real number venn day 1 activity sheet .

9514 1404 393

Answer:

  1. (f+g)(x) = 2x^2 +4x +2

  2. (f -g)(x) = -2x^2 +4x -4

  5. (f+g)(x) = x^2 +2x -1

  6. (g -f)(x) = x^2 -2x -1

Step-by-step explanation:

None of these are compositions. They are only sums or differences.

  (f±g)(x) = f(x) ± g(x)

__

1. (f+g)(x) = f(x) +g(x) = (4x -1) +(2x^2 +3)

  (f+g)(x) = 2x^2 +4x +2

__

2. (f -g)(x) = f(x) -g(x) = (4x -1) -(2x^2 +3)

  (f -g)(x) = -2x^2 +4x -4

__

5. (f +g)(x) = f(x) +g(x) = (2x) +(x^2 -1)

  (f+g)(x) = x^2 +2x -1

__

6. (g -f)(x) = g(x) -f(x) = (x^2 -1) -(2x)

  (g -f)(x) = x^2 -2x -1

Answer:

1.8 cm to the nearest tenth.

Step-by-step explanation:

The angle opposite side a = 180 - 105 - 15 = 60 degrees.

By the Sine Rule:

a / sin 60 = 2 / sin 105

a = 2 * sin60/ sin 105

= 1.79315

Answer:

[tex]\displaystyle \theta = \left\{\frac{7\pi}{6}, \, \frac{3\pi}{2}, \frac{11\pi}{6}\right\}[/tex]

Step-by-step explanation:

We want to solve the equation:

[tex]2\sin ^2 \theta + 3\sin \theta + 1 = 0[/tex]

In the interval [0, 2π).

Notice that this is in quadratic form. Namely, by letting u = sin(θ), we acquire:

[tex]\displaystyle 2u^2 + 3u + 1 = 0[/tex]

Factor:

[tex]\displaystyle (2u+1)(u+1) = 0[/tex]

By the Zero Product Property:

[tex]\displaystyle 2u + 1 = 0\text{ or } u + 1 = 0[/tex]

Solve for each case:

[tex]\displaystyle u = -\frac{1}{2} \text{ or } u = -1[/tex]

Back-substitute:

[tex]\displaystyle \sin \theta = -\frac{1}{2} \text{ or } \sin \theta =-1[/tex]

Use the Unit Circle. Hence, our three solutions in the interval [0, 2π) are:

[tex]\displaystyle \theta = \left\{\frac{7\pi}{6}, \, \frac{3\pi}{2}, \frac{11\pi}{6}\right\}[/tex]

Answer:

9

Step-by-step explanation:

Let Benjamin's age be=x.

Let Lucas's age be=y.

Then, x=2y-6

When x=12, 12+6=2y.

18/2=y, y=9

Answer:

do you mean PEMDAS?

Step-by-step explanation:

parenthesis, exponents, multiplication, division, addition, and subtraction

you solve in order and go left to right

if you give an equation i can explain it better, but it's basically that

Step-by-step explanation:

1- solve operation in parantheses or brackets.

2- we solve any exponent

3- solve all multiplication and division left to right

Answer:

ab^2 + oa^2

Step-by-step explanation:

It is pathagorus theorem basically

hypotenuse²= perpendicular²+base²

Answer:

no solutions

Step-by-step explanation:

5(1+2m)=1/2(8+20m)

5+10m = 4+10m

10m-10m= 4-5

No solutions

Answer:

12

Step-by-step explanation:

Substitute x = 4 into the expression

4² - 3(4) + 8 = 16 - 12 + 8 = 12

Answer:

12

Step-by-step explanation:

x²-3x+8

Plug in:

(4)²-3(4)+8

Use PEMDAS:

P - Parentheses

E - Exponents

M - Multiplication

D - Division

A - Addition

S - Subtraction

(4)²-3(4)+8

16 - 3(4) + 8

16 - 12 + 8

4 + 8

  12

Hope this helped.

Answer:

100,000 coins

Step-by-step explanation:

We can use a ratio to solve

1 apple        1000 apples

------------   = ---------------

100 coins        x coins

Using cross products

1x = 100 * 1000

1x = 100,000

We need 100,000 coins

Answer:

100,000 coins

Step-by-step explanation:

1 apple cost 100 coins

We want to find the amount of coins needed to get 1000 apples.

To do so we simply multiply the coins it takes to get 1 apple (100) by 1000

1000 * 100 = 100,000

Answer:

A cookie is $1.50.

Step-by-step explanation:

Variable x = cost of cookies

For each child means the 7 guests plus Mrs. Perkins' son which equals 8.

Set up an equation:

(2x)8 + (2.75)8 = 46

Use distributive property:

16x + 22 = 46

Isolate variable x by subtracting both sides by 22:

16x = 24

Isolate variable x by dividing both sides by 16

x = 1.5

Check your work:

2(1.5) × 8 + (2.75)8 = 46

3 × 8 + 22 = 46

24 + 22 = 46

46 = 46

Correct!

Answer: $1.50 per cookie

Step-by-step explanation:

We know that each cupcake is worth $2.75 and the total bill of all her purchases is $46.

Therefore, lets multiply the cost of a cupcake times the amount of people eating them. (the sons and 7 guests which add up to 8)

2.75(8) = $22

Now take the total cost of 8 cupcakes and subtract it from the total.

