Find these common multiple for five and nine

The trapezium is an isosceles trapezium. Then the measure of all angles will be 54°, 36°, 36°, and 54°.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezium, one pair of opposite sides are parallel.

In the adjoining figure, ABCD is an isosceles trapezium in which angle ∠BCD = 2x and angle ∠ABC = 3x.

Then all the angles of the trapezium will be

Agngle ∠BCD = ∠ADC and angle ∠ABC = ∠BAD because the trapezium is an isosceles trapezium. Then we have

Then the value of x will be

∠ABC + ∠BCD + ∠CDA + ∠DAB = 180°

                        3x + 2x + 2x + 3x = 180°

                                              10x = 180°

                                                  x = 18°

Then the measure of all angles will be

∠ABC = ∠BAD = 3x = 3 × 18 = 54°

∠BCD = ∠ADC = 2x = 2 × 18 = 36°

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Answer:

i

Step-by-step explanation:

Answer:

8\(\sqrt{3}\)

Step-by-step explanation:

This is a special right triangle with angle measures 90-60-30 degrees

The side lengths are like the following :

The side length that sees 90 degrees is represented with x

The side length that sees 60 degrees is represented with x\(\sqrt{3}\)

The side length that sees 30 degrees is represented with 2x

the side that sees 90 degrees is given as 16 so x = 8 and so  a = 8\(\sqrt{3}\)

The distance between the Pluto and the sun is about 5,905,800,000 kilometers.

Distance between Mercury  and the sun is = 57,900,000 kilometers.

The distance of Pluto from the sun

=  Pluto is about 1.02 x 10^2 times farther away from the sun than Mercury.

⇒Distance of Pluto from the sun

= Distance of Mercury from the sun x 1.02 x 10^2

⇒Distance of Pluto from the sun = 57,900,000 km x 1.02 x 10^2

⇒Distance of Pluto from the sun = 57,900,000 km x 102

⇒ Distance of Pluto from the sun = 5,905,800,000 kilometers

Therefore, the distance of Pluto is about 5,905,800,000 kilometers away from the sun.

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Answer:

5555555555555555555 i dont know what this maens sorry

The critical path is the path with the longest duration, which in this case is A -> B -> D -> E with a duration of 11 days.

To determine the critical path of the project, we need to find the longest path of activities that must be completed in order to finish the project on time. This is done by calculating the earliest start time (ES) and earliest finish time (EF) for each activity.

Starting with activity A, ES = 0 and EF = 4. Activity B can start immediately after A is complete, so ES = 4 and EF = 7. Activity C can start after A is complete, so ES = 4 and EF = 6. Activity D can start after B is complete, so ES = 7 and EF = 9. Finally, activity E can start after C and D are complete, so ES = 9 and EF = 11.

The variance for each activity is also given, which allows us to calculate the standard deviation and determine the probability of completing the project on time. The critical path is the path with the longest duration, which in this case is A -> B -> D -> E with a duration of 11 days.

Using the expected durations and variances, we can calculate the standard deviation of the critical path. This information can be used to determine the probability of completing the project on time.

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The multiplication law states that

So

Answer:

1 = 1

Step-by-step explanation:

We all know the law of exponents,the one we'll use to solve this is the multiplication law:

Solved:

x^0 = 1

Alternate method:

5^3 and 5^3 cancels, which results to

d...................................

Since you have basic knowledge of computer hardware, an action which you should take as an ethical employee include the following: A. Initiate help by offering to check the computer.

A computer hardware can be defined as a physical component of a computer system or an information technology (IT) that can be seen, touched and replaced.

In Computer technology, there are various examples of a computer hardware and these include the following:

Based on ethical principles, we can reasonably infer and logically conclude that an ethical employee should initiate help by offering to help check the colleague’s computer since he or she has basic knowledge of computer hardware.

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Answer:

x=24

Step-by-step explanation:

35x = 105x8

35x=840

x=24

if the equation is 35/8 = 105/x= then your answer is x=24

Answer:

-2 > -8

Step-by-step explanation:

Since they are negative, -2 is greater than -8

Answer:

>

Step-by-step explanation:

Do remember the three symbols :

> - Greater than

< - Less than

= Equal to

An analogy you can use to always do this question is to think of the sign as a hungry alligator, and it wants to eat a bigger portion, so the opening of the teeth will revolt towards the bigger number. But there is a problem here, we're dealing with is negatives, it is the opposite than positives. The lower the number is in a negative is the bigger number in general, because it's closer to 0.

