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3 years ago

What is the most precise name for a quadrilateral with the following vertices:

Mathematics

1 answer:

pashok25 [27]3 years ago

3 0

<h2>Therefore it is a parallelogram.</h2>

Step-by-step explanation:

Given the vertices of the quadrilateral are A(2,3) , B(7,2), C(6,-1) and D(1,0)

The length of AB is $=\sqrt{(2-7)^2+(3-2)^2}$ $=\sqrt{26}$ units

The length of BC is $=\sqrt{(7-6)^2+(2+1)^2}$ $=\sqrt{10}$ units

The length of CD is $=\sqrt{(6-1)^2+(-1-0)^2}$ $=\sqrt{26}$ units

The length of DA is $=\sqrt{(1-2)^2+(0-3)^2}$ $=\sqrt{10}$ units

The length of AC is $=\sqrt{(2-6)^2+(3+1)^2}$ $=4\sqrt{2}$ units

The length of BD is $=\sqrt{(7-1)^2+(2-0)^2}$ = $2\sqrt{10}$ units

Here length of AB = length of CD ,

length of BC= length of DA and

length of AC ≠ length of BD

In this quadrilateral, the opposite sides are equal but the diagonals are not equal

Therefore it is a parallelogram.

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The measure of one base angle of an isosceles triangle is 35 degrees. What is the measure of the vertex angle?

Elis [28]

Answer:

110 degrees

Step-by-step explanation:

The measures of the two base angles of an isosceles triangle are the same so 180 - 2(35) = 110 which is the vertex angle.

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3 years ago

Quinzel earns $1254 each month. His total deductions are 20% of his pay. How much is deducted from his pay each month ?

vova2212 [387]

20% = 0.20

1254 x 0.20 = 250.80

so he has $250.80 deducted every month

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3 years ago

Thirty percent of all customers who enter a department store will make a purchase. Suppose that 6 customers enter the store and

torisob [31]

Answer:

Step-by-step explanation:

Let's use binomial distribution, because we are interested in find the total number of successes in a sequence of n independent experiments.

In probability, a binomial distribution is used in a Bernoulli process. That is, a sequence of experiments of n independent trials, each asking a dichotomous question, that means it only has two answers. One answer is a success (probability: p) and the other is a failure (probability: 1-p). In this case, every customer who enters in the store is the experiment. If they make a purchase is a success event, taking into account that every purchase decision has to be independent.

$P(X=x) = C(n,x)p^{x} (1-p)^{n-x}$

x= total number of success

n= total number of experiments

p=probability of success on an indivual trial

$C(n,x) = \frac{n!}{x!(n-x)!}$

a) x= 5 ------> customers that make a purchase

n= 6 ------> total customers

p=0.3

$p(X=5)= C(6,5)(0.3)^{5} (1-0.3)^{6-5} \\p(X=5)=0.102$

b) At least 3 customers make a purchase. x ≥ 3

$P(X\geq 3)=1-P (X=0)-P(X=1)-P(X=2)\\P(X\geq 3)=1-(C(6,0)(0.3^{0})(0.7)^{6}) - (C(6,1)(0.3^{1})(0.7)^{5}) - (C(6,2)(0.3^{2})(0.7)^{4})\\ P(X\geq 3) = 1-0.11765-0.30253-0.32414\\P(X\geq3)= 0.2557$

c) At most 2 customers make a purchase. x ≤ 2

$P(X\leq2) = P(X=0) + P(X=1) + P(X=2)\\P(X\leq2) = (C(6,0)(0.3^{0})(0.7)^{6}) + (C(6,1)(0.3^{1})(0.7)^{5}) + (C(6,2)(0.3^{2})(0.7)^{4})\\P(X\leq2) = 0.11765-0.30253-0.32414\\P(X\leq2)=0.7443$