Which transformation

Answer:

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a) An equation representing the number of pages of the book that Bentley is on at the end of t days is A = 39 + 16t.

b) An equation representing the number of pages of the book that Arianys is on at the end of t days is B = 19 + 18t.

c) Arianys is farther along in the book after 15 days than Bentley because Arianys is on page 289 of the book while Bentley lags on page 279.

An equation is a statement showing the equality of two or more mathematical expressions.

Equations are depicted using the equation symbol (=).

The pages of the book already covered by Bentley at the beginning of the month = 39

The pages of the book already covered by Arianys at the beginning of the month = 19

Bentley's reading speed per day = 16 pages

Arianys' reading speed per day = 18 pages

The page already read by Bentley = A

The page already read by Arianys = B

For the pages already read by Bentley, A = 39 + 16t

For the pages already read by Arinys, B = 19 + 18t

After 15 days, who has read more?

Bentley, A = 39 + 16t = 39 + 16(15) = 279 pages

Arianys, B = 19 + 18t = 19 + 18(15) = 289 pages

Thus, using equations, we can conclude that Arianys can conclude the book faster than Bentley if it takes up to 15 days in the month to complete the book.

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The value of the algebraic expression -2y³ + y² - 3y + 4, when y = 3 is evaluated as: -50.

An algebraic expression contains a variable. To find the value or evaluate the algebraic expression, plug in the the value of the variable and solve accordingly.

Given the algebraic expression,

-2y³ + y² - 3y + 4, when y = 3

Substitute the value of y into the algebraic expression:

-2(3)³ + (3)² - 3(3) + 4

Evaluate the exponents in the expression:

-2(27) + 9 - 9 + 4

-54 + 9 - 9 + 4

Add together to get the value of the algebraic expression:

-54 + 0 + 4

-54 +  4

= -50

In summary, the value of the algebraic expression -2y³ + y² - 3y + 4, when y = 3 is evaluated as: -50.

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Answer:

A

Step-by-step explanation:

Only one that make sense

Answer:

x(7y)x(7y)

Step-by-step explanation:

The given expression: 7(xy)7(xy)

i.e. a product of 7 and xy.

The operation used here: Multiplication.

Commutative property of multiplication :-

a\times b=b\times aa×b=b×a for any numbers a and b.

Associative property of multiplication :-

a\times(b\times c)=(a\times b\times c)a×(b×c)=(a×b×c) for any numbers a , band c.

Now, 7(xy)=(7x)y7(xy)=(7x)y [Associative property of multiplication]

=(x7)y=(x7)y [Commutative property of multiplication]

=x(7y)=x(7y) [Associative property of multiplication]

Randi's speed when she pressed on the brakes was approximately 129.26 feet per second.

To calculate Randi's speed when she pressed on the brakes, we can use the following formula:

Speed = (Skid Mark Length / Drag Factor) * Square Root(2 * Efficiency)

Given information:

- Skid Mark Length = 94 feet

- Drag Factor = 0.92

- Efficiency = 80% = 0.8

Let's substitute these values into the formula to find Randi's speed:

Speed = (94 / 0.92) * √(2 * 0.8)

     ≈ 102.17 * √(1.6)

     ≈ 102.17 * 1.2649

     ≈ 129.26 feet per second

Therefore, Randi's speed when she pressed on the brakes was approximately 129.26 feet per second.

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Step-by-step explanation:

x = 3

y = - 2

z = 6

\(7xyz\)

Solution,

= 7 × 3 ( - 2 ) × 6

= 21 ( - 2 ) × 6

= - 42 × 6

= - 252

hence the answer is - 252....

The area οf the actual bridge deck in square feet is 1,280 square feet.

Area refers tο the measurement οf the size οf a twο-dimensiοnal surface, usually measured in square units such as square inches, square feet, οr square meters. It represents the amοunt οf space that is inside the bοundary οf a flat οbject οr shape.

The scale οf the drawing is 40:1, which means that the dimensiοns οf the scaled bridge deck are 40 times smaller than the actual bridge deck. Tο find the area οf the actual bridge deck in square feet, we need tο cοnvert the dimensiοns οf the scaled bridge deck frοm inches tο feet and then multiply by the square οf the scale factοr (40² = 1600).

The dimensiοns οf the scaled bridge deck in feet are:

24 inches = 2 feet

4 and 4/5 inches = 0.4 feet

Sο, the area οf the scaled bridge deck in square feet is:

2 feet x 0.4 feet = 0.8 square feet

Tο find the area οf the actual bridge deck in square feet, we need tο multiply the area οf the scaled bridge deck by the square οf the scale factοr:

Area οf actual bridge deck = 0.8 square feet x (40²) = 1280 square feet

Therefοre, the area οf the actual bridge deck in square feet is 1,280 square feet.

