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GalinKa [24]
3 years ago
6

2.What is the most precise name for quadrilateral ABCD with vertices A(-2,4), B(5,6), C(12,4), and D(5,2)?<br />

Mathematics
2 answers:
ExtremeBDS [4]3 years ago
7 0
<span>2.What is the most precise name for quadrilateral ABCD with vertices A(-2,4), B(5,6), C(12,4), and D(5,2)?

First, plot the points given and from there determine what kind of quadrilateral is ABCD. The answer is B) Rhombus

</span><span>3. What is the most precise term for quadrilateral ABCD with vertices A(1,2), B(2,6), C(5,6), and D(5,3)?
</span>
Again, plot the points given and identify the type of quadrilateral ABCD. The answer is <em>parallelogram. </em>
zalisa [80]3 years ago
7 0

Answer:  The correct options are (2). A, (3). B, (9). C and (10). A.

Step-by-step explanation:  The calculations are as follows:

(2) The vertices of the quadrilateral ABCD are A(-2,4), B(5,6), C(12,4), and D(5,2).

The length of the sides are calculated using distance formula as follows:

AB=\sqrt{(5+2)^2+(6-4)^2}=\sqrt{49+4}=\sqrt{53},\\\\BC=\sqrt{(12-5)^2+(4-6)^2}=\sqrt{49+4}=\sqrt{53},\\\\CD=\sqrt{(5-12)^2+(2-4)^2}=\sqrt{49+4}=\sqrt{53},\\\\DA=\sqrt{(-2-5)^2+(4-2)^2}=\sqrt{49+4}=\sqrt{53}.

The slopes of the sides are calculated as:

\textup{Slope of }AB=\dfrac{6-4}{5+2}=\dfrac{2}{7},\\\\\\\textup{Slope of }BC=\dfrac{4-6}{12-5}=-\dfrac{2}{7},\\\\\\\textup{Slope of }CD=\dfrac{2-4}{5-12}=\dfrac{2}{7},\\\\\\\textup{Slope of }DA=\dfrac{4-2}{-2-5}=-\dfrac{2}{7}.

Since the lengths of all sides are equal and the opposite sides are parallel, because the slopes of two parallel lines are equal.

Therefore, ABCD is a parallelogram because opposite sides are parallel and congruent.

Thus, (A) is the correct option.

(3) The vertices of the quadrilateral ABCD are A(1, 2), B(2,6), C(5, 6), and D(5, 3).

The length of the sides are calculated using distance formula as follows:

AB=\sqrt{(2-1)^2+(6-2)^2}=\sqrt{1+16}=\sqrt{17},\\\\BC=\sqrt{(5-2)^2+(6-6)^2}=3=,\\\\CD=\sqrt{(5-5)^2+(3-6)^2}=3,\\\\DA=\sqrt{(1-5)^2+(2-3)^2}=\sqrt{16+1}=\sqrt{17}.

The slopes of the diagonals are

\textup{Slope of }AC=\dfrac{6-2}{5-1}=1,\\\\\\\textup{Slope of }BD=\dfrac{3-6}{5-2}=-1.

So, slope of AC × slope of BD = 1 × (-1) = - 1. Hence the diagonals are perpendicular.

Therefore, ABCD is a kite, because adjacent sides are congruent and diagonals are perpendicular to each other.

Thus, (B) is the correct option.

(9) A 16-gon is a polygon with 16 sides.

So, the measure of one exterior angle of a regular 16-gon is

E_a=\dfracx{360^\circ}{16}=22.5^\circ.

Therefore, the measure of one angle is given by

I_a=180^\circ-22.5^\circ=157.5^\circ.

Thus, (C) is the correct option

(10)  The measure of exterior angle of a regular 5-gon is

E_5=\dfrac{360^\circ}{5}=72^\circ,

and the measure of each exterior angle of a regular 9-gon is

E_9=\dfrac{360^\circ}{9}=40^\circ,

Therefore, The measure of exterior angle of a regular 5-gon is greater the measure of each exterior angle of a regular 9-gon.

Thus, (A) is the correct option.

Hence, the correct options are (2). A, (3). B, (9). C and (10). A.

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6.8
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A NASA mathematician used a system of equations to determine the point in space where a satellite crossed paths with a massive p
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Option D.

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8 0
3 years ago
Justo ayer fue el cumpleaños de Mauricio. Si a la edad e Mauricio, le sumo 13, al resultado le resto 10, luego al nuevo resultad
bezimeni [28]

Answer:

Mauricio nació en el año 2000.

Step-by-step explanation:

Supóngase que el cumpleaños se celebra en el año 2020, si x es la edad actual de Mauricio, entonces la expresión matemática que traduce el enunciado del problema es:

\frac{(x+13)-10}{23} +20 = 21

Ahora, se desarrolla y se simplifica la ecuación:

\frac{x+3}{23}+20 = 21

\frac{x+3}{23} = 1

Se despeja x:

x +3 = 23

x = 20

Mauricio tiene 20 años.

Ahora, el año de nacimiento de Mauricio es la sustracción de la edad de Mauricio del año actual:

y = 2020-20

y = 2000

Mauricio nació en el año 2000.

3 0
3 years ago
If $25, 000 is invested into an account paying 4.5% per year, compounded quarterly, how much money can be withdrawn from the acc
pogonyaev

The money can be withdrawn from the account every two months for the next 6 years is $20, 625, 000

<h3>What is compound interest?</h3>

The formula for compound interest is given as;

A = P ( 1 + \frac{r}{n} )^n^t

P = principal interest = $25, 000

r = rate = 4. 5%

n = 2 months

t = 6 years

A = 25, 000 ( 1 + \frac{4. 5}{2} )^2 ^*^6

A = 25, 000(1 + 0. 75)^1^2

A = 25, 000( 825. 00)

A = $20, 625, 000

Thus, the money can be withdrawn from the account every two months for the next 6 years is $20, 625, 000

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7 0
2 years ago
Question 1
Tanzania [10]

Answer:

Mortality rate is 0.5 per 1000 habitant

the number of deaths have increased (from 210 to 250)

Step-by-step explanation:

Hello

Mortality rate is the number of deaths in a specific population,usually expressed in units of deaths per 1,000 individuals per year

Mortality\ rate\ (S)= \frac{(D)}{(P)} *10^{n} \\\\\\\\

where

S=Mortality rate

D=deaths

P= population

n= is a conversion form ,such as multiplying by  10^{3}=1000, to  get mortality rate per 1,000 individuals( we will use n=3)

step 1

asign

S=unknown

D=250

P=500000

n=3, (for each  1000 people)

step 2

Replace

S=\frac{250}{500000}*1000\\S=\ 0.5\ per\ 1000

Mortality rate is 0.5 per 1000 habitant

step 3

what if S=0.42

S=0.42(assuming it is 0.42 per 1000,n=3)

D=unknown

P=500000

(S)= \frac{(D)}{(P)} *10^{n}\\\\isolatin D\\\\S*P=D*10^{n}\\ D=\frac{S*P}{10^{n} } \\\\and\ replacing\\\\D=\frac{(0.42)*(500000)}{10^{3} }\\\\ Deaths=210\\

the number of deaths have increased (from 210 to 250)

Have a great day

5 0
3 years ago
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