MATHEMATICS HIGH SCHOOL

Are the graphs of y=3/8x -5 and y=3/8x +2 parallel?

Answers

Answer 1
Answer:

The graph of y = (3/8)x - 5 and y = (3/8)x + 2 are parallel since both graphs have the same slope.

What is an equation of a line?

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The graph of two equations is parallel if the slope of each of the equations is the same.

The two equations are:

y = (3/8)x - 5 _____(1)

y = (3/8)x + 2 _____(2)

This is in the form of y = mx + c

Where m is the slope.

Now,

From (1 ) and (2) we see that,

m = 3/8

Thus,

The graphs are parallel.

Learn more about equation of a line here:

brainly.com/question/23087740

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Answer 2
Answer: yes because they have the same slope of 3/8

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The sum of the digits of a two-digit number is 9. If the digits are reversed, the new number is 27 less than the original. Find the original number.

Answers

I did another one just like this about an hour ago.  I did it the elegant, tedious way,
and it took about 2 feet of screen.  Then I realized there was a totally bourgeois but
easy way to do it.  For 5 points, I'll give you the method for the masses:

List all the possible pairs of digits that add up to 9, along with their flips:

18 . . . . . 81
27 . . . . . 72
36 . . . . . 63
45 . . . . . 54

Do you see any pair that are different by 27 ?
How about 36 and 63 ?

So the original number is 63, and when you flip it, it becomes 36, which is 27 less.

In an isosceles trapezoid, each pair of base angles is __________. A. right B. Supplementary C. complimentary D. congruent

Answers

I'm totally sure that inn an isosceles trapezoid, each pair of base angles is D. congruent

At an icecream parlor, ice cream cones cost $1.10 and sundaes cost $2.35. One day, the receipts for a total of 172 cones and sundaes were $294.20. How many cones and sundaes were sold?

Answers

2.35 + 1.10 = 3.45
2.35 / 3.45
1.10 / 3.45

294.20 / 3.45 x 1.10 = 93.80 to 4sf
294.20 / 3.45 x 2.35 = 200.40 to 4sf

93.80 + 200.40 = 294.20

93.80 / 1.10 = 85.2727272727
200.40 / 2.35 = 85.2765957447

85 + 85 = 170      need two more

84 x 1.10 = 92.40    84 x 2.35 = 197.4
88 x 2.35 = 206.8    88 x 1.10 = 96.8
                = 299.2                    = 294.20

Answer: 84 sundaes and 88 ice cream cones were sold.

I guess I spent too long and the working out was probably more long-winded than it should've been.

5.567 round hundredths

Answers

5.57 because 5 is the tenths 6 is hundredths 7 is thousandths
556.7, I am really good at decimals and fractions, just mainly math, science, literature, and some Economics

Solve the system x+y=54
x-5y=0
A. (-45, -9)
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Answers

   
\displaystyle \n \begin{cases} x+y = 54 \n x-5y = 0~~~~~| \cdot (-1) \end{cases} \n \n \n \begin{cases} x+y = 54 \n -x+5y = 0 \end{cases} \n \texttt{-------------- gather equations} \n .~~/~~~~~6y = 54 \n \n y = (54)/(6) = \boxed{9} \n \n x = 54 - y = 54 - 9 = \boxed{45} \n \n \texttt{Problem solution: } \boxed{x = 45 ~~ and ~~ y = 9 }

Find three arithmetic means between -2 and 12.

Answers

a_1=-2;\ a_2;\ a_3;\ a_4;\ a_5=12\n\na_5-a_1=4d\n\n4d=12-(-2)\n4d=14\ \ \ /:4\nd=3.5\n\na_2=a_1+d\to a_2=-2+3.5=1.5\n\na_3=a_2+d\to a_3=1.5+3.5=5\n\na_4=a_3+d\to a_4=5+3.5=8.5\n\nSolutions:1.5;\ 5\ and\ 8.5
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