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3 years ago

Solve w2+13w+42=0 by factoring.

Mathematics

2 answers:

Lesechka [4]3 years ago

7 0

Answer:

w = -7, -6

Step-by-step explanation:

Solve the equation by factoring:

(w+7)(w+6) = 0

Set each parenthesis equal to zero, and solve for w:

w = -7, -6

Hope this helps!

-EmV

Nezavi [6.7K]3 years ago

4 0

Hope it helps you!!!!!!

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Ax +by = 16

Talja [164]

Answer:

The system has infinitely many solutions when a = 3/4 and b = 1/2

<h3>Given </h3>

System of linear equations

ax +by = 16
3x+2y=64

Values of a and b that leads to infinitely many solutions

<h3>Solution</h3>

The linear system of equations has infinitely many solutions when lines overlap, so both have same slope and y-intercept.

We can solve it in two different ways

1. Note that when the first equation is multiplied by 4, it has same value of constant as the second equation, which is 64.

4ax + 4by = 64
3x + 2y = 64

When compared it gives us:

4a = 3 ⇒ a = 3/4
4b = 2 ⇒ b = 2/4 = 1/2

2. Convert both equations from standard to slope-intercept form and compare:

ax + by = 16
by = -ax + 16
y = - (a/b)x + 16/b

3x + 2y = 64
2y = - 3x + 64
y = - (3/2)x + 32

Work out values of a and b:

16/b = 32 ⇒ b = 16/32 ⇒ b = 1/2
- (a/b) = - 3/2 ⇒ a/b = 3/2 ⇒ a = 3b/2 ⇒ a = 3(1/2)/2 ⇒ a = 3/4

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Maggie is considering two investments. Investment A Investment B Principal $10,000 $8,000 Interest rate 3% 2.8% Time in years 5

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To solve this we are going to use the simple interest formula: $A=P(a+rt)$
where
$A$ is the final amount.
$P$ is the initial investment.
$r$ is the interest rate in decimal form.
$t$ is the time in years.

Investment A. We know that the initial investment is $10,000, so $P=10000$ . We also know that the number of years is 5, so $t=5$ . To convert the interest rate to decimal form, we are going to divide the rate by 100%
$r= \frac{3}{100} =0.03$
Lets replace those values in our formula to find $A$ :
$A=P(a+rt)$
$A=10000(1+0.03*5)$
$A=11500$

Investment B. $P=8000$ , $t=15$ , and $r= \frac{2.8}{100} =0.028$ .
$A=P(a+rt)$
$A=8000(1+0.028*15)$
$A=11360$

We can conclude that investment A will be worth than investment B at the end of the investment period.

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