Given:
The function is
[tex]f(x)=-x^2-5x+12[/tex]
To find:
The average rate of change of the function over the interval −5 ≤ x ≤ 4.
Solution:
The average rate of change of a function f(x) over the interval [a,b] is
[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]
Putting x=-5 in the given function, we get
[tex]f(-5)=-(-5)^2-5(-5)+12[/tex]
[tex]f(-5)=-25+25+12[/tex]
[tex]f(-5)=12[/tex]
Putting x=4 in the given function, we get
[tex]f(4)=-(4)^2-5(4)+12[/tex]
[tex]f(4)=-16-20+12[/tex]
[tex]f(4)=-24[/tex]
Now, the average rate of change of the function over the interval −5 ≤ x ≤ 4 is
[tex]m=\dfrac{f(4)-f(-5)}{4-(-5)}[/tex]
[tex]m=\dfrac{-24-12}{4+5}[/tex]
[tex]m=\dfrac{-36}{9}[/tex]
[tex]m=-4[/tex]
Therefore, the average rate of change of the function over the interval −5 ≤ x ≤ 4 is -4.
which linear any qualities could represent the given table of values
Can anyone help me pls???
Answer:
It's
Step-by-step explanation:
9a-3b
because 3×3a is 9a and 3×-b is -3b hope this helps
Answer:
8) A 9) B
Step-by-step explanation:
For question 8 just combine like terms, combine the numbers that have the same variables. Number 9, distribute the 3 to the rest of the equation.
Hope this helped :)
Which of the following constants can be added to x ^2 - x to form a perfect square trinomial?
1/4
1/2
1
urgent
Answer:
Its 1/4 boys dont worry i got you
Step-by-step explanation:
What’s the answer and can someone please explain it?
add x³-2x²y+4xy²-y³,2x³-5xy²+3x²y-4y³
Step-by-step explanation:
the answer is x times (x^2 +xy-y^2 - x^2 y^32)
Can somebody plz help answer these questions correclty (like what the letters=) thanks :D
WILL MARK BRAINLIEST WHOEVER ANSWERS FIRST :DD
Answer:
6. p = 4
7. m = 7
8. n = 13
9. z = 5
10. x = 4
11. y = 9
Step-by-step explanation:
You can divide the solution by the number next to the letters/variables.
For example, to find 9p = 36 you can do 36 ÷ 9 which equals 4.
To double check, you can multiply your quotient by the divisor.
So to check if p = 4, you can do 9 x 4 which equals 36, therefore it is the solution.
PLEASE HELP ASAP?!?
What are the sine, cosine, and tangent ratios for
Explain how to find the distance between 1.5 and any point, n, on a number line.
A model of a famous statue is 3 1/2 inches tall. The actual statue is 5 1/4 feet tall. What is the ratio of the height of the model to the height of the actual statue in simplest form?
Given:
A model of a famous statue is [tex]3\dfrac{1}{2}[/tex] inches tall. The actual statue is [tex]5\dfrac{1}{4}[/tex] feet tall.
To find:
The the ratio of the height of the model to the height of the actual statue in simplest form.
Solution:
We have,
Height of the model = [tex]3\dfrac{1}{2}[/tex] inches
Height of the actual statue = [tex]5\dfrac{1}{4}[/tex] feet.
Now, the ratio of the height of the model to the height of the actual statue is:
[tex]\text{Ratio}=\dfrac{\text{Height of model}}{\text{Height of actual statue}}[/tex]
[tex]\text{Ratio}=\dfrac{3\dfrac{1}{2}\ in.}{5\dfrac{1}{4}\ ft}[/tex]
[tex]\text{Ratio}=\dfrac{\dfrac{3(2)+1}{2}\ in.}{\dfrac{5(4)+1}{4}\ ft}[/tex]
[tex]\text{Ratio}=\dfrac{\dfrac{7}{2}\ in.}{\dfrac{21}{4}\ ft}[/tex]
We know that 1 ft = 12 in.
[tex]\text{Ratio}=\dfrac{\dfrac{7}{2}\ in.}{\dfrac{21}{4}\times 12\ in.}[/tex]
[tex]\text{Ratio}=\dfrac{\dfrac{7}{2}\ in.}{21\times 3\ in.}[/tex]
[tex]\text{Ratio}=\dfrac{7}{2\times 21\times 3}[/tex]
[tex]\text{Ratio}=\dfrac{1}{2\times 3\times 3}[/tex]
[tex]\text{Ratio}=\dfrac{1}{18}[/tex]
Therefore, the ratio of the height of the model to the height of the actual statue in simplest form is [tex]\dfrac{1}{18}[/tex].
6. A piece of carpet is 240cm long.
Mr Jones cuts it into three pieces in the ratio 1 : 2 : 5
Work out the length of the longest piece of carpet.
Answer:
150 cm.
Step-by-step explanation:
The number of parts = 1 + 2 + 5 = 8 so:
the largest part = 5/8 * 240
= 5 * 30
= 150 cm.
y=2x2+3 is this a linear or nonlinear function
Answer:
y=7
Step-by-step explanation:
2x2=4 +3 =7 y
Rob is saving to buy a new MP3 player. For every $11 he earns babysitting, he save $5. On Saturday, Rob earned $33 babysitting. How much money did he save?
Answer:
15
Step-by-step explanation:
if every $11 dollars he save $5, and sense he made $33 ( he done three babysitting)
11-5= 5 (does that three times) [5+5+5} when you add the three five , u should have 15 dollars.
so he save 15 dollars.
i don't understand this! can someone help me
Answer:
oh dang i hated doing these when i was in sixth grade lol umm 55?????
