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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) ?

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 .