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3 years ago

Find an equation for the line with the given properties. Perpendicular to the line 7x - 3y = 68; containing the point (8, -8)

Mathematics

1 answer:

Sever21 [200]3 years ago

6 0

Answer:

$y=\dfrac{-3}{7}x-\dfrac{32}{7}$

Step-by-step explanation:

Given that,

A line 7x - 3y = 68 and containing the point (8, -8).

The equation can be written as :

$-3y=68-7x\\\\y=\dfrac{68}{-3}+\dfrac{7x}{3}\\\\y=\dfrac{7x}{3}+(\dfrac{-68}{3})$

The slope is :7/3

Line is perpendicular so use m = –3/7

$-8=(-\dfrac{3}{7})\times 8+b\\\\-8+\dfrac{3}{7}\times 8=b\\\\b=\dfrac{-32}{7}$

So, required equation is :

$y=\dfrac{-3}{7}x-\dfrac{32}{7}$

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A vcr and tv were bought for 8000 each. The shopkeeper made a loss of 4 per cent on vcr and 8 per cent prophit on the tv. Find t

aleksley [76]

Answer:

2% gain

Step-by-step explanation:

We assume the shopkeeper bought the appliances at the indicated prices, and that gain is computed on the basis of that cost price.

Since the base cost is the same for each appliance, the percentages can be added directly to find the percentage gain on 8000. However, the shopkeeper's total outlay was 16000, not 8000, so the final gain percentage is half of that total.

gain percent = (-4% + 8%)/2 = 2%

_____

If you want to see the actual numbers:

Loss on VCR = 4% × 8000 = 320.

Gain on TV = 8% × 8000 = 640.

Total gain on 16000 is -320 +640 = 320. As a percentage, that is ...

320/16000 × 100% = 2%

7 0

3 years ago

An open box is formed from a rectangular piece of cardboard whose length is 8cm more than its width by cutting squares of 2cm fr

Serggg [28]

If the width of the cardboard = x cm then its length is given by x + 8 cm.
Then the length of the box will be x + 8 - 2(2) = x + 4
and the width = x - 2(2) = x - 4 cm The height is 2 cm

Volume = h*w*l = 2(x - 4)(x + 4) = 256
2(x^2 - 16) = 256
x^2 - 16 = 128
x^2 = 144
x = 12 cm

Dimensions of the box are:-

length = 12 + 4 = 16cm
width = 12 - 4 = 8 cm
height = 2 cm

3 0

3 years ago

The hypotenuse of a right triangle is 6 inches. if one of the legs is 2 inches, find the degree measure of each angle

miskamm [114]

A and b are the 2 smaller sides, and c = hypotenus; only for right triangles,
Pythagorean Theorem states that:
${c}^{2} = {a}^{2} + {b}^{2}$
given c = 6 in., a = 2 in.
${c}^{2} = {a}^{2} + {b}^{2} \\ {6}^{2} = {2}^{2} + {b}^{2} \\ {b}^{2} = {6}^{2} - {2}^{2} = 36 - 4 \\ \sqrt{ {b}^{2} } = \sqrt{36 - 4} = \sqrt{32}$
$b = \sqrt{32} = \sqrt{16} \times \sqrt{2} = 4 \sqrt{2} \\ b = 5.66 \: inches$
So the three side are 2, 6, and 5.66 inches

5 0

3 years ago

Help me with this question please

mojhsa [17]

Step-by-step explanation:

so, he will not wear any pants ? socks ? not to mention underwear ?

anyway, we have to deduct the $35 for the shoes, as he is seemingly buying them in any case.

so, we are left with 100 - 35 = $65 for shirts.

as one shirt costs $15, we need to see how often 15 fits into 65, as that is the answer how many shirts he can buy for this money.

65 / 15 = 4.333333333...

since he cannot buy a part shirt, we can only rely on the integer part of the calculation.

so, he can buy 4 shirts and will have $5 left.

8 0

2 years ago

Solve the following system using the substitution method. Show all work! <br> 4x+y=14 <br> x-2y=8

Serjik [45]

Answer:

Step-by-step explanation:

4x+y=14

x-2y=8

then;

x=8-2y

substitute;

4(8-2y)+8-2y=14

32-8y+8-2y=14

40-10y=14

26=10y

y=2.6 , work out 4x+2.6=14 to get x

6 0

3 years ago

Read 2 more answers