Answer:
18.87 km/hr
Step-by-step explanation:
First boat is heading North with a speed of 10 km/hr.
Second boat is heading West with a speed of 16 km/hr.
Time for which they move = 2.5 hours
To find:
The speed at which the distance is increasing between the two boats.
Solution:
Let the situation be represented by the attached diagram.
Their initial position is represented by point O from where they move towards point A and point B respectively.
[tex]Distance = Speed \times Time[/tex]
[tex]Distance\ OA = 10 \times 2.5 = 25\ km[/tex]
[tex]Distance\ OB = 16 \times 2.5 = 40\ km[/tex]
We can use Pythagorean Theorem to find the distance AB.
AB is the hypotenuse of the right angled [tex]\triangle AOB[/tex].
According to Pythagorean theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AB^{2} = OA^{2} + OB^{2}\\\Rightarrow AB^2 = 25^2 + 40^2\\\Rightarrow AB^2 = 2225^2\\\Rightarrow AB^2 \approx 47.17\ km[/tex]
The speed at which distance is increasing between the two boats is given as:
[tex]\dfrac{47.17}{2.5} \approx 18.87\ km/hr[/tex]
we have 2 fractions 5/8 and 5/4
Due Today, Help me pls. I will MARK AS BRAINLIEST.
What are the solutions of the equation x4 - 5x2 - 14 = 0? Use factoring to solve.
x = +/- √7 and x = +/- √2
x = +/- i√7 and x = +/- i √2
x = +/- i √7 and x = +/- √2
x = +/- √7 and x = +/- i √2
Answer:D
Step-by-step explanation:
The solution is: x = +/- √7 and x = +/- i √2 are the solutions of the equation x^4 - 5x^2 - 14 = 0.
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
given that,
we have to factorize the equation,
The given equation is
x^4 - 5x^2 - 14 = 0
To factor this expression, we can change variables to make easier to see the solution.
x^4 = y^2
and
x^2 = y
Applying the change, we have
y^2 - 5y - 14 = 0
Now, you can observe that to factor this expression, we just need to find two number which product is 14 and which difference is 5, such numbers are 7 and 2.
y^2 - 5y - 14 = 0
or, (y-7) ( y+2) = 0
However, remember that , y = x^2
so, (x^2-7) ( x^2+2) = 0
Applying the zero property, we have
x = +/- √7
and x = +/- i √2
As you can see, the equation has two real solutions and two complex solutions.
Therefore, the right answer is the last choice.
To learn more on simplification click:
brainly.com/question/28996879
#SPJ7
Help I’m being timed!!!
Answer:
50.24 square inches
Step-by-step explanation:
A circles area is:
[tex]\pi r^{2}[/tex]
Insert the values:
(3.14)(4^2)
3.14(16)
50.24 square inches
95 to 155 as a percentage
Answer:
61.290322580645% or 61%
Step-by-step explanation:
I put your question into a percentage calculator and got this for the answer. Wish you luck.
Answer:
Convert the decimal to a percentage by multiplying the decimal by 100
9515500%
Step-by-step explanation:
don't know if this the answer your looking for.
Eric and Shiloh each have a savings account. The ratio of Eric's account balance to Shiloh's account balance is 4:3. Together they have a total of $140 in their accounts. In the tape diagram below, how much money does each bar represent? [Type your answer as a number.]
Answer:
20
Step-by-step explanation:
E:S
4:3
4u+3u=140
7u=140
u=20
398 divided by 344?
Please help me.
Answer:
1.15697674419
Step-by-step explanation:
Answer:
1.15697674419 is the answer
please can some one solve this for me thankyou :-)
its sudoku
In the .docx file is a SUDOKU that needs to be resolved.
See the solution in the attached image.
Help please! Could you put an explanation as well?
Answer:
y=-(4x/3) -1
Step-by-step explanation:
Slope=m= -4/3
y intercept = c = -1
now using equation;
y= mx+c
y= (-4/3)x+(-1)
y=-(4x/3) -1
30 cupcakes he spreads 1/5 mint icing and 1/2chocolate how many will have vanilla icing
what are terms
answer choices...
1. the number in front of the variable
2. a letter that represents a number
3. the individual parts of an expression
4. the number that stands Alone with no variable...
please answer
Answer:
3. the individual parts of an expression.
Step-by-step explanation:
an example would be 5x + 2y - 6
5x, 2y, and 6 are all terms that are separated by symbols like +,-,× etc.
Simplify and Factorise a(a + b - c) - bc
Step-by-step explanation:
[tex] = a(a + ab - c) - bc[/tex]
[tex] = {a}^{2} + {a}^{2} + ab - ac - bc[/tex]
[tex] = {2a}^{2} + ab - ac - bc[/tex]
Put these substances in order of density with the most dense first and the least dense last.
Answer:
iron
rubber
cotton ball
helium
Solve
1+−=0
2 − ^2 = 4
Answer:
Both are inaccurate things.
pls help me answer this
can anyone help me thanks
Answer:
C
Step-by-step explanation:
We can use the vertex form of a quadratic equation, given by:
[tex]f(x)=a(x-h)^2+k[/tex]
Where a is the leading coefficient and (h, k) is the vertex.
