What is x? 30=5(z+1)

There are 112 seats in the school auditorium. There are 7 seats in each row. There are 70 people seated, filling up full rows of

MatroZZZ [7]

112 Seats/ 7 Seats= 16 Total Rows
70Seats / 7Seats = 10 Full Rows
16-10=
6 Remaining Rows that tell us that there are a total of 42 empty seats.

5 0

2 years ago

Find the length of AB

aniked [119]

FIRST QUESTION
Given points are:
A(2, -4) and B(6, 2)
Now, Use the distance formula.
distance formula = $\sqrt{ (x_{2}- x_{1})^{2} + ( y_{2} - y_{1} )^{2} }$

Now, plug the values into the formula, So,
distance = $\sqrt{ (6- 2)^{2} + ( 2 - (-4))^{2} }$

= $\sqrt{ (6- 2)^{2} + ( 2 +4))^{2} }$

= $\sqrt{ (4)^{2} + ( 6))^{2} }$

= $\sqrt{ 16+36}$

= $\sqrt{52}$

= $2 \sqrt{13}$

So, the length of AB is $2 \sqrt{13}$ .

THIRD QUESTION
Two points given are:
A(3, -2) and B(1, 1)
Also given that B is the midpoint of AC.

Let, the co-ordinates of C be C(a, b).
Now, using midpoint formula,
Midpoint = $(\frac{ x_{1}+ x_{2} }{2} , \frac{ y_{1}+ y_{2} }{2} )$

$(1, 1)=(\frac{ 3+ a }{2} , \frac{ -2+b }{2} )$

Now, equaling the ordered pair, we have,

$1=\frac{ 3+ a }{2}$ .............equation (1)

$1=\frac{ -2+b }{2}$ ................equation (2)

Now, taking equation (1)
$1=\frac{ 3+ a }{2}$

$1*2=3+a$

$2-3=a$

$a=-1$

Now, taking equation (2)
$1=\frac{ -2+b }{2}$

$1*2=-2+b$

$2+2=b$

$b=4$

So, the co ordinates of C are (a, b) which is (-1 , 4)


SECOND QUESTION:
Given equations are:
2x + 3y = 14.....................equation (1)
-4x + 2y = 4 .....................equation (2)
Taking equation (2)
-4x + 2y = 4
2y = 4 + 4x
y = (4 + 4x) / 2
y = 2 + 2x .......................equation (3)
Now, Taking equation (1)
2x + 3y = 14
Substituting the value of y from equation (3), we get,
2x + 3(2 + 2x) = 14
2x + 6 + 6x = 14
8x = 14 - 6
x = (14 - 6) / 8
x = 1

Taking equation (3)
y = 2 + 2x
Now, substituting the value of x in equation (3), we get,
y= 2 + 2 (1)
y = 2 + 2
y = 4

So, x=1 and y=4

6 0

3 years ago

Which formula would be used to find the measure of angle 1?

Stels [109]

What’s angle 1? U need to post a pic

7 0

2 years ago

Greg is riding his bicycle. He rides

Sauron [17]

6.4 kilometers an hour

3 0

2 years ago

Read 2 more answers

What does Descartes' rule of signs tell you about the possible number of positive real zeros and the possible number of negativ

Sergio039 [100]

Answer:

3 or 1 positive real zeros
0 negative real zeros

Step-by-step explanation:

The signs of the coefficients of the given terms are ...

+ - + -

There are three sign changes, so the number of positive real zeros is 3 or 1.

When odd-degree terms have their signs changed, the signs become ...

- - - -

There are no sign changes, hence no negative real zeros.

_____

A graph confirms this evaluation.

8 0

2 years ago