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The pie chart above shows the budget of Pen Consulting Company for the coming year. If the budget for Payroll is `$31,980` more than the budget for general, how much is the total budget of Pen Consulting Company for the coming year?

`v=20sqrt(t+273)`   

The model above gives the speed, v, in meter per second (m/s), of sound in air at a temperature, `t^o C` . Using the model, find the temperature, in `^o C` , of a place at a certain time if the speed of sound produced at that time in the place is measured to be `340m/s` .

|`6x+6|=14+4x` 

Which of the following is the solution set to the equation above?

In a statistics exam, `3/8` of the boys that sat for the exam failed and `1/8` of the girls that sat for the exam failed. If `88` students sat for the exam and `64` of them are boys, how many students passed the exam?

Simpson rode his bicycle at a speed of `20` miles per hour (mph) for `x` hours, then he increased his speed and rode the bicycle at `38` mph for `y` hours. If it took him `3` hours to cover a distance of `96` miles, how many miles into the journey was he after 1 hour?

If `log_{8}128=x`  , what is the value of `3x^2` ?

In the figure above, ABCD is a quadrilateral. If the measure of `\angleA` is `98^o` and the measure of `\angleC` is `26^o` more than the measure of `\angleA` , what is the value of `x` ?

The graph of `f(x)` and `g(x)` are shown above. if `g(x)=f(x)+k` , what is the value of `k` ?

Eloise earns `$7,000` per month. He spends `$960` on rent and `$400` for transportation to and from his office every month. If he spends `47%` of the remainder on foods and groceries and saves the rest, about what percent of his earning does he save?

`f(x)=(8(3x-9))/(4+a)`  

 For the function `f` defined above, `a` is a constant and `f(4)=6` . What is the value of `f(-6)` ?

Choose the correct answer
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` .