Question

Maths question

Answer 1

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Answer 2

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Answer 3

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Answer 4

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Answer 5

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Answer 6

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Answer 7

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Answer 8

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Answer 9

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Answer 10

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Answer 11

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Answer 12

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Answer 13

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Answer 14

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Answer 15

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Answer 16

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Answer 17

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Answer 18

solve the eqn.
\(x^{2}+6x-3=0\)

Answer 19

use the quadratic formula to solve this eqn.

Answer 20

Quadratic formula
\(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\)

Answer 21

\(\color{red}{a}x^{2}+\color{blue}{b}x+\color{green}{c}=0\)
\(\color{red}{1}x^{2}+\color{blue}{6}x\color{green}{-3}=0\)

Answer 22

a=1
b=6
c=-3

Answer 23

sub. these values into the quadratic formula.

Answer 24

\(x=\frac{-(6)\pm\sqrt{(6)^{2}-4(1)(-3)}}{2(1)}\)

Answer 25

\(x=\frac{-6\pm\sqrt{48}}{2}\)

Answer 26

\(x=\frac{-6+\sqrt{48}}{2}\)
\(x=\frac{-6+\sqrt{16\times3}}{2}\)
\(x=\frac{-6+\sqrt{16}\times\sqrt{3}}{2}\)
\(x=\frac{-6+4\sqrt{3}}{2}\)
\(x=\frac{2(-3+2\sqrt{3})}{2}\)
\(x=-3+2\sqrt{3}\)

Answer 27

\(x=\frac{-6-\sqrt{48}}{2}\)
\(x=\frac{-6-\sqrt{16\times3}}{2}\)
\(x=\frac{-6-\sqrt{16}\times\sqrt{3}}{2}\)
\(x=\frac{-6-4\sqrt{3}}{2}\)
\(x=\frac{2(-3-2\sqrt{3})}{2}\)
\(x=-3-2\sqrt{3}\)

Answer 28

Therefore,answer is D.

Answer 29

...

Answer 30

8. Solve the eqn.
\(3x^{2}+x=\frac{2}{3}\)

Answer 31

We don't like fractions when solving the quadratic eqn.

Answer 32

First,multiply both sides by 3.

Answer 33

\(3(3x^{2}+x)=\frac{2}{3}\times3\)

Answer 34

\(9x^{2}+3x=2\)

Answer 35

Then,make it into its general form.
\(ax^{2}+bx+c=0\)

Answer 36

\(9x^{2}+3x-2=0\)

Answer 37

Use the quadratic formula to solve the eqn.

Answer 38

Quadratic formula
\(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\)

Answer 39

\(\color{red}{9}x^{2}+\color{blue}{3}x\color{green}{-2}=0\)
\(\color{red}{a}x^{2}+\color{blue}{b}x+\color{green}{c}=0\)

Answer 40

a=9
b=3
c=-2

Answer 41

sub. these values into the quadratic formula.

Answer 42

\(x=\frac{-3\pm\sqrt{(3)^{2}-4(9)(-2)}}{2(9)}\)

Answer 43

\(x=\frac{-3\pm\sqrt{81}}{18}\)
\(x=\frac{-3\pm9}{18}\)

Answer 44

\(x=\frac{-3+9}{18}\)
\(x=\frac{6}{18}\)
\(x=\frac{1}{3}\)

Answer 45

\(x=\frac{-3-9}{18}\)
\(x=\frac{-12}{18}\)
\(x=-\frac{2}{3}\)

Answer 46

Thus,the values of x are \(\frac{1}{3}\) and \(-\frac{2}{3}\)

Answer 47

Therefore,answer is B.

Answer 48

...

Answer 49

4. Rewrite the eqn in vertex form.Name the vertex and y-intercept.
\(y=x^{2}-10x+15\)

Answer 50

use completing the square method to rewrite the eqn in vertex form.

