-15x + 20y = 15
0=18x + 24y - 18

Answer:

20π [in].

Step-by-step explanation:

1. formula is:

C=π*2r;

2. the circumference according to the formula is:

C=π*10*2=20π.

The equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

To find an equation in slope-intercept form that passes through the point (1, -2) and is perpendicular to the given equation y = 5x + 4, we need to determine the slope of the perpendicular line.

The given equation y = 5x + 4 is already in slope-intercept form (y = mx + b), where m represents the slope. In this case, the slope of the given line is 5.

To find the slope of a line perpendicular to this, we use the fact that the product of the slopes of two perpendicular lines is -1. So, the slope of the perpendicular line can be found by taking the negative reciprocal of the slope of the given line.

The negative reciprocal of 5 is -1/5.

Now that we have the slope (-1/5) and a point (1, -2), we can use the point-slope form of the equation:

y - y1 = m(x - x1)

Substituting the values:

y - (-2) = (-1/5)(x - 1)

Simplifying:

y + 2 = (-1/5)(x - 1)

To convert the equation into slope-intercept form (y = mx + b), we need to simplify it further:

y + 2 = (-1/5)x + 1/5

Subtracting 2 from both sides:

y = (-1/5)x + 1/5 - 2

Combining the constants:

y = (-1/5)x - 9/5

Therefore, the equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

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Answer:

c $99,400

Step-by-step explanation:

$195,00-$120,000=$75,000

$75,000+$5,000+$1,400=81,400

$81,400+$38,000-$20,000=$99,400

Ben’s net worth is $99400 which is the correct answer would be an option (C).

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operation is called the arithmetic operator.

Operators which let do a basic mathematical calculation

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

Given that Ben owns a townhome valued at $195,000,

To determine Ben’s net worth

But still owes $120,000 on the loan.

So, 19500 - 120000

⇒ 75000

He has $5,000 in savings and a balance of $1,400 on his credit cards.

So, 75000 + 5000+ 1400

⇒ 81400

There is a balance of $20,000 owed on Ben’s car which is valued at $38,000.

So, 81400 + 38000 - 20000

⇒ 99400

Thus, Ben’s net worth is $99400.

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The equation for the transformed function g(x) is: g(x) = 2.323 (4) raise to the power x-0.872/2

How to solve a function?

If the function f(x) is vertically compressed by a factor of 1/2, the equation for the new function g(x) is given by:

g(x) = a(4) raise to the power x-k/2

where "a" and "k" are constants that need to be determined. To find these constants, we can use the fact that the original function f(x) is equal to g(x) when the compression is applied:

f(x) = g(x)/2

Substituting the expression for g(x) into this equation and simplifying, we get:

4raise to the power x - 6 = a(4)raise to the power x-k/2

To solve for "a" and "k", we need to find two equations involving these variables. One way to do this is to evaluate the expression for f(x) at two different values of x, and then set those equal to the corresponding values of g(x)/2. For example, we can choose x = 0 and x = 1:

f(0) = 4 - 6 = -5

f(1) = 4- 6 = -2

Using the equation g(x)/2 = f(x), we can write:

g(0)/2 = -5

g(1)/2 = -2

Substituting the expression for g(x) into these equations, we get:

a(4) raise to the power -k/2 = -10

a(4) raise to the power 1-k/2 = -4

Taking the ratio of these two equations, we can eliminate the variable "a" and solve for "k":

(4)raise to the power -k/2 / (4)  raise to the power 1-k/2 = -10 / -4

Simplifying this equation, we get:

4.raise to the power(1-k/2) = 5

Taking the logarithm of both sides (with base 4), we get:

1-k/2 = log4(5)

Solving for "k", we get:

k = 2 - 2 log4(5)

Substituting this value of "k" back into one of the equations we derived earlier, we can solve for "a":

a = -10 / (4)   raise to the power  -k/2

Substituting the numerical value of "k", we get:

k = 2 - 2 log4(5) ≈ 0.872

a = -10 / (4) raise ti the power  -k/2 ≈ 2.323

Therefore, the equation for the transformed function g(x) is:

g(x) = 2.323 (4)raise to the power x-0.872/2

or equivalently:

g(x) = 1.1615 (4) raise to the power -x0.872

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Answer:

g(x) = 1/2 (4)^x - 3

Step-by-step explanation:

A vertical compression by a factor of 1/2

means that the entire function f is multiplied by 1/2:

1/2 f (x) = 1/2 (4^x - 6)

= 1/2 (4)^x - 3

Answer:1/2

Step-by-step explanation:

because three is half of six and you can get numbers larger than three also

Answer:

Step-by-step explanation: the y would be 50

To find the unit rate, we need to determine how much distance Margo covers in one unit of time. We can do this by dividing the distance by the time.

