Identify the transformation that does NOT map the figure onto itself.
A) Reflect across the line y = 1
B) Reflect across the line x = 1
C) Rotate 180° about the point (1, 1)
D) Rotate 180° about the origin (0, 0)

The statement that is always true is: D. adjacent linear pairs of angles are supplementary.

Linear pairs of angles are angles that lie on the straight line. The sum of a linear pair is always 180 degrees, thus, they are regarded as supplementary angles.

Therefore, the statement that is always true is: D. adjacent linear pairs of angles are supplementary.

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The Pythagorean theorem is applied to a right triangle with the longer leg being one inch longer than the shorter leg and the hypotenuse being nine inches longer than the shorter leg. The side lengths of the triangle are found to be 5 inches, 6 inches, and 14 inches.

The subject of this question is mathematics, specifically the part of geometry that deals with right triangles and the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c), is equal to the sum of the squares of the other two sides (a and b), i.e., a² + b² = c².

In this problem, the longer leg (a) is represented as b = a + 1 and the hypotenuse (c) as c = a + 9. If you substitute these two equations into the Pythagorean theorem, you get (a + 1)² + a² = (a + 9)². Solving this equation gives a = 5 inches.

Substituting a = 5 inches into the expressions for b and c, we get b = 6 inches and c = 14 inches. Therefore, the sides of the triangle are 5 inches, 6 inches, and 14 inches.

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Answer:

The required function is [tex]h(T)=30\sin (\frac{\pi T}{15})+25[/tex].

Step-by-step explanation:

The general sine function is

[tex]y=A\sin (Bx+C)+D[/tex]             .... (1)

Where, A is amplitude, [tex]\frac{2\pi}{B}[/tex] is period, C is phase shift and D is midline.

It is given that the maximum height above the ground is 55 feet and the minimum height above the ground is 5 feet.

The amplitude of the function is

[tex]A=\frac{Maximum+Minimum}{2}=\frac{55+5}{2}=30[/tex]

The Midline of the function is

[tex]D=\frac{Maximum-Minimum}{2}=\frac{55-5}{2}=25[/tex]

A ferris wheel rotates around in 30 seconds. So, the period of the function is 30.

[tex]\frac{2\pi}{B}=30\Rightarrow B=\frac{2\pi}{30}=\frac{\pi}{15}[/tex]

[tex]2\pi=30B[/tex]

Substitute A=30, [tex]B=\frac{\pi}{15}[/tex], C=0 and D=25 in equation (1), to find the required function.

[tex]y=30\sin (\frac{\pi}{15}x+0)+25[/tex]

The required variable is T. Replace the variable x by T. So the height function is

[tex]h(T)=30\sin (\frac{\pi}{15}T+0)+25[/tex]

Therefore the required function is [tex]h(T)=30\sin (\frac{\pi T}{15})+25[/tex].

The given linear equation will have only one possible solution

A function is a relation between a dependent and independent variable. We can write the examples of functions as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is to find the total number of solutions for the linear equation -

10(x + 6) 2 - 9 = (15x + 1) 3 - 8

A linear equation is a equation of degree one. The number of solutions of a equation are equal to its degree. So, the given linear equation will have only one solution.

Therefore, the given linear equation will have only one possible solution.

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Answer:

The drop is -198 3/4

Step-by-step explanation:

Answer:

16 feet

Step-by-step explanation:

The relationships between displacement (position), velocity and acceleration are:

[tex]\boxed{\boxed{\begin{array}{c}\textbf{DISPLACEMENT (s)}\\\\\text{Differentiate} \downarrow\qquad\uparrow\text{Integrate}\\\\\textbf{VELOCITY (v)}\\\\\text{Differentiate}\downarrow\qquad\uparrow \text{Integrate}\\\\\textbf{ACCELERATION (a)}\end{array}}}[/tex]

To find the distance a particle travels in its first 4 seconds of travel, we first need to determine if the particle changes direction at any point during this time.

