The zeros and their multiplicities of the function f(x)=2x^(5)+11x^(4)-2x^(3)-74x^(2)-60x+48 are:
x = -4, multiplicity 1
x = (-5 + √(41))/(2), multiplicity 1
x = (-5 - √(41))/(2), multiplicity 1
The zeros of a function f(x) are the values of x that make f(x) equal to 0. The multiplicity of a zero is the number of times that zero appears as a solution. To find the zeros and their multiplicities of the given function f(x)=2x^(5)+11x^(4)-2x^(3)-74x^(2)-60x+48, we can use synthetic division or factoring.
First, let's use synthetic division to find one of the zeros:
2x^(5)+11x^(4)-2x^(3)-74x^(2)-60x+48 = 0
Using synthetic division, we can find that x = -4 is a zero of the function:
(-4) | 2 11 -2 -74 -60 48
| 0 -8 20 88 104 -176
---------------------------
2 3 18 14 44 -128
Now we can divide the original function by (x+4) to find the remaining zeros:
f(x) = (x+4)(2x^(4)-x^(3)+14x^(2)+10x-32)
Using the quadratic formula, we can find the remaining zeros of the function:
x = (-b ± √(b^(2)-4ac))/(2a)
x = (-(10) ± √((10)^(2)-4(2)(-32)))/(2(2))
x = (-10 ± √(164))/(4)
x = (-10 ± √(4*41))/(4)
x = (-10 ± 2√(41))/(4)
x = (-5 ± √(41))/(2)
So the zeros of the function are x = -4, x = (-5 + √(41))/(2), and x = (-5 - √(41))/(2).
The multiplicity of each zero is 1, since each zero appears only once as a solution.
Therefore, the zeros and their multiplicities of the function f(x)=2x^(5)+11x^(4)-2x^(3)-74x^(2)-60x+48 are:
x = -4, multiplicity 1
x = (-5 + √(41))/(2), multiplicity 1
x = (-5 - √(41))/(2), multiplicity 1
Learn more about quadratic formula
brainly.com/question/9300679
#SPJ11
2566 concert tickets were sold for a total of $10,348.
if students paid $3 and nonstudents paid $5, how many student
tickets were sold?
1241 student tickets were sold. Below, you will learn how to solve the problem.
2566 concert tickets were sold for a total of $10,348, and if students paid $3 and nonstudents paid $5, then the number of student tickets sold can be calculated.
To solve this problem, we can set up an equation using the given information.
X + Y = 2566
3X + 5Y = 10348
Find the value of X:
Y = 2566 - X
3X + 5(2566 - X) = 10348
3X + 12830 - 5X = 10348
2X = 12830 - 10348
2X = 2482
X = 1241
Therefore, 1241 student tickets were sold.
For more information about equation, visit:
https://brainly.com/question/22688504
#SPJ11
PLEASE ANSWER THIS QUICK
-12
WHAT COULD THE INTEGER BE??????
Answer: its all 3
Step-by-step explanation: https://socratic.org/questions/is-12-an-integer-rational-or-real-number#:~:text=Reals%3A%20any%20number%20that%20is%20rational%20or%20irrational,be%20found%20on%20the%20number%20line.%20Answer%20link
HELP PLS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
-3/2
Step-by-step explanation:
To find:-
Slope of the line.Answer:-
We are interested in finding out the slope of the given line . We can see that the line passes through the points (1,0) and (-1,3) . For finding out the slope we can use the formula,
[tex]:\implies \sf m =\dfrac{y_2-y_1}{x_2-x_1} \\[/tex]
Now on substituting the respective values, we have;
[tex]:\implies \sf m = \dfrac{0-3}{1-(-1)} \\[/tex]
[tex]:\implies \sf m = \dfrac{-3}{1+1}\\[/tex]
[tex]:\implies \sf \pink{m=\dfrac{-3}{2}}\\[/tex]
Hence the slope of the line is -3/2.
The vector ü has length 16 and points at an angle of 5° The vector ü has length 11 and points at an angle of 25°
The sum of the two vectors is a vector with length 26.56 and an angle of 12.72°.
The vector ü can be represented in Cartesian coordinates as (16cos5°, 16sin5°) and the vector ü can be represented as (11cos25°, 11sin25°).
