From an 80ft building the angle of elevation of the top of a taller building is 59 degrees and the angle of depression of the base of this building is 65 degrees determine the height of the taller building

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Explanation:

Let's focus on the root x = 2i. Square both sides to get rid of the imaginary component and then get everything to one side.

x = 2i

x^2 = (2i)^2

x^2 = 4i^2

x^2 = -4

x^2+4 = 0

You should find that the root x = -2i leads to x^2+4 = 0 as well.

So the equation x^2+4 = 0 produces the complex roots x = 2i and x = -2i. This tells us that x^2+4 is a factor of the answer. The other factor is x-5 due to the real number root x = 5.

We'll multiply those two factors mentioned:

(x-5)(x^2+4)

w(x^2+4) ..... let w = x-5

wx^2 + 4w

x^2(w) + 4(w)

x^2(x-5) + 4(x-5) .... plug in w = x-5

x^3 - 5x^2 + 4x - 20

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The last step is to triple each term so that we go from the leading term of x^3 to 3x^3. This will give us a lead coefficient of 3.

So we go from this

x^3 - 5x^2 + 4x - 20

to this

3x^3 - 15x^2 + 12x - 60

after tripling everything. This expression has the same roots as the previous one. Scaling the function only stretches it vertically, but the roots aren't changed.

Answer in the pic hope it helps

Answer:

A

Step-by-step explanation:

[tex]\huge \sf༆ Answer ༄[/tex]

Let's solve ~

Hence, the correct choice is ~ A

Answer:

r = -28/9

Step-by-step explanation:

use slope formula of (y₂-y₁) / (x₂-x₁)

5/9 = [r - (-2)] / [-7 - (-5)]

5/9 = (r+2) /-2

cross-multiply to get:

-2(5) = 9(r+2)

-10 = 9r + 18

-28 = 9r

r = -28/9

Answer:

1/4 or .25

Step-by-step explanation:

You cross multiply which would give you 4x=1.

Answer:

65 hot dogs, 96 sodas

Step-by-step explanation:

x + (x + 31) = 161

2x + 31 = 161

2x = 130

x = 65

65 hotdogs

65 + 31 = 96

96 sodas

z²-2i=0

Answer:

Solution given:

z⁴=-4

doing square root on both side

[tex]\sqrt{z⁴}=\sqrt{2²*-1}[/tex]

we know i²=-1

substituting i² we get

z²=[tex]\sqrt{2²*i²}[/tex]

z²=2i

z²-2i=0 is a required answer. where

z² and 2 is real number.

Answer:

  z = {-1 -i, -1 +i, 1 -i, 1 +i}

Step-by-step explanation:

Using Euler's formula, we can write the equation as ...

  z^4 = 4e^(i(π +2πn)) . . . . . . where n is any integer

Then the 4th root is ...

  z = (√2)e^(i(π +2πn)/4 = (√2)e^(i(π/4 +nπ/2)) . . . . . for n = 0–3

  z = √2(cos(π/4+nπ/2) +i·sin(π/4 +nπ/2)) . . . . . for n = 0–3

  z = ±1 ±i

  z = {1 +i, -1 +i, -1 -i, 1 -i}

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Additional comment

Values of n are only needed in the range 0–3, because the answers repeat for values other than those.

Answer:

2 lines are used fro their respected two centers one Is vertical or one is horizontal it's dice into 4 squares

Answer:

13/6 or 2 1/6 is a fraction and is rational number, so yes it is rational

In the original equation, x is a variable, hence f(x). If that term in the parenthesis changes, such as to 0 or -2, we will plug in that number in place of the current variable.

f(0) = 4(0)^2 + 3 = 0 + 3 = 3

f(-2) = 4(-2)^2 + 3 = 4(4) + 3 = 16 + 3 = 19

Hope this helps! :)

Answer: slope (m) = -2

Step-by-step explanation:

y-3=-2(x+5)

put it into y=mx+b

use PEMDAS-Parantheses, Exponents, Mult. Div. Add. Sub. for your order of operations.

first, parantheses.

-2(x+5)

-2 times x = -2x

-2 times 5 = -10

your new equation is y-3 = -2x-10

now, to get y by itself, cancel out the -3 by adding a positive 3 to both sides.

you final equation will be y=-2x-7

in the form y=mx+b, m is your slope.

therefore, -2 is your answer, or slope.

Answer:96

Step-by-step explanation:

Answer:

114

x_shun

jdebh

jejeu

Answer:

54 km/h

Step-by-step explanation:

use s=½(u+v)t

600=½(x+x+12)10

600=½(2x+12)10

600=(2x+12)5

600=10x+60

540=10x

x=54 km/h

I think this is how to do it, I'm so sorry if I do it wrong!

