All categories

1 year ago

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

Mathematics

2 answers:

mezya [45]1 year ago

8 0

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

givi [52]1 year ago

4 0

To find the perpendicular slope, you find the reciprocal of the slope (in this case, 1/3) and multiply that by -1 (in this case, it gets -1/3)

You might be interested in

The widths (in meters) of a kidney-shaped swimming pool were measured at 3-meter intervals as indicated in the figure. Use the M

forsale [732]

We can used the Simpson's Rule says to approximate the area under a given curve using the following formula:

(Δx/3)[f(x0) + 4f(x1) + 2f(x2) + 4f(x3) + ... + 2f(xn-2) + 4f(xn-1) + f(xn)] 

The pool is divided into 8 subintervals. We integrate the given function from 0 to 24, while the graph provides values of f(x) at 7 different points. The first value given, 6.2, is NOT f(0). It is f(3). Using Simpson's Rule, and dividing the lake of 24 meters into 8 subintervals, we write the equation: 

area = (3/3)[f(0) + 4f(3) + 2f(6) + 4f(9) +2f(12) + 4f(15) + 2f(18) + 4f(21) + f(24)] 

Pool area = 0 + 4(6.2) + 2(7.2) +4(6.8) + 2(5.6) + 4(5.0) +2(4.8) +4(4.8) + 0 = 126.4 m^2 

Rounding to the nearest square meter, the area of the lake is approximately 126 m^2

6 0

2 years ago

Read 2 more answers

A set of speakers costs $22 and songs cost $1.25 each. The sales tax rate is 7.5%. The expression 0.075(22 + 1.25s) can be used

kykrilka [37]

Answer:

1.65 + 0.09s

Step-by-step explanation:

Given that :

Cost of speaker = $22

Cost per song = $1.25

Sales tax rate = 7.5%

Expression to obtain the amount of sales tax on entire purchase : 0.075(22 + 1.25s)

Expanding the expression :

0.075(22 + 1.25s)

(0.075 * 22) + (0.075 * 1.25s)

1.65 + 0.09375s

Rounding to the nearest hundredth :

Sales tax on entire purchase :

1.65 + 0.09s

4 0

1 year ago

At Royston's favorite clothing store, the cost of a pair of jeans is $4 more than twice the cost of a shirt. The cost of a pair

MrRa [10]

J(jeans) = 2s + 4
d(dress pants) = 2.5s - 2
s = shirt

he spent : 2s + 4 + 2.5s - 2 = 4.5s + 2

8 0

1 year ago

What is the unit price of 8 mugs for $38.32

jarptica [38.1K]

Answer:

4.79$ for each mug

Step-by-step explanation:

38.32/8 = 4.79 and to double-check do 4.79*8

8 0

1 year ago

Read 2 more answers

The box which measures 70cm X 36cm X 12cm is to be covered by a canvas. How many meters of canvas of width 80cm would be require

grigory [225]

Answer:

142.2 meters.

Step-by-step explanation:

We have been given that a box measures 70 cm X 36 cm X 12 cm is to be covered by a canvas.

Let us find total surface area of box using surface area formula of cuboid.

$\text{Total surface area of cuboid}=2(lb+bh+hl)$ , where,

$l$ = Length of cuboid,

$b$ = Breadth of cuboid,

$w$ = Width of cuboid.

$\text{Total surface area of box}=2(70\cdot36+36\cdot 12+12\cdot 70)$

$\text{Total surface area of box}=2(2520+432+840)$

$\text{Total surface area of box}=2(3792)$

$\text{Total surface area of box}=7584$

Therefore, the total surface area of box will be 7584 square cm.

To find the length of canvas that will cover 150 boxes, we will divide total surface area of 150 such boxes by width of canvass as total surface area of canvas will also be the same.

$\text{Width of canvas* Length of canvass}=\text{Total surface area of 150 boxes}$