To find the sum of these two vectors, we add their corresponding coordinates:
(16cos5° + 11cos25°, 16sin5° + 11sin25°)
Using a calculator, we can approximate these values:
(25.82, 5.81)
Therefore, the sum of the two vectors is approximately (25.82, 5.81) in Cartesian coordinates. To find the length and angle of this vector, we can use the Pythagorean theorem and the inverse tangent function:
Length = √(25.82² + 5.81²)
≈ 26.56
Angle = tan⁻¹(5.81/25.82)
≈ 12.72°
So the sum of the two vectors is a vector with length 26.56 and an angle of 12.72°.
For more about vector:
https://brainly.com/question/29740341
#SPJ11
This also means your digital upload should these answers to rece Find all zeros. One zero has been given. hen write the factored form of the polynomial f(x)=x^(4)+x^(3)+2x^(2)-22x-60;-2
The factored form of the polynomial is f(x) = (x + 2)(x + 10)(x - 6) .
The given polynomial is f(x) = x4 + x3 + 2x2 - 22x - 60.
To find the zeros of the polynomial, set f(x) = 0 and solve for x. This gives us the following equation:
x4 + x3 + 2x2 - 22x - 60 = 0
The given zero is -2. To factor the polynomial, use the zero(-2) as one factor. To find the other factors, set (x + 2) = 0 and solve for x. This gives us the following equation:
x3 + 2x2 - 22x - 60 = 0
To solve this equation, use the Quadratic Formula. This gives us two factors, (x + 10) = 0 and (x - 6) = 0. Therefore, the factored form of the polynomial is:
f(x) = (x + 2)(x + 10)(x - 6)
To know more about factored form click on below link:
https://brainly.com/question/29065045#
#SPJ11
Your friend asks you for help to check a geometry exercise. Below is vour friend's paper.
What error did your friend make? Explain.
The error is made because two or more shapes are said to be similar if they have common corresponding properties of sides and/ angles. The Option D is correct.
What is the explanation of the Geometric error?All similar shapes are two or more given shapes that share some properties in terms of their corresponding sides or angles. As a result, if the corresponding sides or angles are related, they are similar. It is important to note that similarity does not imply congruency.
When the sides and angles of the given triangles LMN and QRS are compared, it is clear that: angle Side Angle (ASA) similarity implies that the included side between two pairs of congruent angles is similar. As a result, the Option D explains the error in the diagram.
Missing options "a.Your friend's paper does not name the triangles correctly for them to be congruent. b. Your friend's paper shows that the SAS Postulate should be used to show congruence because a pair of congruent angles is included between two pairs of congruent sides. c. The ASA Postulate cannot be used to prove the congruence of the two triangles as shown because the triangles do not have two pairs of congruent angles. d. The ASA Postulate cannot be used to prove the congruence of the two triangles as shown because the included sides between the two pairs of congruent angles are not marked as congruent in both triangles.
Read more about similar properties
brainly.com/question/28887532
#SPJ1
Pls help!
In a video game each player earns 5 pts for reaching the next level and 15 pts for each coin collected. Make a table to show the relationship between the num of coins collected c and total pts p graph the ordered pairs and analyze the graph.
Answer:
Here is a table showing the relationship between the number of coins collected and the total points earned:
Number of coins (c) Total points (p)
0 0
1 20
2 35
3 50
4 65
5 80
6 95
7 110
8 125
9 140
10 155
To graph these ordered pairs, we can plot the number of coins collected (c) on the x-axis and the total points earned (p) on the y-axis. Then we can plot each ordered pair as a point on the graph and connect the points with a line. The resulting graph should show a linear relationship between c and p, with a slope of 15 and a y-intercept of 0.
Analyzing the graph, we can see that as the number of coins collected increases, the total points earned also increases at a constant rate. This suggests that collecting coins is an important part of the game, as it significantly increases the player's total score. Additionally, the slope of the line (15) tells us that each additional coin collected is worth 15 points, while reaching the next level is worth only 5 points.
QUESTION 2.
Consumer Reports did a study of ice cram bars (only vanilla flavored) in their 2001 report. Eleven bars having taste-test ra)ng of at least "fair" were listed, and calories per bar was included. Calories vary quite a bit partly because bars are not of uniform size.
439 111 201 182 197 209 147 190 151 131 151
i) Find range of the data,
ii) Find the 1st quar)le, median and 3rd, quar)le. iii) Find the IQR
iv) Draw the box plot.
iv) Are there any outliers in the data?
