a ship leaves a harbor. it travels 35 miles due east and then adjusts its course 40 degrees northward. after traveling 45 miles in that direction,The distance from the ship's point of departure is approximately 59.9 miles.
To determine the distance from the ship's point of departure, we must first break down the distance traveled into x and y components. Initially, the ship traveled 35 miles due east, which can be represented as 35 miles on the x-axis. When the ship adjusted its course 40 degrees northward, it traveled 45 miles in that direction. This can be represented as 45 miles in the y direction, forming a triangle with the origin (point of departure). Using the Pythagorean theorem, we can calculate the hypotenuse of the triangle, which is equal to the distance from the point of departure. The hypotenuse of the triangle is equal to the square root of (35^2 + 45^2), which is equal to approximately 59.9 miles. Therefore, the distance from the ship's point of departure is approximately 59.9 miles.
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HELP QUICK!!
An item on sale costs 35% of the original price. If the original price was $60, what is the sale price?
use the graphs of f and g to graph h(x) = (f + g)(x). (graph segments with closed endpoints.)
Different x values must be taken into account in order to graph h (x). So the graph of the h(x) is given below.
In the given question, we use the graphs of f and g to graph h(x) = (f + g)(x).
A diagram that compares the fluctuation of one variable to that of one or more other variables, such as a collection of points, lines, line segments, curves, or regions.
The graph is given below:
h (x) = (f + g) (x)
The function h(x) can be written as
h (x) = f (x) + g (x)
Different x values must be taken into account in order to graph h (x).
h (0) = f (0) + g (0) = 2 - 1 = 1
h (1) = f (1) + g (1) = 3 + 0 = 3
h (2) = f (2) + g (2) = 1 + 0.5 = 1.5
h (3) = f (3) + g (3) = 2 + 0 = 2
So the graph of the h(x) is given below:
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Write a triangle congruence statement
Answer:
1. ΔCDE≅ΔJEH
2. ΔIHG≅ΔIHD
3. ΔIHJ≅ΔIXT
4. ΔIJT≅ΔJIH
5. ΔEFD≅ΔDKJ
6.ΔGWY≅ΔGHI
solve each equation by completing the square
[tex]x^{2} -34x+289=0[/tex]
After completing the square, the equation is ____ and the solution is _________
WHOEVER ANSWERS CORRECTLY WILL BE MARKED BRAINLIEST
Answer:
x = 17------------------------------------------------
Complete the square as follows:
x² - 34x + 289 = 0x² - 2*17*x + 17² = 0 Identity (a ± b)² = a² ± 2ab + b²(x - 17)² = 0x - 17 = 0 Square root both sidesx = 17if you use 1 pound of mirepoix in a recipe that yields 1 gallon of soup, how much mirepoix do you need to make 31/2 gallons of soup?
we need 31/2 pounds mirepoix to make 31/2 gallons of soup.
let we need x% (percent) of mirepoix to make 1 gallon of soup
given we have 1 pound of mirpoix which yeilds 1 gallon soup of soup
so total amount of mirepoix that required in the solution is = [tex]\frac{x}{100} *1 pound[/tex]
so x/100 = 1 gallon / pound
we will use this equation for further calculation
let we need y pounds of mirepoix to make 31/2 gallon of soup ans we know that x% of mirepoix is required for this solution.
so [tex]\frac{x}{100} * y = 31/2[/tex]
ans in the above equation x/100 =1 gallon / pound
so 1 * y= 31 /2
and hence y = 31/2 pounds
so we need 31/2 pounds of mirepoix to form requied amount of soup.
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Given g(x)=-5x+2 find g(-4)
Answer:_18
replace _4 instead of x
-5*-4=_20
_20+2=_18
Step-by-step explanation:
What is the first quartile of the given data set?
The value of first quartile of the given data set is 2.5
What is first quartile?The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order.
Given is a data set,
According to the data,
The lower quartile is between 0 and 2.5, which under 25% of the data.
Hence, The value of first quartile of the given data set is 2.5
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here is a famous problem: nn guests arrive at a party. each person is wearing a hat. we collect all hats and then randomly redistribute the hats, giving each person one of the nn hats randomly. what is the probability that at least one person receives his/her own hat?hint: use the inclusion-exclusion principle.
The probability that at least one person receives his/her own hat is 1 - (1/n)^n, using the inclusion-exclusion principle.
