Factor: 81y^2-49
Your answer

The system of equations as an augmented matrix is \(\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]\)

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

x                  = 100

   -5m  - 7c  = 350

   -5m  - 9c  = 200

The above means that the variables in the system of equations are

x, m and c

So, we have the following representation

x    m     c        

1    0      0        100

0   -5    -7        350

0   -5    -9        200

When represented as an augmented matrix, we have

\(\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]\)

Hence, the augmented matrix is \(\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]\)

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Answer:

C. 4 hours

Step-by-step explanation:

I know this because it needs to be increased 20 mph more and since it increases 5 mph each hour then it would need to be increased the 5 mph 4 times to reach 75 mph.

Answer: Yes

Step-by-step explanation:It can because math works like that.

Answer:

Step-by-step explanation:

\( \frac{5}{ {3b}^{3} - {2b}^{2} - 5 } = \frac{2}{ {b}^{3} - 2 } \\ 5( {b}^{3} - 2) = 2( {3b}^{3} - {2b}^{2} - 5) \\ {5b}^{3} - 10 = {6b}^{3} - {4b}^{2} - 10 \\ 10 - 10 = {6b}^{3} - {5b}^{3} - {4b}^{2} \\ 0 = {b}^{3} - {4b}^{2} \\ 0 = {b}^{2} (b - 4) \\ \)

b = 0 or b - 4 = 0

b = 0

b = 4

Answer:

a= 0

b= \(-\frac{\sqrt{42} }{12}\)

Step-by-step explanation:

We can rewrite the expression to be:

\(\frac{i\sqrt{7} }{i^{2}\sqrt{24} }\)

We then can cancel out the i and we get

\(\frac{\sqrt{7} }{\sqrt{24} i}\)

Can be rewritten as

\(\frac{\sqrt{7} }{2\sqrt{6} i}\)

We then rationalize and get

\(-\frac{\sqrt{42} }{12} i\)

The mode for the given series of numbers, which are 100, 150, 200, 150, 175, 160, 150, 225, 250, is 150.

In statistics, the mode is the value that appears most frequently in a given set of data. In the series of numbers given, we can see that the number 150 appears three times, which is more than any other number in the series. This means that 150 is the mode of the series.

To further illustrate, let's count the frequency of each number in the series

100 appears once

150 appears three times

160 appears once

175 appears once

200 appears once

225 appears once

250 appears once

As we can see, the number 150 appears most frequently, and thus is the mode.

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Answer:

BODMAS RULE

(c-3)²=100

c²-6c+9=100

c²-6c=100-9

c²-6c=91

c²-6c-91=0

then factories

Answer:

Yield on this bond = 4.5%

Step-by-step explanation:

Given:

Face value of bond = $10,000

Annual interest receives from bond = $450

Find:

Yield on this bond

Computation:

Yield on bond = [Annual interest / Face value]100

Yield on this bond = [Annual interest receives from bond / Face value of bond]100

Yield on this bond = [450 / 10,000]100

Yield on this bond = [0.045]100

Yield on this bond = 4.5%

The range is 3.5, and it means that it is the value that occurs the most.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

We find the range by subtracting the smallest value from the largest value.

The smallest value on the number line is 4 (with two dots) and

the largest value is 7.5.

Therefore, the range is:

7.5 - 4 = 3.5

So the range is 3.5, but it does not mean that the data varies by a value of 3.5.

The range tells us how spread out the data is, specifically the difference between the highest and lowest values in the data set.

A range of 5.0 means that there is a difference of 5.0 between the largest and smallest values.

Hence, the range is 3.5, and it means that it is the value that occurs the most.

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Answer:

-8p+64

Step-by-step explanation:

Multiply each term in parentheses by 8

8×-p= -8p

-8p+8×8 (8×8=64)

= -8p+64

Answer:

8 is the correct answer because coefficient lies before Exponent. Exponent is variable

So 8 is the coefficient.

