boat speed= 8 m/s
river current= 5 m/s
to find:the resultant speed of the motorboat rounded to the nearest 10.
solution:use pythagorean theorem.
let the unknown be "x".
[tex] {a}^{2} = {b}^{2} + {c}^{2} [/tex]
[tex] {c}^{2} = \sqrt{ {a}^{2} + {b}^{2} } [/tex]
[tex]x = \sqrt{ {8}^{2} + {5}^{2} } [/tex]
[tex]x = \sqrt{64 + 25} [/tex]
[tex]x = 9.4 \: m |s[/tex]
hence, the resultant speed of the motorboat is 9.4 m/s
y=x^4-x^3-5x^2-x-6
Show steps
Answer:
The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x. x= i, −i, 3,−2
Step-by-step explanation:
Answer:
[tex](x-3)({x}^{2}+1)(x+2)[/tex]
Step-by-step explanation:
1) Factor [tex]x^4 - x^3 - 5x^2 - x - 6[/tex] using Polynomial Division.
1 - Factor the following.
[tex]x^4 - x^3 - 5x^2 - x - 6[/tex]
2 - First, find all factors of the constant term 6.
[tex]1, 2, 3, 6[/tex]
3 - Try each factor above using the Remainder Theorem.
Substitute 1 into x. Since the result is not 0, x-1 is not a factor..
[tex]1^4 - 1^3 - 5 * 1^2 - 1 - 6 = - 12[/tex]
Substitute -1 into x. Since the result is not 0, x+1 is not a factor..
[tex]( - 1 ) ^ 4 - ( - 1 ) ^ 3 - 5 ( - 1 ) ^ 2 + 1 - 6 = - 8[/tex]
Substitute 2 into x. Since the result is not 0, x-2 is not a factor..
[tex]{2}^{4}-{2}^{3}-5\times {2}^{2}-2-6 = -20[/tex]
Substitute -2 into x. Since the result is 0, x+2 is a factor..
[tex]{(-2)}^{4}-{(-2)}^{3}-5{(-2)}^{2}+2-6 = 0[/tex]
⇒ [tex]x+2[/tex]
4 - Polynomial Division: Divide [tex]{x}^{4}-{x}^{3}-5{x}^{2}-x-6[/tex] by [tex]x+2[/tex]
[tex]x^3[/tex] [tex]-3x^2[/tex] [tex]x[/tex] [tex]-3[/tex]
--------------------------------------------------------------
[tex]x+2[/tex] | [tex]x^4[/tex] [tex]-x^3[/tex] [tex]-5x^2[/tex] [tex]-x[/tex] [tex]-6[/tex]
[tex]x^4[/tex] [tex]2x^3[/tex]
------------------------------------------------------------
[tex]-3x^3[/tex] [tex]-5x^2[/tex] [tex]-x[/tex] [tex]-6[/tex]
[tex]-3x^3[/tex] [tex]-6x^2[/tex]
---------------------------------------
[tex]-3x[/tex] [tex]-6[/tex]
[tex]-3x[/tex] [tex]-6[/tex]
---------------
5 - Rewrite the expression using the above.
[tex]{x}^{3}-3{x}^{2}+x-3[/tex]
2) Factor out common terms in the first two terms, then in the last two terms.
[tex]({x}^{2}(x-3)+(x-3))(x+2)[/tex]
3) Factor out the common term [tex]x-3[/tex].
[tex](x-3)({x}^{2}+1)(x+2)[/tex]
Which statement about odd functions is correct?
A. They are symmetric over the x-axis.
B. They have rotational symmetry.
C. They are symmetric over the y-axis.
D. They are transformations of the parent function.
No one because odd functions are symmetric about the origin.
What is an odd function?It is a function such that f (x) =f (x) with the sign reversed but the absolute value unchanged if the independent variable's sign is reversed.
If f(x) Equals f(x) for every x, a function is odd. An odd function's graph will be symmetrical around the origin.
For instance, f(x) = x3 is an odd number. That is, the function on one side of the x-axis is sign inverted in relation to the function on the other side, or graphically, symmetric about the origin.
Therefore the odd functions are symmetric about the origin.
