Help !!!!!!!!!!!!!!!!!!!!

Step-by-step explanation:

x - y = 0.77

5x - y = 77

let's subtract the first from the second equation :

5x - y = 77

- x - y = 0.77

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

4x 0 = 76.23

x = 76.23/4 = 19.0575

x - y = 0.77

y = x - 0.77 = 19.0575 - 0.77 = 18.2875

The rectangular coordinate from the given polar coordinate is (2.73, -0.73)

To find the rectangular coordinate from the polar coordinates, we can rewrite this as;

x = r cosθ

y = r sinθ

x = r cosθ

Let's substitute the values into it;

x = (2√2)* cos(-π/12)

x =(2√2)cos(-15)

x = √3 + 1

x = 2.73

y = r sin θ

y = (2√2)sin(-π/12)

y = (2√2) * sin (-15)

y = -√3 + 1

y = -0.73

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The segments AB and CD are, parallel, perpendicular or neither, depending on the slopes obtained from the coordinates on the segments as follows;

Parallel lines or line segments are line segments that have the same slope.

1. The slope of the segment [tex]\overline{AB}[/tex] is; (3 - 13)/(0 - (-2)) = -10/2 = -5

The slope of the segment [tex]\overline{CD}[/tex] is;  (3 - 0)/(10 - (-5)) = 3/15 = 1/5

The slope of  [tex]\overline{AB}[/tex] is the negative inverse of the slope of  [tex]\overline{CD}[/tex] therefore;

[tex]\overline{AB}[/tex] ⊥  [tex]\overline{CD}[/tex],   [tex]\overline{AB}[/tex] is perpendicular to  [tex]\overline{CD}[/tex]

2. The slope of the segment [tex]\overline{AB}[/tex] is; (1 - 7)/(-6 - 3) = -6/-9 = 2/3

The slope of the segment [tex]\overline{CD}[/tex] is;  (-1 - (-5))/(0 - (-6)) = 4/6 = 2/3

The slope of  [tex]\overline{AB}[/tex] is the same as the slope of  [tex]\overline{CD}[/tex] therefore;

 [tex]\overline{AB}[/tex] ║ [tex]\overline{CD}[/tex],   [tex]\overline{AB}[/tex] is parallel to [tex]\overline{CD}[/tex]

3. The slope of the segment [tex]\overline{AB}[/tex] is; (4 - 2)/(-2 - (-6)) = 2/4 = 1/2

The slope of the segment [tex]\overline{CD}[/tex] is;  (-7 - 11))/(5 - (-1)) = -18/6 = -3

The slope of [tex]\overline{AB}[/tex] is different from and not the negative inverse of the slope of  [tex]\overline{CD}[/tex] therefore;

 [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are neither parallel or perpendicular

4. The slope of the segment [tex]\overline{AB}[/tex] is; (3 - 8)/(2 - (-3)) = -5/5 = -1

The slope of the segment [tex]\overline{CD}[/tex] is;  (2 - 6)/(-8 - (-4)) = -4/(-4) = 1

The slope of  [tex]\overline{AB}[/tex] is the negative inverse of the slope of  [tex]\overline{CD}[/tex] therefore;

 [tex]\overline{AB}[/tex] ⊥ [tex]\overline{CD}[/tex]

5. The slope of the segment [tex]\overline{AB}[/tex] is; (2 - (-1))/(-4 - (-8)) = 3/4

The slope of the segment [tex]\overline{CD}[/tex] is;  (6 - (-3))/(12 - 0) = 9/12 = 3/4

The slope of  [tex]\overline{AB}[/tex] is the same as the slope of  [tex]\overline{CD}[/tex] therefore;

 [tex]\overline{AB}[/tex] ║  [tex]\overline{CD}[/tex]

6. The slope of the segment [tex]\overline{AB}[/tex] is; (-1 - 5)/(3 - 6) = -6/-3 = 2

The slope of the segment [tex]\overline{CD}[/tex] is;  (7 - (-5))/(-4 - 2)) = 12/(-6) = -2

The slope of  [tex]\overline{AB}[/tex] is different from and not the negative inverse of the slope of  [tex]\overline{CD}[/tex] therefore;

 [tex]\overline{AB}[/tex] and  [tex]\overline{CD}[/tex] are neither parallel nor perpendicular.

