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2 years ago

9

125 tickets were sold for the jazz band concert for a total of $1,022. Student tickets cost $6 each, and general admission ticke

ts cost $10 each. How many of each kind of ticket were sold?

1 answer:

Phoenix [80]2 years ago

5 0

Answer:

The number of student tickets was $57$

The number of general admission tickets was $68$

Step-by-step explanation:

Let

x----> the number of student tickets

y---> the number of general admission tickets

we know that

$x+y=125$

$x=125-y$ ---> equation A

$6x+10y=1,022$ ----> equation B

Substitute equation A in equation B and solve for y

$6(125-y)+10y=1,022$

$750-6y+10y=1,022$

$4y=1,022-750$

$4y=272$

$y=68$

Find the value of x

$x=125-68=57$

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Karens possabilty is 15/50 chance

Makiah possability is 12/50 chance

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1 year ago

Sum of positive roots of the equation (x2 - 12x + 35) (x2 + 10x + 24) = 504 is

Digiron [165]

Answer:

(3)11

Step-by-step explanation:

We are given that

$(x^2-12x+35)(x^2+10x+24)=504$

We have to find the sum of positive roots of the equation.

$x^2(x^2+10x+24)-12x(x^2+10x+24)+35(x^2+10x+24)=504$

$x^4+10x^3+24x^2-12x^3-120x^2-288x+35x^2+350x+840=504$

$x^4-2x^3-61x^2+62x+840-504=0$

$x^4-2x^3-61x^2+62x+336=0$

Factor of 336

2,3,4,6,8,7,

Let x=2

$2^4-2^4-61(2^2)+62(2)+336\neq0$

x=2 is not the root of equation

x=-2

$(-2)^4-2(-2)^3-61(-2)^2+62(-2)+336=0$

Hence x=-2 is the root of equation.

x+2 is a factor of equation.

x=3

$3^4-2(3^3)-61(3^2)+62(3)+336=0$

Therefore, x=3 is the root of equation.

$(x+2)(x-3)(x^2-x-56)=0$

$(x+2)(x-3)(x^2-8x+7x-56)=0$

$(x+2)(x-3)(x(x-8)+7(x-8))=0$

$(x+2)(x-3)(x-8)(x+7)=0$

$x-8=0\implies x=8$

$x+7=0\implies x=-7$

Positive roots are 3 and 8

Sum of positive roots=3+8=11

Option (3) is true.

4 0

1 year ago

if BD is perpendicular to AC M angle DBE equals 2x - 1 + m angle CBE equals 5x - 42 find the value of x

Paha777 [63]

<h2>Answer:</h2>

<h2>Step-by-step explanation:</h2>

I've drawn a graph in order to a better understanding of this problem. We know that:

BC is perpendicular to AC

∠DBE = 2x - 1

∠CBE = 5x - 42

Let's call the intersection of line BC and AC the point P, so:

∠P=90°

And points B, P and C form the triangle ΔBPC. On the other hand, ∠CBE and ∠PCB are Alternate Interior Angles, so:

∠PCB = ∠CBE = 5x - 42

Moreover:

∠PBC = 2x - 1 - (5x - 42)

∠PBC = 2x - 1 - 5x + 42

∠PBC = -3x + 41

The internal angles of any triangle add up to 180°. Hence for ΔBPC:

90° + ∠PBC + ∠PCB = 180°

90° - 3x + 41 + 5x - 42 = 180°

2x + 89 = 180

2x = 91

x = 45.5°

7 0

1 year ago

#6) Beth saved a total of $30 per month for her first car. Beth saved

cluponka [151]

Answer:

1) The domain In interval notation is [0, 20]

2) The range in interval notation is [100, 700]

Step-by-step explanation:

The given parameters are;

The amount Beth saved per month = $30

The number of months Beth saved = 20 months

The amount with which Beth opened her account = $100

Therefore, the amount of money Beth saved with respect to time is given as follows;

Y = $100 + $30 × X

Where;

Y = The amount of money Beth saved

X = The time (number of months) Beth saved

The domain is given as follows;

$\{X | \ 0 \leq X \leq 20 \}$

The domain in interval notation is [0, 20]

For the range, when X = 0, Y = $100

When X = 20, Y = $100 + $30 × 20 = $700

Therefore, the range is given as follows;

$\{Y | \ 100 \leq Y \leq 700 \}$

Which the range in interval notation is [100, 700].

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2 years ago

How many numbers are 10 units from zero on number line

Lelu [443]

Answer:

I think 2.

Step-by-step explanation:

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1 year ago

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