Write the expression (y 7)^2 -100 as the product of two linear binomials

Answers

Answer 1

Answer: To answer this problem, you have to have a good foundation in factoring polynomial expressions. It has to be taken into account the knowledge in division and fractions.

The expression
(y+7)^2 - 100

can be factored as
[ (y+7) + 10 ] [ (y+7) - 10 ]

Further simplifying the expressions
[ y + 7 + 10 ] [ y + 7 - 10 ]
( y + 17 ) ( y - 3)

So the product of two linear binomials is
(y+17)(y-3)

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The John Jay Theater Dept has tickets at $6 for adults, $4 for teachers, and $2 for students. A total of 280 tickets were sold for one showing with a total revenue of $1010. If the number of adult tickets sold was twice the number of teacher tickets, how many of each type of ticket were sold for the showing?

Answers

Answer:

number of adults tickets sold = x = 90

number of teachers tickets = y = 45

number of students tickets = z = 145

Step-by-step explanation:

Cost of tickets

Adults = $6

Teachers = $4

Students = $2

Total tickets sold = 280

Total revenue = $1010

Let

x = number of adults tickets

y = number of teachers tickets

z = number of students tickets

x + y + z = 280

6x + 4y + 2z = 1010

If the number of adult tickets sold was twice the number of teacher tickets

x = 2y

Substitute x=2y into the equations

x + y + z = 280

6x + 4y + 2z = 1010

2y + y + z = 280

6(2y) + 4y + 2z = 1010

3y + z = 280

12y + 4y + 2z = 1010

3y + z = 280 (1)

16y + 2z = 1010 (2)

Multiply (1) by 2

6y + 2z = 560 (3)

16y + 2z = 1010

Subtract (3) from (2)

16y - 6y = 1010 - 560

10y = 450

Divide both sides by 10

y = 450/10

= 45

y = 45

Substitute y=45 into (1)

3y + z = 280

3(45) + z = 280

135 + z = 280

z = 280 - 135

= 145

z = 145

Substitute the values of y and z into

x + y + z = 280

x + 45 + 145 = 280

x + 190 = 280

x = 280 - 190

= 90

x = 90

Therefore,

number of adults tickets sold = x = 90

number of teachers tickets = y = 45

number of students tickets = z = 145

At what value of x do the graphs of the equations below intersect?2x – y = 6

5x + 10y = –10

Answers

The intersection is the point where two equations meet. It is calculated by substituting terms into the equations involved. For the given systems of equation, calculations are as follows:

2x - y = 6
y = 2x - 6

We substitute the equation above to the second equation.

5x + 10y = –10
5x + 10( 2x - 6 )= –10

Simplifying,

5x + 20x - 60 = -10
25x = 50
x = 2

Therefore, the intersection has the value of x equal to 2.

c (2) is the value in where the equations intersect

Can anyone please help with this question

Answers

so 4(x+5)=x+8
first we distribute
using the distributive property of multiplication which is a(b+c)=(ab)+(ac)

4(x+5) is also (4x)+(4(5))=4x+20

4x+20=x+8
subtract x from both sides
3x+20=8
subtract 20 from both sides
3x=-12
divide both sides by 3
x=-4

4(x+5)=x+8
4x+4*5=x+8
4x+20=x+8
4x-x+20=x+8-x
3x+20-20=8-20
3x=-12
3x/3=(-12)/3
x=-4

Computer usage has increased over time. But has the increase been more linear or more exponential? In 1997, 22.2% of the population over three years of age, or about 60 million people, used the internet. In 1998, 32.7% of the population over three years of age, or about 90 million people, used the internet. a. If the usage increased linearly, write the linear function that would give 60 million people in year 0 and 90 million in year 1.

Answers

That's an increase of 30,000,000 people in one year, a slope of 30 million and a good year for the internet.

If t is the year, and p is number of internet users,

p = 30000000(t - 1997) + 60000000

Answer: p = 30000000(t - 1997) + 60000000

As for linear versus exponential, one year of data can't really distinguish.

A dance floor is made from square wooden tiles with a side length of 1 foot. the floor can be laid out as a square or as a rectangle. Yeasmin chooses a rectangular dance floor for her party. The width of the rectangular dance floor is 10 feet less than the width of the square dance floor, and its length is 15 greater than the length of the square floor.how much greater is the length of the rectangular dance floor than its width?
The perimeter of the rectangular dance floor is 130 feet. What are the length and width of the dance floor?
If the unit rate is $0.50 per tile, how much would it cost Yeasmin to buy the number of tiles needed to make up the dance floor

Answers

legnth/width for square = x
width of rectangle= x-10
legnth of rectangle=x+15
so (x-10)+25=x+15 which is the first part

part two
the perimiter of rectangle floor =130
perimiter= 2width+2legnth so 130/2=width+height
width=x-10 and legnth=x+15 so
x-10+x+15=130/2
2x+5=75
minus 5 from both sides
2x=70
divide by two
x=35 which is legnth/width of the square, but we want the legnth and width of the rectangle so
x-10=width=25
x+15=legnth=50
so the cost of the floor is (50 times 25)times $0.50 or
(50 times 25)/2 so
$525

0.3151515 as a fraction

Answers

That's. 3,151,515/10,000,000. It's prettier if you simplify it.

0.3(15) = $(315-3)/(990) = (312)/(990)$

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Last one Please show your work