The height of a triangle is 6 m more than its base. The area of the triangle is 56 m2. Find the length of the base. 7 m 8 m 14 m 15 m
Determine two pairs of polar coordinates for the point (3, -3) with 0° ≤ θ < 360°
The two pairs of polar coordinates are : [tex]( 3\sqrt{2}, 315^{0} ) , ( -3\sqrt{2}, 135^{0} )[/tex]
Polar coordinates are coordinates labeled as ( r, θ ) , where r = radial coordinate while θ is known as the angular coordinate. Polar coordinates are also plotted on a polar grid.
Using the given data
Point ( 3 , - 3 )
[tex]r = \sqrt{3^2 + (-3)^2} = 3\sqrt{2}[/tex]
θ =
[tex]tan^{-1} (\frac{-3}{3}) = \pi - \frac{\pi }{4} , 2\pi - \frac{\pi }{4} \\\\= 3\pi , \frac{7\pi }{4} , -\frac{\pi }{4}[/tex]
In degrees = 135° , 315° , -45° ( neglecting -45° )
Hence the two pairs of polar coordinates for the point ( 3 , -3 ) can be taken as ; [tex]( 3\sqrt{2}, 315^{0} ) , ( -3\sqrt{2}, 135^{0} )[/tex]
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Answer:
c on edge
Step-by-step explanation:
What is the formula for an eastbound car is going 4 miles per hour faster than a westbound car. the cars are 208 miles apart 2 hours after passing each other on a highway. what is the speed, in miles per hour, of the eastbound car?
The speed of the eastbound car is 56 miles per hour.
Explanation:Let x be the speed of the westbound car. Since the eastbound car is going 4 miles per hour faster, the speed of the eastbound car is x + 4 .
The combined speed of both cars is x + (x + 4) = 2x + 4 miles per hour. In 2 hours, the cars cover a distance of 2(2x + 4) = 4x + 8 miles. This distance is equal to the sum of the distances covered by each car when moving towards each other.
Given that the cars are 208 miles apart, we can set up the equation:
4x + 8 = 208
Subtracting 8 from both sides:
4x = 200
Dividing both sides by 4:
x = 50
So, the speed of the westbound car is 50 miles per hour, and the speed of the eastbound car is 50 + 4 = 54 miles per hour. Therefore, the eastbound car is moving at 54 miles per hour.
In the end, the eastbound car's speed is 54 miles per hour, which is 4 miles per hour faster than the westbound car's speed of 50 miles per hour.
Full Question:An eastbound car is going 4 miles per hour faster than a westbound car. the cars are 208 miles apart 2 hours after passing each other on a highway. what is the speed, in miles per hour, of the eastbound car?
I won tickets to a trip for four to the Super Bowl. I have eight friends but I can only bring three of them. In how many ways can I form my Super Bowl party?
Rip the 4 tickets in half lol
Question 3: In les Miserables Monsier, Thenardier, and Madame Thenardier are married and during act two, Cosette and Marius become married. If Thenardiers must sit next to one another and Cosette and Marius must sit next to one another, but there are no restrictions on how others can sit, how many different ways can you sit 13 people around a circular table?
In Les Miserables, given specific seating arrangements around a circular table with 13 people, there are 16,320 ways to seat them as per the specified conditions.
Step-by-step explanation:
Calculate the number of ways to seat Cosette and Marius together: 2 ways as they are a pair.Calculate the number of ways to seat Thenardiers together: 2 ways as they are a pair.Calculate the number of ways to arrange the remaining 9 people using the circular permutation formula: (9-1)! = 8!.Multiply the three results together: 2 * 2 * 8! = 16,320 ways.Multiply 8 times the square root of 3 by 9 times the square root of 27.
8 times the square root of 3 multiplied by 9 times the square root of 27 is equal to 1944.
To multiply 8 times the square root of 3 by 9 times the square root of 27, we can simplify the expression using the properties of square roots and perform the multiplication.
First, let's simplify the square roots:
Square root of 3 can be written as √3.
Square root of 27 can be written as √(9 * 3), which further simplifies to √9 * √3 = 3 * √3.
Now, we have:
8 * √3 * 9 * √27 = 8 * √3 * 9 * (3 * √3) = 8 * 9 * 3 * √3 * √3 = 216 * 3 * √3 * √3.
Since the square root of 3 multiplied by itself (√3 * √3) simplifies to 3, we have:
216 * 3 * 3 = 1944.
Therefore, 8 times the square root of 3 multiplied by 9 times the square root of 27 is equal to 1944.