The range of the data is 328. The 1st quartile, median and 3rd quartile is 147, 182, and 197, respectively. The IQR is 50. There is only one outlier in the data, which is 439.
i) The range of the data is the difference between the highest and lowest values. In this case, the range is 439 - 111 = 328.
ii) The 1st quartile is the 25th percentile of the data, the median is the 50th percentile, and the 3rd quartile is the 75th percentile. To find these values, we need to first sort the data in ascending order:
111, 131, 147, 151, 151, 182, 190, 197, 201, 209, 439
Then we can find the quartiles:
1st quartile = 147
Median = 182
3rd quartile = 197
iii) The interquartile range (IQR) is the difference between the 3rd and 1st quartiles. In this case, the IQR is 197 - 147 = 50.
v) Outliers are values that are more than 1.5 times the IQR above the 3rd quartile or below the 1st quartile. In this case, the upper bound for outliers is 197 + (1.5 * 50) = 272.5 and the lower bound is 147 - (1.5 * 50) = 71.5. The only value that falls outside of these bounds is 439, so there is one outlier in the data.
Learn more about Outliers here: https://brainly.com/question/29546240.
#SPJ11
olve the following linear programming problem. Restrict x ≥ 0 and y ≥ 0. Maximize f = 2x + 4y subject to x + y ≤ 7; 2x + y ≤ 12; y ≤ 4.
(x,y)=
f=
The solution to this linear programming problem is (x,y) = (3,4) and f = 22.
To solve this linear programming problem, we need to find the feasible region by graphing the constraints and then use the objective function to find the maximum value of f.
1. Graph the constraints:
x + y ≤ 7 can be rewritten as y ≤ -x + 7
2x + y ≤ 12 can be rewritten as y ≤ -2x + 12
y ≤ 4
2. Find the feasible region:
The feasible region is the area that satisfies all of the constraints. In this case, it is the area bounded by the three lines and the x and y axes.
3. Use the objective function to find the maximum value of f:
f = 2x + 4y
To find the maximum value of f, we need to find the corner points of the feasible region and plug them into the objective function. The corner points are (0,4), (3,4), and (4,3).
f(0,4) = 2(0) + 4(4) = 16
f(3,4) = 2(3) + 4(4) = 22
f(4,3) = 2(4) + 4(3) = 20
The maximum value of f is 22 at the point (3,4).
Therefore, the solution to this linear programming problem is (x,y) = (3,4) and f = 22.
Answer:
(x,y) = (3,4)
f = 22
Learn more about Programming
brainly.com/question/11023419
#SPJ11
How do you know which factor to use for the trinomials?
To factor a trinomial, you need to find two binomials that, when multiplied together, give you the original trinomial.
How do you know which factor to use for the trinomials?The key to finding binomials is to identify the factors of the quadratic term and the constant term, and then use those factors to construct the binomials.
Here's a step-by-step process for factoring a trinomial:
Write the trinomial in the form ax^2 + bx + c, where a, b, and c are constants.Identify the factors of the quadratic term (ax^2). These are the numbers that multiply to give you a, the coefficient of x^2. For example, if the trinomial is 2x^2 + 5x + 3, the factors of 2 are 1 and 2.Identify the factors of the constant term (c). These are the numbers that multiply to give you c, the constant term. For example, if the trinomial is 2x^2 + 5x + 3, the factors of 3 are 1 and 3.Find two factors of a and two factors of c that add up to b, the coefficient of x. For example, in the trinomial 2x^2 + 5x + 3, we need to find two factors of 2 and two factors of 3 that add up to 5. We can see that 2 and 1 are factors of 2, and 3 and 1 are factors of 3, and 2+3=5. So we use these factors to write the middle term as 2x+3x, and then we factor by grouping.Use the factors you've identified to write the trinomial as a product of two binomials. For example, in the trinomial 2x^2 + 5x + 3, we can write it as (2x + 3)(x + 1).It's important to note that not all trinomials can be factored using this method.
Learn more about trinomials here: https://brainly.com/question/29827487
#SPJ1
For a given rational function, n < m. what does this mean about the graph of the function?
There are both horizontal and oblique asymptotes.
There is no horizontal asymptote.
There is a horizontal asymptote at y=a/b
There is a horizontal asymptote at y=0 .