We are given that the vertex is (-3, 1).
Hence, h = -3 and k = 1. By substitution:
[tex]f(x)=a(x-(-3))^2+(1)[/tex]
Simplify:
[tex]f(x)=a(x+3)^2+1[/tex]
With this, we can eliminate B and D.
Notice that our parabola is curving downwards.
Therefore, our leading coefficient must be negative.
The only choice that leaves us with is C.
So, our function is:
[tex]f(x)=-(x+3)^2+1[/tex]
And our final answer is C.
Linda and Rob open an online savings account that has a 2.89% annual interest rate, compounded
weekly. If they deposit $35 every week, how much will be in the account after 15 years?
Answer:
FV= $34,222.33
Step-by-step explanation:
First, we need to calculate the weekly interest rate:
Weekly interest rate= 0.0289/52= 0.00056
To calculate the future value (FV), we need to use the following formula:
FV= {A*[(1+i)^n-1]}/i
A= weekly deposit
n= 15*52= 780
A= $35
FV= {35*[(1.00056^780) - 1]} / 0.00056
FV= $34,222.33
The owner of Carlisle Construction is a little
overprotective of his brand new cement mixer,
so each night, he parks it in a storage facility
that is 120 feet long, 45 feet wide, and 45
feet high. What is the facility's volume in cubic
yards?
Answer:
The facility's volume in cubic yards is 9000
Step-by-step explanation:
The volume of the facility is given by the multiplication of it's dimensions.
We want the volume in cubic yards, so the dimensions have to be in yards.
Each feet has a third of an yard. So the dimensions are:
120 feet = 40 yards
45 feet = 15 yards
45 feet = 15 yards
What is the facility's volume in cubic yards?
[tex]V = 40*15*15 = 9000[/tex]
The facility's volume in cubic yards is 9000
27 students are learning to make balloons animals. There are 3,172 balloons to be shared equally among the students. How many balloons are left over after sharing them equally? Show all necessary work.
Answer:
you would do 3,172 divided 27 which would be 117 then subtract that by 3,172
Step-by-step explanation:
answer number 11 pls
Answer:
121.52 feet
Step-by-step explanation:
9.8+2.6 = 12.4
12.4 * 9.8 = 121.52
Afla 3 numere naturale știind ca produsul primelor doua este 54, produsul ultimelor doua este 12,iar suma dintre primul și al treilea este 11
Answer:
Cele 3 numere naturale sunt:
Primul număr = a = 9
Al doilea număr = b = 6
Al treilea număr = c = 2
Step-by-step explanation:
Fie cele 3 numere naturale reprezentate ca:
Primul număr = a
Al doilea număr = b
Al treilea număr = c
Produsul primelor două este de 54
a × b = 54
ab = 54 ...... Ecuația 1
a = 54 / b
Produsul ultimelor două este 12
b × c = 12
bc = 12 ........ Ecuația 2
c = 12 / b
Suma primului și celui de-al treilea este 11
a + c = 11 ...... Ecuația 3
Înlocuim
54 / b pentru a și 12 / b pentru c
54 / b + 12 / b = 11
54 + 12 / b = 11
Cross Multiply
66 / b = 11
11b = 66
b = 66/11
b = 6
Rezolvarea pentru un
a = 54 / b
a = 54/6
a = 9
c = 12 / b
c = 12/6
c = 2
Prin urmare, cele 3 numere naturale sunt:
Primul număr = a = 9
Al doilea număr = b = 6
Al treilea număr = c = 2
simplify the expression 12( a+ 5)
Answer:
12a+60 i think lol
Step-by-step explanation:
this is how i did it though:
12(a+b)
12a+60
Plsss help ASAP pls this is due at 12:00
Answer:
$74.49
(basically $74.50)
Step-by-step explanation:
hope that helps :))
please help and explain!! I got 14x +0
Answer:
[C] 16
Explanation:
7x + 8 − 7x + 8= 7x + 8 + −7x + 8
Combine Like Terms= 7x + 8 + −7x + 8
= (7x + −7x) + (8 + 8)
= 16
What is the value of the expression three less than the quotient of ten and a number, increased by six" when n = 2?
Answer:
The Answer is 8.
Step-by-step explanation:
I just took the test on Edge and got it right, hope this helps! :)
What is the value of x?
−3/4(12−8x)=5x+15−7x
Answer:
x = 3
Step-by-step explanation:
step 1: distribute -3/4 among 12 and 8x to get: -36/4 + 6x
step 2: combine 'like terms' on right side to get -2x + 15
-9 + 6x = -2x + 15
-9 + 8x = 15
8x = 24
x = 3
How much interest is earned on a principal amount of $400 invested at an interest rate of 5% for 3 years
Answer:$63.05
Step-by-step explanation:400*1.05*1.05*1.05=463.05
463.05-400=63.05
What is the area of a rectangular cake with a length of 10 inches and width of 6 inches?
Answer:the area of the cake is 60 inches
Step-by-step explanation: length times width. hope this helps.
(18 ÷ 3) + (3² - 7) =
finish brackets first.
(6) + (9-7)
= 6+2
=8
Mike had $800. He now has $500. What is the percent decrease?