The domain of the function f(x) = -3x + 2 is (-∞, +∞), representing all real numbers, and the range is (-∞, 2], representing all real numbers less than or equal to 2.

The function f(x) = -3x + 2 is a linear function defined by a straight line. To determine the domain of this function, we need to identify the range of values for which the function is defined.

The domain of a linear function is typically all real numbers unless there are any restrictions. In this case, there is no explicit restriction mentioned, so we can assume that the function is defined for all real numbers.

Therefore, the domain of the function f(x) = -3x + 2 is (-∞, +∞), which represents all real numbers.

Now, let's analyze the range of the function. The range of a linear function can be determined by observing the slope of the line. In this case, the slope of the line is -3, which means that as x increases, the function values will decrease.

Since the slope is negative, the range of the function f(x) = -3x + 2 will be all real numbers less than or equal to the y-intercept, which is 2.

Therefore, the range of the function is (-∞, 2] since the function values cannot exceed 2.

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Answer:

6

Step-by-step explanation:

8x+6x+6 = 90

14x = 84

x = 6

Answer:

\( \huge{ \red{ \bold{SOLUTION:-}}}\)

\( \rm{The \: sum \: of \: all \: the \: angles = 90 {}^{ \circ} }\)

\( \rm{i.e.(8 {x}^{ \circ} ) + ( {6x}^{ \circ} + {6}^{ \circ} ) = {90}^{ \circ} }\)

\( \implies{ \rm{ {14}^{ \circ} + {6}^{ \circ} = 90}}\)

\( \implies{ \rm{ {14}^{ \circ} = {90}^{ \circ} - {6}^{\circ} }}\)

\( \implies{ \rm{14x {}^{ \circ} = {84}^{\circ} }}\)

\( \implies{ \displaystyle\rm{ {x}^{\circ} = \frac{8 {4}^{\circ} }{14} }}\)

\( \implies{ \rm{ {x}^{\circ} = {6}^{\circ} }}\)

\( \therefore{ \rm{The \: value \: of \: x \: is \: {6}^{ \circ} .}}\)

\(\red {\rule{35pt}{2pt}} \green{ \rule{35pt}{2pt}}\orange{ \rule{35pt}{2pt}}\pink{ \rule{35pt}{2pt}}\blue{ \rule{35pt}{2pt}}\purple{ \rule{35pt}{2pt}}\red{ \rule{35pt}{2pt}}\)

Hope this helps you....

Answer:

B

Step-by-step explanation:

Yes, because for each input there is exactly one output. You can have two of the same x values but you cannot have 2 of the same y values. if you have two of the same y values, it is not a function as it doesn't pass the vertical line test.

Answer:

Percent change = 600 - 30 |30| × 100% = 570 30 × 100 = 1900% (increase). Where: 30 is the old value and 600 is the new value.

Step-by-step explanation:

The airplane will take 0.0095 seconds to cover 272 meters at a rate of 769 kilometers per hour, which is equivalent to 213.6 meters per second.

(272 m) / (769 km/h) x (1 h/3600 s) = 0.0095 s

1. Convert km/h to m/s: 769 km/h x (1000 m/1 km) x (1 h/3600 s) = 213.6 m/s

2. Divide the distance to travel (272 m) by the rate (213.6 m/s): 272 m / 213.6 m/s = 0.0095 s

The airplane's speed on this certain flight is 769 kilometers per hour. In order to calculate how long it will take to cover a distance of 272 meters, we must first convert the speed to meters per second. 769 kilometers per hour is equivalent to 213.6 meters per second. Once we have the rate, we can divide the distance by the rate, which is 272 meters divided by 213.6 meters per second. This calculation yields a result of 0.0095 seconds. Therefore, the airplane will take 0.0095 seconds to cover 272 meters.

The airplane will take 0.0095 seconds to cover 272 meters at a rate of 769 kilometers per hour, which is equivalent to 213.6 meters per second.

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The mean of the test is 20.

