What is the result of subtracting the second equation from the first?
х – 3y = 6
-83 – y = 6

The equation that could be used to determine x is \(\frac{11+x}{53+x} \leq 0.300\).

Inequality is a relation that makes a non-equal comparison between two expressions.

Batting average of William = 11/53

Desired batting average = 0.300

Suppose the number of more hits in a row to have desired batting average =x

Number of hits now =11+x

Number of bats now =53+x

It is given that the batting average should be a minimum of 0.300.

This means \(\frac{11+x}{53+x} \leq 0.300\)

Therefore, the equation that could be used to determine x is \(\frac{11+x}{53+x} \leq 0.300\).

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Maci and 2 appointments and Logan had 3 appointments.

The linear equation that represents the total amount earned by Maci is:

Total amount earned = (amount per appointment x number of appointments)  + tips

$170 = ($60 x a) + $50

$170 = $60a + $50

$170 - $50 = $60a

$120 = $60a

a = $120 / $60

a = 2

The linear equation that represents the total amount earned by Logan is:

Profit = total revenue - total cost

Profit = (fee per appointment  x number of appointments) + amount received in tips - (rental fee x number of appointments)

$235 = ($75 x a) + $40 - ($10 x a)

$235 = $75a + $40 - $10a

$235 = $65a + $40

$235 - $40 = $65a

$195 = $65a

a = $195 / 65

a = 3

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Answer:

y = -3/4x + 6.75

Step-by-step explanation:

Slope intercept form is y = mx + b, where m is the slope and b is the y intercept.

Plug in the given point and slope into the equation, then solve for b:

y = mx + b

3 = -3/4(5) + b

3 = -3.75 + b

6.75 = b

Then, plug in the slope and y intercept into the equation:

y = -3/4x + 6.75 is the equation of the line in slope intercept form

The coordinates of the image if triangle ABC is translated 4 units down would be: A′(1, -6), B′(9, -6), C′(5, -2)

To translate the triangle 4 units down, we need to subtract 4 from the y-coordinate of each vertex.

Vertex A has coordinates (1, -2), so its image A' after the translation is (1, -2 - 4) = (1, -6).

Vertex B has coordinates (9, -2), so its image B' after the translation is (9, -2 - 4) = (9, -6).

Vertex C has coordinates (5, 2), so its image C' after the translation is (5, 2 - 4) = (5, -2).

Therefore, the coordinates of the vertices of triangle ABC after it is translated 4 units down are A′(1, −6), B′(9, −6), and C′(5, −2).

So, the answer is option A: A′(1, −6), B′(9, −6), C′(5, −2)..

How can you use the coordinates of the vertices of a figure to determine its image after a translation?

To determine the image of a figure after a translation, you can add or subtract the same amount from the x- and/or y-coordinates of each vertex, depending on the direction and distance of the translation.

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Answer:

Blue stars are the hottest stars.

Your total would be $7.02

The factor of the polynomial, the area of the pool and the simplified expression are all algebraic expressions

Factor of the polynomial

The polynomial is given as:

2x^3 + 6x^2 + 6x + 18

Factor out 2

2x^3 + 6x^2 + 6x + 18 = 2(x^3 + 3x^2 + 3x + 9)

Factorize

2x^3 + 6x^2 + 6x + 18 = 2(x^2(x + 3) + 3(x + 3))

Factor out x + 3

2x^3 + 6x^2 + 6x + 18 = 2(x^2 + 3)(x + 3)

Expand

2x^3 + 6x^2 + 6x + 18 = (2x^2 + 6)(x + 3)

Hence, 2x^2 + 6 is a factor of the polynomial 2x^3 + 6x^2 + 6x + 18

The length of the pool

The given parameters are:

Area = 2x^3 - 29x + 12

Width = x + 4

The length is calculated as:

Length = Area/Width

This gives

Length = 2x^2 - 29x + 12/x + 4

Factorize the numerator

Length = (2x^2 - 8x + 3)(x + 4)/x + 4

Cancel out x + 4

Length = 2x^2 - 8x + 3

Hence, the length of the pool is 2x^2 - 8x + 3

Simplify the expression

The expression is given as:

(3s^2 - 2s + 1) \(\div\) (s^2 - s + 2)

Evaluate the quotient

3 + (s - 5)/(s^2 - 5 + 2)

Hence, the simplified expression is 3 + (s - 5)/(s^2 - 5 + 2)

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\({ \bf{ \underbrace{Given :}}}\)

Radius of the circle "\(r\)" = 9 in.

