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alexandr1967 [171]
3 years ago
5

A pack of pencils contains 20 pencils. If Trish uses 3/4 of the pack, how many pencils will she use?

Mathematics
1 answer:
Sergeu [11.5K]3 years ago
5 0
20/4 = 5
5X3 = 15

C is your answer
You might be interested in
−2x=x^2−6
Iteru [2.4K]

Step-by-step explanation:

Example 1

Solve the equation x3 − 3x2 – 2x + 4 = 0

We put the numbers that are factors of 4 into the equation to see if any of them are correct.

f(1) = 13 − 3×12 – 2×1 + 4 = 0 1 is a solution

f(−1) = (−1)3 − 3×(−1)2 – 2×(−1) + 4 = 2

f(2) = 23 − 3×22 – 2×2 + 4 = −4

f(−2) = (−2)3 − 3×(−2)2 – 2×(−2) + 4 = −12

f(4) = 43 − 3×42 – 2×4 + 4 = 12

f(−4) = (−4)3 − 3×(−4)2 – 2×(−4) + 4 = −100

The only integer solution is x = 1. When we have found one solution we don’t really need to test any other numbers because we can now solve the equation by dividing by (x − 1) and trying to solve the quadratic we get from the division.

Now we can factorise our expression as follows:

x3 − 3x2 – 2x + 4 = (x − 1)(x2 − 2x − 4) = 0

It now remains for us to solve the quadratic equation.

x2 − 2x − 4 = 0

We use the formula for quadratics with a = 1, b = −2 and c = −4.

We have now found all three solutions of the equation x3 − 3x2 – 2x + 4 = 0. They are: eftirfarandi:

x = 1

x = 1 + Ö5

x = 1 − Ö5

Example 2

We can easily use the same method to solve a fourth degree equation or equations of a still higher degree. Solve the equation f(x) = x4 − x3 − 5x2 + 3x + 2 = 0.

First we find the integer factors of the constant term, 2. The integer factors of 2 are ±1 and ±2.

f(1) = 14 − 13 − 5×12 + 3×1 + 2 = 0 1 is a solution

f(−1) = (−1)4 − (−1)3 − 5×(−1)2 + 3×(−1) + 2 = −4

f(2) = 24 − 23 − 5×22 + 3×2 + 2 = −4

f(−2) = (−2)4 − (−2)3 − 5×(−2)2 + 3×(−2) + 2 = 0 we have found a second solution.

The two solutions we have found 1 and −2 mean that we can divide by x − 1 and x + 2 and there will be no remainder. We’ll do this in two steps.

First divide by x + 2

Now divide the resulting cubic factor by x − 1.

We have now factorised

f(x) = x4 − x3 − 5x2 + 3x + 2 into

f(x) = (x + 2)(x − 1)(x2 − 2x − 1) and it only remains to solve the quadratic equation

x2 − 2x − 1 = 0. We use the formula with a = 1, b = −2 and c = −1.

Now we have found a total of four solutions. They are:

x = 1

x = −2

x = 1 +

x = 1 −

Sometimes we can solve a third degree equation by bracketing the terms two by two and finding a factor that they have in common.

6 0
3 years ago
Read 2 more answers
What’s the total value of 20 quarters, 40 dimes, 30 nickels, and 15 pennies
Inessa [10]

Answer$10 65 cents

Step-by-step explanation:

20/4= $5 40/10= $4  .05 x 30= $1.50 and add those together to get $10.50 then add the 15 pennies which is $10.65

6 0
3 years ago
Read 2 more answers
The slope of the line whose equation is 2x + 5y + 1 = 0 is<br> 0-2/5<br> 05/2<br> 0-1/5
Leto [7]

Answer:

0-2/5

I think this is it ;-;

7 0
3 years ago
Please help due today!!!!!!!:(
Alchen [17]

Answer:

D

Step-by-step explanation:

∠AXD = 180°

∠AXB = 32°

so you do 180 - 32 and you get 148. hope I helped:)

8 0
2 years ago
The next day Shaina another container of lemonade her sister drinks 1/3 of it her mother the drinks 3/4 of the remaining 2/3 How
zheka24 [161]
<h3>Answer: 1/2 of the container</h3>

Explanation:

Draw a circle and split it into thirds. The sister will take one of the slices, so we have 2 left over. That accounts for the 2/3 left over.

Then split each of those two slices in half to get 2*2 = 4 smaller slices. The mother takes 3 of those smaller slices which represents 1/2.

Or you could say (2/3)*(3/4) = (2*3)/(3*4) = 2/4 = 1/2.

The diagram is shown below. The white portion is the 1/3 the sister gets at first. The pink portion represents the fractional amount the mother drank, which is 3/6 = 1/2.

7 0
3 years ago
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