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3 years ago

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Mathematics

1 answer:

Ray Of Light [21]3 years ago

5 0

x=12,y=12√3

sin60=y/24

√3/2×24=y

y=12√3

again

24^2=x^2+y^2

576=x²+12×12×3

x²=576-432

x=√144

x=12

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Which expression is equivalent to *picture attached*

DiKsa [7]

Answer:

The correct option is;

$4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )$

Step-by-step explanation:

The given expression is presented as follows;

$\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right )$

Which can be expanded into the following form;

$\sum\limits _{n = 1}^{50} \left (4\cdot n^2 + 3 \cdot n\right ) = 4 \times \sum\limits _{n = 1}^{50} \left n^2 + 3 \times\sum\limits _{n = 1}^{50} n$

From which we have;

$\sum\limits _{k = 1}^{n} \left k^2 = \dfrac{n \times (n+1) \times(2n+1)}{6}$

$\sum\limits _{k = 1}^{n} \left k = \dfrac{n \times (n+1) }{2}$

Therefore, substituting the value of n = 50 we have;

$\sum\limits _{n = 1}^{50} \left k^2 = \dfrac{50 \times (50+1) \times(2\cdot 50+1)}{6}$

$\sum\limits _{k = 1}^{50} \left k = \dfrac{50 \times (50+1) }{2}$

Which gives;

$4 \times \sum\limits _{n = 1}^{50} \left n^2 = 4 \times \dfrac{n \times (n+1) \times(2n+1)}{6} = 4 \times \dfrac{50 \times (50+1) \times(2 \times 50+1)}{6}$

$3 \times\sum\limits _{n = 1}^{50} n = 3 \times \dfrac{n \times (n+1) }{2} = 3 \times \dfrac{50 \times (51) }{2}$

$\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right ) = 4 \times \dfrac{50 \times (50+1) \times(2\times 50+1)}{6} +3 \times \dfrac{50 \times (51) }{2}$

Therefore, we have;

$4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )$ .

4 0

3 years ago

Find the discriminant.

qwelly [4]

In order to find the discriminant:
b^2-4ac

A= 1, B= 6, C=8

(6)^2-4(1)(8) = 4

Therefore, the equation has one real solution

4 0

3 years ago

Hey, can anyone help me with this? Okay, so in the equation 10 + 3x= -17 . The answer or (x) = -9 because you minus 10 on both s

Delvig [45]

Answer:

You do -17 + -10 inorder to change the operation used because both negatives does not mathematically look nice.

Step-by-step explanation:

To isolate the unknown, we need to move all the numbers on one side of the equal sign and all the unknow variables on one side.

Here we move 10 on the other side by taking away 10 both sides

10 + 3x = -17

-10 -10

then we are left with only 3x on one side and -27 on the other side because -17 - -10 = -27 , in this case it is acknowledge to change the operation from minus to add because the two minus are together, so we say -17 + -10 .

3x = -27

/3 /3

x = -9

6 0

4 years ago

Help me.............

geniusboy [140]

Answer:

28.) c.

29.) a and c.

30.) a.

y=3x/5 +18/5

(-6, 0)

31.) y=x-4

Step-by-step explanation:

28.)

pounds is equal to the y value of a graph, while months is equal to the x value of the graph. slope is equal to y/x. Therefore, it is the slope.

29.) rearrange the equation to isolate the y value and then divide every equation by 2. you will then get y=4x+8. When you plug each of the points in, you will notice only a and c are true.

30.) a.

The line equation is: y=mx+b. First find the slope. You can do that with subtracting y values over dividing x values. You should get: 3-6/-1-4=3/5.

With this slope, plug in one of the points for the x and y values, and solve for b. I used the point (-1, 3) and got b=18/5

For this, I found that 0= 3(-6)/5+18/5

31.) Find the slope by subtracting the y values over subtracting the x values. This should give you a slope of 1. After you find the slope, plug in your slope as m in the line equation: y=mx+b. Next, find a point in that plot and plug those in to find the y intercept (b). I chose (-2, -6) and (2, -2) and got a slope of -4. However, you can also see that when x=0, y=-4, so that could also be a nice shortcut.

Hope this helps!

7 0

4 years ago

NEED HELP DUE TODAY !

podryga [215]

The right way to go is C

6 0

3 years ago