Plz help please i need it soon

Step-by-step explanation:

Here you go, I hope this is helpfull

The length of the other side of the wall is √500 ft

To get the length of 'd', we will use the pythagoras theorem as shown below:

Given the following

According to the theorem;

\(h^2=a^2+d^2\\30^2 = 20^2 + d^2\\900 = 400 + d^2\\d^2 = 900 - 400\\d = \sqrt{500} ft\)

Hence the length of the other side of the wall is √500 ft

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Answer:

\(sin 2 \theta = \frac{4 \sqrt5}{9}\)

Step-by-step explanation:

Identities used :

\(1. sin^2 \theta = 1 - cos^2\theta\\\\2. tan^2 \theta + 1 = sec^2 \theta\\\\3.cos \theta = \frac{1}{sec \theta} \\\\4. sin 2 \theta = 2 sin\theta cos\theta\)

\(Given \ tan \theta = -\frac{2 \sqrt5}{5}\\\)

\(we \ know \ tan ^2 \theta + 1 = sec^2\theta\)

            \((-\frac{2 \sqrt 5}{5})^2 + 1 = sec^2 \theta\\\\\frac{4 \times 5}{25 } + 1 = sec^2 \theta \\\\\frac{20 + 25}{ 25} = sec^2 \theta \\\\\frac{45}{25} = sec^2 \theta \\\\sec \theta = \sqrt{ \frac{45}{25}}\\\\sec \theta = \sqrt{ \frac{9 \times 5}{5 \times 5}} \\\\sec \theta = \frac{3 \sqrt {5}}{5}\\\\\)

\(We \ know \ cos \theta = \frac{1}{ sec \theta}\)

\(So , \cos \theta = \frac{5}{3 \sqrt5}\)

\(Next \ sin^2 \theta = 1 - cos^2 \theta\)

                 \(= 1 - (\frac{5}{3 \sqrt5})^2\\\\=1 - \frac{25}{9 \times 5}\\\\=1 - \frac{25}{45}\\\\=\frac{45 - 25}{45}\\\\=\frac{20}{45}\\\\=\frac{4}{9}\)

    \(sin \theta = \sqrt{ \frac{4}{9}} = \frac{2}{3}\)

\(Find \ sin 2 \theta\)

\(sin 2 \theta = 2 (sin \theta \times cos \theta)\)

        \(= 2 \times \frac{2}{3} \times \frac{5}{3\sqrt5}\\\\= \frac{4 \times \sqrt5 \times \sqrt5}{9 \times \sqrt 5}\\\\=\frac{4 \sqrt5}{9}\)

The commonly used name for the table used by statisticians that provides probabilities associated with different areas under a bell-shaped curve is the standard normal distribution table or the z-table.

The standard normal distribution table is a reference table that helps statisticians and researchers determine the probabilities associated with specific z-scores (standardized values) in a standard normal distribution. It provides the cumulative probabilities or areas under the curve to the left of various z-scores.

By looking up the corresponding z-score in the table, one can find the probability or area under the curve, which aids in various statistical calculations and hypothesis testing. The standard normal distribution table is a valuable tool for analyzing and interpreting data that follows a normal distribution.

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Buy yellow or green ticket for best chance of winning.

To determine which color ticket to buy, we need to calculate the probability of winning with each color.

First, we need to determine the total number of possible combinations of one ticket of each color. This can be calculated by multiplying the number of tickets of each color together:

Total number of possible combinations = 369 x 488 x 523 x 331 = 39,123,833,144

Next, we need to determine the probability of winning with each color. Since there are four identical prizes, the probability of winning with any one color is the same. We can calculate the probability of winning with a specific color by dividing the number of tickets of that color by the total number of possible combinations:

Probability of winning with blue ticket = 369 / 39,123,833,144 ≈ 0.00000943

Probability of winning with green ticket = 488 / 39,123,833,144 ≈ 0.00001248

Probability of winning with yellow ticket = 523 / 39,123,833,144 ≈ 0.00001337

Probability of winning with red ticket = 331 / 39,123,833,144 ≈ 0.00000846

From the calculations above, we can see that the highest probability of winning is with the yellow ticket, followed closely by the green ticket. Therefore, if we want to maximize our chances of winning one of the prizes, we should buy the yellow or green ticket.

