Answer two questions about system a and b

The distance of the flag pole from point Y is 0.8 km and it is placed at an bearing of N40°E

An equation is an expression that shows the relationship between two or more numbers and variables.

Sine rule shows the relationship between the sides and angles of a triangle.

The triangle formed has angles A = 10°, B = 50°, C = 120°, c = 4 km, a = distance from point y.

Hence:

a / sinA = c / sinC

a / sin(10) = 4 / sin(120)

a = 0.8 km

The distance of the flag pole from point Y is 0.8 km and it is placed at an bearing of N40°E

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Answer:

$2,999

Step-by-step explanation:

Answer:

2x(x^2 - 3)(x^2 + 9)

Step-by-step explanation:

2x^5 + 12x^3 − 54x

2x(x^4 + 6x - 27)

Since -3 + 9 = 6 and -3 x 9 = -27:

2x(x^2 - 3)(x^2 + 9)

Answer:

[tex]2x(x^2-3)(x^2+9)[/tex]

Step-by-step explanation:

Given polynomial:

[tex]2x^5+12x^3-54x[/tex]

Factor out the common term [tex]2x[/tex]:

[tex]\implies 2x(x^4+6x^2-27)[/tex]

To factor the trinomial [tex]x^4+6x^2-27[/tex]:

[tex]\textsf{Let }u=x^2 \implies u^2+6u-27[/tex]

Factor the quadratic by finding two numbers that multiply to -27 and sum to 6:  9 and -3

Rewrite the middle term as the sum of these two numbers:

[tex]\implies u^2+9u-3u-27[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies u(u+9)-3(u+9)[/tex]

Factor out the common term (u + 9):

[tex]\implies (u-3)(u+9)[/tex]

Substitute back [tex]u=x^2[/tex]:

[tex]\implies (x^2-3)(x^2+9)[/tex]

Therefore, the factored form of the given polynomial is:

[tex]\implies 2x(x^2-3)(x^2+9)[/tex]

Answer:

x = 11.5

Step-by-step explanation:

Formula

a^2 = b^2 + c^2 - 2*b*c * cos(A)                     Substitute givens in formula

Givens

Solution

a^2 = 31^2 + 26^2 - 2 * 31 * 26 * cos(21)       Find -2*31*26*cos(21)

a^2 = 961 + 676  -1504.93                             Combine

a^2 = 1637 -1504.93                                      Combine again

a^2 = 132.07                                                   Take the √ on both sides

√a^2 = √132.07

a = 11.5 Rounded.

Answer

x = 11.5

-5/7 x 1/5

-5 x 1 = -5

7 x 5 = 35

-5/35 = -1/7

Happy to help :P

Step-by-step explanation:

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The weight of the full steel bead tire in pounds is 1.76 pounds

The weight of the lighter steel bead tire in pounds is 1.54 pounds.

Division is the process of dividing a number into equal parts using another number. The sign used to denote division is ÷.

The weight of the full steel bead tire in pounds = 800 / 453.592 = 1.76

The weight of the lighter steel bead tire in pounds = 700 / 453.592 = 1.54

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The probabilities are as follows:-

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

The probability will be calculated as follows:-

Total combinations are = 10⁴ = 10000

A) if none of the digits are repeated:-The combinations will be 10 x 9 x 8 x 7 = 5040

Probability =  5040 /  10000

Probaility = 0.504

B) If any of the digits can be repeated:- The combinations will be 10 x 10 x 10 x 10 = 10000

Probabilityy = 10000 / 10000 = 1

C )If any of the digits can be repeated but the 3 and 8 are not in the combination the combinations will be 7 x 7 x 7 x 7 = 2401

Probability = 2401 / 10000 = 0.24

Therefore if none of the digits is repeated 0.50.If any of the digits can be repeated 1.If any of the digits can be repeated but the 3 and 8 are not in the combination 0.24.

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Answer:

  n = 61

Step-by-step explanation:

The subscripted values of x and y in the formula refer to the coordinates of the points:

  [tex](x_1,y_1)=(-3,-2)\qquad(x_2,y_2)=(2,4)[/tex]

Substitute the given values and do the arithmetic.

