What is the solution to this system of equations?

Answer: [tex]R=20.84\ lb\quad 22.57^{\circ},15.43^{\circ}[/tex]

Step-by-step explanation:

Given

Two forces of 9 and 13 lbs acts [tex]38^{\circ}[/tex] angle to each other

The resultant of the two forces is given by

[tex]\Rightarrow R=\sqrt{a^2+b^2+2ab\cos \theta}[/tex]

Insert the values

[tex]\Rightarrow R=\sqrt{9^2+13^2+2(9)(13)\cos 38^{\circ}}\\\Rightarrow R=\sqrt{81+169+184.394}\\\Rightarrow R=\sqrt{434.394}\\\Rightarrow R=20.84\ lb[/tex]

Resultant makes an angle of

[tex]\Rightarrow \alpha=\tan^{-1}\left( \dfrac{b\sin \theta}{a+b\cos \theta}\right)\\\\\text{Considering 9 lb force along the x-axis}\\\\\Rightarrow \alpha =\tan^{-1}\left( \dfrac{13\sin 38^{\circ}}{9+13\cos 38^{\circ}}\right)\\\\\Rightarrow \alpha =\tan^{-1}(\dfrac{8}{19.244})\\\\\Rightarrow \alpha=22.57^{\circ}[/tex]

So, the resultant makes an angle of [tex]22.57^{\circ}[/tex] with 9 lb force

Angle made with 13 lb force is [tex]38^{\circ}-22.57^{\circ}=15.43^{\circ}[/tex]

Answer:

Step-by-step explanation:

Answer:

x = - 5

Step-by-step explanation:

[tex]Let \ (x _ 1 , y _ 1 ) \ and \ (x _ 2 , y _ 2 ) \ be \ the \ points. \\\\The \ distance \ between \ the \ points \ be ,\ d = \sqrt{(x_2 - x_1)^2 + ( y _ 2 - y_1)^2}[/tex]

Given : d = 10 units

         And the points are ( x , - 4) and ( 3 , 2 ).

Find x

[tex]d = \sqrt{( 3 - x)^2 + ( -4 - 2)^2} \\\\10 = \sqrt{( 3 - x)^2 + ( -6)^2} \\\\10^2 = [ \ \sqrt{( 3 - x)^2 + 36} \ ]^2 \ \ \ \ \ \ \ \ \ [ \ squaring \ both \ sides \ ] \\\\100 = ( 3 - x )^2 + 36\\\\100 - 36 = ( 3 - x )^ 2\\\\( 3 - x ) = \sqrt{64}\\\\3 - x = \pm 8\\\\3 - x = 8 \ and \ 3 - x = - 8\\\\-x = 8 - 3 \ and \ -x = - 8 - 3\\\\-x = 5 \ and \ -x = - 11\\\\x = - 5 \ and \ x = 11\\\\[/tex]

Check which value of x satisfies the distance between the points.

x = 11

[tex]d = \sqrt{(3-11)^2 + (-2--4)^2} = \sqrt{(-8)^2 + (-2+4)^2}= \sqrt{64+4} = \sqrt {68} \ units[/tex]

does not satisfy.

x = - 5:

[tex]d = \sqrt{ (3 -- 5)^2 + ( - 4 - 2)^2} = \sqrt{8^2 + 6^2} = \sqrt{100} =10 \ units[/tex]

Therefore , x = - 5

Answer:

The answer is below

Step-by-step explanation:

a) A cube is a three dimensional solid with 6 square faces.

A cube has 8 vertices

b) A rectangular prism is a three dimensional solid with two parallel rectangular bases.

A rectangular prism has 6 faces.

c) A rectangular prism is a three dimensional solid with two parallel rectangular bases.

A rectangular prism has 12 edges.

d) A square-based pyramid is a pyramid with a square base.

A square-based pyramid has 8 edges

e) A triangular prism is a three dimensional solid with two parallel triangular bases.

A triangular prism has 5 faces.

f) A triangular prism is a three dimensional solid with two parallel triangular bases.

A triangular prism has 6 vertices.

Answer:

(I) yessssssssssssssssssssssss

Answer:

yes it is.

Step-by-step explanation:

i did this and it was correct

Answer:

170

Step-by-step explanation:

rititifigkgkrkfjdjfjtjgjgg

Answer:

2.43

Step-by-step explanation:

1.80 x 0.35 + 1.80

Answer:

82,680,328,109,068

Step-by-step explanation:

Use the on-line Big Number calculator

it might take 19 hours i might be wrong

Step-by-step explanation:

Answer:

Step-by-step explanation:

your solution is almost true h=V/πr^2 but the final answer is 36/9π= (4π)cm

--->4×3.14=12.56cm

Answer:

a=5

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

The minimum point of the curve is (2, 0). Hence, axis of symmetry is x = 2

Answer:

1,773.33 Mexican pesos

Step-by-step explanation:

