₁)=L₂W₂

x(40)=160

x=40

Answer:

I believe they donated 4% to the hospitals

Answer:

24

Step-by-step explanation:

2b = b+24

2b-b = 24

b = 24

Answer:

Yes 40/5 is 8

Step-by-step explanation:

40/5=8

Answer:

47 minutes

Step-by-step explanation:

In elapsed time, it's better to make your problem more readable so it's easier to solve. Add 2 minutes into 10:28 so it turns into 10:30. Then add 30 minutes so it turns into 11:00 AM. Finally, add 15 minutes so it turns into the 11:15 you were looking for. When you combine the minutes allotted (2, 30, and 15) you get 47 minutes.

Answer:

The student's claim is incorrect. While it is true that √x^2 = x for all non-negative values of x, this property does not apply to expressions with multiple terms, such as 4√x^2.

Step-by-step explanation:

consider the case where x = -1. Then, √x^2 = √(-1)^2 = 1, but 4√x^2 = 4√1 = 4. On the other hand, √x = √(-1) is undefined, so the equation 4√x^2 = √x is not true for this value of x.

Therefore, the student's claim is not true for all values of x, and it is important to be careful when applying algebraic properties to expressions with multiple terms.

The numbers represented by the statement are 17 and 10

Represent the larger number with x and the smaller number with y

So, we have the following representation from the question

x = 2y - 3

x + y = 27

Substitute x = 2y - 3 in the equation x + y = 27

So, we have the following representation

2y - 3 + y = 27

Evaluate the like terms

3y = 30

Divide both sides by 3

y = 10

Recall that

x = 2y - 3

So, we have

x = 2 * 10 - 3

Evaluate

x = 17

Hence, the numbers are 17 and 10

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The slope in the equation p = 52 + 0.04w represents the rate of change in the water bill payment for each additional unit of water consumed.

Specifically, the slope of 0.04 indicates that for every increase of one unit in the number of water units (w), the water bill payment (p) will increase by 0.04 dollars.

This means that the slope represents the incremental cost of each additional unit of water.

In practical terms, the slope of 0.04 implies that for every additional unit of water consumed, the water bill will increase by $0.04.

This indicates a constant rate of increase in the water bill for each additional unit of water used.

It's important to note that the slope remains constant throughout the equation, suggesting a linear relationship between the amount of water consumed and the corresponding bill payment.

Therefore, The slope, in this case, is the coefficient of the variable w, which is 0.04.

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The probable question may be:

What is the meaning of the slope in the equation p = 52 + 0.04w, which models the relationship between the water bill payment p in dollars and the number of units of water w ?

Answer:

D

Step-by-step explanation:

It's D

Answer:

Answer D

Step-by-step explanation:

Its right I just took the test.

Answer:

I believe the answer is A.

Answer:

the answer is D I believe

Answer:

98

Step-by-step explanation:

Hello There!

The angle that has a measure of 82 degrees and the angle labeled "2" are supplementary angles.

This meaning that the sum of the two angles is 180

So to find the missing angle (2) we subtract the given angle (82 in this case) from 180

so ∠2 = 180 - 82

180 - 82 = 98

Hence, the answer is 98°

Answer:

\(The \ general \ term \ of \ the \ sequence = \frac{n + 1}{n}\)

\(\lim_{n \to \infty} (\frac{n+1}{n}) = \lim_{n \to \infty} (\frac{1}{n} +1 ) = 1 + \lim_{n \to \infty} \frac{1}{n} = 1 + 0 = 1\)

Option 3 : The sequence converges to 1

Answer:percentage answer is 41.7% and for the fractions its 5/12

Step-by-step explanation:

for percentage to need to get the fraction to where the twelve in 7/12 is 100 so you multiply 8.3 to 12 and get 100 but you need to multiply it to the top too so you're left with 58.3/100 but that's the fraction of the goal made so what you do is subtract 58.3 from one hundred and you get 41.7 making your total 41.7%.

the way to solve the fraction is to start by subtracting the overall point to the points made and the sum would be the points missed and the point missed are 5/12 and that fraction is simplified to the max

The common ratio of the resulting sequence is 1.4.

Given that, the three terms are 60, 100 and 180.

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.

Let the same constant is added to the given number is x.

60+x, 100+x and 180+x

Now, the common ratio is

(100+x)/(60+x) = (180+x)/(100+x)

⇒ (100+x)(100+x)=(180+x)(60+x)

⇒ (100+x)²=10800+180x+60x+x²

⇒ 10000+200x+x²=10800+180x+60x+x²

⇒ 10000+200x=10800+180x

⇒ 20x=800

⇒ x=40

The three number are 100, 140 and 220

The common ratio is 140/100 =1.4

Therefore, the common ratio of the resulting sequence is 1.4.

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Answer:

11/6

Step-by-step explanation:

6*2=12

11-6=5

As a fraction, 6 does not go into 11 2times. Only once. 1 5/6

Answer:

6/7

Step-by-step explanation:

11/6 is equal to 1.83 (rounded off) which is more than 1.

4/5 is equal to 0.8 while 5/6 is equal to 0.83 (also rounded off)

4/7 is equal to 0.57 (rounded off once again) and is lesser than 5/6

As 6/7 is equal to 0.86 (rounded off), we can safely say that it is between 1 and 5/6 even if we didn't eliminate the other fractions.

Margaret drove 30 miles one way and 30 miles back, totaling 60 miles.

Given that Margaret drove to a business appointment at 30 mph, and her average speed on the return trip was 20 mph, and the return trip took 1/2 hr longer because of heavy traffic, to determine how far did she travel to the appointment the following calculation must be performed:

Therefore, Margaret drove 30 miles one way and 30 miles back, totaling 60 miles.

