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Mathematics

1 answer:

arsen [322]4 years ago

6 0

Answer:

2x² + 5x + 3 = (2x + 3)(x + 1)

Step-by-step explanation:

* Lets explain how to factor a trinomial in the form ax² ± bx ± c:

- Look at the last term c

# If the c term is a positive number, then its factors r , s will both

be positive or both be negative

# a has two factors h and k

# The brackets are (hx ± r)(kx ± s) where a = hk , c = rs and b = rk + hs

# If the c term is a negative number, then either r or s will be negative,

but not both.

# a has two factors h and k

# The brackets are (hx + r)(kx - s) or (hx - r)(kx + s)where a = hk ,

c = rs and b = rk - hs

* Lets solve the problem

∵ The equation is 2x² + 5x + 3 = 0

∵ The general form of the equation is ax² + bx + c = 0

∴ a = 2 , b = 5 , c = 3

∵ c is positive

∴ Its factors r and s have same sign

∵ c = 3

∵ 3 = 3 × 1

∴ r = 3 and s = 1

∵ a = 2

∵ The factors of a are h , k

∵ 2 = 2 × 1

∴ h = 2 and k = 1

∵ The brackets are (hx + r)(kx + s)

∴ 2x² + 5x + 3 = (2x + 3)(x + 1)

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Write an equation for: melissa has 6 times as many quarters as Michelle. Together they have 896 quarters. How many quarters, q,

butalik [34]

Okay, so in this equation we will use the following variables:

a: for the number of quarters Michelle has
b: for the number of quarters Melissa has
q: for total number of quarters

So first, we will write out the statement "Melissa has 6 times as many quarters as Michelle" in the form of an equation:

6 times the number of quarters Michelle has is equal to the number of quarters Melissa has, or:
6(a)=b

So, we now know that Melissa has 6 times as many quarters as Michelle.

So, if the have 896 quarters total, then you can write the problem as the number of quarters Michelle has added to the number of quarters Melissa has. This can be expressed as:

a+b=q

Since we know that Melissa has 6 times the quarters as Michelle, 6a is equivalent to b:

(6×a)=b

Since we know the total number of quarters is 896, we can rewrite it as this:

a+(6×a)= 896

Now that we know this, we can solve the problem with the following steps:

6a+a=7a

7a=896

896÷7= 128

a= 128

So, now that we know that know that Michelle has 128 quarters, we can find out how many Melissa has:

128×6= 768

Melissa has 768 quarters.

Now we check our work:

128+ (6×128)= 768

If everything is correct the following should be true:

a=128

and

b=768

So, Michelle has 128 quarters.

6 0

3 years ago

Brenda invests $4,848 in a savings account with a fixed annual interest rate of 5% compounded 2 times per year. What will the ac

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She invests some amount in a saving account of fixed interest compounded half-yearly. It says to find its Future Value after six years.

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We know the formula of Future Value is given by :-

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