10. Find y. x is 127° w is 53°

True of False: (log x)^2=2log x. Explain your answer and show your work

Lubov Fominskaja [6]

False.
Only log(x^2)=2log(x)
For example, let x=10
(log(10))^2=1^2=1
yet 2log(10)=2*1=2

8 0

4 years ago

Hello, I am currently very stuck with this problem and I am unsure as to how I would solve it.

borishaifa [10]

We have the equation

$20y=x^2-10-15$

Let's complete the square, to do it let's add and subtract 25 on the right side

$\begin{gathered} 20y=x^2-10-15+25-25 \\ \\ 20y=(x-5)^2-15-25_{} \\ \\ 20y=(x-5)^2-40 \\ \\ \end{gathered}$

Now we can have y in function of x

$\begin{gathered} y=\frac{1}{20}(x-5)^2-2 \\ \\ \end{gathered}$

Now we can already identify the vertex because it's in the vertex form:

$y=a(x-h)+k$

Where the vertex is

$(h,k)$

As we can see, h = 5 and k = -2, then the vertex is

$(5,-2)$

Now we can continue and find the focus, the focus is

$\mleft(h,k+\frac{1}{4a}\mright)$

We have a = 1/20, therefore

$\begin{gathered} \mleft(5,-2+5\mright) \\ \\ (5,3) \end{gathered}$

The focus is

$(5,3)$

And the last one, the directrix, it's

$y=k-\frac{1}{4a}$

Then

$\begin{gathered} y=-2-5 \\ \\ y=-7 \end{gathered}$

Hence the correct answer is: vertex (5, -2); focus (5, 3); directrix y = -7

5 0

1 year ago

How to do this step by step?

serg [7]

The answer is 27.6
angle version of the law of cosines:

cos(C) = (a^2 + b^2 − c^2)/2ab

cos(A) = (b^2 + c^2 − a^2)/2bc

cos(B) = (c^2 + a^2 − b^2)/2ca

cos A = (b^2 + c^2 − a^2) / 2bc
cos A = (10^2+20^2-14^2)/200
cos A = (100+400-196)/200
cos A = (500-196)/200
cos A = (304)/200
cos A = (1.52)
A = cos^-1(1.52) = 40.54 degrees

cos B = (c^2+a^2-b^2)/2ca
cos B = (20^2+14^2-10^2)/280
cos B = (400+196-100)/280
cos B = (496)/280
cos B ≈ 1.77
B = cos^-1(1.77) = 27.66 degrees

we have two methods left to find the measure of angle C:
method 1 :
cos C = (a^2+b^2-c^2)/2ab
cos C = (14^2+10^2-20^2)/140
cos C = (196+100-400)/140
cos C = (-104)/140
cos C ≈ -0.74

C = cos^-1(-0.74) = 111.8 degrees

method 2: 40.54+27.66 = 68.2
180-68.2=111.8

The measure of angle A: 40.54
The measure of angle B: 27.66
The measure of angle C: 111.8

6 0

4 years ago

Make x the subject: y=x+p/x-p step-by-step explanation please

Vedmedyk [2.9K]

Answer:

x = p + yp / y - 1

Step-by-step explanation:

y = x+p / x-p

y(x-p) = x + p

y(x-p) -x = p

yx - yp - x = p

yx - x = p + yp

x(y - 1) = p + yp

x = p + yp / y - 1

3 0

2 years ago

ian picked 5 times as many beries as michelle joe picked 7 times as many berries as michelle together they picked 208 berries ho

Levart [38]

Let x represent the amount michelle has.
The equation would be: 5x+7x+x=208
And to solve it you need to combine like terms: 5x+7x+x=13x
13x=208 divide both sides by 13 and you get that x equals to 16.
And this is how much each person got:
Michelle-16
Ian-80
Joe-112.
Plz thank you me. bye :)

6 0

3 years ago