if a line is tangent to a circle,then it is perpendicular to the radius drawn to that point of tangent.

To find the intervals over which a function is increasing, you need to find its derivative, set it greater than 0 and solve for x. The solutions give the intervals where the function is increasing.

In mathematics, to find the intervals over which a function is increasing, you first need to find its derivative. The derivative of a function at a certain point gives the slope of the tangent line at that point. If the derivative is positive, the function is increasing. If it's negative, the function is decreasing.

For example, let's say we have a function f(x) = x^3 - 3x. The derivative of this function is f'(x) = 3x^2 - 3. To find the interval where the function is increasing, we set the derivative greater than 0 and solve for x: 3x^2 - 3 > 0. The solution to this inequality gives the intervals over which the function is increasing .

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To determine the number of units produced by Assembly Line A when Line B produces 555 units, we use the ratio of their production rates (45/37) to find that Assembly Line A would produce 675 units.

The question asks how many units Assembly Line A produces when Assembly Line B produces 555 units, given that Line A produces 45 units in the same time that it takes Line B to produce 37 units. To find the answer, we can use the concept of ratio and proportion.

Since Line A produces 45 units at the same time Line B produces 37 units, we have a ratio of 45/37. With Line B producing 555 units, we can set up a proportion to find how many units Line A produces:

45/37 = x/555

Multiplying both sides of the equation by 555, we get:

x = (45/37) * 555

Calculating the value of x gives us:

x = 675

Therefore, Assembly Line A produces 675 units in the same time that Assembly Line B produces 555 units.

The function rule in slope-intercept form is y = 3x + 9.

The function rule in slope-intercept form is given by the equation y = mx + b, where m represents the slope of the line and b represents the y-intercept.

In this case, the given y-intercept is 9, so b = 9.

The slope of the line is 3, which means that for every increase of 1 on the horizontal axis (x-axis), there is a rise of 3 on the vertical axis (y-axis). Therefore, m = 3.

Putting these values into the slope-intercept form, we get the function rule to be y = 3x + 9.

The answer came from Rgwoot Ambitious

from another post in case anyone else needs it

What we know:

shape is rectangle which means the 2 long sides have equal distance and the 2 short sides have equal distance

we just need to find the distance of one long side and one short side for the perimeter which is the outline of the rectangle. Imagine the perimeter is the fence around the rectangle  that you would probably have to paint every 3 years and the area would be where the grass would grow in the rectangle which you would probably have to cut every weekend.

perimeter=2l+2w

What we need to find: PERIMETER

Using pythagorean method a² +b²=h² to find length:

From point (-6,1) to point (3,8) is a rise of 9 and a run of 9 right to get from one point to another, those are my a and b in the pythagorean formula.

a² +b²=h²

(9)²+(9)²=h²         substitution

81+81=h²            simplified

162=h²

√162=√h2           used radical properties

√162=h               length =√162

Using pythagorean method a² +b²=h² to find width:

From points (-6,-1) to point (-3,-4) is a down 3 units and left 3 units to reach from one point to another, these are my a and b for the pythagorean formula.

a² +b²=h²

(3)²+(3)²=h²

9+9=h²

18=h²

√18=√h²

√18=h           this is the width=√18

Now we find perimeter:

p=2l+2w

p=2(√162)+2(√18)

p≈33.9

D. 33.9 units

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To find the equation of a line perpendicular to y=(4/9)x-2 that passes through the point (4,3), we need to determine the slope of the original line and then find the negative reciprocal of that slope. The equation of the perpendicular line is y = -(9/4)x + 12.

To find the equation of a line perpendicular to y=(4/9)x-2 that passes through the point (4,3), we need to determine the slope of the original line and then find the negative reciprocal of that slope. The original line has a slope of 4/9, so the perpendicular line will have a slope of -9/4. Using the point-slope form of a line, we can plug in the slope and the given point to find the equation of the perpendicular line:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope. Plugging in the values, we get:

y - 3 = -(9/4)(x - 4)

Simplifying the equation, we get:

y = -(9/4)x + 12

Therefore, the equation of the line perpendicular to y=(4/9)x-2 that passes through the point (4,3) is y = -(9/4)x + 12.