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Answer:

Step-by-step explanation:

The scale factor indicates the actual bridge is 40 times larger than the drawing.

Increase the scale dimensions by the factor of 40.

24 times 40 = 960"

4.8 times 40 = 192" (I changed 4 4/5 to 4.8)

Area = length times width

960 times 192 = 184320 sq inches actual bridge deck in square inches

Divide 183320 by 144 (sq inches in a square foot) = 1280 sq feet

Answer:

Since the slope of KM and ST are different, they are not parallel

Step-by-step explanation:

Slope of line KM = \(\frac{5}{8}\)

 Slope of ST = \(-\frac{8}{5}\)

Determine whether the lines are perpendicular;

Solution:

We can use the slope of a line to determine whether they are perpendicular or parallel to one another.

Parallel lines do not meet one another

Perpendicular lines cross one another at an angle of 90°

Two lines are parallel if their slopes are the same;

  Since the slope of KM and ST are different, they are not parallel

Answer:

5x+3

Step-by-step explanation:

1.  Subtract 1 from 4

4+5x-1

2. Solution

5x+3

The profit function is P(x) = -500.523x^2 + 600x - 200.

To find the profit function, P(x), we need to subtract the cost function, C(a), from the revenue function, R(x).

Given:

Cost function: C(a) = 500x^2 + 300

Revenue function: R(x) = -0.523x^2 + 600x - 200 + 300

Profit function, P(x), is obtained by subtracting the cost function from the revenue function:

P(x) = R(x) - C(a)

P(x) = (-0.523x^2 + 600x - 200 + 300) - (500x^2 + 300)

Simplifying the expression:

P(x) = -0.523x^2 + 600x - 200 + 300 - 500x^2 - 300

P(x) = -500x^2 - 0.523x^2 + 600x + 300 - 200 - 300

P(x) = -500x^2 - 0.523x^2 + 600x - 200

Combining like terms:

P(x) = (-500 - 0.523)x^2 + 600x - 200

Simplifying further:

P(x) = -500.523x^2 + 600x - 200

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Using the formula for finding area of a rectangle we can get the area of the shaded region = 106 sq. meters.

The formula for calculating a rectangle's area can be used to determine how much space the rectangle takes up within its perimeter. The area of a rectangle is determined by multiplying its length by its width (breadth). The following formula can be used to get the area of a rectangle whose length and breadth are "l" and "w," respectively. L * W = the rectangle's area. Hence, the area of a rectangle is equal to length × width

Here, in the given figure, area of the small rectangle =

length × breadth

= 7 × 2

= 14 sq. meters

Now area of the shaded region =

12 × 10

=120 sq. meters.

Therefore, area of the shaded region = 120 - 14

= 106 sq. meters

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Answer:

1/3

Step-by-step explanation:

4/3=1 1/3

1  2/3 - 1 1/3= 1/3

Hope this helps!

Answer:

9

Step-by-step explanation:

The \(n\)term is \(2n+1\).

\(S_n=\frac{3+2n+1}{2}(n)=99 \\ \\ \frac{n(2n+4)}{2}=99 \\ \\ n(n+2)=99 \\ \\ n^2+2n-99=0 \\ \\ (n+11)(n-9)=0 \\ \\ n=9 \text{ } (n>0)\)

The number of terms that needed to make the sum to 99 is 9

The first term of the arithmetic progression = 3

The common difference = 2

The sum of n term is = (n/2) [2a+(n-1)d]

Where a is the initial term

d is the common difference

Substitute the values in the equation

(n/2) [2(3)+(n-1)2] = 99

(n/2) [6 + 2n - 2] = 99

(n/2)[4+2n] = 99

n(2 + n) = 99

2n + \(n^2\) = 99

\(n^2\) + 2n - 99 = 0

Split the terms

\(n^2\) - 9n +11n - 99 =0

n(n -9) + 11(n - 9) = 0

(n + 11)(n - 9) = 0

n = -11 or 9

Since n cannot be a negative number, therefore n = 9

Hence, the number of terms that needed to make the sum to 99 is 9

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the absolute change in the percentage increase amounts from Paula's investments is 74.5%.

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

The absolute change in the percentage increase amounts is the difference between the two percentages.

Absolute change = |87.4% - 12.9%| = |74.5%| = 74.5%

Therefore, the absolute change in the percentage increase amounts from Paula's investments is 74.5%.

