simplify 4x^2+2x/x^2+x-2/8x^2+4x/3x^2+10x+8
Answer:
[tex]\frac{4x^{3} }{3} +\frac{15x^{2} }{4} +11x+\frac{2}{x} +8[/tex]
Step-by-step explanation:
Answer:
3x+4/2(x-1)
Step-by-step explanation:
I took the quiz
A boat is traveling due North at 27mph. A current is flowing at a bearing of 60° west of south at 8mph. Find the actual speed and direction of the boat written in magnitude and direction form.
Answer: [tex]24.02\ mph[/tex]
Step-by-step explanation:
Given
Boat is traveling due to north at [tex]v_{bf}=27\ mph[/tex]
The current is flowing [tex]60^{\circ}[/tex] west of south at [tex]v_f=8\ mph[/tex]
Suppose the actual velocity of boat is [tex]\vec{v_b}[/tex]
In vector notation we can write
[tex]\Rightarrow \vec{v_{bf}}=\vec{v_b}-\vec{v_f}\\\\\Rightarrow \vec{v_b}=\vec{v_{bf}}+\vec{v_f}[/tex]
Flow of current can be written as
[tex]\Rightarrow \vec{v_f}=-8\sin 60^{\circ}\hat{i}-8\cos 60^{\circ}\hat{j}[/tex]
Insert the values of vectors
[tex]\Rightarrow \vec{v_b}=27\hat{j}-8\sin 60^{\circ}\hat{i}-8\cos 60^{\circ}\hat{j}\\\\\Rightarrow \vec{v_b}=-4\sqrt{3}\hat{i}+27\hat{j}-4\hat{j}\\\\\Rightarrow \vec{v_b}=-4\sqrt{3}\hat{i}+23\hat{j}[/tex]
Magnitude of the velocity is
[tex]=\sqrt{(4\sqrt{3})^2+(23)^2}\\=\sqrt{48+529}\\=24.02\ mph[/tex]
The actual direction and magnitude of the velocity of the boat is the sum of
the velocity of the boat and the velocity of the current both in vector form.
The actual velocity and direction of the boat are approximately 24.02 m/s at a bearing of 16.76° west of north.Reasons:
Direction of the boat = North
Speed of the both = 27 mph
Direction of the current = 60° west of south
Speed of the current = 8 mph
Required:
The actual speed and direction of the boat written in magnitude and
direction.
Solution:
The velocities given in vector form are;
Velocity of the boat, [tex]\vec {v}_{boat}[/tex] = 27·j
60° west of south = 30° south of west
Therefore;
Velocity of the current, [tex]\vec{v}_{current}[/tex] = -8 × cos(30°)·i - 8×sin(30°)·j
The actual velocity of the boat, [tex]\vec{v}_{actual}[/tex] = [tex]\mathbf{\vec {v}_{boat}}[/tex] + [tex]\mathbf{\vec{v}_{current}}[/tex]
Which gives;
[tex]\vec{v}_{actual}[/tex] = 27·j - 8 × cos(30°)·i - 8 × sin(30°)·j
[tex]\vec{v}_{actual}[/tex] = 23·j - (4·√3)·i
Therefore;
[tex]\vec{v} _{actual}[/tex] = -(4·√3)·i + 23·j
Which gives;
[tex]|v_{actual}|[/tex] = √((-4·√3)² + 23²) = √(577) ≈ 24.02
The magnitude of the velocity of the boat, [tex]\mathbf{|v_{actual}|}[/tex] ≈ 24.02 m/s
The actual direction of the boat, θ, is given by the arctangent of the ratio
of the vertical to the horizontal component of the velocity as follows;
[tex]\displaystyle \theta = arctan \left(\frac{23}{-4 \cdot \sqrt{3} } \right) \approx \mathbf{-73.24^{\circ}}[/tex]
Based on the horizontal and vertical component, the above angle θ is
approximately 73.24° relative to the negative x-axis, which is 90° - 73.24° =
16.76° west of north.
Therefore;
The actual direction of the both is on a bearing of approximately 16.76° west of north.Learn more about vector quantities here:
https://brainly.com/question/1614684
Answer quickly!!!!!!!!!!
Answer:
-4/5
Step-by-step explanation:
Rise over run helps, since the line is negative the slop will be to. Just pick a spot that is whole/on the dot, and rise/fall as down or up until the next spot that's whole, then you 'run' over to the point. (Ex. (0,0) (5,4))
Una pequeña empresa dedicada a la fabricación de muebles lanzará al mercado un nuevo modelo de escritorio para escolares a un precio de S/ 125. Los costos fijos son S/ 4,750 y los costos variables S/ 75. Entonces, ¿cuántos escritorios se deben fabricar y vender para obtener S/ 25 000 de utilidad?
Answer:
Se debe fabricar y vender 553 escritorios para lograr una utilidad de S/ 25000.