For rational function, n < m. There is a horizontal asymptote at y = 0.
Explain about the rational function?A rational function is one whose denominator is not zero and which can be expressed as the ratio between two polynomials.
f(x) = p(x) / q(x)
A horizontal line is only an asymptote to the graph's extreme left and right. Anything beyond the vertical asymptotes as well as x-intercepts is considered to be "far" left or "far" right. The midpoint of horizontal asymptotes is not asymptotic. A horizontal asymptote can be crossed in the middle.By examining the degrees of a numerator (n) and denominator, we can locate the horizontal asymptote (m).
The horizontal asymptote is at y=0 if nm, the x-axis, is true.Y=an/bm is the horizontal asymptote if n=m. The ratio of the main coefficients, in other words.There isn't a horizontal asymptote if n>m. It has an oblique or slant asymptote, though, if n=m+1.Thus, For rational function, n < m. There is a horizontal asymptote at y = 0.
Know more about rational function
https://brainly.com/question/19044037
#SPJ1
What is the solution of the system?
2x+3y=−26
5x+3y=−29
Answer:
x = -1
y = -8
Step-by-step explanation:
2x+3y= −26
5x+3y= −29
Time the first equation by -1
-2x - 3y = 26
5x + 3y = -29
3x = -3
x = -1
Now put -1 in for x and solve for y
2(-1) + 3y = - 26
-2 + 3y = -26
3y = -24
y = -8
Let's check
2(-1) + 3(-8) = -26
-2 - 24 = -26
-26 = -26
So, x = -1 and y = -8 is the correct answer.
[tex]2x + 3y = - 26 \\ \implies \: 2x + 3y + 26 = 0[/tex]
[tex]5x + 3y = - 29 \\ \implies \: 5x + 3y + 29 = 0[/tex]
For finding what sort of solution the pair of equations give , we need to check the type of equality between
[tex] \frac{ a_{1}}{ a_{2} \: } , \: \frac{ b_{1} }{ b_{2} } , \: \frac{ c_{1}}{ c_{2} } \\ [/tex]
The following results can be obtained ,
[tex]if \: \: \frac{ a_{1} }{a _{2} } \neq \: \frac{ b_{1}}{ b_{2}} \\ \\ \implies \: we \: obtain \: a \: unique \: solution[/tex]
[tex]if \: \: \frac{ a_{1} }{a _{2} } = \: \frac{ b_{1}}{ b_{2}} \: \neq \: \frac{ c_{1}}{ c_{2}} \\ \\ \implies \:we \: obtain \: no \: solution[/tex]
[tex]if \: \: \frac{ a_{1} }{a _{2} } = \: \frac{ b_{1}}{ b_{2}} \: = \: \frac{ c_{1}}{ c_{2}} \\ \\ \implies \:we \: obtain \: infinitely \: many \: \: solutions[/tex]
Considering the equations provided ,
[tex] a_{1} = 2 \: \: , \: \: b_{1} = 3 \: \: , \: \: c_{1} = 26 \\ a_{2} = 5 \: \: , \: \: b_{2} = 3 \: \: , \: \: c_{2} = 29[/tex]
[tex]\therefore \frac{ a_{1}}{ a_{2} } = \frac{2}{5} \: \: \: , \: \: \: \frac{ b_{1}}{ b_{2} } = \frac{3}{3} = \frac{1}{1} \: \: \: , \: \: \: \frac{ c_{1} }{ c_{2} } = \frac{26}{29} \\ [/tex]
Since ,
[tex] \frac{ a_{1} }{ a_{2}} \neq \: \frac{ b_{1} }{ b_{2}} \\ [/tex]
The system of equations has a unique solution .
On further calculations done by elimination method , the solution of the equations comes out to be
[tex]\boxed{x = - 1} \\ \boxed{y = - 8}[/tex]
let's have a look at how it'll be done now.
the equations given in the question are -
[tex]2x + 3y + 26 = 0 \: ...(1) \\ 5x + 3y + 29 = 0...(2) \\ \\ multiplying \: equation \: (1) \: by \: - 1 \\ \implies \: - 2x - 3 - 26 = 0...(3) \\ \\ solving \: eqs. \: (2) \: and \: (3) \\ \\ 5x + \cancel{3y} + 29 = 0 \\ \underline{ - 2x \cancel{- 3y} - 26 = 0} \\ 3x + 3 = 0 \\ \\ \implies \: 3x = - 3 \\ \implies \: \boxed{x = - 1} [/tex]
substiting the value of x in equation 1
[tex]2( - 1) + 3y + 26 = 0 \\ 3y + 26 - 2 = 0 \\ 3y + 24 = 0 \\ 3y = - 24 \\ \implies \: \boxed{y = - 8}[/tex]
hope helpful! :)
▪ (n³ - 11n² +21n-24)÷(n-9)
The result obtained from the long division of the polynomial is n² + 2n - 1 + 3/(n - 9).
