Half of j minus 5 is the sum of k and 13

The lines y=3x-1 and y=ax+2 are perpendicular if a=___

mezya [45]

Answer:

$a = \frac{-1}{3}.$

Step-by-step explanation:

The equation of line in the form .

y = mx + c

Where m is the slope and c is the y- intercept .

As given

The lines y=3x-1 and y=ax+2 are perpendicular .

Here 3 is slope for equation of line y=3x-1 and a is slope for equation of line

y=ax+2 .

Now by using properties of the perpendicular lines property .

When two lines are perpendicular than slope of one line is negative reciprocal of the other line .

Thus

$a = \frac{-1}{3}$

Therefore $a = \frac{-1}{3}.$

8 0

1 year ago

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A parallelogram has a length of 6 centimeters and a width of 4.5 centimeters. This parallelogram is dilated by a scale factor of

Arada [10]

Scale factor is given by:
(length of larger figure)/(length of smaller figure)=(width of larger figure)/(width of the smaller figure)=3.4
The length of the larger figure will be given by:
length=(scale factor)*(length of smaller figure)
=3.4*6=20.4 cm
width of the larger figure will be given by:
width=(scale factor)*(width of smaller figure)
=3.4*4.5
=15.3 cm
Therefore the dimension of the new parallelogram will be 20.4 cm by 15.3 cm

3 0

2 years ago

A gardener brought 5 rabbits, after 2 months rabbits became 10, and after 4 months they became 20. If the growth continues on th

kramer

Answer:

Initial population of Rabbit = 5 rabbit

After 2 months

Population of Rabbit = 10

After 4 months

population of rabbit = 20

Formula for growth is :

G = $G_{0}[1 + R]^n$ , where G is final population and $G_{0}$ is initial population, and R is growth rate.

1. 10 = 5 [1 +R]²

Dividing both sides by 5 , we get

2 = (1 + R)²

→ R + 1 = √2 ⇒ taking positive root of 2

→R = √2 -1

Amount of rabbit after 1 year = $20(1 + \sqrt2 -1)^8= 20 \times (\sqrt2)^8= 20 \times 2^4= 20 \times 16= 320$

6 0

2 years ago

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The perimeter of the base of a regular quadrilateral prism is 60 cm, the area of one of the lateral faces is 105 cm2.

yawa3891 [41]

For a better understanding of the solution, please follow the diagram in the attached file.

A regular quadrilateral is basically a square.

So, if the base of the prism has a perimeter of 60 cm, then the length of the side of the square will be $\frac{60}{4}=15 cm$ . It is shown of the diagram.

Now, from the diagram, it is clear that the lateral face area, which is given as 105 cm^2, is the product of the side of the square, which is known, and the unknown height, let us call it h. Thus, we will get the following equation:

$15\times h=105$

$\therefore h=\frac{105}{15}=7 cm$

This is depicted on the diagram.

Now, all our required parameters are in place. Thus, let us find what has been asked.

<u>SURFACE AREA</u>

Surface Area (SA) will be the sum of the areas of the two bases (squares) and the areas of the four lateral faces.

Since the side of one square base is 15 cm, therefore, the area of one square base will be $15^2$ .

Likewise, the area of one lateral surface is actually the area of a rectangle with length 15 cm and height 7 cm. Thus, it's area will be given as: $15\times 7$ .