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3 years ago

81^5=3^x What does “x” equal?

Mathematics

1 answer:

Lynna [10]3 years ago

7 0

Answer:

$x =2 0$

Step-by-step explanation:

${81}^{5} = {3}^{x}$

We know that 3^4 = 81. So :

$= > { ({3}^{4}) }^{5} = {3}^{x}$

$= > {3}^{4 \times 5} = {3}^{x}$

$= > {3}^{20} = {3}^{x}$

Here both the Right hand side & Left hand side has same base i.e. have 3 as base in both the sides.

So , eliminating the base gives :-

$x = 20$

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How many solutions does the following equation have? -3z + 9 -2z = -12 - 5z

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Juanita bought 3 apples, 2 oranges, and 8 lemons What is the ratio of oranges to apples?

Oduvanchick [21]

The ratio to oranges to apples is 2:3,2-3 or 2 to 3

Hopes this helps

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3 years ago

Find an equation for the plane containing the point (1, 2, 3) and parallel to the plane x 2y 3z

sergeinik [125]

Answer:

Step-by-step explanation:

Heres the full question and solution:

Find an equation for the plane containing the point (1,2,3) and parallel to the plane x+2y+3z=5.

solution

Any plane parallel to $x+2y+3z=5$ is $x+2y+3z=d
$

since the plane is passing through $(1,2,3)$

we substitute point in equation

$1+2\times 2+3\times 3=d\\d=14
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equation of the line is $x+2y+3z=14$

4 0

3 years ago

For a direct variation, describe how the constant variation affects whether y increases or decreases as x increases.

Nataly_w [17]

<span>A direct variation is of the form
y = kx
where k is the constant of variation

In most cases k is positive in which case
y increase in direct proportion to an increase in x
Example
k = 2
x = 1,       y = kx = 2(1)= 2
x = 3,       y = kx = 2(3) = 6

Occasionally k is negative in which case
y decreases in direct proportion to an increase in x
Example
k = -2
x = 1,       y = kx = (-2)(1) = -2
x = 3,       y = kx = (-2)(3) = -6
---------------------------

This is not to be confused with an indirect variation which is of the form
y = k/x
where k is the constant of variation
Example

When k is positive y decreases inversely as x increases
k = 2
x = 1,       y = k/x = 2/1 = 2
x = 3, y = k/x = 2/3 = 2/3

When k is negative y increases inversely as x increases
k = -2
x = 1,       y = k/x = -2/1 = -2
x = 3        y = k/x = -2/3 = -2/3</span>

8 0

3 years ago

The line (x, y, z) = (1 − 2t, 2t − 1, t), with t as the parameter, is denoted by L. The point Q is (1, 2, 3).

inessss [21]

Answer:

P = (-1,1,1)

Step-by-step explanation:

for the line

L (t) = (1 − 2t, 2t − 1, t)

since the vector that is tangent to L is its derivative L'=dL/dt , then

L'= dL/dt (t) = (−2, 2 , 1)

then the vector PQ (P to Q) is

PQ = (x,y,z) - (1, 2, 3) = ( x-1 , y-2 ,z-3)

since P belongs to L → x= 1-2t . y=2t-1 and z=t ,

PQ = ( x-1 , y-2 ,z-3) = (-2t , 2t-3 , t-3)

to be ortogonal to L , PQ should be ortogonal to L' , then the dot product between PQ and L should be 0

PQ * L' = 0

(-2t , 2t-3 , t-3)* (−2, 2 , 1) =0

4t + (4t-6) + (t-3) = 0

9t - 9= 0

t = 1

then

P = L(t=1) = ( 1-2*1 , 2*1-1 , 1 ) = (-1,1,1)

P = (-1,1,1)

5 0

3 years ago