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Answer: B
Step-by-step explanation:
Find the area of the triangle. area triangle 4
Answer:
12
Step-by-step explanation:
because when u plus 4+4+4 it's 12
Problem 4.2
A textbook has 428 numbered pages, starting with 1.
A textbook has 428 numbered pages, starting with 1.
You are equally likely to stop on any of the pages if you flip through the book randomly.
What is the probability that you turn to an even-numbered page?
Answer:
50%
half of the numbers are even
Step-by-step explanation:
Sum interior angle on a regular pentagon
Answer:
540°
Step-by-step explanation:
Formula: note that n means nr of sides
(n-2)×180°
(5-2)×180°=3×180=540°
Where each angle are 540°÷5=108°
Answer:
540
Step-by-step explanation:
108 is one interior angle from a regular pentagon
And a pentagon has 5 interior angles
So 180x5=540
What is the polynomial function of lowest degree with lead coefficient 1 and roots 1 and 1 i? f(x) = x2 – 2x 2 f(x) = x3 – x2 4x – 2 f(x) = x3 – 3x2 4x – 2 f(x) = x2 – x 2
The polynomial with the lowest degrees and a leading coefficent of 1 will be f(x) = x^2 – x
Polynomial functionThese are function with leading degree of 3 and above
Given the standard polynomial function of degree 3
ax³+bx²+cx+d
The leading coefficient is "a"
The polynomial with the lowest degrees and a leading coefficent of 1 will be f(x) = x^2 – x
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2. Mrs.Anub is sad because 75% of her pupils failed in the Summative Test.If 40 pupils failed in the test,how many pupils does she have.in the class?
Copy and answer:
a. What is asked in the problem?
b.What are the given facts?
c. What is the formula to be used to solve the problem?
d.What is the number sentence?
e.Solve and show your solution...
e.Write the answer...
Answer:
1. How many pupils does Mrs.Anub have in all
I am sorry but I could only solve question 1
Step-by-step explanation:
Answer:
Step-by-step explanation:
a. How many pupils does she have in the class?
b. 40 pupils failed in the test.
c. x = all pupil in the class
percentage
d. 75/100 x = 40
e. 75/100 x = 40
x = 40*100/75
= 53.33
pupils = 53 people
f. There are 53 pupils in the class.
A cylinder has radius 14 inches and height 12 inches. A cone has the same radius and height.
Round Volume answers to the nearest hundredth.
A) Find the volume of the cylinder. V=
B) Find the volume of the cone. V=
C) What fraction of the cylinder's volume is the cone's volume?
A. The volume of the cylinder is: 7389.03 in.³
B. The volume of the cone is: 2463.01 in.³
C. The volume of the cone is one-third (1/3) of the volume of the cylinder.
What is the Volume of a Cone and a Cylinder?Volume of cone = 1/3πr²hVolume of cylinder = πr²hA. Volume of the cylinder = πr²h = π(14²)(12) = 7389.03 in.³
B. Volume of the cone = 1/3πr²h = 1/3π(14²)(12) = 2463.01 in.³
C. The volume of the cone is one-third (1/3) of the volume of the cylinder.
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A proportional relationship is shown in the table below:
x 0 2 4 6 8
y 0 1.2 2.4 3.6 4.8
What is the slope of the line that represents this relationship?
_______
Graph the line that represents this relationship.
ill attach the table and the graph
The Answer is 10/13 :)
Explanation: (13−0)
= 10/13
(10−0)
13,10
The slope of the line that represents this relationship is 10/13 .
What is the slope of the lineThe graph of the line representing the proportional relationship will be a straight line passing through these two points.
The x-axis represents the "x" values, and the y-axis represents the "y" values. The line should have a positive slope and go through the points (0, 0).
From the graph (13−0) = 10/13
From the graph one can see that (10−0) will lead to the points of 13,10 So, the slope of the line that represents this relationship is 10/13 .
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The probability for event A is 0.4, the probability for event B is 0.2, and the probability of events A and B is 0.1.
Why are the events not independent?
The sum of P(A) and P(B) is greater than P(A and B).
The product of P(A) and P(B) is greater than P(A and B).
The product of P(A) and P(B) is not equal to P(A and B).
