The boat that sailed in the direction closest to due north is the both that has lesser angle to the vertical ,which is the boat that that sailed 30 miles west and 22 miles north.
How to find the boat that traveled in the direction closest to due northGiven data
One boat sails 30 miles west and 22 miles north
Another boat sails 55 miles west and 40 miles north
Say boat A sail 30 miles west and 22 miles north while boat B sails 55 miles west and 40 miles north
Boat A
let the angle boat A made with the vertical be a. This is given as
tan a = 30 / 22
a = arc tan ( 30 / 22 )
a = 53.746 degrees
Boat B
let the angle boat B made with the vertical be b. This is given as
tan b = 55 / 40
b = arc tan ( 55 / 40 )
b = 53.973 degrees
Comparing angle a and angle b shows that angle a is lesser hence boat A is the boat that sailed in the direction closest to the north
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What is the solution to the system of equations?A. The solution is (2, 7) because the solution to the system must satisfy both equations simultaneously.B. The solution is (1, 6) because the solution to the system must satisfy one equation or the other equation.C. The solution is (3, 5) because the solution to the system must represent the y-intercepts of both equations.D. The solution is (-1.5, -5) because the solution to the system must represent the x-intercepts of both equations.
GIven a graph.
to find the solution of the system of equaion.
The intersection point is the soution of the system of equation in the graph.
thus, (2,7) is the solution of the given system of equation.
The answer is, option A The solution is (2, 7) because the solution to the system must satisfy both equations simultaneously.
On your own paper, graph the system of equations and identify the solution.=2−4=−12+1
The Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
You have the first line:
[tex]=2x-4[/tex]You can identify that the y-intercept is:
[tex]b_1=-4[/tex]You can find the x-intercept substituting the following value of "y" into the equation of the line:
[tex]y=0[/tex]And, after the substitution, you can solve for "x":
[tex]\begin{gathered} 0=2-4 \\ 4=2x \\ \\ \frac{4}{2}=x \\ \\ x=2 \end{gathered}[/tex]Now you know that the first line passes through these points:
[tex]\begin{gathered} (0,-4) \\ (2,0) \end{gathered}[/tex]Then, you can graph it.
Given the second line:
[tex]y=-\frac{1}{2}x+1[/tex]You can identify that:
[tex]b_2=1[/tex]And you can find the x-intercept by following the same procedure applied for the first line:
[tex]\begin{gathered} 0=-\frac{1}{2}x+1 \\ \\ -1=-\frac{1}{2}x \\ \\ (-1)(2)=-x \\ \\ -2=-x \\ x=2 \end{gathered}[/tex]Then, this line passes through these points:
[tex]\begin{gathered} (0,1) \\ (2,0) \end{gathered}[/tex]Now you can graph it.
See the graph below:
By definition, when the lines intersect, the solution of the System of equations is the point where the two lines intersect.
The answer is: First option.
What numbers are between 2/10 and 75% on a number line?
Solve for x to the nearest tenth.
Answer:
Step-by-step explanation:
first from the lower triangle, the unknown length is [tex]\sqrt{10^2-4^2} =\sqrt{100-16}=\sqrt{84}[/tex] so then x is equal to [tex]\sqrt{84-4^2}=\sqrt{68}[/tex] or about 8.2
A gymnast joined a yoga studio to improve his flexibility and balance. He pays a monthly fee and a fee per class he attends. The equation y = 20 + 10x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.
Which graph represents this situation?
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 20 through the point 1 comma 30
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 20 through the point 1 comma 10
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point 1 comma 30
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point one half comma zero
The graph of the linear equation y = 20 + 10x for the given scenario is attached below.
The Cartesian coordinates of a specific point on the Euclidean plane can be thought of as each solution inside the scenario involving two variables.
A linear equation's solutions define a line inside the Euclidean plane, and each line may be viewed as the aggregate of all solutions to a linear model with two variables. This is how this category of equations came to be known as "linear." The solutions to a system of equations with integer variables collectively constitute a hyperplane in the Euclidean space with size n. (a subdomain of dimension n₁).Because linear equations may frequently accurately represent non-linear systems, they are used extensively in all branches of mathematics as well as in physics and engineering.Here the equation is given as y = 20 + 10x
Therefore at x = 0 , y = 20 and at y = 0, x = -2
This represents that the fixed monthly fee is 20 and the daily fee is 10.
