1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sveta [45]
3 years ago
13

The function f(x) = −(x + 5)(x + 1) is shown. What is the range of the function? all real numbers less than or equal to 4 all re

al numbers less than or equal to −3 all real numbers greater than or equal to 4 all real numbers greater than or equal to −3
Mathematics
2 answers:
Tpy6a [65]3 years ago
6 0

all real numbers such that y is less than or equal to 4

qaws [65]3 years ago
4 0

ANSWER

all real numbers less than or equal to 4.

EXPLANATION

The given function is

f(x) =  - (x + 5)(x + 1)

Expand

f(x) =  - ( {x}^{2}  + x + 5x + 5)

f(x) =  - ( {x}^{2}  + 6x + 5)

f(x) =  - {x}^{2}   - 6x  - 5

a=-1,b=-6,c=-5

The x-value of the vertex is given by

a=-1,b=-6,c=-5

x =  \frac{ - b}{2a}

x =  -  \frac{ - 6}{2( - 1)}  =  - 3

The y-value of the vertex is

f( - 3) =  - ( - 3  + 5)( - 3 + 1)

f( - 3) =  - ( 2)( - 2) = 4

Since a=-1, the function opens downwards.

The highest value is the y-value of the vertex which is 4.

Therefore the range is all real numbers less than or equal to 4.

The correct choice is A.

You might be interested in
A building makes a 90° angle with the ground. A ladder leans against the building, making a 110° exterior angle with the ground.
liberstina [14]

<u>Answer:</u>

A building makes a 90^{\circ} angle with the ground .The two interior angles are 70^{\circ} and 20^{\circ}

<u>Solution: </u>

Given, a ladder which is against the building wall makes an exterior angle of 110^{\circ}

And building makes a  90^{\circ} angle with the ground.

So, altogether it makes a right angle triangle with ladder as hypotenuse and ground as base leg and building as another leg.  

Now, we know that, sum of exterior angles and interior angles equals to 180^{\circ}

Here, in the case of ground and ladder, exterior angle is 110^{\circ} and interior angle is unknown.

Exterior angle + interior angle = 180

110 + interior angle = 180

Interior angle = 180 – 110

Interior angle = 70^{\circ}

We have found one of the two interior angles of right angle triangle.

We know that, sum of angles in a triangle is 180 degree

Known Interior angle + unknown interior angle + right angle = 180

70 + unknown interior angle + 90 = 180

Unknown interior angle + 160 = 180

Unknown interior angle = 180 - 160

Unknown interior angle = 20^{\circ}

Hence the two interior angles are  70^{\circ} and 20^{\circ}

7 0
3 years ago
How would we rewrite the equation of y = 1/3x -10 if we moved its graph down six units?
levacccp [35]

If you didn't change the slope of the line, but you moved it
down 6 units on the graph, then its y-intercept would become
6 less.  The equation of the new line would be ...

                  y = 1/3 x - 16 .

3 0
3 years ago
Which shows the following in order from least to greatest: 85%, 15/18, 0.84 PLEASE HELP
Marrrta [24]

Answer:

15/18, 0.84, 85%

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

6 0
2 years ago
Read 2 more answers
Does there exist a di↵erentiable function g : [0, 1] R such that g'(x) = f(x) for all x 2 [0, 1]? Justify your answer
agasfer [191]

Answer:

No; Because g'(0) ≠ g'(1), i.e. 0≠2, then this function is not differentiable for g:[0,1]→R

Step-by-step explanation:

Assuming:  the function is f(x)=x^{2} in [0,1]

And rewriting it for the sake of clarity:

Does there exist a differentiable function g : [0, 1] →R such that g'(x) = f(x) for all g(x)=x² ∈ [0, 1]? Justify your answer

1) A function is considered to be differentiable if, and only if  both derivatives (right and left ones) do exist and have the same value. In this case, for the Domain [0,1]:

g'(0)=g'(1)

2) Examining it, the Domain for this set is smaller than the Real Set, since it is [0,1]

The limit to the left

g(x)=x^{2}\\g'(x)=2x\\ g'(0)=2(0) \Rightarrow g'(0)=0

g(x)=x^{2}\\g'(x)=2x\\ g'(1)=2(1) \Rightarrow g'(1)=2

g'(x)=f(x) then g'(0)=f(0) and g'(1)=f(1)

3) Since g'(0) ≠ g'(1), i.e. 0≠2, then this function is not differentiable for g:[0,1]→R

Because this is the same as to calculate the limit from the left and right side, of g(x).

f'(c)=\lim_{x\rightarrow c}\left [\frac{f(b)-f(a)}{b-a} \right ]\\\\g'(0)=\lim_{x\rightarrow 0}\left [\frac{g(b)-g(a)}{b-a} \right ]\\\\g'(1)=\lim_{x\rightarrow 1}\left [\frac{g(b)-g(a)}{b-a} \right ]

This is what the Bilateral Theorem says:

\lim_{x\rightarrow c^{-}}f(x)=L\Leftrightarrow \lim_{x\rightarrow c^{+}}f(x)=L\:and\:\lim_{x\rightarrow c^{-}}f(x)=L

4 0
3 years ago
Which postulate or theorem proves that these two triangles are congruent?
Olenka [21]

Answer:

SAS congruence postulate. sweetheart.

Step-by-step explanation:


4 0
3 years ago
Read 2 more answers
Other questions:
  • Did i do #7 correctly?
    15·2 answers
  • What word describes the quadrilateral
    15·2 answers
  • On a coordinate grid, point A is at (−2.0, −3.4) and point B is at (2.0, −3.4). Point B is a reflection of point A across the __
    6·1 answer
  • What is a name for a marked angle ? Answers to choose from :
    7·2 answers
  • Write the equation of the line with an x-intercept at (0,2) and perpendicular to 3x+4y=12.
    5·2 answers
  • I need to find all possible roots for x
    6·1 answer
  • In the figure below, m
    6·2 answers
  • 100 people at dinner. 90 had French heritage, 80 had English heritage, and 75 had Native American heritage. At least how many ha
    14·2 answers
  • This box plot shows the weights, in ounces, of some kittens.
    15·2 answers
  • Evaluate 4a3 + 5b4 when a=2 and b=5​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!