Four lab rats stage a daring escape in broad daylight, eventually establishing a colony behind the laboratory's parking garage. After one month, the population of the colony has risen to eight rats. After two months, the population is sixteen; after three months, thirty-two, and so on. If the pattern continues, how many months will it take for the colony population to reach 1,024 rats?

Answer:

10

Step-by-step explanation:

substitute -3 in for x

f(-3)=(-3)²+1=

9+1=10

(You can ignore the g(x) part - it has nothing to do with this question.)

Answer:

 2xy4 • (11x2 + 14xy + 17)

Step-by-step explanation:

(((22•(x3))•(y4))+((28•(x2))•(y5)))+(2•17xy4)

(((22•(x3))•(y4))+((22•7x2)•y5))+(2•17xy4)

 (((2•11x3) • y4) +  (22•7x2y5)) +  (2•17xy4)

5.1     Pull out like factors :

  22x3y4 + 28x2y5 + 34xy4  =   2xy4 • (11x2 + 14xy + 17)  

Trying to factor a multi variable polynomial :

5.2    Factoring    11x2 + 14xy + 17

Final result :

 2xy4 • (11x2 + 14xy + 17)

Answer:

Associative Property

Step-by-step explanation:

The associative property states that it doesn't matter where the parenthesis are put, the answer will always be the same

Answer: It should be 50% or 0.5

Step-by-step explanation:

Answer:

320 miles per hour

Step-by-step explanation:

Speed=800miles/2.5 hours

320milesperhour

Answer:

Both Triangle are congruent because they have equal sides (the same amount of ticks on each side) The triangles are congruent.

Step-by-step explanation:

Answer:

Pythagorean Thereom is the method in which finds the lengths of each side of a triangle. The formula is [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

Each letter in the formula defines a certain side of a triangle.

The picture shown shows the sides of each triangle and how they correspond with the formula.

This helps solve triangles to find its sum, as well as, to figure out a side depending on what is given.

Answer

8x>10+4x  for x=>3

Just two games.

for the third game you would have paid $24 in total

Step-by-step explanation:

Given that

gamers charge $8

Discount Club charges $4 after  a membership of $10

total for the Discount club is given by the expression

let x be the number of games rent

Y=10+4  

So at the first rent, you will pay Discount Club

$14 and the second rent you would have spent

14+4= $18

and the third rent you would have spent

18+4= $22

the inequality is given as

for x=>3

8x>10+4x

Answer:

Domain: 8,4,0,1

Range: 7,9,0,17

Answer:

Y = 14

Step-by-step explanation:

6 times 2 = 12

7 times 2 = 14

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

x = − 38

Step-by-step explanation:

Answer:

−38

Step 1: Simplify both sides of the equation.

−(6x+8)=4(17−x)

−6x+−8=(4)(17)+(4)(−x)(Distribute)

−6x+−8=68+−4x

−6x−8=−4x+68

Step 2: Add 4x to both sides.

−6x−8+4x=−4x+68+4x

−2x−8=68

Step 3: Add 8 to both sides.

−2x−8+8=68+8

−2x=76

Step 4: Divide both sides by -2.

−2x−2=76−2

x=−38

Answer:

30

Step-by-step explanation:

Answer:

50 and 90

Step-by-step explanation:

(180-40)/(5 + 9) = 10

=> 50 and 90

Answer:

55 dollars

Step-by-step explanation:

y = total cost, x = number of sessions attended

Non-members equation:   y = 5x              

Members equation: y = 3x + 25

y = 3(10) + 25

y = 30 + 25

y = 55 dollars

Hope this helps!

Answer:

0.5

Step-by-step explanation:

4a+5=7

4a=7-5

4a=2

a=2/4

Answer:

a = 1/2

Step-by-step explanation:

4a + 5 = 7

4a = 2

a = 1/2

8 inches on the map. To approach this problem, just set up a proportion:

2in =10 mi x in =40 mi.

If we use that to set up an equation we get

80 =10x.

Solve that, you get 8.

Hope this helps, let me know if you need more help.

Answer:

A) 2

Step-by-step explanation:

For this problem, you can create an equation.

2n+4=4n

Then, divide by 2.

n+2=2n

Finally, subtract n from both sides.

2=n

Step-by-step explanation:

first u need to pick a random coordinate to substitute the X . example 0

y = 2(0) + 1

y =1 , X= 0

X= 1

y= 2(1) + 1

y= 3, X= 1

then you continue this same process and again until u have at least two points to draw a straight line. it kinda depended if u want to fill the entire graph.

Answer:

The number 8 goes in the blank,

Step-by-step explanation:

Its basic commutative property.

Hope this helps!

Answer:

Yes

Step-by-step explanation:

You can use the Vertical line test to figure this out, and sure enough none of the points touch the vertical line.

Answer:

69

\

Step-by-step explanation:

88 degrees.

Total measure of triangle's angles is 180 degrees.

angle <2 and 42 degrees are corresponding so <2 is also 42 degrees.

50 + 42 = 92.

180 - 92 = 88 degrees

If this helped, please mark branliest.

Answer: per 1 ticket sold it costs 10 dollars

Step-by-step explanation:

1 and ten meet on the graph constantly

Answer:

Gigi Jojo Jojo hip-hop Dutch him

so do Cob zoom from chick dunno drink gum

Step-by-step explanation:

hjjjhb. bjkn

jkk.

hj. hm.

gin

ghb.

8vb.

ucnluh itg.hboy

Answer:

3x=4

Step-by-step explanation:

3x+3=7

3x=4

Answer:

A:-1

Step-by-step explanation:

According to Khayyam-Pascal triangle ,

the value of n is 8.

[tex] look \: \\ \\ {(x + 1)}^{8} = {x}^{8} + 8 {x}^{7} + 28 {x}^{6} + 56 {x}^{5} + 70 {x}^{4} + 56 {x}^{3} + 28 {x}^{2} + 8x + 1 \\ \frac{56}{28} = 2 [/tex]

Recall the binomial theorem:

[tex](a+b)^n=\displaystyle\sum_{k=0}^n\binom nk a^k b^{n-k}[/tex]

where

[tex]\dbinom nk=\dfrac{n!}{k!(n-k)!}[/tex]

is the binomial coefficient. So

[tex](x+1)^n=\displaystyle\sum_{k=0}^n\binom nk x^k[/tex]

The x² term occurs for k = 2, which has coefficient

[tex]\dbinom n2=\dfrac{n!}{2!(n-2)!}=\dfrac{n(n-1)}2[/tex]

The x³ occurs for k = 3, with coefficient

[tex]\dbinom n3=\dfrac{n!}{3!(n-3)!}=\dfrac{n(n-1)(n-2)}6[/tex]

The latter coefficient is twice the other one, so that

[tex]\dfrac{n(n-1)(n-2)}6=2\cdot\dfrac{n(n-1)}2[/tex]

Solve for n :

[tex]\dfrac{n(n-1)(n-2)}6=n(n-1)[/tex]

[tex]n(n-1)(n-2)=6n(n-1)[/tex]

[tex]n-2=6[/tex]

[tex]\boxed{n=8}[/tex]

Answer:

Step-by-step explanation:

280÷8=35+5=$40