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Lisa [10]
3 years ago
10

Eric is looking up at an object. eric points one arm at the object and the other arm at aaron. the angle formed by his outstretc

hed arms measures 50 degrees. Aaron is also looking up at the object. He points one arm at the object and the other arm at eric. the angle formed by his outstreatched arms measures35 degrees. the distance between the two men is 80 feet. which of the following best represents the distance between eric and the object?
A. 46.1 ft
B. 49.3 ft
C. 52.6 ft
D. 42.4 ft

Use law of sines and please show work. need ASAP

Mathematics
1 answer:
elixir [45]3 years ago
8 0

Answer:

A. 46.1 ft

Step-by-step explanation:

You need to look at this scenario as a triangle, with the object, Eric and Aaron being 3 different points.

<u>Refer to the attached image for clarity.</u>

To solve this, we will use the Sine Rule.


To apply this, we need to know two angles that correspond to the side of the triangle opposite of them, and the length of those to sides.

<h3><u>Finding the unknown angle</u></h3>

The sum of a triangle is 180 degree, and we can subtract the value of the known two angles from this to obtain the value of the unknown angle (A)

180 - 35 - 50 = 95 degree

<h3><u>Apply Sine Rule</u></h3>

To solve for the distance between Eric and the Object, we will apply this as follows:

Sine A / a = Sine C / c

<em>Note: We are using the angle C because the corresponding angle directly opposite is the side of the triangle we need to find</em>

Sine 95 / 80 = Sine 35 / c

Rearrange the equation

c = Sine 35 x 80 / Sine 95

c = 46.06

c ~ 46.1 ft


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2/3 (3x+9)=-2 (2x+6)​
rosijanka [135]

Answer: x=−3

Step-by-step explanation: Let's solve your equation step-by-step.

2

3

(3x+9)=−2(2x+6)

Step 1: Simplify both sides of the equation.

2

3

(3x+9)=−2(2x+6)

(

2

3

)(3x)+(

2

3

)(9)=(−2)(2x)+(−2)(6)(Distribute)

2x+6=−4x+−12

2x+6=−4x−12

Step 2: Add 4x to both sides.

2x+6+4x=−4x−12+4x

6x+6=−12

Step 3: Subtract 6 from both sides.

6x+6−6=−12−6

6x=−18

Step 4: Divide both sides by 6.

6x

6

=

−18

6

x=−3

5 0
3 years ago
Read 2 more answers
1 2 3 4 5 6 7 8 9 10 11 12 13
Rina8888 [55]

Answer:

The mean will increase more than the median, but both will increase.

[third option listed]

Step-by-step explanation:

the <em>median </em>of a data set is the number in the middle [when listed from lowest to highest in value]

1 2 3 4 5 6 7 8 9 10 11 12 13

is the current median

let's consider what adding 12 would mean--it would mean that we move the median slightly higher [further along in the data set] because there are more numbers (but let's try this out to confirm:)

1 2 3 4 5 6 7 8 9 10 11 12 12 13

[if a median placement is shared between two numbers, the mean/average of those two numbers is taken, and that is considered to be the median]

so, 7.5 is the current median

(this is an increase of 0.5)

--

the <em>mean</em> of a data set is what we commonly refer to as the "average"

[you find this value by adding all of the numbers in the data set together and dividing by the number of terms in the data set]

1 2 3 4 5 6 7 8 9 10 11 12 13

mean of original data set:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 [= 91]

_______________________________________

                                    13

[91 ÷ 13 = 7]

because our number is <em>greater </em>than our original mean [12 > 7], we know that the mean must increase:

[91 + 12 = 103]

[103 ÷ 14 ≈ 9.36]

[we had an increase of 2.36]

so, median increased by 0.5, mean increased by 2.36

so, both values increased, whilst the mean increased by <em>more </em>than the median [as to be expected]

you could also express this as "The mean will increase more than the median, but both will increase." [third option listed]

hope this helps!! :)

3 0
2 years ago
Will give brainliest if right
inn [45]

As the Remainder Theorem points out, if you divide a polynomial p(x) by a factor x – a of that polynomial, then you will get a zero remainder. Let's look again at that Division Algorithm expression of the polynomial:

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p(x) = (x – a)q(x) + r(x)

If x – a is indeed a factor of p(x), then the remainder after division by x – a will be zero. That is:

p(x) = (x – a)q(x)

In terms of the Remainder Theorem, this means that, if x – a is a factor of p(x), then the remainder, when we do synthetic division by

x = a, will be zero.

The point of the Factor Theorem is the reverse of the Remainder Theorem: If you synthetic-divide a polynomial by x = a and get a zero remainder, then, not only is x = a a zero of the polynomial (courtesy of the Remainder Theorem), but x – a is also a factor of the polynomial (courtesy of the Factor Theorem).