The inclusion-exclusion principle states that the probability of event A or B occurring is equal to the probability of event A plus the probability of event B minus the probability of event A and B occurring. In this case, the probability of at least one person receiving his/her own hat is the probability of one person receiving his/her own hat plus the probability of two people receiving their own hats minus the probability of three people receiving their own hats, and so on. This can be expressed mathematically as 1 - (1/n)^n, where n is the number of guests. This formula can be applied to any situation where a random event is being repeated multiple times with the same set of outcomes.1 - (1/10)^10 = 0.99.
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You just signed a 2 years lease for a one bedroom apartment in Brooklyn. The rent is $2,657 per month pulse $200 security deposit. Thinking long-term, you are wondering if it is better to rent or own a property. How will the total amount of rent you pay change over time?
After the end of the lease period the pay, the rent would increase to $3030.83 approx.
What is a Lease agreement?A lease is a legal agreement by which the owner of a building, a piece of land, or something such as a car allows someone else to use it for a period of time in return for money.
Given here, a 2-year lease is - $2,657 per month plus a $200 security deposit. Now, the average increase in the rate in the U.S is 14.07%
thus, at the end of the two-year lease period, the new rent would be
= (1+14.07/100) × $2,657
= $3030.83
Hence, the new rent with a security deposit is $3030.83 + security deposit.
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suppose you want to encrypt the message 10101111 by encrypting the decimal number that corresponds to the message. what is the decimal number
To find the decimal number that corresponds to the message "10101111", you can convert the binary number to decimal.
By using the following formula:
decimal = [tex]sum(binary[i] X 2^{(n-i-1)})[/tex]
binary = converting binary number
i = index of the current digit in the binary number
n = total number of digits in the binary number
[tex]2^{(n-i-1)}[/tex] is the corresponding power of 2
use the following steps to convert the binary number "10101111"
Calculate the decimal value for each digit in the binary number:
binary[0] = 1, [tex]2^{(8-0-1)}[/tex] = [tex]2^7[/tex] = 128
binary[1] = 0, [tex]2^{(8-1-1)}[/tex] = [tex]2^6[/tex] = 64
binary[2] = 1, [tex]2^{(8-2-1)}[/tex] = [tex]2^5[/tex] = 32
binary[3] = 0, [tex]2^{(8-3-1)}[/tex] = [tex]2^4[/tex] = 16
binary[4] = 1, [tex]2^{(8-4-1)}[/tex] = [tex]2^3[/tex] = 8
binary[5] = 1, [tex]2^{(8-5-1)}[/tex] = [tex]2^2[/tex] = 4
binary[6] = 1, [tex]2^{(8-6-1)}[/tex] = [tex]2^1[/tex] = 2
binary[7] = 1, [tex]2^{(8-7-1)}[/tex] = [tex]2^0[/tex] = 1
Adding decimal values for each digit
Total decimal value = 1128 + 064 + 132 + 016 + 18 + 14 + 12 + 11
= 128 + 0 + 32 + 0 + 8 + 4 + 2 + 1
= 175
Hence, the decimal number that corresponds to the binary number "10101111" is 175.
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Subtract the expressions.
(7.43n − 2.2) − (6 + 10.5n)
−30.70n − 4.5
−3.07n − 8.2
9.63n − 4.5
17.93n + (−8.2)
The solution to the expression is (b) -3.07n - 8.2
How to subtract the expressions?From the question, we have the following parameters that can be used in our computation:
(7.43n − 2.2) − (6 + 10.5n)
Remove the brackets
So, we have
(7.43n − 2.2) − (6 + 10.5n) = 7.43n − 2.2 − 6 - 10.5n
Evaluate the like terms
(7.43n − 2.2) − (6 + 10.5n) = -3.07n - 8.2
Hence, the solution is (b) -3.07n - 8.2
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Moussa is younger than Sophia. Their ages are consecutive even integers. Find Moussa's age if the product of their ages is 24.
Moussa's age if the product of their ages is 24 is 4 years.
How to calculate their age?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Moussa is younger than Sophia. Their ages are consecutive even integers.
Let the ages be x and x + 2.
This will be illustrated as:
x(x + 2) = 24
x² + 2x = 24
x² + 2x - 24 = 0
x² + 6x - 4x - 24 = 0
x(x + 6) -4(x + 6) = 0
x - 4 = 0
x = 4
x + 2 = 4 + 2 = 6
The ages are 4 and 6 years.
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If the product of Sophia age and Moussa age is 24, the age of Moussa is 4 years.
How to find the Moussa's age?Moussa is younger than Sophia. Their ages are consecutive even integers.