To determine the mean of the test, we need to use the information provided about the scores falling above the mean in terms of standard deviations.

Let's denote the mean of the test as μ, and the standard deviation as σ.

We are given that a score of 29 falls three standard deviations above the mean, so we can write this as:

29 = μ + 3σ

Similarly, we are told that a score of 23 falls one standard deviation above the mean, which can be expressed as:

23 = μ + σ

Now we have a system of two equations with two variables (μ and σ). We can solve this system of equations to find the values of μ and σ.

From the second equation, we can isolate μ:

μ = 23 - σ

Substituting this value into the first equation, we have:

29 = (23 - σ) + 3σ

Simplifying the equation, we get:

29 = 23 + 2σ

2σ = 29 - 23

2σ = 6

σ = 3

Substituting the value of σ back into the second equation, we find:

μ = 23 - 3

μ = 20

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The total cost of the fence needed for the Perimeter of the work site is $8,800. So the answer is option B.

Because the question involves many units of measurement, we must convert them all to the same unit in order to determine the answer.

1/4 mile is equivalent to 1320 feet (1 mile = 5280 feet).

The length of the fence required to surround the work site equals the perimeter of the work site. To calculate the length of the fence in yards, divide 1320 feet by 3 (since a yard is 3 feet long).

1320 feet ÷ 3 = 440 yards

So the length of the fence needed is 440 yards.

The fence costs $20.00 per yard, thus to get the total cost, multiply the length of the fence by the cost per yard:

440 yards x $20.00/yard = $8,800.00

Therefore, the total cost of the fence needed for the perimeter of the work site is $8,800.00.

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Answer:

C) between 3 and 6 hours (5 to 13 cars)

Step-by-step explanation:

**see attached image for question**

To read the graph, find the revelant "number of hours" section.  Look at the dots in that section and write down the approx lowest value and highest value - this is the range.

For example, between 0 and 2 hours, there is only one dot at 2 hours. Reading across to the y-axis, this is at 39 cars.

Looking at the part of the graph between 10 and 12 hours, the lowest dot is at y = 3 and the highest dot is at approx y = 34.  Therefore the number of cars in this time bracket is 3 to 34.

Reading the graph:

8 - 11 hours:  3 - 34 cars

0 - 2 hours:  39 cars

3 - 6 hours:  5 - 13 cars

10 - 12 hours: 3 - 34 cars

Therefore, the answer is C) as it is the only one that concurs with the above graph readings.

To find the limit of a convergent sequence, we can simply take the limit as n approaches infinity. Let's calculate the limits for each of the given sequences:

A. \(\sf\:\lim_{n \to \infty} \frac{5n}{n+7} \\\)

To find the limit, we divide the leading terms by n:

\(\sf\:\lim_{n \to \infty} \frac{5n/n}{(n+7)/n} = \frac{5}{1} = 5 \\\)

Therefore, the limit of the sequence A is 5.

B. \(\sf\:\lim_{n \to \infty} \frac{4-7n}{8+n} \\\)

Again, divide the leading terms by n:

\(\sf\:\lim_{n \to \infty} \frac{4/n - 7}{8/n + 1} = \frac{0 - 7}{0 + 1} = -7 \\\)

So, the limit of sequence B is -7.

C. \(\sf:\lim_{n \to \infty} \frac{8n - 500\sqrt{n}}{2n + 800\sqrt{n}} \\\)

Divide the leading terms by n:

\(\sf\:\lim_{n \to \infty} \frac{8 - 500\sqrt{n}/n}{2 + 800\sqrt{n}/n} \\\)

As n approaches infinity, the terms involving \(\sf\:\sqrt{n}/n \\\) tend to 0:

\(\sf\:\lim_{n \to \infty} \frac{8 - 500(0)}{2 + 800(0)} = \frac{8}{2} = 4 \\\)

Therefore, the limit of sequence C is 4.

