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Irina-Kira [14]
3 years ago
8

4a – 16 = a - 15 how do I solve ​

Mathematics
1 answer:
miv72 [106K]3 years ago
8 0

Answer:

a = \frac{1}{3}

Step-by-step explanation:

4a -16 = a - 15

both left and right -a

then

4a - 16 -a = a - 15 -a

then

4a -a -16 = a -a -15

then

3a -16 = -15

both left and right + 16

then

3a -16 + 16 = -15 + 16

then

3a = 1

both left and right ÷3

then

3a ÷ 3 =1 ÷ 3

then

a = \frac{1}{3}

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Write the vector v in the form aiplusbj​, given its magnitude left norm Bold v right norm and the angle alpha it makes with the
photoshop1234 [79]

Answer:

6\sqrt{3}i-6j

Step-by-step explanation:

Given:

The magnitude, v=12

The angle \alpha it makes with the positive​ x-axis =150^0

Now for a vector (x,y)

  • \alpha =tan^{-1}(\frac{y}{x} ) ; and
  • v=\sqrt{x^2+y^2}

Therefore:

150 =tan^{-1}(\frac{y}{x} )\\\frac{y}{x} =tan 150\\\frac{y}{x}=-\frac{\sqrt{3} }{3}

y=-\frac{x \sqrt{3}}{3}

Similarly:

v=\sqrt{x^2+y^2}\\12=\sqrt{x^2+y^2}\\12^2=x^2+y^2\\144=x^2+y^2

144=x^2+(-\frac{x \sqrt{3}}{3} )^2\\144=x^2+\frac{3x^2}{9} \\144=\frac{4x^2}{3}\\4x^2=144 X 3=432\\x^2=108\\x=6\sqrt{3}

Recall that:

y=-\frac{x \sqrt{3}}{3}\\y=-\frac{6\sqrt{3}  \sqrt{3}}{3}=-6

Therefore: (x,y)=(6\sqrt{3}, -6)

The vector in the form ai+bj is therefore:

6\sqrt{3}i-6j

6 0
4 years ago
I need help on this question
max2010maxim [7]
Answer A
21 mm
7 x 3 = 21
4 0
3 years ago
Find lim x→3 sqrt 2x+3-sqrt 3x/ x^2-3x. you must show your work or explain your work in words plsss I need help
sineoko [7]

I'm assuming the limit is supposed to be

\displaystyle\lim_{x\to3}\frac{\sqrt{2x+3}-\sqrt{3x}}{x^2-3x}

Multiply the numerator by its conjugate, and do the same with the denominator:

\left(\sqrt{2x+3}-\sqrt{3x}\right)\left(\sqrt{2x+3}+\sqrt{3x}\right)=\left(\sqrt{2x+3}\right)^2-\left(\sqrt{3x}\right)^2=-(x-3)

so that in the limit, we have

\displaystyle\lim_{x\to3}\frac{-(x-3)}{(x^2-3x)\left(\sqrt{2x+3}+\sqrt{3x}\right)}

Factorize the first term in the denominator as

x^2-3x=x(x-3)

The x-3 terms cancel, leaving you with

\displaystyle\lim_{x\to3}\frac{-1}{x\left(\sqrt{2x+3}+\sqrt{3x}\right)}

and the limand is continuous at x=3, so we can substitute it to find the limit has a value of -1/18.

7 0
3 years ago
How much money will you have if you started with $1200 and put it in an account that earned 7.3% every year for 10 years?
andrezito [222]
So an exponential equation is gonna be used for this problem. The formula for such is y=ab^x , in which the a variable is the initial value and the b variable is the growth/decay rate.

For this situation, 1200 is gonna be your a variable since you've started out with it. And as for your b variable, its gonna be 107.3%, or 1.073, since it's increasing.

Your equation should look like this: y=1200(1.073)^x and from here just plug in 10 into the x variable and solve.

Multiply (1.073)^10 (don't round answers until the end), and take that answer and multiply it with 1200, your answer should be $2427.61.

y=1200(1.073)^{10} \\ y=2427.61
8 0
3 years ago
What fraction of a gallon is 3 pints?
Nitella [24]
<span>There are 8 pints in 1 gallon, so 3 pints is 3/8 of a gallon </span>
4 0
3 years ago
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