\({ \bf{ \underbrace{To\:find:}}}\)

The circumference of the circle.

\({ \bf{ \underbrace{Solution :}}}\)

\(\sf\orange{The\:circumference \:of\:the\:circle\:is\:56.52\:in.}\)

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

We know that,

\(\sf\purple{Circumference\:of\:a\:circle \:=\:2πr }\)

\( = 2 \times 3.14 \times 9 \: in \\ \\ = 56.52 \: in\)

Therefore, the circumference of the circle is 56.52 in.

\(\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}\)

Answer:

x=11

Step-by-step explanation:

Explanation is in photo, hope this helps!

Answer:

its d or to be more specific its the right of the coordinate plane

Step-by-step explanation:

A relative max is like the top of every mountain in a mountain range. In that area, it's the highest point.

A relative min is like the bottom of every valley in a mountain range. In that area, it's the lowest point.

If you talk about *absolute* maxs and min, then those are the highest peak in the entire mountain range or the lowest valley in the entire mountain range.

See the picture for a visual of where the relative max and min are.

Relative minimum

x coordinate=1

y coordinate=1

Relative maximum

x coordinate=0

y coordinate=2

Here there is no absolute maxima or minima as no particular interval is given

Answer:

9.5

Step-by-step explanation:

6 kiloliters are approximately equal to 202,884.14 fluid ounces.

We have,

To convert 6 kiloliters (kL) to fluid ounces (fl oz), we need to use the conversion factor between these two units.

The conversion factor states that 1 kiloliter is equal to 33814.0227 fluid ounces.

This means that for every kiloliter, there are 33814.0227 fluid ounces.

To convert 6 kiloliters to fluid ounces, we multiply the given value (6 kL) by the conversion factor (33814.0227 fl oz/kL).

= 6 kL x 33814.0227 fl oz/kL

= 202884.1362 fl oz

Therefore,

6 kiloliters are approximately equal to 202,884.14 fluid ounces.

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The data that can be determined from the box plots are

a)

This is because the line in the middle of the box plot is the median of the box plot.

b)

The upper quartile of a box plot is the part of the box plot that is to the right of the line. In this case the median line is at the same location and the upper quartile ends at the same location.

and

The data that can not be determined is

c)

The reason this can not be determined is because the median is the average of the grades. This could mean some students scored in the higher levels and more scored below the median, which in turn drags it down.

d)

Would be following the same reason as C. It can be determined that there was a larger range lower grades in period 5 over period 3, but it can't be determined how many.

Answer:

the answer is 15840

Step-by-step explanation:

Answer:

y=\(\frac{1}{10} x^2\)

Step-by-step explanation:

You're partially correct.

Let me explain:

When a parabola is scaled vertically, think of it this way: a parabola is being stretched up or smooshed downwards, by some math god who can defy all forms of life and dimensions.

When a parabola, in y=a\(x^{2}\), is shifted vertically, when a>1, it appears 'skinnier'. The parabola went on a diet! However, when 0<a<1, the parabola seems wider and fat.

Knowing this knowledge, when factored vertically by a factor of x, it means that it is the coefficient of the parent graph  y=a\(x^{2}\), which means 1/10 goes before \(x^{2}\).

Summing all of this up, your answer would have the equation of the new parabola as y=\(\frac{1}{10} x^2\)

Scaled vertically means not reflected over x axis .

Here

Now it's vertically scaled

so

New equation

Therefore, the solution to the given problem is that the upper bound for P(X>15) is 3/25

The variance is the difference between the numbers in a set of data, to put it simply. Each number's variability is a statistical statistic that indicates how far off from the mean and from each other number in the set it is.

Here,

Given : mean = 10

varience = 3

Using chebyshevs inequality we have

P(|X-u| ≥ k)≤ \(\sigma^{2}\)/\(k^{2}\)

hence we can have,

=> P(X>15)  ≤ 3/\(5^{2}\)

=> P(X>15)  ≤ 3/25

Therefore, the solution to the given problem is that the upper bound for P(X>15) is 3/25

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Answer:

Mean for Male=72.13

Median for male = 65

Mean for Female= 79.93

Median for female= 83

There are differences in the results of mean and median for the males' data compared to the mean and median results calculated from the females' data.

