Write the equation of the line with a slope of 3/4 and a y-intercept of -7 in slope - intercept and point -slope form.

Answer:

The answer is C. 168 in^2

Step-by-step explanation:

(Area = Base x Height)

21 * 8 = 168

Answer:

11 duh

Step-by-step explanation:

Answer:

=======================

Equation of circle:

The center is the radius long distance from the x- axis to left and y-axis up same distance, this makes it in the second quadrant.

So the coordinates of the center are:

The equation is:

Answer:

\((x+8)^2+(y-8)^2=64\)

Step-by-step explanation:

Required conditions:

If the circle is tangent to both axes, its center will be the same distance from both axes.  That distance is its radius.

If the center of the circle is in quadrant II, the center will have a negative x-value and a positive y-value → (-x, y).

Therefore, the coordinates of the center will be (0-r, 0+r) where r is the radius.

If the radius is 8 units, then the center is (-8, 8).

\(\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Substitute the found center and given radius into the formula to create an equation for the circle that satisfies the given conditions:

\(\implies (x-(-8))^2+(y-8)^2=8^2\)

\(\implies (x+8)^2+(y-8)^2=64\)

Using the Pythagoras theorem, the longest leg has the length of 24 feet.

Given that,

A ladder of length (2x+6) feet is positioned x feet from a wall.

Height of the ladder = (2x + 6) feet

Distance of ladder from the wall = x feet

Height of the wall that the ladder is placed = (2x + 4) feet

These three lengths form s right triangle where (2x + 6) feet is the hypotenuse.

Longest leg is (2x + 4) feet

Using the Pythagoras theorem,

(2x + 6)² = (2x + 4)² + x²

4x² + 24x + 36 = 4x² + 16x + 16 + x²

4x² + 24x + 36 = 5x² + 16x + 16

x² - 8x - 20 = 0

(x - 10) (x + 2) = 0

x = 10 or x = -2

x = 2 is not possible.

So x = 10

Longest leg = 2x + 4 = 20 + 4 = 24 feet

Hence the length of the longest leg is 24 feet.

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The coordinates of the turning point on the curve with the equation y = 9 + 18x - 3x² is (3,36).

Any equation of the form \(\rm ax^2+bx+c=0\) where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

It is given that:

The quadratic equation is:

y = 9 + 18x - 3x²

To find the turning point:

Graph the above quadratic equation;

From the graph:

The maximum point from where the graph starts to decrease is (3,36)

Thus, the coordinates of the turning point on the curve with the equation y = 9 + 18x - 3x² is (3,36).

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Answer:

B - 108

Step-by-step explanation:

A regular pentagon is 540 degrees. Divide 540 by 5 (since there are five sides) which equals 108 degrees.

Answer:

The sales tax is given as a percent.

To find the dollar amount of the sales tax, divide the sales tax percent by 100 and multiply by the price.

Once you know the sales tax amount, add it to the price to find the total purchase price.

The various answers to the question are:

a)

A number of extension lines needed to accommodate $90 in calls immediately:

Use the calculation for busy k servers.

\($$P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{k} \frac{\left(\frac{\lambda}{\mu}\right)^{t}}{i !}}$$\)

The probability that 2 servers are busy:

The likelihood that 2 servers will be busy may be calculated using the formula below.

\(P_{2}=\frac{\frac{\left(\frac{20}{12}\right)^{2}}{2 !}}{\sum_{i=0}^{2} \frac{\left(\frac{20}{12}\right)^{t}}{i !}}$$\approx 0.3425$\)

Hence, two lines are insufficient.

The probability that 3 servers are busy:

Assuming 3 lines, the likelihood that 3 servers are busy may be calculated using the formula below.

\(P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{2} \frac{\left(\frac{\lambda}{\mu}\right)^{i}}{i !}}$ \\\\$P_{3}=\frac{\frac{\left(\frac{20}{12}\right)^{3}}{3 !}}{\sum_{i=0}^{3} \frac{\left(\frac{20}{12}\right)^{1}}{i !}}$$\approx 0.1598$\)

Thus, three lines are insufficient.

The probability that 4 servers are busy:

Assuming 4 lines, the likelihood that 4 of 4 servers are busy may be calculated using the formula below.

