Solve the following equation 4x = 3/7

Factor completely:

Sergio [31]

Answer:

a.-(p-1)(p-6)

b.(a+2)(a+2-b)

c 3(b-2)^2

d.(c-5)(1+2x)

Step-by-step explanation:

5 0

2 years ago

What is the measurement of the longest line segment in a right rectangular prism that is 26 inches long, 2 inches wide, and 2 in

EastWind [94]

Answer:

$6\sqrt{19} \approx 26.153$ inches.

Step-by-step explanation:

The longest line segment in a right rectangular prism is the diagonal that connects two opposite vertices. On the first diagram attached, the green line segment connecting A and G is one such diagonals. The goal is to find the length of segment $\mathsf{AG}$ .

In this diagram (not to scale,) $\mathsf{AB} = 26$ (length of prism,) $\mathsf{AC} = 2$ (width of prism,) $\mathsf{AE} = 2$ (height of prism.)

Pythagorean Theorem can help find the length of $\mathsf{AG}$ , one of the longest line segments in this prism. However, note that this theorem is intended for right triangles in 2D, not the diagonal in a 3D prism. The workaround is to simply apply this theorem on two different right triangles.

Start by finding the length of line segment $\mathsf{AD}$ . That's the black dotted line in the diagram. In right triangle $\triangle\mathsf{ABD}$ (second diagram,)

Segment $\mathsf{AD}$ is the hypotenuse.
One of the legs of $\triangle\mathsf{ABD}$ is $\mathsf{AB}$ . The length of $\mathsf{AB}$ is $26$ , same as the length of this prism.
Segment $\mathsf{BD}$ is the other leg of this triangle. The length of $\mathsf{BD}$ is $2$ , same as the width of this prism.

Apply the Pythagorean Theorem to right triangle $\triangle\mathsf{ABD}$ to find the length of $\mathsf{AB}$ , the hypotenuse of this triangle:

$\mathsf{AD} = \sqrt{\mathsf{AB}^2 + \mathsf{BD}^2} = \sqrt{26^2 + 2^2}$ .

Consider right triangle $\triangle \mathsf{ADG}$ (third diagram.) In this triangle,

Segment $\mathsf{AG}$ is the hypotenuse, while
$\mathsf{AD}$ and $\mathsf{DG}$ are the two legs.

$\mathsf{AD} = \sqrt{26^2 + 2^2}$ . The length of segment $\mathsf{DG}$ is the same as the height of the rectangular prism, $2$ (inches.) Apply the Pythagorean Theorem to right triangle $\triangle \mathsf{ADG}$ to find the length of the hypotenuse $\mathsf{AG}$ :

$\begin{aligned}\mathsf{AG} &= \sqrt{\mathsf{AD}^2 + \mathsf{GD}^2} \\ &= \sqrt{\left(\sqrt{26^2 + 2^2}\right)^2 + 2^2}\\ &= \sqrt{\left(26^2 + 2^2\right) + 2^2} \\&= 6\sqrt{19} \\&\approx 26.153\end{aligned}$ .

Hence, the length of the longest line segment in this prism is $6\sqrt{19} \approx 26.153$ inches.

5 0

2 years ago

Goods available for sale are $40000, beginning inventory is $16000, ending inventory is $20000, the cost of goods sold $50000, w

zlopas [31]

Answer:

Step-by-step explanation:

Inventory turn over is the same as the inventory turn over ratio. Inventory turn over is defined simply as the ratio of the cost of goods that was sold (net sales) to the average inventory at the selling price.

Inventory turn over = Cost of goods/average inventory

Cost of goods sold = $50000

Average inventory = beginning of inventory + ending inventory/2

Average inventory = $16000+$20000/2

Average inventory = $36000/2

Average inventory = $18000

Inventory turn over = $50000/$18000

Inventory turn over= 2.78

6 0

2 years ago

1.Graph the equation y = 6x -18:

RSB [31]

Answer:

1. Given the equation: y =6x-18 ......[1]

The intercepts of a line are the points where the line intercepts or crosses the horizontal and vertical axes.

(A)

Horizontal intercept(x) states that the point where the line crosses the x-axis and at this point y=0

Put y=0 in equation [1]

$0=6x-18$ or

$6x=18$

Ordered pair of horizontal intercept(x) = (3,0)

(B)

Vertical intercept(y) states that the point where the line crosses the y-axis and at this point x=0.

Put x=0 in equation [1]

$y=6\cdot 0-18$ or

$y=-18$

Ordered pair of vertical intercept(y) = (0,-18)

You can also see the graph of the function y =6x-18 as shown in Figure-1.

2.

Graph the equation y+2x =4

to find the horizontal intercept and vertical intercept we follow the same process as done in 1

(A)

Horizontal intercept (x) = 2

Ordered pair = (2,0)

(B)

Vertical intercept (y) = 4

Ordered pair = (0,4)

Also, you can see these in the graph as shown in the Figure-2

3.

Given: The slope(m) of a line is $\frac{3}{4}$

Two lines are parallel if their slopes are equal and they have different y - intercepts.

(A).

The slope of a line parallel to it is, $\frac{3}{4}$

(B)

The slope of the original line is $\frac{3}{4}$ .

A line perpendicular to another line has a slope that is the negative reciprocal of the slope of the other line.

Therefore, slope of a line perpendicular to it is; $-\frac{1}{m} = -\frac{4}{3}$

4.

The graph of the equation y =4x+5 as shown in figure 3

The x-intercept of this line is $\frac{-5}{4}$ = -1.25

And the y-intercept of this line is y =5.

5.

Graph of the equation y = -3 represents the line as shown in figure 4.

6.

Solve the equation:

6y-18x = -18

6y = 18x-18

Divide by 6 to both sides of an equation ; we get

y = 3x-3 or

y = 3(x-1)

8 0

3 years ago

Can someone please help? I’ll put u as brainliest (whatever it’s called)

frez [133]

Answer:

B.

Step-by-step explanation:

7 0

2 years ago

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