= Homework: Section 9.6
Question 16, 9.6.61
O Point
The perimeter of a rectangle is to be no greater than 160 centimeters and the width must be 35 centimeters. Find the maximum length of the rectangle.

Answer:

The answer is 0.04a² - 0.04ab - 0.15b²

Step-by-step explanation:

(0.2a - 0.5b) ( 0.2a + 0.3b)

0.04a² + 0.06ab - 0.1ba - 0.15b²

0.04a² + 0.06ab - 0.1ab - 0.15b²

0.04a² - 0.04ab - 0.15b²

Thus, The answer is

0.04a² - 0.04ab - 0.15b²

-TheUnknownScientist 72

Answer:

1. 19 (x) = 7

2. -32 + x = 2

3. x ÷ -27 = 8

4. x - 12 = 5

5. 1/3 (x) = 3

Step-by-step explanation:

:)

Answer: first a it’s left side is shorter while on the other polygoes there left sides longer for the first two

in the third one it goes size wise

Step-by-step explanation:

There is a total of 53 Yr 11 students. 18 in math 13 in science making 31 students, leaving 22 Year 11 students for english. 37 total students picked english, so that makes 15 the remaning amount which is put into the Yr12 students.

There are 100 students total. 53 of which are Yr 11 students leaving 47 to be Yr12 students.

12 Yr 12 students chose science, 15 Yr 12 kids chose english, leaving 20 Yr12 students to have chosen math.

12+15+20=47 Yr 12 students.

22+18+13=52 Yr 11 students.

15 Yr 12 students chose english.

20 Yr 12 students chose math.

12 Yr 12 students chose science.

There are 47 Yr 12 students total.

22 Yr 11 students chose english.

18 Yr 11 students chose math.

13 Yr 11 students chose science.

There are 53 Yr 11 students.

Answer: [tex]\frac{17}{4}[/tex]

Step-by-step explanation:

Simply convert 3/1 into 12/4, then add it to 5/4, to get 17/4.

Hope it helps :) and let me know if you want me to elaborate.

Answer:

A.54

Step-by-step explanation:

because 162 divided by 3 equal 54.3

Answer:

52 units^2

Step-by-step explanation:

The area of the dresser is simple. It is just a rectangle that is 4 units by 3 units.

A_dresser = LW = 4(3) = 12 units^2

The area of the bed is a little more complicated, but you can get by using just areas of rectangles.

See the picture below.

Notice that the entire bed fits within a square (shown in blue) that is 9 units by 9 units.

The area of the square is 81 units^2.

We need to subtract the areas of the 4 triangles at the corners.

There are two triangles, top left and bottom right (shown in green), that have a base of 5 and a height of 5. They combine to for a square that is 5 units by 5 units. The area of this square is 25 units^2.

There are two triangles, top right and bottom left (shown in red), that have a base of 4 and a height of 4. They combine to for a square that is 4 units by 4 units. The area of this square is 16 units^2.

Now subtract 25 and 16 from 81 to get the area of the bed.

81 - 25 - 16 = 40

A_bed = 40 units^2

Combined area of bed and dresser:

A = 40 units^2 + 12 units^2 = 52 units^2

Answer: 52 units^2

Here's another way of finding the area of the bed:

Count the number of full squares inside the bed (there are 31). Each full square is 1 unit^2. Then count the number of half-squares inside the bed (there are 18). Each half-square is 1/2 units^2. Add them all up:

31 + 1/2 * 18 = 31 + 9 = 40

You get 40 units^2

Answer/Step-by-step explanation:

2x-5y=9

Add 5y  to both sides of the equation.

2x=9+5y

Divide each term by 2 and simplify.

Divide each term in 2x=9+5y by 2

[tex]\frac{2x}{2} =\frac{9}{2} +\frac{5y}{2}[/tex]

Cancel the common factor of 2.

Divide x by 1.

[tex]x=\frac{9}{2} +\frac{5y}{2}[/tex]

[tex]y=\frac{-9}{5} +\frac{2x}{5}[/tex]

----------------------------------------------------------------------------------------------------------------

3x+4y=2

Add 4y to both sides of the equation

3x=2+4y

Divide each term by 3 and simplify.

Divide each term in 3x=2+4y by 3.

[tex]\frac{3x}{3} =\frac{2}{3} +\frac{4y}{3}[/tex]

Cancel the common factor of 3.