Distance = 1/4 mile

Time = 1/12 hour

Unit rate = Distance ÷ Time

Unit rate = (1/4 mile) ÷ (1/12 hour)

We can simplify this division by multiplying both the numerator and denominator by the least common multiple of 4 and 12, which is 12.

Unit rate = (1/4 mile) ÷ (1/12 hour) x (12/12)

Unit rate = (3/4 mile) ÷ 1 hour

Unit rate = 3/4 mile per hour

Therefore, Margo's unit rate is 3/4 mile per hour. This means that she can cover a distance of 3/4 mile in one hour of walking.

Answer:

3mph

Step-by-step explanation:

1/12 of an hour will be 5 min. In 5 min she can walk 1/4 mile then in one hour she can walk 1/4 x 12. This means her rate will be 3 miles per hour.

60/12 = 5

12 x 1/4 = 12/4 = 3

Answer:

A. All atoms of the same elements are identical

Step-by-step explanation:

Two atoms of the same chemical element are typically not identical. They can be different if their electrons are in different states,

The option that is to equal to the ratio,  4,200 to 5,000, is 0.84

What is ratio?

Ratio mean expressing one variable as a fraction of the other variable, in this case, 4,200 is expressed as a fraction of a bigger number which is 5,000, intuitively, the correct answer in this scenario is 0.84 because when viewed in percentage terms, 4000 is 80%,hence, 4,200 is greater than 4000, it would be more 80% which is 84%, without mincing words, the computation can be done as shown below:

ratio 4,200 to 5,000=4,200/5,000

ratio 4,200 to 5,000=0.84

Invariably, as stated earlier, all the options from a-c are incorrect as they are not even up 0.80, which means 0.84 is the most appropriate

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Points obtained on the quiz increases when the points are earned from

correct responses.

Reasons:

The number of questions in the quiz = 25 questions

Number of points for correct answers = 3 points

Number of points lost for incorrect answers = 2 points

Points for question not answered = 0 points

Nature of total points = Positive and negative

Required:

The minimum score one can get on the quiz.

Solution:

The minimum score that can be obtained is when all responses result in a

loss of points, due to the questions being incorrect.

Therefore;

The minimum score = 25 × (-2) = -50

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Answer:

you can use a website called wolfram alpha to help with any math equation

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

x=3/4

Step-by-step explanation:

Answer:

\(Radius = 1.997\ in\) and \(Height = 7.987\ in\)

\(Cost = \$1.05\)

Step-by-step explanation:

Given

\(Volume = 100in^3\)

\(Cost =\$0.014\) -- Top and Bottom

\(Cost =\$0.007\) --- Sides

Required

What dimension of the cylinder minimizes the cost

The volume (V) of a cylinder is:

\(V = \pi r^2h\)

Substitute 100 for V

\(100 = \pi r^2h\)

Make h the subject

\(h = \frac{100 }{\pi r^2}\)

The surface area (A) of a cylinder is:

\(A = 2\pi r^2 + 2\pi rh\)

Where

\(Top\ and\ bottom = 2\pi r^2\)

\(Sides = 2\pi rh\)

So, the cost of the surface area is:

\(C = 2\pi r^2 * 0.014+ 2\pi rh * 0.007\)

\(C = 2\pi r(r * 0.014+ h * 0.007)\)

\(C = 2\pi r(0.014r+ 0.007h)\)

Substitute \(h = \frac{100 }{\pi r^2}\)

\(C = 2\pi r(0.014r+ 0.007*\frac{100 }{\pi r^2})\)

