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
Misha Larkins [42]
3 years ago
6

Without graphing, determine the range of the function f(x) = 4|x+6|-5 over the interval [-10,5].

Mathematics
1 answer:
spin [16.1K]3 years ago
3 0

Answer:

[-5,39]

Step-by-step explanation:

The vertex is at (-6,-5)

The interval is from -10 to 5 (inclusive of both endpoints...

Absolute function is open up because 4 is positive

I will plug in both endpoints now:

f(-10)=4|-10+6|-5                               f(5)=4|5+6|-5

f(-10)=4(4)-5                                      f(5)=4(11)-5

f(-10)=11                                             f(5)=39

So the highest reached by f(5) which is 39 so our range will go up to 39 (inclusive)

11 is not the lowest reached, -5 is because our vertex was included within the domain

So the range is [-5,39]

You might be interested in
Which is equivalent to V180x11 after it has been simplified completely?
inna [77]

Question:

Which is equivalent to \sqrt{180x^{11}} after it has been simplified completely?

Answer:

\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}

Step-by-step explanation:

Given

\sqrt{180x^{11}}

Required

Simplify

We start by splitting the square root

\sqrt{180x^{11}} = \sqrt{180} * \sqrt{x^{11}}

Replace 180 with 36 * 5

\sqrt{180x^{11}} = \sqrt{36 * 5} *  \sqrt{x^{11}}

Further split the square roots

\sqrt{180x^{11}} = \sqrt{36} *\sqrt{5} *  \sqrt{x^{11}}

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{11}}

Replace power of x; 11 with 10 + 1

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10 + 1}}

From laws of indices; a^{m+n} = a^m * a^n

So, we have

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10} * x^1}

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10} * x}

Further split the square roots

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10}} * \sqrt{x}

From laws of indices; \sqrt{a} = a^{\frac{1}{2}}

So, we have

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{10*\frac{1}{2}} * \sqrt{x}

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{\frac{10}{2}} * \sqrt{x}

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{5} * \sqrt{x}

Rearrange Expression

\sqrt{180x^{11}} = 6 *  x^{5} * \sqrt{5} * \sqrt{x}

\sqrt{180x^{11}} = 6x^{5} * \sqrt{5} * \sqrt{x}

From laws of indices; \sqrt{a} *\sqrt{b} = \sqrt{a*b} = \sqrt{ab}

So, we have

\sqrt{180x^{11}} = 6x^{5} * \sqrt{5*x}

\sqrt{180x^{11}} = 6x^{5} * \sqrt{5x}

\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}

<em>The expression can no longer be simplified</em>

Hence, \sqrt{180x^{11}} is equivalent to 6x^{5}\sqrt{5x}

7 0
2 years ago
Read 2 more answers
If the height of a triangle
Dvinal [7]

Answer:

75 cm

Step-by-step explanation:

To find the area of a traingle you use the following equation

b*h*.5

We know that the height of the triange is three times the base and that the area is 937.5

This means that

b*3b*.5=937.5

We can combine this and get 1.5b^2=937.5

We can then divide by 1.5 to get b by itself

b^2=625

Then take the square root for our answer and get b=25 (while be also can be -25 it doesn't make sense to have a negative answer in the context of this problem)

So we know that b=25 and that h=3b which means that the height is 75 cm

5 0
3 years ago
Billy stacked six pieces of wood on top of one another. If each piece
Sliva [168]
The answer would be 175 feet tall

6 0
3 years ago
Read 2 more answers
On the same winter morning, the temperature is -28f in Anchorage,Alaska and 65f in Miami,Florida. How many degrees warmer was it
Xelga [282]
C. 90 degrees warmer
5 0
3 years ago
Read 2 more answers
Ruth wants to buy a skateboard for $44. She has $100 in her account. She spent $11.36 to buy stationary. She also wants to buy s
djverab [1.8K]

Given :

Ruth wants to buy a skateboard for $44.

She has $100 in her account. She spent $11.36 to buy stationary.

She also wants to buy some comic books for $3.72 each.

To Find :

The maximum number of comic books, n, that Ruth can buy so that she has enough money left to buy the skateboard.

Solution :

Money left after buying skateboard and stationary is :

Money left = $(100 - 11.36 - 44)

Money left = $44.64

Number of comic she can buy is :

n = \dfrac{44.64}{3.72}\\\\n = 12

Therefore, she can buy a maximum of 12 books.

Hence, this is the required solution.

4 0
2 years ago
Read 2 more answers
Other questions:
  • 100, 88, 76, 78, 92, 94, 84, 98, 82, 90 What is the Nicole’s median score?
    8·2 answers
  • How do you find the product of a fraction then put it in simplest form
    8·2 answers
  • A soup recipe calls for 6 cups of broth a chef will triple this recipe he wants to know how many quarts of broth he will need
    10·1 answer
  • Of all the species in the world, 4 out of every 5 are insects.
    12·1 answer
  • The system of equations y=-1/2 x + 4 and y= 2x - 1 is shown on the graph below According to the graph what is the solution to th
    7·2 answers
  • -3x-4y=-12<br> Need to find the slope and y-intercept
    9·2 answers
  • What is the slope of a ramp that rises 6 inches for every horizontal change of 12 inches?
    7·1 answer
  • Examples from your surroundings where we use negative rational number​
    8·1 answer
  • Equations on both sides
    6·2 answers
  • Suppose a candy bar weighs 5.47 ounces. How much does a pack of 6 bars weight
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!