The graph of the function f(x) = –(x + 6)(x + 2) is shown below.

On a coordinate plane, a parabola opens down. It goes through (negative 6, 0), has a vertex at (negative 4, 4), and goes through (negative 2, 0).

Which statement about the function is true?

The function is increasing for all real values of x where
x < –4.
The function is increasing for all real values of x where
–6 < x < –2.
The function is decreasing for all real values of x where
x < –6 and where x > –2.
The function is decreasing for all real values of x where
x < –4.

Answer:

4a

Step-by-step explanation:

4ax^2 + 4ax + 4a

here in every term there is 4 and a so take 4 and a common

4a(x^2 + x + a)

Answer:

Step-by-step explanation:

you can see this is a geometric progression which a ratio of [tex]{2\over{5}}[/tex]. the sum of the firs n term is:

[tex]S=a_1\frac{(1-r^n)}{(1-r)}=175\frac{1-(\frac{2}{5})^{10}}{1-\frac{2}{5}}=291.6360832[/tex]

the nearest integer would be:

292

The sum of the first 10 terms of the series 175, 70, 28, ...   is  291.636

Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number. This fixed number is called common ratio.. This progression is also known as a geometric sequence of numbers that follow a pattern.

Common ratio = (Any term) / (Preceding term)

It means the sum of all the first "n" numbers in the series. The formula for first "n" natural numbers is

Sn = a + a r + ar2 + ar3 +…+ arn-1

or

Sₙ = a[(rⁿ – 1)/(r – 1)]

where "r" is called common ratio

"a" is called the first term in the series

From the given question the given series is  175, 70, 28, ...

70/175 = 0.4 (or) 28?70 = 0.4

As each succeeding term is produced by multiplying each preceding term by 0.4 .Here the common ratio (r) is 0.4

let first term "a" be 175

then Sₙ = 175[(0.4¹⁰-1)/(0.4 - 1)

      Sₙ= 291.636

Thus the sum of the first 10 terms of the series 175, 70, 28, ...   is  291.636

To know more about geometric progression click here

https://brainly.com/question/4853032

#SPJ2

Answer:

Step-by-step explanation:

Please use parentheses around the denominator:

              2x

f(x) = -------------- or   f(x) = 2x / (1-x^2)

          1 - x^2

to eliminate any ambiguity.  The graph of this function passes thru the origin (0,0) and has vertical asymptotes at x = -1 and x = + 1.  The function is negative on (-1,0) and positive on (0,1).  

Additionally, there are two horizontal asymptotes.   As x grows large and negative, f(x) approaches zero from above.  As x grows large and positive, f(x) approaches zero from below.

The graph approaches -2 as x approaches infinity, this describes the behavior of the function f(x) = 2x/1-x2.

The behavior of the function [tex]f(x) = 2x/(1-x^2)[/tex] as x approaches infinity depends on the degree of the numerator and denominator. In this case, both the numerator and denominator have degree 1, so we can use the ratio of the leading coefficients to determine the behavior.

The leading coefficient of the numerator is 2, and the leading coefficient of the denominator is -1. Therefore, as x approaches infinity, the function approaches -2.

So, the statement that describes the behavior of the function is: "The graph approaches -2 as x approaches infinity."

For more details regarding graph, visit:

https://brainly.com/question/17267403

#SPJ7

9514 1404 393

Answer:

  8

Step-by-step explanation:

The notation n=1 .. 8 means that n takes on all integer values from 1 to 8. Each value of n gives one term that is added to the series.

  The number of terms is 8.

Answer:

[tex] \displaystyle 1)48.2 \: \: \text{sec}[/tex]

[tex] \rm \displaystyle 2)3021.6 \: m[/tex]

Step-by-step explanation:

so when flash down occurs the rocket will be in the ground in other words the elevation(height) from ground level will be 0 therefore,

to figure out the time of flash down we can set h(t) to 0 by doing so we obtain:

[tex] \displaystyle - 4.9 {t}^{2} + 229t + 346 = 0[/tex]

to solve the equation can consider the quadratic formula given by

[tex] \displaystyle x = \frac{ - b \pm \sqrt{ {b}^{2} - 4 ac} }{2a} [/tex]

so let our a,b and c be -4.9,229 and 346 Thus substitute:

