Explanation :

**Choice D is correct.**

Let `x` be the total budget, then `59%` of `x` is greater than `20%` of `x` `by 31,980` .

Thus, `0.59x-0.2x=31,980`

⇒ `0.39x=31,980`

⇒ `x=(31,980)/0.39=82,000`

**Choice A is correct.**

`340=20sqrt(t+273)`

⇒ `sqrt(t+273)=340/20=17`

⇒ `t+273=17^2=289`

⇒ `t=289-273=16^o C`

**Choice C is correct. **

`|6x+6|=14+4x`

⇒ `6x+6=14+4x` or `6x+6=-(14+4x)=-14-4x`

If `6x+6=14+4x` , then `6x-4x=14-6`

⇒ `2x=8`

⇒`x=8/2=4` .

If `6x+6=-14-4x` ,

⇒ `6x+4x=-14-6`

⇒`10x=-20`

⇒ `x=(-20)/10=-2`

Substituting `x=4` and `x=-2` into the original equation shows that both are valid solutions.

**Choice A is correct. **

The number of boys that sat for the exam is `64` out of which `3/8xx64=24` failed which means that `64-24=40` boys passed the exam.

Similarly, the number of girls that sat for the exam is `88-64=24` out of which `1/8xx24=3` failed which means that `24-3=21` girls passed the exam.

Therefore, the number of students that passed the exam is `40+21=61` .

**Choice A is correct. **

Writing in alegbric equation gives `20x+38y=96` and `x+y=3` .

From the second equation, `x=3-y` ,

Substitute `x` in the furst equation

`20(3-y)+38y=96`

⇒ `60-20y+38y=96`

⇒`18y=96-60=36`

⇒ `y=36/18=2`

⇒ `x=3-y=3-2=1` .

Since `x=1` , it means he rode his bicycle at `20` mph for `1` hour and covered a distance of `20xx1=20` miles .

**Choice B is correct.**

`x=log_{8}128=(log128)/(log8) =(log(2^7))/(log(2^3))=(7(log2))/(3(log2))=7/3 `

⇒ `3x^2=3(7/3)^2=3(49/9)=49/3`

**Choice C is correct.**

The sum of the interior angles of a quadrilateral is `360^o` .

The measure of `\angleC=98^o + 26^o=124^o` .

`98+x+18+124+2x-15=360`

⇒ `3x+225=360`

⇒ `3x=360-225=135`

⇒ `x=135/3=45`

**Choice B is correct.**

`g(x)` is `4` units above `f(x)` for all values of `x` .

**Choice C is correct.**

The remainder after rent and transportation is `$7,000-$960-$400=$5,640` .

`47%` of `$5,640=0.47xx$5,640=$2,650.80` .

Thus, the amount saved is `$5,640-$2,650.80=$2,989.2` which is `(2,989.2)/(7,000)=0.427=42.7%` of `$7,000` .

**Choice C is correct. **

`f(4)=6`

⇒ `(8(3(4)-9))/(4+a)=6`

⇒ `8(12-9)=6(4+a)`

⇒ `8(3)=24+6a`

⇒ `6a=24-24=0`

⇒ `a=0/6=0`

Thus, `f(x)=(8(3x-9))/4` and `f(-6)=(8(3(-6)-9))/4=2(-18-9)=2(-27)=-54` .