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3 years ago

Find the measure of the numbered angle. a. 62.5 b. 105 c. 112.5 d. 115

Mathematics

1 answer:

Anit [1.1K]3 years ago

6 0

Answer:

115

Step-by-step explanation:

The angle is vertically opposite to 115. vertically opposite angles are equal

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20 is 60% of what number

Oxana [17]

33.33? im not sure, but you do a/b=p/100. p is the percent, a is the part of the whole number, b. so the equation would be 20/b=60/100. then you do cross multiplication (60b=2000) then you divide.

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3 years ago

A truck is carrying a cars weighing an average of 4500 pounds each what is the total weight in tons of cars on the truck

Yuliya22 [10]

Answer:

2.25 tons

Step-by-step explanation:

It is a conversion problem. The connection between ton and pound is in the following order:

1 pound = 0.0005 tons

By multiplying each side by 4500 we can easily find the answer of this problem:

4500 pounds = 2.25 tons

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3 years ago

Divide 3 by 8, then multiply z by the result

Sonbull [250]

3÷ 8 ·z

3/8 ·z

3/8z

I think i'm just supposed to simplifiy it??

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3 years ago

A price is decreased by 24% and is now £372.40.<br>Work out the original price.

goldfiish [28.3K]

Answer:

Step-by-step explanation:

Subtract the discount from 100 to get the percentage of the original price.

Multiply the final price by 100.

Divide by the percentage in Step One

5 0

3 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

3 years ago