46 - 22 =  $24

24 dollars is equal to the cost times the amount of cookies purchased. Therefore, let X equal to the cost per cookie and multiply it times the amount of cookies purchased. The amount of cookies is equal to 2 cookies times 8 children.

(2*8)X = 24

16x=24

x= $1.50

Check:

8[ (1)(2.75) + 2X ] = 46

8[ 2.75 + (2) (1.50) ] = 46

22 + 24 = 46

46 = 46

Answer: The answer is D

Step-by-step explanation:

Answer:

5 years

Step-by-step explanation:

Let x be the unknown numer of years ago when the product of the man and his child's age was 96.

》 x years ago, the man's age = 37 - x

the child's age = 8 - x

(37 - x)(8 - x) = 96

296 - 37x - 8x + x² = 96

x² - 45x - 296 - 96 = 0

x² - 45x - 200 = 0

x² - 5x - 40x - 200 = 0

x(x - 5) -40(x - 5) = 0

(x - 5)(x - 40) = 0

x = 5 years ago or x = 40 years ago

but x = 40 > son's present age.

Thus, x = 5.

Therefore, 5 years ago the product of the ages of the man and his child was 96.

Answer:

500, 500, 50, 10.

Step-by-step explanation:

5000 ÷ 500 = 10,

500 ÷ 50 = 10

50 ÷ 5 = 10

Answer:

5,000/500 = 10

50 /5 = 10

500/50 = 10

Method:

Calculator ;)

Answer:

7.29

Step-by-step explanation:

Answer:

60

12 inches=1 foot so 12 ×5=60

Answer:

60

Step-by-step explanation:

lol

Answer:

[tex]\frac{-4xy}{x^2-y^2}[/tex]

Step-by-step explanation:

[tex]\frac{x-y}{x+y}-\frac{x+y}{x-y} \\\\\\=>\frac{(x+y)(x-y)}{(x-y)(x-y)} -\frac{(x+y)(x-y)}{(x+y)(x+y) } \\\\=> \frac{(x-y)(x-y)-(x+y)(x+y)}{(x+y)(x-y)} \\\\=>\frac{x^2-xy-xy+y^2-x^2-xy-xy-y^2}{(x+y)(x-y)} \\\\=>\frac{-4xy}{(x+y)(x-y)} \\\\=>\frac{-4xy}{x^2 - y^2}[/tex]

Answer:

Here,

A=-7

B=12

Length of AB=?

Now, We know that,

Length of AB=-7-12

=-19

Thus, the length of AB is -19

Answer:

Answer:

[tex]4(3 + c) + c = 4 + c \\ 12 + 4c + c = 4 + c \\ 12 + 5c = 4 + c \\ 12 - 4 = c - 5c \\ \\ 8 = - 4c \\ c = \frac{ - 8}{4} \\ c = - 2 \\ thank \: you[/tex]

Answer: c = -2

Step-by-step explanation:

Given

4 (3 + c) + c = c + 4

Expand parentheses and apply the distributive property

4 · 3 + 4 · c + c = c + 4

12 + 4c + c = c + 4

Combine like terms

12 + (4c + c) = c + 4

12 + 5c = c + 4

Subtract 12 on both sides

12 + 5c - 12 = c + 4 - 12

5c = c - 8

Subtract c on both sides

5c - c = c - 8 - c

4c = -8

Divide 4 on both sides

4c / 4 = -8 / 4

[tex]\boxed{c=-2}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

a= 1 , b= 3 , c= –3

[tex]x = \frac{ - b \frac{ + }{} \sqrt{ {b}^{2} - 4ac} }{2a} \\ x = \frac{ - 3 \frac{ + }{} {} \sqrt{ {3}^{2} - 4(1)( - 3)} }{2(1)} \\ = \frac{ - 3 \frac{ + }{} \sqrt{9 + 12} }{2} = \frac{ - 3 \frac{ + }{} \sqrt{21} }{2} \\ \\ x = \frac{ - 3 \frac{ + }{} \sqrt{21} }{2} \\ \\ x = 0.79 \\ x = - 3.79[/tex]

I hope I helped you^_^

Answer:

SEE IMAGE FOR SOLUTION

Hope it helps

Have a great day

Answer:

[tex]-\frac{11}{3} \leq x\leq -1[/tex]

Hope this helps!! <3

Answer:

The answer is

The measure of c is 63

Answer:

x+y=$8,000 i guess

Step-by-step explanation:

Answer:

720

Step-by-step explanation:

|16+4(3(-6)+(2)|

|20(-18*2)|

|20*-36|

|-720|

720

Step-by-step explanation:

[tex] |16 + 4(3q + p)| \\ p = 2 \\ q = - 6 \\ then \\ = |16 + 4(3 \times - 6 + 2)| \\ = |16 + 4( - 18 + 2)| \\ = |16 + 4( - 16)| \\ |16 + - 64| \\ = | - 48| \\ take \: out \: side \: of \: mode \: then \: it \: become \: = 48 \\ \\ thank \: you[/tex]

Step-by-step explanation:

For x-intercept:

put y=0

0=-7x+3

7x=3

x=3/7

points(3/7,0)

For y-intercept:

x=0

y=-7(0)+3

y=3

points(0,3)

Answer:

It is 0.6

Step-by-step explanation:

[tex] \frac{12}{20} [/tex]

divide numerator and denominator by 2:

[tex] = \frac{12 \div 2}{20 \div 2} \\ \\ = \frac{6}{10} [/tex]

since it's a tenth, it becomes a value with out decimal place:

[tex] = 0.6[/tex]