The maximum number of turns for the graph given by the function is; 2.
What is the maximum number of turns for the graph?It follows from the task content that the graph given is that of a cubic function. On this note, it follows that the graph has 2 turning points.
This follows from the fact that the degree of the polynomial is 3 and hence, the maximum number of turns on the graph is 2.
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help! asap! algebra 2
We can subtract the function that represents the cost in 2000 from the function that represents the cost in 1990.
Doing this gives us [tex](-20t^{2}+1000)-(-10t^{2}+1500)=\boxed{-10t^{2}-500}[/tex]
What is the area of the polygon given below?
Answer:
340 i am pretty sure
Step-by-step explanation:
Please SHOW THE WORK. How many miles are in 10 kilometers?
Name the property that justifies the statment If AB - BC = 12, then AB = 12 + BC.
The property that justifies the statement is the commutative law of addition
Commutative law of additionThis law occurs if the same number or constant is added to both sides of an equation.
Given the equation
AB - BC = 12
Add BC to both sides
AB - BC + BC = 12 + Bc
AB = 12 + BC
Hence the property that justifies the statement is the commutative law of addition
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Curved surface area of a right circular cylinder is 4.4 m². If the radius of the base of the cylinder is 0.7 m, find its height. [Assume π = 22/7]
[tex]{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}[/tex]
★ Curved surface area of right circular cylinder is 4.4 m².
★ Radius of base of the cylinder is 0.7 m.
★ [tex]\tt \pi = \dfrac{22}{7}[/tex]
[tex]{\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}[/tex]
★ The height of cylinder.
[tex] {\large{\textsf{\textbf{\underline{\underline{Using \: Formula :}}}}}}[/tex]
[tex] \star \: \tt C.S.A \: of \: cylinder = \boxed{ \tt \pink{{ 2πrh}}}[/tex]
[tex] {\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}[/tex]
Let,
❍ The height of circular cylinder be [tex]h[/tex]
❍ Radius [r] of base of cylinder be 0.7 m
We know,
[tex] \star \: \tt C.S.A \: of \: cylinder = 2πrh[/tex]
Putting,
☆ [tex]\tt \pi = \dfrac{22}{7}[/tex]
☆ r as 0.7
[tex] \longrightarrow \tt 4.4 {m}^{2} = 2πrh[/tex]
[tex] \longrightarrow \tt 4.4 {m}^{2} = \bigg( 2 \times \dfrac{22}{7} \times 0.07 \times h \bigg)m[/tex]
[tex] \longrightarrow \tt \dfrac{44}{10} {m}^{2} = \bigg( {2 }\times \dfrac{22}{ \cancel{7}} \times \dfrac{ \cancel{7}}{10} \times h \bigg)m[/tex]
[tex] \longrightarrow \tt \dfrac{44}{10} {m}^{2} = \bigg( 44 \times \dfrac{ {1}}{10} \times h \bigg)m[/tex]
[tex] \longrightarrow \tt \dfrac{44}{ \cancel{10}} \times \cancel{10} \: m = \bigg( 44 \times 1 \times h \bigg)[/tex]
[tex] \longrightarrow \tt 44 m = 44h[/tex]
[tex]\longrightarrow \tt \dfrac{44}{44} m = h[/tex]
[tex]\longrightarrow \tt \red{ 1 m } = h[/tex]
Therefore, the height of cylinder = 1 m.
[tex]\begin{gathered} {\underline{\rule{290pt}{2pt}}} \end{gathered}[/tex]
What is the difference when estimating?
Answer:
1 1/6 = 1
5/9 = 45/99
Step-by-step explanation:
When rounding, make sure that anything that's above half will be rounded up if anything is below half it will be rounded down.
e.g. Round to the nearest half or whole
1. 5/9
Answer: 45/99
Why: 5/9 is 4 units to 9 while 5/9 is half of a unit closer to 45/99
2. 8/10
Answer: 10/10 or 1
Why: 8/10 is 2 units from 10 while 8/10 is 3 units from 5
Hopefully this helped!
()
8
What is 11 - 2³?
Answer:
[tex]11 - 2 {}^{3} [/tex]
[tex]11 - 8[/tex]
[tex]3[/tex]
Are the two triangles congruent?
Answer:
yes.......................
Step-by-step explanation:
NEED ASAP !!!!!
Which table represents a linear function?
Which of the following rational functions is graphed below?
