MATHEMATICS MIDDLE SCHOOL

A college raises its tuition in each of three consecutive years. If the percent increase by 5%, 9%, and 7%, determine the overall percent increase at the end of the three-year period?

Answers

Answer 1

Answer:

The overall increment at the end of the three-year period is 22.5%

The increments are given as:

$\mathbf{Year\ 1 =5\%}$

$\mathbf{Year\ 2 =9\%}$

$\mathbf{Year\ 3 =7\%}$

So, the overall increment is calculated as:

$\mathbf{Overall = (1 + Year\ 1) * (1 + Year\ 2) * (1 + Year\ 3) -100\%}$

Substitute known values

$\mathbf{Overall = (1 + 5\%) * (1 + 9\%) * (1 + 7\%) -100\%}$

Express as decimals

$\mathbf{Overall = (1 + 0.05) * (1 + 0.09) * (1 + 0.07) -100\%}$

$\mathbf{Overall = (1.05) * (1.09) * (1.07) -100\%}$

Multiply

$\mathbf{Overall = 1.224615 -100\%}$

Express as percentage

$\mathbf{Overall = 122.4615\% -100\%}$

Subtract

$\mathbf{Overall = 22.4615\%}$

Approximate

$\mathbf{Overall = 22.5\%}$

Hence, the overall increment is 22.5%

Read more about percentage change at:

brainly.com/question/11639405

Answer 2

Answer:

The overall percentage increase is 22.5%.

step-by-step explanation

Percentage increase in the first year=5%

Percentage increase in the second year=9%

Percentage increase in the third year=7%

we have to calculate the overall percentage increase

Let the initial tuition fees be x

tuition fees after three years=

= $x* (100+a)/(100) *(100+b)/(100)* (100+c)/(100) \n=x* (105)/(100) *(109)/(100) *(107)/(100) \n\n=x* (1224615)/(1000000) \n=x*(122.4625)/(100) \n=x*(100+22.4625)/(100)$

The overall percentage increase is 22.5%.

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Help pleaseif we have100 applesand jim eats20and kellie eats5what is the eqation to solve

What is the equation of the line that passes through the point (5,0) and has a slope of 1

Answers

Answer:

y = x - 5

Step-by-step explanation:

In point slope form (y=a(x-h)+k):

y = 1(x - 5) + 0

simplifies to:

y = x - 5

What is the perpendicular adjacent sides in the triangle

Answers

"Adjacent" means next to each other. "Perpendicular" means at an angle of 90 degrees.
Rectangles (this includes squares) have adjacent perpendicular sides. So do right triangles.

adjecent basically means "next to" and perpindicular is meeting at an right angle (90 degrees) so squares have them and right angle triangles do to.

25e² + n 4= 20e

don't know what to do so please help

Answers

Answer:

see explanation

Step-by-step explanation:

This is a quadratic equation

Rearrange into standard form : ax² + bx + c = 0 : a ≠ 0

subtract 20e from both sides

25e² - 20e + 4 = 0 ← in standard form

This is a perfect square of the form

(a - b)² = a² - 2ab + b²

25e² = (5e)² ⇒ a = 5e and 4 = 2² ⇒ b = 2, and

- 2ab = - 2 × 5e × 2 = - 20e, hence

25e² - 20e + 4 = (5e - 2)²

⇒ (5e - 2)² = 0 ⇒ e = $(2)/(5)$ with multiplicity 2

A garden contains 20 different species of plants. Five of these plants are ferns. What percent of the garden is made up if ferns?

Answers

Answer:

25%

Step-by-step explanation:

A garden contains 20 different species of plants. Five of these plants are ferns.

Total number of species = 20

In that 20 species , 5 are ferns

WE need to find out how much percentage of 20 is 5

LEts make an equation. x be the percentage

x% of 20 is 5

$(x)/(100) \cdot 20 = 5$

$(x)/(5)= 5$

Now multiply both sides by 5

x= 25

So 25% of 20 species plans is equal to 5 ferns

5 out of 20 plants can be written as 5/20.

A percentage is just a fraction with the denominator being 100.
100 / 20 = 5.
5 X 5 = 25
25/100

25% of the garden is made up of ferns

What is an equation of the line that is perpendicular to y-3 =-4(x+2)

Answers

Answer:

$y - 3 = (1)/(4)(x+2)$ or choose any line with slope 1/4

Step-by-step explanation:

The slope of this line is -4. The slope of the line perpendicular to this line will be the negative reciprocal or 1/4.

Write the equation using the slope m=1/4 and the point slope form.

$y-y_1=m(x-x_1)\ny-3=(1)/(4)(x+2)$

This is the equation of the line that is perpendicular and passes through the same point (-2,3) as the equation listed.

Answer:

$y=(1)/(4) x+c$ where $c$ can be any number.

Step-by-step explanation:

First we need to clear for y:

$y-3 =-4(x+2)\ny=-4(x+2)+3\ny=-4x-8+3\ny=-4x-5$

and now we have an equation of the form:

$y=mx+b$

where m is the slope and b is the y-intercept.

in this case $m=-4$ and $b=-5$

to find and equation perpendicular to this line, the following must be true: $m*m_(1)=-1$

where m is the slope of the original line that i just mentioned, and $m_(1)$ is the slope of the new line. Substituting $m=-4$

$-4*m_(1)=-1$

clearing for $m_(1)$

$m_(1)=(-1)/(-4) \nm_(1)=(1)/(4)$

thus, the new perpendicular line must have the form:

$y=m_(1)x+c\ny=(1)/(4)x+c$

where the y-intecept $c$ can be any number, some examples are:

$y=(1)/(4)x+3\ny=(1)/(4)x-8$

and so on, the important thing to be a perpendicular line is that the slopes are related to the equation $m*m_(1)=-1$ .

The rule is applied to ΔFGH to produce ΔF"G"H".What are the coordinates of vertex F" of ΔF"G"H"?

(4, –1.5)
(4, –0.5)
(–1.5, 4)
(–0.5, 4)

ITS TIMED. I REALLY NEED HELP!!!

Answers

Answer:

(4, –1.5)

Step-by-step explanation:

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