The boat and the whale are about 218.5 miles apart.
Solving for the distance between the boat and the whale:Using the Pythagorean theorem to calculate the distance between the boat and the whale.
Let's call the distance between the boat and the whale "d" and the time they moved apart "t".
1st movement:
d = 45t
2nd movement:
d = (45t + 25(t+35))²
To calculate the final distance, we need to square d from the second movement and add the result from the first movement.
d² = (45t)² + (25(t+35))²
We know that the boat and the whale were moving apart for 35 minutes and 25 minutes, so we can substitute t = 35 and t = 25 in the equation.
d² = (4535)² + (2560)²
Taking the square root of the result and get the final distance between the boat and the whale.
d = ([tex]\sqrt{4535 ^{2} +2560^{2} }[/tex])
d ≈ 218.5 miles
Hence, the boat and the whale are about 218.5 miles apart.
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the mean of 1 2 3 4 5
Answer: 3
Hope this helps :)
Step-by-step explanation:
1+2+3+4+5=15
15/5=3
The age of a father is three times that of his son, but six years ago, the sum of their ages was 45. What is the present age of the son?
Answer: Let's call the present age of the son x and the present age of the father y.
We know that y = 3x and that six years ago, the sum of their ages was 45.
So, we can write the equation:
x + (y-6) = 45
x + (3x-6) = 45
4x = 51
x = 12.75
The present age of the son is 12.75 years.
Step-by-step explanation:
What is the inverse of the function? f(x)= 1/3 x −5
Answer:
The inverse of a function, denoted as f^-1 (x), is a new function that "undoes" the original function. To find the inverse of a function, you need to switch the x and y variables and then solve for y. To find the inverse of f(x) = 1/3 x - 5, you need to switch the x and y variables and then solve for y:
Step-by-step explanation:
To solve for y, you need to get x alone on one side of the equation:
x + 5 = 1/3 y
3x + 15 = y
The inverse of f(x) = 1/3 x - 5 is f^-1 (x) = 3x + 15
It is important to note that not all functions have an inverse, only functions that are one-to-one or "injective" functions have inverses.
Answer: 3x + 15 = the inverse function of f(x)
Explanation:
First of all, arrange the equation and leave the "x" alone.
x/3 - 5 = y (Multiply both sides by 3)
x - 15 = 3y (Then, leave "x" alone)
x = 3y + 15 (As the final step, change x and y variables.)
y = 3x + 15 (This is the inverse function of f(x).)
Accurate to the nearest hundredth, the larger root of
On solving the provided question, we can say that the value of the quadratic equation would be x = 0.18
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.
The roots of a quadratic equation ax^2 + bx + c = 0 can be found using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
The given equation is 2x² + 5x - 1 = 0
Hence, the larger root of the given quadratic equation would be x = 0.18.
[tex]x = \frac{-5 + \sqrt{5^2 - 4(2)(-1)} }{2(2)} \\x = 0.18\\or \\x = -2.68\\[/tex]
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Hellllllllllp me please
Step-by-step explanation:
different between each value is 4
5 situati de lipsa de respect in familie
Answer:
1. Nevoia de a te certa sau de a-i critica pe cei din familie prin limbaj cu conotatii negative sau prin tonul vocii.
2. Nerespectarea deciziilor familiei sau nerespectarea responsabilitatilor asumate.
3. Abuzul verbal sau emotional, inclusiv insultele sau minciunile.
4. Negarea dreptului la intimitate sau la spatiu personal.
5. Ignorarea afectiunii si a momentelor importante din familie.
Greg washes cars on Saturdays at his dad’s car dealership. His dad pays him $50 plus $5 for each car that he washes. Greg washed 11 cars last Saturday. Use function notation to write an equation that gives the total amount Greg earns as a function of the number of cars he washes. Use the equation to find how much he earned last Saturday.