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Actual time is much longer than the 50-year timeframe suggested by the speaker.

How to verify the statement?

This claim is based on the assumption that the rate of pollution reduction from each factory remains constant at 80%, and the number of factories increases by 3% per annum.

To verify this claim, we can use the following formula to calculate the expected total pollution after n years:

Total pollution after n years = \(Present \: pollution \: level x (1 + 0.03)^n \times (1 - 0.8)^n\)

Here, the first factor represents the increase in pollution due to the growth in the number of factories, and the second factor represents the reduction in pollution due to the 80% reduction in pollution from each factory.

We can set the expected total pollution after n years equal to the present pollution level and solve for n:

\(Present \: pollution \: level = Present \: pollution \: level \times (1 + 0.03)^n \times (1 - 0.8)^n\)

Simplifying this equation, we get:

\(1 = 1.03^n \times 0.2^n\)

Taking the logarithm of both sides of the equation, we get,

\(n \times log(1.03) + n \times log(0.2) = 0 \\ n \times (log(1.03) + log(0.2)) = 0 \\ n = \frac{0} { (log(1.03) + log(0.2))} \\ n = 271.56\)

Therefore, according to this calculation, it would take approximately 272 years for the total annual pollution to return to its present level if the number of factories in the country increases by 3% per annum, and they all immediately reduce the amount of pollution they produce by 80%. This is much longer than the 50-year timeframe suggested by the speaker.

It is important to note that this calculation assumes that the pollution reduction from each factory remains constant at 80% and does not take into account any other factors that may affect pollution levels, such as changes in technology or regulations. Therefore, this should be considered as a rough estimate and not as an exact prediction.

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Correct question is "A speaker claimed that if the number of factories in the country increases by 3% per annum, then even if they all immediately reduced the amount of pollution they produce by 80%, the total annual pollution will be back to its present level in about 50 years. Verify the statement. (use logarithm)"

Ahab's total change to funds is -$175, which means he spent more than he gained.

Ahab spent 3 tires at $50 each, which is a total of 3 x $50 = $150.

Later, he returned one tire, so he gets $50 back.

He also found a $5 bill, so he has an extra $5.

He then bought 2 jackets at $40 each, which is a total of 2 x $40 = $80.

The total amount Ahab spent is $150 + $80 = $230.

However, he also received $50 back and found $5, so his total change to funds is $50 + $5 - $230 = -$175.

Therefore, Ahab's total change to funds is -$175, which means he spent more than he gained.

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In the class, Lucy's score is 6.

In statistics, the median is the middle value in a sorted, ascending or descending list of numbers. Thus, it represents the midpoint of the data.

The median is often compared with other descriptive statistics such as the mean (average), mode, and standard deviation.

Since Lucy is one of the 29 students in the class and her score was the same as the median score for her class.

Thus, the median score will be 15th score (i.e. the midpoint of 29). Using the frequency in of each score from the figure, let's keep adding the frequency until we reach 15 and we will then check the corresponding score at the 15th position:

2 + 2 + 4 + 7 = 15

Thus, the the corresponding score at the 15th position is 6.

Therefore, the median score is 6 and consequently Lucy's score is 6.

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Answer:

g(-4) = 1

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

What g(-4) is saying is what the output of the function g(x) when x= -4. According to the graph, when x = -4, y = 1.

∴ g(-4) = 1

Answer:

a) The mean is 225 and the standard deviation is 11.12.

b) It means that in samples of 500 adult Americans, the number of those who believe that the overall state of moral values in the United States is poor is expected to be around 225.

c) No, since 240 is less than 2.5 standard deviations from the mean.

Step-by-step explanation:

For each adult American, there are only two possible outcomes. Either they believe the overall state of moral values in the US is poor, or they do not. The adults are independent of other adults. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

\(E(X) = np\)

The standard deviation of the binomial distribution is:

\(\sqrt{V(X)} = \sqrt{np(1-p)}\)

In the binomial distribution, a value is considered to be unusual if it is more than 2.5 standard deviations from the mean.

45% of adult Americans believe that the overall state of moral values in the United States is poor.

This means that \(p = 0.45\)

(a) Compute the mean and standard deviation of the random variable X, the number of adults who believe that the overall state of moral values in the United States is poor based on a random sample of 500 adult Americans.

Sample of 500 means that \(n = 500\)

Mean:

\(E(X) = np = 500*0.45 = 225\)

Standard deviation:

\(\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{500*0.45*0.55} = 11.12\)

The mean is 225 and the standard deviation is 11.12.

(b) Interpret the mean.

It means that in samples of 500 adult Americans, the number of those who believe that the overall state of moral values in the United States is poor is expected to be around 225.

(c) Would it be unusual to identify 240 adult Americans who believe that the overall state of moral values in the United States is poor based on a random sample of 500 adult Americans

2.5 standard deviations above the mean is:

225 + 2.5*11.12 = 252.8

So 253 or more would be unusual, 240 no.

\(12x\sqrt{\cfrac{3}{2}}~~ = ~~6\sqrt{3}\implies (6)(2)x\cdot \cfrac{\sqrt{3}}{\sqrt{2}}~~ = ~~6\sqrt{3}\implies \cfrac{(2x)(6\sqrt{3})}{\sqrt{2}}=6\sqrt{3} \\\\\\ \cfrac{2x}{\sqrt{2}}=\cfrac{6\sqrt{3}}{6\sqrt{3}}\implies \cfrac{2x}{\sqrt{2}}=1\implies 2x=\sqrt{2}\implies x=\cfrac{\sqrt{2}}{2}\)