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An experience that I had outside the academia was when I worked as a marketing coordinator for a small start-up company.

A product launch event had been planned by the team for several weeks, and everything appeared to be going according to plan. However, we learned the day before the event that our keynote speaker, who was an important component of it, had unexpectedly become unwell and would not be able to attend.

I had to evaluate the situation as the marketing coordinator and decide right away. Either we could cancel the event or we could locate a another speaker.

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The value of the expressions are;

a. 4n - 8

b. 64

c. 18

d. 5(n + 3)

Algebraic expressions are described as expressions that consists of terms, constants, coefficients, factors and variables.

They are also identified to consist of mathematical operations which includes;

Using the distributive property, we have;

a. 4(n - 2)

expand the bracket, we get;

4n - 8

b. . 8(2+6)

8(8)

expand the bracket

64

c. 6•8-6•5

48 - 30

Subtract

18

d. 5n+15

factorize the expression

5(n + 3)

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The value of the variable x for the triangle base length is derived as 5.

Using the proportionality theorem for evaluating x as follows:

JD/DK = PJ/PK

3x/(4x + 1) = 20/28

3x × 28 = 20(4x + 1) {cross multiplication}

84x = 80x + 20

84x - 80x = 20 {collect like terms}

4x = 20

x = 20/4 {divide through by 4}

x = 5

Therefore, the value of the variable x for the triangle base length is derived as 5.

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Check the picture below.

The account's total value is $498,174.72.

The total interest paid is $174,174.72.

We can utilize the calculation for the future value of a compound interest annuity to resolve this issue:

FV = P*(((1 + r/n)(n*t))-1) / (r/n).

where

When we enter the values, we obtain:

FV = 600 * (((1 + 0.12/4)^(4*60)) - 1) / (0.12/4) = 498,174.72

After the 60th deposit, the account's total value is $498,174.72.

We can deduct the total amount deposited from the account's total value to calculate the cumulative interest:

Added interest is calculated as follows: FV - (P * t * n) = 498,174.72 - (600 * 60 * 4) = 174,174.72

Therefore, the total interest paid is $174,174.72.

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Answer:

We can use the formula to find the length of a circular arc given the measure of the central angle and the radius:

Length of arc = (central angle measure / 360) x 2πr

where r is the radius of the circle.

Given that the central angle measure is 40° and the length of the arc is 6 cm, we can set up the equation:

6 = (40/360) x 2πr

Simplifying the fraction and solving for r, we get:

6 = (1/9) x 2πr

r = 9 x 6 / 2π

r = 27/π

So the radius of the circle is 8.59 cm (rounded to two decimal places).

The transformation that maps the pre-image (red) onto the image (blue) is reflection

Given that

the pre-image (red) and the image (blue)

From the figure, we can see that

Both triangles are mirrors of one another

As a general rule

When two shapes with the same orientation and properties mirror one another, then the transformation between the shapes is the reflection transformation

This means that the transformation of the two triangles is a reflection transformation

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Point T is the orthocenter of this triangle because it is the point where all the three altitudes of the triangle are intersecting each other.

Circumcenter : The point of intersection of the three perpendicular bisectors.

Incenter : The point of intersection of the three angle bisectors.

Centroid : The point of intersection of the three medians.

Orthocenter : The point where all the three altitudes of the triangle meet or intersect each other.

In conclusion, based on the information, Point T is the orthocenter of this triangle because it is the point where all the three altitudes of the triangle are intersecting each other.

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The point of tangency and the equation of the tangent line are (x, y) = (- 5, 0) and x = - 5, respectively. (Correct choice: D)

A figure representing a circle and a tangent line, from which we need to determine the point of tangency and the equation of the tangent line. The point of tangency is a point where the tangent line and the circle meet each other.

Thus, by direct inspection, we have the following results:

Point of tangency

(x, y) = (- 5, 0)

Tangent line

x = - 5

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Check the picture below.

The volume of a cylinder whose diameter measures 2.5 cm and has a height of 15.5 cm is equal to 76.10 cubic centimeters.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

Note: Radius = diameter/2 = 2.5/2 = 1.25 cm.

By substituting the parameters, we have:

Volume of cylinder, V = 3.142 × 1.25² × 15.5

Volume of cylinder, V = 76.10 cubic centimeters.

