1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Veseljchak [2.6K]
3 years ago
8

Write the equation for a line in standard form (Ax+By+C) that is perpendicular to y = 3x -

Mathematics
1 answer:
salantis [7]3 years ago
8 0

Answer:

x+3y-6=0

Step-by-step explanation:

given eqn is y=3x-2 which is 3x-y-2=0

the eqn of line perpendicular to given eqn is -x+3y+k=0

it passes through (6,4)

-6+3*4+k=0

or,. -6+12+k=0

or, k= -6

therefore, the eqn of line perpendicular to given eqn is x+3y-6=0

You might be interested in
What is (528^5 x 2419^9)^6 - 328?
damaskus [11]

Answer:

Exact Form:

(41036433850368 ^6  x  2419 ^54 )− 328

Decimal Form:

2.48516121  x  10 ^264

6 0
3 years ago
Match the numerical expressions to their simplest forms.
Aloiza [94]

Answer:

(a^6b^1^2)^\frac{1}{3} = a^2b^4

\frac{(a^5b^3)^\frac{1}{2}}{(ab)^-^\frac{1}{2}} = a^3b^2

(\frac{a^5}{a^-^3b^-^4})^\frac{1}{4} = a^2b

(\frac{a^3}{ab^-^6})^\frac{1}{2} = ab^3

Step-by-step explanation:

Simplify each of the expressions:

1

(a^6b^1^2)^\frac{1}{3}

Distribute the exponent. Multiply the exponent of the term outside of the parenthesis by the exponents of the variable.

(a^6b^1^2)^\frac{1}{3}

a^6^*^\frac{1}{3}b^1^2^*^\frac{1}{3}

Simplify,

a^2b^4

2

Use a similar technique to solve this problem. Remember, a fractional exponent is the same as a radical, if the denominator is (2), then the operation is taking the square root of the number.

\frac{(a^5b^3)^\frac{1}{2}}{(ab)^-^\frac{1}{2}}

Rewrite as square roots:

\frac{\sqrt{a^5b^3}}{\sqrt{(ab)}^-^1}

A negative exponent indicates one needs to take the reciprocal of the number. Apply this here:

\frac{\sqrt{a^5b^3}}{\frac{1}{\sqrt{ab}}}

Simplify,

\sqrt{a^5b^3}*\sqrt{ab}

Since both numbers are under a radical, one can rewrite them such that they are under the same radical,

\sqrt{a^5b^3*ab}

Simplify,

\sqrt{a^6b^4}

Since this operation is taking the square root, divide the exponents in half to do this operation:

a^3b^2

3

(\frac{a^5}{a^-^3b^-^4})^\frac{1}{4}

Simplify, to simplify the expression in the numerator and the denominator, the base must be the same. Remember, the base is the number that is being raised to the exponent. One subtracts the exponent of the number in the denominator from the exponent of the like base in the numerator. This only works if all terms in both the numerator and the denominator have the operation of multiplication between them:

(\frac{a^8}{b^-^4})^\frac{1}{4}

Bring the negative exponent to the numerator. Change the sign of the exponent and rewrite it in the numerator,

(a^8b^4)^\frac{1}{4}

This expression to the power of the one forth. This is the same as taking the quartic root of the expression. Rewrite the expression with such,

\sqrt[4]{a^8b^4}

SImplify, divide the exponents by (4) to simulate taking the quartic root,

a^2b

4

(\frac{a^3}{ab^-^6})^\frac{1}{2}

Using all of the rules mentioned above, simplify the fraction. The only operation happening between the numbers in both the numerator and the denominator is multiplication. Therefore, one can subtract the exponents of the terms with the like base. The term in the denomaintor can be rewritten in the numerator with its exponent times negative (1).

(a^3^-^1b^(^-^6^*^(^-^1^)^))^\frac{1}{2}

(a^2b^6)^\frac{1}{2}

Rewrite to the half-power as a square root,

\sqrt{a^2b^6}

Simplify, divide all of the exponents by (2),

ab^3

7 0
3 years ago
Suppose it takes 4 hours for a certain strain of bacteria to reproduce by dividing in half. If 70 bacteria are present to begin
Sauron [17]

Answer:

1 day: 4480

2 days: 8960

3 days: 13440

f^{-1}(x) = \sqrt{\frac{x -4}{4}} ---- function inverse

Step-by-step explanation:

Given

f(x) = 70 \cdot 64x

Solving (a): The amount present after 1 day.

Here, x =1

So:

f(1) = 70 \cdot 64*1= 4480

Solving (b): The amount present after 2 days.

Here, x =2

So:

f(2) = 70 \cdot 64*2= 8960

Solving (c): The amount present after 3 days.

Here, x = 3

So:

f(3) = 70 \cdot 64*2= 13440

Solving (d): The inverse function of:

f(x)= 4x^2 + 4

Replace f(x) with y

y= 4x^2 + 4

Swap x and y

x= 4y^2 + 4

Rewrite as:

4y^2 = x -4

Divide by 4

y^2 = \frac{x -4}{4}

Take square roots

y = \sqrt{\frac{x -4}{4}}

Replace y with function inverse

f^{-1}(x) = \sqrt{\frac{x -4}{4}}

6 0
3 years ago
Based on the graph below, how would you describe the curve?​
motikmotik

Answer:

It's A.

Step-by-step explanation:

For every value of x there is one value of y  - we can draw a vertical line through any value of x and it will pass through only one value of y.

Therefore it is a one-to-one function.

8 0
3 years ago
Read 2 more answers
A bag of marbles contains 1 green, 5 red, and 2 blue. Find the probability of picking a red marble, putting it back in the
sleet_krkn [62]

Answer:

Red = 25/32768

Blue = 4/64

Step-by-step explanation:

Green Marbles = 1

Red Marbles = 5

Blue Marbles = 2

Probability of picking a red marble = 5/8 x 5/8 x 5/8 x 5/8 x 5/8 = 25/32768

Probability of picking a blue marble = 2/8 x 2/8 = 4/64

6 0
3 years ago
Other questions:
  • How to simplify (-12)-7×(-12)7
    12·1 answer
  • PPPLLLEEEZZZ HHHEEELLLPPP Select from the drop-down menu to correctly identify the property shown.
    10·2 answers
  • Help please... extra points
    5·2 answers
  • 12=x÷8<br> I need help please
    11·2 answers
  • An airplane needs to head due north, but there is a wind blowing from the northeast at 50 km/hr. The plane flies at an airspeed
    12·1 answer
  • What is the range of this function?​
    7·1 answer
  • Which sign makes the statement true? -3 ? |3| is it greater than, less than, or equal to?​
    15·1 answer
  • I been confused about this for the longest whats this answer 1500g+10.0m/s^2.
    11·1 answer
  • A mistake was made in the steps shown to simplify the expression. Which step includes the mistake?
    5·1 answer
  • What is the area of a parallelogram if is length is x+1 and height is x+8?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!