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Answer:
i think its c because every time the it goe it goes were its suposefd to
Step-by-step explanation:
hope this helps dont minf my typing
If BC=5 in and AB=12in. Find the exact circumference of the circle.
EXPLANATION
We can get the circunference of the circle by applying the Pythagorean Theorem as shown as follows:
[tex]\text{AC}^2=AB^2+BC^2[/tex]Repalcing terms:
[tex]AC^2=12^2+5^2=144+25=169[/tex]Aplying the square root to both sides:
[tex]AC^{}=\sqrt[]{169}=13\text{ inches}[/tex]The circunference is 13 inches.
$15 per hour is the basic rate at a factory. After a 48-hour basic work week, overtime is paid time and a half.
(a) If no one worked overtime and the factory paid $15 840 in wages one week, how many workers are in the factory?
(b) During another week, a worker in the factory earns $810 in wages for himself. How many hours did he work for?
Answer:
(a) There are 22 workers are available in the factory.
Step-by-step explanation:
(a) Let the number of workers in the factory be x.
Basic rate = $15
Working hours in a week = 48 hours
Total wages in a week = $ 15840
If no overtime is to be paid then according to question,
Amount paid to 1 worker = 48 X 15 = $ 720
Amount paid to x worker = 720x
15840 = 720
x = 15840/720
x = 22
June, Gavyn and Alex share some sweets in the ratio 3:5:4. June gets 39 sweets. How many sweets are there altogether?
Answer:
156
Step-by-step explanation:
This is a question in proportion and ratio
Since the ratio in which the sweets are shared is 3: 4 : 5 we can say that the proportion of total sweets that June gets is 3/(3 + 4 + 5) = 3/12 = 1/4
Let the total number of sweets be S
Then 1/4th of this will be June's share and we are given that the actual number June gets is 30
So we have 1/4 x S = 39
Multiplying both sides by 4:
4 x 1/4 x S = 39 x 4
S = 156
So there were 156 sweets altogether
tia charges a set up fee of 2$ and then 0.75 a square foot to power wash driveways which equation properly displays the amount she charges to power wash a driveway
Step-by-step explanation:
0.75x+2
2 is taken and 0.75 is not optional therfore
0.75=x(per square foot) =0.75x
and
$2 fee is required
so they must pay 2 dollars plus 0.75 everysquare foot
answer:
0.75x+2
My little sister decided that she had to have a new Softball so she went to the bank where she holds her money and emptied it out completely in order to get my recent need it for the ball the money was in the form of 45 coins with me your personal little heavy for her to carry and also took a long time for her to come out the money at the store I had to take her and I got bored wedding how many pennies nickels dimes quarters and a half dollars did she have with her
Answer:
you know it's a very good question
Step-by-step explanation:
I have no idea
Plot 2.379 on a number line on which the long tick marks are tenths.
A number line which represents the given number (2.379) is plotted and shown in the image attached below.
What is a place value?A place value can be defined as a numerical value which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsUnitTensHundredsThousands.Tens of thousands.Hundred of thousands.Millions.Tens of millions.Hundreds of millions.Billions.What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.
In conclusion, the number (2.379) should be placed close to 4 as plotted on the number line shown in the image attached below.
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1. Identify 4x + 2(x -6) = 7 as an equation, an expression, or neither A. Expression B. Equation C. Neither
Answer:
Equation
Step-by-step explanation:
Equations require equal signs.
Please help I’ll mark you as brainliest if correct!!
Slope intercept form for points through (0,-4) and (2,1)
Answer:
y = (5/2)x - 4
Step-by-step explanation:
(0, -4) and (2, 1)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 1 - (-4) 1 + 4 5
m = ------------- = ------------ = --------- = --------
x₂ - x₁ 2 - 0 2 2
y - y₁ = m(x - x₁)
y - (-4) = (5/2)(x - 0)
y + 4 = (5/2)x - 0
-4 -4
----------------------------
y = (5/2)x - 4
I hope this helps!
need help answering
ieven
raph of the fucnction
ind
quation of the fuctcion
xpolanation
s we see it i s the graph of exponential function.
from graph we find point (0 , 2)
now , we substitute this point to find the equation.
[tex]\begin{gathered} y=0.5^x+1 \\ y=0.5^0+1 \\ y=1+1 \\ y=2 \end{gathered}[/tex]so , this exponential function satisfy the point.