The instant(s) when the particle changes direction is when its velocity is zero. Therefore, set the velocity function v(t) to zero and solve for t:

[tex]\begin{aligned}v(t)&=0\\-t^2+4&=0\\-t^2&=-4\\t^2&=4\\t&=\pm 2 \end{aligned}[/tex]

So, the particle changes direction at t = 2 seconds in its first 4 seconds of travel. This means that to find the distance the particle travels in its first 4 seconds of travel, we need to integrate the velocity function over the two intervals [0, 2] and [2, 4] seconds to find the particle's displacement over these intervals.

The displacement of the particle in its first 2 seconds of travel is:

[tex]\begin{aligned}\displaystyle \int^2_0 (-t^2+4)\; \text{d}t&=\left[\dfrac{-t^{2+1}}{2+1}+4t\right]^2_0\\\\&=\left[-\dfrac{t^{3}}{3}+4t\right]^2_0\\\\&=\left(-\dfrac{(2)^{3}}{3}+4(2)\right)-\left(-\dfrac{(0)^{3}}{3}+4(0)\right)\\\\&=-\dfrac{8}{3}+8+0-0\\\\&=\dfrac{16}{3}\end{aligned}[/tex]

The displacement of the particle in its next 2 seconds of travel is:

[tex]\begin{aligned}\displaystyle \int^4_2 (-t^2+4)\; \text{d}t&=\left[\dfrac{-t^{2+1}}{2+1}+4t\right]^4_2\\\\&=\left[-\dfrac{t^{3}}{3}+4t\right]^4_2\\\\&=\left(-\dfrac{(4)^{3}}{3}+4(4)\right)-\left(-\dfrac{(2)^{3}}{3}+4(2)\right)\\\\&=-\dfrac{64}{3}+16+\dfrac{8}{3}-8\\\\&=-\dfrac{32}{3}\end{aligned}[/tex]

The negative value means that the particle is travelling in the opposite direction.

So, the particle travels 16/3 feet in its first 2 seconds of travel, changes direction at t = 2 seconds, and travels 32/3 feet in the opposite direction in the next 2 seconds of travel.

Therefore, the total distance the particle travelled is the sum of the absolute values of the two displacements:

[tex]\textsf{Distance}=\dfrac{16}{3}+\dfrac{32}{3}=\dfrac{48}{3}=16\;\sf feet[/tex]

So, the particle travels 16 feet in its first 4 seconds of travel.

The distance a particle travels in the first 4 seconds, moving according to the velocity equation v(t)= -t² + 4, is found by integrating the velocity function over that interval, which yields 5.33 feet.

To find the distance a particle travels given its velocity equation v(t)= -t² + 4 (in feet/sec), we need to integrate the velocity function over the desired time interval.

Since velocity is the rate of change of position with respect to time, the integral of the velocity function from 0 to 4 seconds will give us the displacement of the particle in that time interval.

The integral of v(t) from 0 to 4 seconds can be computed as follows:

However, the absolute value of -5.33 feet is needed, because distance must be positive. Hence, the particle travels 5.33 feet in the first 4 seconds.

David’s score at the end of round 3 is calculated by adding the net points gained during the round to his initial score, resulting in a final score of 2000 points.

Calculating David's Score

To determine David's score at the end of round 3, we need to account for both his correct answers and incorrect answers during the round.

David's initial score at the start of round 3 is -1500 points.

During round 3:

He answered five 1000-point questions correctly. Each correct answer adds 1000 points. So, 5 correct answers add:

5 × 1000 = 5000 points

He answered three 500-point questions incorrectly. Each incorrect answer subtracts 500 points. So, 3 incorrect answers subtract:

3 × 500 = 1500 points

Next, we calculate the net change in his score by adding the points gained and subtracting the points lost:

Net change = 5000 points (gained) - 1500 points (lost) = 3500 points

Finally, we add this net change to his initial score:

Final score = -1500 points (initial score) + 3500 points (net change) = 2000 points

Thus, David's score at the end of round 3 is 2000 points.

the correct answer is =

The slope of the line is 3.5

This means that every pound

of dried fruit cost $3.50

   Slope of the line is 3.5. This means that every of dried fruit costs $3.5 per lb.

