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3 years ago

(03.01 MC) Factor completely 3x2 + 9x − 54. (6 points)

Mathematics

2 answers:

Bad White [126]3 years ago

5 0

3x^2+9x-54
= 3(x-3)(x-6)
That’s your answer 3(x-3)(x-6)

Genrish500 [490]3 years ago

3 0

The answer is 3(x - 3)(x + 6)

Factor common term from 3x^2 + 9x - 54
In this case, 3 is the common term. Hence:
3(x^2 + 3x - 18)

Simplify by factoring (x^2 + 3x - 18). Hence:
(x - 3)(x + 6)

Therefore: 3(x - 3)(x + 6)

You might be interested in

10(2^×) + 7(3^×) = 6^× + 70

Mkey [24]

Answer:

x = 2.81 and 2.096

Step-by-step explanation:

Given the expression

10(2^x) + 7(3^x) = 6^x + 70

This can also be expressed as;

10(2^x) + 7(3^x) = (2*3)^x + 70

10(2^x) + 7(3^x) = 2^x*3^x + 70

Let a = 2^x and b = 3^x

10a + 7b = ab + 70

10a + 7b - ab = 70

10a-ab + 7b - 70 = 0

a(10-b)+7(b-10) = 0

a(10-b)-7(10-b) = 0

a-7 = 0 and 10-b = 0

a = 7 and b = 10

Since a = 2^x

7 = 2^x

log 7 = log2^x

log7 = xlog2

x = log7/log2

x = 2.81

Similarly

10 = 3^x

log 10 = log 3^x

log 10 = xlog3

x = log 10/log 3

x = 1/0.4771

x = 2.096

Hence the values of x that satisfies the equation are 2.81 and 2.096

8 0

2 years ago

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

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

###

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

2 years ago

If a circle has a radius length of 2x units, what is the circle's circumference?

Brut [27]

Answer: 12.56

Step-by-step explanation:

If I remember correctly, the equation for circumference is C=2r*pi (R representing radius). For this problem, if 2 is your radius 2R would equal 4. Take this number and multiply it by 3.14 (pi) to get your final answer.

4 0

3 years ago

Which expressions are equivalent to the expression −6x + 8? Select all that apply. 1. −2(3x + 4) 2. 2(−3x + 4) 3. 5(x + 1) − 11x

ki77a [65]

1)
-2(3x+4)=-6x-8≠-6x+8

2)
2(-3x+4)=-6x+8

3)
5(x+1)-11x+3=5x+5-11x+3=-6x+8

4)
x+2-7x+6=-6x+8

5)
8-6x=-6x+8

Answer: The expressions 2,3,4 and 5 are equivalents.

6 0

2 years ago

Simplify 2x2a^2 x2a^2

horrorfan [7]

Step-by-step explanation:

> 2×2a²×2a²

8a⁴

> 36a³×1/4a²

9a³×1/a²

> 2⁶

> 5²m²

6 0

2 years ago