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What is the arc length when 0=3pi over 5 and the radius is 7?
Describe how the graphs of functions f and g are related: f (x) = 2cos(pi x) g(x) = 2cos(2pi x)
Factor the following.
How many right triangles have a hypotenuse that measures 2x+5 meters and legs that measure 22xminus−33 meters and x+8 meters? what are the dimensions of the triangle(s)?
Please help!
Factor the expression.
9b^2+48b+64
Answer:
(3x+8)^2
Step-by-step explanation:
(3x+8)^2
The arithmetic mean (i.e., average) of a set of 7 numbers is 20. the mean of a second set of 13 numbers is 40. what is the mean of all 20 numbers?
Using the weighed mean, it is found that the mean of all 20 numbers is of 33.
What is the weighed mean?The weighed mean is given by the sum of all elements in a data-set multiplied by it's weight, divided by the sum of the weights.
In this problem, the means are divided as follows.
Mean of 20 with a weight of 7.Mean of 40 with a weight of 13.Hence:
[tex]M = \frac{20(7) + 40(13)}{20} = 33[/tex]
The mean of all 20 numbers is of 33.
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I was wondering if anybody had the questions to the module 8 DBA for FLVS. I usually dont do well unless I see the question, I dont need the answers just the question.
An expression is shown below: 3pf^2 - 21p^2f + 6pf - 42p^2. Rewrite the expression completely factored. Show the steps of your work.
The final expression will be equal to 3p(f - 7p)( f + 2).
What is an expression?
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The given expression will be solved as below:-
First find the GCF - this is 3p which we take out:-
E= 3p(f² - 7pf + 2f - 14p)
Factor the terms in the parentheses by grouping:-
E= 3p [f(f - 7p) + 2(f - 7p)]
E= 3p(f - 7p)( f + 2)
Therefore, the final expression will be equal to 3p(f - 7p)( f + 2).
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Suppose there is a strong positive correlation between v and w which of the following must be true
?
A.)when V increases, w tends to increase
B.)An increase in a V causes W to decrease
C.)An increase in V causes W to increase
D.)When V increases, W tends to decrease
The truth is when V increases, W tends to increase. Positive correlation between two variables in which both variables move in tandem. Positive correlation exists when one variable decreases as the other also decreases or one variable increases while others increase too.
Answer: A.) when V increases, w tends to increase
Step-by-step explanation:
Positive correlation is a relationship between two variables in which both variables move with the same ratio. A positive correlation exists when one variable increases as the other variable increases, or vice-versa.
A perfect positive correlation means that both variables move by the exact same percentage.
Therefore, if there is a strong positive correlation between v and w then when V increases, w tends to increase .
Given a standard deck of playing cards, what is the probability of randomly selecting a card that is either red or a face card or both
Final answer:
This detailed answer explains the probability of selecting a heart or a face card from a standard deck of cards and the calculation involved.
Explanation:
Calculate the probability of selecting a heart or a face card from a standard deck of cards:
There are 52 cards in a deck, with 13 hearts and 12 face cards (3 each of Jacks, Queens, Kings).The probability of selecting a heart card is 13/52 = 1/4.The probability of selecting a face card is 12/52 = 3/13.By the principle of inclusion-exclusion, you add the probabilities of selecting a heart and a face card and subtract the probability of both (heart face cards, which are only the face cards that are hearts - 3 cards):
(1/4) + (3/13) - (3/52) = 39/52 = 3/4
Henry is putting money into a checking account. Let y represent the total amount of money in the account (in dollars). Let x represent the number of weeks Henry has been adding money. Suppose that x and y are related by the equation y=20x+650 . Answer the questions below. Note that a change can be an increase or a decrease.
For an increase, use a positive number. For a decrease, use a negative number.
What was the starting amount of money in the account? $
What is the change per week in the amount of money in the account? $
Update: solved
one pinball games 25 cents to play.how much will it cost to play 10 pinball games?
It would cost 2.50 dollars to play 10 pinball games
Medical researchers have determined that for exercise to be beneficial, a person’s desirable heart rate, R, in beats per minute, can be approximated by the formulas
for women
for men,
where a represents the person’s age. If the desirable heart rate for a man is 135 beats per minute, how old is he?
a.
22.5 years old
b.
40 years old
c.
45 years old
d.
42.5 years old
Please select the best answer from the choices provided
Elisa needs to make a scale drawing of his school building for art class. If the building is 256.25 meters long, and Elisa scales it down using a ratio of 25 meters to 1 inch, how long will the building be in the sketch? (in inches)
The cost of a daily newspaper varies from city to city. however, the variation among prices remains steady with a standard deviation of 20?. a study was done to test the claim that the mean cost of a daily newspaper is $1.00. ten costs yield a mean cost of 96? with a standard deviation of 18?. do the data support the claim at the 1% level?
First, we establish our hypothesis:
Null hypothesis H0: μ = $1.00
Alternative hypothesis Ha: μ ≠ $1.00
Let’s say X = the sample average cost of a daily newspaper = 0.96
u = population mean cost = 1.00
S = sample standard deviation = 0.18
Calculating for z value:
z = (X – u) / S
z = (0.96 – 1) / 0.18
z = – 0.222
From the standard distribution table at this z value, p-value = 0.4129
Since alpha = 0.01, the decision therefore is:
Do not reject the null hypothesis because the p-value is greater than 0.01. There is enough evidence to support the claim that the mean cost of newspapers is $1.
The two-way table shows the number of students in a class who help in an animal shelter and/or library.
Help in Animal Shelter
Do Not Help in Animal Shelter
Total
Help in Library
12
?
15
Do Not Help in Library
11
10
21
Total
23
13
36
What is the missing number in the table?
3
5
25
27
Answer: The number 3 is missing from the table!
Step-by-step explanation:
Evaluate m – n when m = –2.6 and n = 7.9.
a. –10.5
b. –5.3
c. 5.3
d. 10.5
Final answer:
The value of m – n when m = –2.6 and n = 7.9 is –10.5, which is an option (a).
Explanation:
To evaluate m – n when m = –2.6 and n = 7.9, we simply substitute the given values into the expression and perform the subtraction:
m – n = –2.6 – 7.9
Since subtracting a positive number is the same as adding its negative, this is equivalent to:
m – n = –2.6 + (–7.9)
Adding these two negative numbers together gives us:
m – n = –10.5
Therefore, the correct answer is a. –10.5.
The vertex of the functions graph is given. Find c. y=2x^2-6x+c;(3/2, 0.5)
select the TWO binomials that are factors of this
since the last number -s -20 you need the 2 that when multiplied together would equal -20
so x-5 and x +4 are the correct answers
Divide 40x/ 64y by 5x/ 8y
A. 1
B. 3/4
C. 25x^2/ 64y^2
D. 25/64
The division to the expression Divide 40x/ 64y by 5x/ 8y is (a) 1
How to evaluate the quotient expression
From the question, we have the following parameters that can be used in our computation:
Divide 40x/ 64y by 5x/ 8y
As an expression we have
40x/ 64y ÷ 5x/ 8y
So, we have
40x/ 64y ÷ 5x/ 8y = 40x/ 64y * 8y/5x
Divide the variables
This gives
40x/ 64y ÷ 5x/ 8y = 40/64 * 8/5
Lastly, we have
40x/ 64y ÷ 5x/ 8y = 1
Hence, the solution to the expression is (a) 1
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Below are two different functions, f(x) and g(x). What can be determined about their y-intercepts? F(x)=-2x-1
The correct statement is:
The function f(x) has a higher y-intercept.Step-by-step explanation:We know that the general form of a slope intercept form of a line is given by:
[tex]y=mx+c[/tex]
where m is the slope of the line and c is the y-intercept of a line.
The function f(x) is given by:
[tex]f(x)=-2x-1[/tex]
Hence, on comparing the function to the slope-intercept form of a line we get
The y-intercept of function f(x) is: -1
Also, the table for the function g(x) is given by:
x g(x)
2 2
4 6
6 10
The function g(x) satisfies the equation:
[tex]g(x)=2x-2[/tex]
The y-intercept of the function g(x) is: -2
Since we know that:
-1 > -2
This means that the y-intercept of the function f(x) is higher than the y-intercept of the function g(x).
Design an equation for the volume of a box made from a cardboard sheet of length q and width p and square cutouts of side length x.
Is the centroid of a triangle equidistant from the three vertices?
Yes, the centroid of a triangle is equidistant from the three vertices.
Explanation:Yes, the centroid of a triangle is indeed equidistant from the three vertices.
The centroid of a triangle is the point where the three medians of the triangle intersect. A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side.
Since the medians of a triangle intersect at the centroid, the distances from the centroid to each vertex along the medians are equal. This property can be proven using properties of similar triangles.
The football team has 30 more members than the basketball teams. If each group had 10 more members, the ratio of their membership would be 3.2. How many members are in each group? Write your answer as football x basketball y
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