30 PIONTS FOR A NEATLY AND CORRECTLY ANSWERED QUESTION + EXTRA IF I GET IT FAST + EXTRA IF IT IS EXPERT VERIFIED + EXTRA IF I GET FULL MARKS

PART 1 PLEASE LOOK FOR PART TWO


Part A

Which angles of the triangles measure 90°?


Part B

To show that the other two angle measurements in each triangle are equal, you can use parallel lines cut by a transversal. Which two pairs of line segments formed by triangle sides are parallel, and what is the transversal for each pair?


Part C

Which angle has the same measurement as angle DEA, and how do you know that the measurement is the same?


Part D

Which angle has the same measurement as angle DAE and why (vertical, corresponding, alternate interior, or alternate exterior angles)?

Answer:

The opposite sides of a rectangle are equal in length ⇒ perimeter = 2(3x +1) +2(x + 1) Also the perimeter = 28.

Answer:

P=2(L+W)

Step-by-step explanation:

p=2(L+W)

    2(2x+1)+2(3x-2)

    4x+2+6x-4

    10x-2

The system of linear inequalities to model the situation is 10x + 20y ≤ 100 and y > 2x

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

Using the following representations:

We have the following system of inequalities from the given statements

10x + 20y ≤ 100

y > 2x

Hence, the system of inequalities is 10x + 20y ≤ 100 and y > 2x

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When we roll three fair coins, there are two possible outcomes for each coin - either it lands heads up or tails up. There are 8 elementary events in the sample space of the experiment of rolling three fair coins.

The sample space of this experiment consists of all possible combinations of three outcomes, which can be calculated by multiplying the number of outcomes for each coin: 2 x 2 x 2 = 8.
Each of these combinations is called an elementary event, which means that there are 8 elementary events in the sample space of the experiment of rolling three fair coins. We can list them as follows:
1. HHH (all three coins land heads up)
2. HHT (two coins land heads up, one lands tails up)
3. HTH (two coins land heads up, one lands tails up)
4. THH (two coins land heads up, one lands tails up)
5. HTT (one coin lands heads up, two land tails up)
6. THT (one coin lands heads up, two land tails up)
7. TTH (one coin lands heads up, two land tails up)
8. TTT (all three coins land tails up)

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Answer:

a) Rectangle:

Length = 12 cm

Breadth = 6 cm

Area = length × breadth

= 12 × 6

= 72 cm²

b) Triangle A:

Base = 3 cm

Height = 6 cm

Area = 1/2 × base × height

= 1/2 × 3 × 6

= 9 cm²

c) Triangle B:

Base = 3 cm

Height = 6 cm

Area = 1/2 × base × height

= 1/2 × 3 × 6

= 9 cm²

d) Parallelogram:

Base = (12 - 3) = 9 cm

Height (distance between two parallel sides – the ones you use as your base) = 6 cm

Area = base × height

= 9 × 6

= 54 cm²

We can see that Jack painted 15/24 of the wall, while Sam painted 14/24 of the wall. Comparing these fractions, we can conclude that Jack painted a larger part of the wall.

To determine who painted a larger part of the wall, we need to compare the fractions 5/8 and 7/12. To make the fractions easier to compare, we need to find a common denominator. In this case, the least common multiple (LCM) of 8 and 12 is 24.

To convert 5/8 to have a denominator of 24, we multiply the numerator and denominator by 3: (5/8) x (3/3) = 15/24.
To convert 7/12 to have a denominator of 24, we multiply the numerator and denominator by 2: (7/12) x (2/2) = 14/24.

Now we can see that Jack painted 15/24 of the wall, while Sam painted 14/24 of the wall. Comparing these fractions, we can conclude that Jack painted a larger part of the wall.

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The new positions are:

\(P1_{new}\) = (3, 0, 0)

\(P2_{new}\)= (0, -2.5√3, 2.5)

\(P3_{new}\) = (0, 0, 7)

To determine the new position of the triangle after rotating 30 degrees counter-clockwise about the x-axis, we can apply a rotation matrix to each of the three vertices of the triangle.

The rotation matrix for a rotation about the x-axis is:

\(\left[\begin{array}{ccc}1 &0&0 \\0&cos(\theta) &sin(\theta)\\ 0&sin(\theta) &cos(\theta)\end{array}\right] \\\)

In this case, since we are rotating 30 degrees counter-clockwise, the angle of rotation (theta) is 30 degrees or π/6 radians.

