--------------------

Answer:

If you divide:

[tex]1+\frac{x+3}{x^2-3x-40}[/tex]

If you simplify:

[tex]\frac{x^2-2x-37}{(x-8)(x+5)}[/tex]

Step-by-step explanation:

The equation for the circle whose endpoints are A(1,4) and B(5,4) is written in diameter form [tex]x^{2} +y^{2}[/tex] -6x -8y + 21 = 0

A circle is a closed two-dimensional object in which every point in the plane is equally spaced from a certain point known as the "center" The symmetry line of reflection is formed by each line that traverses the circle. Additionally, it is rotationally symmetric about the center for all angles. In the plane, the circle formula is as follows:

The coordinate coordinates (x,y) are equal to (x-h)2 + (y-k)2 = r2.

The centre of a circle is located at (h,k), and its radius is measured in units of r.

The equation of a circle having end points of the diameter as (x1​,y1​) and (x2​,y2​) is (x−x1​)(x−x2​)+(y−y1​)(y−y2​)=0.

we have (1,4) and (5,4) as (x1​,y1​) and (x2​,y2​)

(x−(1))(x−(5))+(y−(4))(y−(4))=0

⇒ ([tex]x^{2}[/tex] -5x -1x + 5 ) + ( [tex]y^{2}[/tex] -4y -4y + 16 ) = 0

[tex]x^{2} +y^{2}[/tex] -6x -8y + 21 = 0

The equation for the circle whose endpoints are A(1,4) and B(5,4) is written in diameter form [tex]x^{2} +y^{2}[/tex] -6x -8y + 21 = 0.

To know more about circle click:

brainly.com/question/29142813

#SPJ1

Answer:

3x + 5y = 5

Multiply by 2 on both sides.

-2x - 8y = -6

Multiply by 3 on both sides.

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases} \;\;\:3x + 5y = 5\\-2x-8y = 6\end{cases}[/tex]

To eliminate the x-terms in the given system of equations:

3x + 5y = 5 → Multiply  by 2 on both sides:

[tex]\implies 2(3x+5y)=2(5)[/tex]

[tex]\implies 6x+10y=10[/tex]

-2x - 8y = 6 → Multiply by 3 on both sides:

[tex]\implies 3(-2x - 8y) = 3(6)[/tex]

[tex]\implies -6x - 24y = 18[/tex]

Add them together to eliminate x:

[tex]\begin{array}{crcccc}&6x&+&10y&=&10\\+&(-6x&-&24y&=&18\\\cline{2-6} &&-&14y&=&28\end{array}[/tex]

a) The amount of money that he earned with the stock was of: $382.05.

b) The return on the investment was of: 96.40%.

The amount of money earned is obtained by the subtraction of the price that the stock was sold by the price the stock was bought. If this amount is negative, it means that money was lost, otherwise money was earned.

Considering the values on the problem, the amount that he earned with the stock is given as follows:

778.38 - 396.33 = $382.05.

The return on the investment is given by the amount earned/lost divided by the initial value, and multiplied by 100% to obtain the value as a percentage, hence it is of:

382.05/396.33 x 100% = 96.40%.

More can be learned about investments and percentages at https://brainly.com/question/1305349

#SPJ1

13.5m × 20.74m or 20.74m × 13.5m can be the possible dimensions.

Height, length, and width are the three dimensions that all of the places we dwell and things we utilize on a daily basis have.

Height, depth, and other dimensions are examples of dimensions.

The dimensions of a line, a square, and a cube are each one, two, and three, respectively.

However, we consider the Universe to have one temporal dimension and three spatial dimensions (north-south, east-west, and up-down).

So, we have the area (A):

A = (54 – 2x)x

A = 54x - 2x²

Differentiate to obtain: dA/dX = 54 - 4x

We shall differentiate and equate to zero for a maximum Area, so dA/dx = 0.

54 – 4x = 0

x = 54/4

x = 13.5 m

It covers 280 m². Consequently, the other potential dimension:

w = 280/13.5

w = 20.74 m

Therefore, 13.5m × 20.74m or 20.74m × 13.5m can be the possible dimensions.

