6. A line passes through the points (-2,5) and (6,9). Calculate the gradient of this line.

Solve the following equation -3=z+4

makkiz [27]

Answer:

z = -7

x = 1.6

There is no equation in what you typed on the third lie so it cannot be solved (equal sign is missing)

x = - 132/7

Step-by-step explanation:

For all cases the goal is to isolate the unknown (represented by a letter) on one side of the equal sign by using mathematical operations simultaneously on both sides.

In the first equation, to isolate z we need to subtract 4 from both sides:

$-3=z+4\\-3-4=z+4-4\\-3-4=z\\z=-7$

In the second equation: in order to isolate x we need to get rid of the factor 4 that is multiplying x, therefore we use the division by 4 on both sides:

$6.4=4x\\\frac{6.4}{4}=\frac{4x}{4} \\1.6=x$

The third expression you wrote doesn't contain an equal sign and therefore it s not an equation (cannot be solved)

In the last equation, in order to isolate x we need to divide both sides by 7 and also to multiply both sides by 33:

$-4=\frac{7}{33} x\\\frac{-4*33}{7} =\frac{7*33}{33*7} x\\\frac{-132}{7} = x\\x=-\frac{132}{7}$

8 0

3 years ago

Find the value of the expression 4 + d For d = 8

yaroslaw [1]

Answer:

12

Step-by-step explanation:

4 + 8

5 0

3 years ago

Read 2 more answers

If the point P( -3/5,v) lies on the unit circle and P is in the third quadrant, what does y equal?

Bad White [126]

Answer:

y = -4/5

Step-by-step explanation:

Both coordinates are negative in the 3rd quadrant. The value of y is the other leg of the right triangle with hypotenuse 1. The Pythagorean theorem is helpful.

y = -√(1 -(-3/5)^2) = -√(1 -9/25) = -√(16/25)

y = -4/5

4 0

3 years ago

Hurry please help I am struggling

Paraphin [41]

Volume = L x W x H

6.1 x 5.4 x 8 = 263.52 cm^3

5 0

3 years ago

The vertices of a rectangle are Q (2, -3), R (2,4), S (5,4), and T (5, -3).

disa [49]

4) $A_{QRST} = A_{Q'R'S'T'} = 9$ .

5) The areas of the rectangles QRST and Q'R'S'T' are the same since the translation of the geometric loci conserved the Euclidean distance.

6) x = 1, w = 3, y = - 1/4, z = 1/3

<h3>How to analyze and apply rigid transformations</h3>

Rigid transformations are transformations applied on geometric loci such that Euclidean distance is conserved. In this question we have applications of translations, a kind of rigid transformation.

Exercise 4

In this part we must determine the areas of rectangles QRST and Q'R'S'T':

Rectangle QRST

A = RS · QT

A = 3 · 3

A = 9

Rectangle Q'R'S'T'

Q'(x, y) = (2, - 3) + (- 3, - 3)

Q'(x, y) = (- 1, - 6)

R'(x, y) = (2, 4) + (- 3, - 3)

R'(x, y) = (- 1, 1)

S'(x, y) = (5, 4) + (- 3, - 3)

S'(x, y) = (2, 1)

T'(x, y) = (5, - 3) + (- 3, - 3)

T'(x, y) = (2, - 6)

A = R'S' · Q'T'

A = 3 · 3

A = 9

The rectangles QRST and Q'R'S'T' have both an area of 9 square units.

Exercise 5

The areas of the rectangles QRST and Q'R'S'T' are the same since the translation of the geometric loci conserved the Euclidean distance.

Exercise 6

In this case, we must solve the following equations:

PQ = A'(x, y) - A(x, y)

(4, 1) = (2 · x + 1, 4) - (- 1, w)

(4, 1) = (2 · x + 2, 4 - w)

(4, 1) = (2 · x, - w) + (2, 4)

(2, - 3) = (2 · x, - w)

(x, w) = (1, 3)

PQ = B'(x, y) - B(x, y)

(4, 1) = (3, 3 · z) - (8 · y - 1, 1)

(4, 1) = (2 - 8 · y, 3 · z)

(4, 1) = (- 8 · y, 3 · z) + (2, 0)

(2, 1) = (- 8 · y, 3 · z)

(y, z) = (- 1/4, 1/3)

To learn more on translations: brainly.com/question/17485121

#SPJ1

3 0

2 years ago