MATHEMATICS HIGH SCHOOL

Expand or condense the following expression: 3log_2y+log_25-log_2 10

Answers

Answer 1

Answer:

Answer:

HI,

Step-by-step explanation:

3log_2y+log_25-log_2 10

should be written like :

$3log_2(y)+log_2(5)-log_2(10)\n\n=log_2(y^3)+log_2(5)-log_2(10)\n\n=log_2((5y^3)/(10) )\n\n=\boxed{log_2((y^3)/(2) )}$

Answer 2

Answer:

Final answer:

To expand or condense the given expression, we can use the properties of logarithms.

Explanation:

To expand or condense the given expression, we can use the properties of logarithms. Based on the properties of logarithms:

Applying these properties, the expanded form of the expression is:

3log2(y) + log2(5) - log2(10) = log2(y3) + log2(5) - log2(10)

This expression cannot be further simplified unless the values of y, 5, and 10 are known.

Learn more about Logarithms here:

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Tara incorrectly estimates 36,591,000,000 meters as 4x10^6 meters explain tara's mistake?

Answers

Answer:

4 * 10¹⁰

Step-by-step explanation:

Estimation:

The estimate value of 36,591,000,000 is 40,000,000,000.

40,000,000,000 = 4 * 10¹⁰

Answer: 4 * 10¹⁰

The bike is on sale for $130. If th original price of the bike is $200, what is the percent discount.

Answers

PERCENT discount=discount/originalprice
rembmer that percent means parts out of 100 so
x%=x/100

find disctount first
200 minus disctount=130
add discount to both sides
200=130+discount
subtract 130 from both sides
70=discount

original parice=200
dscount=70
percent discount=70/200
convert bottom number to 100 by dividind top and bottom by 2
70/2=35
200/2=100
35/100=35%

answer is 35% discount

Review the graph.What is the magnitude of the vector shown?

5
13
StartRoot 5 EndRoot
StartRoot 13 EndRoot

Answers

The required magnitude of the vector is √13. Option D is correct.

A graph is given, that shows the vector, the magnitude of the vector is to be determined.

What is vertex form?

Vector form is defined as representing any point in space that has both magnitude and direction. A point k in space is represented as a vector OKi + OKj, which denotes the vector line, OK joining the line from the origin O to the point k. The vector form is used to define a line or a plane in a 3D space.

From the figure,
given vector can be expressed as,
$\bar v = 3\bar i+2\bar j$
now the magnitude of vactor,
$|\bar v| = √(3^2+2^2)\n|\bar v| = √(9+4)\ \n|\bar v| = √(13)\$

Thus, the required magnitude of the vector is √13. Option D is correct.

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Answer:

D. sqrt 13

Step-by-step explanation:

took on edge :)

N to the first power divided by (n - r) to the first power

Answers

$(n^1)/((n-r)^1)=(n)/(n-r)$

What is the equation of a parabola whose vertex is at the origin and whose directrix is y = 3?

Answers

The equation of a parabola whose vertex is at the origin and whose directrix is y = 3 will be y = 12x².

What is the parabola?

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

Let the point (h, k) is the vertex of the parabola and a is the focus.

Then the equation of the parabola will be given as,

y = 4a(x - h)² + k

The vertex of the parabola is at the origin, then the equation of the parabola will be

y = 4a(x - 0)² + 0

y = 4ax²

We know that the distance between the directrix - graph and focus graph is the same.

Then the value of focus will be 3.

Then the equation of the parabola will be

y = 4 × 3 × x²

y = 12x²

The equation of a parabola whose vertex is at the origin and whose directrix is y = 3 will be y = 12x².