(SHOW WORK)
Answer:
605
Step-by-step explanation:
11x55=605
Let A and B be sets, where:
A = {3, 6, 8}
B = {0, 2, 4, 5, 9}
Which of the following are square roots to the number below? Check all that apply.  625
A. 625^1/2
B.-625^1/2
C.-25
D.15
E.125
F.25
The square root of 625 is 25 and the square root of 25 is 5. Therefore, option A and F are the correct answers.
What is the square root?The square root of a number is the inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number.
A) [tex]625^{\frac{1}{2}[/tex]
= [tex](25^2)^{\frac{1}{2}[/tex]
= 25
F) 25
= 5
Therefore, option A and F are the correct answers.
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The cost of 2 bottles of water and 3 bags of pretzels is $7.05. The cost of a bag of pretzels is $1.35. Write a system of equations to represent this situation. Solve and explain what the answer means.
(SHOW WORK)
Answer:
The cost of the water is $5.70.
Step-by-step explanation:
7.05-1.35=5.70 You just have to - 7.05 by 1.35
Rewrite 15 + (72 + 19) using the Associative Law of Addition.
Answer: (15 + 72) + 19
Explanation: "Associative Law = (a + b) + c = a + (b + c)"
Suppose A = {2, 5, 7, 9, 13, 25, 26}.
(a) Find n(A).
n(A) = _________
(b) T/F: 20 A
True
False
Answer:
a) n(A)7
b) 140
Step-by-step explanation:
a) numbers in the set
b)since n(A)=7
20A=20×7
=140
Which of the following fractions have the same value as 16 ÷ (–3)? Check all that apply.
StartFraction 16 over negative 3 EndFraction
StartFraction negative 16 over negative 3 EndFraction
StartFraction negative 16 over 3 EndFraction
StartFraction 16 over 3 EndFraction
Negative (StartFraction 16 over 3 EndFraction)
Negative (StartFraction 16 over negative 3 EndFraction)
Find the quotient:
–20 ÷ 5 =
The fractions that have the same value as 16 ÷ (–3), include:
16 over negative 3negative 16 over 3Negative (StartFraction 16 over 3 EndFraction)The quotient of the problem given is - 4.
How to find the equivalent fractions ?To find the equivalent fractions to ,16 ÷ (–3), first solve for the quotient:
= 16 ÷ (–3)
= - 5. 33
Then, solve the fractions in the options to see if they give the same result as when you solved 16 ÷ (–3).
Fraction : 16 over negative 3
= 16 / -3
= - 5.333
This has the same value
Fraction : negative 16 over negative 3
= -16 / -3
= 5. 333
This does not have the same value
Fraction : negative 16 over 3
= - 16 / 3
= - 5. 333
This has the same value
Fraction : 16 over 3
= 16 / 3
= 5. 333
This is not the same value
Fraction: Negative (StartFraction 16 over 3 EndFraction)
= - ( 16 / 3 )
= - 5. 33
This is the same
The quotient of - 20 / 5 :
= - 20 / 5
= - 4
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Janice drives to the grocery store and
back every Tuesday. The drive home
takes twice as long because of traffic.
If her total travel time is forty-eight
minutes, how long does it take Janice
to drive to the grocery store?
Solve the equation
4sinxcosx^2 - 1 = 2cos(sin x - 1)
Answer:
Step-by-step explanation:
To solve this equation, we can start by using the identity cos(A-B) = cosAcosB + sinAsinB. Substituting A=sin x and B=1, we have:
2cos(sin x - 1) = cos(sin x)cos(1) + sin(sin x)sin(1)
We can then substitute this expression on the left-hand side of the original equation and simplify:
4sinxcosx^2 - 1 = cos(sin x)cos(1) + sin(sin x)sin(1)
Rearranging terms, we have:
4sinxcosx^2 - cos(sin x)cos(1) - sin(sin x)sin(1) = 1
We can now use the identity sin^2x+cos^2x=1 to simplify the left-hand side further:
4sinxcosx^2 - (sin^2x + cos^2x)cos(1) = 1
Simplifying further:
4sinxcosx^2 - (cosx)cos(1) = 1
Now we can divide both sides by cos(1):
4sinxcosx^2/cos(1) - cosx = 1/cos(1)
Rearranging terms:
cosx(4sinxcosx^2/cos(1) - 1) = 1/cos(1)
Finally, we can use the identity cos2x = 2cos^2x - 1 to simplify the left-hand side further:
(2cos^2x - 1)(4sinxcosx^2/cos(1) - 1) = 1/cos(1)
We can then divide both sides by (4sinxcosx^2/cos(1) - 1):
2cos^2x - 1 = 1/cos(1) (4sinxcosx^2/cos(1) - 1)
And finally, we can solve for cosx:
cosx = 1/2 + 1/2cos(1) (4sinxcosx^2/cos(1) - 1)
This is the solution to the equation.
