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3 years ago

6

Please help me simplify these expressions

1 answer:

yKpoI14uk [10]3 years ago

3 0

Answer:

first must times the number

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sketch the curve represented by the parametric equations (indicate the orientation of the curve), write the corresponding rectan

pychu [463]

Answer:

Reduced equaton is $5x-3y+\frac{28}{3}=0$ .

Step-by-step explanation:

Given parametric equation is,

$x=3t-5$ and $y=5t+1$

Now, $x=3t-5\implies t=\frac{x+5}{3}$ substitute in second equation we get,

$y=\frac{5}{3}(x+5)+1$

$y=\frac{5}{3}x+\frac{28}{9}$

$\implies 5x-3y+\frac{28}{3}=0$

which is the corresponding rectangular equation after eliinating the parameter.

Now consider,

$y=\frac{5}{3}x+\frac{28}{9}$

Of which,

Slope : $\frac{5}{3}$

when,

$x=0, y=\frac{28}{9}=3.1$

$x=1, y=\frac{43}{9}=4.8; x=-1, y=\frac{13}{9}=1.4$

$x=2, y=\frac{58}{9}=6.4; x=-2, y=\frac{-2}{9}=-0.2$

$x=3, y=\frac{73}{9}=8.1; x=-3, y=\frac{-17}{9}=-1.8$

$x=4, y=\frac{88}{9}=9.8; x=-4, y=\frac{-32}{9}=-3.6$

$x=5, y=\frac{103}{9}=11.4; x=-5, y=\frac{-47}{9}=-5.2$

ans so on. Thus sketching th curve will look like given,

5 0

3 years ago

A pair of shorts are £15 in a 40%. What was the non-sale price

lana66690 [7]

Answer:

£10.71

Step-by-step explanation:

Given the original price including discount od shorts = £15

Percent discount = 40%

Original price = x

Using the expression to calculate x

x + (40%of x) = 15

x +0.4x = 15

1.4x = 15

x = 15/1.4

x = £10.71

Hence the non sale price is £10.71

4 0

3 years ago

Piper works at a camera store. He is paid an hourly rate +16% commission on everything he sells. One week, he was paid $515 for

umka21 [38]

His hourly rate is $13.75.

Let x be the hourly rate. Since he works 20 hours that week, the hourly wages are given by 20x. We add to that his commission, which is 16% of the $1500 in sales, or 0.16(1500). This totals to 515:

20x + 0.16(1500) = 515
20x + 240 = 515

Subtract 240 from both sides:
20x + 240 - 240 = 515 - 240
20x = 275

Divide both sides by 20:
20x/20 = 275/20
x = 13.75.

8 0

3 years ago

Alik [6]

The answer would be 7

7 0

3 years ago

At the beginning of each of her four years in college, Miranda took out a new Stafford loan. Each loan had a principal of $5,500

kaheart [24]

Answer:

D. $31,337.27

Step-by-step explanation:

We have that the initial amount of the loan is $5500.

Miranda took the loan for 4 years. So, the total present value is $5500×4 = $22,000.

The rate of interest on the loan is 7.5% i.e. 0.075 and it was for the duration of 10 years.

Also, it is given that the loan was compounded annually.

We have the formula as,

$P=\frac{\frac{r}{n}\times PV}{1-(1+\frac{r}{n})^{-t\times n}}$

i.e. $PV=\frac{P\times [1-(1+\frac{r}{n})^{-t\times n}]}{\frac{r}{n}}$

Substituting the values, we get,

i.e. $PV=\frac{P\times [1-(1+\frac{0.075}{12})^{-10\times 12}]}{\frac{0.075}{12}}$

i.e. $22000=\frac{P\times [1-(1+0.00625)^{-120}]}{0.00625}$

i.e. $22000=\frac{P\times [1-(1.00625)^{-120}]}{0.00625}$

i.e. $22000=\frac{P\times [1-0.4735]}{0.00625}$

i.e. $22000=\frac{P\times 0.5265}{0.00625}$

i.e. $P=\frac{22000\times 0.00625}{0.5265}$

i.e. $P=\frac{137.5}{0.5265}$

i.e. $P=261.16$

Thus, the total lifetime cost to pay of the loans compounded annually = 261.16 × 120 = $31,339.2

Hence, the total cost close to the answer is $31,337.27

7 0

3 years ago

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