Just as with the Remainder Theorem, the point here is not to do the long division of a given polynomial by a given factor. This Theorem isn't repeating what you already know, but is instead trying to make your life simpler. When faced with a Factor Theorem exercise, you will apply synthetic division and then check for a zero remainder.

Use the Factor Theorem to determine whether x – 1 is a factor of

    f (x) = 2x4 + 3x2 – 5x + 7.

For x – 1 to be a factor of  f (x) = 2x4 + 3x2 – 5x + 7, the Factor Theorem says that x = 1 must be a zero of  f (x). To test whether x – 1 is a factor, I will first set x – 1 equal to zero and solve to find the proposed zero, x = 1. Then I will use synthetic division to divide f (x) by x = 1. Since there is no cubed term, I will be careful to remember to insert a "0" into the first line of the synthetic division to represent the omitted power of x in 2x4 + 3x2 – 5x + 7:

completed division: 2  2  5  0  7

Since the remainder is not zero, then the Factor Theorem says that:

x – 1 is not a factor of f (x).

Using the Factor Theorem, verify that x + 4 is a factor of

     f (x) = 5x4 + 16x3 – 15x2 + 8x + 16.

If x + 4 is a factor, then (setting this factor equal to zero and solving) x = –4 is a root. To do the required verification, I need to check that, when I use synthetic division on  f (x), with x = –4, I get a zero remainder:

completed division: 5  –4  1  4  0

The remainder is zero, so the Factor Theorem says that:

x + 4 is a factor of 5x4 + 16x3 – 15x2 + 8x + 16.

In practice, the Factor Theorem is used when factoring polynomials "completely". Rather than trying various factors by using long division, you will use synthetic division and the Factor Theorem. Any time you divide by a number (being a potential root of the polynomial) and get a zero remainder in the synthetic division, this means that the number is indeed a root, and thus "x minus the number" is a factor. Then you will continue the division with the resulting smaller polynomial, continuing until you arrive at a linear factor (so you've found all the factors) or a quadratic (to which you can apply the Quadratic Formula).

Using the fact that –2 and 1/3 are zeroes of  f (x) = 3x4 + 5x3 + x2 + 5x – 2, factor the polynomial completely.   Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved

If x = –2 is a zero, then x + 2 = 0, so x + 2 is a factor. Similarly, if x = 1/3 is a zero, then x – 1/3 = 0, so x – 1/3 is a factor. By giving me two of the zeroes, they have also given me two factors: x + 2 and x – 1/3.

Since I started with a fourth-degree polynomial, then I'll be left with a quadratic once I divide out these two given factors. I can solve that quadratic by using the Quadratic Formula or some other method.

The Factor Theorem says that I don't have to do the long division with the known factors of x + 2 and x – 1/3. Instead, I can use synthetic division with the associated zeroes –2 and 1/3. Here is what I get when I do the first division with x = –2:

completed divison: bottom row:  3  –1  3  –1  0

The remainder is zero, which is expected because they'd told me at the start that –2 was a known zero of the polynomial. Rather than starting over again with the original polynomial, I'll now work on the remaining polynomial factor of 3x3 – x2 + 3x – 1 (from the bottom line of the synthetic division). I will divide this by the other given zero, x = 1/3:

completed division:  bottom row:  3  0  3  0

 

3x2 + 3 = 0

3(x2 + 1) = 0

x2 + 1 = 0

x2 = –1

x = ± i

If the zeroes are x = –i and x = i, then the factors are x – (–i) and x – (i), or x + i and x – i. I need to   divided off a "3" when I solved the quadratic; it is still part of the polynomial, and needs to be included as a factor. Then the fully-factored form is:

3x4 + 5x3 + x2 + 5x – 2 = 3(x + 2)(x – 1/3)(x + i)(x – i)

7 0
3 years ago
Hey i was wondering can i move +7 from inside the absolute value in the left side to -7 outside the absolute value on the right
pashok25 [27]

Answer:

  • A) Zero

Step-by-step explanation:

<u>Given equation:</u>

  • |x + 7| = - 4

The left side is absolute value, we know it is zero or positive value but never negative.

The right side is negative so the equation can't have solutions as we have contradiction above.

5 0
2 years ago
Read 2 more answers
1. Classify the polynomial 2x4 + 6x − 3 by number of terms. constant trinomial binomial cubic
goldenfox [79]
Polynomial are classified according to their number of terms. 5x^3+8y+6x^2 has three terms, 2xy has 1 term and 15-y^2. A polynomial with 1 term is called a monomial, A polynomial with 2 terms is called a binomial while a polynomial with 3 terms is called a trinomial. Thus our polynomial 2x^4+6x-3 is called a trinomial.
5 0
3 years ago
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