What is the result of the long division?
The quotient of the polynomial is obtained by applying long division method as shown below.
n² + 2n - 1
________________________
n - 9 √ (n³ - 11n² + 21n - 24)
(n³ - 9n²)
____________
-2n² + 21n
-2n² + 18n
__________
3n - 24
3n - 27
______
3
Therefore, the quotient is n² + 2n - 1 and the remainder is 3.
n³ - 11n² + 21n - 24 = (n - 9)(n² + 2n - 1) + 3.
So when we divide the polynomial using long division method we would obtain the following result.
(n³ - 11n² + 21n - 24) ÷ (n - 9) = n² + 2n - 1 + 3/(n - 9)
Learn more about long division here: https://brainly.com/question/25289437
#SPJ1
Find the quotient of this long division; (n³ - 11n² +21n-24)÷(n-9)
(p ↔ r) → (∼q → (p ∧ r))
simply this by propostional algebra
answer must be verifiable by truth table
Truth Table
This statement can be simplified using proportional algebra as follows: (p ∨ ∼r) ∧ (q ∨ (p ∧ r)). This can be verified using a truth table.
Learn more about proportional algebra
brainly.com/question/19306970
#SPJ11
find (gof)(x) if f(x)=X^2-3, and g(x)=2x-1,
The composite result function ( g o f )(x) in the functions f(x) = x² - 3 and g(x) = 2x - 1 is 2x² - 7.
What is the function operation ( g o f )(x) in the given functions?A function is simply a relationship that maps one input to one output.
Given the data in the question;
f(x) = x² - 3g(x) = 2x - 1(g o f)(x) = ?First, set up the composite result function (g o f)(x).
(g o f)(x) = g( f(x) )
g( x ) = 2x - 1
g( f(x) ) = 2( f(x) ) - 1
g( f(x) ) = 2( x² - 3 ) - 1
Now, simplify the function by applying distributive property.
g( f(x) ) = 2( x² - 3 ) - 1
g( f(x) ) = 2 × x² - 2 × 3 - 1
g( f(x) ) = 2x² - 6 - 1
Add -6 and -1
g( f(x) ) = 2x² - 7
Therefore, the function operation ( g o f ) is 2x² - 7.
Learn more about functions here: brainly.com/question/2541698
#SPJ1
HELP PLEASE DUE TODAY WILL GIVE BRAINLIST
The volume of the given shapes are listed below with their options:
11.) 12 in³ = C
12.) 108 in³ = D
13.) 293.33 cm³ = C
14.) 287 mi³ = B
15.) 3801.33 cm³ = D
16.) 452.39 yd³ = C
17.) 3619.11 in³= B
18.) 16 ft³ = C
19.) 64 m³ = A
20.) 769.69 cm³ = C
How to calculate the volume of a pyramid, cylinder and a cone?The formula used to calculate the volume of a cylinder= πr²h
The formula used to calculate the volume of triangular prism = 1/3Bh
For a square based pyramid = 1/3b²h
For a rectangular pyramid = 1/3 lwh
Volume of a cone = 1/3πr²h
For question 11;
Volume of the triangular pyramid =1/3Bh= 1/3×6×6 = 12 in³
For question 12;
Volume of square pyramid =1/3b²h = 1/3 ×6×6×9 = 108 in³
For question 13.)
Volume of a rectangular pyramid = 1/3 lwh= 1/3×11*8*10=293.33 cm³
For question 14.)
Volume of square pyramid =1/3b²h = 1/3*9*9*11= 287 mi³
For question 15.)
Volume of a cylinder = πr²h = 3.14×11*11*10 = 3801.33 cm³
For question 16.)
Volume of a cone= 1/3πr²h= 1/3*3.14*6*6*12= 452.39 yd³
For question 17.)