   From the graph attached,

Points shown on the graph are (4, 14) and (8, 28).

Since, slope of a line passing two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,

Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Therefore, slope of the line passing through (4, 14) and (8, 28) will be,

Slope = [tex]\frac{28-14}{8-4}[/tex]

          = [tex]\frac{14}{4}[/tex]

          = 3.5

This means that every of dried fruit costs $3.5 per lb.

       Therefore, slope of the line is 3.5. This means that every of dried fruit costs $3.5 per lb.

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To calculate the cost of diesel for Steve's trip from Leeds to Edinburgh, divide the distance by the car's mpg to find the number of gallons needed. Then, multiply the gallons by the cost of diesel per gallon to get the total cost.

To determine the cost of diesel for Steve's trip, we need to calculate the number of gallons he will need and then multiply by the cost per gallon. Steve's car does 42 miles per gallon (mpg), and he is driving a distance of 215 miles. Therefore, he will need 215/42 = 5.12 gallons of diesel. Since a gallon is 4.55 liters, Steve will need 5.12 * 4.55 = 23.36 liters of diesel. The cost of diesel per liter is £1.38, so the total cost for diesel will be 23.36 * £1.38 = £32.19.

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x^2 - 2x -4 =0

Using the quadratic formula -b +/- √b^2 - 4(ac) / 2a

Replace the letters with the values from the equation:

2 +/- √-2^2 -4*(1*-4) / 2*1

X = 2 +/- 2√5 / 2

x = 1 +/-√5

The answer is:  x^2 - 2x -4 =0

Test has a mean of 80 and standard deviation of 4 than after one deviation from the mean, most of the score will fall in the interval ([tex]\mu - \sigma\;,\; \mu + \sigma[/tex]) which is (76 , 84).

Given :

Mean, [tex]\mu = 80[/tex]

Standard Deviation, [tex]\sigma = 4[/tex]

After one deviation from the mean, most of the score will fall in the interval ([tex]\mu - \sigma\;,\; \mu + \sigma[/tex]). Where [tex]\mu[/tex] is the mean which is arithmetic average of all values and [tex]\sigma[/tex] is the standard deviation which is the square root of its variance.

Now, the value of  [tex]\mu - \sigma = 80-4 = 76[/tex].

And the value of  [tex]\mu + \sigma = 80+4=84[/tex].

After one deviation from the mean, most of the score will fall in the interval ([tex]\mu - \sigma\;,\; \mu + \sigma[/tex]) which is (76 , 84).

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Final answer:

After converting 7/20 to a decimal, we find that Rose bought 0.35 kilogram of ginger candy, which is less than the 0.4 kilogram of cinnamon candy; therefore, Rose bought more cinnamon candy.

Explanation:

Rose bought 7/20 kilogram of ginger candy and 0.4 kilogram of cinnamon candy. To determine which she bought more of, we need to compare these amounts. The fraction 7/20 can be converted into a decimal to make the comparison easier. To convert a fraction to a decimal, you divide the numerator by the denominator.

So, 7 ÷ 20 = 0.35. This means that Rose bought 0.35 kilogram of ginger candy, which is less than the 0.4 kilogram of cinnamon candy. Therefore, Rose bought more cinnamon candy than ginger candy.

B. 2-x = 4x+3

x 2-x 4x+3

-3 5 -9
-2 4 -5
-1 3 -1
0 2 3
1 1 7
2 0 11
3 -1 15

The table shows that none of the integers from [-3,3] work because in no case does
2-x = 4x+3

To find the solution we need to rearrange the equation to the form x=n
2-x = 4x+3
2 -x + x = 4x + x +3
2 = 5x + 3
2-3 = 5x +3-3
5x = -1
x = -1/5

The only point that satisfies both equations is where x = -1/5
Find y: y = 2-x = 2 - (-1/5) = 2 + 1/5 = 10/5 + 1/5 = 11/5
Verify we get the same in the other equation
y = 4x + 3 = 4(-1/5) + 3 = -4/5 + 15/5 = 11/5