Know more about dimensions here:

https://brainly.com/question/19819849

#SPJ1

Answer:

Step-by-step explanation:

Sophie was offered a job after college earning a salary of $30,000. She will get a raise of $2,000 after each year working for the company. Answer the questions below regarding the relationship between salary and the number of years working at the company.

Reflection across the y-axis on a coordinate plane.

What is the short definition of a coordinate plane?

Two number lines combine to produce the coordinate plane, a two-dimensional surface. The x-axis is a single horizontal number line. The y-axis is a vertical number line, which is the other number line. A place known as the origin is where the two axes collide. The coordinate plane allows us to graph points, lines, and more.

What is reflaction of coordinate plane?

Transformation is the process of making each point in a shape appear at the same distance on the other side of a specified line.

                           The term "line of reflection" refers to introspection with relation to that line. A line is crossed to flip the image.

Learn more about coordinate plane.

brainly.com/question/13611766

#SPJ4

The number of bacteria after 4 hours is 800

The complete question is added at the end of this solution

Given that,

This means that the rate of production is by doubling

So, we have the following parameters

a = 50

r = 2

An exponential function is represented as

A(n) = arⁿ

Substitute the known values in the above equation, so, we have the following representation

A(n) = 50(2)ⁿ

We have to find,

Find the number of bacteria after 4 hours.

This means that n = 4

So, we have

A(4) = 50(2)⁴

Evaluate

A(4) = 800

Hence, the population is 800

Read more about exponential functions at

https://brainly.com/question/11464095

#SPJ1

Complete question

in a biology lab, a population of 50 bacteria reproduce by splitting. Every hour, on the hour, each bacterium splits into two bacteria.

Find the number of bacteria after 4 hours.

Square root of 3 cos

Consider the given data.

[tex]$$\begin{aligned}& \sin \theta+\sin ^2 \theta=1 \\& \sin \theta=1-\sin ^2 \theta \\& \sin \theta=\cos ^2 \theta\end{aligned}$$[/tex]

We have,

[tex]$$\begin{aligned}& =\cos ^{12} \theta+3 \cos ^{10} \theta+3 \cos ^8 \theta+\cos ^6 \theta+2 \cos ^4 \theta+2 \cos ^2 \theta-2 \\& =\cos ^{12} \theta+3 \cos ^{10} \theta+3 \cos ^8 \theta+\cos ^6 \theta+2\left(\cos ^4 \theta+\cos ^2 \theta-1\right) \\& =\left(\cos ^4 \theta+\cos ^2 \theta\right)^3+2\left(\cos ^4 \theta+\cos ^2 \theta-1\right)\end{aligned}[/tex]

[tex]$$Since, $\sin \theta=\cos ^2 \theta$Therefore,$$\begin{aligned}& =\left(\sin ^2 \theta+\sin \theta\right)^3+2\left(\sin ^2 \theta+\sin \theta-1\right) \\& =1^3+2(1-1) \\& =1+0\end{aligned}[/tex]

[tex]=1[/tex]

Hence, the required value is 1.

To more learn about Square root visit:

https://brainly.com/question/3120622

#SPJ1

Answer:

$221

Step-by-step explanation:

The reasonable domain is { 1,2,3,4,5 }

What are domain and range of a function ?

The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

The collection of all feasible independent variable values is known as the mathematical domain. The set of all independent variable values that are conceivable yet make sense in the context at hand is known as the reasonable domain.  

Here, the situation is not given.

So, the reasonable domain is { 1,2,3,4,5 }

To learn more about the domain and range from the given link

https://brainly.com/question/28801359

#SPJ1

Answer:

20

Step-by-step explanation:

Triangle inequality says that the third side can only be 18-3...15, that is bigger than 15.

And 18+3... 21, that is smaller than 21.

If the third side is 21, the 18 and the 3 will just lay right on top of the 21 and not make a triangle. So it has to be 20 in order to be a whole number.

The sample size of 502 should be the required size to perform the experiment.