Volume of a cone= 1/3πr²h= 1/3*3.14*12*12*24= 3619.11 in³.
For question 18.)
Volume of the triangular pyramid =1/3Bh = 1/3*6*8= 16 ft³
For question 19.)
Volume of the triangular pyramid =1/3Bh = 1/3*24*8= 64 m³
For question 20.)
Volume of a cylinder = πr²h = 3.14×7*7*5 = 769.69 cm³
Learn more about volume here:
https://brainly.com/question/27710307
#SPJ1
PLEAAAASEEEE HELPP!!!!!!!!!!! I WILL GIVE BRAINLIEST!!!!!!!!!!
The median of class A is equal to 40.
The median of class B is equal to 8.
The difference between the median of the two classes is 32.
What is a dot plot?In Mathematics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.
Based on the dot plot, the median of class A can be determined by sorting the data set in ascending order;
10, 10, 10, 20, 20, 30, 40, 40, 40, 40, 50, 50, 50, 70, 70
Median of class A = 40.
Based on the dot plot, the median of class B can be determined by sorting the data set in ascending order;
4, 6, 6, 6, 6, 8, 8, 8, 8, 10, 10, 10, 12, 12, 16
Median of class B = 8.
For the difference, we have:
Difference = 40 - 8
Difference = 32.
Read more on dot plots here: brainly.com/question/18466974
#SPJ1
Shea runs a carpet cleaning business. The average cost to shea per cleaning is $30. Shea charges $60 per cleaning. Shea’s fixed plus variable costs per month total $1,500. How many carpet cleaning does shea need to do per year to break even?
Shea needs to do 600 carpet cleaning per year to break even.
What is revenue?
Total revenue is the total amount of money earned by a business from the sale of its products or services during a particular period of time.
To break even, the total revenue Shea generates from the carpet cleaning business must be equal to the total cost of running the business.
Let's first calculate the total cost of running the business per year:
Total Cost = Fixed Costs + Variable Costs
Since the fixed plus variable costs per month total $1,500, the total cost per year would be:
Total Cost = $1,500 x 12
Total Cost = $18,000
Now, let's calculate the profit that Shea makes per cleaning:
Profit per Cleaning = Price per Cleaning - Cost per Cleaning
Profit per Cleaning = $60 - $30
Profit per Cleaning = $30
So, Shea makes a profit of $30 per cleaning.
To break even, the total profit generated by the number of cleanings Shea does per year should be equal to the total cost of running the business per year:
Total Profit = Total Revenue - Total Cost
If x is the number of carpet cleaning Shea needs to do per year to break even, then:
Total Revenue = Price per Cleaning x Number of Cleanings per Year = $60x
Total Profit = Profit per Cleaning x Number of Cleanings per Year = $30x
Setting Total Profit equal to Total Cost:
$30x = $18,000
x = $18,000 / $30
x = 600
Therefore, Shea needs to do 600 carpet cleaning per year to break even.
To learn more about the revenue, visit:
https://brainly.com/question/29087694
#SPJ1
ill give brainlyist Please someone help me asap :(
The value of probabilities are,
P (1, 1) = 1 / 36 = 0.027
P (both odd) = 0.166
P (even, odd) = 0.25
P (2 anywhere) = 0.3055
P (sum 8) = 0.1389
P (sum 1) = 0
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one
Given that;
Two dice are rolled at the same time.
Hence, There are total number of possibilities = 36
Thus, The value of P (1, 1) is,
P (1, 1) = 1 / 36
Since, There are 6 possibilities when both dice have rolled to get odd.
Hence, The value of P (both odd) is,
P (both odd) = 6 / 36
= 1/ 6
Since, There are 9 possibilities to get first dice even and second odd.
Hence, The value of P (even, odd) is,
P (even, odd) = 9/36
= 1/4
Since, There are 11 possibilities when 2 is in anywhere.
Hence, The value of P (2 anywhere) is,
P (2 anywhere) = 11/36
Since, There are 5 possibilities to get sum 8.
Hence, Value of P (sum 8) is,
P (sum 8) = 5/36
Since, There are no possibilities to get sum 1.
Hence, P (sum 1) = 0
Learn more about the probability visit:
https://brainly.com/question/13604758
#SPJ1
Intense trig problem.
The answer is [5sqrt(6)] / (12).
How do I get there?
