The distances of the ships makes a right angled triangle. Ship A sails at 25 mph in direction QP, towards north. Ship B sails at 14 mph in direction QR, towards east.
Therefore, the distance between the two ships at 1 P.M. would be the distance between PR.
Applying Pythagoras Theorem,
[tex]P^{2} +B^{2} = H^{2}[/tex]
[tex](PQ)^{2} + (QR)^{2} = (PR)^{2} \\PR= \sqrt{(PQ)^{2} + (PR)^{2} } \\= \sqrt{(25)^{2} + (14)^{2} } \\= \sqrt{821} mph[/tex]
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for the following exercises, find the lengths of the missing sides if side a is opposite angle a, side b is opposite angle b, and side c is the hypotenuse.
Using relations in a right triangle and the Pythagorean Theorem, it is found that the missing side lengths are as follows:
a = 14.4.c = 15.24.What are the relations in a right triangle?There are three relations in a right triangle, given as follows:
The sine of an angle of the triangle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle of the triangle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle of the triangle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.For this problem, we have that:
tan(A) = b/a.
Hence:
5/12 = 6/a
Applying cross multiplication, the side a is found as follows:
5a = 72
a = 72/5
a = 14.4.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
Hence the hypotenuse c is given as follows:
c² = 5² + 14.4²
c = sqrt(5² + 14.4²)
c = 15.24.
What is the missing information?For the triangle, we have that:
tan A = 5/12.b = 6.More can be learned about relations in a right triangle and the Pythagorean Theorem at https://brainly.com/question/26396675
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After how much time to the nearest minute Will the cost of plan a be equal to the cost of plan b
Let
y ----> total charge in a month
x ----> number of minutes
so
Plan A
y=0.21x+11
Plan B
y=0.10x+20
Equate both equations
0.21x+11=0.10x+20
solve for x
0.21x-0.10x=20-11
0.11x=9
x=9/0.11
x=81.82 minutes
Convert to hours and minutes
81.82 minutes=60+21.82=1 hour 22 min
therefore
the answer is option APlease help, I’ve been trying to do this for a couple of hours now but I can’t seem to figure it out.
The tables show a Linear function that represents your earnings y in dollars after x working hours
(Picture below)
What is the totals earnings for the 6th hour?
$
What is your hourly wage?
$
Answer:
total earnings at 6th hour: 111
hourly wage (slope): 18.5
Step-by-step explanation:
A linear function has a linear relationship, which essentially states as x increases by one, the y-value increases by some constant amount yielding a straight line.
The slope, or how much the y-value changes as x changes by 1 is generally written as: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We can choose any two points and this should yield the slope of the function, but it's a lot easier to choose y-values that are only separated by an x-value of one.
Let's say: [tex](x_1, y_1)=(4,\ 74)\text{ and }(x_2,y_2)=(5,\ 92.50)[/tex]
If we plug the values into the slope formula we just get: [tex]\frac{92.50-74}{5-4}=\frac{92.50-74}{1}=92.50-74[/tex]
And this makes sense, since by definition of a slope, it's just the change in y over change in x. This is equivalent to how much the y-value changes as x increases by one, so if we select two values with a difference of one in their x-values, the slope just turns out to be the difference between the two numbers.
Simplifying our expression we get: [tex]92.50-74=18.5[/tex]
This slope in this context represents how earnings increases as the hour increases, or in other words the hourly wage.
To calculate the earnings of the 6th hour we can just use the definition of a slope. From the x-value 5 to the x-value 6, the y-value should simply increase 18.5
So adding 18.5 to the y-value at x=5 we get: [tex]92.5+18.5=111[/tex]
Giving anyone that gets it right 100 points!
Six cantaloupes are cut up and served into thirty-two equal portions for a catering event. Which of the following shows the amount of cantaloupe in each portion?
A. 0.1875
_
B. 0.1875
C. 0.533
_
D. 0.53
Answer: pretty sure its B
hope this helps :)
write an equation relating cost per student c to number of students n
Answer:
t=n*c where t=total cost
Step-by-step explanation:
Which of the following is a true statement?
All negative numbers are above zero on the number line.
All positive numbers are to the left of zero on the number line.
All negative numbers are to the left of zero on the number line.
All statements are correct.
Answer:
Step-by-step explanation:
The correct statement is all negative number are to the left of zero on a number line.
When you look at a number line you will see negative numbers, 0, then positive numbers ( -# ------- 0 -------- +#), you an see the negative numbers are on the left.
The height h in feet that a pole vaulter can reach can be estimated using
the formula h = 20, where v is the velocity of the athlete in feet per second.
