The average rate of change of the function f( x ) = x² + 7x + 6 at the interval of −4 ≤ x ≤ −1 is 2
What is the average rate of change the function?The average rate of change the function is simply the change in y-values of the two points divided by the change in x-values of the two points.
It is expressed as;
Given the data in the question;
f( x ) = x² + 7x + 6Interval: −4 ≤ x ≤ −1 ⇒ [-4.-1]Average rate of change = ( f(-1) - f(-4) ) / ( (-1) - (-4) )
Average rate of change = ( (-1)² + 7(-1) + 6 ) - ( (-4)² + 7(-4) + 6 ) ) / ( (-1) - (-4) )
Average rate of change = ( (1 + -7 + 6 ) - ( 16 - 28 + 6 ) ) / (-1 + 4 )
Average rate of change = ( ( 0 ) - ( -6 ) ) / (-1 + 4 )
Average rate of change = ( 0 + 6 ) / ( 3 )
Average rate of change = 6 / 3
Average rate of change = 2
Therefore, the average rate of change of the function is 2.
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Horizontally translated 4 units left, vertically translated 2units down, and shrunk vertically by one half.
Solution
We will consider each and every statement and the translate what it mean appropriately
Horizontally translate 4 units left
That means
[tex](x-(-4))=x+4[/tex]The option to choose is
[tex](x+4)^3[/tex]Vertically translate 2 units down
That basically mean is to subtract 2
That is
[tex]-2[/tex]Shrunk vertically by one half
That is
[tex]a=\frac{1}{2}[/tex]The image below shows what to select
Intelligence Quotient (IQ) scores are often reported to be normally distributed with μ=100.0 and σ=15.0. A random sample of 61 people is taken.What is the probability that the mean IQ score of people in the sample is less than 98? Round your answer to 4 decimal places, if necessary.
To find the probability that the mean IQ score of people in the sample is less than 98, first we need to convert the value into z-score by using the formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Then, when x=98:
[tex]\begin{gathered} z=\frac{98-100.0}{15.0} \\ z=\frac{-2.0}{15.0} \\ z=-0.1333 \end{gathered}[/tex]By checking in a standard normal table z=-0.1333 has a p-value=0.4471.
Then the probability is 0.4471 that also can be expressed as 44.71%
Find the value of x that makes A || B.
B
2
42= 3x20 and 25 = x + 20
x = [?]
Translate this sentence into an equation.
Goran's score increased by 18 is 69.
Use the variable g to represent Goran's score.
Answer:
g + 18 = 69
Step-by-step explanation:
Translate this sentence into an equation. Goran's score increased by 18 is 69. Use the variable g to represent Goran's score.
g + 18 = 69
solve:
g + 18 = 69
subtract 18 from both sides:
g + 18 - 18 = 69 - 18
g = 51
THERE IS 5 QUESTIONS I NEED TO GET DONE IN TOTAL, BUT IT WONT LET ME PUT MANY PICS IN ONE QUESTION SO PLS GO TO MY ACC AND VIEW THE OTHER 2!!I NEED THIS BY **TODAY**
Answer:
given in picture
Step-by-step explanation:
(-2,10) (-1,7) (0,4) (1,1) (2,-2) (3,-5)
simplify a5/a2. can someone help fast
Answer:
a^3
Step-by-step explanation:
a^5/a^2
When dividing exponents with the same base, we can subtract the exponents
a^ ( 5-2)
a^3
Answer:
a³
Step-by-step explanation:
We know that,
[tex] \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ [/tex]
In the same way, let us solve the given sum.
[tex] \frac{ {a}^{5} }{ {a}^{2} } = {a}^{5 - 2} = {a}^{3} \\ [/tex]
Select the lesser of the two given numbers.
-5, -11
Which is the lesser of the two numbers?
I just need help solving this problem.
Answer:
see below
Step-by-step explanation:
sum of angles in right triangle is 180
90 + 50 = 140
b = 180 - 140 = 40 deg
find c
cos(50) = 20/ c
c = 20/cos(50) = 31.1
find a
tan(40) = 20/a
a = 20/tan(40) = 23.8
Can you please help me with this problem?
