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Leona [35]
3 years ago
12

Solve for www. Give an exact answer in simplified form. 53w+13 < 56w + 16

Mathematics
1 answer:
ki77a [65]3 years ago
5 0

The solution will be:  w>-1

<em><u>Explanation</u></em>

The given inequality is:   53w+13 < 56w + 16

First we will subtract 56w from both sides. So.....

53w+13-56w

Now we will subtract 13 from both sides. So.....

-3w

Then we need to divide both sides by -3. As here we are <u>dividing the inequality by a negative number, so we need to switch the inequality symbol</u>. So, we will get.......

\frac{-3w}{-3}>\frac{3}{-3}\\ \\ w>-1

Thus, the solution will be:  w>-1

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If possible help me in this. I need to find the two odd numbers...​
Lelechka [254]

Part (a)

Consecutive odd integers are integers that odd and they follow one right after another. If x is odd, then x+2 is the next odd integer

For example, if x = 7, then x+2 = 9 is right after.

<h3>Answer:  x+2</h3>

========================================================

Part (b)

The consecutive odd integers we're dealing with are x and x+2.

Their squares are x^2 and (x+2)^2, and these squares add to 394.

<h3>Answer: x^2 + (x+2)^2 = 394</h3>

========================================================

Part (c)

We'll solve the equation we just set up.

x^2 + (x+2)^2 = 394

x^2 + x^2 + 4x + 4 = 394

2x^2+4x+4-394 = 0

2x^2+4x-390 = 0

2(x^2 + 2x - 195) = 0

x^2 + 2x - 195 = 0

You could factor this, but the quadratic formula avoids trial and error.

Use a = 1, b = 2, c = -195 in the quadratic formula.

x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(2)\pm\sqrt{(2)^2-4(1)(-195)}}{2(1)}\\\\x = \frac{-2\pm\sqrt{784}}{2}\\\\x = \frac{-2\pm28}{2}\\\\x = \frac{-2+28}{2} \ \text{ or } \ x = \frac{-2-28}{2}\\\\x = \frac{26}{2} \ \text{ or } \ x = \frac{-30}{2}\\\\x = 13 \ \text{ or } \ x = -15\\\\

If x = 13, then x+2 = 13+2 = 15

Then note how x^2 + (x+2)^2 = 13^2 + 15^2 = 169 + 225 = 394

Or we could have x = -15 which leads to x+2 = -15+2 = -13

So, x^2 + (x+2)^2 = (-15)^2 + (-13)^2 = 225 + 169 = 394

We get the same thing either way.

<h3>Answer: Either 13, 15  or  -15, -13</h3>
4 0
2 years ago
Given f(x)=x-7 and h(x)=2x+3 what is the rule for h(f(x))
Paul [167]

Answer:

h(f(x)) = 2x - 11

Step-by-step explanation:

To evaluate h(f(x)) substitute x = f(x) into h(x)

h(x - 7)

= 2(x - 7) + 3

= 2x - 14 + 3

= 2x - 11

6 0
3 years ago
Anthony wanted to get a job after school. His
Leto [7]
$8 per hour
Work for 4 hours a day so
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2 years ago
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Chris Christina collects stamps she is 47 stamps and all she has 20 from Europe the number of African stamps is 2 times the numb
AVprozaik [17]

Answer:

Step-by-step explanation:

Let x represent the number of stamps from Europe.

Let y represent the number of stamps from Africa.

Let z represent the number of stamps from Asia.

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y = 2z

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z = 27/3 = 9

y = 2z = 2 × 9

y = 18

She has 20 stamps from Europe, 18 stamps from Africa and 9 stamps Asia.

7 0
3 years ago
There are 12 boys and 13 girls in a class. If the teacher randomly chooses a student's name out of a hat, what is the probabilit
balu736 [363]
If there are 12 boys and 13 girls, there are 25 kids in the class total.  This means that 13/25 are girls.  In order to know the probability, you must divide 13 by 25, which gets an answer of 0.52, which is equal to 52%.

52%
7 0
3 years ago
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