Answer:

A.-4x^2y^4

that the answer

Answer:y=4x+4

Step-by-step explanation:

Answer: 49/30 or, 1 19/30

Answer:

8:10

Step-by-step explanation:

8 parts for brown sugar and 10 parts flour.

In simplest, 4:5 (divide 8 and 10 by 2)

[tex](i)\\\\2A = \begin{pmatrix}3x \times 2 & 1 \times 2 & 5 \times 2\\0\times 2 & 2x \times 2 & -3 \times 2\end{pmatrix} = \begin{pmatrix}6x & 2 & 10\\0 & 4x & -6\end{pmatrix}\\\\\\(ii)\\\\2A + B = C\\\\\implies \begin{pmatrix}6x & 2 & 10\\0 & 4x & -6\end{pmatrix} + \begin{pmatrix}y & 0 & -4\\1 & -3y & 2\end{pmatrix} = \begin{pmatrix}31& 2 & 6\\1 & 17& -4\end{pmatrix}[/tex]

[tex]\implies \begin{pmatrix}6x+y & 2+0 & 10-4\\0+1 & 4x-3y & -6+2\end{pmatrix} = \begin{pmatrix}31 & 2 & 6\\1 & 17& -4 \end{pmatrix}\\\\\\\implies \begin{pmatrix}6x+y & 2 & 6\\1 & 4x-3y & -4\end{pmatrix} = \begin{pmatrix}31 & 2 & 6\\1 & 17& -4 \end{pmatrix}\\\\\text{System of equations},\\\\6x +y =31,~~ 4x -3y = 17\\\\\\(iii)\\\\6x +y-31 =0 \\\\4x-3y -17=0\\\\\text{Solving by cross multiplication method}\\\\\\\dfrac x{1(-17) - (-31)(-3)} = \dfrac y{4(-31) - 6(-17)} = \dfrac 1{6(-3) - 4(1)}[/tex]

[tex]\implies \dfrac{x}{-17 -93} = \dfrac{y}{-124 +102} = \dfrac 1{-18-4}\\\\\\\implies -\dfrac{x}{110} = -\dfrac{y}{22} = -\dfrac 1{22}\\\\ \implies \dfrac{x}{110} = \dfrac{y}{22} = \dfrac 1{22}\\\ \\\text{Hence,}\\\\\\x=\dfrac{110}{22}=5,~~~~ y= \dfrac{22}{22} =1[/tex]

Answer:

  (i)

  [tex]2A=\left[\begin{array}{ccc}6x&2&10\\0&4x&-6\end{array}\right][/tex]

  (ii) 6x+y=31; 4x-3y=17

  (iii) (x, y) = (5, 1)

Step-by-step explanation:

The matrix 2A is written by multiplying each element of A by 2.

  [tex]2A=\left[\begin{array}{ccc}6x&2&10\\0&4x&-6\end{array}\right][/tex]

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Variables are seen in elements (1, 1) and (2, 2) of the matrices A and B, so the simultaneous equations can be chosen from those elements of the equation 2A+B=C.

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A graphing calculator shows the solution to be (x, y) = (5, 1).

Answer:

$237.50

Step-by-step explanation:

5/100=.05

250•.05=12.5

250-12.5=237.50

Step-by-step explanation:

If you swim 575 yards in 3 days, you swim 575 yards.

If you swim 575 yards per day for 3 days, then you swim 3 × 575 yd = 1725 yd

Answer:

y=6+8

y=14

Step-by-step explanation:

y=14 is the answer to this question

Answer:

Draw a straight line through these two points (0, 0) and (1, 3).

Step-by-step explanation:

"Proportional relationship" implies line or curve that goes through the origin; there is no "y-intercept" in this case.  

Plot a dot at (0, 0).  Next, move your pencil point 1 unit to the right (you'll end up at (1, 0), and then move it from there up to (1, 3).  Draw a straight line through these two points (0, 0) and (1, 3).

Answer: yes

Step-by-step explanation:

It is because for every x value there is a y and the x value does not repeat to any y values.

Answer:

No because the slope isnt constant, the y changes higher and higher while the x stays constant

Step-by-step explanation:

Hope this helps!:)

Answer:

A. 4

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

See image

Step-by-step explanation:

Simple way: The cost of three items is given. Divide by 3 to find the cost of one item.

Next level: write a proportion by comparing like quantities (compare things that are the same in the same order)

Cost/numbers of items = Cost/number of items

We know all but one piece of information:

4.76/3 = x/1

Solve for x to find the price of one carton.

Answer:

cant see

Step-by-step explanation:

Step-by-step explanation:

1- 2x(x -4)

2- 3x(2-3x)

3- 4x²(3x-1)

Answer:

y=2(x+5)^2-4.

Step-by-step explanation:

By solving a little bit, we get the vertex to be (-5, -4). Plugging the info given and the vertex into the vertex form, we get y=2(x+5)^2-4. You have a happy holiday season, too!