Answer: Draw a line from (2, 2) to (6, 2) for the run.
Draw a line from (6, 2) to (6, 8) for the rise.
The slope of the line is represented by rise/run, so in this case it would be 6/4.
The single inequality y > |x + 2| is equivalent to which of the following systems?
Answers:
1.y > x + 2
y > –x + 2
2.y > x + 2
y > –x – 2
3.y > x + 2
y < –x + 2
4.y > x + 2
y < –x – 2
The single inequality y > |x + 2| is equivalent to:
4. y > x + 2
y < –x – 2
What is an inequality?It should be noted that an inequality is simply used to show the relationship between the expressions that aren't equal.
The non-negative value of a real number x, regardless of its sign, is its absolute value or modulus | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5. One way to think about a number's absolute value is as its distance from zero on the real number line.
It should be noted that based on the information, the inequality is:
y > |x + 2|. This is the positive part of the modulus.
This is the same as y < –x – 2 when the signs are changed. This is the negative part of the modulus.
In conclusion, the correct option is 4.
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the number of DVDs shipped to an online retailer was 20000 less that the previous year use an integer to describe the change in number of DVDs shipped
The number of DVDs shipped is, 20000 less that the previous year ,
Therefore, the integer -20000 can be used to describe the change.
y = 3x + 5
y = 4x² + x
The system of equations has two solutions, these are:
(-0.89, 2.33) and (1.4, 9.2)
How to solve the system of equations?Here we have the following system of equations:
y = 3x + 5
y = 4x² + x
We can see that y is already isolated in both equations, so we can write the equation:
3x + 5 = y = 4x² + x
3x + 5 = 4x² + x
now we can solve this for x, this is just a quadratic equation:
3x + 5 - 4x² - x = 0
-4x² + 2x + 5 = 0
Using the quadratic formula, we can see that the two solutions are:
[tex]x = \frac{-2 \pm \sqrt{2^2 - 4*(-4)*5} }{2*-4} \\\\x = \frac{-2 \pm 9.17}{-8}[/tex]
So the solutions are:
x = (-2 +9.17)/-8 = -0.89
x = (-2 - 9.17)/-8 = 1.4
Evaluating the linear equation in these values, we get:
y = 3*(-0.89) +5 = 2.33
y = 3*(1.4) + 5 = 9.2
So the solutions of the system are:
(-0.89, 2.33) and (1.4, 9.2)
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please help
Also explain it so my brain gets it :)
Hello!
To solve for the y-values in the table:
[tex]\hookrightarrow \text{ Must plug in the corresponding x's value into the equation}[/tex]
Thus when x = -2[tex]y = 2(-2) + 3 = -4 + 3 = -1[/tex]
Thus when x = 0[tex]y = 2(0) + 3 =3[/tex]
Thus when x = 1[tex]y = 2(1) +3=5[/tex]
Thus when x = 3[tex]y = 2(3) + 3=6 + 3=9[/tex]
Hope that helps!
6. Select the operations that would increase the value of a given number.
A. Multiply the number by 10.
B. Multiply the number by 0.1.
C. Divide the number by 10.
D. Divide the number by 0.1.
7.Select the operations that would decrease the value of a given number.
A. Multiply the number by 10.
B. Multiply the number by 0.1.
C. Divide the number by 10.
D. Divide the number by 0.1.
The operations that would increase the value of a given number include the following:
A. Multiply the number by 10.
D. Divide the number by 0.1.
The operations that would decrease the value of a given number include the following:
B. Multiply the number by 0.1.
C. Divide the number by 10.
How to increase the value of a number?Multiplication is a mathematical operation which can be used to increase the value of a given number, especially by multiplying the number by a value that is greater than 1. Similarly, the value of a given number can also be increased by dividing it by a number that is lesser than 1 such as 0.1
How to decrease the value of a number?Multiplication is a mathematical operation which can be used to decrease the value of a given number, especially by multiplying the number by a value that is lesser than 1. Similarly, the value of a given number can also be decreased by dividing it by a number that is greater than 1 such as 10.
