line a'b is the translated image of ab. which could be the coordinates of a' and b

Algebra transformation

for  Graph1 f(x)=f(x)+4

for  Graph2 f(x)=-f(x-4)

for  Graph3 f(x)=f(x-7)

for  Graph4 f(x)=f(x-2)-5

In mathematics, the reflection of a graph is a transformation that produces a mirror image of the original graph across a specific line or point. The line or point across which the reflection occurs is called the axis of reflection.

Graph1

Transform the graph by +4 units in y direction.

f(x)=f(x)+4

Graph2

Transform the graph by +4 units in x direction.

f(x)=f(x-4)

Now take the reflection of graph about x axis

f(x)=-f(x-4)

Graph3

Transform the graph by +7 units in x direction.

f(x)=f(x-7)

Graph5

Transform the graph by -5 units in y direction.

f(x)=f(x)-5

Now Transform the graph by -2 units in x direction.

f(x)=f(x-2)-5

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Answer:

[tex] \frac{19 + 6 \sqrt{3} }{2} [/tex]

Step-by-step explanation:

[tex]2a - \frac{1}{ \sqrt{a} } + \frac{1}{a} \: \: \: when \: \: a = 4 + 2 \sqrt{3} [/tex]

[tex]2 \times (4 + 2 \sqrt{3} ) - \frac{1}{ \sqrt{4 + 2 \sqrt{3} } } + \frac{1}{4 + 2 \sqrt{3} } [/tex]

Expand the brackets (multiply every term inside the bracket by the term on the outside) and make the denominator the same (4 + 2√3):

[tex] \frac{(8 + 4\sqrt{3} )\times(4 + 2 \sqrt{3} ) }{4 + 2 \sqrt{3} } - \frac{ \sqrt{4 + 2 \sqrt{3} } }{4 + 2 \sqrt{3} } + \frac{1}{4 + 2 \sqrt{3} } [/tex]

[tex] \frac{32 + 16 \sqrt{3} + 16 \sqrt{3} + 24 - \sqrt{4 + 2 \sqrt{3} } + 1}{4 + 2 \sqrt{3} } [/tex]

Collect like-terms:

[tex] \frac{57+ 32 \sqrt{3} - \sqrt{4 + 2 \sqrt{3} } }{4 + 2 \sqrt{3} } [/tex]

[tex] \frac{57 + 32 \sqrt{3} - \sqrt{( {1 + \sqrt{3}) }^{2} } }{4 + 2 \sqrt{3} } [/tex]

[tex] \frac{57 + 32 \sqrt{3} - (1 + \sqrt{3} )}{4 + 2 \sqrt{3} } [/tex]

Eliminate the parentheses:

[tex] \frac{57 + 32 \sqrt{3} - 1 - \sqrt{3} }{4 + 2 \sqrt{3} } [/tex]

Collect like terms:

[tex] \frac{56 + 31 \sqrt{3} }{4 + 2 \sqrt{3} } [/tex]

[tex] \frac{56 + 31 \sqrt{3} }{4 + 2 \sqrt{3} } \times \frac{4 - 2 \sqrt{3} }{4 - 2 \sqrt{3} } = \frac{224 - 112 \sqrt{3} + 124 \sqrt{3} - 186}{16 - 4 \times 3} = \frac{38 + 12 \sqrt{3} }{4} [/tex]

[tex] \frac{2(19 + 6 \sqrt{3}) }{4} = \frac{19 + 6 \sqrt{3} }{2} [/tex]

The food stand located at the amusement park is located at the centroid, which is the point of concurrency.

The centroid is the point of intersection of the three medians of a triangle. The medians are the lines drawn from each vertex to the midpoint of the opposite side of the triangle.

In this case, the medians are drawn from each of the three attractions to the food stand. The centroid is the point at which all three medians intersect, making it the point of concurrency.

The centroid can be found by taking the mean of the x and y coordinates of each vertex of the triangle.

The centroid is the point at which the sum of the distances from the vertices to the centroid is at its minimum. This is why the food stand is located at the centroid of the triangle formed by the roller coaster, merry-go-round, and go karts.

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When x3 + x² + 2kx + 6 is divided by (x - 2), the remainder is 30 and k = ±1.

An equation is a mathematical statement that establishes an equality between two expressions. It consists of two expressions separated by an equal sign (=). The expressions on either side of the equal sign represent the same value and can be used to solve for a desired quantity. Equations can be used to express relationships between variables, calculate unknowns, and describe physical phenomena.

