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4 years ago

X/-2=10 (one step equations )

Mathematics

2 answers:

SVEN [57.7K]4 years ago

6 0

Answer:

x= -20

Step-by-step explanation:

Multiply each side by -2 to get x= -20

kiruha [24]4 years ago

3 0

$\frac{x}{ - 2} = 10 \\ \: x = - 20$

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4 years ago

If Tanisha has $1000 to invest at 7% per annum compounded semiannually, how long will it be before she has $1600? If the co

Sphinxa [80]

Answer:

Using continuous interest 6.83 years before she has $1600.

Using continuous compounding, 6.71 years.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

$A(t) = P(1 + \frac{r}{n})^{nt}$

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.

Continuous compounding:

The amount of money earned after t years in continuous interest is given by:

$P(t) = P(0)e^{rt}$

In which P(0) is the initial investment and r is the interest rate, as a decimal.

If Tanisha has $1000 to invest at 7% per annum compounded semiannually, how long will it be before she has $1600?

We have to find t for which $A(t) = 1600$ when $P = 1000, r = 0.07, n = 2$

$A(t) = P(1 + \frac{r}{n})^{nt}$

$1600 = 1000(1 + \frac{0.07}{2})^{2t}$

$(1.035)^{2t} = \frac{1600}{1000}$

$(1.035)^{2t} = 1.6$

$\log{1.035)^{2t}} = \log{1.6}$

$2t\log{1.035} = \log{1.6}$

$t = \frac{\log{1.6}}{2\log{1.035}}$

$t = 6.83$

Using continuous interest 6.83 years before she has $1600

If the compounding is continuous, how long will it be?

We have that $P(0) = 1000, r = 0.07$

Then

$P(t) = P(0)e^{rt}$

$1600 = 1000e^{0.07t}$

$e^{0.07t} = 1.6$

$\ln{e^{0.07t}} = \ln{1.6}$

$0.07t = \ln{1.6}$

$t = \frac{\ln{1.6}}{0.07}$

$t = 6.71$

Using continuous compounding, 6.71 years.

7 0

4 years ago

The difference between the roots of the quadratic equation x2+x+c=0 is 6. Find c.

NemiM [27]

We have that
$x_{1} - x_{2} = 6$
Let y be the first root, then y - 6 will be the second one. Since both roots make the quadratic equation equal to 0, we have that:
$y^{2} + y + c = (y - 6)^{2} + (y - 6) +c$
Solve for y:
$y^{2} +y +c = y^{2} - 12y + 36 + y - 6 +c \\ y + 12y - y = 30 \\ y = \frac{5}{2}$
Plug in y = 5/2 into original quadratic equation and solve for c:
$( \frac{5}{2}) ^{2} + \frac{5}{2} +c = 0 \\ c= - \frac{5}{2} - \frac{25}{4} \\ c = - \frac{35}{4}$
So, the answer is c = -35/4

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4 years ago