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3 years ago

9

Examine this system of equations. Which numbers can be multiplied by each equation so that when the two equations are added toge

ther, the x term is eliminated? 1 5 3 4 TY - y = 8 0-10 times the first equation and 3 times the second equation O 10 times the first equation and 3 times the second equation 0 -3 times the first equation and 5 times the second equation O 3 times the first equation and 5 times the second equation

1 answer:

Anna11 [10]3 years ago

3 0

Answer:

The correct answer is A.

Step-by-step explanation:

1/5*-10/1=-10/5= -2

2/3*3/1=6/3= 2

----------------------------

0.

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Prove that the segments joining the midpoint of consecutive sides of an isosceles trapezoid form a rhombus.

sergiy2304 [10]

Answer:

See explanation

Step-by-step explanation:

a) To prove that DEFG is a rhombus, it is sufficient to prove that:

All the sides of the rhombus are congruent: $|DG|\cong |GF| \cong |EF| \cong |DE|$
The diagonals are perpendicular

Using the distance formula; $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$|DG|=\sqrt{(0-(-a-b))^2+(0-c)^2}$

$\implies |DG|=\sqrt{a^2+b^2+c^2+2ab}$

$|GF|=\sqrt{((a+b)-0)^2+(c-0)^2}$

$\implies |GF|=\sqrt{a^2+b^2+c^2+2ab}$

$|EF|=\sqrt{((a+b)-0)^2+(c-2c)^2}$

$\implies |EF|=\sqrt{a^2+b^2+c^2+2ab}$

$|DE|=\sqrt{(0-(-a-b))^2+(2c-c)^2}$

$\implies |DE|=\sqrt{a^2+b^2+c^2+2ab}$

Using the slope formula; $m=\frac{y_2-y_1}{x_2-x_1}$

The slope of EG is $m_{EG}=\frac{2c-0}{0-0}$

$\implies m_{EG}=\frac{2c}{0}$

The slope of EG is undefined hence it is a vertical line.

The slope of DF is $m_{DF}=\frac{c-c}{a+b-(-a-b)}$

$\implies m_{DF}=\frac{0}{2a+2b)}=0$

The slope of DF is zero, hence it is a horizontal line.

A horizontal line meets a vertical line at 90 degrees.

Conclusion:

Since $|DG|\cong |GF| \cong |EF| \cong |DE|$ and $DF \perp FG$ , DEFG is a rhombus

b) Using the slope formula:

The slope of DE is $m_{DE}=\frac{2c-c}{0-(-a-b)}$

$m_{DE}=\frac{c}{a+b)}$

The slope of FG is $m_{FG}=\frac{c-0}{a+b-0}$

$\implies m_{FG}=\frac{c}{a+b}$

5 0

4 years ago

EastWind [94]

<span>A=12h(a+b)
Solve for h.

</span>All these answers are incorrect
<span>A. h=2Aa+b
B.h=a+b2A
C.h=A2(a+b)
D.h=2(a+b)A

The answer is
h = A / 12(a+b)
$h = \frac{A}{12(a+b)}$ </span>

6 0

3 years ago

At the Rue’s zoo there are 400 total animals. 100 of them are reptiles. What percentage of the total amount of animals are not r

Mariana [72]

Answer:

I´ll say 75% because basically well..lets say that there are 400 animals then you divide them all to 100 so there is 100 animals in each box and lets say 100 animals = 25% so we add another animal and that gives us 50% then another and 75% so you get wear im going with this right?

Step-by-step explanation:

But the answer is 75%

4 0

3 years ago

If x + 3/ 3 = y + 2/ 2 , then x/ 3 = _______.

Naddik [55]

Answer:

The correct answer is y/2

Step-by-step explanation:

It is given that,

(x + 3)/ 3 = (y + 2)/ 2

<u>To find x/3</u>

(x + 3)/ 3 = (y + 2)/ 2

⇒ x/3 + 3/3 = (y + 2)/2

x/3 + 1 = (y + 2)/2

x/3 = (y + 2)/2 - 1

x/3 = (y + 2)/2 -2/2

x/3 = (y + 2 - 2)/2

x/3 = y/2

Therefore the correct answer is x/3 = y/2

4 0

3 years ago

Which of the following are solutions to the equation below?

nalin [4]

$\qquad\qquad\huge\underline{{\sf Answer}}$

Let's solve the given equation ~

$\qquad \tt \dashrightarrow \:4 {x}^{2} + 20x + 25 = 49$

$\qquad \tt \dashrightarrow \:4 {x}^{2} + 20x + 25 - 49 = 0$

$\qquad \tt \dashrightarrow \:4 {x}^{2} + 20x - 24 = 0$

$\qquad \tt \dashrightarrow \:4( {x}^{2} + 5x - 6) = 0$

$\qquad \tt \dashrightarrow \: {x}^{2} + 5x - 6 = 0$

$\qquad \tt \dashrightarrow \: {x}^{2} + 6x - x - 6 = 0$

$\qquad \tt \dashrightarrow \:x(x + 6) - 1(x + 6) = 0$

$\qquad \tt \dashrightarrow \:(x + 6)(x - 1) = 0$

Hence, we get -6 and 1 as our roots ~

So, the correct choices are : B and D

3 0

2 years ago