The sum of P(A) and P(B) is not equal to P(A and B).
Let x = 0.147 and let y = 0.147.
Answer:
X is a rational number, y is not a rational number, and y is larger.
Step-by-step explanation:
The line above the 0.147 means that the number goes on forever and never stops. This is a characteristic of an irrational number. Rational numbers, however, do stop, so x is rational. Because y goes on forever, it has more values after the 0.147, making it larger.
Having trouble with this problem, can someone help me understand how to solve this.
Answer:
448m^3
Step-by-step explanation:
volume of pyramid = 1/3*area of base * perpendicular height
12*16=192m^2
1/3*192*7=448m^3
Simplify this expression
20f-4(5f+4)+16
Solve step by step
20f - 4 (5f + 4) + 16
= 20f - 20f - 16 + 16
= 0
Answer:
0
Step-by-step explanation:
Distribute terms in the parentheses
20f - 4(5f + 4) + 1620f - 20f - 16 + 16 0 + 0 [20f and -20f, and -16 and 16 cancel out]0what is -7/6 simplified
-7/6 = - 1.167 in simplest form
Answer:
Step-by-step explanation:
You cant simply this into fraction but you can simplify it to decimal form
which is - 1.17 round off
MULTIPLE CHOICE QUESTION
Which is the greater number
0.23 or 0.111
Answer:
0.23
Step-by-step explanation:
0.23 - 0.111 = 0.119
Meaning that it's greater in value.
Answer:
0.23
Step-by-step explanation:
When you look in the tenths place 2 is greater than one :) hope this helps!!
Please help me with this
The probability of not picking a red marble is 0.2.
The probability of picking a yellow or green marble is 0.5
The probability of drawing an even number of a number greater than 4 is 1.
The probability of getting heads and an even number is 1.
The probability of drawing a 2 or a 4 is 0.25.
What are the probabilities?Probability determines how likely it is for an event to happen. The chances of the event occurring lies between 1 and 0.
The probability of not picking a red marble = (number of all the marbles - red marbles) / total marbles
4/20 = 0.2
The probability of picking a yellow or green marble = (number of yellow marbles / total number of marbles) + (number of green marbles / total number of marbles)
2/20 + 8/20 = 10/20 = 0.5
The probability of drawing an even number of a number greater than 4 = (number of even numbers / total numbers) + (numbers greater than 4 / total numbers)
5/10 + 5/10 = 1
The probability of getting heads and an even number is = (side that is head / total sides) x (even numbers on a die / total numbers on a die)
1/2 x 3/6 = 1
The probability of drawing a 2 or a 4 = 1/8 + 1/8 = 2/8 = 0.25
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kite EFGH is graphed on the coordinate plane. three of its verticies are E(1,6), F(3,5), and G(4,-3). what are the coordinates of the fourth vertex, H?
The coordinates of the fourth vertex, H is; (-6.056, 7.302)
How to find the Coordinates of a Kite?
A kite has 4 sides and we know that a pair of diagonally opposite angles of a kite are said to be congruent.
We are given the coordinates of its' vertices as;
E(1,6), F(3,5), and G(4,-3).
The two diagonals are perpendicular;
Slope of EG = (-3 - 6)/(4 - 1)
Slope of EG = -9/5
Equation of line passing through G is;
y = mx + c
-3 = -9/5(4) + c
-15 = -36 + 15c
c = 51/15 = 17/5
y = (-9/5)x + 17/5 ------(1)
Equation of line passing through F is;
y = mx + c
6 = (5/9)(1) + c
54 = -9 + 9c
c = 7
y = (5/9)x + 7 -----(2)
Solving eq 1 and eq 2 simultaneously gives;
x = -1.528 and y = 6.151
If (a, b) are coordinates of vertex H, then;
(a + 3)/2 = -1.528 and (b + 5)/2 = 6.151
Thus;
a = -6.056 and b = 7.302
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Luke gets paid $13/hour. He got an
additional bonus of $50 for staying late one
day. He got paid $641.50 this month.
Write an equation, define your variable and
solve. How many hours did he work?
Answer:
13x+50=641.50, where x is the about of hours Luke worked. (x=45,5[h])
Cuanto es El 15% de1.340 es
Hey there!