To solve this problem, we can use the Remainder Theorem, which states that when a polynomial is divided by a linear expression, the remainder is equal to the value of the polynomial at the x-intercept of the linear expression.

In this case, when we divide x3 + x² + 2kx + 6 by (x - 2), we get the following:

(x - 2)(Q(x)) + R = x3 + x² + 2kx + 6

Where Q(x) is the quotient and R is the remainder (in this case, 30).

We can use the Remainder Theorem to find k. Since the x-intercept of (x - 2) is x = 2, we can plug this into the equation to find R:

(2 - 2)(Q(2)) + R = 23 + 22 + 2k2 + 6

R = 30

Therefore, we can solve for k:

30 = 23 + 22 + 2k2 + 6

30 - 23 - 22 - 6 = 2k2

k2 = 1

Therefore, k = ±1.

In conclusion, when x3 + x² + 2kx + 6 is divided by (x - 2), the remainder is 30 and k = ±1.

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Answer:

y = sin(3x)

Step-by-step explanation:

Amplitude = A = 1

Period = 2π/B = 2π/3

B = 3

Equation of a sine wave:  y = Asin(B(x + C)) + D

There is no phase shift or vertical shift, so C and D are 0 (zero)

Therefore, the equation of the graph is:

y= Asin(Bx) = sin(3x)

The area of the sector is  30. 52 square units

To determine the area of the sector, we need to consider the formula.

The formula for calculating the area of a sector is expressed with the formula;

A = (θ/360º) × πr2

Such that the parameters of the formula are;

From the information given, we have;

Substitute the values

Area = 140/360 × 3.14 × 5²

Find the square value

Area = 140/360 × 3.14 × 15

Multiply the values

Area = 0. 389  × 3.14 × 25

Multiply

Area = 30. 52 square units

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Answer:

z>-4

Step-by-step explanation:

You start with -2z-3<5 add 3 to both sides -2z<8 and divided by negative which flips your sign so you get z>-4 hope this helps :)

Answer:

give brainliest if correct

Step-by-step explanation:

Let's call the distance from the ball to the base of the goal "x". We can use the tangent function to set up an equation:

tan(27°) = opposite/adjacent

In this case, the opposite side is the height of the goal (9 feet) and the adjacent side is the distance we want to find (x). So we can rewrite the equation as:

tan(27°) = 9/x

To solve for x, we can cross-multiply and then divide by tan(27°):

tan(27°) * x = 9

x = 9 / tan(27°)

Using a calculator, we get:

x ≈ 17.20 feet

So the distance from the ball to the base of the goal is approximately 17.20 feet.

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The total change to Ahab's funds is -$175, which means he spent more money than he received and is now $175 poorer

To solve this problem, we need to calculate the total amount of money Ahab spent and the total amount of money he received. We can then subtract the total amount spent from the total amount received to get the total change to Ahab's funds.

The total amount spent on tires is 3 x $50 = $150.

When he returned one tire, he received a refund of $50.

He found a five dollar bill, which adds $5 to his funds.

The total amount spent on jackets is 2 x $40 = $80.

Therefore, the total amount spent is $150 + $80 = $230, and the total amount received is $50 + $5 = $55.

To find the total change to Ahab's funds, we subtract the total amount spent from the total amount received:

$55 - $230 = -$175

Therefore, the total change to Ahab's funds is -$175, which means he spent more money than he received and is now $175 poorer.

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The value of angle QSR is determined as 50⁰.

The value of angle QSR can be obtained if we calculate the value of x.

The value of x is calculated by setting up the following equation as shown below;

(4x - 8) + 34 + (76 - x) = 180 (sum of angles in a straight line )

4x - 8 + 34 + 76 - x = 180

3x = 180 - 102

3x = 78

x = 78/3

x = 26

The value of angle QSR;

∠QSR = 76 - x

∠QSR = 76 - 26

∠QSR =  50⁰

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The probability that she selects a blue floss is 14% greater than the probability that she selects an orange floss.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of spools is given as follows:

8 + 5 + 7 + 10 + 3 + 6 + 4 + 7 = 50 spools.

10 are blue, hence the probability is of:

10/50 = 20%.

3 are orange, hence the probability is of:

3/50 = 6%.

The difference is of:

20 - 6 = 14%.

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Answer:

⇒ X = (-2/7, 48/7)

Step-by-step explanation:

Use this formula to find the point X.

([mx₂ + nx₁] / [m+n], [my₂ + ny₁] / [m+n])

Where m:n is the ratio, and the points are x₁, y₁ and x₂, y₂.

