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3 years ago

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A problem states: "There are 9 more children than parents in a room. There are 25 people in the room in all. How many children a

re there in the room?" Let c represent the number of children. Which expression represents the number of parents? c + 9 c−9 9−c c⋅9

1 answer:

Elza [17]3 years ago

4 0

C = number of parents
c+9 = number of children
2c+9=25
2c=16
c=8
8 parents, 17 children

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Advocard [28]

Well, 50 points total given, 25 points per user and 13 bonus for brainliest

anyway

1.
add them equations, the y's will cancel
x+2y=4
<span>3x-2y=4 +</span>
4x+0y=8

4x=8
divide by 4 both sides
x=2
sub back
x+2y=4
2+2y=4
minus 2
2y=2
divide 2
y=1
x=2
y=1
(x,y)
(2,1) is solution

2.
the solution is where they intersect
multiply 2nd equation by 2 and add to first
4x-14y=6
<span>-4x+14y=-6 +</span>
0x+0y=0
0=0
infinite solutions

that is because they are actually the same line
the solutions are (x,y) such that they satisfy -2x+7y=-3 or 4x-14y=6 (same equaiton)
infinite solutions

3.
multiply first equation by 2 and add to first
4x+2y=-6
<span>1x-2y=-4 +</span>
5x+0y=-10

5x=-10
divide by 5 both sides
x=-2
sub bac
x-2y=-4
-2-2y=-4
add 2
-2y=-2
divide by -2
y=1

x=-2
y=1
(x,y)
(-2,1)

4.
coincident means they are the same line
so

we see that we have to multiply 4 by 2 to get 8
multiply top equation by 2
8x+10y=16
8x+By=C
B=10 and C=16

5.
a. false, either 0, 1, or infinity solutions
change the word 'two' to 'one' or 'zero' or 'infinite', or change 'can' into 'can't'

b.false
'sometimes' to 'always'

c. true

d. false, change 'sometimes' to 'always'

EC
total cost=150
TC=childC+adultC
TC=3c+5a
150=3c+5a

40 tickets, c+a
40=c+a

the equations are
150=3c+5a and
40=c+a

eliminate
multiply 2nd equaton by -3 and ad to first one

150=3c+5a
<span>-120=-3c-3a +</span>
30=0c+2a

30=2a
divide by 2
15=a

sub back
40=c+a
40=c+15
minus 15
25=c

25 children tickets and 15 adult tickets were sold

ANSWERS:

1.
(2,1) is solution

2.
infinite solutions

3.
(-2,1)

4.
B=10 and C=16

5.
a. false,
change the word 'two' to 'one' or 'zero' or 'infinite', or change 'can' into 'can't'

b.false
'sometimes' to 'always'

c. true

d. false, change 'sometimes' to 'always'

EC
the equations are
150=3c+5a and
40=c+a
25 children tickets and 15 adult tickets were sold

7 0

3 years ago

Read 2 more answers

Three expressions equivalent to the following: -90x + 60

Deffense [45]

Answer:

33beacuse you i have -90×+60=9×6=369-63

3 0

3 years ago

Work out the size of one of the exterior angles

hodyreva [135]

<u>Given</u><u> </u><u>Information</u><u> </u><u>:</u><u>-</u>

⠀

A polygon with 10 sides ( Decagon )

⠀

<u>To</u><u> </u><u>Find</u><u> </u><u>:</u><u>-</u>

⠀

The value of one of the exterior angles

⠀

<u>Formula</u><u> </u><u>Used</u><u> </u><u>:</u><u>-</u>

⠀

$\qquad \diamond \: \underline{ \boxed{ \pink{ \sf Exterior ~angle = \dfrac {360^\circ}{no. ~of~sides}}}} \: \star$

⠀

<u>Solution</u><u> </u><u>:</u><u>-</u>

⠀

Putting the given values, we get,

⠀

$\sf \dashrightarrow Exterior ~angle = \dfrac{360 ^\circ}{10} \: \: \\ \\ \\ \sf \dashrightarrow Exterior ~angle = \frac{36 \cancel{0}^\circ}{ \cancel{10}} \: \: \\ \\ \\ \sf \dashrightarrow Exterior ~angle = \underline{ \boxed{ \frak{ \red{36^\circ}}}} \: \star \\ \\$

Thus, the value of the exterior angles of a Decagon is 36°.

⠀

$\underline{ \rule{227pt}{2pt}} \\ \\$

8 0

2 years ago

Read 2 more answers

Point A lies on the circle and has an x-coordinate of –3. Which value could be the y-coordinate for point A? 2.5 2.8

vodka [1.7K]

Answer:

the other point could be 2.8

Step-by-step explanation:

in circle values of both x and are almost equal in magnitude

since 2.8 is closest to 3 i magnitude

hence 2.8 will be correct option

this point will lie in third coordinate

as third coordinate has points

(-x,y)

and coordinates of points lie on the circle are

(-3,2.8)

8 0

2 years ago

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If one root is the square of the other in the equation 8+mx+27x²=0,find the value of m

aleksklad [387]

Answer:

The value of $m$ is -30.

Step-by-step explanation:

Let $27\cdot x^{2}+m\cdot x +8 = 0$ , we notice that expression is a second order polynomials. We can rearrange the polynomial and use factorization to calculate all roots:

$x^{2}+\frac{m}{27}\cdot x + \frac{8}{27} = 0$ (1)

$-x^{2}-x = \frac{m}{27}$ (2)

$x^{3} = \frac{8}{27}$ (3)

From (3) we find the least root:

$x = \sqrt [3]{\frac{8}{27}}$

$x = \frac{2}{3}$

By (2) we have the value of $m$ :

$m = -27\cdot (x^{2}+x)$

$m = -30$

3 0

3 years ago