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2 years ago

What is the slope of the line through the points (2, 8) and (5, 7)?3- 1/3-31/3

Mathematics

1 answer:

cluponka [151]2 years ago

4 0

Answer:

Option B

Step-by-step explanation:

In order to find the answer to this question you need to use the slope formula and solve by subtracting the numerator and the denominator.

$slope=\frac{y^2-y1}{x^2-x^1}$

$x^1,x^2=(2,5)$

$y^2,y^1=(8,7)$

Substitute:

$\frac{8-7}{2-5}$

Subtract:

$8-7=1$

$2-5=-3$

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

Hope this helps.

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3 years ago

For the following amount at the given interest rate compounded continuously, find (a) the future value after 9 years, (b) the

Stella [2.4K]

Answer:

(a) The future value after 9 years is $7142.49.

(b) The effective rate is $r_E=4.759 \:{\%}$ .

(c) The time to reach $13,000 is 21.88 years.

Step-by-step explanation:

The definition of Continuous Compounding is

If a deposit of $P$ dollars is invested at a rate of interest $r$ compounded continuously for $t$ years, the compound amount is

$A=Pe^{rt}$

(a) From the information given

$P=4700$

$r=4.65\%=\frac{4.65}{100} =0.0465$

$t=9 \:years$

Applying the above formula we get that

$A=4700e^{0.0465\cdot 9}\\A=7142.49$

The future value after 9 years is $7142.49.

(b) The effective rate is given by

$r_E=e^r-1$

Therefore,

$r_E=e^{0.0465}-1=0.04759\\r_E=4.759 \:{\%}$

(c) To find the time to reach $13,000, we must solve the equation

$13000=4700e^{0.0465\cdot t}$

$4700e^{0.0465t}=13000\\\\\frac{4700e^{0.0465t}}{4700}=\frac{13000}{4700}\\\\e^{0.0465t}=\frac{130}{47}\\\\\ln \left(e^{0.0465t}\right)=\ln \left(\frac{130}{47}\right)\\\\0.0465t\ln \left(e\right)=\ln \left(\frac{130}{47}\right)\\\\0.0465t=\ln \left(\frac{130}{47}\right)\\\\t=\frac{\ln \left(\frac{130}{47}\right)}{0.0465}\approx21.88$

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2 years ago

As an estimation we are told £3 is €4.<br> Convert €52 to pounds.

kati45 [8]

Answer:

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Step-by-step explanation:

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3 years ago

X + (2x + 40) + (3x – 50) = 15,002

Charra [1.4K]

Answer:

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Step-by-step explanation:

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2 years ago

Read 2 more answers

Find how many years it would take for an investment of $3700 to grow to $6000 at an annual interest rate of 6.2% compounded semi

lorasvet [3.4K]

Answer:

7 years 11 months

Step-by-step explanation:

The future value formula for the value of a principal P invested at annual rate r compounded n times yearly for t years is ...

FV = P(1 +r/n)^(nt)

For the given numbers, we want to find t:

6000 = 3700(1 +.062/2)^(2t)

Dividing by 3700 and taking the logarithm, we get ...

6000/3700 = 1.031^(2t)

log(60/37) = 2t·log(1.031)

Dividing by the coefficient of t gives ...

t = log(60/37)/(2log(1.031)) ≈ 7.92 . . . . . years

It will take about 7 years 11 months for the investment to grow to $6000.

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2 years ago

What is the slope of the line through the points (2, 8) and (5, 7)?3- 1/3-31/3​

What is the slope of the line through the points (2, 8) and (5, 7)?3- 1/3-31/3