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lara [203]
3 years ago
11

Plsss help!!!!!!!!!!!

Mathematics
1 answer:
olga55 [171]3 years ago
6 0
You’re correct, it’s the first option
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Combine the like terms to create an equivalent expression:
Nesterboy [21]

Answer:

-2z+8

Step-by-step explanation:

3z+2+(-5x)+6\\\\=3z+2-5x+6\\\\=(3z-5z)+(2+6)\\\\=(-2z)+(8)\\\\=-2z+8

6 0
3 years ago
PLEASEEE HELP !!
miss Akunina [59]

Answer: b+95+34=180, b+129=180, 51

Step-by-step explanation:

b+95+34=180 works because the angles add to form a straight angle.

From this, we can obtain b+129=180 by adding the two constants.

Subtracting 129 from both sides, we get b=51.

6 0
2 years ago
A hiker travels 45 degrees north of east for 30 km. What is his NORTH (or y) displacement component? Round your answer and inclu
miv72 [106K]

consider X-axis along the east-west direction and north-south direction along Y-axis

A = magnitude of distance traveled by hiker in north-east direction = 30 kilometer

θ = angle of direction of displacement of the hiker relative to x-axis or east direction = 45 degree counterclockwise

A' = component of distance traveled by the hiker along the east direction.

Since the angle is given with the x-axis, the Sin provides the component in Y-direction. hence

Using the equation

A' = A Sinθ

Inserting the values

A' = (30) Sin45

A' = 21.2 km

8 0
3 years ago
Verify that the points are the vertices of a parallelogram and find its area. (2,-1,1), (5, 1,4), (0,1,1), (3,3,4)
Gelneren [198K]

Answer:

Area = 13.15 square units

Step-by-step explanation:

Let the given vertices be represented as follows:

A(2, -1, 1) = 2i - j + k

B(5, 1, 4) = 5i + j + 4k

C(0, 1, 1) = 0i + j + k

D(3, 3, 4) = 3i + 3j + 4k

(i) Let's calculate the vectors of all the sides:

\\AB = B - A =  (5i + j + 4k) - (2i - j + k)

AB = 5i + j + 4k - 2i + j - k                 [Collect like terms]

AB = 3i + 2j + 3k

BC = C - B =  (0i + j + k) - (5i + j + 4k)

BC = 0i + j + k - 5i - j - 4k                 [Collect like terms]

BC = -5i + 0j - 3k

CD = D - C =  (3i + 3j + 4k) - (0i + j + k)

CD = 3i + 3j + 4k - 0i - j - k                [Collect like terms]

CD = 3i + 2j + 3k

DA = A - D =  (2i - j + k) - (3i + 3j + 4k)

DA = 2i - j + k - 3i - 3j - 4k                [Collect like terms]

DA = -i - 4j - 3k

AC = C - A =  (0i + j + k) - (2i - j + k)

AC = 0i + j + k - 2i + j - k                [Collect like terms]

AC = -2i + 2j

BD = D - B = (3i + 3j + 4k) - (5i + j + 4k)

BD = 3i + 3j + 4k - 5i - j - 4k                [Collect like terms]

BD = -2i + 2j

(ii) From the results in (i) above, we can deduce that;

AB = CD This implies that AB || CD  [AB is parallel to CD]

AC = BD This implies that AC || BD  [AC is parallel to BD]

(iii) Therefore, ABDC is a parallelogram since opposite sides (AB and CD) are parallel. Hence, the points are vertices of a parallelogram

<u>Now let's calculate the area</u>

To find the area of the parallelogram, we find the magnitude of the cross product of any two adjacent sides.

In this case, we'll choose AB and AC

Area = |AB X AC|

Where;

AB X AC = \left[\begin{array}{ccc}i&j&k\\3&2&3\\-2&2&0\end{array}\right]

<u></u>

AB X AC = i(0 - 6) - j(0 + 6) + k(6 + 4)

AB X AC = - 6i - 6j + 10k

|AB X AC| = \sqrt{(-6)^2 + (-6)^2 + (10)^2}

|AB X AC| = \sqrt{172}

|AB X AC| = 13.15

Area = 13.15 square units.

<u></u>

<u></u>

<u>PS: </u> ACBD is also a parallelogram. The diagram has also been attached to this response.

6 0
3 years ago
Complete the square and graph: 9y²−x − 18y +10=0 ​
Nitella [24]

Answer:

See below ~

Step-by-step explanation:

Completing the square :

  • 9y² - x - 18y + 10 = 0
  • 9y² - 18y + 9 - 9 - x + 10 = 0
  • <u>(3y - 3)² - x + 1 = 0</u>

<u></u>

Graph :

4 0
2 years ago
Read 2 more answers
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