Classify the system of equations
Answer:
The correct answer is: parallel
The two equations are in the form of y = mx + b and y = mx + b, which are the standard forms of linear equations.
and the slope of the two equations are different, so they are not coincident and not intersecting. They are parallel lines that never meet, so the system of equations is parallel.
Graphing Lines How would you graph 10x-3y=15
Answer:
Step-by-step explanation:
To graph 10x-3y=15, start by rearranging the equation to the slope-intercept form of y = mx + b, where m = the slope and b = the y-intercept. 10x-3y=15 becomes 3y = 10x - 15. Solve for y by dividing both sides by 3 to get y = (10/3)x - 5.
Now that the equation is in the slope-intercept form, draw a graph on a coordinate plane. Start by plotting the y-intercept at (0, -5). Next, use the slope of 10/3 to determine the rise and run of the line. The rise is +10 and the run is +3. Starting at the y-intercept, draw a line that moves up 10 and to the right 3, and continue doing this until you reach the end of the graph. This line is the graph of 10x-3y=15.
Answer:
y=10/3x+5
(0,5), (3,15)
Step-by-step explanation:
First, put the graph in slope-intercept form. We can do this by subtracting 10x from both sides.
-3y=-10x-15
Next, we divide by -3.
y=10/3x+5
If you don't know how to graph an equation with slope-intercept form,
it is in the format of y=mx+b, where m is the slope (in this case, 10/3) and b is the y-intercept (in this case 5, or (0,5)). First graph the y-intercept.
(0,5).
Then implement the slope. Here we would go up by 10 and then go right by 3. This makes our second point (3,15).
Now that we have two points (0,5) and (3,15), just construct your line.
Your business requests a 3-month loan for
$450,000. What will be the interest paid at the
end of the term if the business risk percentage is
assessed at 2.0% and LIBOR is at 2.8%?
interest paid = $ [?]
Round to the nearest hundredth.
Enter
PH
The interest paid at the term end will be $5400.
What is interest and its types(Simple and compound interest)?
Interest is the cost of borrowing money, where the borrower pays a fee to the lender for the loan. The interest, typically expressed as a percentage, can be either simple or compounded. Simple interest is based on the principal amount of a loan or deposit. In contrast, compound interest is based on the principal amount and the interest that accumulates on it in every period. Simple interest is calculated only on the principal amount of a loan or deposit, so it is easier to determine than compound interest.
The formula for these are
Simple Interest= P×r×n
where:
P=Principal amount
r=Annual interest rate
n=Term of loan, in years
Compound Interest=P×(1+r)^t−P
where:
P=Principal amount
r=Annual interest rate
t=Number of years interest is applied
Here,
Interest rate will be risk percentage + LIBOR
i.e.4.8%
Hence, the interest can be found by using formula for simple interest
Therefore,
SI=P*r*t
=$450000*0.048*0.25 (Time is 3 month or 0.25 years.)
SI (Interest paid)=$5400
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The total interest paid for the period of three months will be $5225 on the loan amount of $450000.
What is interest?
The interest is the charges levied on the amount which we borrow from any bank for a particular period of time.
Here in the question given data is
P= $450000
R=2.2%+2.8%=5%
T=1/4 years or three months
So from the simple interest formula
SI= PNR/100
SI=15000×5×1/`100×4
SI=$5625
Hence the total interest paid for the period of three months will be $5225 on the loan amount of $450000.