If the height for a women's pole vault is about 9.8 feet, about how fast was
the holder running? How far will the pole vaulter run in 2 seconds?
Using the numeric value of functions, it is found that the pole vaulter will run 50 feet farther in 2 seconds.
How to find the numeric value of a function/expression?To find the numeric value of a function, we replace each instance of the variable by the desired value.
The formula for the velocity is given as;
v=8√h
where h is the height.
we have the height is of h = 9.8,
hence:
v = 8√(9.8) = 25 feet per second.
The holder was running at the rate of 25 feet per second.
Then, within two seconds, the distance is given as;
d = 25 x 2 = 50 feet.
Hence, The pole vaulter will run 50 feet farther in 2 seconds.
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26. a)prove that a strictly increasing function from r to itself is one-to-one. b)give an example of an increasing function from r to itself that is not one-to-one.
a) f is strictly increasing function then f is one to one
b) f: R-> R such that f(x) = x^n where n is even is not one to one
suppose that f is strictly increasing function
we have to prove that f is one to one
let us assume f(x1) = f(x2)
we have to prove x1=x2
since f is strictly increasing function
then x2>x1 and x1> x2
this implies that x1=x2
and Hence f is one to one function
b) f:R->R such that f(x) = x^ n where n is even is not one to one
because f(1)= f( -1)
but -1 is not equal to 1 therefore f is not one to one function
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Analyze the definition below and complete the instructions that follow.
Alaska is the biggest state in the United States of America.
Write the given definition as a biconditional.
A.
A state is Alaska if and only if it is the smallest state in the United States of America.
B.
A state is the biggest state in the United states of America if and only if it is not Alaska.
C.
If a state is Alaska, then it is the biggest state in the United States of America.
D.
A state is Alaska if and only if it is the biggest state in the United States of America.
When written as a biconditional statement, the definition becomes D. A state is Alaska if and only if it is the biggest state in the United States of America.
How to write a biconditional statement?When writing a biconditional statement, you are to combine the statement in question, with the converse of the same equation and then join them by using the words, "if and only if."
This kind of statement lets it be known that if the first statement is correct, then the second definition or statement is correct as well. The biconditional definition here is that a state can only be Alaska if and only if that state is the largest in the country.
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Let a = $125.36, b = $729.35, c = $49.53, d =$500, f =$3.50, p =$1,450, and w =
$60.
Answer:
a = $125.36, b = $729.35, c = $49.53, d =$500, f =$3.50, p =$1,450, and w =
$60
Step-by-step explanation:
Amol drives his truck at an average speed of 50 km/h. He leaves at 07 00 and arrives at 11 15. Calculate the distance he drives.
Answer:
209km/h
Step-by-step explanation:
4hrs 15mins was the time.
4hrs x 50km/h = 200km/h
15 percent of 60: how many minutes is in an hour, is 9.
Hence, The answer would be 209km/h.
SOMEONE please please pleaseee help me out...
Graph the lines in standard form.
A graph of the linear equation (3x + 2y = 6) in standard form is shown in the image attached below.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
In Mathematics, the graph of any proportional relationship such as a linear equation is characterized by a straight line as shown in the image attached below.
Next, we would rewrite the linear equation in standard form as follows:
3x + 2y = 6
2y = 3x + 6
Dividing all through by 2, we have:
2y/2 = 3x/2 + 6/2
y = 3x/2 + 3
In conclusion, a graph which represents the linear equation (y = 3x/2 + 3) shows a proportional relationship between the value of x and y.
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75 [Chercher]
On considère l'expression suivante définie pour tout
ne Z par U(n)=n²+14n+33.
Résoudre U(n)=0.
Answer:
-11, -3
Step-by-step explanation:
[tex]n^2 + 14n+33=0 \\ \\ (n+11)(n+3)=0 \\ \\ n=-11, -3[/tex]
What is 7 divided by 534
Answer:
0.0131086142
Step-by-step explanation:
I just put in the calculator.
what is the fastest way to find the radius of a circle that's daimeter is 679.756
Answer:
divide it in half it would be 339.878
Step-by-step explanation:
radius is half of a diameter
Hello
By definition:
⇒ the diameter of a circle is twice the length of the radius of the circle
Thus if the diameter is 679.756:
[tex]\text{radius} = \dfrac{679.756}{2} = 339.878[/tex]
Hope that helps!
←++
2. The 7th grade class plans to collect at least 600 pairs of socks for people in need. So far, 135
pairs have been collected. How many pairs of socks does the class need to collect over the
next 5 days?