Thus the only actual solution, being the point where the lines cross, is the point (-1/5, 11/5)

C. To solve graphically 2-x=4x+3
we would graph both lines... y = 2-x and y = 4x+3
The point on the graph where the lines cross is the solution to the system of equations ...
[It should be, as shown above, the point (-1/5, 11/5)]

To graph y = 2-x make a table....
We have already done this in part B

x 2-x x 4x+3
_ __
-1 3 -1 -1
0 2 0 3
1 1 1 7

Just graph the points on a Cartesian coordinate system and draw the two lines. The solution is, as stated, the point where the two lines cross on the graph.

I hope I helped! 

I will still trying to see if I can solve them another way that might be clearer.

The sum of 100.0 g and 0.01 g, expressed in scientific notation and written with the correct number of significant figures is 1.0001 * 10².

Sum is the output of the mathematical operation, Addition.

The sum of two numbers a and b is written as a +b.

The first number is 100.0 g

The second number is 0.01 g.

Scientific notation is the method used to write very small and large quantities.

It makes it easy to understand and interpret.

The rules followed while writing significant figures is that, the digits which are not zero is always significant, zeroes between two significant digits are significant.

The number of the form 0.0001 = 1 * 10⁻⁴,

and the number 45000000 is written as = 4.5 * 10⁷.

The sum of 100.0 g and 0.01 g has to be determined.

Let x represent the sum of the numbers, then

x = 100.00 + 0.01

x = 100.01

The sum is 1.0001 * 10²

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Final answer:

To calculate the new price of an item after a 55% reduction from an original price of $75, you multiply $75 by 55% to get the reduction amount of $41.25. Subtracting this from the original price gives a new price of $33.75.

Explanation:

The student is asking how to calculate the new price of an item after a percentage decrease, specifically a 55% reduction from the original price. To find the new price, we can apply the percentage decrease to the original price and then subtract that amount from the original price.

Original price = $75
Percentage decrease = 55%

First, calculate the amount of the reduction:
Reduction amount = (Original price) × (Percentage decrease)
Reduction amount = $75 × 0.55
Reduction amount = $41.25

Now, subtract the reduction amount from the original price to get the new price:
New price = Original price - Reduction amount
New price = $75 - $41.25
New price = $33.75

So the new price of the item after a 55% reduction is $33.75.

Answer:

C

Step-by-step explanation:

Cause i'm a genius

Reza made monthly payments for 24 months to pay off her car after making a $4,500 down payment. The total cost of the car was $10,500, and she paid the remaining amount in installments of $250 per month.

Reza's car payments can be calculated using a simple algebraic function. She made an initial down payment of $4,500 and paid off the remaining balance with equal monthly payments of $250. The total cost of the car was $10,500. To find out how many months Reza made payments on the car, you can use the following function:

Total Cost = Down Payment + (Monthly Payment × Number of Months)

First, we subtract the down payment from the total cost:

$10,500 - $4,500 = $6,000

This is the amount Reza paid in monthly installments. Now we divide this amount by the monthly payment amount to find the number of months:

$6,000 / $250 = 24 months.

Therefore, Reza made payments for 24 months.

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Answer

The answer is

D) Kyle's class is making banners for a fund raiser. Each banner takes

2

5

yard of material. They have 4 yards of material. How many banners can they make?

Step-by-step explanation:

Let b = number of banners

(

2

5

yd)b = 4 (total material available)

2

5

b = 4

A perfect square is a figure that can be conveyed as the product of two identical integers.

The first ten positive perfect squares are the following:

1 = 1 x 1

4 = 2 x 2

9 = 3 x 3

16 = 4 x 4

25 = 5 x 5

36 = 6 x 6

49 = 7 x 7

64 = 8 x 8

81 = 9 x 9

100 = 10 x 10

Using a zero as a placeholder so that both decimals ahve the same number of digits after their decimal point is a good strategy while adding decimals because it helps you line the decimals up in the correct way to get the correct sum.