The confidence interval (1 - alpha )% for population percentage p is as follows,

CI =p +- z √pq/n

The following formula is used to determine the margin of error,

MOE = z * √pq/n

The information provided is, with a margin of error of 0.03 and = 0.32.

The z-value for an 85% degree of confidence is,

For the z-value, use a z-table.

The sample size n is then determined by,

MOE = z * √pq/n

= 1.44 √ 0.32( 1 - 0.32 ) ²/ 0.03

= ( 22.392 )²

= 502

Therefore, a sample of size 502 would be needed to assess the percentage of subjects that experience blackouts at 6 or more Gs.

To learn more about sample size

brainly.com/question/18398606

#SPJ4

24 students received an A on the test.

What is the system of linear equations?

A system of linear equations is a group of one or more linear equations that can be solved by using a simultaneous equation or elimination method. Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).

If 80% of 120 students passed the test, the number of students who passed is 120 * 80% = 96 students.

If (1)/(4) of these students received an A on the test, the number of students who received an A is (1)/(4) * 96 = 24 students.

Therefore, 24 students received an A on the test.

To learn more about the system of linear equations visit,

https://brainly.com/question/2226590

#SPJ1

The null hypothesis of a test always predicts no effect or no association between variables, but the alternative hypothesis reflects the effect or relationship that your research predicts.

Hypothesis;-

A put forward explanation for a phenomenon is called a hypothesis (plural: hypotheses).

A hypothesis cannot be called a scientific hypothesis unless it can be tested using the scientific process. Observations from the past that cannot be fully explained by the body of knowledge at this time often serve as the foundation for scientific ideas.

A scientific hypothesis is distinct from a scientific theory, despite the fact that the phrases "hypothesis" and "theory" are sometimes used interchangeably.

A working hypothesis is a theory that has been accepted provisionally and is put forth for further investigation[1], beginning with an educated guess or way of thinking.

As a result, the alternative hypothesis of a test indicates the effect or relationship that your research predicts, whereas the null hypothesis of a test always predicts that there will be no effect or no association between variables.

Learn more about hypothesis here;

https://brainly.com/question/29708875

#SPJ4

Decimal of  5% = 0.05,  0.274 to Percent:%  27.4%

A percentage is a figure or ratio that shows a portion of one hundred. A dimensionless connection between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals. The sign "%" is frequently put after the number to indicate percentages.

A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole amounts.

a).

so we have to write this in decimal that is remove percentage

To remove % we have , divide it by 100

suppose x% to remove % we divide it by 100,  x% = x/100

5% = 5/100 =0.05 which is in decimal

b). The model was 0.274 of the size that the original was. we need to add percentage so to add percentage multiple it by 100

making x to percentage

x*100 = x%

so 0.274 to % will be

0.274 *100

27.4%

Decimal of  5% = 0.05,  0.274 to Percent:% 27.4%

To know more about percentage click the link:

brainly.com/question/29306119

#SPJ1

The graph has an asymptote at y = 0.

Option (A) is correct.

What is the asymptote of the graph?

An asymptote is a straight line that constantly approaches a given curve but does not meet at an infinite distance. In other words, an Asymptote is a line that a curve approaches as it moves toward infinity.

The given function is:

                                [tex]y = 12.(\frac{1}{2})^x[/tex]

Now let's draw the graph for this given function,

By observing the graph we can conclude that the graph has an asymptote at y = 0 cause it is not meeting to the x-axis when it is approaching infinity.

Hence, the graph has an asymptote at y = 0.

To learn more about asymptote of the graph, visit:

https://brainly.com/question/10712512

#SPJ1

The two  statements that are logically true as per the given data is q=>p and  p ∧ q .

p = raining

q = Robert is laughing

q=>p   this is because the entire proposition is logically true when the conclusion of the condition is true.

and

p ∧ q   means that it is raining and Robert is laughing which is again logically true.

If two logical statements have the same truth value in all circumstances, they are said to be comparable. This fact can occasionally be used to demonstrate a mathematical result by switching out one expression for an equivalent one while maintaining the original compound proposition's truth value.

