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solmaris [256]
2 years ago
14

160% of what number is 144

Mathematics
1 answer:
givi [52]2 years ago
6 0

Step-by-step explanation:

Let the number be x

160% of x=144

160x \div 100 = 144

then we cross multiply

160x = 100 \times 144

160x = 14400

divide both sides by 160

160x \div 160 = 14400 \div 160

x = 90

therefore the number is 90

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Peter says if you subtract 13 from my number and multiply the difference by -6, the result is -42. What is Peters's number?
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I think the answer is 20, may be wrong tho
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3 years ago
Determine the number and type of roots for the equation using one of the given roots. Then find each root. (inclusive of imagina
dmitriy555 [2]

Step-by-step explanation:

<em>"Determine the number and type of roots for the equation using one of the given roots. Then find each root. (inclusive of imaginary roots.)"</em>

Given one of the roots, we can use either long division or grouping to factor each cubic equation into a binomial and a quadratic.  I'll use grouping.

Then, we can either factor or use the quadratic equation to find the remaining two roots.

1. x³ − 7x + 6 = 0; 1

x³ − x − 6x + 6 = 0

x (x² − 1) − 6 (x − 1) = 0

x (x + 1) (x − 1) − 6 (x − 1) = 0

(x² + x − 6) (x − 1) = 0

(x + 3) (x − 2) (x − 1) = 0

The remaining two roots are both real: -3 and +2.

2. x³ − 3x² + 25x + 29 = 0; -1

x³ − 3x² + 25x + 29 = 0

x³ − 3x² − 4x + 29x + 29 = 0

x (x² − 3x − 4) + 29 (x + 1) = 0

x (x − 4) (x + 1) + 29 (x + 1) = 0

(x² − 4x + 29) (x + 1) = 0

x = [ 4 ± √(16 − 4(1)(29)) ] / 2

x = (4 ± 10i) / 2

x = 2 ± 5i

The remaining two roots are both imaginary: 2 − 5i and 2 + 5i.

3. x³ − 4x² − 3x + 18 = 0; 3

x³ − 4x² − 3x + 18 = 0

x³ − 4x² + 3x − 6x + 18 = 0

x (x² − 4x + 3) − 6 (x − 3) = 0

x (x − 1)(x − 3) − 6 (x − 3) = 0

(x² − x − 6) (x − 3) = 0

(x − 3) (x + 2) (x − 3) = 0

The remaining two roots are both real: -2 and +3.

<em>"Find all the zeros of the function"</em>

For quadratics, we can factor using either AC method or quadratic formula.  For cubics, we can use the rational root test to check for possible rational roots.

4. f(x) = x² + 4x − 12

0 = (x + 6) (x − 2)

x = -6 or +2

5. f(x) = x³ − 3x² + x + 5

Possible rational roots: ±1/1, ±5/1

f(-1) = 0

-1 is a root, so use grouping to factor.

f(x) = x³ − 3x² − 4x + 5x + 5

f(x) = x (x² − 3x − 4) + 5 (x + 1)

f(x) = x (x − 4) (x + 1) + 5 (x + 1)

f(x) = (x² − 4x + 5) (x + 1)

x = [ 4 ± √(16 − 4(1)(5)) ] / 2

x = (4 ± 2i) / 2

x = 2 ± i

The three roots are x = -1, x = 2 − i, x = 2 + i.

6. f(x) = x³ − 4x² − 7x + 10

Possible rational roots: ±1/1, ±2/1, ±5/1, ±10/1

f(-2) = 0, f(1) = 0, f(5) = 0

The three roots are x = -2, x = 1, and x = 5.

<em>"Write the simplest polynomial function with integral coefficients that has the given zeros."</em>

A polynomial with roots a, b, c, is f(x) = (x − a) (x − b) (x − c).  Remember that imaginary roots come in conjugate pairs.

7. -5, -1, 3, 7

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f(x) = (x² + 6x + 5) (x² − 10x + 21)

f(x) = x² (x² − 10x + 21) + 6x (x² − 10x + 21) + 5 (x² − 10x + 21)

f(x) = x⁴ − 10x³ + 21x² + 6x³ − 60x² + 126x + 5x² − 50x + 105

f(x) = x⁴ − 4x³ − 34x² + 76x − 50x + 105

8. 4, 2+3i

If 2 + 3i is a root, then 2 − 3i is also a root.

f(x) = (x − 4) (x − (2+3i)) (x − (2−3i))

f(x) = (x − 4) (x² − (2+3i) x − (2−3i) x + (2+3i)(2−3i))

f(x) = (x − 4) (x² − (2+3i+2−3i) x + (4+9))

f(x) = (x − 4) (x² − 4x + 13)

f(x) = x (x² − 4x + 13) − 4 (x² − 4x + 13)

f(x) = x³ − 4x² + 13x − 4x² + 16x − 52

f(x) = x³ − 8x² + 29x − 52

5 0
2 years ago
25 students are learning how to make balloon animals. There are 194 balloons to be shared equally among the students. How many b
alexdok [17]
25 students
194 balloons

194/25 = 7.76
Each student gets 7 balloons, 7 x 25 = 175 balloons will be used
194 - 175 = 19 balloons remaining (Answer to part 1 of this question)

If each student needs 8 balloons
8 * 25 = 200
200 - 194 = 6 ballons needed (Answer to part 2 of this question)

We also could have found the answer to part 2 by saying that we had 19 balloons left over when the students each were given 7 balloons
Each student needs another 1 balloon = 25 balloons, 
We have 19 left over
25 - 19 = 6 balloons need to be purchased (we got the same answer both ways so it is very likely we have the correct answer)
6 0
3 years ago
Find the value of x.
melisa1 [442]
To find the value of X, simply know that for this parallelogram, the angles on each end that are diagonal with respect to each other are the same. And knowing that the angles in a parallelogram add up to equal 360 degrees. Simply make an algebraic expression equal to the value of 360 and then solve for x.

X + X + (X - 26) + (X - 26) = 360
2X + X - 26 + X - 26 = 360
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X = 103.

The value for X, I believe would be 103 degrees. You can verify this by plugging in the value into both expressions, X and X-26 and see that if adding all the expressions together does it equal 360 degrees.
7 0
3 years ago
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