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sergiy2304 [10]
2 years ago
10

One Step Equations (Multiplication) -4=2y

Mathematics
1 answer:
Katena32 [7]2 years ago
8 0
The answer will be y= -2.
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5x + 8 - 7x = -4x + 1
irakobra [83]

Step-by-step explanation:

5x+8-7x=4x+1

5x+7x-4x=8+1

8x=9

6 0
3 years ago
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The vertices of a parallelogram are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which of the following must be true if paral
Iteru [2.4K]

The answer is really none of the above, because all of these have divisions by difference in x, and there are perfectly fine rectangles where those will mean dividing by zero.

To do the problem the way they want us to, we note segments with the same slope are parallel (or collinear); segments with slopes which multiply to -1 are perpendicular.

Let's figure out what each choice is trying to tell us by translating it into parallel and perpendicular. Remember A is point 1, ...

A. ((y_4-y_3)/(x_4-x_3)= (y_3-y_2)/(x_3-x_2)) and ((y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2))=-1

translated, that's CD║BC and CD⊥BC - contradictory; second half right

B. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and ((y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1))=-1

CD ║ AB and CD ⊥ AB - only the parallelogram half is right

C. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and (y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2)=-1

CD║AB and CD⊥BC - that's TRUE

D. (y_4-y_3)/(x_4-x_3)= (y_3-y_1)/(x_3-x_1) and (y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1)=-1

CD║AC and CD⊥AB - nope

Answer: C

The way I'd get the proper expression is with the dot product.

A parallelogram is a rectangle when adjacent sides are perpendicular. It only takes one right angle to make them all right.

Two sides are perpendicular when the dot product of their direction vectors is zero. All the answers have y_4 - y_3 so one side is CD. The other side must be BC or AD; AD would give y_4 - y_1 terms which don't appear among the answer, so let's go with BC.

The direction vectors are

D-C = (x_4 - x_3, y_4 - y_3)

C-B = (x_3 - x_2, y_3 - y_2)

For perpendicularity we need a zero dot product:

0 = (D-C)\cdot(C-B) = (x_4 - x_3)(x_3 - x_2) + (y_4 - y_3)(y_3 - y_2)

- (x_4 - x_3)(x_3 - x_2) = (y_4 - y_3)(y_3 - y_2)

That's the correct expression, given it's a parallelogram, to demonstrate it's a rectangle. The divisions make it iffy.

8 0
2 years ago
A tangerine juice container is in the shape of a rectangular prism. The width is 26
geniusboy [140]

Answer:

V = 26d^2 + 624d

Step-by-step explanation:

Volume = Width x Depth x Height

V = 26 (d) (d+24)

Now distribute 26

V = 26d(d+24)

Then distribute 26d

V = 26d^2 + 624d

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3 years ago
Write -8 in simplest radical form.
Nadya [2.5K]
2.8 or if rounded to the nearest tenth so 2.8√8
4 0
2 years ago
In a class of 40 students, the number of girls is 10 more than the number of boys. We have to find the number of girls and the n
Nadusha1986 [10]

Answer:

b=15 g=25

Step-by-step explanation:

lets translate that story problem to mathematics equations

the problem told that no. of girls are 10 more than no of boys so this will =

g=b+10

then in class there are 40 students that means

g+b=40

now we have to equations with two variables then we should substitute

(b+10)+b=40

lets remove the brackets

2b+10=40 subtract 10 from both sides

2b=30 now divide both by 2

b=15 so g=25 after you write the equation once again with the new proof or number

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