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3 years ago

Find the area of the shaded region.

Mathematics

1 answer:

Iteru [2.4K]3 years ago

4 0

Keeping in mind that the area of a rectangle is simply width * length, if we get the area of the larger rectangle, and then subtract the area of the smaller rectangle, we're in effect making a hole in the larger rectangle's area and thus what's leftover is the shaded area.

$\bf \stackrel{\textit{area of the larger rectangle}}{(2x+2)(3x-4)}~~-~~\stackrel{\textit{area of the smaller rectangle}}{(x-3)(x-6)}
\\\\\\
\stackrel{FOIL}{6x^2-2x-8}~~~~-\stackrel{FOIL}{(x^2-9x+18)}\implies 6x^2-2x-8-x^2+9x-18
\\\\\\
5x^2+7x-26$

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A toll collector on a highway receives $8 for trucks and $7 for cars. At the end of a 33-hour period, she collected $296. H

frosja888 [35]

Answer:

The required list is: 0 car and 37 truck; 8 car and 30 truck; 16 car and 23 truck; 24 car and 16 truck; 32 car and 9 truck;

Step-by-step explanation:

Consider the provided information.

A toll collector on a highway receives $8 for trucks and $7 for cars, at the end she collected $296.

Let t represents the number of trucks and c represents the number of cars pass through highway.

$8t+7c=296$

$8t=296-7c$

$t=37-\frac{7c}{8}$

The number of trucks should be natural number.

Substitute c=0 in $t=37-\frac{7c}{8}$

$t=37-\frac{7(0)}{8}$

$t=37$

Substitute c=8 in $t=37-\frac{7c}{8}$

$t=37-\frac{7(8)}{8}$

$t=37-7$

$t=30$

Substitute c=16 in $t=37-\frac{7c}{8}$

$t=37-\frac{7(16)}{8}$

$t=37-14$

$t=23$

Substitute c=24 in $t=37-\frac{7c}{8}$

$t=37-\frac{7(24)}{8}$

$t=37-21$

$t=16$

Substitute c=32 in $t=37-\frac{7c}{8}$

$t=37-\frac{7(32)}{8}$

$t=37-28$

$t=9$

Hence, the required list is: 0 car and 37 truck; 8 car and 30 truck; 16 car and 23 truck; 24 car and 16 truck; 32 car and 9 truck;

8 0

3 years ago

A sequence is defined recursively by f(1)=16 and f(n)= f(n-1)+2n. Find f(4)

lord [1]

Hi,

f(1)=16
f(2)=f(1)+2*2=16+4=20
f(3)=f(2)+2*3=20+6=26
f(4)=f(3)+2*4=26+8=34

8 0

3 years ago

What is the slope of the line on the graph?<br> Enter your answer in the box.

Firlakuza [10]

Answer:

I think this is the answer you are looking for. (See below)

Step-by-step explanation:

From the given graph it is noticed that the line is passing through many points.

The coordinates of three given points are (1,5), (-1,-1), (-1,-7)

If a line passing through two points (x1 ,y1) and (x2, y2) , the slope of the lie is defined by, m= y2 - y1/x2 - x1

The line passing through two points (-1,1) and (1,5). So the slope of the line is, m= 5 - 1 / 1 minus -1

m=4/2

Therefore, the slope of the line is 2.

Pls if this is wrong, let me know in the comments. I'm not really good at this topic in math but I hope it helps you. Sorry if it is wrong. Have a good day. :)

6 0

2 years ago

We roll a fair die repeatedly until we see the number four appear and then we stop. The outcome of the experiment is the number

muminat

Answer:

Step-by-step explanation:

given that we roll a fair die repeatedly until we see the number four appear and then we stop.

the number 4 can appear either in I throw, or II throw or .... indefinitely

So X = the no of throws can be from 1 to infinity

This is a discrete distribution countable.

Sample space= {1,2,.....}

b) Prob ( 4 never appears) = Prob (any other number appears in all throws)

= $\frac{5}{6} *\frac{5}{6} *\frac{5}{6} *\frac{5}{6} *...\\=(\frac{5}{6} )^n$

where n is the number of throws

As n tends to infinity, this becomes 0 because 5/6 is less than 1.

Hence this probability is approximately 0

Or definitely 4 will appear atleast once.

8 0

3 years ago

An initial investment is $6100.

gtnhenbr [62]

32,533.3>
Because 6100x16=97,600divided by 3=32,533.3

6 0

3 years ago