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IRINA_888 [86]
3 years ago
9

Solve the inequality. 1/3b + 1 < -6​

Mathematics
2 answers:
olga_2 [115]3 years ago
5 0

Answer:

b<-21

Step-by-step explanation:

1/3b+1<-6

1/3b<-7

*3     *3

b<-21

nadezda [96]3 years ago
4 0

Answer:

b <  - 21

Step-by-step explanation:

\frac{1}{3} b + 1 < - 6 ( subtract 1 from both sides )

\frac{1}{3} b < - 7 ( multiply both sides by 3 to clear the fraction )

b < - 21

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Evaluate the following
IRINA_888 [86]

(a) [\frac{9}{2.6}  - \frac{2.5^{2} }{2.5} ]^{2}

Answer:

[\frac{9}{2.6}  - \frac{2.5^{2} }{2.5} ]^{2}

= [\frac{9}{2.6}  - \frac{2.5*2.5 }{2.5} ]^{2}

= [\frac{9}{2.6}  - \frac{2.5}{1} ]^{2}

*canceling 2.5 in numerator and denominator*

= [\frac{9-(2.5)(2.6)}{2.6} ]^2\\*Using L.C.M of 2.6 and 1 which comes out to be '2.6'= [\frac{9-(6.5)}{2.6} ]^2\\= [\frac{2.5}{2.6} ]^2\\*multiplying and dividing by '10'= [\frac{2.5*10}{2.6*10} ]^2\\= [\frac{25}{26} ]^2\\= \frac{25^2}{26^2}\\= \frac{625}{676}\\= 0.925

Properties used:

Cancellation property of fractions

Least Common Multiplier(LCM)

The least or smallest common multiple of any two or more given natural numbers are termed as LCM. For example, LCM of 10, 15, and 20 is 60.

(b) [[\frac{3x^{a}y^{b}} {-3x^{a} y^{b} } ]^{3}    ] ^{2}

Answer:

[[\frac{3x^{a}y^{b}} {-3x^{a} y^{b} } ]^{3}] ^{2}\\

*using [x^{a}]^b = x^{ab}*

= [\frac{3x^{3a}y^{3b}} {-3x^{3a} y^{3b} }] ^{2}        

*Again, using [x^{a}]^b = x^{ab}*

= \frac{3x^{2*3a}y^{2*3b}} {-3x^{2*3a} y^{2*3b} }  \\= (-1)\frac{3x^{6a}y^{6b}} {3x^{6a} y^{6b} }\\[\tex]*taking -1 common, denominator and numerator are equal*[tex]= -(1)\frac{1}{1}\\= -1

Property used: 'Power of a power'

We can raise a power to a power

(x^2)4=(x⋅x)⋅(x⋅x)⋅(x⋅x)⋅(x⋅x)=x^8

This is called the power of a power property and says that to find a power of a power you just have to multiply the exponents.

3 0
3 years ago
Math help please? w/ only two questions.
Law Incorporation [45]
Maybe: 1. When I play basketball i wear cletes. 2. If a quadrilateral figure has four right angles then it is a square <span> </span> my best guess. Let me know if it helps
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Lina20 [59]
It’s the 3rd option!

-5 (the bubble shaded black), the arrow going left towards -9.

Hope this helps!
4 0
2 years ago
Evaluate the expression for the given value of the variable(s).
Lesechka [4]
The answer to what you have there is -55 using order of operations. 5 times -6 is -30. 5 times -5 is -25. add. You get -55.
3 0
3 years ago
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Prime numbers problem :)
Hatshy [7]

Answer:

The answer to your question is (2)(3)(11)

Step-by-step explanation:

Data

154

Process

1.- Find the prime factors of 154, starting with 2, then, 3, 5, 7, etc

                    154  2

                       77  7

                       11   11

                        1

2.- Write 154 as a composition of prime factors

                    154 = (2)(7)(11)

3.- Conclusion

The prime factors of 154 are 2, 3 and 11

7 0
2 years ago
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