Let's apply the rotation matrix to each vertex of the triangle:

P1(3, 0, 0):

\(\left[\begin{array}{ccc|c}1&0&0 & 3\\0&cos(\pi/6)&-sin(\pi/6) | * &0\\0&sin(\pi/6)&cos(\pi /6)&0\end{array}\right] \\\)

Simplifying the matrix multiplication gives:

\(P1_{new}\) = (3, 0*cos(π/6) - 0*sin(π/6), 0*sin(π/6) + 0*cos(π/6))

      = (3, 0, 0)

P2(0, 5, 0):

\(\left[\begin{array}{ccc|c }1&0&0&0\\0&cos(\pi/6)&-sin(\pi/6) * &5\\0&sin(\pi/6)&cos(\pi /6) & 0 \end{array}\right] \\\)

Simplifying the matrix multiplication gives:

\(P2_{new}\) = (0, 0*cos(π/6) - 5*sin(π/6), 0*sin(π/6) + 5*cos(π/6))

      = (0, -2.5√3, 2.5)

P3(0, 0, 7):

\(\left[\begin{array}{ccc|c }1&0&0&0\\0&cos(\pi/6)&-sin(\pi/6) * &0\\0&sin(\pi/6)&cos(\pi /6) & 7 \end{array}\right] \\\)

Simplifying the matrix multiplication gives:

\(P3_{new}\) = (0, 0*cos(π/6) - 0*sin(π/6), 0*sin(π/6) + 0*cos(π/6))

      = (0, 0, 7)

Therefore, the new positions of the triangle vertices after rotating 30 degrees counter-clockwise about the x-axis are:

\(P1_{new}\) = (3, 0, 0)

\(P2_{new}\)= (0, -2.5√3, 2.5)

\(P3_{new}\) = (0, 0, 7)

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A boy told me he rearrange my guts like Naruto when he punched Sasuke in the stomach. Then one boy told me he gonna eat my refrigerator if I don't shut up.

The center of a dilation is a fixed point in the plane about which all points are expanded or contractedAnswer:

Step-by-step explanation:

Answer:

1) \( = 10 \frac{2}{5} = \frac{52}{5} \)

2) \( = \frac{252}{25} = 10 \frac{2}{25} \)

Step-by-step explanation:

\(6 \frac{4}{5} + 3 \frac{3}{5} \\ (6 + 3) + ( \frac{4}{5} + \frac{3}{5} ) \\ 9 + \frac{7}{5} = 9 + 1 \frac{2}{5} \\ 9 + 1 + \frac{2}{5} = 10 + \frac{2}{5} \)

\( \boxed{\green{= 10 \frac{2}{5} = \frac{52}{5}}} \)

•◇•◇•◇•◇•◇•◇•◇•◇•◇•◇•

\(2 \frac{4}{5} \times 9 \frac{2}{5} \\ \frac{14}{5} \times 9 \times \frac{2}{5 } \)

\(\boxed{\green{ = \frac{252}{25} = 10 \frac{2}{25}}} \)

Answer:

x=1 I'm not sure if I'm correct

Step-by-step explanation:

4x2x=8x

4x3=12

4x3x=12x

4x2=8

8x+12=12x+8

8x-12x= 8-12

-4x=-4 divide -4x in both side so the answer should be x=1

a) The correct line chart for these time series data is Graph (iii).

b)  When a linear trendline is fitted to the data, it shows a positive linear trend.

(a) The correct line chart for these time series data is Graph (iii). From the chart, we can see that the average price per gallon of conventional regular gasoline has fluctuated over the 36-month period. It started around $2.27 per gallon and reached its peak around $3.90 per gallon before coming back down to around $3.56 per gallon at the end of the period.

(b) When a linear trendline is fitted to the data, it shows a positive linear trend. This indicates that, on average, the price of gasoline has been increasing over the 36-month period. The slope of the trendline provides an estimate of the average rate of increase per month, which can be used to forecast future prices.

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: The following table contains time series data for regular gasoline prices in the United States for 36 consecutive months: Month Price ($) Month Price ($) Month Price ($) 3.91 1 2.27 13 2.84 25 2 2.63 14 2.73 26 3.68 3 2.53 15 2.73 27 3.65 4 2.62 16 2.73 28 3.64 5 2.55 17 2.71 29 3.61 6 2.55 18 2.80 30 3.45 7 2.65 19 2.86 31 3.38 8 2.61 20 2.99 32 3.27 9 2.72 21 3.10 33 3.38 10 2.64 22 3.21 34 3.58 11 2.77 23 3.56 35 3.85 12 2.85 24 3.80 36 3.90 (a) Choose the correct line chart for these time series data. What interpretations can you make about the average price per gallon of conventional regular gasoline over these 36 months? (i) Price $ 4.50 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 i 3 Сл 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 Month (ii) Price $ 4.50 4.00 3.50 3.00 um Muuwi www 2.50 2.00 1.50 1.00 0.50 i 35 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 Month Price ($) 4.50 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 Month (iv) Price ($) 4.50 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 Month - Select your answer Select your answer - Graph (1) Graph (ii) Graph (iii) Graph (iv) (b) Fit a linear trendline to the data. What does the trendline indicate about the price of gasoline over these 36 months? - Select your answer - - Select your answer Positive non-linear trend Positive linear trend Negative linear trend Negative non-linear trend

Using binomial theorem we can expand the equation but We are not given the value of a or n, so we cannot determine c exactly.