Step-by-step explanation:
La utilidad por cada escritorio se obtiene al sustraer los costes fijos y variables del precio, es decir:
[tex]u = S/ \,125 -S/\,4,75 - S/\,75[/tex]
[tex]u = S/\,45.25[/tex]
El número de escritorios a vender para obtener [tex]S/\,25000[/tex] se calcula mediante la siguiente regla de tres simple:
[tex]x = \frac{S/\,25000}{S/\,45,25} \times 1\,esc[/tex]
[tex]x = 552.486[/tex]
Puesto que la cantidad a vender es una variable entera, se debe redondear al entero más cercano. En consecuencia, se debe fabricar y vender 553 escritorios para lograr una utilidad de S/ 25000.
A mug can hold 15.38 oz of coffee without overflowing. The radius of the mug is 4 cm. Given that 1 cm3 equals approximately 0.034 oz, what is the height of the mug to the nearest centimeter?
A. 13 cm
B. 9 cm
C. 11 cm
D. 7 cm
If your inequality has these signs, will you have an Opened or Closed circle on your number line graph? > or <
Answer:
it will be opened but if it's for the < and > with a line underneath each of them, the circle with be closed
Help please! Using the Counting Principle, determine how many outcomes are possible.
A car comes in 7 different colors, 4 different interior packages, and 4 different tire types.
Answer:
112
Step-by-step explanation:
7 x 4 x 4 = 112
112 unique outcomes
Skyler has 20 comic books about the Avengers. He goes to the comic book
store and after he leaves, he now has 26 Avengers comics. What is Chris'
percent increase in Avenger comics? *
Answer:
6%
Step-by-step explanation:
Niall has half dollar mary has a tenth of a dollar and jack has a hundredth of a dollar if they combine their money do the 4 students have more or less than a dollar
Answer: Students have less than a dollar.
Step-by-step explanation:
Niall has $1/2
Mary has $1/10
Jack has $1/100
Add these up to see if they reach 1.
= 1/2 + 1/10 + 1/100
Convert to decimals by dividing the numerator by the denominator:
= 0.5 + 0.1 + 0.01
= $0.61
Students have less than a dollar.
Maggie has 7 bills, all tens and twenties, that
total $100 in value. Find the number of tens, x, and
the number of twenties, y, that Maggie has.
Answer:
4 tens, 3 twenties
Step-by-step explanation:
4 tens ($40) and 3 ($60) twenties work. I’m sorry I don’t have a formula for it though.
Which fraction is equal to 7/-9? A. -7/9 B. -7/-9 C. 7/--9 D. --7/9
Answer:
A = -7/9
Step-by-step explanation:
7 / -9
Move the negative to the top
-7 / 9
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]\text{A) }\frac{-7}{9}[/tex]
»»————- ★ ————-««
Here’s why:
We can apply the rules for products and quotients of values with different signs. If the signs of two numbers are the same, then the product/quotient would be positive. If the signs are different, the sign of the product/quotient would be negative.⸻⸻⸻⸻ [tex]\boxed{\text{Equivalent Faction}}\\\\\rightarrow \frac{7}{-9}= -0.77777...... \leftarrow\\\\------------\\\text{Option A: } \frac{-7}{9} = -0.77777......\\\\\text{Option B: } \frac{-7}{-9}= 0.77777......\\\\\boxed{\text{Recall that if two numbers have the same sign then the product or quotient would be positive.}}\\\\\text{Option C: }\frac{7}{-(-9)}=\frac{7}{9} = 0.77777......\\\\\text{Option D: } \frac{-(-7)}{9}=\frac{7}{9} = 0.77777......[/tex]⸻⸻⸻⸻
Option A's fraction is equivalent.
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Chris has a bag of four apples. Three of the apples are red and one of them is green. He also has two
sandwiches. One of the sandwiches is ham and the other is turkey, If he reaches into both bags without looking, what is the probability that he will grab a red apple and a ham sandwich?
A. 1/8
B. 1/2
C. 3/8
D. 2/3
Answer: 3/8
Step-by-step explanation:
It’s the answer :>
Answer:
c. 3/8
Step-by-step explanation:
3/4 * 1/2 = 3/8
i multiplied both probabilities
A box contains 60 identical marbles where x of them are red while the rest are yellow. If a marble is drawn and the probability that it is white is 1/12, find the value of x.
b: How many white marbles must be added to the box so that the probability of choosing a white marble is 5/16?
Please answer I will make brianliest!!
