Answer:
21
Step-by-step explanation:
The average rate of change of function f(x) from x = a to x = b is
[tex] \dfrac{f(b) - f(a)}{b - a} [/tex]
Here we have
a = -1
b = 2
f(a) = f(-1) = 1
f(b) = f(2) = 64
[tex] \dfrac{f(b) - f(a)}{b - a} = [/tex]
[tex] = \dfrac{f(2) - f(-1)}{2 - (-1)} = [/tex]
[tex] = \dfrac{64 - 1}{2 + 1} [/tex]
[tex] = \dfrac{63}{3} [/tex]
[tex] = 21 [/tex]
I am stuck on a geometry lesson. It is on the Angle Sum Theorem. It said we have an obtuse trisngle with angles 1, 2, and 3. Then they extend the line out as a dashed line top and bottom parallel to each other. It then he says we have angle 1 value would also be true on the opposite side of the triangle like as a transeversal intersected 2 parallel lines making those angles alternate interior angles. He does the sme with 2. then says 1 plus 2 plus 3 equal 180 and says it twice. What does that mean?
A wooden beam is (3y2 + 7y+1) meters long. If a piece of length (y2 - 10) meters is cut off, express the length of the
remaining piece of beam as a polynomial in y.
Answer:
2y^2 +7y +11
Step-by-step explanation:
The remaining length is the difference between the original and the length cut off:
remaining = whole length - piece length
remaining = (3y^2 +7y +1) -(y^2 -10)
= 3y^2 +7y +1 -y^2 +10 = (3 -1)y^2 +7y +(1 +10)
remaining = 2y^2 +7y +11
Renata moved to her new home a few years ago. Back then, the young oak tree in her back yard was 190 centimeters tall. She measured it once a year and found that it grew at a constant rate. 3 years after she moved into the house, the tree was 274 centimeters tall
How fast did the tree grow?
How many years passed from the time Renata moved in until the tree was 344 centimeters tall?
Answer:
Answers below
Step-by-step explanation:
How fast did the tree grow?
28 centimeters per year
How many years passed from the time Renata moved in until the tree was 344 centimeters tall?
5.5 years
Hope this helps!
+
What is the quotient when (16x4 + 40x3 - 24x2) is divided by 8x??
OA.
2x + 5x-3
OB. 2x + 3x-5
OC. 2x - 5x+5
D. 2x3 + 5X-3
+
Relat
Next
Answer: [tex]2x^{2} + 5x -3[/tex]
Step-by-step explanation:
Find the quotient of [tex]\frac{16x^4+40x^3-24x^2}{8x^2}[/tex]
Step 1: Break down the polynomial equation
[tex]\frac{16x^4}{8x^2}[/tex] + [tex]\frac{40x^3}{8x^2}[/tex] - [tex]\frac{24x^2}{8x^2}[/tex]
Step 2: Divide each piece by dividing the coeffients and subtracting the variables.
16 ÷ 8 = 2
[tex]x^{4}[/tex] - [tex]x^{2}[/tex] = [tex]x^{2}[/tex] → 2[tex]x^{2}[/tex]
40 ÷ 8 = 5
[tex]x^{3}[/tex] - [tex]x^{2}[/tex] = [tex]x[/tex] → 5[tex]x[/tex]
- 24 ÷ 8 = - 3
[tex]x^{2}[/tex] - [tex]x^{2}[/tex] = 1 → - 3
Step 3: Put the polynomial together
2[tex]x^{2}[/tex] + 5[tex]x[/tex] - 3
How does the equation change when the radius changes? Unlike h and k, why is r always positive?
Answer:
When the radius is changed, the constant term (r2) in the equation changes—it becomes bigger as the radius becomes bigger. The term r is always positive because it denotes the length of the radius, which is a distance and not a position or location.
Step-by-step explanation:
Only right answers! Please hurry.
A food truck did a daily survey of customers to find their food preferences. The data is partially entered in the frequency table. Complete the table to analyze the data and answer the questions:
Answer:
Part A: about 8%
Part B: about 65%
Step-by-step explanation:
To form a hyperbola what is the relationship between the base of the cone and the angle of the plane that intersects the cone
A. The plane is a parallel to the base of the cone
B. The plane may be perpendicular to the base of the cone
C. the plane must be at a 45 degree angle to the base of the cone
D. The plane is at an angle that is neither parallel nor perpendicular to the base of the cone
BRAINLIEST
Please solve at least one of these problems. I would love it if you could do all of them but I know you probably won’t have time for it. Ty!