Using the definition of the tangent function, we will get that:
5√(6)/12 = sin(θ)
How to find the sine of theta?Here you need to remember how the tangent function is defined, we know that:
tan(θ) = sin(θ)/cos(θ)
Here we know that:
tan(θ) = √15/3
cos(θ) = √10/4
Replacing that we can write:
√15/3 = sin(θ)*(4/√10)
Solving for the sine, we will get:
(√15/3)*(√10/4) = sin(θ)
(√15*√10)/(3*4) = sin(θ)
(√150)/(12) = sin(θ)
(√(25*6))/(12) = sin(θ)
5√(6)/12 = sin(θ)
That is the answer.
Learn more about the sine function:
https://brainly.com/question/9565966
#SPJ1
−2x−8y=10
2x−6y=18
−2x+9y=−4
2x+3y=−20
2x+5y=0
x + 5y = −10
−4x+y=9
−4x+9y=17
−5x−4y=−11
−4x + 4y = 20
−5x − 4y =
−15 −x + 4y = −3
3x + 2y =
−12 4x − 2y = −2
7x + 8y = 20
7x − y = 29
−3x − y = 8
−8x − y = 23
−6x − y =
−1 6x + 6y = −24
Please I need help like now I’m going to fail
The solution of the system of equation is
1) The solution to the system of equations is x = -7 and y = -2.
2) The solution to the system of equations is x = -7 and y = -2.
3) The solution to the system of equations is any point on the line 2x + 5y = 0
4) The solution to the system of equations is x = -2 and y = 1.
5) The solution to the system of equations is x = 1 and y = -16.
In mathematics, a system of equations refers to a set of two or more equations that must be solved simultaneously. Solving a system of equations involves finding the values of the variables that satisfy all the given equations. In this response, we will go through the process of solving five different systems of equations.
−2x−8y=10 and 2x−6y=18, in order to solve this system of equations, we need to eliminate one of the variables, x or y. One way to do this is to add the two equations together. When we add them, the x term cancels out, leaving us with -14y = 28. Solving for y, we get y = -2. Substituting this value of y into either equation, we get x = -7.
And then the equations, −2x+9y=−4 and 2x+3y=−20, to solve this system of equations, we can use the method of elimination again. If we add the two equations, the x term cancels out, leaving us with 12y = -24. Solving for y, we get y = -2. Substituting this value of y into either equation, we get x = -7.
Then the third one 2x+5y=0 and x + 5y = −10 is in this system of equations, we notice that the second equation is just the first equation with a constant term added. Therefore, these equations are dependent, meaning that they represent the same line. Any point that satisfies one equation will also satisfy the other equation.
And the fourth one has −4x+y=9 and −4x+9y=17, to solve this system of equations, we can use the method of substitution. We can solve the first equation for y, getting y = 4x + 9. Substituting this expression for y into the second equation, we get -4x + 9(4x + 9) = 17. Simplifying, we get 25x + 72 = 17. Solving for x, we get x = -2. Substituting this value of x into the first equation, we get y = 1.
−6x − y = 10 and −16x + 6y = −24, To solve this system of equations, we can use the method of elimination. If we multiply the first equation by -6 and the second equation by -1, we can add the two equations to eliminate y. Doing so, we get 80x = 80. Solving for x, we get x = 1. Substituting this value of x into either equation, we get y = -16.
To know more about equation here
https://brainly.com/question/10413253
#SPJ4
Complete Question:
Solve the system of equations
1) −2x−8y=10 and 2x−6y=18
2) −2x+9y=−4 and 2x+3y=−20
3) 2x+5y=0 and x + 5y = −10
4) −4x+y=9 and −4x+9y=17
5) −6x − y = 10 and −16x + 6y = −24
Are the triangles similar? if yes , write a similarity statement and explain how you know they are similar?
The both triangles are not similar.
How do you know similar triangle?
Similar triangles are triangles that have the same shape but may have different sizes. Two triangles are considered similar if their corresponding angles are equal, and their corresponding sides are in proportion or have the same ratio.
In other words, if two triangles have the same angles, then they are similar. The ratio of the lengths of the corresponding sides of similar triangles is the same, and this ratio is called the scale factor.
Learn more similar triangles:https://brainly.com/question/2773823
#SPJ1
How long does it take for a deposit of $800 to double at 8% compounded continuously?
