The coordinates of the endpoints of AB and CD are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which condition proves that AB||CD ?

Answers

Answer 1

Answer:

Based on the concept of coordinates and the available information, the correct answer is option D. (y2 - y1)(y4 - y3) = (x2 - x1)(x4 - x3)

What is Coordinates?

Coordinate is a mathematical term that is used to describe the values on which mathematical operations occur in an algebraic expression.

In this case, to determine if AB is parallel to CD check if the slopes of the two lines are equal since parallel lines have the same slope.

The slope of a line passing through two points (x1 y1) and (x2 y2) is given by the formula:

m = (y2 - y1) / (x2 - x1)

So the slope of line AB is:

m_AB = (y2 - y1) / (x2 - x1)

And the slope of line CD is:

m_CD = (y4 - y3) / (x4 - x3)

If AB is parallel to CD then the slopes m_AB and m_CD should be equal.

Therefore the condition to prove that AB is parallel to CD is:

m_AB = m_CD

If the condition m_AB = m_CD is true it proves that line AB is parallel to line CD.

Hence, in this case, the correct answer is option D. (y2 - y1)(y4 - y3) = (x2 - x1)(x4 - x3)

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The option is in the image attached to the answer.

Answer 2

Answer:

Answer:

c= -1

Step-by-step explanation:

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1. (k+7)² =2892. (2s-1)² =225
3. (x-4)² =169

please help me answer these :)

Answers

$1. \ \ \ (k+7)^2 =289\n\n\Leftrightarrow\ \ \ k+7= √(289) \ \ \ or\ \ \ \ k+7=- √(289)\n\nk=17-7=10\ \ \ \ \ \ \ or\ \ \ \ k=-17-7=-24 \n\n2.\ \ \ (2s-1)^2 =225\n\n\Leftrightarrow\ \ \ 2s-1= √(225) \ \ \ or\ \ \ \ 2s-1=- √(225)\n\n2s=15+1\ \ \ \ \ \ \ or\ \ \ \ 2s=-15+1\n2s=16\ \ \ \ \ \ \ \ \ \ \ \ or\ \ \ \ 2s=-14\ns=8\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ or\ \ \ \ s=-7 \n\n$

$3.\ \ \ (x-4)^2 =169\n\n\Leftrightarrow\ \ \ x-4= √(169) \ \ \ or\ \ \ \ x-4=- √(169)\n\nx=13+4=17\ \ \ \ \ \ \ or\ \ \ \ x=-13+4=-9$

$(k+7)^2 =289\n |k+7|=17\n k+7=17\vee k+7=-17\n k=10 \vee k=-24$

$(2s-1)^2 =225\n |2s-1|=15\n 2s-1=15\vee 2s-1=-15\n 2s=16 \vee 2s=-14\n s=8 \vee s=-7$

$(x-4)^2 =169\n |x-4|=13\n x-4=13 \vee x-4=-13\n x=17 \vee x=-9$

What is the value of (4 minus 2) cubed minus 3 times 4?
Negative 20

Answers

The expression $((4 - 2)^3 - 3) * 4$ simplifies to 20, as of the given operations.

To calculate the expression $((4 - 2)^3 - 3) * 4$ , we follow the order of operations (PEMDAS/BODMAS).

First, we evaluate the parentheses: (4 - 2) = 2.

Next, we calculate the cube of 2³= 8.

Then, we subtract 3 from 8:
8 - 3 = 5.

Finally, we multiply the result by 4:
5 × 4 = 20.

Therefore, the value of the expression $((4 - 2)^3 - 3) * 4$ is 20.

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Answer:

-4

Step-by-step explanation:

(4-2)³ = 8

so 8 - 3 x 4

is equal to -4

Please help the question is in the picture x

Answers

$E\to1\ *\ 1\ *\ 24\n\nF\to1\ *\ 2\ *\ 12\n\nG\to1\ *\ 3\ *\ 8\n\nH\to1\ *\ 4\ *\ 6\n\nI\to2\ *\ 2\ *\ 6\n\nJ\to2\ *\ 3\ *\ 4$

E is 1 x 1 x 24
F is 1 x 2 x 12
G is 1 x 3 x 8
H is 1 x 4 x 6
I is 2 x 2 x 6
J is 2 x 3 x 4
Happy to Help!

Is 31.010 greater or less than 31.01

Answers

31.010 is equal to 31.01. This is because 31.010 and 31.01 is the same thing. 31.010 is just adding a zero at d end and 31.01 has no zero but it is the same thing as 31.010.

So, 31.010 = 31.01

Hope I helped ya!!

They are equal, you just can add 0's to the last digits of number and it's still the same.

T/9=35/6 what is this portion

Answers

Hello,this is your answer. :)

What are the approximate solutions of 2x2 + 9x = 8 to the nearest hundredth?a. x ≈ 1.22 and x ≈ 3.28
b. x ≈ −0.76 and x ≈ 5.26
c. x ≈ −1.22 and x ≈ −3.28
d. x ≈ −5.26 and x ≈ 0.76