The formula can be thought like this:

When the midpoint of a line is taken, we take the average of the x coordinates and the average of the y coordinates. This is in the ratio 1:1.

If we were to take the point on a line in a ratio [m:n], we take the weighted average.

X = ([3*2 + 4*-2] / [3 + 4], [3*4 + 4*9] / [3 + 4])

∴ X = (-2/7, 48/7)

Answer:

So I did the work, but it won't let me upload a picture of it, so when I solved it my answer that I had gotten foe this solution was x(-2/7,48/7).

I hope it was correct for you.

The zeros of the function y = -16x² + 246x + 100 are x = -0.4 and x = 15.8

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

y=-16x^2+246x+100

Express properly

So, we have

y = -16x² + 246x + 100

Divide through the equation by 2

So, we have

y = -8x² + 123x + 50

We set the value of y to 0, in order to solve the equation

So, we have

-8x² + 123x + 50 = 0

When solved graphically, we have

x = -0.396 and x = 15.771

Approximate

x = -0.4 and x = 15.8

Hence, the x values are x = -0.4 and x = 15.8

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The above prompts have to do with Accounting Principles especially journal entries, income statements and Inventory Mangement. See the answers below.

1) The journal entries are given as follows:

Oct. 4: Purchased 180 bicycles at a cost of $145 each from the Nixon Bicycle Company, terms 2/10, n/30.

Inventory (180 x $145) 26,100

Accounts Payable 26,100

Oct. 5: Paid freight of $900 on the October 4 purchase.

Freight-In 900

Cash 900

Oct. 6: Sold 10 bicycles from the October 1 inventory to Team America for $250 each, terms 2/10, n/30.

Accounts Receivable 2,500

Sales Revenue 2,500

Cost of Goods Sold:

Inventory (10 x $150) 1,500

Cost of Goods Sold 1,500

Oct. 7: Received credit from the Nixon Bicycle Company for the return of 8 defective bicycles.

Accounts Payable 1,160

Inventory 1,160

Oct. 13: Issued a credit memo to Team America for the return of a wrong clear bicycle.

Sales Returns and Allowances 2,500

Accounts Receivable 2,500

Cost of Goods Sold:

Cost of Goods Sold 1,500

Inventory 1,500

Oct. 14: Paid Nixon Bicycle Company in full, less discount.

Accounts Payable 25,452

Inventory 648

Cash 24,804

Explanation:

On October 4, the company purchased 180 bicycles at a cost of $145 each for a total of $26,100. The journal entry is a debit to Inventory for $26,100 and a credit to Accounts Payable for $26,100.

On October 5, the company paid freight costs of $900 on the October 4 purchase. The journal entry is a debit to Freight-In for $900 and a credit to Cash for $900.

On October 6, the company sold 10 bicycles from the October 1 inventory to Team America for $250 each. The total sales revenue is $2,500. The cost of goods sold is calculated by multiplying the number of bicycles sold (10) by the cost per unit ($150), which equals $1,500. The journal entry for the sale is a debit to Accounts Receivable for $2,500 and a credit to Sales Revenue for $2,500. The cost of goods sold is recorded as a debit to Cost of Goods Sold for $1,500 and a credit to Inventory for $1,500.

On October 7, the company received a credit from Nixon Bicycle Company for 8 defective bicycles. The journal entry is a debit to Accounts Payable for $1,160 and a credit to Inventory for $1,160.

On October 13, the company issued a credit memo to Team America for the return of a wrong clear bicycle. The journal entry is a debit to Sales Returns and Allowances for $2,500 and a credit to Accounts Receivable for $2,500. The cost of goods sold is recorded as a debit to Cost of Goods Sold for $1,500 and a credit to Inventory for $1,500.

On October 14, the company paid Nixon Bicycle Company in full, less discount. The company received a 2% discount for paying within the discount period. The journal entry is a debit to Accounts Payable for $25,452, a debit to Inventory for $648, and a credit to Cash for $24,804.



