LAM 1 Mod 6 Question 3-2.

Answer:

(-1, -5)

Step-by-step explanation:

since it is reflected across the y- axis, the y coordinate remains the same while the x coordinate changes sign so we get,

(1,-5) goes to (-1, -5)

Answer:

100

Step-by-step explanation:

0.3n - 15 = 0.2n - 5

0.3n - 0.2n = - 5 + 15

0.1n = 10

10/0.1 = n

n = 100

The area of the land is 289/4 square units

The area of a shape is the amount of space on the shape

For most regular quadrilaterals, you multiply the side lengths to determine the area

The given parameters are

Shape = Square

Side length = 17/2

The area of a square shape is

Area = Side length^2

So, we have

Area = (17/2)^2

Evaluate the exponent

Area = 289/4

Hence, the area of square plot of land whose each side measures 17/2 is 289/4 square units

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Statistics report that the average successful quitter is able to stop smoking after multiple attempts, usually between 8 to 10 times.  everyone's journey to quitting smoking is unique and may take more or fewer attempts to achieve success.

According to statistics, the average successful quitter is able to stop smoking after attempting to quit 6 to 30 times. This number varies due to individual factors and the methods used for quitting. Remember, persistence is key, and it is never too late to quit smoking for a healthier lifestyle.

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Answer:

81*x^8 / 256

Step-by-step explanation:

Answer:\(\frac{81x^8} {256}\)

Step-by-step explanation:

Answer:

1) The image of the line has the same slope as the pre-image but a different y-intercept.

hope this helps ;)

Check the picture below.

Answer:

8.41

Step-by-step explanation:

Answer:

it's 8.41

Step-by-step explanation:

Answer: 39.66

Step-by-step explanation: hope this helps!!!!

Answer:

(x, y) -> (-x,-y)

180

Step-by-step explanation:

The rule for the rotation about the origin that maps triangle ABC to triangle A'B'C' is:

(x', y') = (-x, -y)

And the triangle has been rotated at 180 degrees.

Each point in a figure is transformed into a rotation by rotating it a certain amount of degrees around another point.

Given information:

A(-1, -2), C(-1, -4) and B(-4, -2)

A'(1, 2), C'(1, 4) and B'(4, 2)

The rule that describes a rotation about the origin is:

(x', y') = (xcosθ - ysinθ, xsinθ + ycosθ)

where (x, y) are the original coordinates, θ is the angle of rotation (in radians), and (x', y') are the new coordinates after rotation.

To find the angle of rotation, we can compare the coordinates of the corresponding vertices of the original and rotated triangles. Since A(-1,-2) maps to A'(1,2), we can see that the triangle has been rotated 180 degrees.

Therefore, the rule for the rotation about the origin that maps triangle ABC to triangle A'B'C' is:

(x', y') = (-x, -y).

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The expression below are correct:

πr_c^2h_c / 4 = πr_p^2h_p / 5

h_c / h_p = (r_p / r_c)^2 * (5 / 4)

To prove that the equation

πr_c^2h_c / 4 = πr_p^2h_p / 5

and

h_c / h_p = (r_p / r_c)^2 * (5 / 4)

are correct, we can use some algebraic manipulation and the properties of ratios.

Starting with the first equation, we can simplify it as follows:

πr_c^2h_c / 4 = πr_p^2h_p / 5

5πr_c^2h_c = 4πr_p^2h_p (multiply both sides by 20 to get rid of fractions)

5r_c^2h_c = 4r_p^2h_p (cancel out π on both sides)

Next, we can rearrange the second equation to solve for h_c:

h_c / h_p = (r_p / r_c)^2 * (5 / 4)

h_c = h_p * (r_p / r_c)^2 * (5 / 4) (multiply both sides by h_p)

Now we can substitute this expression for h_c into the simplified version of the first equation:

5r_c^2h_c = 4r_p^2h_p

5r_c^2(h_p * (r_p / r_c)^2 * (5 / 4)) = 4r_p^2h_p (substitute h_c)

5r_c^2r_p^2(5/4) = 4r_p^2h_p (simplify)

5r_c^2 = (16/25)h_p (divide both sides by 4r_p^2)

Finally, we can substitute this expression for h_p into the earlier expression we found for h_c:

h_c = h_p * (r_p / r_c)^2 * (5 / 4)

h_c = (5/16)r_c^2 (substitute for h_p)

h_c / r_c^2 = 5/16

This means that the ratio of the height to the radius squared for cylinder c is 5/16, which is a constant value. We can also rearrange the simplified first equation to solve for h_p in terms of r_c and r_p:

5r_c^2h_c = 4r_p^2h_p

h_p = (5/4)h_c(r_c/r_p)^2 (divide both sides by 4r_p^2 and multiply by 5/4)

Substituting this expression for h_p into the second equation, we get:

h_c / h_p = (r_p / r_c)^2 * (5 / 4)

h_c / ((5/4)h_c(r_c/r_p)^2) = (r_p / r_c)^2 * (5 / 4) (substitute for h_p)

1 / ((5/4)(r_c/r_p)^2) = (r_p / r_c)^2 * (5 / 4) (simplify)

Now we can simplify this expression using the fact that (r_p / r_c)^2 = 1 / (r_c / r_p)^2:

1 / ((5/4)(r_c/r_p)^2) = (1 / (r_c/r_p)^2) * (5/4)

1 / (5/4) = (r_c/r_p)^4 * (5/4)

4/5 = (r_c/r_p)^4

(r_c/r_p)^2 = √(2/√5) or -(√2/√(√5))

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Answer:

11

Step-by-step explanation:

You put the 3 in the place of the X

which means X^2 would be 3^2

That would be 9

You would then add 9 + 2

11 would be your answer

a) The binary representation of 17 is 10001. To convert 17 into binary, we divide it successively by 2, keeping track of the remainders. The remainder at each step forms the binary representation in reverse order.

