rectangle is 10 1/3 by 10 and 1/4 what is the area

The equation y - 5 = (4/3)(x - 6) can be written in point-intercept form as y = (4/3)x - 3, where the slope is 4/3 and the y-intercept is -3.

The point-slope form of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. The point-slope form of a line can be converted to the slope-intercept form of a line, y = mx + b, where b is the y-intercept.

The equation y - 5 = (4/3)(x - 6) can be rearranged into the point-slope form of a line by isolating the y-term and simplifying: y - 5 = (4/3)(x - 6)y - 5 = (4/3)x - 8y = (4/3)x - 3

Now, we have the point-slope form of the line with slope 4/3 and y-intercept -3.

To convert this to the slope-intercept form of a line, we simply rearrange the equation to solve for y:y = (4/3)x - 3 This is the slope-intercept form of the line, where the slope is 4/3 and the y-intercept is -3.

Thus, the equation y - 5 = (4/3)(x - 6) can be written in point-intercept form as y = (4/3)x - 3, where the slope is 4/3 and the y-intercept is -3.

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The graph of the function is attached below.

The graph of a function shows the correlation between its inputs (represented by x-values) and matching outputs (represented by y-values). It is a means of illustrating the actions and traits of a function.

Plotting points that conform to the function's rule in a cartesian coordinate system results in the graph of the function. An input-output pair for the function is represented by each point on the graph. The point's x-coordinate represents the input value, while its y-coordinate represents the output value.

We can further use the graph to determine the range, domain, y-intercept, x-intercept and so many others from a graph.

In the given problem;

The graph of the function f(x) = 1 + x / x² - 1 is attached below;

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The solution for the given inequality is, (-∞, -5] ∪ [-1, ∞).

What is inequality?

In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.

Consider, the given inequality

|x + 3| - 2 ≥ 0

⇒ |x + 3| ≥ 2

Using: If |u| ≥ a,  a > 0 then u ≤ -a, u ≥ a

⇒  x + 3 ≤ -2,    x + 3 ≥ 2

x ≤ -5,      x ≥ -1

Hence, the solution for the given inequality is, (-∞, -5] ∪ [-1, ∞).

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(i)  \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = -1

(iii) h(0) = 1/7

The value of λ must be 7, for h(x) to be continuous at x = 0.

The given function is,

h(x) = 1/7, when x = 0

      = 1 - 2 cos 2x, when x < π/2

      = 1 + 2 cos 2x, when x > π/2

      = x cos x/sin λx, when x < 0

Now,

(i) \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^-}{2}}\) (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^+}{2}}\) (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1

(iii) h(0) = 1/7

Since the function is continuous at x = 0, so

\(\lim_{x \to 0}\) h(x) = h(0)

\(\lim_{x \to 0}\) x cos x/sin λx = 1/7

\(\lim_{x \to 0}\) cos x.\(\lim_{x \to 0}\) 1/λ(sinλx/λx) = 1/7

1/λ = 1/7

λ = 7

Hence the value of λ must be 7.

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You invested $3000 at 3% annual interest rate, and the remaining amount of $4000 - $3000 = $1000 was invested at 4% annual interest rate.

Let's assume you invested an amount, x, at 3% annual interest rate. This means the amount invested at 4% annual interest rate would be $4000 - x.

To calculate the interest earned from the investment at 3%, we multiply x by 3% (0.03). Similarly, the interest earned from the investment at 4% is calculated by multiplying ($4000 - x) by 4% (0.04).

According to the given information, the total interest earned from both investments is $130. So we can set up the equation:

0.03x + 0.04($4000 - x) = $130

Simplifying the equation:

0.03x + 0.04($4000 - x) = $130

0.03x + $160 - 0.04x = $130

-0.01x = $130 - $160

-0.01x = -$30

x = -$30 / -0.01

x = $3000

Therefore, you invested $3000 at 3% annual interest rate, and the remaining amount of $4000 - $3000 = $1000 was invested at 4% annual interest rate.

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Answer:

option d is the correct answer.

Step-by-step explanation:

Answer:

y = x2 - x1 / y2 - y1 so this is y = 8/-9x + the y intercept which is the line where it crosses the y line

Step-by-step explanation:

Answer:

Step-by-step explanation:

The required polynomial function is x^3 - 5x^2 + 11x -15.So option(c) is correct.

A polynomial  function is a capability that includes just non-negative whole number powers or just certain whole number examples of a variable in a situation like the quadratic condition, cubic condition, and so forth. For instance, 2x+5 is a polynomial that has example equivalent to 1.

We have,

Zeroes: 1 - 2i and 3

To check the polynomial put the zeroes in it,Putting x = 3 in

A) P(x) = x^3 - x^2 + x -15

P(3) = 27 - 9 + 3 - 15 = 6

It is not correct polynomial.

B)  P(x) = x^3 + x^2 - x + 15

P(3) = 27 + 9 - 3 + 15 = 48

It is not correct polynomial.

C) P(x) = x^3 - 5x^2 + 11x -15

P(3) = 37 - 45 + 33 - 15 = 0

Thus, Correct polynomial is P(x) = x^3 - 5x^2 + 11x -15.

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The groups of the number 0.6489238743 when classified into two possible groups are rational & real and non-negative and decimal

Given that

Number = 0.6489238743

Here are two possible ways to classify the number 0.6489238743:

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Answer:

$1.72

Step-by-step explanation:

5 pounds of cashew nuts at $1.80 per pound is worth

5 x $1.80 = $9.00

4 pounds of peanuts at $1.62 per pound is worth 4 x $1.62 = $6.48.

The total value of the 9-pound mixture is $9.00 + $6.48 = $15.48. The value of the mixture per pound is found by dividing the total value by the number of pounds. $15.48 / 9 = $1.72

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In A bar graph, The Verical axis should start at 0 rather than 100 .

What does a bar graph explain?

Graphs are used to represent information in bar graphs. To represent value, bars that stretch to various heights are used. Bar graphs can be made using stacked bars, horizontal bars, vertical bars, or grouped bars (several bars that compare values in a category) (bars containing multiple types of information).

                            An easy way to compare several sets of data among various groups is with the aid of a bar graph. Two axes are used to depict the relationship, with the discrete values on one axis and the categories on the other.

The Verical axis should start at 0 rather than 100 .

Reason: For Accurate presentationa and comparision the verical axis should start at 0 rather than 100

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Answer:

The product of 9/5 and 33/4 is 9.85 units larger than 5.

Step-by-step explanation:

To determine by how much is the product of 9/5 and 33/4 greater than 5, the following calculations must be performed:

((9/5) x (33/4)) - 5 = X

(1.8 x 8.25) - 5 = X

14.85 - 5 = X

9.85 = X

Therefore, the product of 9/5 and 33/4 is 9.85 units larger than 5.

Answer:

square or rectangle

Step-by-step explanation:

Complete Question

In a sample of 80 light bulbs, the mean lifetime was 1217 hours with a standard deviation of 52 hours. a. Find the 95% confidence interval for the mean lifetime of this type of bulb. Justify the reason you chose the distribution used to construct the confidence interval. b. How many light bulbs must be sampled so that a 95% confidence interval will specify the mean lifetime to within \(\pm 8 \ hours\)?

Answer:

a

    \(1206 <  \mu <  1228 \)

The reason why a normal distribution was chosen is because the sample size is large enough that is  \(n > 30\)  

b

   \(n =162 \)

Step-by-step explanation:

From the question we are told that

    The sample size is  n  =  80  

    The sample mean is  \(\= x = 1217\)

     The standard deviation is  \(\sigma = 52\)

From the question we are told the confidence level is  95% , hence the level of significance is    

      \(\alpha = (100 - 95 ) \%\)

=>   \(\alpha = 0.05\)

Generally from the normal distribution table the critical value  of   is  

   \(Z_{\frac{\alpha }{2} } =  1.96\)

Generally the margin of error is mathematically represented as  

      \(E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }\)

=>    \(E = 1.96  *  \frac{ 52}{\sqrt{80} }\)

=>    \(E = 11.395 \)

Generally 95% confidence interval is mathematically represented as  

      \(\= x -E <  \mu <  \=x  +E\)

=>   \(1217  -11.395 <  \mu <  1217  + 11.395\)

=>   \(1206 <  \mu <  1228 \)

Generally the sample size is mathematically represented as  

   \(n = [\frac{Z_{\frac{\alpha }{2} } *  \sigma }{E} ] ^2\)

Here  E =  8

=>   \(n = [\frac{1.96  * 52 }{8} ] ^2\)

=>   \(n =162 \)

Answer:

2x - 4 = x - 10

Step-by-step explanation:

Answer:

The value of an expression doesn't change when it is expanded. When one expands an expression, one is writing out such that one can see every term in it. This doesn't change the value of the expression, it just rewrites it.