Step-by-step explanation:

Mean for Male: 96 75 53 94 79 55 62 65 61 91 64 81 60 63 83 ​

X= 96, 75, 53, 94, 79, 55, 62, 65, 61, 91, 64, 81, 60, 63, 83 ​

Total number of value, n=15

Mean is average value, which gives: addition of X, divided by n

Mean= (96+75+53 +94+ 79+ 55+ 62+ 65+ 61+ 91+ 64+ 81+ 60+ 63+ 83) / 15

Mean= 1082 / 15

Mean=72.13

Median for male: 96 75 53 94 79 55 62 65 61 91 64 81 60 63 83 ​

The values should be rearranged in numerical order to get the middle value

53 55 60 61 62 63 64 65 75 79 81 83 91 94 96

The middle value is the 8th value since there are 15 values

Median = 65

Mean for Female: 71 73 92 86 90 67 89 76 89 86 69 88 68 83 72

X= 71 73 92 86 90 67 89 76 89 86 69 88 68 83 72

Total number of value, n=15

Mean is average value, which gives: addition of X, divided by n

Mean= (71 +73+ 92 +86 +90 +67 +89+ 76+ 89+ 86+ 69+ 88+ 68+ 83+ 72) / 15

Mean= 1199 / 15 = 79.93

Median for female: 71 73 92 86 90 67 89 76 89 86 69 88 68 83 72

The values should be rearranged in numerical order to get the middle value: 67 68 69 71 72 73 76 83 86 86 88 89 89 90 92    

 The middle value is the 8th value since there are 15 values

Median = 83

There are differences in the results of mean and median for the males' data compared to the mean and median results calculated from the females' data.

Answer:

option (d) is correct.

Step-by-step explanation:

Given the table

x       -3       0       3

y       -6       0       6

An ordered pair (x, y) is a composition of the x-coordinate and y-coordinate.

For example, the ordered pair (1, 2) is a composition of the x-coordinate i.e. x = 1 and y-coordinate i.e. y = 2.

The relation can be determined by converting all the points in the table via the ordered pairs and combining all of them such as ordered pairs:

{(-3, -6), (0, 0), (3, 6)}

Therefore, option (d) is correct.

Answer:

rational

Step-by-step explanation:

rational + rational=rational

Answers

x= -3/2

x= 3i

x= -3i

Step-by-step explanation:

f (x) = 2x3 + 3x2 + 18x + 27

Set 2x^3 + 3x^2 + 18x + 27 equal to 0.

2x^3 + 3x^2 + 18x + 27 = 0

Solve for x.

Factor the left side of the equation.

Factor out the greatest common factor from each group.

x^2 (2x + 3) + 9 (2x + 3) = 0

Factor the polynomial by factoring out the greatest common factor, 2x + 3. (2x + 3) (x^2 + 9) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

2x + 3 = 0

x^2 + 9 = 0

Set 2x + 3 equal to 0 and solve for x.

Set 2x + 3 equal to 0. 2x + 3 = 0

Solve 2x + 3 = 0 for x. Tap for more steps...  

3 x = − 2

Set x2 + 9 equal to 0 and solve for x.

Set x2 + 9 equal to 0. x2 + 9 = 0

Solve x2 + 9 = 0 for x.

x = 3i, −3i

The final solution is all the values that make (2x + 3) (x2 + 9) = 0 true.

x = − 3/2 , 3i, −3i

SOLUTION

Since t is the number of years since 1950, we will take 1950 to be 0, then the other years in multiples of 5, since it is 5 years interval. The table and the model from a graphing calculator is shown below

From the model

Substituting, we have

Hence the linear function is

The exponential function

From the calculator

We have

Plugging the values we have

Hence the exponential function is

Mortality rate in 2022.

1950 to 2022 is 72 years. So we substitute 72 for t in the exponential function, we have

Hence the answer is 31.8 to one decimal place

For the transformations of the triangle, we have that:

1. The translation of triangle ABC preserves side lengths and angles.

2. The dilation of triangle ABC preserves angles but not side lengths.

Hence the correct options are, respectively, C and B.