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7:8:9 = .... : 12 : ....
Answer:
7:8:9=21/2:12:27/2
Step-by-step explanation:
12/8=3/2
3/2*7=21/2
3/2*9=27/2
Pls brainliest
1. Ali collects comic books. He buys 2
comic books a week. This year after 5
weeks he has 17 comic books in his
collection. Write an equation relating
the number of comic books c to the
number of weeks w.
xw + 5w - 17 = 0 is the required equation.
How to find the required related equation?Given,
Ali buys 2 comic books a week.
After 5 weeks he has 17 comic books this year.
Solution:
Let w be weeks and c be comic books.
Since Ali buys 2 comic books a week.
1w = 2c
For 5 weeks, he would have,
5w = 10c, if he bought 2books per week.
But he had 17 books,
i.e, he would have collected some books last year.
Let x be the no of unknown weeks last year.
(x + 5)w = 17c
(x+5)w-17c= 0
xw + 5w - 17 = 0 is the required equation.
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Help
Help me simplify this equation
Answer:
-100000
Step-by-step explanation:
[tex](-1000)^{5/3} \\ \\ =(\sqrt[3]{-1000})^5 \\ \\ =(-10)^5 \\ \\ =-100000[/tex]
2. Write in standard form: one hundred dollars and fourteen cents
1
A man ordered 3 times as many boxes of ballpoint pens as boxes of felt-tip pens. Ballpoint pens cost $4.31 per box, and felt-tip pens cost $3.42. If the man's order of pens totaled $98.10. how many boxes of each type pen did he buy? How many boxes of felt-tip pens did he buy? How many boxes of ballpoint pens did he buy?
let x be the number of ballpoint boxes and y the number of felt tip boxes
so we get
[tex]\begin{gathered} \begin{cases}4.31x+3.42y=98.10 \\ x=3y\end{cases}\rightarrow \\ 4.31\cdot3y+3.42\cdot y=98.10 \\ 12.93y+3.42y=98.10 \\ 16.35y=98.10 \\ y=\frac{98.10}{16.35}=6 \end{gathered}[/tex]so we get that the number of felt tip boxes is 6, and therefore the number of ballpoint boxes is 6*3=18
help me its so hard !!!
For the rectangle given, considering its diagonal properties, the value of x=4, while the angle VUR=36°
Angles and properties of plane shapesTo answer this question, let us recall the following:
The diagonals of a rectangle bisects each other into four eqaul length.The base angles of an Isosceles triangle are equal.Complementary angles add up to give a total of 90°.Hence;
the lengths RV and SV are
so, 3x+8=6x-4
6x-3x=8+4 [collecting like terms]
3x=12
when we divide both sides of the equation by 3, we have the value of x=4.
the angles VRS and VRU are complementary
so, 54°+VRU = 90°
VRU = 90°-54°
VRU = 36°
The triangle RUV is an Isosceles
so, angles VRU and VUR are equal, therefore angle VUR = 36°.
We can reduce from our workings that the value of x = 4 and the angle VUR is 36°.
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Jane wants to buy a CD for $12. She has saved $7. How much money does she still need if 6% sales tax will be added to the cost of the CD.
Using the sales tax, the amount of money she still needs is $5.72
What is sales tax?A sales tax is a consumption tax imposed by the government on the sale of goods and services.
Jane wants to buy a CD for $12. She has saved $7.
The amount she needs if 6% sales tax is added to the cost can be calculated as follows;
Let's find the sales tax,
sales tax = 6% of 12
sales tax = 6 / 100 × 12
sales tax = 72 / 100
sales tax = $0.72
Therefore,
amount she needs to save = 12 + 0.72 - 7
amount she needs to save = 12.72 - 7
amount she needs to save = $5.72
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Write 80% as a rate per 100.