It's important to note that the difference in probabilities between the yellow and green tickets is very small, so the decision of which color to choose ultimately depends on personal preference.

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Answer:  A. - 5/4

Step-by-step explanation:

m = y2-y1/x2-x1

m=3+2/1-5

m=5/-4

Answer:

Step-by-step explanation:

Putting value of n = 12

f(12) = 128 + 15(12 - 1)

= 128 + 180 - 15

= 293

Step-by-step explanation:

C + 1 = 2(L-1)

C +1= 2L -2

C- 2L = -3 ......(eq.1)

L+1 = C-1

C- L = 2 .....(eq.2)

by elimination :

C - 2L = -3

C - L = 2

________-

- L = -5

L = 5

C = 2+5 = 7

so, Leo has 5 cars and Charlie has 7 cars

Answer:

Charlie=7, Leo=5

Step-by-step explanation:

cant explain

The result of 2/3 in decimals is 0.667

To convert a fraction to a decimal, you simply need to divide the numerator (the top number) by the denominator (the bottom number).

In this case, we have:

2 ÷ 3 = 0.666666...

This decimal representation of 2/3 is a repeating decimal, which means that the digit 6 repeats indefinitely.

To write this number as a decimal with a finite number of decimal places, we can round it off to a certain number of decimal places.

For example, rounding to two decimal places gives:

2/3 ≈ 0.67

Rounding to three decimal places gives:

2/3 ≈ 0.667

And so on. The number of decimal places to which you round depends on how precise you need the answer to be.

Therefore, 2/3 is 0.667

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We have shown that if zo is a zero of a linear phase filter, then zo¹ = zo + Δz is also a zero. This holds true because the linear phase property ensures that the filter's phase response varies linearly with frequency, and hence, any frequency offset from zo will yield a corresponding zero in the transfer function.

For a linear phase filter, the phase response is linearly proportional to the frequency. Let's consider a linear phase filter with a zero at frequency zo. The transfer function of the filter can be expressed as H(z) = A(z - zo), where A is a constant and z represents the complex frequency variable.

To find the zero at zo¹, we need to analyze the filter's transfer function at a frequency offset from zo. Let's substitute z with (z - Δz) in the transfer function, where Δz represents a small frequency offset. The new transfer function becomes H(z - Δz) = A((z - Δz) - zo).

Now, let's evaluate the new transfer function at the frequency zo¹ = zo + Δz. Substituting zo¹ into the transfer function, we have H(zo¹ - Δz) = A((zo¹ - Δz) - zo).

Expanding the equation, we get H(zo¹ - Δz) = A(zo¹ - Δz - zo) = A(zo - zo + Δz - Δz) = A(0) = 0.

Therefore, we have shown that if zo is a zero of a linear phase filter, then zo¹ = zo + Δz is also a zero. This holds true because the linear phase property ensures that the filter's phase response varies linearly with frequency, and hence, any frequency offset from zo will yield a corresponding zero in the transfer function.

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Answer:

D)  x² -x - 10  =0

Step-by-step explanation:

Given that

             \(\frac{2}{3x-6} - \frac{1}{3x+6} = \frac{1}{3}\)

L.C.M

         \(\frac{2(3x+6)-(3x-6)}{(3x+6)(3x-6)} = \frac{1}{3}\)

        \(\frac{(6x+12-3x+6)}{(3x+6)(3x-6)} = \frac{1}{3}\)

          \(\frac{(3x+18)}{((3x)^{2} )-(6)^{2} } = \frac{1}{3}\)

    ⇒ \(3(3x+18) = 9 x^{2} - 36\)

   ⇒ 9 x + 54 = 9 x² - 36

  ⇒ 9 x² - 36 - 9x - 54 =0

⇒ 9 x²  - 9x - 90 =0

⇒ 9(x² -x - 10 ) =0

⇒ x² -x - 10  =0

Answer:

The answer is below!

Step-by-step explanation:

Answer:.....

Step-by-step explanation:

Answer:

3.5 in

Step-by-step explanation:

84 ÷ 8 = 10.5

10.5 ÷ 3 = 3.5

Answer:

slope: m=8/7

Step-by-step explanation:

Karabo's net salary after deductions is R29,659 per month where he earns a gross salary of R34600.

