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2 years ago

What is the value of x?

Mathematics

2 answers:

disa [49]2 years ago

7 0

Answer:

x = 98

Step-by-step explanation:

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle, thus

x = 45 + 53 = 98

bixtya [17]2 years ago

6 0

Answer:

98°

Step-by-step explanation:

53 + 45 = x

because two interior angles in a triangle that is not adjacent to exterior angle is equal to that exterior angles

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Find the solution of the given initial value problem. ty' + 6y = t2 − t + 1, y(1) = 1 6 , t > 0

gtnhenbr [62]

Answer:

Step-by-step explanation:

Given is a differential equation as

$ty' + 6y = t^2 - t + 1, y(1) = 1 6 , t > 0$

Divide this by t to get in linear form

$y'+6y/t = t-1+1/t$

This is of the form

y' +p(t) y = Q(t)

where p(t) = 1/t $e^(\int 1/tdt) = t$

So solution would be

$yt = \int t^2-t+1 dt\\= t^3/3-t^2/2+t+C$

siubstitute y(1) = 16

$16 = 16^3/3-128+1+C\\C = -1206$

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2 years ago

How do you graph -1/5x-1 and 4/5x-6

kakasveta [241]

Answer:

The points for the given to linear equations is (5 , - 2) and (5 , - 1)

The points is plotted on the graph shown .

Step-by-step explanation:

Given as :

The two linear equation are

y = $\dfrac{-1}{5}$ x - 1 ...........1

y = $\dfrac{4}{5}$ x - 6 ...........2

Now, Solving both the linear equations

Put the value of y from eq 2 into eq 1

I.e $\dfrac{4}{5}$ x - 6 = $\dfrac{-1}{5}$ x - 1

Or, $\dfrac{4}{5}$ x + $\dfrac{1}{5}$ x = 6 - 1

Or, $\dfrac{4 + 1}{5}$ x = 5

or, $\dfrac{5}{5}$ x = 5

∴ x = 5

Now, Put the value of x in eq 1

So, y = $\dfrac{-1}{5}$ x - 1

Or, y = $\dfrac{-1}{5}$ × 5 - 1

or, y = $\dfrac{-5}{5}$ - 1

Or, y = - 1 - 1

I.e y = -2

So, For x = 5 , y = - 2

Point is ( $x_1$ , $y_1$ ) = (5 , - 2)

Again , put the value of x in eq 2

So, y = $\dfrac{4}{5}$ x - 6

Or, y = $\dfrac{4}{5}$ × 5 - 6

Or, y = $\frac{4\times 5}{5}$ - 6

Or, y = 4 - 6

I.e y = - 2

So, For x = 5 , y = - 2

Point is ( $x_2$ , $y_2$ ) = (5 , - 2)

Hence, The points for the given to linear equations is (5 , - 2) and (5 , - 2)

The points is plotted on the graph shown . Answer

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2 years ago

Jose could win $17 for guessing the correct number of Jelly Beans in a fat. The estimates that there are 450 Jelly Beans in the

Shkiper50 [21]

Answer:

Step-by-step explanation:

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2 years ago

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2 years ago

Prove that an = 4^n + 2(-1)^nis the solution to

olga nikolaevna [1]

Answer:

See proof below

Step-by-step explanation:

We have to verify that if we substitute $a_n=4^n+2(-1)^n$ in the equation $a_n=3a_{n-1}+4a_{n-2}$ the equality is true.

Let's substitute first in the right hand side:

$3a_{n-1}+4a_{n-2}=3(4^{n-1}+2(-1)^{n-1})+4(4^{n-2}+2(-1)^{n-2})$

Now we use the distributive laws. Also, note that $(-1)^{n-1}=\frac{1}{-1}(-1)^n=(-1)(-1)^{n}$ (this also works when the power is n-2).

$=3(4^{n-1})+6(-1)^{n-1}+4(4^{n-2})+8(-1)^{n-2}$

$=3(4^{n-1})+(-1)(6)(-1)^{n}+4^{n-1}+(-1)^2(8)(-1)^{n}$

$=4(4^{n-1})-6(-1)^{n}+8(-1)^{n}=4^n+2(-1)^n=a_n$

then the sequence solves the recurrence relation.

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2 years ago