[tex] \rm\displaystyle t = \frac{ - (229) \pm \sqrt{ {229}^{2} - 4.( - 4.9)(346)} }{2.( - 4.9)} [/tex]

remove parentheses:

[tex] \rm\displaystyle t = \frac{ - 229 \pm \sqrt{ {229}^{2} - 4.( - 4.9)(346)} }{2.( - 4.9)} [/tex]

simplify square:

[tex] \rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 52441- 4( - 4.9)(346)} }{2.( - 4.9)} [/tex]

simplify multiplication:

[tex] \rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 52441- 6781.6} }{ - 9.8} [/tex]

simplify Substraction:

[tex] \rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 45659.4} }{ - 9.8} [/tex]

by simplifying we acquire:

[tex] \displaystyle t = 48.2 \: \: \: \text{and} \quad - 1.5[/tex]

since time can't be negative

[tex] \displaystyle t = 48.2 [/tex]

hence,

at 48.2 seconds splashdown occurs

to figure out the maximum height we have to figure out the maximum Time first in that case the following formula can be considered

[tex] \displaystyle x _{ \text{max}} = \frac{ - b}{2a} [/tex]

let a and b be -4.9 and 229 respectively thus substitute:

[tex] \displaystyle t _{ \text{max}} = \frac{ - 229}{2( - 4.9)} [/tex]

simplify which yields:

[tex] \displaystyle t _{ \text{max}} = 23.4[/tex]

now plug in the maximum t to the function:

[tex] \rm \displaystyle h(23.4)- 4.9 {(23.4)}^{2} + 229(23.4)+ 346 [/tex]

simplify:

[tex] \rm \displaystyle h(23.4) = 3021.6[/tex]

hence,

about 3021.6 meters high above sea-level the rocket gets at its peak?

Answer:

2.13%

Step-by-step explanation:

assume that the distribution is approximately normal

[tex]\frac{6700-5000}{850} =2[/tex]

the value is 2 s.d. more than the mean

according to normal distribution, approximately 2.13% of the data is 2 s.d. more than the mean.

Answer: y= -1

Step-by-step explanation:

2+y=1  

y=1-2

y=-1

Answer:

I believe the question was written twice on accident

y=7x-38

Step-by-step explanation:

y-4=7(x-6)

y-4=7x-42

y=7x-38

Answer:

Step-by-step explanation:

Given

Find (g - f)(x):

Correct choice is A

Answer:

exponential form = 2.1^2

evaluation = 4.41

Step-by-step explanation:

it is times-ing 2.1 two times, therefore its 2.1^2

2.1 times 2.1 = 4.41

Answer:

-2

Step-by-step explanation:

f(x) = 3x^2 + 5x - 14

substitute -3 inplace of x

f(-3) = 3*(-3)^2 + 5*(-3) - 14

=3*9 - 15 - 14

=27 - 15 - 14

= -2

Answer:

Answer: (C)A picnic table is on sale for 60 percent off.

Step-by-step explanation:

well someone copied me but okay :[

Answer:

The appropriate solution is Option D (22 m/sec).

Step-by-step explanation:

The given equation is:

[tex]s(t)= -(t-15)^2 + 225[/tex]

Now,  

The instantaneous velocity at t = 4 will be:

= [tex][-2(t-15)(1)+0][/tex]

= [tex]-2(4-15)[/tex]

= [tex]-2\times (-11)[/tex]

= [tex]22 \ m/sec[/tex]

Thus, the above is the correct option.

Answer:

314 m²

Step-by-step explanation:

the formula for the surface area of a sphere (As) is

As = 4×pi×r²

the radius r (half of the diameter) is clearly indicated as 5m.

so, As = 4×3.14×5² = 4×3.14×25

I don't even need a calculator for this, as 4×25 = 100

so, As = 100×3.14 = 314

(you know, when multiplying by 10, the decimal point moves right one position. multiply by 100 it moves 2 positions, and so on).

Answer:

Hello There!!

Step-by-step explanation:

The answer is 3,9,15,21.

hope this helps,have a great day!!

~Pinky~

Answer:

the common difference is 6. So, the missing two terms are 9 and 15 using

3 + (n-1)(6)

Answer:

fjjjjjjjjjjjjjj?

aefieoapowiejfie

Answer:

I don't no answer sorry

Step-by-step explanation:

give me brainliest

Answer:

976 ÷ 8 =

8 groups of n = 976

n groups of 8 = 976

122

____

8 | 976

- 8

____

176

- 16

_____

160

- 160

______

0

Answer:

.43 · 80 = 34.4

Step-by-step explanation:

percentages into decimals = move decimal place to left two places

'of' means multiply in math

equations have equal (=) signs

Answer:

4.196.754

Step-by-step explanation:

god bless stay safe po

Answer:

The volume of the prism is 243 ft^3.