Answer 51

\(y=x^{2}-10x+(\frac{-10}{2})^{2}-(\frac{-10}{2})^{2}+15\)

Answer 52

\(y=x^{2}+(-5)^{2}-(5)^{2}+15\)

Answer 53

\(y=(x-5)^{2}-25+15\)
\(y=(x-5)^{2}-10\)

Answer 54

Now,lets find the vertex point
\(x-5=0\)
\(x=5\)
vertex point: (5,-10)

Answer 55

when x=0,y-intercept is
\(y=(0-5)^{2}-10\)
\(y=25-10\)
\(y=15\)

Answer 56

Therefore,answer is B.

Answer 57

...

Answer 58

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Answer 59

7. Solve the eqn.
\(2x^{2}+2x-5=x^{2}\)

Answer 60

use the quadratic formula to solve the eqn.

Answer 61

Quadratic formula
\(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\)

Answer 62

Before using the quadratic formula,make the eqn into its general form.
\(ax^{2}+bx+c=0\)

Answer 63

\(x^{2}+2x-5=0\)

Answer 64

\(\color{red}{1}x^{2}+\color{blue}{2}x\color{green}{-5}=0\)
\(\color{red}{a}x^{2}+\color{blue}{b}x+\color{green}{c}=0\)

Answer 65

a=1
b=2
c=-5

Answer 66

sub. these values into the quadratic formula.

Answer 67

\(x=\frac{-2\pm\sqrt{(2)^{2}-4(1)(-5)}}{2(1)}\)

Answer 68

\(x=\frac{-2\pm\sqrt{24}}{2}\)

Answer 69

\(x=\frac{-2\pm\sqrt{4\times6}}{2}\)

Answer 70

\(x=\frac{-2\pm\sqrt{4}\times\sqrt{6}}{2}\)
\(x=\frac{-2\pm2\sqrt{6}}{2}\)
Factorise 2
\(x=\frac{2(-1\pm\sqrt{6})}{2(1)}\)
\(x=-1\pm\sqrt{6}\)

Answer 71

Therefore,answer is A.

Answer 72

...

Answer 73

2. Calculate the height of the trapezoid.

Answer 74

Lets sketch a diagram of a trapezoid.

Answer 75

shorter base=h+3
longer base=h+77
area of the trapezoid=225
h=?

Answer 76

sub. these values into the given formula...

Answer 77

area=\(\frac{1}{2}h(b_{1}+b_{2})\)

Answer 78

\(225=\frac{1}{2}h(h+3+h+7)\)

Answer 79

\(225=\frac{1}{2}h(2h+10)\)
\(225=h(h+5)\)

Answer 80

\(h^{2}+5h=225\)
\(h^{2}+5h-225\)
use the quadratic formula to solve the eqn.

Answer 81

\(h^{2}+5h=225\)
\(h^{2}+5h-225=0\)
use the quadratic formula to solve the eqn.

Answer 82

\(\color{red}{1}h^{2}+\color{blue}{5}h\color{green}{-225}=0\)
\(\color{red}{a}h^{2}+\color{blue}{b}h+\color{green}{c}=0\)

Answer 83

a=1
b=5
c=-225

Answer 84

sub. these values into the quadratic formula.

Answer 85

\(x=\frac{-5\pm\sqrt{(5)^{2}-4(1)(-225)}}{2(1)}\)
\(x=\frac{-5\pm\sqrt{925}}{2}\)

Answer 86

\(x=\frac{-5+\sqrt{925}}{2}\)
\(x=12.71\)

Answer 87

\(x=\frac{-5-\sqrt{925}}{2}\)
\(x=-17.71\)
This value is not accepted bcoz it has negative sign...

Answer 88

Therefore,answer is D.

Answer 89

1. Complete the square.
\(x^{2}+18x+(~~~)\)
Answer is D.
2. Complete the square.
\(x^{2}-x+(~~~)\)
Answer is A.
3. Complete the square.
\(x^{2}-24x+(~~~)\)
4. Complete the square.
\(m^{2}-3m+(~~~)\)
Answer is D.

Answer 90

1. Complete the square.
\(x^{2}+18x+(~~~)\)
Answer is D.
2. Complete the square.
\(x^{2}-x+(~~~)\)
Answer is A.
3. Complete the square.
\(x^{2}-24x+(~~~)\)
Answer is C.
4. Complete the square.
\(m^{2}-3m+(~~~)\)
Answer is D.