\(C = 2\pi r(0.014r+ \frac{0.007*100 }{\pi r^2})\)

\(C = 2\pi r(0.014r+ \frac{0.7}{\pi r^2})\)

\(C = 2\pi (0.014r^2+ \frac{0.7}{\pi r})\)

Open bracket

\(C = 2\pi *0.014r^2+ 2\pi *\frac{0.7}{\pi r}\)

\(C = 0.028\pi *r^2+ \frac{2\pi *0.7}{\pi r}\)

\(C = 0.028\pi *r^2+ \frac{2 *0.7}{r}\)

\(C = 0.028\pi *r^2+ \frac{1.4}{r}\)

\(C = 0.028\pi r^2+ \frac{1.4}{r}\)

To minimize, we differentiate C w.r.t r and set the result to 0

\(C' = 0.056\pi r - \frac{1.4}{r^2}\)

Set to 0

\(0 = 0.056\pi r - \frac{1.4}{r^2}\)

Collect Like Terms

\(0.056\pi r = \frac{1.4}{r^2}\)

Cross Multiply

\(0.056\pi r *r^2= 1.4\)

\(0.056\pi r^3= 1.4\)

Make \(r^3\) the subject

\(r^3= \frac{1.4}{0.056\pi }\)

\(r^3= \frac{1.4}{0.056 * 3.14}\)

\(r^3= \frac{1.4}{0.17584}\)

\(r^3= 7.96178343949\)

Take cube roots of both sides

\(r= \sqrt[3]{7.96178343949}\)

\(r= 1.997\)

Recall that:

\(h = \frac{100 }{\pi r^2}\)

\(h = \frac{100 }{3.14 * 1.997^2}\)

\(h = \frac{100 }{12.52}\)

\(h = 7.987\)

Hence, the dimensions that minimizes the cost are:

\(Radius = 1.997\ in\) and \(Height = 7.987\ in\)

To calculate the cost, we have:

\(C = 2\pi r(0.014r+ 0.007h)\)

\(C = 2* 3.14 * 1.997 * (0.014*1.997+ 0.007*7.987)\)

\(Cost = \$1.05\)

Answer:

Step-by-step explanation:

Ronald's walking speed is 3 miles per hour, and he walks for 2 hours, so he covers 3 * 2 = 6 miles. In the next hour, he runs at a speed of 6 miles per hour, covering an additional 6 miles. Therefore, Ronald traveled a total of 6 + 6 = 12 miles.

Answer:

Yes, he is correct.

Step-by-step explanation:

Took the test

The astronomer is wrong, the numerator and denominator need to be switched in the expression.

Difference in distance = Distance from Earth to Neptune ÷ Distance from Earth to Mercury

= 2.7 × 10^9 ÷ 5.7 × 10^7

= 2.7 × 10^9 × 1 / 5.7 × 10^7

= 2.7 × 10^9 / 5.7 × 10^7

= (2.7 - 5.7) × 10^9-7

= -3 × 10² miles

Therefore, the astronomer is wrong,the numerator and denominator need to be switched in the expression.

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The range of the data is 30, and the interquartile range (IQR) is 15.

To create a box plot using the given data, we first need to determine the five-number summary, which includes the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value.

From the given data, we can determine the five-number summary as follows:

Minimum: 60

Q1: 70

Median (Q2): 80

Q3: 85

Maximum: 90

Now, let's create a box plot using this information:

```

  |         |         |         |         |

60 |––––––––|––––––––|         |

  |         |         |         |         |

70 |––––––––|––––––––|––––––––|––––––––|

  |         |         |         |         |

80 |––––––––|––––––––|––––––––|––––––––|

  |         |         |         |         |

90 |––––––––|––––––––|         |

  |         |         |         |         |

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

    60       70        80        90

```

In the box plot, the line within the box represents the median (Q2), the box represents the interquartile range (IQR) from Q1 to Q3, and the lines extending from the box (whiskers) represent the minimum and maximum values. Any data points falling outside the whiskers would be considered outliers.

The range can be calculated as the difference between the maximum and minimum values:

Range = Maximum - Minimum = 90 - 60 = 30

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1):

IQR = Q3 - Q1 = 85 - 70 = 15

Therefore, the range of the data is 30, and the interquartile range (IQR) is 15.