Integers are real numbers that only comprise positive and negative whole integers as well as natural numbers. Because of rational and irrational numbers, real numbers may include fractions, whereas integers cannot.

A real number is a quantity in mathematics that may be expressed as an infinite decimal expansion. Real numbers, as opposed to natural numbers such as 1, 2, 3,..., which are generated from counting, are used in measures of continually changing quantities such as size and time.

by applying the binomial theorem:

\((1 + ax)^n = C(n, 0) + C(n, 1)(ax) + C(n, 2)(ax)^2 + C(n, 3)(ax)^3 + ...\)

where C(n, k) is the binomial coefficient, which equals\(n!/(k!(n-k)!).\)

The first few terms of this expansion are:

\((1 + ax)^n = 1 + nax + n(n-1)(a^2/2)x^2 + n(n-1)(n-2)(a^3/6)x^3 + ...\)

Comparing with the given expression [1 - 20x + 150x^2 + cx^3], we have:

\(1 - 20x + 150x^2 + cx^3 = 1 + nax + n(n-1)(a^2/2)x^2 + n(n-1)(n-2)(a^3/6)x^3 + ...\)

Equating coefficients of \(x^3\) on both sides, we get:

\(c = n(n-1)(n-2)(a^3/6)\)

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A rhombus is a quadrilateral that has four sides of equal length. A rhombus also has two diagonals, which are perpendicular bisectors of each other. This formula is given as follows: Perimeter = 4 × a, where a is the length of each side of the rhombus.

To find the perimeter of a rhombus using diagonals, follow these steps:

Step 1: Obtain the length of each diagonal of the rhombus.

Step 2: Use the length of the diagonals to find the length of each side.

Step 3: Add the length of each side to find the perimeter of the rhombus.

The perimeter is the sum of all the sides of a figure. To get the perimeter of a rhombus using diagonals, the length of each diagonal has to be found first. The formula for finding the length of each side of a rhombus is:  where the diagonal is the measure of the diagonal of the rhombus.

To find the perimeter of a rhombus, add the length of all the sides of the rhombus. This formula is given as follows: Perimeter = 4 × a, where a is the length of each side of the rhombus.

Therefore, the perimeter of a rhombus using diagonals can be found by following the above procedure and then using the formula to add all the sides of the rhombus.

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Answer:

Step-by-step explanation:

(-1,4) (1,4) 2,0

The endpoint of the line segment will be (-1, 4) and (2, 0). Then the correct options are B and E.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

A line segment in mathematics has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a path that joins two places.

Section Stomach muscle has endpoints A(- 2, 8) and B(4,0). The section is widened at the beginning by a scale variable of 0.5 to make a fragment of the Stomach muscle.

The endpoint of the line segment is given as,

A = 0.5(-2, 8)

A = (-1, 4)

B = 0.5(4, 0)

B = (2, 0)

The endpoint of the line fragment will be (- 1, 4) and (2, 0). Then the right choices are B and E.

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Answer:

95°

Step-by-step explanation:

(x+49)+(x+59)=180

2x+108=180

2x=72

x=36

36+59=95

Answer:

22

Step-by-step explanation:

the terms are counting by 3. making it by adding three to the lest term will give you the answer.

Answer:

0

Step-by-step explanation:

because the carrot is wrong

Answer:

Assuming you are using the zero product property, x = 2, √(3), -√(3)

Step-by-step explanation:

first I factored the (2x^2-7+1) into 2(x^2 - 3)

I also factored the (3x-6) into 3(x - 2)

Now I have the equation 6(x - 2)(x^2 - 3) = 0

I'll start with the easiest one, which is x - 2 = 0, which gives me 2

Now I solve for x^2 - 3 = 0, and I end up with two answers:

√(3) and -√(3)

So in total, x as 3 answers

Answer:

Height = 2 yards

Longer base = 8 yards

Step-by-step explanation:

From the figure attached :

