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sp2606 [1]
2 years ago
7

Find all the points that are on the x-axis that are a distance of 13 units from the point (12,-5).

Mathematics
1 answer:
Viefleur [7K]2 years ago
6 0

Let point A(x,y) be the point on the x-axis. All points that lie on the x-axis have y-coordinate equal to 0, then A(x,y).

Find the distance from point A to point (12,-5):

d=\sqrt{(x-12)^2+(0-(-5))^2}=\sqrt{(x-12)^2+25}.

This distance is equal to 13, then

\sqrt{(x-12)^2+25}=13,\\ \\(x-12)^2=169-25,\\ \\(x-12)^2=144,\\ \\x-12=12 \text{ or } x-12=-12,\\ \\ x=24 \text{ or }x=0.

You get two ponts (0,0) and (24,0).

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Infinite over E n=1 4(0.5)^n-1
yan [13]

Answer:

S = 8

Step-by-step explanation:

An infinite geometric series is defined as limit of partial sum of geometric sequences. Therefore, to find the infinite sum, we have to find the partial sum first then input limit approaches infinity.

However, fortunately, the infinite geometric series has already set up for you. It’s got the formula for itself which is:

\displaystyle \large{\lim_{n\to \infty} S_n = \dfrac{a_1}{1-r}}

We can also write in summation notation rather S-term as:

\displaystyle \large{\sum_{n=1}^\infty a_1r^{n-1} = \dfrac{a_1}{1-r}}

Keep in mind that these only work for when |r| < 1 or else it will diverge.

Also, how fortunately, the given summation fits the formula pattern so we do not have to do anything but simply apply the formula in.

\displaystyle \large{\sum_{n=1}^\infty 4(0.5)^{n-1} = \dfrac{4}{1-0.5}}\\\\\displaystyle \large{\sum_{n=1}^\infty 4(0.5)^{n-1} = \dfrac{4}{0.5}}\\\\\displaystyle \large{\sum_{n=1}^\infty 4(0.5)^{n-1} = 8}

Therefore, the sum will converge to 8.

Please let me know if you have any questions!

6 0
2 years ago
How do you get the number 24 with the numbers 2,6,4,1
elena55 [62]

Answer:

(2+6)*(4-1) = 24

(2-1)*(6*4) = 24

(2-1)*6*4 = 24

(2-1)*(4*6) = 24

(2-1)*4*6 = 24

(6+2)*(4-1) = 24

6*(2-1)*4 = 24

6*(2-1)*4 = 24

6/(2-1)*4 = 24

6/(2-1)*4 = 24

3 0
3 years ago
The given statement is true or t<br> (-4+6i)-(12-5i) = -16+ i
Pavel [41]
The answer is x=mc^2
8 0
1 year ago
Read 2 more answers
Jackson is starting an exercise program. The first day he will spend 30 minutes on the treadmill. He will increase his time on t
yulyashka [42]

Answer:

40 minutes.

Step-by-step explanation:

  • time spent on the thread mill as a function of d(day) = t(d)

= 30 +2(d-1) minutes

[where d represents day number]

(when d is 1 the time spent should be 30

so substitute d=1 and check it will be 30 only.

on first day he will spend 30 minutes so, I added 30 .

and on every additional day( these additional days are excluding first day), he will increase the time by 2 minutes.so, I added 2(d-1) to initial 30 minutes)

  • so, T(6), the minutes he will spend on the treadmill on day 6=

=30+2(6-1)

=30+2(5)

=30+10

=40 minutes

3 0
3 years ago
The coordinates of the 3 of the vértices of a parallelogram are (-7, 3), (-6, 1), and (-4, 5). What is the equation for the line
Natali [406]

We know, opposite sides are parallelogram is parallel, therefore slopes are equal.

Slope of line one :

m=\dfrac{-7-(-6)}{3-1}\\\\m =\dfrac{-1}{2}\\\\m= -0.5

So, equation of other line passing through (-4,5) and have slope of -0.5 is :

y-5 = -0.5( x-(-4))

y-5 = -0.5x - 2

y  + 1/2x = 3

2y + x = 6

Therefore, equation of line containing the (-4, 5) is 2y + x = 6.

Hence, this is the required solution.

6 0
3 years ago
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