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Answer:

2/8

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

First found amount yielded

A = P(1+r)^nt

P is amount deposited 50,200

r is interest rate 13% = 13/100 = 0.13

t = 3

A = 50,200(1+0.13)^3

A = 50,200(1,13)^3

A = 72,433.42939999998

A is approximately 72,433.43

interest = A - P = 72,433.43-50,200 = 22,233.43= 22,233 to the nearest GHS

Answer:

3) x = -4 and y = 6

4) x = -1 and y = 0

5) x = 1 and y = -3

6) x = -4 and y = -3

Step-by-step explanation:

3) Add the equations:

(3x + 4y = 12) + (-3x - y = 6) (eliminate the x)

= 3y = 18

y = 18/3

y = 6

3x + 4(6) = 12

3x = 12 - 24

x = -12/3 = 4

4) Add the equations:

(-5x - 6y = 5) + (-6x + 6y = 6)

-11x = 11

x = -1

-5(-1) -6y = 5

-6y = 5 - 5

y = 0

5) 7x -4y = 19

10x - 2y = 16

Multiply the second equation by -2 to eliminate the y and add both equations.

-2(10x -2y = 16) =

(-20x + 4y = -32) + (7x - 4y = 19)

-13x = -13

x = 1

7(1) - 4y = 19

-4y = 19-7

y = 12/-4

y = 3

6) multiply the second equation by -2 to eliminate the x and then add the equations.

-2(5x - 3y = - 11) =

(-10x + 6y = 22) + (10x - 9y = - 13)

= -3y = 9

y = - 3

10x - 9(-3) = - 13

10x = -13 - 27

x = -40/10

x = -4

Answer:

san po jan

The orthogonal projection of vector v onto vector w in R^3 is (-54/14, -159/70, -159/35).

To find the orthogonal projection of v onto w, we need to calculate the scalar projection of v onto w and multiply it by the unit vector of w. The scalar projection of v onto w is given by the formula:

proj_w(v) = (v⋅w) / (w⋅w) * w

where ⋅ denotes the dot product.

Calculating the dot product of v and w:

v⋅w = (-7)(-5) + (6)(-3) + (-6)(-6) = 35 + (-18) + 36 = 53

Calculating the dot product of w with itself:

w⋅w = (-5)(-5) + (-3)(-3) + (-6)(-6) = 25 + 9 + 36 = 70

Now, substituting these values into the formula, we have:

proj_w(v) = (53/70) * (-5,-3,-6) = (-54/14, -159/70, -159/35)

Therefore, the orthogonal projection of v onto w is (-54/14, -159/70, -159/35).

In simpler terms, the orthogonal projection of v onto w can be thought of as the vector that represents the shadow of v when it is cast onto the line defined by w. It is calculated by finding the component of v that aligns with w and multiplying it by the direction of w. The resulting vector (-54/14, -159/70, -159/35) lies on the line defined by w and represents the closest point to v along that line.

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Answer:

Step-by-step explanation:

2 lbs.  x    1 wk.  

   wk.       7 days

= 2/7 lbs./day

or

= 0.29 lbs./day

Answer:

Triangles A and B are acute, C is right, and I think D might be obtuse.

Step-by-step explanation:

Acute means that the angles are less than 90 degrees, and obtuse means that at least one angle is more than 90 degrees.

Answer:

Triangle A: Acute

Triangle B: Acute

Triangle C: Obtuse

Triangle D: Right

Step-by-step explanation:

Acute angle: 0°-90°

Right angle: 90°

Obtuse angle: 90°-180°

An acute triangle only has acute angles. A right triangle has one right angle. An obtuse triangle has one obtuse angle.

Answer:0.25

Step-by-step explanation: 1.50÷6

The slope of the graph in dollars per roll is 0.25.

The slope of a line indicates the direction and the steepness of the line.

Given that, the bakery sells 6 rolls for $1.50.

The slope of the line in dollars per roll is given by:

(total cost)/(total roll)

= 1.50/6

= 0.25

Hence, the slope of the graph in dollars per roll is 0.25.

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