Divide 72 rolls into 2 groups so the ratio is 3 to 5

100 POINTS PRE-CALCULUS

Sonja [21]

Answer:

not sure for the 1st one but pretty sure 2nd one is B

Step-by-step explanation:

3 0

3 years ago

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40 POINTS is (4,7) a solution of equations? Explain your answer 2x+4y=36 3x-4y=-6

dsp73

2x + 4y = 36
3x - 4y = -6
--------------add
5x = 30
x = 6

2x+4y=36
2(6)+4y=36
12 + 4y = 36
4y = 24
y = 6

answer
(6, 6) is a solution of equations
(4,7) is NOT a solution of equations

6 0

3 years ago

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If a,b,c and d are positive real numbers such that logab=8/9, logbc=-3/4, logcd=2, find the value of logd(abc)

Eva8 [605]

We can expand the logarithm of a product as a sum of logarithms:

$\log_dabc=\log_da+\log_db+\log_dc$

Then using the change of base formula, we can derive the relationship

$\log_xy=\dfrac{\ln y}{\ln x}=\dfrac1{\frac{\ln x}{\ln y}}=\dfrac1{\log_yx}$

This immediately tells us that

$\log_dc=\dfrac1{\log_cd}=\dfrac12$

Notice that none of $a,b,c,d$ can be equal to 1. This is because

$\log_1x=y\implies1^{\log_1x}=1^y\implies x=1$

for any choice of $y$ . This means we can safely do the following without worrying about division by 0.

$\log_db=\dfrac{\ln b}{\ln d}=\dfrac{\frac{\ln b}{\ln c}}{\frac{\ln d}{\ln c}}=\dfrac{\log_cb}{\log_cd}=\dfrac1{\log_bc\log_cd}$

so that

$\log_db=\dfrac1{-\frac34\cdot2}=-\dfrac23$

Similarly,

$\log_da=\dfrac{\ln a}{\ln d}=\dfrac{\frac{\ln a}{\ln b}}{\frac{\ln d}{\ln b}}=\dfrac{\log_ba}{\log_bd}=\dfrac{\log_db}{\log_ab}$

so that

$\log_da=\dfrac{-\frac23}{\frac89}=-\dfrac34$

So we end up with

$\log_dabc=-\dfrac34-\dfrac23+\dfrac12=-\dfrac{11}{12}$

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Another way to do this:

$\log_ab=\dfrac89\implies a^{8/9}=b\implies a=b^{9/8}$

$\log_bc=-\dfrac34\implies b^{-3/4}=c\implies b=c^{-4/3}$

$\log_cd=2\implies c^2=d\implies\log_dc^2=1\implies\log_dc=\dfrac12$

Then

$abc=(c^{-4/3})^{9/8}c^{-4/3}c=c^{-11/6}$

So we have

$\log_dabc=\log_dc^{-11/6}=-\dfrac{11}6\log_dc=-\dfrac{11}6\cdot\dfrac12=-\dfrac{11}{12}$

4 0

3 years ago

Lim. √2x -√3x-a/√x-√a x approaches a

Ludmilka [50]

Answer: $\sqrt{2}a-\sqrt{3}a-2\sqrt{a}$

Step-by-step explanation:

$\lim _{x\to \:a}\left(\sqrt{2}x-\sqrt{3}x-\frac{a}{\sqrt{x}}-\sqrt{a}\right)$

$=\sqrt{2}a-\sqrt{3}a-\frac{a}{\sqrt{a}}-\sqrt{a}$

$=\sqrt{2}a-\sqrt{3}a-2\sqrt{a}$

3 0

3 years ago

If $580 is invested in an account which earns 9% interest compounded annually, what will be the balance of the account at the en

joja [24]

The formula for compounded interest is A = P (1+r/n)^nt.
P=580
r = .09
n = 1
t = 9

To find how much the balance is at the end of nine years, plug in all of the knows into the formula.
A = 1259.698 is how much the balance will be. (Rounded to 1259.70 if you round to the nearest cent).

8 0

3 years ago