Net salary refers to the amount of money that an employee takes home after all of the deductions and taxes have been subtracted from their gross salary. In other words, it is the actual amount of money that an employee earns and receives in their bank account or as a paycheck

To calculate Karabo's net salary after deductions, we need to subtract the deductions from his gross salary. Let's start by calculating the deductions:

Pension = 7.5% of R34,600 = 0.075 x R34,600 = R2,595

Medical Aid = Let's assume that the medical aid deduction is R2,000 per month (this is just an estimate, the actual amount may vary based on the specific medical aid plan).

UIF = 1% of R34,600 = 0.01 x R34,600 = R346

Now we can calculate Karabo's net salary:

Net Salary = Gross Salary - Deductions

Net Salary = R34,600 - R2,595 - R2,000 - R346

Net Salary = R29,659

Therefore, Karabo's net salary after deductions is R29,659 per month.

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The circumference of the circle in terms of π whose radius is given would be = 63π. That is option D.

To calculate the circumference of a circle, the formula that should be used would be given below.

That is;

circumference of circle= 2πr

The radius = 31½

circumference = 2×π × 31½

= 2×π× 63/2

= 63π

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Answer:

y=(x+1/2)^2-21/4

Step-by-step explanation:

Answer:

63/100

Step-by-step explanation:

0.63 = 63/100

Answer: nswer ; x , we can find ; y with the first equation :.

1 answer

·

We know that y=5x−7 so we are just going to replace the y in the other equation : −3x−

Step-by-step explanation:

Answer:

C. P = 30

Step-by-step explanation:

Parallelogram opposite (or parallel) sides are equal,

so:

2x = x + 2

5y - 9 = 2y + 3

For x:

2x = x + 2

2x - x = 2

x = 2

For y:

5y - 9 = 2y + 3

5y - 2y = 3 + 9

3y = 12

y = 4

the smallest sides are equal 2x and x + 2 => 2 * 2 = 4

the biggest sides are equal 5y - 9 and 2y + 3 => 2 * 4 + 3 = 11

P = 2 * (a + b)

P = 2 * (4 + 11)

P = 2 * 15

P = 30

Answer:

55/7 in simplest form is 7 6/7

Answer:

\(x>1/2\)

Step-by-step explanation:

\(2(4x-3)>-3(3x)+5x\)

Expand the brackets.

\(8x-6>-9x+5x\)

Add -9x and 5x

\(8x-6>-4x\)

Add 4x and 6x on both sides.

\(8x+4x>6\)

Add the like terms.

\(12x>6\)

Divide 12 into both sides.

\(12x/12>6/12\)

\(x>1/2\)

Answer:

x > 1/2

Step-by-step explanation:

We have the inequality 2(4x - 3) > -3(3x) + 5x.

Let's first expand all the parentheses on the left side. When doing so, remember that we take the sum of the products of the outside number with each of the inside numbers:

2 * 4x + 2 * (-3) > -9x + 5x

8x - 6 > -4x

Add 4x and 6 to both sides:

8x + 4x > 6

12x > 6

Divide by 12:

x > 6/12

x > 1/2

Thus, any x value greater than 1/2 works: x > 1/2.

~ an aesthetics lover

Solution to given logarithmic equations and inequalities are;

x = 1

x = 9

x = 261

x = 10/3

x = 4

3x² - 2x - 1 = 0

x = 1 or x = -1/3

x = 13

x = 0

x = 0 or x = 5

1. 3x = log6 216

Using the definition of logarithm, we have:

\(6^{3x} = 216\)

\(6^{3x} = 6^3\)

3x = 3

x = 1

2. x - 4 = log3 243

Using the definition of logarithm, we have:

\(3^{x - 4} = 243\)

\(3^{x - 4} = 3^5\)

x - 4 = 5

x = 9

3. log4 (4x - 20) = 5

Using the definition of logarithm, we have:

4⁵ = 4x - 20

1024 = 4x - 20

4x = 1044

x = 261

4. log9 (3 - x) = log9(5x – 15)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

3 - x = 5x - 15

20 = 6x

x = 10/3

5. log81 (x + 20) = log81 (6x)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

x + 20 = 6x

20 = 5x

x = 4

6. log9 (3x²) = log9 (2x + 1)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