Answer:
Step-by-step explanation:
PLS HELP WILL MARK BRAINLIEST!
Answer:
81 x² - 4 y²
Answer C is correct.
Step-by-step explanation:
First, you have to find the area of the larger square.
Area of the larger square = (9x) × (9x)
= 81 x²
Then you have to find the area of the un shaded square,
Area of the unshaded square = (2y) × (2y)
= 4 y²
Now to find the area of shaded region you have to subtract the area of the unshaded square from the area of the larger square.
Area of the shaded region = Area of the larger square - Area of the unshaded square
= 81 x² - 4 y²
Hope this helps you.
Let me know if you have any other questions :-)
The product of two positive numbers is 9. The reciprocal of one of these numbers is 4 times the reciprocal of the other number. What is the sum of the two numbers?
Answer:
7 and 1 / 2
Step-by-step explanation:
xy = 9
( 1 / x ) = 4 ( 1 / y )
y = 4x
x ( 4x ) = 9
4x^2 = 9
x = 3 / 2
( 3 / 2 ) y = 9
y = 6
6 + ( 3 / 2 ) = 7 and 1 / 2
The two numbers are 3/2 and 6.
What are reciprocal numbers?The reciprocal of a number is this fraction flipped upside down.
Given that, The product of two positive numbers is 9. The reciprocal of one of these numbers is 4 times the reciprocal of the other number.
Let the numbers be a and b.
ab = 9.......(i)
1/a = 4/b
a = 4b..........(ii)
Using (i) in (ii)
4b×b = 9
b² = 9/4
b = 3/2
a×3/2 = 9
a = 6
Hence, The two numbers are 3/2 and 6.
For more references on reciprocal numbers, click;
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A book has 12 chapters. The mean length of the chapters is 38 pages. How many total pages are there in the 12 chapters
The decimal approximation for cot(235°36') is approximately -0.9503.
To find the decimal approximation for cot(235°36'), we first need to convert the angle to degrees.
The given angle is 235°36'. We can convert this to decimal degrees by adding the fraction of minutes to the degree value. There are 60 minutes in a degree, so we divide 36 by 60 to convert it to a fraction of a degree:
36 / 60 = 0.6 degrees
Now, we can add this fraction to the degree value:
235 + 0.6 = 235.6 degrees
The cotangent function is the reciprocal of the tangent function. To find the cotangent of an angle, we can use the following formula:
cot(x) = 1 / tan(x)
Since we want to find cot(235.6°), we can find tan(235.6°) first and then take the reciprocal.
Using a scientific calculator or software, we can find
tan(235.6°) ≈ -1.0529
Now, we can take the reciprocal to find cot(235.6°):
cot(235.6°) ≈ 1 / (-1.0529) ≈ -0.9503
Therefore, the decimal approximation for cot(235°36') is approximately -0.9503.
for such more question on fraction
https://brainly.com/question/28372533
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Please simplify
(6-√-16)+(-4+√-25)
Answer:
2+i
Step-by-step explanation:
Which product is negative?
−2⋅(−4)⋅8⋅(−1)
−7⋅(−3)⋅(−5)⋅(−8)
−3⋅(−4)⋅(−9)⋅0
6⋅(−2)⋅(−3)⋅1
[tex]-2(-4)\cdot 8 (-1)\\\\=8 \cdot (-8)\\\\=-64\\\\\text{This one is negative.}[/tex]
The perimeter of the table shown is 16 feet. Write an equation in the form px+q=r to solve for x.
p = 2
q = 6
r = 16
x = 5 feet
Step-by-step explanation:
The perimeter of the rectangle is
In your case,
Width = 3 feet
Length = x feet
So, the perimeter is
Since the perimeter is 16 feet, we have
Hence,
p = 2
q = 6
r = 16
Solve this equation for x:
Help me out I need it
Answer:
27 Chairs (See below)
Step-by-step explanation:
A: You will put 9 chairs in each row, and have 3 rows.
For a visual example I will use the symbol "O" for the number of chairs.
OOOOOOOOO
OOOOOOOOO
OOOOOOOOO
B: The multiplication problem, using the information 3 Rows, and 9 Chairs in each row, is 9x3
C: The factors are the numbers you are multiplying with, and the product, is your outcome when you multiply the two factors, 9, and 3.