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In ΔEFG, e = 690 inches, ∠F=94° and ∠G=46°. Find the length of g, to the nearest inch.
If In ΔEFG, e = 690 inches, ∠F=94° and ∠G=46° then the length of g is 800 inches.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The sum of interior angles of a triangle are 180 degrees.
In ΔEFG, e = 690 inches, ∠F=94° and ∠G=46
We need to find the ∠E then the length of g.
∠E+∠F+∠G=180
∠E+94+46=180
∠E+140=180
∠E=40 degrees
By using sinE rule we have to find the length of g.
SinE/E=sinG/G
sin40/690=sin46/x
0.642/690=0.72/x
0.00093=0.72/x
x=0.72/0.0009
x=800 inches
Hence, the length of g is 800 inches.
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Use technology to find points and then graph the function y = x + 2| -4,
following the instructions below.
Plot at least five points that fit on the axes below. Click a point to delete it.
-10
done plotting points
63
-3
A graph of the absolute function y = |x + 2| - 4 with five points that fit on the axes is shown in the image attached below.
What is an absolute value function?In Mathematics, an absolute value function is a type of function that is composed of an algebraic expression, which is placed within absolute value symbols and it typically measures the distance of a point on the x-axis to the x-origin (0) of a cartesian coordinate (graph).
Next, we would use an online graphing calculator to plot the given absolute value function y = |x + 2| - 4 as shown in the graph attached below.
By observing critically the graph (see attachment), the five ordered pairs (points) that fit on its axes include the following:
Ordered pair = (-6, 0).Ordered pair = (-4, -2).Ordered pair = (-2, -4).Ordered pair = (0, -2).Ordered pair = (2, 0).Read more on absolute value function here: brainly.com/question/28308900
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Find the solutions of the equation on the indicated interval. List the smaller answer first. Round to 3 decimal places. 3 cos ( x ) + 4 = 5 with − π ≤ x ≤ π .
Answer:
Step-by-step explanation:
The solutions to this equation are x = 1.273 and x = -0.273.
When x = 1.273, 3 cos (x) + 4 = 5.
When x = -0.273, 3 cos (x) + 4 = 5.
Rounding to 3 decimal places, the solutions to the equation on the indicated interval are x = 1.273 and x = -0.273.
An isosceles triangular prism can be unfolded into the net shown
below. Find the lateral surface area of the triangular prism.
8.3 in
9 in
7 in
17 in
The latera surface area of the triangular prism is 425 inches².
How to find the lateral surface area of a triangular prism?The isosceles triangular prism is unfolded into the net shown below. Therefore, the lateral surface area of the triangular prism can be found as follows:
The lateral surface area of the triangular prism is the product of the perimeter of the triangle and the height of the prism.
Hence,
lateral surface area of the triangular prism = ph
where,
p = perimeter of the triangleh = height of the prismTherefore,
lateral surface area of the triangular prism = (9 + 9 + 7)17
lateral surface area of the triangular prism = 25 × 17
lateral surface area of the triangular prism = 425 inches²
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What is the domain and range of the function ?
The domain of the function is (-∞, 1), (1, ∞).
the correct option is (C)
What is domain and Range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
Given:
As, we know the domain are the input values in the function.
So, From the graph the domain starts from -∞ to reach 1 then there is change in slope.
Next the domain starts from to ∞.
Now, range is the output value as (-4, 1).
Hence, the domain is (-∞, 1), (1, ∞).
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Guys please help me!!!!!
1)what is 50% of R1,00
2)what is 0,5 of R1, 00.
3) what is 1\2 of R1,00
1.) The 50% of R100 = R50
2.) The 0.5 of R100 = R50
3.) The ½ of R100 = R50.
What is percentage?Percentage is defined as the part of a whole which is represented per 100 and the symbol which is used is %.