Final Answer
ence , the correct option is 1,.
one hundred and twenty one million, two hundred and twelve thousand and eighty-eight in number
I need help with the following
Let x be the number of miles and y the total cost; therefore, the equations that model the two plans are
[tex]\begin{gathered} PlanA: \\ y_A=30+0.20x \\ PlanB \\ y_B=50 \end{gathered}[/tex]Then, set y_A=y_B as shown below
[tex]\begin{gathered} y_A=y_B \\ \Rightarrow30+0.20x=50 \\ \Rightarrow0.20x=20 \\ \Rightarrow x=\frac{20}{0.20}=100 \end{gathered}[/tex]Therefore, once the mileage is greater than 100 miles, the total cost of plan B will be less than that of plan A.
The answer is 100 miles.48 candies 12 are red and 14 are yellow what is the raito to red to yellow
Answer:
12:14
Step-by-step explanation:
RED=12
YELLOW=14
what is the ratio red to yellow u put the amount of red first then the amount of yellow
If jack drives 876 miles to Mexico Tuesday, and 986 miles wens day , what-is the total miles he drove?
The distance travelled by Jack to Mexico on Tuesday is 876 miles.
The distance travelled by Jack to Mexico on Wednesday is 986 miles.
To determine the total miles he drove ,
The sum of the distance travelled by Jack to Mexico on Tuesday and Wednesday.
Let the total miles drove is denoted as T.
[tex]T=876+986[/tex][tex]T=1862\text{ miles.}[/tex]Thus the total miles drove is 1862 miles.
The animals at a safari park include gorillas, buffalo and wallabies. There are 24 more buffalo than there are gorillas. There are 7 times as many wallabies as there are gorillas. There are the same number of buffalo as there are wallabies. How many gorillas are there at the safari park?
The number of gorillas at the safari park is 4.
Let the number of gorillas at the safari park be x.
It is given that there are 24 more buffalo than there are gorillas.
Number of buffalo at the safari park = 24 + x
There are 7 times as many wallabies as there are gorillas.
Number of wallabies at the safari park = 7x
Now, the number of buffalo is the same as the number of wallabies.
So, we equate their numbers to find the value of x i.e. number of gorillas.
24 + x = 7x
7x - x = 24
6x = 24
x = 4
Therefore, the number of gorillas at the safari park is 4.
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Find two numbers that the quotient 3,382/6 is between
The most appropriate choice for division will be given by
Quotient of [tex]\frac{3382}{6}[/tex] is between 563 and 564
What is division?
The process of dividing a certain number into equal parts is called division
The answer obtained after division is called quotient and the other part is the remainder. The number which is divided is called the dividend and the number by which the dividend is divided is called divisor.
General rule of division
Divisor x Quotient + Remainder = Dividend
Here,
Quotient of [tex]\frac{3382}{6}[/tex] = 563
563 is between 562 and 564
So, quotient of [tex]\frac{3382}{6}[/tex] is between 563 and 564
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A runner has a track lap time of 1 minute while at a run, 4 minutes while at a jog, and 7 minutes while at a walk. If 2/5 of the lap is paced at a run, 1/3 at a jog, and 4/15 at a walk, what is the total track lap time of the runner? Write the solution as a mixed number or a fraction in lowest terms.
The track lap time of the runner will be 3 3/5 minutes.
How to illustrate the information?From the information, the runner has a track lap time of 1 minute while at a run, 4 minutes while at a jog, and 7 minutes while at a walk. If 2/5 of the lap is paced at a run, 1/3 at a jog, and 4/15 at a walk.
The track lap time of the runner will be:
= (2/5 × 1 minute) + (1/3 × 4 minutes) + (4/15 × 7 minutes)
Note that 1 minute = 60 seconds
(2/5 × 1 minute) + (1/3 × 4 minutes) + (4/15 × 7 minutes)
= 24 seconds + 80 seconds + 112 seconds
= 216 seconds
= 3 minutes 36 seconds.
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Complete the frequency table for the following set of data. =
Given the set of data:
12, 4, 11, 3, 4, 0, 13, 13, 2, 6, 11, 0, 10, 11, 3, 4, 0, 10, 13, 2, 11, 9.
Let's complete the given frequency table using the set of data given.