So your answer is 27.
Hope this helps!
which number sentence can be used to find 42 divied by 7
Answer: isn't it 42÷7=6?
Answer:
42 / 7 = 6
Step-by-step explanation:
Just use a multiplication table.
Solve -3(x-2)=2(x-7) and write a reason for each step
Answer:
4=x
Step-by-step explanation:
-3(x-2)=2(x-7)
Distribute -3 and 2.
-3x+6=2x-14
Add 3x to both sides of the equation.
6=5x-14
Add 14 to both sides of the equation.
20=5x
Divide 5 from both sides of the equation.
4=x
Hope this helps :)
Answer:
x=5
Step-by-step explanation:
Our equation is
-3(x-2)=2(x-7)
First we will distribute -3 and 2, because in math when we have a number being multiplied into parenthesis we multiply both things inside of it
Our equation is now
-3x+6=2x-14
Next we subtract 6 from both sides because we want x to be on only one side
-3x=2x-20
Next we subtract 2x from both sides because we want x to equal something exactly
-5x=-20
Now we divide -5 from both sides because we only want x
x=5
Brainliest please :)
solve pls brainliest
Answer:
Step-by-step explanation:
|x|=x,if x>0
|x|=-x,if x<0
(a)
|7-9|=|-2|=-(-2)=2
(b)
|7|-9=7-9=-2
HELP PLS! Suppose the year of car accidents per day in Wilmington NC has been recorded for the past year. The table below is a probability distribution table representing the data collected.
1) what is the probability that on a randomly selected day there were no accidents?
2) find the probability there will be at least 2 accidents
3) on any given day how many accidents should the Wilmington police expect to have.
According to the discrete distribution given:
1) There is a 0.18 = 18% probability that on a randomly selected day there were no accidents.
2) There is a 0.7 = 70% probability that there will be at least 2 accidents.
3) On any given day, the Wilmington police should expect to have 2.03 accidents.
The distribution is:
[tex]P(X = 0) = x[/tex]
[tex]P(X = 1) = 0.12[/tex]
[tex]P(X = 2) = 0.32[/tex]
[tex]P(X = 3) = 0.25[/tex]
[tex]P(X = 4) = 0.13[/tex]
Item 1:
The sum of the probabilities has to be 100% = 1, hence:
[tex]x + 0.12 + 0.32 + 0.25 + 0.13 = 1[/tex]
[tex]x + 0.82 = 1[/tex]
[tex]x = 0.18[/tex]
0.18 = 18% probability that on a randomly selected day there were no accidents.
Item 2:
This probability is:
[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.32 + 0.25 + 0.13 = 0.7[/tex]
0.7 = 70% probability that there will be at least 2 accidents.
Item 3:
The expected value is the sum of each outcome multiplied by it's respective probability, hence:
[tex]E(X) = 0.18(0) + 0.12(1) + 0.32(2) + 0.25(3) + 0.13(4) = 2.03[/tex]
On any given day, the Wilmington police should expect to have 2.03 accidents.
A similar problem is given at https://brainly.com/question/25653146
Which equation has the solution x = 5?
Select each correct answer.