Answer:
a. x is 55
b. 20 white marbles
Step-by-step explanation:
Question: A box contains 60 identical marbles where 'x' of them are red while the rest are white; (given that in the original question, the box only contains red and yellow marbles, the yellow can be replaced by white to explain the question idea)
a. The number of identical marbles in the box, n = 60
The number of red marbles = x
The number of white marbles = The rest of the marbles which are not red
The probability that a marble drawn is white, P(y) = 1/12
Let 'y' represent the number of white marbles
From probability theory, we have;
The number of white marbles, y = n × P(y) = 60 × 1/12 = 5
The number of red marbles, x = n - y = 60 - 5 = 55
x = 55
b. The number of white marbles that must be added to make the probability of choosing a white marble = 5/16 is given as follows;
Let Δy represent the number of white marbles added, therefore;
P(y) = (y + Δy)/(y + Δy + x)
∴ P(y) = (5 + Δy)/(5 + Δy + 55) = 5/16
5 × (60 + Δy) = 16 × (5 + Δy)
300 + 5·Δy = 80 + 16·Δy
16·Δy - 5·Δy = 300 - 80
11·Δy = 220
Δy = 220/11 = 20
The number of white marbles that must be added, Δy = 20 white marbles
People were surveyed about the types of pets they own and their housing situation. Each person has only one pet. For people who live in a condo, what is the relative frequency with which a person owns a cat?
Answer:
The answer is 6.3
Step-by-step explanation:
Help plsss anyone help plsss
Answer:
[tex]\frac{1}{70}[/tex]
Step-by-step explanation:
P(gold) = [tex]\frac{gold}{total}[/tex] = [tex]\frac{5}{350}[/tex] = [tex]\frac{1}{70}[/tex]
40:√100 + √9.√36
????
Answer:
28
Step-by-step explanation:
[tex]\sqrt{100} + (\sqrt{9} \cdot \sqrt{36}) = 10 + (3 \cdot 6) = 10 + 18 = 28[/tex]
The dimensions of two square pyramids formed of sand are shown. How much more sand is in the pyramid with the greater volume?
Answer:
Answer: There is 32in² more sand in the pyramid with greater volume.
step explanation:
A girl works a basic week of 40 hours and her basic rate is $6.25 per hour. Calculate her basic wage for the week
Answer:
$250
Step-by-step explanation:
To find the total multiply 6.25 and 40 together
6.25x40
$250 (Don't forget the dollar sign)
Answer:
250
Step-by-step explanation:
If she work 40 hours and earns $6.25 per hour for 40 hours you multiply howmuch she makes by the amunt of time she worked, so 6.25x40 = 250
Please help, don’t understand
Answer:
x = 9 degrees
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp side/ hypotenuse
sin x = 15/91
Taking the inverse sin of each side
sin ^-1 (sin (x)) = sin ^ -1( 15/91)
x =9.487658996
To the nearest degree
x = 9 degrees
Quadrilateral ABCD is translated 5 units right. What are the coordinates of quadrilateral
Answer:
it should be C sry if I'm wrong <3
What is the area of the triangle?
10
8
6
Answer:
10
Step-by-step explanation:
What is the area of a rectangle with side length of 5/12 foot and 2/ 3 foot
Answer:
5/12 x 2/3 = 10/36 = 5/18 foot2
The book fair sold 60% of the books
donated to the book fair. They sold
72 books. How many books were
donated in all?
Answer:
120 Books
Step-by-step explanation:
60% of 120 is 72
pliss give me the aswer
Answer:
AA
Step-by-step explanation:
AA
Answer:
15+ 8d
After d day,she has read 15 +8d pages
What is the product of 3.8\times 10^23.8×10
2
and 6.4 \times 10^66.4×10
6
expressed in scientific notation?
Answer:
2.432 * 10⁹
Step-by-step explanation:
Given the expression;
3.8*10² × 6.4*10⁶
= (3.8*6.4)× (10²*10⁶)
= 24.32*10⁸
= 2.432* 10¹ * 10⁸
= 2.432 * 10⁹
Hence the product expressed as a scientific notation is 2.432 * 10⁹
Please give me a detailed step by step explanation of how to solve y ≥ 5.
♣ explanation ♣
--------------------------------------------------------------------------------------
It may seem crazy that the value of Y > 5 can be anything, but it can be. Y greater than 5 basically means that Y is any number over 5 and has no exact value.
--------------------------------------------------------------------------------------
Remember, Y is a variable!
Find the slope of the line that crosses through the points (-2, 5) and (-5, -4)
Answer:
umm i believe it is positive 5
Step-by-step explanation:
i hope i helped
Use the function p(x)=4x-3
what is p(3)
Answer:
9!
Step-by-step explanation:
Use the given functions to set up and simplify p ( 3 ) .
-barbara
Answer:
9
Step-by-step explanation:
p(x)= 4X-3
P(3)= 4×3-3=9
Give the most precise selection
for the quadrilateral with the
following vertices.
P(0,0), Q(0,2a), R(2a,2a), S(2a,0)
A. Parallelogram
B. Rectangle
C. Square
D. Rhombus
Answer:
Its definitley square to be precise so that's my answer, but its also a rhombus
Step-by-step explanation:
assuming a is 1, regardless, graph would always be square, which is a rhombus. hope square is correct :)
What are the angles labeled ?
Answer:
90° angle
Step-by-step explanation:
Every time you see an angle that has a box, it measures 90°