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Musya8 [376]
3 years ago
6

Find the length of the longest side of the rectangle whose vertices are given. a(2, 1), b(5, 4), c(0, 3), d(3, 6)

Mathematics
1 answer:
aleksandr82 [10.1K]3 years ago
5 0
First, you plot the coordinates to visualize the problem clearly. As you can see in the picture, the longest sides could either be one of those marked in red. This could be initially determined when you use visual estimation. We measure this using the distance formula: d = √[(x2-x1)^2 + (y2-y1)^2)]

Between coordinates (0,3) and (3,6)
d = √[(3-0)^2 + (6-3)^2)]
d= 4.24 units

Between coordinates (2,1) and (5,4)
d = √[(5-2)^2 + (4-1)^2)]
d= 4.24 units

They are of equal length. Both are the longest sides which measures 4.24 units.

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At a restaurant last night, 8 people ordered salads, 10 ordered steaks, 18 ordered chicken, and 14 ordered pasta.
tatyana61 [14]

Answer:

36 people would order chicken.

Step-by-step explanation:

Case I: (50 People in Total)

Total Number of People Ordering=8+10+18+14=50

Percentage of People ordering chicken=people ordering chicken/total number of people=18/50=0.36%

Case II: (100 People in Total)

Number of People ordering chicken=percentage of people ordering chicken x total number of people=0.36 x 100=36

6 0
3 years ago
Create an expression equivalent to 3 (4x -2) -5x+10 using the least number of terms. please show your work.
marusya05 [52]

Answer:

7x+4

Step-by-step explanation:

Distribute:

=(3)(4x)+(3)(−2)+−5x+10

=12x+−6+−5x+10

Combine Like Terms:

=12x+−6+−5x+10

=(12x+−5x)+(−6+10)

=7x+4

7 0
3 years ago
The sets G and M are given below.
Varvara68 [4.7K]

union=( -2,-1,0,1,2,5,7,8) intersection= -1,1

6 0
3 years ago
Solve the equations
Minchanka [31]

Answer:

#1 - All real numbers are solutions.

#2 - All real numbers are solutions.

Step-by-step explanation:

#1 -

Let's solve your equation step-by-step.

12(6t−4)=3t−2

Step 1: Simplify both sides of the equation.

12(6t−4)=3t−2

(12)(6t)+(12)(−4)=3t+−2(Distribute)

3t+−2=3t+−2

3t−2=3t−2

Step 2: Subtract 3t from both sides.

3t−2−3t=3t−2−3t

−2=−2

Step 3: Add 2 to both sides.

−2+2=−2+2

0=0

Same for #2

8 0
3 years ago
In the expression below, a is an integer. 12^3+ax-20 if 3x+4 is a factor of the expession above, what is the value of a
SVEN [57.7K]

Our function is:

f(x)=12^3+ax-20

Now, if 3x+4 is a factor of f(x) then x=\frac{-4}{3} must satisfy the equation:

So, f(\frac{-4}{3} )=0

Putting x=\frac{-4}{3}

We get,

f(\frac{-4}{3} )=12^3+a(\frac{-4}{3} )-20=0

12^3+\frac{-4}{3} a-20=0

\frac{-4}{3} a=20-12^3=20-1708

a=-1708 \times \frac{-3}{4} =1281

So, the value of 'a' for the given expression is 1281.

4 0
3 years ago
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