15% * 1.340
= 15/100 * 1.340
= 0.15 * 1.340
= .15 * 1.34
= 0.201
Therefore, the answer should be: 0.201
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Find the midpoint M of the line segment joining the points A = (7, - 8) and B = (- 3, - 4)
Answer:
The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.
Use this calculator to calculate the midpoint, the distance between 2 points, or find an endpoint given the midpoint and the other endpoint.
Step-by-step explanation:
Step-by-step explanation:
(7+(-3))/2 , (-8+(-4))/2(7-3)/2 , (-8-4)/24/2 , -12/2midpoint = (2,-6)help plssssssssssssssssssss
Answer:
The circumference is 75.36 inches.
Step-by-step explanation:
Hi there! Please take a look at the following explanation and let me know in the comment if you have any doubts!
Given:We are given the radius that’s equal to 12 inches and π = 3.14
Problem:We want to find the circumference.
Circumference Formula:[tex]\displaystyle \large{C=2\pi r}[/tex] which simply means circumference = 2*π*radius or sometimes can also be written as [tex]\displaystyle \large{C=\pi d}[/tex] which means circumference = π*diameter since 2r means two times of radius and that’s technically diameter.
Step:Determine the following:
π = 3.14 as givenr = 12 as givenApply the circumference formula.
[tex]\displaystyle \large{C=2\cdot 3.14 \cdot 12}\\\\\displaystyle \large{C = 24 \cdot 3.14}\\\\\displaystyle \large{C=75.36}[/tex]
Hence, the circumference is 75.36 inches.
Answer:
75.36 in^2
Step-by-step explanation:
24*3.14
=75.36 in^2
Identify the equations of ellipses whose major axis lengths are twice their minor axis lengths.
The equations of ellipses whose major axis lengths are twice their minor axis lengths are
(x - h)²/4b² + (y - k)²/b² = 1 and (x - h)²/b² + (y - k)²/4b² = 1To answer the question, we need to know what an ellipse is.
What is an ellipse?An ellipse is part of a conic section.
The equation of the ellipseThe equation of an ellipse centered at (h,k) with major axis on the x-axis and major axis length, 2a and minor axis length 2b is
(x - h)²/a² + (y - k)²/b = 1
The equation of ellipse with major axis x-axis
The equations of ellipses whose major axis lengths are twice their minor axis lengths with ellipse centered at (h,k) with major axis on the x-axis. Since the major axis is twice the length of the minor axis, a = 2b.
So, (x - h)²/a² + (y - k)²/b² = 1
(x - h)²/(2b)² + (y - k)²/b² = 1
(x - h)²/4b² + (y - k)²/b² = 1
The equation of ellipse with major axis y-axis
The equations of ellipses whose major axis lengths are twice their minor axis lengths with ellipse centered at (h,k) with major axis on the y-axis. Since the major axis is twice the length of the minor axis, a = 2b.
So, (x - h)²/b² + (y - k)²/a² = 1
(x - h)²/b² + (y - k)²/(2b)² = 1
(x - h)²/b² + (y - k)²/4b² = 1
So, the equations of ellipses whose major axis lengths are twice their minor axis lengths are
(x - h)²/4b² + (y - k)²/b² = 1 and (x - h)²/b² + (y - k)²/4b² = 1Learn more about ellipse here:
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Hello guys can someone please help me?
ASAP?
Ill give points and brainliest
THANK YOU!!!
Answer:
[tex]4^{4}[/tex]
[tex](-7)^{6}[/tex]
5x5x5x5
Step-by-step explanation:
The exponent sign shows how many times you will multiply the base number by itself
[tex]4^{4}[/tex] is saying "multiply 4 by itself 4 times" which is the same as 4x4x4x4
[tex](-7)^{6}[/tex] is saying "multiply -7 by itself 6 times" which is the same as -7x-7x-7x-7x-7x-7
Complete the recursive formula of f (n)
The value of the given function will be written as:-
a) f(1)= 12
b) [tex]f(n-1)= -48(\dfrac{-1}{4})^{n-1}[/tex]
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
The given function is :-
[tex]f(n)= -48(\dfrac{-1}{4} ) ^{n}[/tex]
So the value of the given function f(1) will be:-
[tex]f(1)= -48(\dfrac{-1}{4} ) ^{1}=12[/tex]
The value of the function f(n-1) will be:-
[tex]f(n-1)= -48(\dfrac{-1}{4})^{n-1}[/tex]
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HOWW DO I DO THIS????
