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2 years ago

Explain why a + b = d. B A C swer

Mathematics

1 answer:

bixtya [17]2 years ago

4 0

Answer:

<em>Explanation below</em>

Step-by-step explanation:

<u>Angles in a Triangle</u>

There are two basic relations of angles we need to recall:

Supplementary angles add up to 180°
Internal angles of a triangle add up to 180°

Note a, b, and c are the internal angles of the triangle. The angle c is what is needed to a+b to complete 180°, thus:

c = 180 - ( a + b )

Also, note c and d are supplementary angles. Again, c is what is needed to d to complete 180°, thus

c = 180 - d

From the two relations above, it follows that:

a + b = d

You might be interested in

Which expression is equivalent to 4 - 10(9m-7)

ira [324]

Step-by-step explanation: multiply both sides by 9m-7 then bring down your 10

that's about all I can remember so your on your own from that point it's been a while since I've did this sorry mate

5 0

3 years ago

You have 14 coins that are nickles and quarters that equals 2 dollars how do you solve using substitution?

sergejj [24]

Answer:

The question is incorrect but if half nickels and quarters exist then you could say the answer is 7.5 nickels and 6.5 quarters.

The problem:

14 coins that are either nickels are quarters

The total dollar amount of these coins is 2 dollars

Step-by-step explanation:

Let n be the number of nickels.

Let q be the number of quarters.

We are given that n+q=14 and that .05n+.25q=2.

I'm going to choose to solve the system by elimination.

Multiplying the first equation by .25 gives:

.25n+.25q=.25(14)

.25n+.25q=3.5

So let's line the equations up now:

.25n+.25q=3.5

.05n+.25q=2

---------------------If we subtract the equations, the variable q will be eliminated. Thus, we will able to solve for the variable n.

.20n+0q=1.5

.20n=1.5

Dividing both sides by .2 gives:

n=7.5

If n=7.5 and n+q=14, then we have 7.5+q=14 by substitution property.

We can subtract 7.5 on both sides giving us:

q=14-7.5=6.5

We cannot have 7.5 nickels and 6.5 quarters but this satisfies the given information.

Check:

7.5+6.5=(7+6)+(.5+.5)=13+1=14

7.5(.05)+6.5(.25)=2

Now, the requested way which is by substitution:

Let n be the number of nickels.

Let q be the number of quarters.

We are given that n+q=14 and that .05n+.25q=2.

We can solve the first equation for either n or q and then substitute that into the other equation allowing us to solve for the other variable.

Let's solve for q by subtraction n on both sides:

q=14-n

We are going to replace q in the second equation with (14-n) giving us:

.05n+.25(14-n)=2

Distribute:

.05n+3.5-.25n=2

Combine like terms:

-0.2n+3.5=2

Subtract 3.5 on both sides:

-0.2n=-1.5

Divide both sides by -0.2:

n=7.5

Since q=14-n and n=7.5, then q=14-7.5=6.5 .

We are already check the solution above.

8 0

2 years ago

The South Coast Air Basin (Los Angeles, Orange, and San Bernardino counties) does not meet the air quality standards for carbon

Archy [21]

Answer:

0.2225 gr/mile

Step-by-step explanation:

Let's work out first the amount of CO sent out in 1990.

The population we estimated in 12.5 million people with a total of driven miles per year of about

12.5 million*8,700 = 108,750 million miles.

With an CO emission factor of 0.9 g per mile, we would have a total of CO emitted rounding 0.9*180,750 = 97,875 million grams

Now, we must estimate the population for 2020.

Since we are assuming an exponential growth, the population in year t is given by a function

$\bf P(t)= Ce^{kt}$

where C and k are constants to be determined.

We can take 1980 as year 0. This way calculations are lighter. 1990 is year 10 and 2020 is year 20.

So P(0) = 10.3 and C=10.3

So far we have

$\bf P(t)= 10.3e^{kt}$

Given that P(10)=12.5

$\bf 10.3e^{k*10}=12.5\rightarrow e^{10k}=\frac{12.5}{10.3}=1.21359\rightarrow \\10k=log(1.21359)\rightarrow k=0.01936$

And the function that models the population growth is

$\bf P(t)= 10.3e^{0.01936t}$

We need P(20)

$\bf P(20)= 10.3e^{0.01936*20}=10.3e^{0.38717}=15.17\;million$

If the miles driven per person per year remains constant at 8700 mi/yr.person, then we have a total miles driven of

15.17*8,700=131,979 million miles, so the CO emitted would be 0.9*131,979=118,781.1 million grams.

The 30% of the CO sent out in 1990 is 0.3*97,875=29,362.5 million grams.

We must reduce 118,781.1 down to 29,362.5

Hence the new CO emission factor would be

29,362.5/131,979 = 0.2225 gr/mile

6 0

3 years ago

The length of a rectangle is 2x+1 and the width is 4x-3. Write an expression to calculate the area. (Note: Area= length • width)

maw [93]

(4x-3)(2x+1) expand the brackets: 8x^2 -2x -3 = area

7 0

2 years ago

I need help with this

gtnhenbr [62]

So what are we trying to find the reduced fraction or inverse operation

5 0

3 years ago