Therefore :

-2 > -8

a) 2x - 4 = 0
2x = 4, x = 2

b) (x-1)(6-2x) = 0

If x-1 = 0
=> x = 0 + 1 = 1

If 6-2x = 0
=> 2x = 6-0 = 6
=> x = 3

Answer:

Step-by-step explanation:

\(\frac{3}{x+3}-\frac{4}{x-3}=\frac{3*(x-3)}{(x+3)(x-3)}-\frac{4(x+3)}{(x-3)(x+3)}\\\\=\frac{3*x-3*3}{(x+3)(x-3)}-\frac{4*x+4*3}{(x+3)(x-3)}\\\\=\frac{3x-9}{x^{2}-3^{2}}-\frac{4x+12}{x^{2}-3^{2}}\\\\=\frac{3x - 9 -(4x + 12)}{x^{2}-3^{2}}\\\\=\frac{3x-9-4x-12}{x^{2}-9}\\\\=\frac{-x-21}{x^{2}-9}\\\\\)

\(\frac{3}{x+3}-\frac{4}{x-3}=\frac{5x}{x^{2}-9}\\\\\frac{-x-21}{x^{2}-9}=\frac{5x}{x^{2}-9}\\\\-x-21=\frac{5x}{(x^{2}-9)}*(x^{2}-9)\\\)

-x - 21 = 5x

Add 'x' to both sides

-x -21 +x = 5x + x

        -21 = 6x

6x = -21

x = -21/6

   = -7/2

x = -3.5

Answer:

The answer is 11.401754

Answer: Approximately 11.4 units

================================================

Work Shown:

(x1,y1) is the first point (-6,-2)

(x2,y2) is the second point (5,1)

Apply the distance formula

\(d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(-6-5)^2+(-2-1)^2}\\\\d = \sqrt{(-11)^2+(-3)^2}\\\\d = \sqrt{121+9}\\\\d = \sqrt{130}\\\\d \approx 11.4017542509913\\\\d \approx 11.4\\\\\)

The distance between the two points is roughly 11.4 units.

Answer:

\(B.\ x^3 - 2x^2 - 4x + 1\)

Step-by-step explanation:

Given

Polynomials A to D

Divisor: x - 2

Required

Which of polynomial A - D has a remainder of -7

We start by equating the divisor to 0

\(x - 2 = 0\)

Make x the subject of formula

\(x = 2\)

Next is to substitute 2 for x in the polynomials to get the remainder;

\(A.\ 4x^3 + 2x^2 + 5\)

\(4(2)^3 + 2(2)^2 + 5\)

Open Brackets

\(4 * 8 + 2 * 4 + 5\)

\(32 + 8 + 5\)

\(Remainder = 45\)

\(B.\ x^3 - 2x^2 - 4x + 1\)

\((2)^3 - 2(2)^2 - 4(2) + 1\)

Open Brackets

\(8 - 2 * 4 - 4 * 2 + 1\)

\(8 - 8 - 8 + 1\)

\(Remainder = -7\)

\(C.\ 3x^2 + 6x - 2\)

\(3(2)^2 + 6(2) - 2\)

Open Brackets

\(3 * 4 + 6 * 2 - 2\)

\(12 + 12 - 2\)

\(Remainder = -2\)

\(D.\ -2x^3 + 4x^2 + 3x - 2\)

\(-2(2)^3 + 4(2)^2 + 3(2) - 2\)

Open Brackets

\(-2 * 8 + 4 * 4 + 3 * 2 - 2\)

\(-16 + 16 + 6 - 2\)

\(Remainder = 4\)

From the calculations above, the polynomial with a remainder of -7 when divided by \(x - 2\) is \(B.\ x^3 - 2x^2 - 4x + 1\)

The value of the polynomial \(x^3-2x^2-4x+1\) is -7 at x = 2. So, option B is correct.

Important information:

According to the Remainder Theorem, if a polynomial is p(x) is divided by (x-c), then the remainder is p(c).

If polynomials have a remainder of -7 when divided by x – 2. So, the value of the polynomial must be -7 at x = 2.

Substitute x = 2 in the first polynomial.

\(4(2)^3+2(2)^2+5=45\neq -7\)

Substitute x = 2 in the second polynomial.

\((2)^3-2(2)^2-4(2)+1=-7\)

Substitute x = 2 in the third polynomial.