To summarize:

A. The limit of sequence A is 5.

B. The limit of sequence B is -7.

C. The limit of sequence C is 4.

Answer:

See below

Step-by-step explanation:

Desmos is a free graphing calculator.

Based on the information, we can infer that the salary a worker earns depends on the hourly wage they earn. In this case we will have to multiply the value of each hour by the number of hours worked. Additionally, I would agree to have a higher minimum wage to benefit workers.

Based on the information in the graph, we can infer that workers will have wages of $5.2, $6.0, and $6.6. According to the above, the salary varies depending on the number of hours.

On the other hand, I believe that you would agree to a salary increase because this would benefit workers who would be better paid for each hour of work.

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Length of scarf before unraveling = 4.75 + 0.75 = 5.5.

Equation: Length before unraveling = 4.75 + 0.75

Sadie is knitting a striped scarf for her grandfather for his birthday, but discovers a mistake and has to unravel 0.75 of the scarf. After unraveling, the remaining part of the scarf is 4.75 long. To calculate the length of the scarf before it was unraveled, we can use an equation. The equation we will use is Length before unraveling = 4.75 + 0.75. We can interpret this equation as the length before unraveling being equal to the length after unraveling plus the amount unraveled. Therefore, the length of the scarf before unraveling is 4.75 + 0.75, which is equal to 5.5. This equation is useful for finding the original length of the scarf, as it takes into account the amount that was unraveled. Therefore, the original length of the scarf is 5.5.

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The equation of the line in slope-intercept form is y = (3/4)x.

To write the equation of a line in slope-intercept form, we need to use the slope-intercept form equation: y = mx + b,

where m is the slope and b is the y-intercept.

Given that the line passes through the point (-8, 5) and has a slope of 3/4, we can substitute the values into the equation to find the y-intercept (b).

First, let's find the value of b using the point-slope form equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line.

Using (-8, 5) as the point and 3/4 as the slope, we have:

5 - 5 = (3/4)(-8 - x)

0 = (3/4)(-8 - x)

0 = (-3/4)(8 + x)

0 = -6 - (3/4)x

Next, we can solve for x:

(3/4)x = -6

x = -6 \(\times\) (4/3)

x = -8

Now that we have the value of x, we can substitute it back into the equation to find the value of b:

0 = -6 - (3/4)(-8)

0 = -6 + 6

0 = 0

So, the value of b is 0.

Finally, we can write the equation of the line in slope-intercept form:

y = (3/4)x + 0

y = (3/4)x.

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The value of the coin in 2019 would be approximately $132.

To calculate the value of the coin in 2019, we need to consider the annual increase rate of 16.9% from 2010 to 2019. We can use the compound interest formula to find the final value.

Starting with the initial value of $40 in 2010, we can calculate the value in 2019 as follows:

Value in 2019 = Initial value * (1 + Rate)^n

where Rate is the annual increase rate and n is the number of years between 2010 and 2019.

Plugging in the values:

Value in 2019 = $40 * (1 + 0.169)^9

Value in 2019 ≈ $40 * 2.996

Value in 2019 ≈ $119.84

Rounding the value to the nearest dollar, we get approximately $120. Therefore, the value of the coin in 2019 would be approximately $120.

However, please note that the exact value may vary depending on the specific compounding method and rounding conventions used.

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Answer:

To simplify the expression (a÷b)³×(b÷c)×(c÷a)³ when a=3, b=a², c=a³, we can substitute the given values and perform the calculations.

Substituting the values of a, b, and c:

a = 3

b = a² = 3² = 9

c = a³ = 3³ = 27

Now let's simplify the expression:

(a÷b)³×(b÷c)×(c÷a)³

(3÷9)³×(9÷27)×(27÷3)³

Simplifying each term:

(3÷9) = 1/3

(9÷27) = 1/3

(27÷3) = 9

Now we can substitute the simplified values back into the expression:

(1/3)³×(1/3)×9

Simplifying further:

(1/27)×(1/3)×9

1/9

Therefore, the simplified expression is 1/9.