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3 years ago

What solves the equation? (Needs to be simplified)

Mathematics

1 answer:

Alja [10]3 years ago

8 0

$\bf \cfrac{4v+1}{6v^2-19v+10}\div \boxed{x}=\cfrac{4v-1}{3v-2}\implies \cfrac{~~\frac{4v+1}{6v^2-19v+10}~~}{x}=\cfrac{4v-1}{3v-2} \\\\\\ \stackrel{\textit{cross-multipying}}{\cfrac{~~\frac{4v+1}{6v^2-19v+10}~~}{\frac{4v-1}{3v-2}}=x}\implies \cfrac{4v+1}{6v^2-19v+10}\cdot \cfrac{3v-2}{4v-1}=x \\\\\\ \cfrac{4v+1}{(\underline{3v-2})(2v-5)}\cdot \cfrac{\underline{3v-2}}{4v-1}=x\implies \cfrac{4v+1}{(2v-5)(4v-1)}=x \\\\\\ \cfrac{4v+1}{8v^2-2v-20v+5}=x\implies \cfrac{4v+1}{8v^2-22v+5}=x$

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What is the exact time t, in years, needed for the balance of an account that earns 5% annual 8. Interest compounded continuousl

Brums [2.3K]

Answer:

It takes 22.52 years for the balance to triple in value.

Step-by-step explanation:

Continuous compounding:

The amount of money earned using continuous compounding is given by the following equation:

$A(t) = A(0)(1+r)^t$

In which A(0) is the initial amount of money and r is the interest rate, as a decimal.

Interest rate of 5%.

This means that $r = 0.05$ , and thus:

$A(t) = A(0)(1+r)^t$

$A(t) = A(0)(1+0.05)^t$

$A(t) = A(0)(1.05)^t$

Time for the balance to triple?

This is t for which $A(t) = 3A(0)$ . So

$A(t) = A(0)(1.05)^t$

$3A(0) = A(0)(1.05)^t$

$(1.05)^t = 3$

$\log{(1.05)^t} = \log{3}$

$t\log{1.05} = \log{3}$

$t = \frac{\log{3}}{\log{1.05}}$

$t = 22.52$

It takes 22.52 years for the balance to triple in value.

3 0

3 years ago

Da A Solve the equation 2x^2+3=0

Anika [276]

Answer:

x = ±i(√6 / 2)

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Algebra I

Solving quadratics

Algebra II

Imaginary root i

√-1 = i

Step-by-step explanation:

Step 1: Define

Identify

2x² + 3 = 0

Step 2: Solve for x

[Subtraction Property of Equality] Subtract 3 on both sides: 2x² = -3
[Division Property of Equality] Divide 2 on both sides: x² = -3/2
[Equality Property] Square root both sides: x = ±√(-3/2)
Simplify: x = ±i(√6 / 2)

4 0

3 years ago

You are researching two glaciers.the first glacier flows at a rate of 75 meters in 3 days.the second glacier flows at a rate of

podryga [215]

Answer:

$1.3\ days$

Step-by-step explanation:

step 1

Find the units rate of the first glacier

$\frac{75}{3}=25\frac{meters}{day}$

using proportion

$\frac{25}{1}\frac{meters}{day}=\frac{200}{x}\frac{meters}{days}\\ \\x=200/25\\ \\x=8\ days$

step 2

Find the units rate of the second glacier

$\frac{107.5}{5}=21.5\frac{meters}{day}$

using proportion

$\frac{21.5}{1}\frac{meters}{day}=\frac{200}{x}\frac{meters}{days}\\ \\x=200/21.5\\ \\x=9.3\ days$

step 3

Find the difference

$9.3\ days-8\ days=1.3\ days$

4 0

3 years ago

The triangle has side lengths 10cm, 24cm, and 28cm, is it a right triangle? Explain please i dont understand

Nitella [24]

In every right triangle, if you add up the squares of the two
shorter sides, you get the square of the longest side. If you
don't then it's not a right triangle.

10² = 100
24² = 576

100 + 576 = 676

676 is the square of 26.
It's NOT the square of 28.

So 10 - 24 - 28 is not a right triangle.

8 0

3 years ago

Read 2 more answers

Which relation is a function

Anon25 [30]

$\{(\boxed{2};\ 3);\ (1;\ 5);\ (\boxed{2};\ 7)\}-NO\\\\\{(-1;\ 5);\ (-2;\ 6);\ (-3;\ 7)\}-YES\\\\\{(\boxed{11};\ 9);\ (\boxed{11};\ 5);\ (9;\ 3)\}-NO\\\\\{(\boxed{3};\ 8);\ (0;\ 8);\ (\boxed{3};\ -2)\}-NO$

3 0

3 years ago