__

Using these values in the formula gives ...

  [tex]d=\sqrt{n}=\sqrt{(2-(-3))^2+(4-(-2))^2}=\sqrt{5^2+6^2}=\sqrt{25+36}\\\\d=\sqrt{n}=\sqrt{61}\\\\\boxed{n=61}[/tex]

Distance

√n=√61

n=61

The direct proportion is shown by table (B)

Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value.

Here the second table shows the direct proportion relation.

This is because the ratio of x/y remain same.

4/2= 7/3.5= 10/5= 11/5.5= 15/7.5 = 2/1

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Answer:

62/235 +95/383

Step-by-step explanation:

P(satisfied or junior)= P(satisfied participant that are junior) + P(junior participant)

P(satisfied or junior)= 62/235 + 95/383

P(satisfied or junior)= 46071/90005

Answer:

.833 (83.3%)

Step-by-step explanation:

There are 6 numbers on a normal die. 5 of them are larger than 1. The odds would be 5/6

Step-by-step explanation:

Given :

1- cosA = 1/2

or, CosA = 1 -1/2

Therefore ; CosA = 1/2 = b/h

According to the Pythagoras theorem,

P = root under h^2 - b^2

= root under (2)^2 - (1)^2

= root under 4 -1

= root 3

Again,

SinA = P/h

= root 3 / 2

Answer:

Equation of parabola is (x+1)²=20(y-3)

Step-by-step explanation:

And the graph above

(x+1)²=20(y-3) is the equation of a parabola with focus (-1, 3) and directrix x = -5.

Two or more expressions with an Equal sign is called as Equation.

Given, focus : (-1, 3)

directrix : x + 5 = 0 or x=-5

Let (x ,y) is the point on the parabola .

∴ distance of point from focus = distance of point from directrix

√(x+1)²+(y-3)²=|x+5|

Let (x ,y) is the point on the parabola .

∴ distance of point from focus = distance of point from directrix

√(x+1)²+(y-3)²=|x+5|

squaring both sides,

(x+1)²+(y-3)²=(x+5)²

(x+1)²=20(y-3)

Hence,  (x+1)²=20(y-3) is the equation of a parabola with focus (-1, 3) and directrix x = -5.

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The graph of the parent function is given below;

The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, the given function is;

         1, if -1<x≤0

f(x) = 2, if 0<x≤1

          3, if 1<x≤2

Now, the graph of given function is given below.

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Answer:

The correct graph is in the image below

Step-by-step explanation:

Answer:

2 & 3

Step-by-step explanation:

2. High Interest Rates

High-interest rates make it more difficult for businesses to invest. For instance, a small store that is just starting is going to find it hard to make repayments at an interest rate of 20 or 30 percent. It also sucks out money from the economy and re-directs it to the banks. As the interest rates are so high, businesses and consumers reduce their demand for credit. In turn, there is a contraction in the money supply which can lead to deflation.

The effects of high interest rates can be dire if not managed correctly and subtly by central banks. If the interest rates are increased too fast, too high, and too rapidly, we will see the aforementioned effects such as lower business investment and deflation. Therefore, it can contribute to a transition towards an economic contraction in the business cycle.

3. Declining Real Incomes

Inflation can create a drain on consumer incomes as it decreases its value year on year. Therefore, if firms do not increase wages in line with inflation, the average worker will be able to afford less than before.

If real incomes decline, it means consumers have less income to spend on goods and services in the economy. In turn, a prolonged period of decline in real incomes can contribute to an economic contraction in the business cycle.

Answer

is 3 just did it on edge

Step-by-step explanation:

Answer:

A. The volume is the product of the area of the base, 5x(x + 3), and

the height, 2x - 1.

Step-by-step explanation:

Volume is defined as the product of the Length, Width, and Height,

V = L*W*H

The Length x Width is the Area of the Base

L*W = Area Base)

Therefore:  

The (L*W) in the equation V = L*W*H can be replaced with [Area of the Base]

[Area of the Base]

[Area of the Base]  = (5x)*(x+3)          [(or 5x^2 + 15x)]

Volume = [Area of the Base]*H

Volume = [(5x)*(x+3)]*(2x-1)

     The volume is the product of the area of the base, 5x(x + 3), and

the height, 2x - 1.