3x² = 2x + 1

3x² - 2x - 1 = 0

7. Using the quadratic formula, we have:

x = (-(-2) ± √((-2)² - 4(3)(-1))) / (2(3))

x = (2 ± √(16)) / 6

x = (2 ± 4) / 6

x = 1 or x = -1/3

8. log4(x - 1) = log4(12)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

x - 1 = 12

x = 13

9. log7(5 - x) = log7 (5)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

5 - x = 5

x = 0

10. logx (5x) = 2

Using the definition of logarithm, we have:

x² = 5x

x² - 5x = 0

x(x - 5) = 0

x = 0 or x = 5

Note that x = 0 is not a valid solution, since log 0 is undefined. Therefore, the only solution is x = 5.

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An inverse does not exist for a parabola.

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics.

It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

An inverse does not exist for a parabola.

One definition of a parabola includes a line and a point (the focus) (the directrix).

The directrix is not the main focus.

The locus of points in that plane that are equally spaced apart from the directrix and the focus is known as the parabola.

A right circular conical surface and a plane parallel to another plane that is tangential to the conical surface intersect to form a parabola, which is also known as a conic section.

Therefore, an inverse does not exist for a parabola.

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Answer:

2/3, 3/7, 2/5.

Step-by-step explanation:

The easiest way to tell which number is larger is by using a common denominator. For example, when comparing 2/3 and 3/7, the common denominator would be 21. I multiplied 3 by 7 to get 21, and multiplied 7 by 3 to get 21. Therefore, we must multiply the  numerator by the same number. Then, our two numbers are 14/21, and 9/21. Now, we can easily see that 2/3 (14/21) is the bigger fraction.

Example Math:

2/3·1/7 = 2/21

2/21·7 = 14/21

3/7·1/3 = 3/21

3/7·3 = 9/21

The value of m∠TUS using exterior angle theorem to solve the triangle  is 97° and the correct option is D) 97°

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

To find the value of m∠TUS, we first use exterior angle theorem to find the value of x

Given:

From the diagram,

Substitute the value of x into equation 1

Hence, the correct option is D) 97°

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The probability of rolling two dice and getting a sum of 7 is 1/6.

The probability is the ratio of the number of favorable outcomes to the total outcomes in that sample space. Probability of an event P(E) = (Number of favorable outcomes) ÷ (Sample space).

Sample space for rolling a pair of dice we have:

=> S {(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)}

n(S) = 36

Let A = sum of numbers is 7 = { (1, 6)(2, 5)(3, 4) (4, 3) (5, 2) (6, 1)}

n(A) = 6

P (Sum of numbers is 7) = n(A) / n(S)

= 6/36 = 1/6

Therefore, the probability of rolling two dice and getting a sum of 7 is 1/6.

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Answer:

Step-by-step explanation:

10% = 15.30

40%=61.20

1% = 1.53

2%=3.06

61.20+3.06=64.26

153+ 64.26=217.26

Answer:

b  ≥ 4

Step-by-step explanation:

12b + 12 ≥ 60

Subtract 12 from each side

12b + 12-12 ≥ 60-12

12b  ≥ 48

Divide each side by 12

12b/ 12 ≥ 48/12

b  ≥ 4

Close circle at 4  line to the right

Answer:

Step-by-step explanation:

12b + 12 ≥ 60

1) add -12 at both members

12b + 12-12 ≥ 60 -12

12b ≥ 48

2) divide both members by 12

12/12 b ≥ 48/12

b ≥ 4

for graph the solutions we have to draw two lines

the first one is an horizontal line that has as equation the right part of the inequality

y = 60

the second one is a line the that passes from the origin and interecpts the first line in (4;60). 4 is the the first number that can be a possible value of the inequality

Equation a line that passes for two points  A (0,0) , B (4,60)

(y-y1)/(y2-y1) = (x-x1)/(x2-x1)

(y - 60)/ (0 -60) = (x - 4) / (0-4)

(-y+60)/60 (-x+4)/4

-y + 60 = -15x + 60

y = 15x

the solutions of the inequality are all the points between the two lines with x≥4 and y≥60

Step-by-step explanation:

Answer:

-20x

Step-by-step explanation: