MATHEMATICS HIGH SCHOOL

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 real 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

Answers

Answer 1

Answer:

we have

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

we know that

The equation of a vertical parabola into vertex form is equal to

$y=a(x-h)^(2)+k$

where

(h,k) is the vertex of the parabola

if $a>0$ ----> the parabola open upward (vertex is a minimum)

if $a<0$ ----> the parabola open downward (vertex is a maximum)

In this problem convert the quadratic equation into vertex form

$f(x)=-(x+5)(x+1)\nf(x)=-(x^(2) +x+5x+5)\nf(x)=-( x^(2) +6x+5)$

$f(x)=-x^(2)-6x-5$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)+5=-(x^(2)+6x)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)+5-9=-(x^(2)+6x+9)$

$f(x)-4=-(x^(2)+6x+9)$

Rewrite as perfect squares

$f(x)-4=-(x+3)^(2)$

$f(x)=-(x+3)^(2)+4$

This is a vertical parabola open down (vertex is a maximum)

the vertex is the point $(-3,4)$

The range is the interval--------> (-∞,4]

$y\leq 4$

All real numbers less than or equal to $4$

therefore

the answer is the option

All real numbers less than or equal to $4$

Answer 2

Answer: 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

Related Questions

The park is 6 mi due east of Freeport High School, and the library is 4 mi due west of the school. The police department is located due north of the school and is 5 mi from the library.How far is the police department from the park? Round to the nearest tenth of a mile. blank mi
If a cube has a volume of 343 cubic yards, what is its surface area?
The graph below shows the distance (y) between Hannah and her home, in km, after a certain time (x), in hours:Which of the following statements best describes Hannah"s distance from her home?
Melissa ran at a constant speed of 509.056 meters in 62.08 seconds. How far did Melissa run in one second?
Use a factor tree to find the prime factorization of 164

Math help? giving 100 points (:

Answers

Answer:

Perimeter = 14 + 2sqrt(17)

Area =28

Step-by-step explanation:

FG = 8 counted

EH = 6 counted

using the pythagorean theorem

height = 4 and the base = 1 in the right triangle

HG^2 = 4^2 + 1 ^2

hg^2 = 16+1

hg^2= 17

hg= sqrt(17)

ef^2 = 4^2 + 1 ^2

ef^2 = 16+1

ef^2= 17

ef=sqrt(17)

Perimeter = EF+FG + GH+HE

sqrt(17)+ 8+ sqrt(17) + 6

14 + 2sqrt(17)

A =1/2 (b1+b2) * h

b1 =EH b2 = FG and h = 4 height that we used in the perimeter

= 1/2 (6+8) * 4

= 1/2 * 14*4

=28

Look at the picture.

$A=(1)/(2)(8+6)\cdot4=(1)/(2)(14)\cdot4=7\cdot4=28$

How do i solve this answer ugh please help

Answers

Separate the quadratic functions into two individual function in x which multiply together to equal the original quadratic.
Eg: x^2-3x-10=0 can be written as (x+2)(x-5)=0
The two solutions for x can then be determined by making each bracket equal to zero.
x+2=0 so x=-2x-5=0 so x=5

Find n.
6/9=n/36
n=_____

Answers

multiple 6 with 36 and divide with 9
n = 24

Answer:

its 24 Hope this have a great day!

Step-by-step explanation:

elizabeth has 3497 cans to put on shelves how many shelves will she use if she put 13 cans on each shelve

Answers

269 shelves because if you divide 3497 by 14 you will get 269

Simplify –2x3y × xy 2. A. –12x4y3

B. –2x3y4

C. –2x4y3

D. –3x4y3

Answers

$-2x^3y\cdot xy^2=-2x^(3+1)y^(1+2)=-2x^4y^3$

Used:

$a^n\cdot a^m=a^(n+m)$

Answer: C. –2x^4y^3

(-47) - 33 ÷ (-3) - 3 × (-7)

Answers

Final answer:

To simplify the expression (-47) - 33 ÷ (-3) - 3 × (-7), use the order of operations (PEMDAS/BODMAS) to calculate step by step. The simplified expression is -15.

Explanation:

To simplify the expression (-47) - 33 ÷ (-3) - 3 × (-7), we need to follow the order of operations (PEMDAS/BODMAS).

PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).