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Complete Question:

Calculate the volume of a cylinder whose diameter measures 2.5 cm and has a height of 15.5 cm.

D. The probability that a randomly selected giraffe will be shorter than 18.5 feet tall is given as follows: 0.7340 = 73.40%.

E. The probability that a randomly selected giraffe will be between 19 and 19.9 ft tall is given as follows: 0.0968 = 9.68%.

F. The 75th percentile for the height of giraffes is given as follows: 18.54 ft.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 18, \sigma = 0.8[/tex]

The probability that a randomly selected giraffe will be shorter than 18.5 feet tall is the p-value of Z when X = 18.5, hence:

Z = (18.5 - 18)/0.8

Z = 0.625

Z = 0.625 has a p-value of 0.7340.

The probability that a randomly selected giraffe will be between 19 and 19.9 ft tall is the p-value of Z when X = 19.9 subtracted by the p-value of Z when X = 19, hence:

Z = (19.9 - 18)/0.8

Z = 2.375

Z = 2.375 has a p-value of 0.9912.

Z = (19 - 18)/0.8

Z = 1.25

Z = 1.25 has a p-value of 0.8944.

Hence:

0.9912 - 0.8944 = 0.0968 = 9.68%.

The 75th percentile is X when Z = 0.675, hence:

0.675 = (X - 18)/0.8

X - 18 = 0.8 x 0.675

X = 18.54 ft.

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The 25th percentile for the math scores is 71.65.

In Mathematics and Geometry, the z-score of a given sample size or data set can be calculated by using this formula:

Z-score, z = (x - μ)/σ

Where:

Note: 25th percentile for the math scores is the same as the first quartile for the math scores.

Based on the z-score table A, 25th percentile (0.25) is equal to a z-score of -0.67;

0.2514 = -0.67

By substituting the parameters, we have:

Z-score, z = (x - μ)/σ

-0.67 = (x - 75)/5

x = 75 - 3.35

x = 71.65

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a. The definite integral ∫₀²f(x)dx = lw

b.  The definite integral ∫₂⁴f(x)dx = πr²/2

A definite integral is an integral evaluated on an interval.

Given the figure, to evaluate the definite integral ∫₀²f(x)dx and ∫₂⁴f(x)dx, we proceed as follows.

a.  The definite integral ∫₀²f(x)dx

Observe the graph, the integral ∫₀²f(x)dx is the area occupied by the square on the interval (0, 2).

So,  ∫₀²f(x)dx = lw

b.  The definite integral ∫₂⁴f(x)dx

Observe the graph, the integral ∫₂⁴f(x)dx is the area occupied by the circle on the interval (2, 4).

So,  ∫₂⁴f(x)dx = πr²/2

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Answer:

0

Step-by-step explanation:

Answer:

Step-by-step explanation:

hello :

6x  the greatest common factor from the polynomial.

 12x² + 30x

The inverse of the function f(x) = 9x²- 12 is p(x) = √(x + 12)/9

Given that the domain of a function f is restricted to x ≥ 0, we need to find the inverse of the function

f(x) = 9x²- 12 for x ≥ 0.

To find the inverse of the function, we proceed as follows.

f(x) = 9x²- 12

Let f(x) = y

So, we have that

y = 9x²- 12

Adding 12 to both sides of the equation, we have that

y + 12 = 9x²- 12 + 12

y + 12 = 9x²

Dividing both sides by 9, we have that

(y + 12)/9 = 9x²/9

(y + 12)/9 = x²

Taking square root of both sides, we have that

√x² = √(y + 12)/9

x = √(y + 12)/9

Now, replacing x with y, we have that

x = √(y + 12)/9

y = √(x + 12)/9

Replacing y with f⁻¹(x), we have that

f⁻¹(x) = √(x + 12)/9

So, the inverse is p(x) = √(x + 12)/9

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Answer:

20%  (D)

Step-by-step explanation:

The equivalent value of the expression are A = -8x + 19 , B = -6x - 2x + 19

Given data ,

Let the expression be represented as A

Now , the value of A is

A = 14 - 8x + 5

On simplifying , we get

A = -8x + 19

And , the equivalent values of the expression are

B = -6x - 2x + 19 = A

C = -8 ( x - 2 ) + 3

Hence , the expression is A = -8x + 19

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The graph of the inequality is added as an attachment

