MATHEMATICS HIGH SCHOOL

Expand the logarithmic expression.
log(b)squrt(13/73)

Answers

Answer 1

Answer:

Answer:

$\frac{log_b{13}-log_b{73}}{2}$

Step-by-step explanation:

$log_b{\sqrt{(13)/(73)}}$

First we remove the square root

$log_b({(13)/(73))^(1)/(2)}$

As per log property we can move the exponent 1/2 before log

$(1)/(2)log_b{(13)/(73)}$

Now we apply log property to expand log (13/73)

log(a/b)= log(a) - log(b)

$(1)/(2)log_b{13}-log_b{73}}$

$\frac{log_b{13}-log_b{73}}{2}$

Answer 2

Answer: $\log_b\sqrt{(13)/(73)}=\frac12\log_b(13)/(73)=\frac{\log_b13-\log_b73}2$

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Which type of triangle is formed with the points A(1, 7), B(-2, 2), and C(4, 2) as its vertices?

Answers

We will have to use the distance formula in order to determine the lengths of each side of the triangle.

Distance formula: $\sqrt{(x_(2) - x_(1))^(2) + (y_(2) - y_(1))^(2) }$

Let's calculate AB first:
A (1, 7) and B (-2, 2)
A: x1 = 1 and y1 = 7
B: x2 = -2 and y2 = 2

so
$\sqrt{(-2 - 1)^(2) + (2 - 7)^(2) }$
$\sqrt{(-3)^(2) + (-5)^(2) }$
$√(9 + 25 )$
AB = $√(34)$ or (rounded to the nearest tenth) ≈ 5.8

Now let's do BC:
B: x1 = -2 and y1 = 2
C: x2 = 4 and y2 = 2

So
$\sqrt{(4 - -2)^(2) + (2 - 2)^(2) }$
$\sqrt{(6)^(2) + (0)^(2) }$
BC = $√(36 )$ or 6

Now let's do CA
C: x1 = 4 and y1 = 2
A: x2 = 1 and y2 = 7

So
$\sqrt{(1 - 4)^(2) + (7 - 2)^(2) }$
$\sqrt{(-3)^(2) + (5)^(2) }$
$√(9 + 25)$
CA = $√(34)$ or (rounded to the nearest tenth) ≈ 5.8

So let's recap:

AB ≈ 5.8
BC = 6
CA ≈ 5.8

So AB and AC are the same length while BC is .2 units longer which means this is an isosceles triangle.

Two lines have given equations. At what point do they intersect? 2x-y=1 3x=y-6

Answers

2x-y=1 and 3x=y-6,
y=2x-1 and y=3x+6,
y=2x-1 and 2x-1=3x+6,
y=2x-1 and 3x-2x=-1-6,
x=-7 and y=-14-1
x=-7 and y=-15

check:
for x=-7 and y=-15:
2x-y=1 is -14-(-15)=1 is 1=1 ok
3x=y-6 is -21=-15-6 is -21=-21 ok

answer:
lines intersect at (-7;-15)

Can some one help me with this

Answers

Answer:

the answer is C the third one 25,500

Step-by-step explanation:

Solve the following expression when b = 12 10 + b/6 + b

Answers

Answer:

Step-by-step explanation:

Given that b = 12,

10 + 12/6 + 12

= 10 + 2 + 12

= 24

Answer:

Step-by-step explanation:

10+(12/6)+12 = 24 use brackets and divide first before adding

What is the y-coordinate of the solution? Round to the nearest hundredth.
( 4x-y= 2
2x+9y= -12)

Answers

$Hi \n \n \begin{cases}4x-y=2~~----\ \textgreater \ (I) \n 2x+9y=- 12~--\ \textgreater \ (II)\end{cases} \n \n \underline{Resolution ~} \n \n~~~~~~4x-y=2 \n =\ \textgreater \ \boxed{y=4x-2}~~--\ \textgreater \ \textcircled{1} \n \n \mathbb{tttttttttttttttttttttttttttttttttttt} \n\textcircled{1}~in (II) \n \n2x+9\underbrace{y}_(4x-2)=-12 \n \n 2x+9(4x-2)=-12 \n \n 2x+36x-18=-12 \n \n \boxed{\boxed{x=0,16}} \n \n \mathbb{tttttttttttttttttttttttttttttttttttt} \n =\ \textgreater \ y=4x-2 \n ~~~~~~y=4(0,16)-2 \n ~~~~~~\boxed{\boxed{y=-1,36}}\n \n \n .$

$\therefore~(x;y)=(0,16; -1,36)$

y=-1.4
all you had to do was the elimination method

Help!
What is one and sixty-seven hundredths added to fifteen and nine tenths?