18−2x=9
x/5+5=6
32−4x=12
11 + 6x = 22
3x + 1 = 9
25/x+4=9
Solve each question with the quadratic formula
6a² + 10 = 0
I know the answer but I'm not to sure how imaginary roots work. I would really appreciate if someone could explain how imaginary roots work! :)
Answer:
[tex]\boxed{\sf a=\cfrac{\sqrt{15i} }{3}}[/tex]
[tex]\boxed{\sf a=-\cfrac{\sqrt{15i} }{3}}[/tex]
Step-by-step explanation:
[tex]\sf 6a^2 + 10 = 0[/tex]
We'll solve this equation using The Quadratic Formula:
[tex]\boxed{\sf \frac{-b\pm \sqrt{b^2-4ac} }{2a} }[/tex]
[tex]\sf 6a^2 + 10 = 0[/tex]
Substitute 6: a, 0: b, 10: c
[tex]\longmapsto\sf a=\cfrac{0\pm\sqrt{0^2-4\times 6\times 10} }{2\times 6}[/tex]
→ Square 0
→ Multiply -4 * 6= -24
→ Multiply -24 * 10 = -240
[tex]\longmapsto\sf a=\cfrac{0\pm\sqrt{-240} }{2\times 6}[/tex]
→ Take the square root of -240:
→ Multiply 2 * 6= 12
Now, Separate solutions:
[tex]\longmapsto\sf a=\cfrac{0\pm 4\sqrt{15i} }{12}[/tex]
Now, Separate solutions:
First, solve the equation when ± is plus:
[tex]\longmapsto \boxed{\sf a=\cfrac{\sqrt{15i} }{3}}[/tex]
___
Now, solve it when ± is minus:
[tex]\longmapsto \boxed{\sf a=-\cfrac{\sqrt{15i} }{3}}[/tex]
__________________________________________
[tex]\sf\longmapsto 6a^2+10=0[/tex]
a=6b=0c=10[tex]\sf\longmapsto a=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex](This a is root of equation)
[tex]\sf\longmapsto a=\dfrac{-0\pm\sqrt{0^2-4(6)(10)}}{2(6)}[/tex]
[tex]\sf\longmapsto a=\dfrac{\pm\sqrt{-240}}{12}[/tex]
[tex]\sf\longmapsto a=\dfrac{\pm\sqrt{240}i}{12}[/tex]
[tex]\sf\longmapsto a=\dfrac{\pm 4√15i}{12}[/tex]
[tex]\sf\longmapsto a=\dfrac{\pm √15i}{3}[/tex]
[tex]\sf\longmapsto a=\dfrac{\pm √3√5i}{3}[/tex]
[tex]\sf\longmapsto a=\pm\dfrac{√5i}{\sqrt{3}}[/tex]
[tex]\sf\longmapsto a=\pm\sqrt{\dfrac{5}{3}}i [/tex]
What is i?i stands for iota.
[tex]\sf\longmapsto i=\sqrt{-1}[/tex]
Find the perimeter. Simplify your answer.
Answer:
24c-14
Step-by-step explanation:
to find the perimeter, simply add up the values of the three sides:
(7c-5) + (7c-5) + (10c-4) = 7c-5+7c-5+10c-4 = (7c + 7c + 10c) + (-5 -5 -4) = 24c -14
help im not good in math
Answer:
4
Step-by-step explanation:
yeah 4/8 is the answer. yeah-ya
What is the answer to the question below, I have been working on it for a while. Plz help!
The quotient of 10 times m and 7
Answer:
10m / 7
Step-by-step explanation:
times = multiplication of 10 and variable m
quotient of = division of 7
Which is the graph of the equation y+2=−12(x−4)?
Answer:
Step-by-step explanation:
y+2 = -12(x-4)
y=-12x+48-2
y = -12x+46
Draw a graph with the points (1,34) and (3,10)
a line has a slope of m=-2 and the point (3, -1) lies on the line.what is the represent the equation of the line in point slope form
Answer:
Step-by-step explanation:
To find out if a point (x, y) is on the graph of a line, we plug in the values and see if we get a true statement, such as 10 = 10.
Find the quotient. 4/12÷4/12=
Answer:
1
Step-by-step explanation:
Factor the numerator and denominator and cancel the common factors.
please help me I really need help
1) 300 squared cm
2) 105 squared cm
3) about 165.75 squared cm
4) about 211.4 squared cm
PLS HELP WILL MARK BRAINLIEST!
Answer:
B 81x^2 + 4y^2 that's the answer I have
Answer:
C. 81x² - 4y²Step-by-step explanation:
The shaded region is the difference of the area of square with side 9x and the area of square with side 2y:
A = (9x)² - (2y)² = 81x² - 4y²Correct choice is C
Haley invested $750 into a mutual fund that paid 3.5% interest
each year compounded annually. Find the value of the mutual
fund in 15 years.
The future value of the mutual fund after 15 years is equal to $1,256.55.
Given the following data:
Principal = $5,000Interest = 3.5% = 0.035Time = 15 years
To find the future value of the mutual fund after 15 years:
Mathematically, compound interest is given by the formula:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Where;
A is the future value.P is the principal or starting amount.r is annual interest rate.n is the number of times the interest is compounded in a year.t is the number of years for the compound interest.Substituting the given parameters into the formula, we have;
[tex]A = 750(1 + 0.035)^{15}\\\\A = 750(1.035)^{15}\\\\A = 750(1.6754)[/tex]
Future value, A = $1,256.55
Read more: https://brainly.com/question/22339845