Step-by-step explanation:

The equation you have to use is A=Bh

Answer: 121.5 ft3

Step-by-step explanation:

Use this formula for volume of triangulsr prism:

1/2 • length • width • height

That will be 1/2 • 4.5 • 9 x 6 = 121.5

Unit of measurement is ft3 (also same as cubic feet)

Welcomeee!

Answer:

30

Step-by-step explanation:

that is the procedure above

(a) Both conditions are satisfied with x = (1, 0) for [tex]\mathbb R^2[/tex] and x = (1, 0, 0) for [tex]\mathbb R^3[/tex]:

||(1, 0)|| = √(1² + 0²) = 1

max{1, 0} = 1

||(1, 0, 0)|| = √(1² + 0² + 0²) = 1

max{1, 0, 0} = 1

(b) This is the well-known triangle inequality. Equality holds if one of x or y is the zero vector, or if x = y. For example, in [tex]\mathbb R^2[/tex], take x = (0, 0) and y = (1, 1). Then

||x + y|| = ||(0, 0) + (1, 1)|| = ||(1, 1)|| = √(1² + 1²) = √2

||x|| + ||y|| = ||(0, 0)|| + ||(1, 1)|| = √(0² + 0²) + √(1² + 1²) = √2

The left side is strictly smaller if both vectors are non-zero and not equal. For example, if x = (1, 0) and y = (0, 1), then

||x + y|| = ||(1, 0) + (0, 1)|| = ||(1, 1)|| = √(1² + 1²) = √2

||x|| + ||y|| = ||(1, 0)|| + ||(0, 1)|| = √(1² + 0²) + √(0² + 1²) = 2

and of course √2 < 2.

Similarly, in [tex]\mathbb R^3[/tex] you can use x = (0, 0, 0) and y = (1, 1, 1) for the equality, and x = (1, 0, 0) and y = (0, 1, 0) for the inequality.

(c) Recall the dot product identity,

x • y = ||x|| ||y|| cos(θ),

where θ is the angle between the vectors x and y. Both sides are scalar, so taking the norm gives

||x • y|| = ||(||x|| ||y|| cos(θ)|| = ||x|| ||y|| |cos(θ)|

Suppose x = (0, 0) and y = (1, 1). Then

||x • y|| = |(0, 0) • (1, 1)| = 0

||x|| • ||y|| = ||(0, 0)|| • ||(1, 1)|| = 0 • √2 = 0

For the inequality, recall that cos(θ) is bounded between -1 and 1, so 0 ≤ |cos(θ)| ≤ 1, with |cos(θ)| = 0 if x and y are perpendicular to one another, and |cos(θ)| = 1 if x and y are (anti-)parallel. You get everything in between for any acute angle θ. So take x = (1, 0) and y = (1, 1). Then

||x • y|| = |(1, 0) • (1, 1)| = |1| = 1

||x|| • ||y|| = ||(1, 0)|| • ||(1, 1)|| = 1 • √2 = √2

In [tex]\mathbb R^3[/tex], you can use the vectors x = (1, 0, 0) and y = (1, 1, 1).

===========================================================

Explanation:

Start at the origin (0,0). Move 2 units up (rise) and move to the right 3 units (run) to arrive at the point (3,2).

This shows that the slope is rise/run = 2/3.

---------------------

You could also use the slope formula, which is,

m = (y2-y1)/(x2-x1)

You can use any two points from the orange line.

Answer:

25x - 45

Step-by-step explanation:

5(5x - 9)

Distribute

5*5x - 5* (9)

25x - 45

Answer:

➛ 25 x - 45

Step-by-step explanation:

➛ 5 ( 5 x - 9 )

Using distributive property multiply both by 5

➛ 5 × 5 x - 5 × -9

➛ 25 x - 45

Answer:

the answer is 220

Step-by-step explanation:

the formula for surface area of a rectangular prism is A=2(wl+hl+hw)

w = width

h= height

l = length

and when you have those lengths, you have to substitute.