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Answer:

Step-by-step explanation:Bó tay

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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The answer is

for parallel : y= 4/7-5x/7

for perpendicular: y=10+7x/5

The slope-intercept form is written as y = mx+b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis). It's usually easy to graph a line using y=mx+b.

Given line: 5x+7y=9

when our intersection point is (5,-3) the constant

5x+7y

= 5(5)+7(-3)

= 25-21

=4

hence, 5x+7y=4

slope intercept form

7y= 4-5x

y= 4/7-5x/7

Now, for perpendicular lines:

swap the coefficients on x and y with negative sign of x in  5x+7y=9

7x-5y= constant

again, when our intersection point is (5,-3) the constant must be

7x-5y

= 7(5)-5(-3)

=35+15

=50

7x-5y=50

slope intercept form so we solve for y:

y= (50+7x)/5

y=10+7x/5

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Answer:

x =  −5 /2

Step-by-step explanation:

Answer:

looking at the straight line, it touches the axis at (-2,0) and (6,0)

Step-by-step explanation:

Answer:

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9.  The stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. The stamp duty payable on a property with a purchase price of K150,000 is K7,500.

To calculate the stamp duty payable on properties with a purchase price of K45,000 and K150,000, we need to apply the corresponding rates of stamp duty based on the given information.

Given:

Value of Property:

Up to K35,000: Stamp Duty Rate - 2%

K35,000 to K70,000: Stamp Duty Rate - 3%

K70,000 to K140,000: Stamp Duty Rate - 4%

Over K140,000: Stamp Duty Rate - 5%

9. Calculate the stamp duty payable on properties whose purchase price is K45,000:

Since the purchase price of K45,000 falls within the range of K35,000 to K70,000, the stamp duty rate applicable is 3%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K45,000 * 3%

= K45,000 * 0.03

= K1,350

Therefore, the stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. Calculate the stamp duty payable on properties whose purchase price is K150,000:

Since the purchase price of K150,000 is above K140,000, the stamp duty rate applicable is 5%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K150,000 * 5%

= K150,000 * 0.05

= K7,500

Therefore, the stamp duty payable on a property with a purchase price of K150,000 is K7,500.

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The x-intercepts are (4,0)(5,0) of the following graph.

In the context of a graph, an x-intercept is a point where a curve or line crosses the x-axis. It is the point at which the value of y is zero. In other words, the x-intercept is the value of x when the function or equation crosses the x-axis.

To find the x-intercepts of a function, you can set y equal to zero and solve for x. The resulting values of x will be the x-intercepts.

In the context of a graph, a y-intercept is a point where a curve or line crosses the y-axis. It is the point at which the value of x is zero. In other words, the y-intercept is the value of y when the function or equation crosses the y-axis.

To find the y-intercept of a function, you can set x equal to zero and solve for y. The resulting value of y will be the y-intercept.

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The tangent of the smaller acute angle in a right triangle is tanФ = 0.42.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, A right triangle with side lengths 5, 12, and 13.

tanФ = 5/12.

tanФ = 0.42.

Ф = tan⁻¹(0.42).

Ф = 22.8°.

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Answer:69.66

r=9 so diameter is 18, and the shape being a square you do 18 x 18 = 324

now the circles area is 254.34 now find the difference... and it is 69.66

Step-by-step explanation:

The required probability is 3 √7 / 32.

Given, a square with sides of length 4 units and a red-shaded triangle with sides 3 units, 3 units and 4 units. We need to find the probability that a randomly selected point within the square falls in the red-shaded triangle.To find the probability, we need to divide the area of the red-shaded triangle by the area of the square. So, Area of square = 4 × 4 = 16 square units. Area of triangle = 1/2 × base × height.

Using Pythagorean theorem, the height of the triangle is found as: h = √(4² − 3²) = √7

The area of the triangle is: A = 1/2 × base × height= 1/2 × 3 × √7= 3/2 √7 square units. So, the probability that a randomly selected point within the square falls in the red-shaded triangle is:  P = Area of triangle/Area of square= (3/2 √7) / 16= 3 √7 / 32.

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Answer:

(1.307 ; 3.893)

Step-by-step explanation:

Given that:

Mean, xbar = 2.6

Standard deviation, s = 0.69

Sample size, n = 5

Confidence interval : xbar ± margin of error

Margin of Error = Tcritical * s/sqrt(n)

Degree of freedom (df) = n - 1 = 5 - 1 = 4

Hence Tcritical = 3.747

Margin of Error = 3.747 * 0.69/sqrt(4)

Margin of Error = 1.293

Lower boundary = (2.6 - 1.293) = 1.307

Upper boundary = (2.6 + 1.293) = 3.893

(1.307 ; 3.893)