Step-by-step explanation:
use equivalent expression 20a+18+16a
Answer:
36a+18
Step-by-step explanation:
20a+16a=36a
18 does not have a "like term", so just leave it.
Write an equation, in standard form, using the following given info: M = 10
and it passes through the point (6,2) *
-10x + y = -58
-10x + y = 58. -10x - y = -58
10x + y = -58
Given:
m = 10
The line passes through the point (6,2).
To find:
The equation of line in the standard form.
Solution:
If a line passes through the point [tex](x_1,y_1)[/tex] with slope m, then the equation of line is
[tex]y-y_1=m(x-x_1)[/tex]
The line passes through the point (6,2) and m = 10. So, the equation of line is
[tex]y-2=10(x-6)[/tex]
[tex]y-2=10x-60[/tex]
[tex]y-10x=-60+2[/tex]
[tex]-10x+y=-58[/tex]
Therefore, the correct option is A.
-2x - y = 1
-6x=3y+3
Answer: All Real Number
Step-by-step explanation:
This is a system of equation, and generally, there are three ways to solve:
eliminationsubstitutionaugmented matrixHere, we are going to use elimination
------------------------------------------------------------------------------------
Given
-2x-y=1
-6x=3y+3
Put them in the same order
-2x-y=1
-6x-3y=3
Multiply 3 on both sides for the first equation
-6x-3y=3
-6x-3y=3
We subtract the first equation from the second equation
0=0
The answer will be All Real Numbers, which means any real number will fit this equation. In the graphing method, these two equations will overlap each other.
Hope this helps!! :)
Please let me know if you have any questions
Factor the expression
27 - 9x + 15y
Answer:
-3(3x-5y-9)
Step-by-step explanation:
Consider sample data with x = 12 and s = 3. (a) Compute the coefficient of variation. % (b) Compute a 75% Chebyshev interval around the sample mean. Lower Limit Upper Limit
Answer: a) 25%
b) 75% Chebyshev interval around the sample mean=(6,18)
Step-by-step explanation:
Given: Sample mean: [tex]\overline{x}=12[/tex]
Sample standard deviation: s= 3
a) Coefficient of variation = [tex]\dfrac{s}{\overline{x}}\times100[/tex]
[tex]\\\\=\dfrac{3}{12}\times100\%=\dfrac{100\%}{4}\\\\=25\%[/tex]
b) According to the Chebychev's theorem,
75% of the population lies within 2 standard deviations from the sample mean.
i.e. 75% Chebyshev interval around the sample mean. = [tex](\overline{x}-2s,\ \overline{x}+2s)[/tex]
[tex]=(12-2(3),\ 12+2(3))\\\\=(6, 18)[/tex]
Hence, the 75% Chebyshev interval around the sample mean=(6,18)
yesterday the temperature was 7 degrees fahrenheit . Today the temperature is 0 degrees fahrenheit . What was the change in the temperature from yesterday to today?
Answer:
-7
Step-by-step explanation:
HOPE THIS HELPS
7+
2-
3+
3-
-
7+
1-
4
Answer:-15
Step-by-step explanation:
Answer:
umm... thirteen....
13
(3) need help plz Asap
Answer:
brainlist plzz
Step-by-step explanation:
D....................................
911÷406 con operaciones
Answer:
2.24384236453
Step-by-step explanation:
division/división
Answer:
Step-by-step explanation:
2.24384236453 divicion y divicion
5x+3y-z-4x-3y-z help please
The simplified version of this x-2z
Step-by-step explanation:
You need to start by combining like terms. You can start with the terms that have the variable x in them. By combining those terms, the equation becomes x+3y-z-3y-z.
From here, you can combine the terms 3y and -3y, which bring the equation to x-z-z.
From here, combine the terms with the variable z. This would bring the equation down too x-2z, your final answer.
How many terms are in this expression? d + 8c + 7
Answer:
2
Step-by-step explanation:
⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️
Answer: lol why so expensive.
Consider the function p(t) show.identify the intervals on which the function appears to be in increasing
Answer:A
Step-by-step explanation:
Function 1 is defined by the equation p= --3/2r - 5. function 2 is defined by the following table. Which function has a greater y-intercept. A: Function 1 B: Function 2 C: The functions have the same y-intercept.
The y-intercept of function 1 is -5.
The y-intercept of function 2 is -5.
Option C is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Consider the function to be in the form of p = mr + c
Where x is the y-intercept.
Function 1.
p = (-3/2)r - 5 _______(1)
y-intercept = -5
Function 2.
Let p = mr + c
Take two pairs from the table.
(0, -5) and (1, -6.5)
m = (-6.5 + 5) / (1 - 0) = -1.5
(0, -5) = (r, p)
-5 = -1.5 x 0 + c
c = -5
Now,
p = -5x - 5 ______(2)
y-intercept = -5
From (1 ) and (2)
Both have the same y-intercept.
Thus,
Function 1 and Function 2 have the same y-intercept.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ2
what is the answer to 1/2d+6
Answer:
Step-by-step explanation:
What you gave, is an expression. There is no answer. The only thing that can be done is factor out the 1/2
[tex]\frac{1}{2}(d+12)[/tex]
Please I don’t understand I need help thank you
Answer:
Step-by-step explanation:
Is there anybody here good at medical terminology??? pls I need help on one of my questions.
Answer:
I could try.
Step-by-step explanation: