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3 years ago

Find the zeros of the function. Write the smaller solution first, and the larger solution second f(x)= (x+6)^2-49

Mathematics

2 answers:

katrin2010 [14]3 years ago

7 0

Answer:

-13,1

Step-by-step explanation:

f(x)= (x+6)^2-49

When we find the zero's we set f(x) =0

0= (x+6)^2-49

Add 49 to each side

49= (x+6)^2-49+49

49= (x+6)^2

Take the square root of each side

±sqrt(49) = sqrt((x+6)^2)

±7 = (x+6)

Subtract 6 from each side

±7-6 = (x+6-6)

±7-6 = x

7-6 =x -7-6 =x

1=x -13=x

Contact [7]3 years ago

3 0

Answer:

x = -13 or x = 1

Step-by-step explanation:

(x+6)^2 is x^2+12x+36

(x+6)^2-49 is x^2+12x-13, looks hard to factor.

BUT (x+6)^2 - 49 is the difference of two squares, so the factorization is

(x+6+7)(x+6-7) = (x+13)(x-1),

which is factorization of x^2+12x-13.

The expression is zero when either factor is zero, x = -13 or x = 1

Check: f(x) = (x+6)^2-49

f(-13) = (-13+6)^2-49 = (-7)^2-49 = 0

f(1) = (1+6)^2-49 = (7)^2-49 = 0

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Pam is taking a train from the town of Rome to the town of Florence. Rome is located 40 miles due west of the town of Paris. Flo

tankabanditka [31]

Answer:

Pan is closest to Paris when she gets to Florence when she is 35 miles away

Step-by-step explanation:

With Paris at (0,0), Rome is 40miles west which is on the negative x axis.

Florence is 35 miles closer (east to Paris) so we have -45 + 35 = -10

and 55 mikes north of Rome which is on the positive y-axis. So Florence is at point (-10,55)

The distance between the two points Florence and Paris is √(x2 - x1)^2 + (y2 - y1)^2

x1 = 0, y1 = 0

x2 = -10, y2 = 55

So we have

√(-10-0)^2 + (55-0)^2

= √(-10)^2 + (55)^2

= √ 100 + 3025

= √3125

= 55.9 mikes from Paris

Pam is closest to Paris when she gets to Florence when she is 35 miles away

3 0

2 years ago

the cab charges $1.75 for the flst fee and $0.25 for each mile. write and solve an inequality to determine how many miles eddie

Dominik [7]

0.25m + 1.75= 15

Move +1.75 to the right side of the equal sign which becomes -1.75

0.25m=15-1.75

subtract 15 and 1.75 which is 13.25

0.25m=13.25

divide 0.25 by both sides. 0.25m divided by 0.25 is 1m and 13.25 divided by 0.25 is 53.

He can travel 53 miles

0.25m + 1.75= 15

6 0

2 years ago

Can I please have some help????

DedPeter [7]

Answer:

avn= -8 + (n-1)(-7)

Step-by-step explanation:

arithmetic sequence formula= avn= av1 + (n-1)d

av1= first number in the sequence

d= common difference

n= the number of the term to find

The common difference is -7 so d=-7 and you plug it into the equation. The first number in the sequence is -8 so av1.

There is no specific n to find so it remains n.

I hope this helps! Let me know if this helps.

8 0

2 years ago

Read 2 more answers

In the figure below, \overline{AD} AD start overline, A, D, end overline and \overline{BE} BE start overline, B, E, end overline

VLD [36.1K]

Answer:

<u>The measure of the arc CD = 64°</u>

Step-by-step explanation:

It is required to find the measure of the arc CD in degrees.

So, as shown at the graph

BE and AD are are diameters of circle P

And ∠APE is a right angle ⇒ ∠APE = 90°

So, BE⊥AD

And so, ∠BPE = 90° ⇒(1)

But it is given: ∠BPE = (33k-9)° ⇒(2)

From (1) and (2)

∴ 33k - 9 = 90

∴ 33k = 90 + 9 = 99

∴ k = 99/33 = 3

The measure of the arc CD = ∠CPD = 20k + 4

By substitution with k

<u>∴ The measure of the arc CD = 20*3 + 4 = 60 + 4 = 64°</u>

6 0

2 years ago

Find all of the equilibrium solutions. Enter your answer as a list of ordered pairs (R,W), where R is the number of rabbits and

zloy xaker [14]

Answer:

$(0,0)$ $(4000,0)$ and $(500,79)$

Step-by-step explanation:

Given

See attachment for complete question

Required

Determine the equilibrium solutions

We have:

$\frac{dR}{dt} = 0.09R(1 - 0.00025R) - 0.001RW$

$\frac{dW}{dt} = -0.02W + 0.00004RW$

To solve this, we first equate $\frac{dR}{dt}$ and $\frac{dW}{dt}$ to 0.

So, we have:

$0.09R(1 - 0.00025R) - 0.001RW = 0$

$-0.02W + 0.00004RW = 0$

Factor out R in $0.09R(1 - 0.00025R) - 0.001RW = 0$

$R(0.09(1 - 0.00025R) - 0.001W) = 0$

Split

$R = 0$ or $0.09(1 - 0.00025R) - 0.001W = 0$

$R = 0$ or $0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

Factor out W in $-0.02W + 0.00004RW = 0$

$W(-0.02 + 0.00004R) = 0$

Split

$W = 0$ or $-0.02 + 0.00004R = 0$

Solve for R

$-0.02 + 0.00004R = 0$

$0.00004R = 0.02$

Make R the subject

$R = \frac{0.02}{0.00004}$

$R = 500$

When $R = 500$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 -2.25 * 10^{-5} * 500 - 0.001W = 0$

$0.09 -0.01125 - 0.001W = 0$

$0.07875 - 0.001W = 0$

Collect like terms

$- 0.001W = -0.07875$

Solve for W

$W = \frac{-0.07875}{ - 0.001}$

$W = 78.75$

$W \approx 79$

$(R,W) \to (500,79)$

When $W = 0$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 - 2.25 * 10^{-5}R - 0.001*0 = 0$

$0.09 - 2.25 * 10^{-5}R = 0$

Collect like terms

$- 2.25 * 10^{-5}R = -0.09$

Solve for R

$R = \frac{-0.09}{- 2.25 * 10^{-5}}$

$R = 4000$

So, we have:

$(R,W) \to (4000,0)$

When $R =0$ , we have:

$-0.02W + 0.00004RW = 0$

$-0.02W + 0.00004W*0 = 0$

$-0.02W + 0 = 0$

$-0.02W = 0$

$W=0$

So, we have:

$(R,W) \to (0,0)$

Hence, the points of equilibrium are:

$(0,0)$ $(4000,0)$ and $(500,79)$

4 0

2 years ago