MATHEMATICS HIGH SCHOOL

The roots of the function f(x) = x2 – 2x – 3 are shown. what is the missing number? x = –1 and x =

Answers

Answer 1

Answer:

we have

$f(x)=x^(2)-2x-3$

Find the roots

Equate the function to zero

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

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$x^(2)-2x=3$

Complete the square. Remember to balance the equation by adding the same constants to each side.

$x^(2)-2x+1=3+1$

$x^(2)-2x+1=4$

Rewrite as perfect squares

$(x-1)^(2)=4$

Square root both sides

$(x-1)=(+/-)2$

$x=1(+/-)2$

$x=1+2=3$

$x=1-2=-1$

therefore

the answer is

$x=3$

Answer 2

Answer: x^2 -2x -3 = 0

(x-3)(x+1)=0

x+1=0
x=-1

x-3=0
x = 3

so the missing number is 3

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The solution to an equation is 21

Answers

an solution to an equation = 21 would be something like 2p + 7

if you wanna know how to solve this
here is how:
Simplifying 2p + 7 = 21 Reorder the terms: 7 + 2p = 21 Solving 7 + 2p = 21 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2p = 21 + -7 Combine like terms: 7 + -7 = 0 0 + 2p = 21 + -7 2p = 21 + -7 Combine like terms: 21 + -7 = 14 2p = 14 Divide each side by '2'. p = 7 Simplifying p = 7

NEED HELP ASAP! The sum of two numbers is 105. The larger number is 6 less than twice the smaller
number. What are the numbers?

Answers

Answer: x=68, y=37

Step-by-step explanation:

The equation for the sum of two numbers is 105 would be x+y=105. You can say the larger number would be x and the smaller would be y. So, x=2y-6. then you plug that into the x in the first equation.

2y-6+y=105

3y-6=105

3y=111

y=37

Then you would plug in the y to one of the equations. I will do the second one but you can do either one.

x=2y-6

x=2*37-6

x=74-6

x=68

Please help how do I do this ??

Answers

for 10 here is the answer and for 9 i’ll reply to my comment

Identify the domain for the following ordered pairs: (3, 5) (-2, 4) (5, 5) (-1, 1).A. (5, 4, 5, 1)
B. (-5, -4, -5, -1)
C. (3, -2, 5, -1)
D. (-3, 2, -5, 1)

Answers

Domain is the x value's
to get your answer, get all the x - values
i.e
(3, -2, 5, -1)
So, You're correct option is C.

What formula tells the cost, in dollars, ifchocolate chip cookies are $1.50/dozen and
lemon frosteds are $ 1.00/dozen? Let c =
number of dozens of chocolate chip cookies; L=
number of dozens of lemon frosteds; T = total
charge.

Answers

Answer:

T = $1.50C + $1.00L

Step-by-step explanation:

Chocolate chip cookies - $1.50/dozen

C: # of dozens of chocolate chip cookies

↓

$1.50C

Lemon Frosteds - $1.00/dozen

L: # of dozens of lemon frosteds

↓

$1.00L

T(total) = $1.50C + $1.00L

Hope that helps.

Can someone show me how to solve this? A boat took 5 hours to travel 60km up a river, against the current. The return trip took 3 hours. Find the speed of the boat in still water and the speed of the current.

Answers

Yes, I can.

And even though you haven't asked to be shown how to do it,
I'll go ahead and do that too:

Call the speed of the boat (through the water) 'B'.
Call the speed of the current (the water) 'C'.

When the boat is going 'up' the river, against the current,
his speed past the riverbank is (B - C).

When the boat is going 'down' the river, the same way as the current,
his speed past the riverbank is (B + C).

The problem says it took him 5 hours to travel 60 km against the current.
Distance = (speed) x (time)
60 km = (B - C) x (5 hours)

The problem also says it took him 3 hours to return.
The distance to return is the same 60 km.
The other direction is the same direction as the current,
so his speed on the return is (B + C).
Distance = (speed) x (time)
60 = (B + C) x (3)

Now we have two equations, so we can find 'B' and 'C'.

5B - 5C = 60
3B + 3C = 60

Multiply each side of the first equation by 3, and
multiply each side of the second equation by 5:

15B - 15C = 180
15B + 15C = 300

Add the second equation to the first one:

30B = 480
B = 480/30 = 16 km per hour.

Subtract the second equation from the first one:

-30C = -120
C = -120/-30 = 4 km per hour.

The speed of the boat through the water (B) is 16 km per hour.
The speed of the water past the riverbank is 4 km per hour.

Check:

-- When the boat is going along with the current, his speed past the riverbank
is (16 + 4) = 20 km per hour. In 3 hours, he covers (3 x 20) = 60.

-- When the boat is going against the current, his speed past the riverbank
is (16 - 4) = 12 km per hour. In 5 hours, he covers (5 x 12) = 60 km.

yay !

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