Create a proportion where x was how many Mexican pesos it was worth:

[tex]\frac{1}{0.075}[/tex] = [tex]\frac{x}{133}[/tex]

Cross multiply and solve for x:

133 = 0.075x

1773.33 = x

So, it was worth approximately 1,773.33 Mexican pesos

Answer:

A. (-2, -5), (0, -7), (1, -4)

Step-by-step explanation:

The following transformation is applied:

[tex](x,y) \rightarrow (y + 2, -x - 4)[/tex]

To find the range:

We apply the transformation to the points in the domain. Thus:

[tex](1,-4) \rightarrow (-4 + 2, -1 - 4) = (-2, -5)[/tex]

[tex](3,-2) \rightarrow (-2 + 2, -3 - 4) = (0, -7)[/tex]

[tex](0,-1) \rightarrow (-1 + 2, 0 - 4) = (1, -4)[/tex]

Thus the correct answer is given by option a.

Answer:

(a)So, there are 2 kings in red- one of hearts and the other of diamonds. Therefore, the probability of selecting a red king from a deck of cards= 2/52 or 1/26.

(b) There are 6 red face cards in a 52-card deck (so 46 other cards). PROBABILITIES compare the number of favorable outcomes to the total number of possible outcomes: The PROBABILITY of getting a red face card is 6/52 = 3/26.

The odds in favor of getting a red king will be 1/26. And the odds against getting a red king will be 25/26.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

You are dealt one card from a 52-card deck.

Total events = 52

The odds in favor of getting a red king will be

Favorable events = 2

Then the probability will be

P = 2/52

P = 1/26

The odds against getting a red king will be

q = 1 – P

q = 1 – 1/26

q = 25/26

More about the probability link is given below.

https://brainly.com/question/795909

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Answer:

si a forse that can t negativo AND f so ITS 0;3

Answer:

(21.064 ; 23.136)

Step-by-step explanation:

Given :

Sample, n = 80

Mean, xbar = 22.1

Standard deviation, s = 5.6

Standard Error, S. E = 0.63

Confidence interval :

Xbar ± Zcritical * S.E

22.1 ± (1.645 * 0.63)

22.1 ± 1.036

Lower boundary = 22.1 - 1.036 = 21.064

Upper boundary = 22.1 + 1.048 = 23.136

(21.064 ; 23.136)

Answer:

[tex]g(x) = \frac{-2}{x-1}+5\\\\[/tex]

The graph is shown below.

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

Explanation:

Notice that if we multiplied the denominator (x-1) by 5, then we get 5(x-1) = 5x-5.

This is close to 5x-7, except we're off by 2 units.

In other words,

5x-7 = (5x-5)-2

since -7 = -5-2

Based on that, we can then say,

[tex]g(x) = \frac{5x-7}{x-1}\\\\g(x) = \frac{5x-5-2}{x-1}\\\\g(x) = \frac{(5x-5)-2}{x-1}\\\\g(x) = \frac{5(x-1)-2}{x-1}\\\\g(x) = \frac{5(x-1)}{x-1}+\frac{-2}{x-1}\\\\g(x) = 5+\frac{-2}{x-1}\\\\g(x) = \frac{-2}{x-1}+5[/tex]

This answer can be reached through alternative methods of polynomial long division or synthetic division (two related yet slightly different methods).

-------------------------

Compare the equation [tex]g(x) = \frac{-2}{x-1}+5\\\\[/tex] to the form [tex]g(x) = \frac{a}{x-h}+k\\\\[/tex]

We can see that

The vertical asymptote is x = 1, which is directly from the h = 1 value. If we tried plugging x = 1 into g(x), then we'll get a division by zero error. So this is why the vertical asymptote is located here.

The horizontal asymptote is y = 5, which is directly tied to the k = 5 value. As x gets infinitely large, then y = g(x) slowly approaches y = 5. We never actually arrive to this exact y value. Try plugging in g(x) = 5 and solving for x. You'll find that no solution for x exists.

The point (h,k) is the intersection of the horizontal and vertical asymptote. It's effectively the "center" of the hyperbola, so to speak.

The graph is shown below. Some points of interest on the hyperbola are

Another thing to notice is that this function is always increasing. This means as we move from left to right, the function curve goes uphill.

Answer:

b = 50°

c = 130°

Step-by-step explanation:

Two angles A and B are complementary if:

A + B = 90°

And two angles are supplementary if:

A + B = 180°

Then, we know that:

a = 40°

b is a complement of a (this means that a and b are complementary angles)

c is a supplement of b (this means that b and c are supplementary angles).

From the first statement, we have that:

b + a = 90°

Replacing the value of a we get

b + 40° = 90°

b = 90° - 40° = 50°

b = 50°

And now we can use that b and c are supplementary, then:

b + c = 180°

replacing the value of b we get:

50° + c  = 180°

c = 180° - 50° = 130°

c = 130°

Then the values we wanted are:

b = 50°

c = 130°

Answer:

a. Yield

c. Pre-Order picked up

e. Pre-Orders placed.