The product of there ages is 24. Moussa's age can be found as follows:
Even numbers are those numbers that can be divided into two equal groups or pairs and are exactly divisible by 2.
Hence,
Let
x = age of Moussa
x + 2 = age of Sophia
Hence, the product of their age will be as follows:
x(x + 2) = 24
x² + 2x = 24
x² + 2x - 24 = 0
lets factorise the quadratic equation. The numbers one can multiply to get -24 and add to get 2 are -4 and 6. Therefore,
x² - 4x + 6x - 24 = 0
x(x - 4) + 6(x - 4) = 0
(x + 6)(x - 4) = 0
Therefore,
x = - 6 and x = 4
We can only use positive numbers.
Therefore, the age of Moussa is 4 years
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pls help having trouble!
Answer:
a is 30 degrees.
Step-by-step explanation:
The degree of a triangle is 180, which means that all the degrees in any triangle will always add up to 180. Since CB and DB are congruent, the angles C and D will be the same. This means that to get the answer, just subtract the value we already have from 180 and divide the sum by 2.
[tex]\frac{180-120}{2} = \frac{60}{2} = 30[/tex]
Please helpppp me with thisss
Answer:
d = 0
Step-by-step explanation:
We have the equation
7.5d = 2.5d
We divided both sides by factors and get
d = 0
Value of d is 0.
According to question
7.5d=2.5d
Lin divides each side by 2.5d
∴7.5d÷2.5d=2.5d÷2.5d
⇒3=1
which is not possible and Lin is doing wrong
Elena subtract 2.5d from each side
∴7.5d-2.5d=2.5d-2.5d
⇒5d=0
⇒d=0
So Elena is right and the value of d is 0.
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f(x)=2x^2
g(x)=x+1
prove fg(x)=gf(x)
Answer:
here is the answer with proper steps.
The tatue i 4. 6 meter high. The angle of elevation from the oppoite corner of the courtyard to the top of the tatue i 8
The statue is 4. 6 meter high. The angle of elevation from the opposite corner of the courtyard to the top of the statue is 8,Tan 8 = 4.6/opposite and opposite = 4.6/tan 8 = 5.8 meters
First, we calculate the opposite side of the triangle using the tangent function. To do this, we need to use the angle of elevation (8 degrees) and the height of the statue (4.6 meters). We use the tangent function to calculate this, which is written as:
tan 8 = 4.6/opposite
Solving for the opposite, we get:
opposite = 4.6/tan 8 = 5.8 meters
This means that the opposite corner of the courtyard to the top of the statue is 5.8 meters away.
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What is the equation of the linear function in point-slope form that passes through (6, 5) and has a slope of?
y-5=(x-6)
x-6=1/(x-5)
Answer:
y – 5 = m(x – 6)
Step-by-step explanation:
using y =mx +c as our guide line
Step 1 : identification of coordinates
(6,5) ;x1= 6,y1 = 5
step 2 : applying the formula
y – y1 = m(x – x1)
y – 5 = m(x – 6)
Angles 2 and 8 are what type of angles?
A. Same side interior angles
B. Alternate exterior angles
C. Alternate interior angles
D. Corresponding angles
Help!!!
Answer:
B. Alternate exterior angles
Step-by-step explanation:
Alternate exterior angles are angles that are outside two lines intersected by the transversal and are located on opposite sides of the transversal. Also, they have the same degree! So, the answer is B.
PLEASE HELP I AM SO BEHIND ON SCHOOL WORK !!!
Which equation represents the same line as the points in the table?
y=−3x+2y is equal to negative 3 x plus 2
y=−34x+83y is equal to negative 3 fourths x plus 8 thirds
y=2x−34y is equal to 2 x minus 3 fourths
y=−34x+2
Answer:
Use this site, it will help you in the long run.
Elie built a large rectangular vegetable garden that i 9 meter long and ha an area of 72 quare meter. What i the perimeter of Elie’ vegetable garden
Answer:
The perimeter of Elie's vegetable garden is 34 meters.
Step-by-step explanation:
The formula for area is: a=w*l.
A = area
W = width
L = length
If the length is 9 meters, then we know two of the values, the area, and the length. Substitute.
72=w*9
You can divide both sides by 9 to get the width, which is 8 meters.
To find perimeter, we add l+w+l+w, or 2l+2w. Substitute for our values:
2(9)+2(8)=34
The perimeter of Elie's vegetable garden is 34 meters.
PLEASE HELP!!!!! 90 POINTS!!!!!
Graph the following system of equations.