Answer:80100
Step-by-step explanation:
Since "per cent" means parts per hundred, if we can convert the fraction to have 100 as the denominator, we then know that the top number, the numerator, is the percentage. Our percent fraction is 80/100, which means that 80100 as a percentage is 80%.
HELP ASAP GIVING ALL THE POAINTS I HAVE LEFT
a container in a shape of a cube uses 64 cubes with side lengths of 1inch to completely fill the container what is the edge length of the container
A farmer harvested 250 fruits. 82 were oranges and there were twice as many sapodillas as paw paws. What percentage of the fruits were paw paws? ||giving 30 points
Answer:
22.4%
Step-by-step explanation:
There were twice as many sapodillas as paw paws--take the sapodillas as 2 units and paw paws as 1 unit.
Form an equation.
2u + 1u + 82 = 250
Simplify and solve for 1 unit.
3u = 168
1u = 56
Number of paw paws is 56.
Formula for finding percentage of an object is given as (number of object/total number of items) x 100.
Percentage of paw paws
= (56/250) x 100
= 22.4%
The population of City A is 8.59 x 10^4. The population of City B is 3.2 x 10^3 Select all of the values that show the difference in population of City A and City B
The difference of population in these two cities are 85900- 3200
= 82,700
How do you calculate difference?
Subtract the largest number from the lowest number to determine the difference between two integers. The difference between the two numbers is the product of this sum. As a result, there are 55 between the numbers 45 and 100.
Given: Population of city A= 8.59 x 10^4
and population of city B = 3.2 x 10^3
This can also be written as :
Population of city A= 85,900
and population of city B = 3200
Thus the difference of population in these two cities are 85900- 3200
= 82,700
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GRAPH GOES WITH MY QUESTION OF NUMBER 20!!!
Question 20.
If the measure of angle 5 = x, which angles have a measure of 180 - x? Select all the apply.
(a) angle 2
(b) angle 3
(c) angle 7
(d) angle 11
Answer:
C) angle 7
Step-by-step explanation:
all i know is angle 5 and 7 are corresponding angles, the only other practical option could be angle 3 but angle 3 and angle 5 have no correlation with one another
5. Find the area of the triangle.
11 ft
5 ft
14 ft
13 ft
Answer:
35ft
Step-by-step explanation:
ignore 11 and 13, you only need the height and one side that corresponds to it. 14*5=70
70/2=35
Determine where f(x) is increasing and/or decreasing.
Answer:
decreasing: (-∞,3)
increasing: (3,∞)
Step-by-step explanation:
HELP PLS Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
The slope of the line is the ratio of the rise to the run, or rise divided by the run. slope of line is 4/3.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The given two points are (3,0) and (0,-4)
y₂=-4, y₁=0, x₁=3, x₂=0
Substitute values in formula
m=-4-0/0-3
m=4/3
Hence slope of line is 4/3.
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help meeeeeeeeeeee pleaseeeeeeeeeeeeee!!
Answer:
a. [tex]y = 21.5x + 376[/tex]
b. [tex]569.5[/tex] or with rounding, [tex]570[/tex].
Step-by-step explanation:
To set up a linear equation in slope-intercept form, we use the formula y=mx+b, where m is slope given by the formula m= [tex]\frac{y_{2}-y_1 }{x_2-x_1}[/tex], and b is the y-intercept (the value of y when x=0). It is given that x is the year, where 2005 is x=0, and y is the number of assistants in thousands, meaning at x=0 (the year 2005), y=376 (376,000 medical assistants). This can be written as the point (0, 376), which is our y-intercept. Using the formula for slope, the slope of this line is found to be [tex]\frac{215}{10}[/tex], or 21.5 ([tex]\frac{591-376}{10-0}[/tex]). This gives us the equation [tex]y = 21.5x + 376[/tex].
For part (b), simply plug in a value for x, then solve for y. The given value is the year 2014, which can be written as x=9 (x=0 is 2005, x=1 is 2006, etc.). This gives us the equation [tex]y=21.5(9)+376[/tex], which gives us y=569.5. However, since this is a real-world problem, you can not have "half" a person, so this rounds up to 570.