MATHEMATICS MIDDLE SCHOOL

The floor of a rectangular meeting room is the same length as the room and is 1/6 the width of the room. What is the width of the raised platform. Length is 7 1/2 and width is 6 2/5.

Answers

Answer 1

Answer:

Length of floor = length of room = 7.5 units

Width of floor = $(1)/(6)$ * Width of Room = $(1)/(6)$ * $(32)/(5)$

⇒ Width of floor = 1.067 units

Answer 2

Answer:

Answer:

Width of raised platform = $1(1)/(15)\text{ units}$ = 1.067 units

Step-by-step explanation:

We are given the following information about the room:

Lenght of room = $7(1)/(2)\text{ units}$

Width of room = $6(2)/(5)\text{ units}$

We are given the following information about the raised platform of meeting room.

Length of raised platform = Length of the room = $7(1)/(2)\text{ units}$

Width of the raised platform = $(1)/(6) * \text{Width of the room}$

= $(1)/(6) * (32)/(5)$

= $(16)/(15) \text{ units}$

= $1(1)/(15)\text{ units}$

= 1.067 units

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If you put 1/5, 2/3, and 5/8 from least to greatest what are they in order
Your school wants to collect at least 5,000 box tops for a fundraiser. Write and graph an inequality to describe the amount of box tops that your school hopes to collect.
In the number 956,783,529, how does the value of the digit 5 in the ten millions place compare to the digit 5 in the hundreds place?

Find the unit rate for the quantities in the table above.

Answers

to find how many dollars per hour, you must choose one ratio of dollars to hours

24:3

we want to get 3 to 1 so we must divide both numbers by 3

now our new ratio is

8:1

the unit rate is

$8 per hour

Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%. Its current value is $2,000. The equation 2,000=16,000(1-r)^t represents the situation, where t is the age of the car in years and r is the rate of depreciation. About how old is Devon’s car? Use a calculator and round your answer to the nearest whole number.1 year
2 years
5 years
8 years

Answers

9514 1404 393

Answer:

Step-by-step explanation:

A graphing calculator shows the function ...

f(t) = 16000(1 -0.35)^t -2000

will be zero for t ≈ 4.83 years. Rounded to the nearest year, the value is expected to be about $2000 after 5 years.

Using a scientific calculator, you can rewrite the equation to make use of logarithms.

2000 = 16000(1 -0.35)^t

2000/16000 = 0.65^t

log(1/8) = t·log(0.65)

t = log(0.125)/log(0.65) ≈ 4.827

Devon's car will be about 5 years old when its value is $2000.

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Additional comment

We expected to see the same sort of formula for continuous depreciation that we see for continuous growth: 2000 = 16000e^(-rt). The value formula given in the problem statement is a continuous function, but it should not be described as modeling continuous depreciation.

Answer:

Step-by-step explanation:

Correct on EDGE 2022

Help meh....................

Answers

Answer:

The Exception: Negative Numbers. There is one very important exception to the rule that multiplying or dividing an inequality is the same as multiplying or dividing an equation. Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign.

Step-by-step explanation:

System of Equations

y=x-5
3x+y=7

Solve?

Answers

$\sf{y=x-5}$
$\sf{3x+y=7}$

Lets solve this by substitution.

Lets plug in y=x-5 into 3x+y=7

So:

$\sf{y=x-5}$
$\sf{3x+y=7}$

Plugging it in:

$\sf{3x+(x-5)=7}$

Solve for x by simplifying that:

$\sf{3x+x-5=7}$

$\sf{4x-5=7}$

Add 5 on both sides

$\sf{4x=12}$

Divide by 4 on both sides

$\sf{x=3}$

Now simply plug x=3 back into any equation and solve for y

So:
$\sf{y=x-5}$

$\sf{y=3-5}$

Simplify that:

$\sf{y=-2}$

So we are left with our final answer which is
$\boxed{\bf{(3,-2)}}$

Y=x-5
-y=3x-7
Add them together
0=4x-12
12=4x
X=3
Y=-2

Which graph shows the solution to the system of inequalities? y<1/2x-2 y≤-2x+4

Answers

Answer:

First of all, we need to graph the equation of the two lines and find each region separately.

The first line is:

$y=(1)/(2)x-2$

This line has been plotted in the first figure below. To find the feasible region, let's take a random point and test the inequality, so let's take $(0,0)$

$y<(1)/(2)x-2 \n \n 0<(1)/(2)(0)-2 \n \n 0<-2 \ False!$

Since for (0,0) the inequality is false, then the region for this inequality is not where the point (0, 0) lies, but the other region, that is, the one under the line as indicated in the second figure. Keep in mind that points on the border of this region, that is, points that lies on the line aren't included in the region because the symbol < tells us that the equality is not included.

The second line is:

$y=-2x+4$

This line has been plotted in the third figure below. To find the feasible region, let's take (0,0) again, so let's take $(0,0)$

$y\leq -2x+4\n \n 0\leq -2(0)+4 \n \n 0<4 \ True!$

Since for the point (0,0) the inequality is true, then the region for this inequality is where this point lies as indicated in the fourth figure. Keep in mind that points on the border of this region, that is, points that lies on the line are included in the region because the symbol ≤ tells us that the equality is included.

_____________________

Finally, the solution to the system of inequalities is the one where the red and blue region overlap as indicated in the fifth figure below.

Answer:

Step-by-step explanation:

Nine tokens are black on one side and white on the other. Initially, four tokens have the black side up (see the picture). In each turn you have to flip three tokens. What is the least number of turns you need to have all tokens showing the same color?