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Maslowich
3 years ago
13

Can someone please help me with this question I don’t understand. Thanks

Mathematics
1 answer:
Ghella [55]3 years ago
7 0
I'm assuming your teacher meant to say "line segment AB" and not "line segment AD". Point D is not given at all. If that assumption holds up, then you can proceed with the rest of the solution below. If not, then you'll have to talk to your teacher. I think its a typo but its possible that there's more context somewhere that I'm not seeing (a diagram maybe?)

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

We're given the two points (2,7) and (5,1). The first thing we need to do is find the slope of the line through those points. Lets assign them to be equal to (x1,y1) and (x2,y2), so,

(x1,y1) = (2,7) and (x2,y2) = (5,1)

which further breaks down into these four items:
x1=2
y1=7
x2=5
y2=1

Plug each of those into the slope formula and simplify
m = (y2 - y1)/(x2 - x1)
m = (1 - 7)/(5 - 2)
m = (-6)/(3)
m = -2

The slope is -2. We'll use this to find the y intercept. We'll also use one of the points given to us, say the point (2,7)

(x,y) = (2,7) ---> x = 2 and y = 7

Plug m = -2, x = 2, and y = 7 into the equation below and solve for b
y = m*x + b
7 = -2*2 + b
7 = -4 + b
7 + 4 = -4 + b + 4
11 = b
b = 11

So we figured out that m = -2 is the slope and b = 11 is the y intercept

Therefore, the equation y = mx+b turns into y = -2x+11

Final Answer: y = -2x+11

-------------------------------------------------
Checking the answer:
plug in x = 2 and we get...
y = -2*x + 11
y = -2*2 + 11
y = -4 + 11
y = 7 
so that proves (x,y) = (2,7) is on the line y = -2x+11

Plug in x = 5 and we get...
y = -2*x + 11
y = -2*5 + 11
y = -10 + 11
y = 1
so that proves (x,y) = (5,1) is on the line y = -2x+11

Both points are on the same line y = -2x+11 so the answer is confirmed
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Step-by-step explanation:

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$120

Step-by-step explanation:

I = Prt

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3x + y = 3
x + y = 2

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2 years ago
can someone help me with this and give an explanation on how to do it? So i can know with the others.
MaRussiya [10]

Answer:

Values of y in order: 0, 2, 4, 6

Step-by-step explanation:

Hi there!

In the table, the first value of x is -2. To find the value of y for this row of the table, we can use the given equation y=2x+4.

y=2x+4

Plug in -2 as the value of x

y=2(-2)+4\\y=-4+4\\y=0

Therefore, y is 0 when x is -2. (In the table, in the row where x is -2, y would be 0.)

We repeat this process for the rest of the values in the table.

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y=2(-1)+4\\y=-2+4\\y=2

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y=2(0)+4\\y=0+4\\y=4

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y=2(1)+4\\y=2+4\\y=6

I hope this helps!

6 0
3 years ago
3. In an auditorium, 1/6 of the students are fifth graders, 1/3 are fourth graders, and 1/4 of the remaining students are second
Katen [24]

12

<h3>Further explanation</h3>

<u>Given:</u>

In an auditorium,

  • \frac{1}{6} of the students are fifth graders,
  • \frac{1}{3} are fourth graders, and
  • \frac{1}{4} of the remaining students are second graders.

There are 96 students in the auditorium.

<u>Question:</u>

How many second graders are there?

<u>The Process:</u>

The least common multiple (LCM) of 3 and 6 is 6.

Let us draw the diagram of all students.

96 \div 6 \ units = 16 \rightarrow \boxed{16}\boxed{16}\boxed{16}\boxed{16}\boxed{16}\boxed{16} = 96 \ students

  • \frac{1}{6} of the students are fifth graders, or 1 of 6 units above, that is \boxed{16} = 16 \ students
  • \frac{1}{3} = \frac{2}{6} are fourth graders, or 2 of 6 units above, that is \boxed{16}\boxed{16} = 32 \ students

The remainder is 6 units - (1 unit + 2 units) = 3 units, that is \boxed{16}\boxed{16}\boxed{16} = 48 \ students. Or, 96 - 16 - 32 = 48 students.

\frac{1}{4} of the remaining students are second graders.

Let us count how many second graders are there.

\boxed{ \ \frac{1}{4} \times 48 \ students = ? \ }

Thus, there are 12 second-graders in the auditorium.

- - - - - - - - - -

Quick Steps

\boxed{ \ \frac{1}{4} \times \bigg(1 - \frac{1}{6} - \frac{1}{3} \bigg) \times 96 = ? \ }

\boxed{ \ = \frac{1}{4} \times \bigg(\frac{6}{6} - \frac{1}{6} - \frac{2}{6} \bigg) \times 96 \ }

\boxed{ \ = \frac{1}{4} \times \frac{3}{6} \times 96 \ }

\boxed{ \ = \frac{3}{24} \times 96 \ }

We crossed out 24 and 96.

\boxed{ \ = 3 \times 4 \ }

\boxed{\boxed{ \ = 12 \ students \ }}

<h3>Learn more</h3>
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Keywords: In an auditorium, 1/6 of the students, fifth graders, 1/3, fourth, 1/4, the remaining students, second, 96, how many, second graders

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