Divide x by 1.

[tex]x=\frac{2}{3} +\frac{4y}{3}[/tex]

[tex]y=\frac{-1}{2} +\frac{3x}{4}[/tex]

Answer:

Q'(-4,0), R'(-4,1), S'(0,0), T'(-3,-3)

Step-by-step explanation:

To solve this, what we need to do is find out what the translation is. So if we are translating those coordinates up two units, then that means we are basically adding two to the y value.

So that means that we will use the mapping (x,y)→(x,y+2)

Now we plug this in. We will start with Q:

Q(-4,-2)→Q'(-4,-2+2)→Q'(-4,0)

So when Q is translated two units up, we get Q'(-4,0).

Now we will do R:

R(-4,-1)→R'(-4,-1+2)→R'(-4,1)

So when R is translated two units up, we get R'(-4,1).

Now we will do S:

S(0,-2)→S'(0,-2+2)→S'(0,0)

So when S is translated two units up, we get S'(0,0).

Next we will do T:

T(-3,-5)→T'(-3,-5+2)→T'(-3,-3)

So when T is translated two units up, we get T'(-3,-3).

Answer:

Step-by-step explanation:

Hello  there !

    [tex]\boxed{\begin{array}{c|c} \boxed{\bf x} & \boxed{\bf y+2} \\ -4 & 0 \\-4&1\\0\!\!\!\!&0 \\ -3 &-3 \end {array }}[/tex]

Answer:

-5(-2)=10

Step-by-step explanation:

Let be x

[tex] - 5 \times - 2 = x \\ take \: minus \: to \: rhs \: from \: lhs \\ 5 \times ( - 2) = - x \\ - 10 = - x \\ cancel \: minus \: on \: both \: sides \\ 10 = x[/tex]

Answer:

80%

Step-by-step explanation:

800-160=640

640/800=.8

.8=80%

25 red, 15 blue

======================================================

Work Shown:

b = number of blue marbles = unknown

r = number of red = 25

T = number total = 25+b

r/T = probability of getting red = 5/8

r/T = 5/8

25/(25+b) = 5/8

25*8 = 5(25+b) .... cross multiplication

200 = 125+5b

200-125 = 5b

75 = 5b

5b = 75

b = 75/5

b = 15

We have 15 blue marbles and 25 red marbles. This means there are T = r+b = 25+15 = 40 marbles total.

The proportion of red is r/T = 25/40 = (5*5)/(5*8) = 5/8 to help confirm we have the correct value for b.

Answer:

Step-by-step explanation:

16.) (3/5)+(-13/5) = (3-13)/5

(3-13)/5 = -10/5, or -2

17.) -1 3/20 - (-3/4)

-(20/20+3/20) + (3/4)

-23/20 + 3/4

-23/20 + 15/20

-8/20

-2/5

18.) (-8/15)/(-1+1/3)

(-8/15)/(-3/3+1/3)

(-8/15)/(-2/3)

(-8/15)*(-3/2)

24/30

4/5

We can convert the line 7x + 3y = 15 into the slope-intercept form (y = mx + c) by making y the subject of the equation. In this form the coefficient of x (m) is the slope.

Since 7x + 3y = 15

                 3y = -7x + 15

                   y = - ⁷/₃x + 5

∴ the slope is NEGATIVE.

Check your answer:

A line with a negative slope is highest to the left and lowest to the right. This is because when x values increase, the y  values decrease, and when x values decrease, y values increase (the two variables are negatively related). If we graph the line this should be true, and it is.

The probability of picking an orange or a cherry flavored candy from the bag is [tex]\frac{8}{15}[/tex].

Given that, total number of candies=15, banana flavoured candies=4, strawberry flavoured candies=3, cherry flavoured candies=6 and orange flavoured candies=2.

We need to find out what would be the probability of picking an orange or a cherry-flavoured candy from the bag.

According to the probability formula, the likelihood that an event will occur is equal to the proportion of favourable outcomes to all outcomes.

The probability of an event[tex]=\frac{Number of favourable outcomes}{Total Number of outcomes}[/tex].

Now, the probability of picking an orange flavored candy from the bag [tex]=\frac{2}{15}[/tex]

The probability of picking a cherry flavored candy from the bag [tex]=\frac{6}{15}[/tex]

The probability of picking an orange or a cherry flavored candy from the bag [tex]=\frac{2}{15}+\frac{6}{15}=\frac{8}{15}[/tex].