The length of the shorter base of the Trapezoid = 4 yards

Hence, if height of Trapezoid is half the length of the shorter base ;

Then ;

Height of Trapezoid = shorter base/2 = 4 /2 = 2 yards

Longer base is twice the length of shorter base :

Longer base = 2 * shorter base = 2 * 4 = 8 yards

Answer:

7.2

Step-by-step explanation:

Answer:

hope these helps

Step-by-step explanation:

y = 5x + 9 m = 5

y = -3x + 4 m = -3

y = 6 – 7x m = -7

y = 15 – 12x m = -12

Answer:

−4; the amount of bait decreases by 4 pieces each hour

Step-by-step explanation

Answer:

−4; the amount of bait decreases by 4 pieces each hour

Step-by-step explanation:

I did the exam and got it right .

hope this helps you! have a Great day!

Applying properties of exponents, the quotient is given as follows:

\(2\sqrt[3]{3} - \sqrt[3]{18}\)

The expression is given by:

\(\frac{6 - 3\sqrt[3]{6}}{\sqrt[3]{9}}\)

The 3 can be inserted into the cube root, as follows:

\(\frac{6 - 3\sqrt[3]{6}}{\sqrt[3]{9}} = \frac{6 - \sqrt[3]{6 \times 3³}}{\sqrt[3]{9}}\)

Applying the subtraction, we have that the expression is:

\(\frac{6}{\sqrt[3]{9}} - \frac{\sqrt[3]{162}}{\sqrt[3]{9}} = \frac{6}{\sqrt[3]{9}} - \sqrt[3]{\frac{162}{9}} = \frac{6}{\sqrt[3]{9}} - \sqrt[3]{18}\)

The denominator can be simplified as follows:

\(\sqrt[3]{9} = \sqrt[3]{3^2} = 3^{\frac{2}{3}}\)

Then:

\(\frac{6}{\sqrt[3]{9}} = \frac{2 \times 3}{3^{\frac{2}{3}}} = 2 \times 3^{1 - \frac{2}{3}} = 2 \times 3^{\frac{1}{3}} = 2\sqrt[3]{3}\)

Hence the quotient is given by:

\(2\sqrt[3]{3} - \sqrt[3]{18}\)

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Answer:

  ∠CBD = 125°

Step-by-step explanation:

The angle sum theorem tells you that ...

  ∠ABC +∠CBD = ∠ABD

  8x -41° +9x +17° = 180° . . . . . . a "straight angle" has a measure of 180°

  17x -24° = 180° . . . simpify

  17x = 204° . . . . . . add 24°

  x = 12° . . . . . . . . . . divide by 17

Now the measures of the angles can be found from their expressions.

  ∠ABC = 8(12) -41° = 55°

  ∠CBD = 9(12) +17° = 125°

Answer:

BRO IS GERMAN LOL

Step-by-step explanation:

Answer: 8 Oranges

Step-by-step explanation:

Given information

3 Oranges = $1.23

Total cost = $3.28

Determine the unit price of an orange

Unit price = Cost ÷ Number of Oranges

Unit price = 1.23 ÷ 3

Unit price = $0.41 / orange

Determine the number of oranges bought

Number of orange × Unit price = Total cost

N × (0.41) = (3.28)

Divide 0.41 on both sides

N = 3.28 ÷ 0.41

\(\Large\boxed{Number~of~oranges=8}\)

Hope this helps!! :)

Please let me know if you have any questions

The blanks when completed is: If 3 = x, then x = 3

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

3 = x x = 3

The above equation is an illustration of the symmetric property of equation

The symmetric property of an equation states that if one side of an equation is equal to the other side, then the other side is equal to the first side.

In other words, if we have an equation that says a = b, then we can use the symmetric property to say that b = a

Using the above as a guide, we have the following:

If 3 = x, then x = 3

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Actually, 0 degrees is not a counterexample for the expression sin(y)*tan(y) = cos(y).

To see why, let's substitute y = 0 degrees into the expression:

sin(y)*tan(y) = cos(y)

sin(0)*tan(0) = cos(0)

0*tan(0) = 1

0 = 1

As we can see, the equation does not hold for y = 0 degrees. However, this does not make 0 degrees a counterexample, because 0 degrees is not in the domain of the tangent function.

The tangent function is undefined at odd multiples of 90 degrees (e.g. 90, 270, etc.), because at those angles the denominator of the tangent function becomes zero. Therefore, we cannot substitute y = 0 degrees into the expression sin(y)*tan(y) = cos(y), because it would result in division by zero.

In summary, 0 degrees is not a counterexample for the expression sin(y)*tan(y) = cos(y), because it is not in the domain of the tangent function.