MATHEMATICS HIGH SCHOOL

The average rate of change of a function f(x) = x2 between x = 3 and x = 5 isaverage rate of change =
X
5-3
8

Help please thank you

Answers

Answer 1

Answer:

Answer:

average rate of change = 8

Step-by-step explanation:

the average rate of change of f(x) in the closed interval [ a, b ] is

$(f(b)-f(a))/(b-a)$

here the closed interval is [ 3, 5 } , then

f(b) = f(5) = 5² = 25

f(a) = f(3) = 3² = 9

Then

average rate of change = $(25-9)/(5-3)$ = $(16)/(2)$ = 8

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Eighty percent of the tourists in a group took a bus and the rest took a taxi. The bus fare per person is 40% less than the taxi fare per person. All together they paid $68 for the tour transportation, and the bus fare per person is $3. How many tourists are in the group?

An arts academy requires there to be 4 teachers for every 100 students and 5 tutors for every 60 students. How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 144 standents?

Answers

Answer: 25 students per teacher and 12 students per tutor. They need 2.4 tutors for the school

Y-1=5/6(x-4) in standard form

Answers

   y - 1 = ⁵/₆(x - 4)
   y - 1 = ⁵/₆(x) - ⁵/₆(4)
   y - 1 = ⁵/₆x - 3¹/₃
   + 1    + 1
             y = ⁵/₆x - 2¹/₃
      ⁻⁵/₆x + y = ⁵/₆x - ⁵/₆x - 2¹/₃
   -6(⁻⁵/₆x + y) = -6(-2¹/₃)
-6(⁻⁵/₆x) - 6(y) = 14
         5x - 6y = 14

If you would like to write the equation Y - 1 = 5/6 * (x - 4) in standard form, you can do this using the following steps:

Y - 1 = 5/6 * (x - 4)
Y - 1 = 5/6 * x - 5/6 * 4
Y - 1 = 5/6 * x - 10/3
Y - 5/6 * x = 1 - 10/3
Y - 5/6 * x = - 7/3 /*6
6 * Y - 5 * x = - 14

The correct result would be 6 * Y - 5 * x = - 14.

in a survey if 27.5 percent of those questioned chose swimming as their favorite. If 11 people chose swimming then how many people were surveyed

Answers

27.5% of x=11 x is the number of people 27.5%=.275 x=11/.275=40 people in the survey participated

Final answer:

To determine the total number of people surveyed when given the number who preferred swimming and the percentage they represent, you set up an equation based on the percentage and then solve for the total. With this data, 40 people were surveyed.

Explanation:

The question pertains to the mathematical concept of percentages. You mention that 27.5 percent of the surveyed population favored swimming and this equaled to 11 people. To calculate the total number of people surveyed, we let the total number be 'x'. Therefore, the mathematical equation, based on the provided data, becomes 27.5% of 'x' = 11. In mathematical terms, it can be written as 0.275x = 11. For finding 'x', divide both sides of the equation by 0.275. Thus 'x' = 11 / 0.275 = 40. Therefore, based on the given percentages and data, it's inferred that a total of 40 people were surveyed.

Learn more about Percentage Problem here:

brainly.com/question/36014670

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2x -y=-1
3x-2y=1
elimination somebody do this for me

Answers

2x-y=-1 (1)
3x-2y=1 (2)
(1) * 2--> 4x-2y=-2 (3)
(3) - (2)
x= -3

sub x= -3 into (1)
2(-3)-y=-1
-6-y=-1
-y=5
y= -5

-2(2x-y)=-1
3x-2y=1

-4x+2y=2
3x-2y=1

-x=3 (x=-3)
(-3,__)

2(-3)-y=-1
-6-y=-1
-y=-1+6
-y=5
y=-5
so..(-3,-5)

Which of the following expressions shows the expression 1/2x+3−2/5x+1 in simplest form?

Answers

Hey there!

1/2x + 3 - 2/5x + 1

COMBINE the LIKE TERMS

= (1/2x - 2/5x) + (3 + 1)

1/2x - 2/5x = 1/10x

3 + 1 = 4

= 1/10x + 4

Therefore, your answer is: 1/10x + 4

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

$\huge\boxed{(1)/(2)x+3-(2)/(5)x+1=(1)/(10)x+4}$

Step-by-step explanation:

$(1)/(2)x+3-(2)/(5)x+1\n\n=\left((1)/(2)x-(2)/(5)x\right)+(3+1)\n\n=\left((1\cdot5)/(2\cdot5)x-(2\cdot2)/(5\cdot2)x\right)+4\n\n=\left((5)/(10)x-(4)/(10)x\right)+4\n\n=(1)/(10)x+4$

How do I make these points (3,-5)(-5,3) into a point slope form equation that contains the given points

Answers

$General\ equation\ for\ line\ in\ slope\ intercept\ form:\n\ny=ax+b\n\nTo\ find\ a\ and\ b\ substitude\ points\ (3,-5),\ (-5,3)\ into\ equation\n\n \left \{ {{-5=3a+b}\ \ \ \ \atop {3=-5a+b\ |*-1}} \right.\n\n \left \{ {{-5=3a+b} \atop {-3=5a-b}} \right. \n+----\n\n-8=8a\ \ \ |:8\na=-1\n\n-5=3\cdot(-1)+b\n-5=-3+b\n-5+3=b\nb=-2\n\ny=-x-2$

Steps:
1. First you have to find the slope
3+5= 8 -5-3=-8 Your slope is -1
2. You plug in one of the points into the point slope form
Y1-Y2=m(x-x1)
Y-3=-1(x+5)
Y-3=-1x+-5
3. Then, you add three to each side
Y=-1x+ (-2)

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