10-
10
-10
-10-
O A. F(x) =
X-2
x(x + 5)
OB. F(x)=
1
(x+5)(x-2)
O C. F(x) = (x+5)(x - 2)
X
O D. F(x) = (x+5)(x-2)
X
The graph of the function f(x) = x(x + 5)(x - 2) have x intercepts at x = 0, -5 and 2
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
f(x) = x(x + 5)(x - 2)
x(x + 5)(x - 2) = 0
x = 0, x + 5 = 0, x - 2 = 0
x = 0, -5 and 2
The graph of the function f(x) = x(x + 5)(x - 2) have x intercepts at x = 0, -5 and 2
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Finding the inverse of the function x^3+3x+1 is beyond the scope of this course. Nevertheless, you should be able to use your knowledge of functions and their inverses as well as your graphing calculator to find the following values of the inverse function.
a. f^-1(1)
b. f^-1(5)
c. f^-1(3)
Step-by-step explanation:
[tex] {x}^{3} + 3x + 1 = 1 = = = > \\ {x}^{3} + 3x = 0 = = = > \\ x({x}^{2} + 3) = 0 \\ x = 0 \: or \\ {x}^{2} + 3 = 0 = = = > \\ {x}^{2} = - 3 = = = > x 1= \sqrt{ - 3} \: or \: i \sqrt{3} \\ x2 = - \sqrt{ - 3} = = = > x2 = - i \sqrt{3} [/tex]
[tex] {x}^{3} + 3x + 1 = 5 = = = > \\ {x}^{3} + 3x - 4 = = = > \\ (x - 1)( {x}^{2} + x + 4) = 0 = = = > \\ x - 1 = 0 = = > x1 = 1 \\ {x}^{2} + x + 4 = 0 = = = > \\ x2 = - 1 + i \sqrt{3} \\ x3 = - 1 - i \sqrt{3} [/tex]
[tex] {x}^{3} + 3x + 1 = 3 = = = > \\{ x}^{3} + 3x - 2 = 0 = = = > x = 0.6[/tex]
The values of the inverse of the function, f(x) = x³ + 3·x + 1, obtained from graphing of the function are;
a. f⁻¹(1) = 0
b. f⁻¹(5) = 1
c. f⁻¹(3) ≈ 0.59607
What is an inverse function?An inverse function is a function that reverses the action of another function, such that the inverse function maps the output of the function to the corresponding input.
The inverse of the function can be found by graphing the function, f(x) = x³ + 3·x + 1, using technology and then using inverse or table function to find the values of the inverse functions at the specified points
a. The value of the inverse function, f⁻¹(1), is the x-value, on the graph that corresponds to the point with a y-coordinate of 1.
The graph of the function indicates that at a y-value of 1, x = 0, therefore;
f⁻¹(1) = 0
b. Similarly, the graph indicates that a y-value of 5, x = 1, therefore;
f⁻¹(5) = 1
c. When the y-value = 3, we get;
x³ + 3·x + 1 = 3
x³ + 3·x - 2 = 0
Solving the above equation with an online tool, we get; x ≈ 0.59607
Therefore; f⁻¹(3) ≈ 0.59607
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Alana, Brianna and Carla divided $171 between them in the ratio 4 colon 7 colon 8. How much did Brianna receive?
Answer:
$63
Step-by-step explanation:
Alana has 4 units of the $171.
Brianna has 7 units of the $171.
Carla has 8 units of the $171.
Total units = 4 + 7 + 8 = 19
19 units = $171
1 unit [tex]\frac{171}{19} \\= $9[/tex]
Brianna has 7 units, so she receives 7 x $9 = $63.
How Do You Answer This Question
Write this fraction as a mixed number.
Answer:
7/6=2/7/6
7/6=2
7/6=27/6
7/6=2
7/6
Solve each inequality and graph the solution set and a number lined, express the Solution set in interval notation. 6 < x + 3 < 8 Solve each inequality and graph the solution set and a number lined , express the Solution set in interval notation . 6 < x + 3 < 8
The solution set for the given inequality is 3<x<5.
The given inequality is 6<x+3<8.
What is the solution set?In mathematics, a solution set is the set of values that satisfy a given set of equations or inequalities.
Now, solve the given inequality:
6<x+3<8⇒6<x+3 and x+3<8
6-3<x ⇒3<x
x+3<8⇒x<5
Thus, 3<x<5.
Therefore, the solution set is 3<x<5.