Propositional types based on Truth values

To learn more about  proportional equivalence

https://brainly.com/question/29334514

#SPJ4

Answer: $53.95

Step-by-step explanation:

Original Price: $83

Discount: 35%

35%=0.35

$83 x 35%, or 83 x 0.35

=29.05

$83-29.05

=$53.95

The coordinates of the vertices with the base b and the height h is  O(0, 0), W(b, 0), T(b, h) and S(0,h).

What is rectangle?

An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions.

The rectangle with  base b and height h.

We know that:

The point O is shown in the graph is at Origin.

So, its coordinates are O(0, 0)

Since, the height of the rectangle is h,

as S and T are h units away from the x-axis.

and the base of the rectangle is b, T and W are b units away from the y-axis.

thus the coordinates of the other vertices are:

S(0, h), T(b, h) and W(b, 0)

Therefore, the coordinates of the vertices of the following rectangle with base b and height h are:

O(0, 0), W(b, 0), T(b, h) and S(0,h)

To learn more about rectangle visit:https://brainly.com/question/15019502

#SPJ4

Step-by-step explanation:

it is an isoceles triangle (both legs are equally long).

that means also both base angles are equal :

angle J = angle L = 40°

the sum of all angles in a triangle is always 180°.

so,

180 = angle J + angle L + angle K = 40 + 40 + angle K

angle K = 180 - 40 - 40 = 100°

The width of a confidence interval for a population mean depends on group of answer choices the sample proportion is population size and sample mean .

Given :

What is population size ?

population is the entire set of items from which you draw data for a statistical study. It can be a group of individuals, a set of items, etc.

What is sample mean ?

The sample mean from a group of observations is an estimate of the population mean .

so the width of a confidence interval is dependent on population size and sample mean .

Learn more about the confidence here:

https://brainly.com/question/16807970

#SPJ4

The correct unit of measure for the mean of the sampling distribution of  (pˆB - pˆC) is Workers , the correct option is (d) .

In the question ,

it is given that ,

the proportion of workers who purchase coffee from company B is = 0.62

the proportion of workers who purchase coffee from company C is = 0.71

the random sample taken from company B is = 40 workers  

the random sample taken from company C is = 40 workers

we know that , a proportion is written as two equivalent fractions.

So , Each ratio compares the same units, percentage of workers purchasing the coffee in the restaurant,

hence,  the unit of measure for the mean of sampling distribution is workers .

Therefore , the unit for the measurement for the mean is (d) Workers .

The given question is incomplete , the complete question is

On a given day, the proportion of workers from Company B who purchase a coffee from the company cafeteria is 0.62 and the proportion of workers from Company C who purchase a coffee from the company cafeteria is 0.71. A random sample of40 workers was selected from Company B and another random sample of 40 workers was selected from Company C. The proportion of workers from Company B who purchased coffee was pˆB=0.70 and the proportion of workers from Company C who purchased coffee was pˆC=0.75.

What is the correct unit of measure for the mean of the sampling distribution of pˆB - pˆC ?

(a) Days

(b) Dollars

(c) Companies

(d) Workers .

Learn more about Mean here

https://brainly.com/question/21928747

#SPJ4

The monthly periodic interest rate on a credit card with a 24.99% APR is 0.0685% .

Hence, the monthly periodic interest rate on a credit card with a 24.99% APR is 0.0685% .

To know more about interest check the below link:

https://brainly.com/question/25793394

#SPJ1

The required value of "a" would be 3.

Perpendicular lines are two lines that cross one other and create a 90-degree angle.

As per the question, we have

Line m has the equation y = −13x − 2

Here slope of line m = -13

The slope of the given line m will be -13,

Line k passes through the points (0,4) and (9, a).

The slope of line k = (a - 4)/(9-0)

The slope of line k = (a - 4)/9

Given line m and line k are both perpendicular to each other,

We know that two lines are perpendicular if the product of their slopes is -1.

