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Assoli18 [71]
2 years ago
8

If (a+b)^2=54, and (a-b)^=46, then a^2+b^2=?

Mathematics
1 answer:
erastovalidia [21]2 years ago
4 0

(a+b)^2 =a^2 +b^2 + 2ab = 54~~~.....(i)\\\\(a-b)^2 = a^2 +b^2 -2ab = 46~~~.....(i)\\\\\\(i)+(ii):\\\\(a+b)^2 +(a-b)^2  = 54+46\\\\\implies a^2 +b^2 + 2ab + a^2 +b^2 - 2ab =100\\\\\implies 2a^2 +2b^2 =100\\\\ \\\implies 2(a^2 +b^2) =100\\\\\implies a^2 +b^2 = \dfrac{100}2 = 50

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Find the value of 5x-6 given that 2x-7=9​
erik [133]

Answer:

34

Step-by-step explanation:

Given that

2x - 7 = 9 ← solve for x

Add 7 to both sides

2x = 16 ( divide both sides by 2 )

x = 8

Substitute x = 8 into 5x - 6

5x - 6 = (5 × 8) - 6 = 40 - 6 = 34

4 0
3 years ago
An investor invested a total of $2500 in two mutual funds. One fund earned a 5% profit while the other earned a 3% profit. If th
7nadin3 [17]

Answer:

$500 and $2000

Step-by-step explanation:

Let x represent the total investment = $2500

also, this total is split into two different funds

Lets represent these funds as a and b, such that fund a yields a profit of 3% and fund b yield a profit of 5%

So,

a + b = x

a + b =  2500   ......eq 1

Profit from each fund gives;

0.03 a + 0.05b = 115     ....eq 2

Solve simultaneously using substitution method

From eq 1;

b = 2500 - a

Slot in this value in eq 2

0.03a + 0.05 (2500 - a) = 115

expand

0.03a + 125 - 0.05a = 115

collect like terms

0.03a - 0.05a = 115 - 125

-0.02a = -10

Divide both sides by -0.02

a =  $500

Put this value of a in eq 1

500 + b =  2500

Subtract 500 from both sides

b = 2500 - 500

b = $2000

3 0
3 years ago
For which value of a does Limit of g(x) as x approaches alpha not exist?​
Hunter-Best [27]

The value of a where the Limit of g(x) as x approaches alpha not exist are -1 and 1

<h3>Limit of a function</h3>

The limit of a function is the limit of a function as x tends to a value.

From the given graph, you can see that the function g(x) goes large at the point where the arrows orange and purple point down from the x-coordinates -1 and 1.

Hence the value of a where the Limit of g(x) as x approaches alpha not exist are -1 and 1

Learn more on limit of a function here: brainly.com/question/23935467

#SPJ1

7 0
1 year ago
Uhbjhbjhbjhbjhbjhbjhbfg
Len [333]

Answer:

2/5 (B)

Step-by-step explanation:

x^\frac{1}{y}=\sqrt[y]{x}

So:

\sqrt{\frac{4}{25}}=\frac{2}{5} because

(\frac{x}{y})^z=\frac{x^z}{y^z}

5 0
2 years ago
A jar contains 8 white marbles, 6 black marbles, and 1 red marbles. If one marble is drawn at random, find the probability that
Mariana [72]

Answer:

Hi there!

6/15 is the probability that the marble is black!

Step-by-step explanation:

Oki, so lets's find the total number of marbles first!

8 + 6 + 1 = 14 + 1 = 15

And just turn it into a fraction!(very simple and easy)

6/15

5 0
3 years ago
Read 2 more answers
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