WEIRD EXACT TRIG QUESTION (cannot use a calculator)
Answer:
[tex]\huge{\red{\angle ABC = \boxed{30}\degree}}[/tex]
Step-by-step explanation:
[tex]\sin \angle ABC =\frac{p}{30}......(1)[/tex] (Given)In [tex] \triangle ABC,[/tex] sin ratio of [tex] \angle ABC[/tex] can be given as:[tex]\sin \angle ABC =\frac{AC}{AB}[/tex][tex]\implies \sin \angle ABC =\frac{2p+10}{80}......(2)[/tex]From equations (1) and (2), we find:[tex] \frac{p}{30}=\frac{2p+10}{80}[/tex][tex]\implies 80(p)=30(2p+10)[/tex][tex]\implies 80p=60p+300[/tex][tex]\implies 80p-60p=300[/tex][tex]\implies 20p=300[/tex][tex]\implies p=\frac{300}{20}[/tex][tex]\implies p=15[/tex][tex]\implies \sin \angle ABC =\frac{15}{30}[/tex][tex]\implies \sin \angle ABC =\frac{1}{2}[/tex][tex]\implies \sin \angle ABC =\sin 30\degree\:\:\:\:(\because \sin 30\degree=\frac{1}{2})[/tex][tex]\implies \huge{\red{\angle ABC = \boxed{30}\degree}}[/tex]Simplify the expression. Write your answer as a power.
64⁴/64³
The simplified expression is
Answer:
[tex]64^1\:\text{or}\:64[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{64^4}{64^3}=64^{4-3}=64^1=64[/tex]
Step-by-step explanation:
64^4/64^3= 64^(4-3)= 64^1= 64
Which best describes the strength of the correlation, and what is true about the causation between the variables? it is a weak positive correlation, and it is not likely causal. it is a weak positive correlation, and it is likely causal. it is a strong positive correlation, and it is not likely causal. it is a strong positive correlation, and it is likely causal.
What best describes the strength of the correlation between variables is that it is a strong positive correlation, and it is likely causal.
What is the correlation between variables?Corresponds to a statistical relationship, which will be positive when both variables, such as x and y move in the same direction, that is, when one variable increases, the other also increases, being a causal relationship.
Therefore, the relationship can also be negative, meaning that when the value of one variable increases, the values of the other will decrease.
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offering tons of points and brainliest for the right answer!
A boat can travel 28 miles up a river in the same amount of time it takes to travel 36 miles down the same river. If the current is traveling at 2 miles per hour, what is the speed of the boat in still water?
Answer:
16 mph
Step-by-step explanation:
You want the speed of a boat in still water if it travels 28 miles upstream in the same time it travels 36 miles downstream in a river that runs 2 mph.
TimeThe relation between time, speed, and distance is ...
t = d/s
If we let b represent the boat speed, the two identical times give the relation ...
28/(b -2) = 36/(b +2)
Solution28(b +2) = 36(b -2) . . . . cross multiply
28b +56 = 36b -72 . . . . eliminate parentheses
128 = 8b . . . . . . . . . . . . add 72 -28b
16 = b . . . . . . . . . . . . divide by 8
The speed of the boat is 16 mph.
<95141404393>
Brian bought 22 pounds of flour for $10. How many pounds of flour did he get per dollar?
Answer:
$2.20
You do 22÷10 and you get 2.20
Stefan sells Jin a bicycle for $138 and a helmet for $18. The total cost for Jin is 130% of what
Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How
much money did he make by selling the bicycle and helmet to Jin?
Stefan originally spent
Answer:
1. $109.20 2. $46.80
Step-by-step explanation:
Doing the math, we find that 30% of 156 (138+18) is 46.80, which answers the second part of this problem. Plugging this value into the first part of the equation gives us what Stefan originally paid.
Good luck! Hope this helps!