Frequency can be said to be the number of times a number occurs in a set of data.
hus, we have:
• 0 - 2
ubmbers between 0 - 2 in the data set: 0, 2, 0, 0, 2 ==> 5 times
• 3 - 5
3 - 5: 4, 3, 4, 3, 4, ==> 5 times
• 6 - 8:
6 - 8: 6, ==> 1 time
• 9 - 11:
: 9 - 119, 11, 11, 10, 11, 10, 11, 9 ==> 7 times
• 12 - 14:
12 - 134: 12, 13, 13, 13 =3 ==> 4 times.
Therefore, the complete table is:
Help ASAP solve for the value of Z
Answer:
z = 6
Step-by-step explanation:
The angle in the middle is a right angle with a measure of 90°
Together, all three angles, makes a stright angle which is measured 180°.
So we can write the following equation to find the value of z:
5z + 1 + 59 = 90 (we don'thave to include the middle angle since we already its measure)
add like terms
5z + 60 = 90 subtract 60 from both sides
5z = 30 divide both sides by 5
z = 6
Josh's mom gave him money to spend at an
amusement park. So far, he's used 3/10 of the
money on games and 1/4 of the money on rides.
What fraction of the money does he have left?
Give your answer as a fraction in simplest form.
Answer:
9/20
Step-by-step explanation:
3/10 + 1/4
find a common denominator, which is 20 here
6/20 + 5/20 = 11/20 he used
left over is 9/20
Please help me help help me please help help me
ANSWER
t = 10.27
EXPLANATION
Step 1: Given
[tex]500e^{0.0675t}\text{ = 1000}[/tex]Step 2: Divide both sides by 500
[tex]\begin{gathered} \frac{500e^{0.0675t}}{500}\text{ = }\frac{1000}{500} \\ e^{0.0675t}\text{ = }2 \end{gathered}[/tex]Step 3: Take the natural logarithm of both sides
[tex]\begin{gathered} 0.0675t\text{ = ln 2} \\ 0.0675t\text{ = }0.69314718056 \end{gathered}[/tex]Step 4: Divide both sides by 0.0675
[tex]\begin{gathered} \frac{0.0675t}{0.0675}\text{ = }\frac{0.69314718056}{0.0675} \\ t\text{ = 10.268847} \end{gathered}[/tex]Hence, t = 10.27 (rounded to the nearest hundredth).
18) Before Santiago donated 84 of his books to the Goodwill store, he had twice as many books
as Alex. After the donation, Alex has twice as many books as Santiago. How many books
does Alex have?
Alex has 56 books.
Let the number of books Santiago has be x. So, after the donation, the number of books with Santiago is (x - 84). Let the number of books with Alex be y.
Before the donation -
x = 2y : equation 1
After the donation -
y = 2(x - 84) : equation 2
Keep the value of x from equation 1 in equation 2
y = 2(2y - 84)
Performing multiplication on Right Hand Side of the equation
y = 4y - 168
Rearranging the equation
4y - y = 168
Performing subtraction on Left Hand Side of the equation
3y = 168
y = 168 ÷ 3
Performing division on Right Hand Side of the equation
y = 56
Therefore, Alex has 56 books.
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The perimeter of the rectangle below is 176 units. Find the length of side BC.
Write your answer without variables
Answer:
(5y-3)+(4y+1)+(5y-3)+(4y+1) = 176
18y - 4 = 176
18y = 180
y = 10
BC = 4y + 1 = 4(10) + 1 = 41 units
Answer this question pls
Answer:
No
Step-by-step explanation:
Two different inputs can not have the same output. Although they can have two different outputs and the same input the reverse is not a thing. Each input has only one output, and the fact that it is the same output does not matter. It is supposed to be a function and by definition, functions are a special kind of relations allowing precisely one output for each input.
The slope of the line below is
-1 over 7
Write a point-slope equation of the line
using the coordinates of the labeled point
The point slope form of the given equation is [tex](y-3)=\frac{-1}{7} (x-3)[/tex] .
What is a equation of line?The equation y = mx + c is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis).
If a line passes through the point with slope m, then the point slope form of the line is
[tex](y-y_{1} )=m(x-x_{1} )[/tex]
Given that,
The slope of the line m = [tex]\frac{-1}{7}[/tex].
From the graph it is clear that the line passes through the point (3,3).
Substitute x₁= 3, y₁= 3 and in the above equation.
[tex](y-3) = \frac{-1}{7}(x-3)[/tex]
Hence, The point slope form of the given equation is [tex](y-3)=\frac{-1}{7} (x-3)[/tex] .
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The above question is not complete.