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

y < -2 + 7

The above expression is an inequality that implies that

The value of y is less than the sum of -2 and 7

Next, we plot the graph

See attachment for the graph of the inequality

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The percentage of people taking the test who score above 654 is 15.87%

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

Mean = 550

Standard deviation = 104

Score = above 654

The z-score is calculated as

z = (Score - Mean)/Standard deviation

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

z = (654 - 550)/104

Evaluate

z = 1

The percentage of people taking the test is then calculated as

P = p(z > 1)

So, we have

P = 0.15866

Express as percentage

P = 15.87%

Hence, the percentage is 15.87%

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The person will travel 62.8 meters farther in one revolution of the Adventure Land ferris wheel than in one revolution of the Kiddie Land ferris wheel.

The above problem is asking how much farther a person will travel in one revolution of the Adventure Land ferris wheel compared to one revolution of the Kiddie Land ferris wheel.

The Adventure Land ferris wheel has a diameter of 30 meters, and the Kiddie Land ferris wheel has a diameter of 10 meters.

This means that the circumference of the Adventure Land ferris wheel (the distance traveled in one revolution) is

3.14×30= 94.2 meters

The circumference of the Kiddie Land ferris wheel is

3.14 ×10= 31.4 meters

Here, 94.2-31.4 =62.8 meters

Therefore, the person will travel 62.8 meters farther in one revolution of the Adventure Land ferris wheel than in one revolution of the Kiddie Land ferris wheel.

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To determine the range you need to evaluate and find a maximum/minimum if you can.

For a function f(x) = y, we define the range as the set of the possible outputs of the function.

So, to find the range of any function, we need to evaluate it and try to find the minimum and maximum values of the function. To do so it is useful to understand the behavior of different types of functions.

For example linear ones have a range of all the real numbers.

Quadratic ones have a range that depends on its vertex, and so on.

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The lower quartile, the median, and the upper quartile are 22, 31 and 90

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

11, 18, 22, 22, 31, 31, 63, 86, 90, 92, 98

Split the data values into 2

So, we have

11, 18, 22, 22, 31,

31,

63, 86, 90, 92, 98

The middle of each set is the quartiles

So, we have

Lower = 22

Median = 31

Upper = 90

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Step-by-step explanation:

use the formula V=1/3hπr².

V=1/3×3 π 2×2

V=1/3×12π

V=4πcm3

The dolphin's weight that differs most from the value predicted by this model is JoJo's (31 lb of difference)

Let's elaborate the model this way:

Snowflake's length - Pax's length = 8.2 - 7.6 = 0.6 ft

Snowflake's weight - Pax's weight = 549 - 519 = 30 lb

Ratio = 30/0.6 = 50 lb/ft

This means that for every foot of length, the dolphin has a variable weight of 50 lb.

However, if we multiply the ratio by the actual length of the two dolphins, we will have these results:

Snowflake = 50 × 8.2 = 410

Pax = 50× 7.6 = 380

Snowflake = Actual weight - Ratio× Length = 549 - 410 = 139

Pax = Actual weight - Ratio × Length = 519 - 380 = 139

The common difference is 139.

Therefore, the linear model that predicts the weight (y) of a dolphin given its length (X) is:

y = 139 + 50x

Now, let's use the linear equation or model to calculate the weight of the remaining four dolphins, as follows:

Blaze  y = 139 + 50 × 6.8 = 479 ⇒ difference of 9 lb (488 - 479)

JoJo   y = 139 + 50 × 5.8 = 429 ⇒ difference of 31 lb (460 - 429)

Corky   y = 139 + 50 ×8.4 = 559 ⇒ difference of 2 lb  (559 - 557)

Shadow  y = 139 + 50 × 7.4 = 509 ⇒ difference of 8 lb  (509 - 501)

Hence, the dolphin's weight that differs most from the value predicted by this model is JoJo's (31 lb of difference)

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The table below shows the lengths and weights of six dolphins at an aquarium. Use the data from Pax and Snowflake to

create a linear model that predicts the weight (y) of a dolphin given its length (X). Which dolphin's weight differs most from th

value predicted by this model?

Name

Snowflake

Shadow

Corky

Pax

JoJo

Blaze

Length (ft)

8.2

74

8.4

7.6

5.8

6.8

Weight (lb)

549

501

557

519

460

488

Blaze

JOJO

Corky

Shadow