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Inequality and graph the solution set and a number line, express the Solution set in interval notation is 3 < x < 5
6<x+3<8
[tex]6 < x+3\quad \mathrm{and}\quad \:x+3 < 8[/tex]
What is the rule of inequality?[tex]\mathrm{If}\:a < u < b\:\mathrm{then}\:a < u\quad \mathrm{and}\quad \:u < b[/tex]
[tex]\mathrm{Combine\:the\:intervals}[/tex]
[tex]x > 3\quad \mathrm{and}\quad \:x < 5[/tex]
[tex]3 < x < 5[/tex]
Therefore the Inequality and graph of the solution set and a number line, express the Solution set in interval notation as 3 < x < 5.
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A graph displays point A (5, 3, 4) and point B (−4, 2, 6). Calculate the approximate distance each point is from the origin. Round to the nearest tenth. Which point is farther from the origin, and by how much?
Distance from the origin to the points ≈ 0.41.
What is the distance between two points ( p,q) and (x,y)?The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
D = √[(x-p)² + (y-q)²]
Point A (5, 3, 4) and point B (−4, 2, 6) are located away from the origin (0,0,0), and the points from the origin to this points are expressed as OB - OA where;
Let OB is the distance from the origin to the point B
Let OA is the distance from the origin to the point A
Using the formula for calculating the distance between two points;
OA = √(z2-z1)²+(y2-y1)²+(x2-x1)²
OA = √(4-0)²+(3-0)²+(5-0)²
OA = √(16)+(9)+(25)
OA = √50
OA = 7.071
Similarly;
OB = √(6-0)²+(2-0)²+(-4-0)²
OB = √(6)²+(2)²+(-4)²
OB = √36+4+16
OB = √56
OB = 7.4833
Distance from the origin to the points = 7.4833 - 7.071= 0.4123
Distance from the origin to the points ≈ 0.41
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Question 3(Multiple Choice Worth 4 points)
Which expression is equivalent to (7³)-2?
1
7-7-7-7-7-7
07
01
7
-1
7-7-7-7-7-7
frm
Finding the Domain and Range of a Graph
Determine the domain and range for the graph below. Write your answer in interval notation.
Answer:
Domain: [tex][-3, 1)[/tex]Range: [tex][-5, 4][/tex]Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Olympic Enterprises has the following inventory data: Assuming average cost, what is the cost of goods sold for the June 14 sale?
Assuming average cost of $55.5, the cost of goods sold by Olympic Enterprises for the June 14 sale is equal to $444.
How to calculate cost of goods?In Financial accounting, the cost of goods sold for a business firm can be calculated by multiplying the total quantity of goods by an average cost. Mathematically, this is given by:
Cost of goods = quantity × average cost
Note: We would assume an average cost of $55.5.
Substituting the parameters into the formula, we have:
Cost of goods sold = 8 × 55.5
Cost of goods sold = $444.
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#40 is it true or false
Answer:
True
Step-by-step explanation:
-77 is less than -76. Since the symbol refers to less than or equal to, this statement will be true.
if a= (-3 -9 -3 -4 -3 9 7 9 -10) and b= (9 1 6 3 -10 5 -1 9 -9) find -7A -4B?
Answer: Choice A
[tex]\begin{pmatrix}-15 & 59 & -3\\16 & 61 & -83\\-45 & -99 & 106\end{pmatrix}[/tex]
===========================================================
Explanation:
In matrix A, the upper left corner is -3
Multiply this with -7 to get -7*(-3) = 21
So we'll have 21 in the upper left corner of matrix -7A. The other entries will be handled in a similar fashion.
Meanwhile, the upper left corner of matrix B is 9. Multiply this with -4 to get 9(-4) = -36 which is the upper left corner entry of matrix -4B
Combine those products: 21 + (-36) = -15
The number -15 is the upper left corner entry in matrix -7A-4B
This points us to choice A as the final answer.
Helppp needed plx as fast as u can
Answer:
The answer is either 30 degrees or 36 degrees.
You need a protractor to measure it.
Most probably, the answer is 30 degrees.
BUT PLEASE MEASURE THE ANGLE WITH A PROTRACTOR!
Answer:
d. 60°
Step-by-step explanation:
Since the clock is a full circle, it has a degree span of 360°.