  That looks a lot like the answer in A:  "The volume is the product of the area of the base, 5x(x + 3), and the height, 2x - 1."

Using the permutation formula, it is found that the number of ways to distribute the books is given by:

c. 8,204,716,800

The order is important, as the books are different, hence the permutation formula is used to solve this question.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, 8 books are distributed among 21 children, hence the number of ways is given by:

[tex]P_{21,8} = \frac{21!}{13!} = 8,204,716,800[/tex]

Which means that option c is correct.

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The division problem that's illustrated based on the information is 3000/75 = 40 without remainder.

A rectangle is defined as a two-dimensional shape having four-sided and opposite sides equal and parallel.

From the information, it was stated that the rectangle with left side labelled 75 and the middle part has 4 above it and 300 inside it.

Therefore, the division problem that's illustrated based on the information is 3000/75 = 40 without remainder.

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Answer:

y = 3x - 5

Step-by-step explanation:

We know that the equation 'y = 3x + ?' intersects the point (1, -2). This means that when x = 1, y = -2 in out equation above. To solve this just plug in the x and y values to get '?'.

[tex]y = 3x + ?\\-2 = 3(1) + ?\\-5 = ?[/tex]

Now that we know '?' is -5, we write it back into slope intercept form, so our final answer is y = 3x - 5

Answer:

pi/6

Step-by-step explanation:

honestly just do it in a calculator that is set to radians.

Answer:

A = 80g B = 200g

Step-by-step explanation for A:

First, you would find what the serving size is divided by to get the number of people needed to feed 6/3 = 2. Then take that number (3) and divided it by the fish (240g) to get 240/3 = 80.

Step-by-step explanation for B:

You will first need to find how much butter goes into ONE pie by dividing 80 by 6 which is 1.33333333333333. Then do 1.333333333333333 times the number of people to feed (15) to get 200.

Answer:

70 is the right answer....

Answer:

70 ways

Step-by-step explanation:

8 C 4 =   8 ! / ( 4! * 4!) = 70 ways

The correct answer is option A which is the equations which represent relationship  between c and f is c = 7 / 3f.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division

Given that:-

From the given data we can see that the amount of flour required is [tex]9\dfrac{1}{3}\[/tex] Cups or [tex]\dfrac{28}{3}[/tex] Cups for making 4 cakes.

So the expression will be written as:-

[tex]9\dfrac{1}{3}f = 4c[/tex]

[tex]\dfrac{28}{3\\}f = 4c[/tex]

[tex]c = \dfrac{28}{3\times 4}f[/tex]

c = [tex]\dfrac{7}{3}[/tex]f

Therefore the correct answer is option A which is the equation that represents the relationship between c and f is c = 7 / 3f.

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Answer:

∠ ABD = 20°

Step-by-step explanation:

since BD bisects ∠ ABC , then

∠ ABD = ∠ CBD ( substitute values )

3x - 1 = 34 - 2x ( add 2x to both sides )

5x - 1 = 34 ( add 1 to both sides )

5x = 35 ( divide both sides by 5 )

x = 7

Then

∠ ABD = 3x - 1 = 3(7) - 1 = 21 - 1 = 20°

The rule represents the translation from the pre-image, ΔABC, to the image, ΔA'B'C' is (x, y) → (x + 7, y - 6).

When a line is translated, it means the line is moved from one position to another. The coordinate for triangle ABC are A(-3 ,4) , B(-4,1) and C(-2,1).

The coordinate of triangle A'B'C' is A'(4,-2), B'(3,-5), and C'(5,-5).

From above, it can be seen that the image A'B'C' is obtained from the pre-image ABC by translating the vertices of the image by 7 units to the right and 6 units down.

Therefore, the rule represents the translation from the pre-image, ΔABC, to the image, ΔA'B'C' is (x, y) → (x + 7, y - 6)

Hence, the rule represents the translation from the pre-image, ΔABC, to the image, ΔA'B'C' is (x, y) → (x + 7, y - 6).

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Answer:

C. Line PQ

Step-by-step explanation:

Tangent means touching, not crossing.