\(3(2)^2+6(2)-2=22\neq -7\)

Substitute x = 2 in the fourth polynomial.

\(-2(2)^3+4(2)^2+3(2)-2=4\neq -7\)

Only the value of the second polynomial is -7 at x = 2. Therefore, the correct option is B.

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\((\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{4}}}\implies \cfrac{-7}{-4}\implies \cfrac{7}{4}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{\cfrac{7}{4}}(x-\stackrel{x_1}{4}) \\\\\\ y-2=\cfrac{7}{4}x-7\implies y=\cfrac{7}{4}x-5\)

The value of x that satisfies the given conditions is 6. Let's solve the problem step by step.

We are given that the apples are shared in the ratios 1:3:x, where x > 3. This means that the total number of parts in the ratio is 1 + 3 + x = 4 + x.

To find the number of apples in each person's share, we divide the total number of apples (60) by the total number of parts in the ratio (4 + x):

Number of apples in each part = Total number of apples / Total number of parts

= 60 / (4 + x)

Now, we are given that the number of apples in Carol's share is 18 more than the number of apples in Betty's share. Therefore, we can set up the equation:

Number of apples in Carol's share = Number of apples in Betty's share + 18

Using the ratios, we can express the number of apples in each person's share:

Number of apples in Betty's share = 3 * (Number of apples in Abbie's share)

Number of apples in Carol's share = x * (Number of apples in Abbie's share)

Substituting these values into the equation, we get:

x * (Number of apples in Abbie's share) = 3 * (Number of apples in Abbie's share) + 18

Simplifying the equation, we have:

x * (60 / (4 + x)) = 3 * (60 / (4 + x)) + 18

To solve for x, we can multiply both sides of the equation by (4 + x) to eliminate the denominators:

x * (4 + x) * (60 / (4 + x)) = 3 * (4 + x) * (60 / (4 + x)) + 18 * (4 + x)

Simplifying further:

60x = 3 * 60 + 18 * (4 + x)

60x = 180 + 72 + 18x

42x = 252

x = 6

Therefore, x = 6.

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The pattern of error seems to be adding 4 and subtracting 10 in each calculation.

In the first example, the student adds 4 to the correct sum of 10 and 6, resulting in 14 instead of the correct answer of 16. In the second example, the student subtracts 10 from the correct difference of 11 - 5, resulting in 1 instead of the correct answer of 6.

From these examples, we can observe a consistent pattern in the errors made by the student. Specifically, the student is adding 4 to the correct sum and subtracting 10 from the correct difference. This suggests that the student may have misunderstood or misapplied the rules of addition and subtraction.

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Answer:

w(x)=2.3x+31

Step-by-step explanation:

From the information given, the function would indicate that the weight of the dolphin after x days would be equal to the 31 pounds the baby weighed when it was born plus 2.3 lbs that is the average rate it is growing for the number of days:

w(x)= 2.3x+31, where:

w(x)= weight of the dolphin

x=number of days

Answer:

x = 17

Step-by-step explanation:

The two given angles are supplementary angles, but also all angles on a straight light must add up to 180°:

3x + 14 + 7x - 4 = 180

Add like terms

3x + 7x + 14 - 4 = 180

10x + 10 = 180

Subtract 10 from both sides to isolate 10x:

10x + 10 - 10 = 180 - 10

10x = 170

Divide both sides by 10:

10x ÷ 10 = 170 ÷ 10

x = 17

Hope this helps!

Dividing two polynomials may produce another polynomial only when the divisor has a lower degree than the dividend. Otherwise, it will generally result in a rational function.

No, dividing two polynomials may not result in another polynomial. It can produce a rational function.

A polynomial is an algebraic expression consisting of terms with non-negative integer exponents. When two polynomials are divided, the result is not always a polynomial.

If the degree of the polynomial being divided (dividend) is higher than the degree of the polynomial dividing (divisor), then the result can be a polynomial with a lower degree. However, if the degree of the divisor is equal to or greater than the degree of the dividend, the result will generally be a rational function, which is a ratio of two polynomials.

A rational function has the form P(x)/Q(x), where P(x) and Q(x) are polynomials and Q(x) is not equal to zero. The division can introduce terms with negative or fractional exponents, making the result a rational function rather than a polynomial.