2) The multiple step income statement for the year ended December 31, 2022 is given as follows:

A) McCoy Company

Income Statement

For the Year Ended December 31, 2022

Sales Revenue $645,000

Less: Sales Returns and Allowances 50,000

Sales Discounts 9,500

________

Net Sales 585,500

Cost of Goods Sold 396,000

________

Gross Profit $189,500

Operating Expenses:

Freight-Out 2,000

Advertising Expense 15,000

Interest Expense 19,000

Salaries and Wages Expense 84,000

Utilities Expense 23,000

Depreciation Expense 3,500

________

Total Operating Expenses 146,500

________

Income Before Taxes 43,000

Other Revenues and Gains:

Interest Revenue 25,000

________

Net Income $ 68,000

=======

B) Profit Margin = Net Income / Net Sales

= $68,000 / $585,500

= 0.1164 or 11.64%

Gross Profit Rate = Gross Profit / Net Sales

= $189,500 / $585,500

= 0.3239 or 32.39%

C) For the third prompt, see the attached.

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The set of parametric equations for the path of the baseball are:

x = (146.67 cos )t

y = 3 + (146.67 sin )t - 16t

where x is the horizontal distance traveled by the ball and y is the vertical height of the ball.

It should be noted that to determine if the ball clears the fence, we need to find the value of t when y = 10, which is the height of the fence. So we solve the equation:

3 + (146.67 sin 220)t - 16t = 10

Simplifying the equation, we get:

(146.67 sin 220 - 16)t = 7

t = 7 / (146.67 sin 220 - 16) ≈ 0.071 seconds

Now we can plug this value of t into the equation for x to find the horizontal distance traveled by the ball:

x = (146.67 cos 220) × 0.071 ≈ -24.4 feet

Since the ball has a negative x-coordinate, it lands behind the fence and is not a homerun.

c) The graph shows the path of the baseball in blue. The important points are labeled on the graph. The point (0,3) represents the initial position of the ball, and the point where the blue curve intersects the red line (y=10) represents the point where the ball hits the top of the  fence. The point where the blue curve intersects the x-axis represents the landing point of the ball.

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The  credit rating higher than 447 will put applicants in the top 2.5%.

We have Probability of X > x = 0.025

1 - p(z < x - 300 / 75)

z(0.975) = x - 300 / 75 = 1.96

x - 300 / 75 = 1.96

from here we have to cross multiply and solve for x

x = 300 + 147

x = 447

credit rating higher than 447 will put applicants in the top 2.5%.

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A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 300 and a standard deviation of 75. Applicants rated in the top 2.5% will have their loan processing fees waived. What credit rating do applicants need to be higher than to receive this extra perk? .

A credit rating higher than ____ will put applicants in the top 2.5%.

The correct answer is Akira should buy 12 daffodil bulbs in packages of 3 and save $1.08.

Given that,

Akira can buy Daffodil bulbs in packages of 3 for $5.28 or in packages of 2 for $3.70.

He needs to buy 12 bulbs at a better price.

Money spent by buying bulbs in packs of 3 = 4 × $5.28 = $21.12.

Money spent by buying bulbs in packs of 2 = 6 × $3.70 = $22.2.

so, we get,

Money saved if bought in packs of 3 = $22.2 - $21.12 = $ 1.08.

Thus Akira should buy 12 daffodil bulbs in packages of 3 and save $1.08.

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The playhouse consists of a cube and a square pyramid on top of it. The pyramid has a base of 5 feet and a height of 6 feet. The total volume of the playhouse is 135 cubic feet.

To find the volume of the playhouse, we need to find the volume of both the cube and the pyramid and then add them together.

Let's start with the pyramid

The pyramid's volume formula is: V = 1/3 * base * height

We are given that the base of the pyramid is 5 feet and the height is 6 feet, so we can plug in those values and solve for the volume

V = 1/3 * 5 feet * 6 feet

V = 10 cubic feet

Next, let's find the volume of the cube

The cube's volume formula is: V = length * width * height

Since it is a square pyramid on top of a cube, we know that the base of the pyramid has the same length and width as the cube. Let's call the length of each side of the cube "s". Then we have

V = s * s * s

V = s³

We need to find the value of "s". To do that, we can use the fact that the base of the pyramid has a side length of 5 feet. Since the base of the pyramid is the top face of the cube, we know that the side length of the cube is also 5 feet. So

V = 5 feet * 5 feet * 5 feet

V = 125 cubic feet

Now we can add the volumes of the pyramid and the cube to get the total volume of the playhouse

Total volume = pyramid volume + cube volume

Total volume = 10 cubic feet + 125 cubic feet

Total volume = 135 cubic feet

So the playhouse has a volume of 135 cubic feet.

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Answer: B: N is odd

Step-by-step explanation:

If 3N + 5 is a multiple of 10, then it can be written as:

3N + 5 = 10k, where k is an integer.

Subtracting 5 from both sides, we get:

3N = 10k - 5

Dividing both sides by 3, we get:

N = (10k - 5) / 3

For N to be an integer, 10k - 5 must be divisible by 3.

