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FrozenT [24]
3 years ago
6

The sum of 4 times a number and -2 is equal to the sum of 5 times the number and -2. Find the number

Mathematics
1 answer:
MArishka [77]3 years ago
6 0
4n(-2)=(5)(-2)
-8n=-10
—— —-
-8 -8

n= 5/4
n= 1 1/4

So the final answer is n= 1.25
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3 years ago
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If a = √3-√11 and b = 1 /a, then find a² - b²​
Serga [27]

If b=\frac1a, then by rationalizing the denominator we can rewrite

b = \dfrac1{\sqrt3-\sqrt{11}} \times \dfrac{\sqrt3+\sqrt{11}}{\sqrt3+\sqrt{11}} = \dfrac{\sqrt3+\sqrt{11}}{\left(\sqrt3\right)^2-\left(\sqrt{11}\right)^2} = -\dfrac{\sqrt3+\sqrt{11}}8

Now,

a^2 - b^2 = (a-b) (a+b)

and

a - b = \sqrt3 - \sqrt{11} + \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{9\sqrt3 - 7\sqrt{11}}8

a + b = \sqrt3 - \sqrt{11} - \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{7\sqrt3 - 9\sqrt{11}}8

\implies a^2 - b^2 = \dfrac{\left(9\sqrt3 - 7\sqrt{11}\right) \left(7\sqrt3 - 9\sqrt{11}\right)}{64} = \boxed{\dfrac{441 - 65\sqrt{33}}{32}}

5 0
2 years ago
3n+7 write the first five terms
harkovskaia [24]

Answer:

10

13

15

17

22

Step-by-step explanation:

the first 5 terms will be 1,2,3,4 and 5.

I guess...

6 0
3 years ago
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Line segment GT contains the point G(−3, 5) and a midpoint at A(1, −4). What is the location of endpoint T?
algol [13]

Imagine you're moving along the segment. Since the midpoint is in the middle of the segment (obviously), it means that when you've traveled from G to A, you're halfway through your journey, along both x and y directions. So, let's break the problem in two and analyze both directions.


Along the x axis, you've moved from -3 to 1, so you moved 4 units forward. This means that you have 4 units still to go, and your journey will end at coordinate 5.


Similarly, along the y axis, you've moved from 5 to -4, so you moved 9 units downward. This means that you have 9 units still to go, and your journey will end at coordinate -13.


So, the coordinates of the endpoint are T = (5,-13)


If you prefer a more analyitical approach, simply write the definition of the midpoint and solve it for the coordinates of T.


We have G = (-3, 5) and T = (x_T,y_T). The midpoint is computed as


A = \left( \frac{-3+x_T}{2},\frac{5+y_T}{2} \right) = (1, -4)


So, you have the equations


\frac{-3+x_T}{2} = 1,\qquad \frac{5+y_T}{2} = -4


Multply both equations by 2 to get


-3+x_T = 2,\qquad 5+y_T = -8


Move the constants to the right hand sides to get


x_T = 5,\qquad y_T = -13

8 0
3 years ago
Which two numbers have a product of 18 and a sum of -11?
ValentinkaMS [17]

Answer:

X=-8

Y=10

Step-by-step explanation:

5 0
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