\(P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{k} \frac{\left(\frac{\lambda}{\mu}\right)^{t}}{i !}}$ \\\\$P_{4}=\frac{\frac{\left(\frac{20}{12}\right)^{4}}{4 !}}{\sum_{i=0}^{4} \frac{\left(\frac{20}{12}\right)^{7}}{i !}}$\)

Generally, the equation for is  mathematically given as

To answer 90% of calls instantly, the organization needs four extension lines.

b)

The probability that a call will receive a busy signal if four extensions lines are used is,

\(P_{4}=\frac{\left(\frac{20}{12}\right)^{4}}{\sum_{i=0}^{4} \frac{\left(\frac{20}{12}\right)^{1}}{i !}} $\approx 0.0624$\)

Therefore, the average number of extension lines that will be busy is Four

c)

In conclusion, the Percentage of busy calls for a phone system with two extensions:

The likelihood that 2 servers will be busy may be calculated using the formula below.

\(P_{j}=\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}$$\\\\$P_{2}=\frac{\left(\frac{20}{12}\right)^{2}}{\sum_{i=0}^{2 !} \frac{\left(\frac{20}{12}\right)^{t}}{i !}}$$\approx 0.3425$\)

For the existing phone system with two extension lines, 34.25 % of calls get a busy signal.

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Answer:

760

Step-by-step explanation:

Subtract the y-intercept from y.

240 - 50 = 190

.25x = 190

Division property of equality:

.25x = 190

/.25     /.25

x = 760

Answer:

21 % increase

Step-by-step explanation:

Lets imagine the sides of the rectangle are 100 & 200 cms.

The area would be 100 x 200 = 20000cm^2

If we added 10% onto each side, the sides would now be 110 & 220 cms.

The area would be 110 x 220 = 24200cm^2

We can now find percentage change:

\(\frac{24200-20000}{20000}\) = 21/100 = 21% increase.

The reason we can just pick random values of sides to do this question with is because we worked out percentage change, which will be the same no matter the proportion of the sides.

Hope this helped! Let me know if you have any questions :)

The joint relative Frequency of students who do not like to run and enjoy swimming, based on the given two-way frequency table, is approximately 62.16%.

The joint relative frequency of students who do not like to run and enjoy swimming, we need to find the intersection of the row and column corresponding to those categories in the two-way frequency table.

Given the following information from the table:

Likes running: 28

Does not like running: 46

Column totals: 74

Enjoys swimming: 62

Enjoys cycling: 90

Row totals: 110

The joint relative frequency, we divide the number of students who do not like running and enjoy swimming by the total number of students:

Joint relative frequency = (Number of students who do not like running and enjoy swimming) / (Total number of students)

From the table, the number of students who do not like running and enjoy swimming is given as 46.

Total number of students is given as 74.

Joint relative frequency = 46 / 74

Calculating this value, we find that the joint relative frequency is approximately 0.6216, which is equivalent to 62.16%.

Therefore, the joint relative frequency of students who do not like to run and enjoy swimming is approximately 62.16%.

In conclusion, the joint relative frequency of students who do not like to run and enjoy swimming, based on the given two-way frequency table, is approximately 62.16%.

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Answers:

A, B, D, E

Nearly everything except choice C is true.

====================================================

Explanation:

This is due to the fact that angles 2, 3, and 5 are interior angles of the triangle, and the total of the inner angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.

A triangle is a closed, two-dimensional geometric object composed of three line segments, known as sides, that intersect at three locations, known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all sides equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles less than 90 degrees), right (one angle equal to 90 degrees), or obtuse (all angles greater than 90 degrees). The area of a triangle can be computed using the formula A = (1/2)bh, where A is the area, b is the triangle's base, and h is the triangle's height.

Regarding the given diagram, the following claims are always true:

m∠3 + m∠4 + m∠5 = 180°

m∠5 + m∠6 = 180°\s= m∠2 (the measure of the external angle at angle 2). (the measure of the exterior angle at angle 2). And because angles 2 and 3 are likewise interior triangle angles, we get m2 + m3 = m6, which can be rearranged to yield m5 + m6 = m3 + m4 + m5 = 180°.

m∠2 + m∠3 + m∠5 = 180°

This is due to the fact that angles 2, 3, and 5 are interior angles of the triangle, and the total of the inner angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.

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Answer:  It take 6.66 min to complete one lap.

Step-by-step explanation:

2.3r - 7 + 6 = 21

2.3r - 1 = 21

2.3r = 22

r = 22/2.3

r = 9.6

2.3(4.23) - y + 6 = 21

9.73 - y + 6 = 21

15.73 - y = 21

-y = 5.27

y = -5.27

The domain of the rational expression (6-x)/(4x+20) is all real numbers except x = -5.