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Answer:

x<2

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

x < 2 x < 2

Interval Notation:

( − ∞, 2)

Answer:

Slower

Step-by-step explanation:

If 100 cans per 20 minutes continues, it would be 200 cans per 40 minutes, which is more than 160 cans per 40 minutes

Answer:

600

Step-by-step explanation

1.5% of /(10,000x2) is 300

3.0% of 10,000 is 300

Add them to get 600

Don't forget to thank me

A percentage is a way to describe a part of a whole. The number of people that enter the restaurant per day is 600 people.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given that You own a restaurant in a lakeside town where 10,000 cars and 10,000 pedestrians pass by per day.

1.5% of cars with 2 people each, and 3% of pedestrians enter your restaurant.

The number of cars that has 2 people in each car passing the restaurant per day.

= 10,000 cars

The number of pedestrians that passes the restaurant each day.

= 10,000 people

The 1.5% of 10,000 cars will be,

= 1.5 / 100 x 10,000

= 150 cars

The number of people in 150 cars.

= 150 x 2

= 300 people _______(1)

The 3% of 10,000 pedestrians will be,

= 3 / 100 x 10,000

= 300 pedestrian

= 300 people ______(2)

The number of people that entered the restaurant.

= 1.5% of cars with 2 person on each car + 3% of pedestrians

From (1) and (2)

= 300 people + 300 people

= 600 people

Thus, the number of people that enter the restaurant per day is 600 people.

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The derivative of the given expression `y=10 ∩_4^(x(x+1)(2x-1))` is `dy/dx = 4^(x(x+1)(2x-1)) * ln 4 * [(2x-1)(x+1) + 4x² - x]`.

Given, `y=10 ∩_4^(x(x+1)(2x-1))`

To find the derivative of the above expression, we can use the Chain rule of differentiation.

The Chain rule of differentiation is used to find the derivative of composite functions. This rule is also known as the function of a function rule.

The Chain Rule: If `f` and `g` are both differentiable functions, then the derivative of their composite is given by the product of the derivative of `g` with respect to `x` and the derivative of `f` with respect to `g`.

That is, if `y = f(g(x))`, then

`dy/dx = f'(g(x))g'(x)`

Hence, the derivative of the given expression `y=10 ∩_4^(x(x+1)(2x-1))` is given by:

dy/dx = d/dx [10 ∩_4^(x(x+1)(2x-1))]

dy/dx = 0 + d/dx [4^(x(x+1)(2x-1))] * d/dx [x(x+1)(2x-1)]

Now we need to find the derivative of the two terms separately.

(i) d/dx [4^(x(x+1)(2x-1))] = 4^(x(x+1)(2x-1)) * ln 4 * d/dx [x(x+1)(2x-1)]

(ii) d/dx [x(x+1)(2x-1)] = x'(x+1)(2x-1) + x(x+1)(2x-1)'= 1(x+1)(2x-1) + x(1)(4x-1)

So, dy/dx = 0 + 4^(x(x+1)(2x-1)) * ln 4 * [1(x+1)(2x-1) + x(1)(4x-1)]

Hence, dy/dx = 4^(x(x+1)(2x-1)) * ln 4 * [(2x-1)(x+1) + 4x² - x]

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Answer:

5593.75

Step-by-step explanation:

To find the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3, we first need to compute the derivative of the function.

f(x) = ln(4sec(x))
f'(x) = (1/sec(x)) * (4sec(x)) * tan(x) = 4tan(x)
Next, we use the arc length formula:
L = ∫ [a,b] √[1 + (f'(x))^2] dx
Substituting in the values, we get:
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
We can simplify this by using the identity 1 + tan^2(x) = sec^2(x):
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
 = ∫ [0,π/3] √[1 + 16tan^2(x)] dx
 = ∫ [0,π/3] √[sec^2(x) + 16] dx
 = ∫ [0,π/3] √[(1 + 15cos^2(x))] dx
 = ∫ [0,π/3] √15cos^2(x) + 1 dx
Using the substitution u = cos(x), we get:
L = ∫ [0,1] √(15u^2 + 1) du
This can be solved using trigonometric substitution, but the details are beyond the scope of this answer. The final result is:
L = 4/3 * √(15) * sinh^(-1)(√15/4) - √15/2
Therefore, the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3 is approximately 3.195 units.

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Answer:

OC.6 ft hope this helps you

Answer: 6 ft

Step-by-step explanation:

L×w×h    36×12×24=10368in

1 cubic foot = 1728in          10368÷1728=6