The 50% of R100 = 50/100 × 100/1 = R50The 0.5 of R100 = 0.5 × 100 = R50The ½ of R100 = 1/2× 100 = R50Therefore, is can be concluded since the same value was gotten that 50% = 0.5 = ½.
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What is the slope of the line shown below?
10
(-5, -1)
10
-10
y
10
5
(5, 11)
10
15
O
A.
B.
O C.
O D.
96
The slope of the line is C) [tex]\frac{6}{5}[/tex].
What is slope?
Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined. The difference between the line's y and x coordinate changes is known as the slope of the line. Any two distinct places along the line can be used to determine the slope of any line.
Here the given point is [tex](x_1,y_1)=(-5,-1)[/tex] and [tex](x_2,y_2)=(5,11)[/tex]
Now using slope formula then,
=> Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> Slope m = [tex]\frac{11-(-1)}{5-(-5)}[/tex]
=> slope m = [tex]\frac{11+1}{5+5}[/tex]
=> slope m = [tex]\frac{12}{10}[/tex]
=> slope m = [tex]\frac{6}{5}[/tex]
Hence the slope of the line is C) [tex]\frac{6}{5}[/tex].
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A store is offering 25% off all shoes Declan purchase shoes and clothes the expression representing his total cost including 8% tax is C+ parentheses one -0.25 parentheses S +0.08 bracket C plus parentheses one -0.25 parentheses as bracket
The term that represents the cost of the shoes after the discount is (1 - 0. 025)s. Option D
What are algebraic expressions?Algebraic expressions are described as mathematical expressions that consist of factors, constants, variables, terms and coefficients.
They are also made up of arithmetic operations, which includes;
DivisionMultiplicationAdditionBracketSubtractionParentheses, etcFrom the information given, we have that there was a 25% discount on all the shoes Declan bought
Given the expression;
c + ( 1 - 0.25)s + 0. 08[c + (1 -0.25)s ]
expand the bracket
c + s - 0. 25s + 0. 08( c - s - 0. 25s)
expand the parentheses
c + s - 0. 25s + 0. 08c - 0. 08s - 0.02
But for the cost of the shoes after the 25% discount, we have;
(1 - 0. 025)s
Hence, the expression is (1 - 0. 025)s
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List all subsets of the given set. {Lennon, McCartney}
{ }, {Lennon}, {McCartney}, {Lennon, McCartney}
{Lennon}, {McCartney}, {Lennon, McCartney}
{ }, {McCartney}, {Lennon, McCartney}
{ }, {Lennon}, {Lennon, McCartney}
{ }, {Lennon}, {McCartney}
The list of all sets which are subsets of the given set; {Lennon, McCartney} as required is; { }, {Lennon}, {McCartney}, {Lennon, McCartney}.
What are the subsets of the set; {Lennon, McCartney}?It follows from the task content that the list of all subsets of the given set is to be determined.
It is noteworthy to know that the empty set, {} is a subset of all sets.
Also, if all the elements of a set A are present in another set B; it can be inferred that the set A is a subset of set B.
On this note, the list of all sets which are subsets of the given set; {Lennon, McCartney} is; { }, { Lennon }, { McCartney }, { Lennon, McCartney }.
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I Fill in the Blanks :-
1) 39Km = ______m
Answer:
39000meter
hope it will help you
Find the factors of each number.
36
Answer:
1, 2, 3, 4, 6, 9, 12, 18, and 36.
Step-by-step explanation:
All of these are factors of 36.
They can all be divisors with no remainder
Which choice correctly expresses the number below in scientific notation? 0.000611
D. 6.11 * 10 ^ - 5
C. 6.11 * 10 ^ - 3
OE. 6.11 * 10 ^ - 4
OF. 611 * 10 ^ - 6
B. 611 * 10 ^ - 4
A. 61.1 * 10 ^ - 5
0.000611
The scientific notation of the given number is 6.11×10⁻⁴. Therefore, option E is the correct answer.
What is scientific notation?Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.
The given decimal number is 0.000611.
0.000611 in scientific notation, we get
6.11×10⁻⁴
Therefore, option E is the correct answer.
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