To find the domain of a rational expression, we need to identify any values of x that would result in division by zero. Division by zero is undefined in mathematics
In this case, we need to set the denominator, 4x+20, equal to zero and solve for x:
4x + 20 = 0
Subtract 20 from both sides:
4x = -20
Divide both sides by 4:
x = -5
Therefore, the value x = -5 makes the denominator zero.
Now, we need to consider the values of x for which the denominator is not zero. Since the denominator is a linear expression (a polynomial of degree 1), it is defined for all real numbers except x = -5.
So, the domain of the rational expression (6-x)/(4x+20) is all real numbers except x = -5.

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Answer:

answer is +4...

Step-by-step explanation:

when x=6, the expression becomes

2(6)^2+ 4-5

2(36)+(-1)

72-1=71

therefore 71+4 gives 75

Answer:

3.245

Step-by-step explanation:

Answer:

YES I ANSWERED IT

Step-by-step explanation:

THX I GOT 100 POINTS :)

The graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

The functions for this problem are defined as follows:

When a function is multiplied by 2, we have that it is vertically stretched by a factor of 2.

Hence the graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

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Using the index notation are a) \($2^3$\) , b) \($3^5$\)  , c) \($4^3 \times 5^2$\) , and d) \($9^4 \times 7^2$\)

Index notation is a method of representing numbers (constants) and variables (e.g., x and y) that have been multiplied by themselves many times. Index notation is used to identify the components of a numerical array.

The use of indices varies in formality depending on the subject. There are several ways to refer to the components of a list, vector, or matrix, depending on whether one is writing a formal academic article for publication or building a computer program.

Therefore,

a)\($2 \times 2 \times 2=2^1 \times2^1 \times2^1$\)

Applying law of indices

\(2^{1+1+1}=2^3\)

b)\($3 \times 3 \times 3 \times 3 \times 3=3^1 \times3^1 \times3^1 \times3^1 \times3^1$\)

Applying law of indices

\(3^{1+1+1+1+1}=3^5\)

c) \($4 \times 4 \times 4 \times 5 \times 5=4^1 \times4^1 \times4^1 \times5^1 \times5^1$\)

Applying law of indices

\(4^{1+1+1} \times5^{1+1}=4^3 \times5^2\)

d) \($9 \times 7 \times 9 \times 9 \times 7 \times 9=9^1 \times7^1 \times9^1 \times9^1 \times7^1 \times9^1$\)

Applying law of indices

\(7^2 \times 9^4\)

Hence, Using the index notation are a) \($2^3$\) , b) \($3^5$\)  , c) \($4^3 \times 5^2$\) , and d) \($9^4 \times 7^2$\)

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Answer:

I hope this helps

Step-by-step explanation:

carbonhydrates protein water fats minerals and vitamins

Answer:

(x,y)=(4,-9)

Step-by-step explanation:

The solution of the equation 7x + 4y = – 8 and 8x + 5y = –13 will be (4, –9).

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The solution of the equation means the value of the unknown or variable.

The system of the equation is given below.

7x + 4y = – 8      …1

8x + 5y = –13     …2

Multiply equation 1 by 5 and equation 2 by 4. Then subtract the equation 1 from 2, then we have

32x – 35x = –52 – (–40)

          –3x = –12

              x = 4

Substitute the value of x in equation 1, then the value of y will be

7(4) + 4y = – 8

 28 + 4y = –8

          4y = –36

            y = –9

The solution of the equation 7x + 4y = – 8 and 8x + 5y = –13 will be (4, –9).

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Answer:

50%

Step-by-step explanation:

Answer:

!

Step-by-step explanation:

Answer:

C)

Step-by-step explanation:

It seperates and makes most sense

The graph of f(x) is the second one, so the correct option is B.

Here we have f(x), a piecewise function, and we want to see which one of the four graphs is the correct one.

You can see that the first domain of the function is:

x ≤ -4

So we must have a closed circle at x = -4, when the parabola ends.

The second domain is:

-4 < x < 1

So x here is not equal to -4 nor 1, so this part starts and ends with open circles.

finally, the linear part starts with a closed circle.

Also, notice that the line has a negative slope, so it goes down, then we can discard the first option.

Then we can see that the correct option is the second graph.

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Answer:

No:

Step-by-step explanation:

No, there is no way to further simplify this equation, unless there is a value for x.

Answer:

No. x-2 can't.

Step-by-step explanation:

Its the same reason why you can't simplify 1+1. You could add them together, but in a case like this, where one number is unknown you can't. The number is already to its simplifiest form.

Answer:

the answer is your welcome

$33.52

Answer:

trueeeeeeee!!!!!!!!!!!

Answer:

Yes, 14 is an integer

Step-by-step explanation:

An integer has to be a whole number, and 14 IS a whole number. So, yes. The answer is true