I NEED HELP RN WHAT IS (3x2.05+(_x1.09)+(2x_)+(_x_)
The value of the expression is 5x + 3.14
How to evaluate the expression?The expression is given as
(3x + 2.05) + (-x + 1.09) + (2x) + (x)
Open the brackets
So, we have the following equation
(3x + 2.05) + (-x + 1.09) + (2x) + (x) = 3x + 2.05 - x + 1.09 + 2x + x
Collect the like terms
So, we have the following equation
(3x + 2.05) + (-x + 1.09) + (2x) + (x) = 3x - x + 2x + x + 2.05 + 1.09
Evaluate the like terms
So, we have the following equation
(3x + 2.05) + (-x + 1.09) + (2x) + (x) = 5x + 3.14
Hence, the value of the expression given as (3x + 2.05) + (-x + 1.09) + (2x) + (x) is 5x + 3.14
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Possible question
What is (3x + 2.05) + (-x + 1.09) + (2x) + (x)
PLEASE HELP!!!
A system of linear inequalities is graphed below.
What are the linear inequalities for the system? Show your work, or explain your answer.
Answer:
System of linear inequalities is x - y + 1 < 0 and x + 2y +6 < 0
Step-by-step explanation:
Given:
The dotted line has two points as (-1,0) and (0,1).The solid line also has two points as (-6,0) and (0,-3).To Find:
Linear inequality for the system.Formula used:
Equation of a line passing through point (x1, y1) and (x2, y2) is given by (y-y1) = (y2-y1)/(x2-x1) * (x-x1)According to question, we have
Inequality for dotted line :
(y-1) > (0-1)/(-1-0) * (x-0)
y - 1 > x
x - y + 1 < 0...(1)
Inequality for solid line:
(y-(-3)) < (0-(-3))/(-6-0) * (x-0)
y + 3 < -x/2
x + 2y +6 < 0...(2)
Using (1) and (2), we get
System of linear inequalities is x - y + 1 < 0 and x + 2y +6 < 0.
Given y=x^2-2x-9 in standard form is y=(x+a)+b in vertexform, use completing the square to find a and b.
y = (x - 1)² - 10 is the vertex form of the equation y = x² - 2x - 9.
Given, y = x² - 2x - 9
The equation is already in standard form : y = ax² + bx + c
where a=1, b=-2 and c=-9 according to the equation y = x² - 2x - 9.
The vertex form of parabola is: y = a (x - h)² + k
The "a" in y = ax² + bx + c equation and the "a" in equation y = a (x - h)² + k are the same attributes of a parabola, therefore, substitute 1 for "a" in equation y = a (x - h)² + k: y = (x - h)² + k.
"h" is the x coordinate of the axis of the vertex: h = [tex]\frac{-b}{2a}[/tex]
Substitute in the values: h = - ( -2 ) ÷ 2(1)
∴ h = 1
Then, Substitute the value of h into the y = (x - h)² + k.
y = (x - 1)² + k.
Using the coordinates x and y from the above equations,
k = 1² - 2(1) - 9
k = 10
Now, Substitute the value of k into the equation y = (x - 1)² + k.
y = (x - 1)² - 10.
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At what speed should you enter an expressway? Question 1 options: 70mph 35mph the prevailing 10 miles below the freeway traffic
At a speed of 10 mph below the freeway traffic one should enter the expressway.
The speed of an object, also known as v in kinematics, is a scalar quantity that depends on the magnitude of the change in that object's position over time or the magnitude of the change in that object's position per unit of time.
The instantaneous speed serves as the upper bound of the average speed as the duration of the time period gets closer to 0. The average speed of an object over a given period is calculated by dividing its total distance traveled over that time by its duration. Velocity and speed are not the same thing.Now of the given options since the respective speeds on various expressways are different it is tangible than to enter an expressway one must use less speed than the speed of the traffic on the expressway.
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What are precise definitions of perpendicular and parallel lines
Answer:
Perpendicular lines: Are lines that intersect at right angles (90°)
Parallel lines: Are lines which have no point of intersection.
Step-by-step explanation:
[tex]{}[/tex]
What is the volume of a cuboid with 10cm 8cm and 6cm
Answer:
480 cm³
Step-by-step explanation:
volume = width × heigh × length
volume = 10 cm × 8 cm × 6 cm
volume = 480 cm³
Hope it Help~
Reshma spends 1/4 of her pocket money on her comic books out of Rs 660.
What is the amount she spent on her comic books and what amount is left with her?