A translation involves shift left, shift right, shift down, or shift up, meaning that just the coordinates of the figure change, not the angles or the side lengths,

1. The translation of triangle ABC preserves side lengths and angles.

For a dilation, the coordinates of the vertices are multiplied by a constant, hence the side lengths change while the angles remain constant, thus:

2. The dilation of triangle ABC preserves angles but not side lengths.

Hence the correct options are, respectively, C and B.

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The amount of Duane's first payment that goes to interest is approximately $26.47.

To determine the amount of Duane's first payment that goes to interest, we need to use the amortization formula for a loan.

The formula to calculate the interest portion of a loan payment is:

Interest = Remaining Balance * Monthly Interest Rate.

Let's calculate the interest for the first payment using the given information:

Loan Amount = $5,000.00

Monthly Payment = $118.57

First, we need to calculate the monthly interest rate:

Monthly Interest Rate = Annual Interest Rate / 12

= 6.5% / 12

= 0.00542

Next, we need to calculate the remaining balance after the first payment:

Remaining Balance = Loan Amount - Principal Paid

= $5,000.00 - $118.57

= $4,881.43

Finally, we can calculate the interest portion of the first payment:

Interest = Remaining Balance * Monthly Interest Rate

= $4,881.43 * 0.00542

= $26.47

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Answer:

A+S=22

A=S/2+4

Multiply second equation by 2 and rearrange.

2A-S=8

Add equations 1 and 3.

3A=30

A=10

Substitute for A in either of the first 2 equations to get

S=12

Step-by-step explanation:

Answer 3/8 is the answer hope this helps

5/8 or 0.625

Equation: 120/192

GCF: 24

Simplifying: 120÷24/192÷24

Simplified: 5/8 or 0.625

Applying angle relationships, the measures of the numbered angles are:

m∠1 = 90°

m∠2 = 68°

m∠3 = 112°

m∠4 = 112°

m∠5 = 68°

m∠6 = 56°

m∠7 = 124°

m∠8 = 124°

To calculate angle measurements that are formed by a transversal and parallel lines, we can apply the knowledge of the angle relationships that exist between the angle pairs in concerned. Some angle relationships are:

m∠1 = right angle [corresponding angles is the angle relationship]

m∠1 = 90°

m∠2 = 180 - m∠1 - 22 [triangle sum theorem]

Substitute

m∠2 = 180 - 90 - 22

m∠2 = 68°

m∠3 = 180 - m∠2

Substitute

m∠3 = 180 - 68

m∠3 = 112°

m∠4 = m∠3

m∠4 = 112°

m∠5 = 180 - m∠4

m∠5 = 180 - 112

m∠5 = 68°

m∠6 = 1/2(180 - m∠5)

m∠6 = 1/2(180 - 68)

m∠6 = 56°

m∠7 = 180 - 56

m∠7 = 124°

m∠8 = m∠7 [alternate interior angles is the angle relationship]

m∠8 = 124°

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Therefore, the package with 40 hooks is the better buy in terms of cost efficiency.

To determine which package is the better buy, we need to compare the cost per hook for each package.

For the package of 25 hooks costing $9.95, we divide the total cost by the number of hooks:

Cost per hook = $9.95 / 25 = $0.398

Rounding to the nearest cent, the cost per hook is $0.40.

For the package of 40 hooks costing $13.99, we divide the total cost by the number of hooks:

Cost per hook = $13.99 / 40 = $0.3498

Rounding to the nearest cent, the cost per hook is $0.35.

Comparing the two costs per hook, we can see that the package with 40 hooks for $13.99 offers a better deal, as the cost per hook is lower at $0.35.

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Answer:

Graph D

Step-by-step explanation:

Move the constant to the opposite side of the equation and group terms that include the same variable.

g(x) + 1 = x^2 + 2x

Finish the square. Remember to keep the equation balanced by using the same constants on both sides.

g(x) + 1 + 1 = x^2 + 2x + 1

g(x) + 2 = x^2 + 2x + 1

Rewrite as perfect squares

g(x) + 2 = (x + 1)^2

Equation in vertex form:
g(x) = (x + 1)^2 - 2

The vertex:

(-1, -2)

* This a minimum *