We know that any multiple of 10 that is divisible by 3 must have a units digit of 0, and the sum of its digits must be divisible by 3.

The units digit of 3N + 5 is 5, which is not 0, so N is not even. Therefore, option A is not correct.

The sum of the digits of 3N + 5 is 3 + 5 = 8, which is not divisible by 3. Therefore, N is not a factor of 30. Therefore, option C is not correct.

Similarly, since 3N + 5 is not divisible by 5, N cannot be a factor of 50. Therefore, option D is not correct.

Therefore, the only possible option is B: N is odd.

To see why, consider the following: if N is odd, then 3N is odd, and 3N + 5 is even. If 3N + 5 is even, then it must be divisible by 2, which means it is also divisible by 10 (since it is given that 3N + 5 is a multiple of 10). Therefore, N must be odd.

Answer:

Solve mentally:

a. 782 x 1000 =782,000

Answer:

C; 4

Step-by-step explanation:

the distance between two points in the smaller triangle is 2 units.

the distance between the same two points in the dilated triangle is 8 units, so because 2*4=8, the scale factor is 4

A point that is graphed at (9, 0) include the following: C. Point D.

In Mathematics and Geometry, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

Based on the cartesian coordinate (grid) below, the coordinates points and quadrants should be identified as follows;

Point A ⇔  (2, 1) → quadrant I.

Point B ⇔  (5, 3) → quadrant I.

Point C ⇔ (8, 8) → quadrant I.

Point D ⇔ (9, 0) → quadrant I.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The slide needs to be approximately 11.66 feet long.

The decimal system is a way of representing numbers using a base 10 positional notation. This means that each digit in a number represents a different power of 10.

"Nearest hundredth" refers to the second digit to the right of the decimal point. It means rounding a number to the nearest value that ends in two decimal places.

To calculate the length of the slide, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the ladder, the slide, and the ground form a right triangle, where the ladder is the vertical side, the slide is the hypotenuse, and the ground is the horizontal side. We know that the ladder is 4 feet tall and the bottom of the slide is 12 feet from the ladder. Let's call the length of the slide "x". Then we can set up the following equation:

4² + x² = 12²

Simplifying and solving for x, we get:

x = [tex]\sqrt{12^2-4^2}[/tex] = 11.66 feet (rounded to the nearest hundredth)

Therefore, the slide needs to be approximately 11.66 feet long.

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The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:

-6x - 5 < 10 - x and -6x + 15 < 10 - 5x.

What is inequality?

In mathematics, an inequality is a statement that compares two quantities or expressions and shows that they are not equal.

To solve the inequality, we can simplify it as follows:

-3(2x – 5) < 5(2 – x)

-6x + 15 < 10 - 5x (distribute the negative sign on the left and the positive sign on the right)

-6x + 5x < 10 - 15 (add 6x and subtract 15 from both sides)

-x < -5 (combine like terms)

x > 5 (multiply both sides by -1 and reverse the inequality)

Therefore, we have x > 5 as the solution to the inequality. The two correct representations of this solution are:

-6x - 5 < 10 - x (simplified from the original inequality)

A number line from 5 to infinity with an open circle at 5 and a bold line pointing to the right. (graphical representation)

Option 2 and 4 are incorrect because they do not accurately represent the solution to the inequality.

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Answer:

86

Step-by-step explanation:

The option that depicts the motion of the rainfall is: Option A graph

When talking about motion graphs, we can also refer to it as speed time graph or distance time graph.

Now, we are told that the rain began slowly and this tells us that the rate of rain fall with time in this phase slowly increased.

Thereafter, we are told that it got much heavier and then tapered off slowly. What this means is that it reached a peak rainfall and then fell at that constant peak before it gradually began to reduce to almost zero.

Looking at the different motion graphs, the correct one is option A.

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Answer:250%

Step-by-step explanation:

so hmmm let's simply get the volume of the outer rectangular prism and then get the volume of the inner rectangular prism, and subtract the inner one from the outer one, what's leftover, is the part we didn't subtract, namely, the vase's volume.

[tex]\stackrel{ \textit{\LARGE Volumes} }{\stackrel{ \textit{outer prism} }{(5)(3)(3)}~~ - ~~\stackrel{ \textit{inner prism} }{(4)(1\frac{1}{2})(1\frac{1}{2})}}\implies 45~~ - ~~9\implies \text{\LARGE 36}~in^3[/tex]