Answer step by step and give brief explanation for 20 points will also mark as brainliest
We need to know about fraction to solve this problem. The amount Reshma spent on comic books is Rs 165 and the amount that is left with her is Rs 495.
We can solve this problem by calculating what 1/4th of 660 will be. In this question we know that Reshma spends 1/4th of her pocket money on comic books out of Rs 660. We can think of 660 being divided in 4 parts equally and that Reshma spends one part of it. The amount that will be left with Reshma is the rest three parts.
Reshma spends= 1/4x660=165
Amount left= 660-165=495
Therefore the amount Reshma spends on comic books is Rs 165 and the amount that is left with her is Rs 495.
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(2x-4)²=2x(x-2)+48 solve this ecuation
Answer:
x = 2, 4
Step-by-step explanation:
[tex](2x-4)^2=2x(x-2)+48 \\ \\ 4x^2 - 16x+16=2x^2-4x+48 \\ \\ 2x^2-12x-32=0 \\ \\ x^2-6x-8=0 \\ \\ (x-2)(x-4)=0 \\ \\ x=2, 4[/tex]
You pay 10.5% sales tax on a $85 purchase. How much was the tax?
Answer:
85x10.5%=8.925
Step-by-step explanation:
Solve the following inequality:
3r-13>14
could I have a demonstration of how it worked out
Answer:
r>9
Step-by-step explanation:
3r-13+13>14+13
3r>27
3r/3>27/3
r>9
Answer:
r > 9
Step-by-step explanation:
Hello!
Treat inequality as an equal sign. The only rule is that when you divide or multiply by a negative number, flip the sign.
Solve for r3r - 13 > 143r > 27r > 9The solution is true for any value of r greater than 9.
Which statement best describes a graph of paired points that form a proportional relationship?
A straight line cannot be drawn through all of the the points, but the line passes through the origin.
A straight line can be drawn through all the points, but the line does not pass through the origin.
A straight line can be drawn through all the points, and the line passes through the origin.
A straight line cannot be drawn through all of the the points, and the line does not pass through the origin.
Answer: A straight line can be drawn through all the points, and the line passes through the origin.
Step-by-step explanation:
A graph (not shown) of the selling prices of homes in a certain city for the month of April reveals that the distribution is skewed to the left. Which of the following statements is the most reasonable conclusion about the selling prices based on the graph?
Responses
The mean is greater than the median.
The mean is greater than the median.
The median is the average of the first quartile and the third quartile.
The median is the average of the first quartile and the third quartile.
There are fewer selling prices between the first quartile and the median than there are between the median and the third quartile.
There are fewer selling prices between the first quartile and the median than there are between the median and the third quartile.
There are more selling prices that are less than the mean than selling prices that are greater than the mean.
There are more selling prices that are less than the mean than selling prices that are greater than the mean.
The value of maximum minus third quartile is less than the value of first quartile minus minimum.
The statement which is the most reasonable conclusion about the selling prices based on the graph is that: E. the value of maximum minus third quartile is less than the value of first quartile minus minimum.
What is a box and whisker plot?A box and whisker plot is also referred to as boxplot and it can be defined as a type of graph that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread. Also, the five-number summary include the following:
Minimum (Min).First quartile (Q₁) or lower quartile.Median (Med).Third quartile (Q₃) or upper quartile.Maximum (Max).In Mathematics, the value of maximum minus third quartile (Max - Q₃) is generally less than value of first quartile minus minimum (Q₁ - Min). Mathematically, this can be represented by this expression:
Data value = (Max - Q₃) < (Q₁ - Min)
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Which polynomial is prime?
x² + 7
x² - 25
3x²-27
2x²-8
answer is (a) just took the quiz
The polynomial function, x² + 7 is prime
What is a polynomial?
A polynomial is an expression in mathematics that consists of indeterminates (also known as variables) and coefficients and includes only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. x² + 4x + 7 is an example of a polynomial with a single indeterminate x. In three variables, consider x³ + 2xyz² - yz + 1.
The polynomial function, x² + 7 is prime.
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Fill in: -5^2=____-5^2
The complete expression that fills the blank is -5^2 = 0 - 5^2
What are mathematical expressions?These are any statements that use variables, operators and coefficients as its representation
How to completely fill the blanks?The expression is given as
-5^2 = __-5^2
Represent the blank with x
So, we have the following expression
-5^2 = x - 5^2
Add 5^2 to both sides of the equation
So, we have
x = 5^2 - 5^2
Evaluate the difference
x = 0
This implies that -5^2 = __-5^2 gives -5^2 = 0 - 5^2
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