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3 years ago

Find a direct relationship between x and y. x = 3t and y = 2t + 7

Mathematics

1 answer:

ikadub [295]3 years ago

6 0

Answer:

y = $\frac{2}{3}$ x + 7

Step-by-step explanation:

Given

x = 3t ( divide both sides by 3 )

$\frac{1}{3}$ x = t

Substitute this value into y = 2t + 7

y = 2 × $\frac{1}{3}$ x + 7 = $\frac{2}{3}$ x + 7

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Danielle earns a 7.25% commission on everything she sells at the electronics store where she works. She also earns a base salary

Nikitich [7]

Answer:

Last week her sales were $4500.

Step-by-step explanation:

Given:

Danielle earns a 7.25% commission on everything she sells at the electronics store where she works.

She also earns a base salary of $750 per week.

Her total earnings for the week were $1,076.25.

Now, to find her sales last week.

Let the sales of last week be $x.$

Base salary = $750.

Total earnings = $1076.25.

So, we deduct the base salary from the total earnings first:

$1076.25-750$

$=326.25.$

Thus, the rest of the earnings is $326.25 which is the 7.25% commission on sales.

Now, to get the sales of last week we put an equation:

$7.25\%\ of\ x=326.25$

$\frac{7.25}{100} \times x=326.25$

$\frac{7.25x}{100} =326.25$

Multiplying both sides by 100 we get:

$7.25x=32625$

Dividing both sides by 7.25 we get:

$x=4500.$

The sales of last week = $4500.

Therefore, last week her sales were $4500.

7 0

3 years ago

65. show that of all the isosceles triangles with a given perimeter, the one with the greatest area is equilateral.

lora16 [44]

Answer:

Below.

Step-by-step explanation:

I can do this using calculus but the algebra will be a bit messy.

Let the 2 equal sides of isosceles triangle be x and the base be y units long.

Then perimeter p = 2x + y.

Area A = 0.5yh where h is the altitude of the triangle.

h = sqrt [x^2 - (0.5y)^2]

= [x^2 - (0.5y)^2]^0.5

So A = 0.5y * [x^2 - (0.5y)^2]^0.5

From the perimeter formula y = p - 2x so:

A = 0.5(p-2x) * [x^2 - (0.5(p-2x)^2]^0.5

A = 0.5(p-2x) * [x^2 - 0.25(p^2 - 4xp + 4x^2)]^0.5

A = 0.5(p-2x) * [x^2 - 0.25p^2 + xp - x^2]^0.5

A = (0.5p-x) * [xp - 0.25p^2]^0.5

We now find the derivative and equate it to zero to find the value of x which corresponds to a maximum area.

We use the product rule:

dA/dx = (0.5p-x)* 0.5(xp - 0.25p^2)^(-0.5) * p - 1(xp - 0.25p^2)^0.5 = 0

p(0.5p - x) / (2((xp - 0.25p^2)^0.5 - (xp - 0.25p^2)^0.5 = 0

p(0.5p - x) / (2((xp - 0.25p^2)^0.5 = (xp - 0.25p^2)^0.5

Now multiplying though by (2((xp - 0.25p^2)^0.5 :-

p(0.5p - x) = 2 (xp - 0.25p^2)

0.5p^2 - px = 2px - 0.5p^2

p^2 = 3px

x = p^2/3p = p/3

So for a maximum value of the area x = p/3.

But y = p - 2x

= p - 2(p/3)

= p - 2/3p

= p/3

- but we've just shown that x = p/3

That means that x = y and the triangle is Equilateral.

4 0

2 years ago

A construction worker needs to put lights on a pole 420 centimeters off the ground. How many meters off the ground do the lights

evablogger [386]

Answer:

4.2 meters

Step-by-step explanation:

The height that the lights will be put is 420 centimeters, and the question asks how many meters off the ground the lights need to be placed, so to solve the question we just need to convert 420 centimeters to meters.

We know that 1 meter is equal to 100 centimeters, so we can solve this using a rule of three:

100 centimeters -> 1 meter

420 centimeters -> X meters

100/420 = 1/X

X = 420/100 = 4.2 meters

The lights need to be placed on the pole at 4.2 meters off the ground.

5 0

3 years ago

8. If the measure of one side of a square is increased by 2 centimeters and the measure of

GalinKa [24]

Answer:

6 cm

Step-by-step explanation:

If the original side length is x, then the modified square has an area of ...

A = LW

32 = (x +2)(x -2) = x^2 -4

36 = x^2 . . . . . . . . add 4

6 = x . . . . . . . . . . take the square root

The original figure has a side length of 6 cm.

Check

The modified figure is 8 cm by 4 cm = 32 cm^2.

8 0

3 years ago

Fins the product of 5/12 And 3/8

Kamila [148]

Answer:

Step-by-step explanation:

( 5/12) × (3/8) =(5×3)/(12×8) = 5/32

4 0

3 years ago