2x + 4y = 8
2x + 6y = 18
What is the solution to the system?
There is no solution.
There is one unique solution, (−6, 5).
There is one unique solution, (−4, 4).
There are infinitely many solutions.
Answer:
There is one unique solution, (−6, 5).
Step-by-step explanation:
2x + 4y = 8
2x + 6y = 18
2x + 4y = 8 ==> solve for 2x
2x + 4y - 4y = 8 - 4y
2x = 8 - 4y
2x + 6y = 18 ==> solve for 2x
2x + 6y - 6y = 18 - 6y
2x = 18 - 6y
8 - 4y = 18 - 6y ==> 2x = 8 - 4y and 2x = 18 - 6y
8 - 4y + 6y = 18 - 6y + 6y ==> solve for y by first adding 6y on both sides to
remove negative y
8 + 2y = 18 ==> simplify
8 - 8 + 2y = 18 - 8 ==> isolate y
2y = 10
y = 5
2x + 4(5) = 8 ==> substitute 5 for y in 2x + 4y = 8
2x + 20 = 8
2x - 20 + 20 = 8 - 20 ==> subtract 20 on both sides to isolate 2x
2x = -12
x = -6
x = -6, y = 5 ==> (6, 5)
Answer: There is one unique solution, (−6, 5).
At a school there are six lessons in a day.
In total, the six lessons last for 4 hours.
a) Assume that each lesson lasts the same amount of time.
How many minutes long is the final lesson?
Optional working
Answer:
40mins
Step-by-step explanation:
4hrsx60
=240mins
240mins/6 lessons
=40mins per lesson
thanks for helping me!
Answer:
<E=180-60=120
t=60 degrees
u=8
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The graphs in this problem that show continuous data are given as follows:
Top right.Bottom left.What are continuous and discrete graphs?Continuous and discrete graphs have different formats to show the data, which are presented as follows:
For a continuous data, the data shown is all the real numbers in an interval, hence a continuous graph is represented by solid lines. This means that the second and third graphs in this problem, that is, the top right and the bottom left graphs represent continuous data.
For discrete data, only certain values are represented in an interval, hence the graph of discrete data is composed only by dots, which is the case for the first and last graphs in this problem, that is, the top left graph and the bottom right graph.
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Which sentence does NOT contain an error in pronoun-antecedent agreement?
a. A large herd of buffalo thundered across the plain and left a cloud of dust in their wake.
b. When the crowd reached the center of town, the mayor was surprised by their size.
c.Our gymnastics team proved their skills during the individual floor exercises.
Answer:
a
Step-by-step explanation:
Each year the value of a car decreases by 12% of its value at the beginning of that year. The original value of the car is $20000. Calculate the value of the car at the end of 3 years
Answer:
The value of the car at the end of 3 years will be $13707.
Step-by-step explanation:
If the original value of the car is $20000, then after the first year, the value of the car will be $20000 - (12/100)*$20000 = $17600.
After the second year, the value of the car will be $17600 - (12/100)*$17600 = $15552.
After the third year, the value of the car will be $15552 - (12/100)*$15552 = $13707.
Therefore, the value of the car at the end of 3 years will be $13707.
FILL IN THE BLANK. the _______ _______ is a statement we are trying to find evidence to support.
Answer:
Alternative Hypothesis
(x + 2)(x+4)²
———————
(x+4)
Answer:
(x + 2)(x + 4)
Step-by-step explanation:
for the denominator we have (x + 2)(x + 4)(x + 4).
divide the denominator by (x + 4), you would be left with (x + 2)(x + 4).
Help asp thank you show your work if you want
Answer:
[tex]y=-\frac{2}{3}x+1[/tex]
Step-by-step explanation:
Parallel means same slope.
[tex]y=-\frac{2}{3}x+b[/tex]
[tex]5=-\frac{2}{3} (-6)+b[/tex]
5 = 4 + b
b = 1
[tex]y=-\frac{2}{3}x+1[/tex]
In a board of directors composed of 14 people, how many different ways can one chief
executive officer, one director, and one treasurer be selected?
Answer:
2184
Step-by-step explanation:
This question involves permutations. We can solve it using the formula
[tex]\frac{n!}{(n-r)!}[/tex]
where n=14 (because we are choosing from 14 people)
and r=3 (because we are choosing 3 people)
and we are using the permutation formula because the order or placement in which these 3 people are choosing matters (having a person 1 being a director is different from having person 1 being a chief executive officer)
14!/(14-3)!
= 14!/11!
= 14 x 13 x 12
= 2184