Step-by-step explanation:

Uncertain random variables are those over which the farmer has no control. These variables are uncontrollable and there can be no prediction for it. The farmer has no control over the yield produced. He can choose what type of fruits to grow and input method but he has no control over output generated.

Option D. The set of transformation that is performed on this triangle (ABCD)' is A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin

The answer choices have been shown to have all solutions to be rotated around their origin.

To shift the triangle, It has to be done through the connection the points ABC ' to the origin in such a way that the line is extended as we can seen in the diagram.

Read more on reflection here:

https://brainly.com/question/1908648

#SPJ1

Answer:

SAA

Step-by-step explanation:

HOPE IT HELPS YOU IN YOUR LEARNING PROCESS.

Answer:

The answer is "58th %".

Step-by-step explanation:

2.4 Mbps in the sort data set is the 30th data point. Therefore 29 numbers out of 50 are less than 2.4 Mbps.

[tex]=\frac{29}{50} = 0.58 =58\%\\\\[/tex]

The X-th percent is just the same as x% below the percent and thus 2,4 Mpbs corresponds to a 58th percent.

Answer:

The range is from 1.62 to 1.98.

Step-by-step explanation:

We have to solve for the percentage of the particular value if the range of the answer should be +/- 10% of the particular value.

The value given is 1.8, we thus want to find 10% of that: 1.8 * 10/100 = 0.18

Then, add this value to the original value of 1.8: 1.8+0.18 = 1.98

Furthermore, subtract .18 from from the original value of 1.8: 1.8-0.18 = 1.62

The range will be between these two numbers, so the range is from 1.62 to 1.98.

Answer:

the answer is x = 2 or B, hope this helps

Step-by-step explanation:

Answer:

The possible values are a = -2.5 or a = 4.5.

Step-by-step explanation:

Composite function:

The composite function of f(x) and g(x) is given by:

[tex](f \circ g)(x) = f(g(x))[/tex]

In this case:

[tex]f(x) = 4x^2 - 8x - 20[/tex]

[tex]g(x) = 2x + a[/tex]

So

[tex](f \circ g)(x) = f(g(x)) = f(2x + a) = 4(2x + a)^2 - 8(2x + a) - 20 = 4(4x^2 + 4ax + a^2) - 16x - 8a - 20 = 16x^2 + 16ax + 4a^2 - 16x - 8a - 20 = 16x^2 +(16a-16)x + 4a^2 - 8a - 20[/tex]

Value of a so that the y-intercept of the graph of the composite function (fog)(x) is (0, 25).

This means that when [tex]x = 0, f(g(x)) = 25[/tex]. So

[tex]4a^2 - 8a - 20 = 25[/tex]

[tex]4a^2 - 8a - 45 = 0[/tex]

Solving a quadratic equation, by Bhaskara:

[tex]\Delta = (-8)^2 - 4(4)(-45) = 784[/tex]

[tex]x_{1} = \frac{-(-8) + \sqrt{784}}{2*(4)} = \frac{36}{8} = 4.5[/tex]

[tex]x_{2} = \frac{-(-8) - \sqrt{784}}{2*(4)} = -\frac{20}{8} = -2.5[/tex]

The possible values are a = -2.5 or a = 4.5.

Answer:

The story tells of a plain-looking little bird (the Ugly Duckling) born in a barnyard. His brothers and sisters as well as the other birds and animals on the farm tease him for being plain and ugly, so he runs off to live with a flock of wild ducks and geese until hunters shoot down the flock. Alone again, the Ugly Duckling finds a home with an old woman, but her cat and hen also tease him, so he doesn't stay there long.

In his wanderings, the Ugly Duckling comes across a flock of migrating swans, and he wishes to join them but can't because he's too young and can't fly well enough. When winter sets in, a farmer rescues the Ugly Duckling, but the farmer's children and other animals frighten him with their noise and teasing, so again, he flees. He spends a cold and lonely winter hiding in a cave until springtime, when the flock of swans comes to the lake near his hiding place.

When the Ugly Duckling approaches the swans, he's delighted to find that they accept him and treat him like one of them. When he looks at his reflection in the lake, he realizes, to his astonishment, that he's matured into a beautiful swan himself. When the swans fly off from the lake, he spreads his wings and joins them, finally having found a family who accepts him.

Answer:

150 m at 10 m/s

350 m at 50 m/s

Step-by-step explanation:

x + y = 500

x/10 + y/50 = 22

~~~~~~~~~~~~~~~~~

x + y = 500

5x  + y  = 1100

~~~~~~~~~~~~~~~~

x + y = 500

-5x  - y  = -1100

-4x = -600

x = 150

y = 350

Answer:

I think 6.............,..........

Answer:

this is the answer I got! i don't know if it helps, but I hope it does