So,  -13 × (a - 4)/9 = -1

⇒ -13a + 52 = 13

⇒ 13a = 52 - 13

⇒ 13a = 39

⇒ a = 39/13

⇒ a = 3

Therefore, the required value of "a" would be 3.

Learn about the perpendicular lines here :

https://brainly.com/question/18271653

#SPJ1

A snowmobile can be rented for $14 per day with a $50 initial fix cost.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here,

Let the initial fee be x and daily fee be y,

92=x+3y

120=x+5y

x+5y=120

x+3y=92

Subtract both,

2y=28

y=$14

x+5y=120

x+70=120

x=$50

The daily fee to rent a snowmobile is $14 per day with a initial fix fee of $50.

To know more about equation,

https://brainly.com/question/649785

#SPJ4

Answer:

d) y = -3x-3

e) y = -3x - 1

f) y = -3x + 2

Step-by-step explanation:

Knowledge Needed:

Slope-Intercept Form: y = mx + b

y and x stay as variables so you can solve for the intercepts and graph.

m is the slope, or the constant amount that the y-value on a line changes when the x-value increases by 1.

b is the y-intercept, or when t he line has an x-value of 0.

When lines are parallel, they have the same slope.

Question

d)

Examine the line: At what y-value does the line have a x-value of 0?

y-value: -3

Alternatively, you could also solve be getting a set of points on the line and plugging in.

(1,0)

Our equation for line d:

y = -3x - b

0 = -3(1)  - b

0 = -3 - b

0 + 3 = -3 + 3 - b

3 = -b

b = -3

d) y = -3x-3

e)

Repeat the same steps.

y-intercept: -1

Because they are parallel, they have the same slope.

e) y = -3x - 1

f)

Repeat the same steps.

y-intercept: 2

Because they are parallel, they have the same slope.

f) y = -3x + 2

Answer:

Yes, both men could drive at the rate of 112 miles in 2 hours. This is because you need to find the unit rate. For Theo's unit rate it is 57 miles per hour while Lex could drive at 62 miles per hour. Finally, the last statement ask if they could drive at a unit rate of 56 miles per hour and yes both men can.

Step-by-step explanation:

Answer: Theo's speed is 240 miles / 4 hours = <<240/4=60>>60 mph.

Lex's speed is 183 miles / 3 hours = <<183/3=61>>61 mph.

To determine whether Theo can drive 118 miles in 2 hours, we can calculate the time it would take him to travel 118 miles at his speed of 60 mph: 118 miles / 60 mph = <<118/60=1.97>>1.97 hours.

Since 1.97 hours is less than 2 hours, Theo could drive 118 miles in 2 hours.

To determine whether Lex can drive 118 miles in 2 hours, we can calculate the time it would take him to travel 118 miles at his speed of 61 mph: 118 miles / 61 mph = <<118/61=1.93>>1.93 hours.

Since 1.93 hours is less than 2 hours, Lex could also drive 118 miles in 2 hours.

Therefore, both Theo and Lex could drive 118 miles in 2 hours.

The given statement " All else being equal, the further the t statistic falls from 0, either in the positive or negative direction, the more likely it is that the difference between two population averages is statistically significant. " is true.

The term t statistics refers the ratio of the departure of the estimated value of a parameter from its hypothesized value to its standard error.

Here we have the statement All else being equal, the further the t statistic falls from 0, either in the positive or negative direction, the more likely it is that the difference between two population averages is statistically significant.

And we need to identify whether the statement is true or not.

As per the definition of t statistics, we have identified that the t statistic falls from 0. which states that is goes on the negative direction.

Therefore, the more likely it is that the difference between two population averages is statistically significant.

So, the statement is correct.

To know more about t statistics here.

https://brainly.com/question/15236063

#SPJ4

Answer:

[tex]y=-\frac{3}{4}x-2[/tex]

Step-by-step explanation:

Substitute into point-slope form and rearrange to slope-intercept form.

[tex]y+8=-\frac{3}{4}(x-8) \\ \\ y+8=-\frac{3}{4}x+6 \\ \\ y=-\frac{3}{4}x-2[/tex]