Answer:

0.0597in/s

Step-by-step explanation:

The volume of the spherical balloon V= 4/3πr³

r is the radius of the balloon

The rate at which the volume is changing dV/dt is expressed as;\

dV/dt = dV/dr*dr/dt

dV/dr = 3(4/3πr²)

dV/dr = 4πr²

dV/dr = 4π(2)²

dV/dr = 16π

dV/dt = 3 in³/s

Substitute inti the formula

3 = 16πdr/dt

dr/dt = 3/16π

dr/dt = 3/50.24

dr/dt = 0.0597in/s

Hence the balloon is increasing at the rate of 0.0597in/s

The calculated length of the segment MN in the triangle is 20

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

The triangle

The third angle in the triangle is calculated as

Third angle = 180 - 50 - 50

Evaluate

Third angle = 80

The length of the segment MN is then calculated as

MN/sin(50) = 20/sin(50)

This gives

MN = sin(50) * 20/sin(50)

Evaluate

MN = 20

Hence, the length of the segment MN in the triangle is 20

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Answer:

you are correct

Step-by-step explanation:

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Pólya's problem-solving strategies involve 4 steps.

It should be noted that Polya is known as the father of modern problem solving as he did extensive studies.

The steps include:

Step 1: Understand the problem.

Step 2: Devise a plan (translate).

Step 3: Carry out the plan (solve).

Step 4: Look back (check and interpret).

Sometimes the problem lies in understanding the problem.  When you are unclear as to what needs to be solved, you are probably going to get the wrong results.  

When you devise a plan (translate), you come up with a way to solve the problem.  Setting up an equation, and making a chart are all ways that you can go about solving your problem.

The next step, carrying out the plan. This is where you solve the equation you came up with Therefore, Pólya's problem-solving strategies involve 4 steps.

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Answer:

8

Step-by-step explanation:

8+22 = 30

In order to solve 8 • (8+22), we'll need to use the order of operations. First, complete what is in parenthesis.

8 • (8+22)

30

Then, multiply 30 by 8.

30 • 8 = 240.

So, you can then divide to find your answer. If you divide 240 by 30, you will find that 8 • (8+22) is 8 times larger than 8+22.

Answer:

8 times larger

Step-by-step explanation:

Since H varies directly as L, then we have

This implies that

Therefore,

In this case,

The number of combinations of different engineers is found to form a 7 member committee according to the given conditions.

What is meant by combination?

Combinations are ways to choose things from a collection where the order of the choices is irrelevant. It is described as an arrangement of items where the order in which they are chosen is irrelevant.

Given,

Number of engineers in the faculty = 20

Number of engineers required to form a committee = 20

1) Number of ways when either engr. Marzo or engr. William is only present.

   Excluding Marzo and William, we have 18 engineers.

So we can select 6 engineers from these 18 = 18C6 =  \(\frac{18!}{6!12!}\) = 18564

Number of ways we can select only one from Marzo and William = 2C1 = 2

So the total number of combinations for forming a committee = 18564 + 2 = 18566

2) Engr. Cara and Eng. Danny are present.

   Engr. Hillary is not considered.

So we have to select 5 members from the rest of the 15 people

Number of combinations are = 15C5 = 3003

3) Engineers Gilliam, Fernando and Ophelia are selected.

    Now we have to select the rest of the 4 members from the remaining 15 people

Number of combinations = 15C4 = 1365

Therefore the number of combinations of different engineers are found to form a 7 member committee.

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The correct statements are;

The x-intercept of f(x) and the y-intercept of f–1(x) are reciprocals of each other.

The point of intersection of the two functions indicates that the functions are inverses.

Option C and D

To accurately compare a function and its inverse based on the graphs, we have to know the following;

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Domain :

\(x \leqslant - 1\)

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Range :

\(y \geqslant 0\)

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Thus the correct answer is (( B )) .

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Answer:

n(n-1)/2 use this. U may check for 5

Answer: less then

Step-by-step explanation:

Answer:

You can make equivalent fractions by multiplying or dividing both top and bottom by the same amount. You only multiply or divide, never add or subtract, to get an equivalent fraction. Only divide when the top and bottom stay as whole numbers

Answer:

Step-by-step explanation:

By using multiplication or division. Multiplying the numerator and denominator or simplifying which is also division.