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Rewrite the systems of inequalities in slope-intercept form, and then graph the lines using the respective inequalities. The shaded area that overlaps will represent the solution to these systems of inequalities.

In order to determine a graph that represents the system of inequalities, y+32x > -3 and y-5 ≤ -6x, you will need to write the systems of inequalities in mathematical terms, known as slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

Firstly, let's rewrite the first inequality as y > -32x - 3. This inequality suggests that y is greater than -32x - 3, therefore the area above the line will be shaded.

Next, the second inequality is rewritten as y ≤ 6x + 5. This suggests y is less than or equal to 6x + 5, thus the area below the line will be shaded.

Remember, when creating the graph, a solid line should be used for ≤ symbol and a dashed line for the > symbol. The overlapping region of the two inequalities on the graph is the solution to the system of inequalities.

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315 x 3 = 945

518 - 315 = 203

203 x 4 = 812

945 + 812 =1757

So the answer is $1,757 total

The total money collected from ticket sales for the high school play, with 315 student tickets sold at $3.00 each and 203 other tickets sold at $4.00 each, is $1,757.00.

To find the total money collected from ticket sales, we need to calculate the revenue from both student tickets and tickets sold to others. We know that 315 student tickets were sold at a price of $3.00 each, and the remaining tickets sold to others were at a price of $4.00 each. Since a total of 518 tickets were sold, the tickets sold to others amount to 518 - 315 = 203 tickets.

Revenue from student tickets = 315 tickets  imes $3.00 per ticket = $945.00

Revenue from other tickets = 203 tickets  imes $4.00 per ticket = $812.00

Total revenue from ticket sales = Revenue from student tickets + Revenue from other tickets = $945.00 + $812.00 = $1,757.00

Therefore, the total money collected from ticket sales is $1,757.00.

A 90% confidence interval will have a width of 2.36 which is false.

Let μ be the mean, σ be the standard deviation, n be the ample size, and z be the z-score. Then we have

Confidence interval = μ ± z (σ / √n)

A sample mean of 2.1 and a sample standard deviation of 0.7 from a sample of 10 data points.

We know that the z-score for 90% of the confidence interval is 1.645. Then we have

Confidence interval = μ ± z (σ / √n)

Confidence interval = 2.1 ± 1.645 (0.7 / √10)

Confidence interval = 2.1 ± 0.364

For positive sign, then the width will be

⇒ 2.1 + 0.364

⇒ 2.46

A 90% confidence interval will have a width of 2.36 which is false.

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Answer:

So, the point-slope form of the equation that represents the line passing through the points [tex]\((-6,4)\) and \((2,0)\)[/tex] is:

[tex]\[ y - 4 = -\frac{{1}}{{2}}(x + 6) \][/tex]

Explanation:

To find the equation of the line passing through the points [tex]\((-6,4)\) and \((2,0)\)[/tex] , we can use the point-slope form of the equation of a line:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

Where [tex]\((x_1, y_1)\)[/tex]  is a point on the line, and [tex]\(m\)[/tex] is the slope of the line.

First, let's find the slope [tex]\(m\):[/tex]

[tex]\[ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} \][/tex]

Using the coordinates of the given points:

[tex]\[ m = \frac{{0 - 4}}{{2 - (-6)}} \][/tex]

[tex]\[ m = \frac{{-4}}{{2 + 6}} \][/tex]

[tex]\[ m = \frac{{-4}}{{8}} \][/tex]

[tex]\[ m = -\frac{{1}}{{2}} \][/tex]

Now that we have the slope, let's choose one of the given points to plug into the point-slope form. We'll use [tex]\((-6,4)\):[/tex]

[tex]\[ y - 4 = -\frac{{1}}{{2}}(x - (-6)) \][/tex]

[tex]\[ y - 4 = -\frac{{1}}{{2}}(x + 6) \][/tex]

