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3 years ago

Factorise 21ax+10by-35ay-6bxwith working pls

Mathematics

1 answer:

wolverine [178]3 years ago

3 0

Answer:

Step-by-step explanation:

21ax + 10by - 35ay - 6bx

21ax - 35ay - 6bx + 10by

7a ( 3x - 5y ) - 2b ( 3x - 5y )

( 7a - 2b ) ( 3x - 5y )

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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

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

###

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

Mariana plans to visit an amusement park where she must pay for admission and purchase tickets to go on the rides. Mariana wants

Ivanshal [37]

Answer: The number 12 represents admission charge in Mariana's equation.

Step-by-step explanation:

As per given ,

Total cost = ( Charge per ticket) (Number of tickets) + (Admission fees) (i)

For x = Number of tickets, the total cost (c) for a day at the amusement park is given as

$c = 1.50x + 12$ (ii)

Here, 12 = Admission fees [Comparing (i) and (ii)]

Hence, the number 12 represents admission charge in Mariana's equation.

3 0

3 years ago

105-84 170-125 what is the answer to both of em'?

prisoha [69]

The answers are
1) 21
2) 45

5 0

3 years ago

Read 2 more answers

Explain the procedure (but don't create the graph) for graphing the quadratic function in factored form f(x) = (x - 2)(x + 4) us

hichkok12 [17]

Answer: You will need to find the x-intercepts and the vertex

Step-by-step explanation: Use the information in the factors and some formulae.

The x- intercepts are the points where the parabola crosses the x-axis. The x-axis is where y = 0

Set each factor equal to 0 and solve:

x-2=0, so x = +2 and x +4 = 0, so x = -4 (you would plot these if creating the graph)

To find the vertex you need the Vertex Formula: x = -b/2a

b is the coefficient of the x term in the middle of the quadratic equation; you can just do the O and I parts of FOIL to get b: -2x + 4x = 2x You know a = 1 because x² will have the implied (missing)(1).

Put the numbers in the Formula: x = -b/2a x = -(2)/2(1) -2/2 = -1

-1 is the "x-value" of the vertex.

The y value is the 'c' in the quadratic formula. You get that from the L part of FOIL -2 × 4 = -8 .

So, your coordinates for the vertex: ( -1, -8 )

If you were creating a graph, you would plot that point, then draw the parabola starting there and through the x-intercepts.

5 0

3 years ago

$1500 computer 7% tax

lina2011 [118]

Answer:

$1605

Step-by-step explanation:

since 100% = 1, just multiply 1 (100% aka given price) and 0.07 (7%) by 1500:

1500(1.07)

= 1605

the computer with tax added would be $1605

3 0

3 years ago

Read 2 more answers

Factorise 21ax+10by-35ay-6bxwith working pls​

Factorise 21ax+10by-35ay-6bxwith working pls