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rodikova [14]
3 years ago
14

Is ab perpendicular to cd A(0,2) B(-3,-3) C(-4,1)D(0,-2)

Mathematics
1 answer:
Nostrana [21]3 years ago
6 0
Find the slopes of the 2 line segments and see if they are negative reciprocals then the lines are perpendicular.
AB slope is -3-2/-3-0= -5/-3=5/3
CD slope is -2-1/0- -4=-3/4

The lines are not perpendicular
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Find the sum of the given arithmetic series. 24 + 48 + 72 + 96 +...+ 480
Alja [10]

Answer:

5040

Step-by-step explanation:

The given series is :

24 + 48 + 72 + 96 +...+ 480

The first term, a= 24

Common difference, d = 24

The last term, a_n=480

Let there are n terms in the AP.

So,

a_n=a+(n-1)d\\\\480=24+(n-1)24\\\\480=24+24n-24\\\\n=20

There are 20 terms in the series. The sum of 20 terms is :

S_{20}=\dfrac{n}{2}(2a+(n-1)d))\\\\=\dfrac{20}{2}\times (2(24)+19(24))\\\\=5040

So, the sum of the given arithmetic series is equal to 5040.

8 0
3 years ago
Mary went to the local market to purchase some fruit. Each box of
musickatia [10]

Answer:

11

Step-by-step explanation:

11 BOXES OF ORANGES IS $33

7 BOXES OF PEARS IS $35

WHICH EQUALS $68

MEANING THERE IS 11 BOXES OF ORANGES

5 0
3 years ago
Simplify the trigonometric expression.
Natasha_Volkova [10]
First we are going to find the common denominator of both fractions. To do that, we are going to multiply their denominators:
(1+sin \alpha )(1-sin \alpha )=1-sin^2 \alpha

Now we can rewrite our expression using the common denominator:
\frac{1-sin \alpha }{1-sin^2 \alpha } + \frac{1+sin \alpha }{1-sin^2 \alpha} = \frac{2}{1-sin^2 \alpha}

Finally, we can use the trig identities: 1-sin^2 \alpha =cos^2 \alpha and sec \alpha = \frac{1}{cos \alpha } to simplify our trig expression:
\frac{2}{cos^2\alpha}=2sec^2 \alpha

We can conclude that the correct answer is the fourth one.
5 0
3 years ago
Read 2 more answers
7×300=7× blank hundreds
VladimirAG [237]
7x300=7x 3 hundres because in 300 hundreds there is 3 hundreds.I know that didnt make sense.so basically just look at the front number number its 3 so 3 hundreds but if your working with thousands and the front number is 5 its 5 thousands.I hope this was helpful.
6 0
3 years ago
What is the sixth term of the sequence shown in the table ​
horsena [70]

Answer:

375

Step-by-step explanation:

trust me

:)

4 0
3 years ago
Read 2 more answers
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