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3 years ago

Write all your answers as a fraction. 1. 8/3 - 8/5/

Mathematics

1 answer:

allsm [11]3 years ago

5 0

Answer:

16/15

Step-by-step explanation:

Simplify the following:

8/3 - 8/5

Put 8/3 - 8/5 over the common denominator 15. 8/3 - 8/5 = (5×8)/15 + (3 (-8))/15:

(5×8)/15 + (3 (-8))/15

5×8 = 40:

40/15 + (3 (-8))/15

3 (-8) = -24:

40/15 + (-24)/15

40/15 - 24/15 = (40 - 24)/15:

(40 - 24)/15

| 3 | 10

| 4 | 0

- | 2 | 4

| 1 | 6:

Answer: 16/15

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Please help solve for x..

aalyn [17]

Answer:

x = 1 or x = -1

Step-by-step explanation:

Given equation:

$x^{100}-4^x \cdot x^{98}-x^2+4^x=0$

Factor out -1:

$\implies -1(-x^{100}+4^x \cdot x^{98}+x^2-4^x)=0$

Divide both sides by -1:

$\implies -x^{100}+4^x \cdot x^{98}+x^2-4^x=0$

Rearrange the terms:

$\implies 4^x \cdot x^{98}-4^x-x^{100}+x^2=0$

$\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c \quad \textsf{to }x^{100}:$

$\implies 4^x \cdot x^{98}-4^x-x^{98}x^2+x^2=0$

Factor the first two terms and the last two terms separately:

$\implies 4^x(x^{98}-1)-x^2(x^{98}-1)=0$

Factor out the common term $(x^{98}-1)$ :

$\implies (4^x-x^2)(x^{98}-1)=0$

Zero Product Property: If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Using the Zero Product Property, set each factor equal to zero and solve for x (if possible):

$\begin{aligned}x^{98}-1 & = 0 & \quad \textsf{or} \quad \quad4^x-x^2 & = 0 \\x^{98} & =1 & 4^x & = x^2 \\x & = 1, -1 & \textsf{no}& \textsf{ solutions for } x \in \mathbb{R}\end{aligned}$

Therefore, the solutions to the given equation are: x = 1 or x = -1

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3 0

2 years ago

Please help me answer this‍♂️

DerKrebs [107]

Answer:

x+x+14=90

2x=90-14

2x=76

x=38 (opp angles =)

8 0

3 years ago

What is the first step to solve this equation: -3x + 12 = -40

ElenaW [278]

Answer:

Your supposed to cancel out 12 on both sides so u subtract 12 on both sides so the equation would be

-3x= -52

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Which inequality matches the graph?

alexdok [17]

The inequality that matches the graph would be C. -3x + 2y ≥ 7.

4 0

3 years ago

if a sequence is defined recursively by f(0)=4 and f(n+1)= -3f(n+1)=-3f(n)+1 for n≥0, then f(3) is equal to? DESPERATELY NEED HE

muminat

f(3) is equal to -101.

Step-by-step explanation:

The sequence is followed by f(0)=4
The given expression is f(n+1)= -3f(n)+1

Put n=0,

f(0+1)= -3f(0)+1

f(1)= -3(4)+1

f(1)= -12+1 = -11

Put n=1,

f(1+1)= -3f(1)+1

f(2)= -3(-11)+1

f(2)= 33+1 = 34

Put n=2,

f(2+1)= -3f(2)+1

f(3)= -3(34)+1

f(3)= -102+1

f(3)= -101

5 0

3 years ago