∴ every 5-min interval on the clock
= 360° ÷ 12 five min intervals
= 30°
∴ acute angle formed by clock in figure
= two 5-min intervals
= 60°
Which of the following options is a 3rd degree polynomial with exactly 1 real
root?
A. F(x)=x²-9x² +27x-27
B. F(x)=x+3x² +9x+27
C. F(x)= x +9x² +27x+27
D. F(x)=x+3x² -9x-27
Which is not a solution of sin 20 = 1?
A = 90
B = 45
C = 225
D = - 135
Scott started his bank account with $150 and is spending $7 per day on lunch. The x-axis would be labeled:
The x axis is labeled as Number of days.
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
let x be the number of days and y be money.
So, the equation is
y = -7x + 150.
Hence, the x axis is labeled as Number of days.
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This table represents a proportional relationship between x and y.
x 0.2 0.4 0.6 0.8
y 0.25 0.5 0.75 1.0
What is the constant of proportionality?
Enter your answer as a decimal in the box.
Answer:
x
Step-by-step explanation:
I got it right.........
A car is purchased for 28,000 after each year, the resale value decreased by 25% what will be the resale value be after 3 years?
Answer:
11,812.5
Step-by-step explanation:
25% = 0.25
(YEAR ONE)
[tex]28,000*0.25 -- > 21,000[/tex]
↓ (why?)
28,000 * 0.25 = 7,000
[tex]28,000 - 7,000 = 21,000[/tex]
(YEAR TWO)
[tex]21,000 * 0.25 -- > 15,750[/tex]
↓ (why?)
[tex]21,000 * 0.25 = 5250[/tex]
[tex]21,000 - 5,250 = 15,750[/tex]
(YEAR THREE)
[tex]15,750 * 0.25 -- > 11,812.5\\[/tex]
↓ (why?)
[tex]15,750 * 0.25 = 3,937.5\\15,750 - 3,937.5 = 11,812.5[/tex]
Answer = 11, 812.5
Select the correct answer.
x
f(x)
2.0 2.8
2.5 1.1
3.0 –0.8
3.5 –1.2
4.0 –0.3
4.5 0.7
For the given table of values for a polynomial function, where must the zeros of the function lie?
A.
between 2.0 and 2.5 and between 4.0 and 4.5
B.
between 2.5 and 3.0 and between 4.0 and 4.5
C.
between 2.0 and 2.5 and between 3.5 and 4.0
D.
between 2.5 and 3.0 and between 3.5 and 4.0
Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients. The correct option is B.
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication, and non-negative exponentiation of variables involved.
Example:
x² + 3x + 5
In order to find the values at which the given polynomial will have zeros of the function, we need to find the values at which f(x) changes from positive to negative or vice versa. Since this is the range at which the function must have crossed the x-axis on the graph.
As per the given table, the value of f(x) is changing from negative to positive and positive to negative are between 2.5 and 3.0 and between 4.0 and 4.5.
Hence, the correct option is B.
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n
Sigma 2k+4
k=1
4th term in sequence?
Answer:
12
Step-by-step explanation:
2k+4= 2*4 +4=8+4=12
hope it will help
Answer:
12
Step-by-step explanation:
Given:
[tex]\displaystyle \sum^n_{k=1}2k+4[/tex]
The 4th term in the sequence is when k = 4.
Therefore, substitute k = 4 into 2k + 4:
⇒ 2k+ 4 = 2(4) + 4
= 8 + 4
= 12
Therefore, the 4th term in the sequence is 12
A polynomial function has a root of -6 with multiplicity 3 and a root of 2 with multiplicity 4. If the function has a negative
leading coefficient and is of odd degree, which could be the graph of the function?
Answer:
Using the formula multiplicity, we find that the equation of the function will be [tex]f(x)=-(x+6)^{3} (x-2)^{4}[/tex]. The graph is in the attachment.
Step-by-step explanation:
Concept: Given that for -6, multiplicity is 3 and for 2 multiplicity is 4.
So, the equation of multiplicity is represented as:
[tex]f(x)=a(x-root)^{mutliplicity}[/tex]
This gives the following function
[tex]f(x)=a(x+6)^{3} (x-2)^{4}[/tex]
The equation has a negative leading coefficient.
This means that, the value of a is less than 0 i.e. a < 0
Assume any value of a (say a = -1), the equation becomes
[tex]f(x)=-(x+6)^{3} (x-2)^{4}[/tex]
The graph is in the attachment.
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Answer:
C
Step-by-step explanation:
trust bro
