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2 years ago

1/2m−5=23. What is the answer please tell me, it's very important.

Mathematics

1 answer:

olga_2 [115]2 years ago

3 0

Answer:

m = 56

Step-by-step explanation:

1/2m - 5 = 23

add 5 to both sides

1/2m - 5 + 5 = 23 + 5

1/2m = 28

multiply both sides by 2

1/2m(2) = 28(2)

m = 56

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In the expansion (ax+by)^7, the coefficients of the first two terms are 128 and -224, respectively. Find the values of a and b

madam [21]

Answer:

a = 2, b = 3.5

Step-by-step explanation:

Expanding $(ax+by)^7$ using Binomial expansion, we have that:

$(ax+by)^7$ =

$(ax)^7(by)^0 + (ax)^6(by)^1 + (ax)^5(by)^2 + (ax)^4(by)^3 + (ax)^3(by)^4 + (ax)^2(by)^5 + (ax)^1(by)^6 + (ax)^0(by)^7$

$= (a)^7(x)^7+ (a)^6(x)^6(b)(y) + (a)^5(x)^5(b)^2(y)^2 + (a)^4(x)^4(b)^3(y)^3 + (a)^3(x)^3(b)^4(y)^4 + (a)^2(x)^2(b)^5(y)^5 + (a)(x)(b)^6(y)^6 + (b)^7(y)^7\\\\\\= (a)^7(x)^7+ (a)^6(b)(x)^6(y) + (a)^5(b)^2(x)^5(y)^2 + (a)^4(b)^3(x)^4(y)^3 + (a)^3(b)^4(x)^3(y)^4 + (a)^2(b)^5(x)^2(y)^5 + (a)(b)^6(x)(y)^6 + (b)^7(y)^7$

We have that the coefficients of the first two terms are 128 and -224.

For the first term:

=> $a^7 = 128$

=> $a = \sqrt[7]{128}\\ \\\\a = 2$

For the second term:

$a^6b = -224$

$b = \frac{-224}{a^6}$

$b = \frac{-224}{2^6} \\\\\\b = \frac{-224}{64} \\\\\\b = 3.5$

Therefore, a = 2, b = 3.5

5 0

3 years ago

Please help worth a lot of points!!!

V125BC [204]

Let's solve this problem step by step

$2x+3=4(x-6)$ | Given Equation

$2x+3=4x-24$ | Distributive Property of Multiplication over subtraction

$3=2x-24$ | Subtraction Property of Equality

$27=2x$ | Subtraction Property of Equality

$\frac{27}{2}=x$ | Division Property of Equality

Definition of each property:

Distributive Property of Multiplication over subtraction: it says that the product of a number and the difference of two other numbers is equal to the difference between the products of the distributed number.
Subtraction Property of Equality: if the same value is subtracted from two equal sides, the differences remain the same
Division Property of Equality: if the same value is divided from two equal sides, the equation remains the same

Hope that helps!

8 0

2 years ago

Please help I really need help

katrin2010 [14]

Answer:

Step-by-step explanation:

Use the vertical line test, you can conclude that this is not a function.

5 0

2 years ago

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QUESTION 2

stiv31 [10]

The first quartile would be 48.5

3 0

3 years ago

Prove that 3(x+1)(x+7)-(2x+5)² is never positive

scZoUnD [109]

Step-by-step explanation:

3(x + 1)(x + 7) − (2x + 5)²

3(x² + 8x + 7) − (4x² + 20x + 25)

3x² + 24x + 21 − 4x² − 20x − 25

-x² + 4x − 4

-(x² − 4x + 4)

-(x − 2)²

A squared number is never negative (provided x is a real number), so -(x − 2)² is never positive.

3 0

3 years ago

Read 2 more answers