[tex]\[ y - 4 = -\frac{{1}}{{2}}x - 3 \][/tex]

Now, let's simplify and put the equation in slope-intercept form:

[tex]\[ y = -\frac{{1}}{{2}}x - 3 + 4 \][/tex]

[tex]\[ y = -\frac{{1}}{{2}}x + 1 \][/tex]

Given

Tom and Martin both worked 9 hours this week and sold $360 worth of meals

Tom's percent of tips was 15% while Martin's was 20%

Find out the most money this week between Tom and Martin

To proof

In this question take two cases

FIRST CASE

Martin worked 9 hours

sold worth of meals = $360

Martin's percent of tip = 20%

First convert 20% in decimal form

= [tex]\frac{20}{100}[/tex]

= 0.20

than the equation becomes

Martin makes money = 9 × 2.50 + 0.20 × 360

                                   = 22.5 + 72

                                   = $ 94.5

SECOND CASE

Tom worked 9 hours

Tom's percent of tips = 15%

sold worth of meals = $360

First 15 % is written in decimal form

= [tex]\frac{15}{100}[/tex]

= 0.15

than the equation becomes

Tom  makes money = 9 × 2.15 + 0 .15× 360

                                =  19.35 + 54

                                = $ 73.35

Thus martin makes money is $94.5

Thus tom makes money is $73.35

Hence Martin makes more money than tom

Hence proved

Answer: Tom made more money than Martin

Step-by-step explanation:

Test results said this was the right answer

Answer:

the answer is 1/8

Step-by-step explanation:

Answer: $5,725

Step-by-step explanation:

Given: The cost of home = $205,000

If there is no down payment, then the mortgage amount = $205,000

We know that one point costs 1 % of mortgage amount .

2 points = 2 % of the mortgage amount =[tex]0.02\times205,000=\$4,100[/tex]

[tex]\text{Closing costs=}\text{cost of points + appraisal fee+processing fee+ title fee}[/tex]

[tex]=\$4,100+\$450+\$575+\$600=\$5,725[/tex]

Hence, her total in closing costs = $5,725.

The sides of the right angle triangle are 20, 48, and 52.

We have given that,

The hypotenuse of a right triangle is 8 feet less than three times the shorter leg and the longer leg is 8 feet more than twice the shorter leg.

Suppose the shortest leg is x, the hypotenuse is then 3x-8, and the longer leg is 2x+8

We use the Pythagorean theorem

[tex]hypotenous^2=side^2+side^2[/tex]

Therefore by using Pythagorean theorem

[tex]x^2+(2x+8)^2=(3x-8)^2\\x^2+(4x^2+32x+64)=(9x^2-48x+64)\\4x^2-80x=0[/tex]

x=0 or x=20

So the sides are 20, 48, and 52.

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Lines can be parallel, perpendicular or have no relationship at all.

The equation of the line is: [tex]\mathbf{y = -3x + 14}[/tex]

First, we calculate the slope of: [tex]\mathbf{y = \frac x3 - 1}[/tex]

A linear equation is represented as:

[tex]\mathbf{y = mx + c}[/tex]

Where:

m represents the slope

So, by comparison:

[tex]\mathbf{m = \frac 13}[/tex]

From the question, we understand that the required line is perpendicular to [tex]\mathbf{y = \frac x3 - 1}[/tex]

This means that, the slope (m2) of the required line is:

[tex]\mathbf{m_2 = -\frac 1m}[/tex]

So, we have:

[tex]\mathbf{m_2 = -\frac 1{1/3}}[/tex]

[tex]\mathbf{m_2 = -3}[/tex]

The equation of the line is:

[tex]\mathbf{y = m_2(x - x_1) + y_1)}[/tex]

Where:

[tex]\mathbf{(x_1,y_1) = (4,2)}[/tex]

So, we have:

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

Open bracket

[tex]\mathbf{y = -3x + 12 + 2}[/tex]

[tex]\mathbf{y = -3x + 14}[/tex]

Hence, the equation of the line is: [tex]\mathbf{y = -3x + 14}[/tex]

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