Therefore, the probability of picking an orange or a cherry flavored candy from the bag is [tex]\frac{8}{15}[/tex].

To learn more about the probability visit:

https://brainly.com/question/11034287.

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Answer:

0.649

Step-by-step explanation:

The probability that the number of people who show up to the plane exceed the capacity of the plane is 0.257.

Binomial distribution in probability is the discrete distribution that results in only two possible values in an experiment. The two possible values are either success/ true/ one which is denoted by probability 'p' or failure/ false/ zero which is denoted by q = 1 - p.

Binomial distribution formula can be written as,

P(x) = ⁿCₓ pˣ qⁿ⁻ˣ

where, n is number of experiments and x = 0, 1, 2, ...

Here, it is given that capacity of plane is 68

Number of people actually booked for flight is 70 ⇒ n = 70

Probability that people booked on their flight actually show up = 0.97

So, p = 0.97

⇒ q = 1 - p = 1 - 0.97 = 0.03

Let P be the probability that the number of people showing up exceed the capacity of the plane.

P = P (x = 69) + P (x = 70)

P = [⁷⁰C₆₉ (0.97)⁶⁹ (0.03)⁷⁰⁻⁶⁹] + [⁷⁰C₇₀ (0.97)⁷⁰ (0.03)⁷⁰⁻⁷⁰]

P = [ 70 × 0.122 × 0.03] + [1 × 0.119 × 0.03]

P = 0.2562 + 0.00357

P = 0.2598 ≈ 0.257

Hence, probability that the number of people who show up will exceed the capacity of the plane is 0.257.

To learn more on binomial probability distribution, click:

https://brainly.com/question/7283210

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Answer:

of the 30 students in the class, 2/3 are wearing jackets. How many students in the class are wearing jackets.

Step-by-step explanation:

For the first one, the equation would be 1/3(30)

for the second, the equation would be 3/2(30)

and the last on would be the same as the first. 1/3(30)

  Angle Q = 31°  

  Angle R = 118°

   Angle S = 31°

Answer:

the answer is 207550

.............................

Answer:

isoseles triangle

explanation: none of the sides are the same

hope this helps

Answer: SCALENE

Step-by-step explanation:

All sides are unequal, ISOSELES has 2 equal sides and EQUILATERAL all sides are equal.

Answer:

y-4=1x-4

Step-by-step explanation:

put in format : y2-y1=m(x2-x1)

y-4 = 1(x-4)

distribute

y-4=1x-4

Answer:

B

Step-by-step explanation:

x = -5

Put in -5 for x, and expand:

-40(k-x) = -40(k+5)

B. -40(k+5)

Answer:

a quadratic function is letter A

Answer:

2 metres per 1 hour

12 metres per 6 hours

30 minutes to glide 1 metre.

Step-by-step explanation:

1. To find the average speed, simply divide the distance covered by the amount of time taken, like so:

4 metres / 2 hours = 2 metres per 1 hour

2. To find how many metres the snail will glide in 6 hours, multiply the 2 metres per 1 hour by 6, like so:

6(2 metres per 1 hour) = 12 metres per 6 hours

3. Because we know that 2 metres take 1 hour to glide over, if we divide 2 in half, we get 1, so we can also divide 1 hour in half to get 30 minutes. Therefore, it takes 30 minutes to glide 1 metre.

Hope this helps :)

Answer: 9

Step-by-step explanation:

-3 1/3 x (-2 7/10)

-3  = -3*(3/3) = -9/3

-3 1/3 = -10/3

(-2 7/10)

-2  = -2(10/10) = -20/10

-2 7/10 = -27/10

(-10/3)*(-27/10) = (270/30) = 9

Answer:

Step-by-step explanation:

The km/minute is different for segment, so "The train does not always go . . ."

Tha average speed in km/minute of the 3 points is 3.2km/min. 10 minutes would be 32km.

===

Divide the cost by the number of people. It is $7/person in each case. The cost for each person appears to be the same. If Sam knew more math, he could charge each person $10 and end the evening $3/person richer. He would need at least 3 people to cover his own expense, and have $2 left for a tip to the attentive waitress who approved his strategy for profiting from his math skills.

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The Correct choice is C

Keegan is correct, Annie didn't line up the decimals correctly.