b) The decimal representation of the binary number 01001011 is 75. To convert a binary number into decimal, we multiply each digit by the corresponding power of 2 and sum them up.

c) Converting 0.635 into binary floating point representation in base 7 involves representing the whole and fractional parts separately. The whole part is 0 in this case, and for the fractional part, we multiply it by the base (7) successively, recording the integer parts until we reach the desired precision.

d) When a variable in a byte data type that has a value of 255 (maximum value) is incremented by 1, it will wrap around and become 0. This is because a byte can store values from 0 to 255, and when the maximum value is reached, the next increment wraps back to the minimum value of 0.

e) To represent -28 in binary using 2's complement notation, we first find the binary representation of 28, which is 11100. Then, we invert all the bits (1s become 0s and vice versa) and add 1 to the result. This gives us the 2's complement representation: 10011100.

f) The binary representation of 0.625 in IEEE 754 format is 0.101. In IEEE 754 format, the number is represented as a sign bit (0 for positive), followed by the binary representation of the normalized fraction (without the leading 1), and finally the biased exponent.

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Answer:

hol up

x=-1/8  negative one over eight

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

so it is just like a regular equation like 30+10=40 but your just finding what A means so 40 yea

Answer:

length = 8

Step-by-step explanation:

l x w = 48

let l = 6w - 48

x(6w - 28) = 48

6w² - 28w - 48 = 0

(6w + 8) (w - 6) = 0

w = 6

l = 6(6) - 28 = 36 - 28 = 8

Answer:

4.5 miles per hour

Step-by-step explanation:

2 1/4 x 2 = 4.5 (As decimal)

30 mins + 30 mins = 1 hour

1 hour = 4.5 miles per hour

Answer:

19.2 lbs of dog food in 5 weeks

Step-by-step explanation:

12 divided by 5 is 2.4

So that means each week the dog consumes 2.4 lbs of food each week.

If we want to see how much he eats in 8 weeks, we'd multiply 2.4 by 8, giving us 19.2

Explanation:

Replace c with 5. Use PEMDAS to simplify

5c - 2 = 5*5 - 2 = 25 - 2 = 23

Step-by-step explanation:

y = 4x - 7

Comparing the given equation with y = mx + c Then

slope (m) = 4

y -intercept (c) = - 7

Hope it will help :)

Answer: the slope is negative 4

Step-by-step explanation:

because its ez

Answer:

10. 85°

11. 70°

12. 50°

Step-by-step explanation:

Please see attached picture for full solution.

Using proportional relationships, we can say that They will walk 12 laps and run 20 laps for a total of 32 miles.

In a direct proportional relationship, the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx.

Given that we know this, they walk 3/8 of the 8 miles that make up the complete distance. Run 5/8 of the route.

The following are the proportional relationships for the distances:

For a total distance of 32 miles, the distances walked and run are given:

therefore, They will walk 12 laps and run 20 laps for a total of 32 miles as per the proportional relation.

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Strong positive relationship means there is direct variation between x and y .

\(\\ \sf\Rrightarrow x\propto y\)

\(\\ \sf\Rrightarrow \dfrac{x}{y}=k\)

The domain of ggg is option D: -7 ≤ x ≤ 4.

To determine the domain of a function, we need to identify the set of all possible values for the independent variable, in this case, x, for which the function is defined.

In option D, the domain is specified as -7 ≤ x ≤ 4. This means that x can take any value within the closed interval from -7 to 4, inclusive.

In other words, the domain of ggg includes all real numbers between -7 and 4, including -7 and 4 themselves. This interval represents the range of values for x that satisfy the given conditions for the function ggg.

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The dollar amount the school will raise is given by the expression 0.25n, where n is the number of students.

A combination of terms through addition, subtraction, multiplication, division, and other operations is known as an algebraic expression (or variable expression).

A connection that compares two numbers or other mathematical expressions inequitably is known as an inequality in mathematics.

Therefore the dollar amount the school will raise is given by the expression 0.25n or \(\frac{1}{4} n\) , where n is the number of students.

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Answer:

The distributive property

Step-by-step explanation:

You have to distribute the 3 to the parenthesis so it is the distributibe property.

Answer:

\(a_{21}\) = 16

Step-by-step explanation:

You add the numbers.  The two top left, two top right, 2 bottom left, 2 bottom right.

8    -6

16    -12

They are asking what number is in the second row, first column.

The equation representing the given transformations is y = 3sin(x - 10°) + 3.

To create an equation in the form y = asin(x - d) + c given the transformations, we can start with the standard sine function and apply the given transformations step by step:

Vertical translation 1 unit up:

The standard sine function has a maximum value of 1 and a minimum value of -1.

To vertically translate it 1 unit up, we add 1 to the function.

This gives us a maximum value of 1 + 1 = 2 and a minimum value of -1 + 1 = 0.

Horizontal translation 10 degrees to the right:

The standard sine function completes one full period (i.e., goes from 0 to 2π) in 360 degrees.

To shift it 10 degrees to the right, we subtract 10 degrees from the angle inside the sine function.

This accounts for the horizontal translation.

Adjusting the amplitude:

To achieve a maximum value of 8, we need to adjust the amplitude of the function.

The amplitude represents the vertical stretch or compression of the graph.

In this case, the amplitude needs to be 8/2 = 4 since the original sine function has an amplitude of 1.

Putting it all together, the equation for the given transformations is:

y = 4sin(x - 10°) + 2

This equation represents a sine function that has been vertically translated 1 unit up, horizontally translated 10 degrees to the right, and has a maximum value of 8 and a minimum value of 2.

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Answer:

Linear functions

Step-by-step explanation: