y + x = 30
xy = 209
y = 30 -x
x(30-x) = 209
30x - x^2 = 209
x^2 - 30x + 209 = 0
x = 19
y = 11
the difference is 19-11 = 8
The numbers are 11 and 19.
Given to us,Sum of the two numbers = 30,Product of the two numbers = 209,AssumptionLet's assume that the first number be a and the second is b.
equation 1,a + b = 30
equation 2,ab = 209
Therefore, in equation 1,
[tex]a\times b = 209\\b= \dfrac{209}{a}[/tex]
substitute the value of b in equation 1,
[tex]a+b=30\\\\a+\dfrac{209}{a}=30\\\\\dfrac{a^2+209}{a} =30\\\\a^2 +209 = 30a\\a^2-30a +209 = 0[/tex]
[tex]a^2 -30a+209= 0\\a^2 -19a-11a+209= 0\\a(a-19)-11(a-19)=0\\(a-11)(a-19)=0[/tex]
Substituting the factor against 0,
[tex](a-11) = 0\\a = 11\\\\(a-19)=0\\a = 19[/tex]
Therefore, the numbers are 11 and 19.
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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.
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 .
For what values of x does f(x)= x^2 +9x +20 reach its minimum value?
The minimum value of the quadratic function f(x)= [tex]x^2[/tex] +9x +20 is achieved at x = -4.5, calculated using the vertex formula -b/2a.
Explanation:The function f(x)= [tex]x^2[/tex] +9x +20 is a quadratic function. The minimum value of a quadratic function is achieved at the vertex. The x-coordinate of the vertex can be found using the formula -b/2a, where a and b are coefficients of [tex]x^2[/tex] and x respectively in the standard form a[tex]x^2[/tex] + bx + c. Here, a=1 and b=9.
So, by applying the formula, the value of x will be -b/2a = -9/(2*1) = -4.5. Hence, the function achieves its minimum value when x = -4.5.
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2. The value of a Plasma TV bought new for $3,700 decreases 25% each year. Identify the function for the value of the television. Does the function represent growth, or decay?
V(t) = 3700(1.25)t; growth
V(t) = 3700(0.75)t; decay
V(t) = 3700(1.25)t; decay
V(t) = 3700(0.75)t; growth
Answer: V(t) = 3700(0.75)t; decay
Step-by-step explanation:
HELP ROUND 479065.389037 TO THE NEAREST THOUSAND
A cubic centimeter of quartz, olivine, and gold weighs 2.5, 3.0, and 19.8 grams, respectively. this indicates that
To solve the problem we must know about density.
The different weight shows that the solids have different density.
Given to us
A cubic centimeter of quartz, olivine, and gold weighs 2.5, 3.0, and 19.8 grams.What are weight and mass?We know that weight is the product of mass and acceleration due to gravity, also, mass is the product of density and volume.
[tex]\rm{ weight = mass \times acceleration\ due\ to\ gravity[/tex]
[tex]\rm{ w = m \times g[/tex]
[tex]\rm{ Mass = density \times volume[/tex]
[tex]m = \rho \times v[/tex]
What is the relationship between weight and mass?In the three solids given, the acceleration due to gravity will be the same, also, it is already mentioned that the volume of the three materials is the same that is 1 cubic centimeter.
[tex]w = m \times g\\w = (\rho \times v) \times g\\\\w = \rho \times 1\ cm^3 \times 9.81[/tex]
Therefore, the only thing that can vary is the density of the solids. Hence, the different weight shows that the solids have different density, the more is the weight the more is the density of the solid.
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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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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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If a system of linear equations has no solution, what do you know about the slopes and y-intercepts of the graphs of the equations?
Answer:
The slopes of the graphs are the same and the y-intercepts of the graphs are different.
Step-by-step explanation:
Please help!
Factor the expression.
9b^2+48b+64
Answer:
(3x+8)^2
Step-by-step explanation:
(3x+8)^2
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?
If you were asked to load 225 boxes onto a truck, and the boxes are crated with each crate containing nine boxes, how many crates would you need to load
Answer:
You should load 25 crates onto a truck.
Step-by-step explanation:
Given:
There are 225 boxes.
Each crate containing 9 boxes.
We need to find the number of crates that containing 225 boxes.
Here we use division to find the answer.
Number of crates = Total number of boxes / Number of boxes in each crate
= 225/9
= 25
You should load 25 crates onto a truck.
Write an equation for ab is congruent to segment bc
Answer:
[tex]\overline {ab}\cong \overline {bc}[/tex]
Step-by-step explanation:
We are asked to write an equation for the given statement.
Statement:
Segment 'ab' is congruent to segment 'bc'.
We know that segment is written by a bar on name of segment as: [tex]\overline {ab}[/tex] and [tex]\overline {bc}[/tex].
Congruent sign is [tex]\cong[/tex]
Therefore, our required equation would be: [tex]\overline {ab}\cong \overline {bc}[/tex]
Solve by using elimination 3x+y=27 -3x+4y=-42
Can someone help me!
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
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.quotient of two more than a number and eight
(06.05 MC)
Dylan surveyed the students at his sports camp to find out if they like diving and/or boxing. The table below shows the results of the survey:
Like Diving
Do Not Like Diving
Total
Like Boxing
28
12
40
Do Not Like Boxing
20
5
25
Total
48
17
65
If a student likes diving, what is the probability that student also likes boxing?
43.1%
58.3%
70.0%
73.8%
without seeing the chart, I hope I have the columns and labels correct,
but it looks like 28 students like both diving and boxing.
there is a total of 65 students
28/65 = 0.4307, which rounds to 0.431
which is 43.1%
Please Help!!!
which statement is true about the system x-3y = 5 and y = x - 7 ?
If f(x)=5x-2 and g(x)=2x+1, find(f-g)(x)
A ball bearing is shaped like a sphere and has a diameter of 2.5 centimetres. What is the volume contained inside the ball bearing? Use 3.14 for pi. Round your answer to the nearest hundredth. 8.18 cubic centimeters 7.15 cubic centimeters 7.08 cubic centimeters 6.89 cubic centimeters
Answer: 8.18 cubic centimeters
Step-by-step explanation:
Given : A ball bearing is shaped like a sphere .
The diameter of ball = 2.5 centimeters
Then , the radius of the ball =[tex]\dfrac{2.5}{2}=1.25\text{ cm}[/tex]
We know that the volume of a sphere is given by :-
[tex]\text{Volume}=\dfrac{4}{3}\pi r^3[/tex]
Then , the volume of ball is given by :-
[tex]\text{Volume}=\dfrac{4}{3}(3.14) (1.25)^3\\\\\Rightarrow\ \text{Volume}=8.17708333333\approx8.18\text{ cubic centimeters}[/tex]
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)?
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.
Question 2: Remember that there are 5 lead male roles and 4 lead female ones. If you must seat the male leads together and the female leads together, the three producers together and the director by himself, how many different ways can you seat 13 people around the circular table?
A purse contains dimes and nickels. The total value of all the coins is, at most, $2.50, and there are at least three of each coin. Which of the following systems correctly shows the system that describes the possible number of nickels (n) and dimes (d) in the purse?
<= That means greater than or equal to or less than or equal to
1.n >= 3
d >= 3
0.05n+0.1d <= 2.50
2. n <= 3
d <= 3
0.05+0.1d <= 2.50
3. n <= 3
d<= 3
n + d >= 2.50
4. n>=3
d >= 3
n + d <=2.50
How to write 0.000028 in scientific notation?
Choose the correct simplification of the expression (7x − 3)(4x2 − 3x − 6).
28x3 − 33x2 − 33x − 18
28x3 + 33x2 − 33x + 18
28x3 − 51x2 − 33x + 18
28x3 − 33x2 − 33x + 18
a b c d
Answer:
The expression (7x − 3) × (4x² − 3x − 6) is equivalent to 28x³ - 33x² - 33x + 18 .
Step-by-step explanation:
As given the expression in the question be as follow .
= (7x − 3) × (4x² − 3x − 6)
= 7x × (4x²- 3x - 6) - 3 × (4x² - 3x - 6)
Now open the bracket
= 7x × 4x² + 7x × -3x + 7x × -6 -3 × 4x² -3 × -3x - 3 × -6
= 28x³ -21x² -42x -12x² + 9x +18
= 28x³ -21x² - 12x² -42x + 9x + 18
= 28x³ - 33x² - 33x + 18
Therefore the expression (7x − 3) × (4x² − 3x − 6) is equivalent to 28x³ - 33x² - 33x + 18 .
True or False.
A binomial is also a polynomial.