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \stackrel{ doubled }{\$ 1600}\\ P=\textit{original amount deposited}\dotfill & \$800\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years \end{cases}[/tex]
[tex]1600 = 800e^{0.08\cdot t} \implies \cfrac{1600}{800}=e^{0.08t}\implies 2=e^{0.08t} \\\\\\ \log_e(2)=\log_e(e^{0.08t})\implies \log_e(2)=0.08t\implies \ln(2)=0.08t \\\\\\ \cfrac{\ln(2)}{0.08}=t\implies 8.66\approx t\qquad \textit{about 8 years and 241 days}[/tex]
Solve for x using the given angles
The value of x is -11
What is sum of angle in a triangle?The sum of angles of a triangle equals the straight angle (180 degrees, π radians, two right angles, or a half-turn). A triangle has three angles, one at each vertex, bounded by a pair of adjacent sides.
represent the other two base angles as z and y
z= 80(opposite angles)
y = 60( opposite angles)
z+y +x+51 = 180
80+60 +x +51 = 180
140+51+x = 180
x+191 = 180
x = 180-191
x = -11
therefore the value of x is -11
learn more about sum of angle in a triangle from
https://brainly.com/question/25215131
#SPJ1
What is the estimated quotient for 2 1/2 divided by 1 7/9
The estimated quotient of the given dividend 2 1 / 2 divided by the divisor 1 7/9 is equal to 1.41 ( round off up to the two decimals ).
Divisor = 1 7/9
Convert the divisor (mixed fraction ) into improper fraction,
1 7 /9
= [( 9× 1 ) + 7]/ 9
= 16/9
Dividend = 2 1 / 2
Convert the dividend (mixed fraction ) into improper fraction,
2 1 / 2
=[ ( 2 ×2 ) + 1] /2
= 5 /2
Divide the 5 / 2 by 16 /9 to get the estimated quotient ,
( 5 / 2 ) ÷ ( 16 / 9)
= ( 5 / 2 ) × ( 9 / 16 )
= ( 5 × 9 ) / ( 2 × 16 )
= 45 / 32
= 1.40625
= 1.41 ( round off up to the two decimals )
Therefore, the estimated quotient of the division is equal to 1.41( round off up to the two decimals ).
Learn more about estimated quotient here
brainly.com/question/14527521
#SPJ4
Solve the system of equations and choose the correct answer from the list of options. d + e = 1 −d + e = −5 Label the ordered pair as (d, e). (4 points) a (0, 0) b (3, −2) c (−2, 3) d (−3, 0)
Answer:
b (3, −2)
Step-by-step explanation:
You want the solution to the system of equations ...
d +e = 1-d +e = -5EliminationWe see the coefficients of d are opposites, so we can add the equations together to eliminate the d variable:
(d +e) +(-d +e) = (1) +(-5)
2e = -4 . . . . . . . . simplify
e = -2
Substituting into the first equation, we have ...
d +(-2) = 1
d = 3 . . . . . . add 2
The solution is (d, e) = (3, -2).
__
Additional comment
We also note that the coefficients of 'e' are identical, so we can eliminate 'e' as a variable by subtracting one equation from the other. We choose to subtract the equation with the lower value coefficient of 'd'.
(d +e) -(-d +e) = (1) -(-5)
2d = 6 . . . . . . . simplify
d = 3 . . . . . . . . divide by 2; matches the solution above.
The attached graph uses x and y, because those are the built-in independent and dependent variables. Your graphing calculator may let you define the variables as you wish.
x=1/2 and y= -5
4(1/2) (4) -3 (-5)
The value of 4x - 3y when x=1/2 and y=-5 is -13. The given equation can be simplified by using the distributive property.
What is an equation?An mathematical equation is a statement that states that two expressions are equal. It is usually written using symbols such as +, -, x, and ÷. They can be used to find unknown values, such as the area of a circle or the speed of a moving object.
The equation 4x - 3y = 0 can be rearranged to 4x = 3y. We can substitute 1/2 for x and -5 for y to determine the value of the equation. The equation becomes 4(1/2) (4) -3 (-5). This equation can be simplified by using the distributive property. The equation simplifies to 4/2 - 15. 4/2 simplifies to 2 and -15 simplifies to -15. The final answer is 2 - 15 = -13.
Therefore, the value of 4x - 3y when x=1/2 and y=-5 is -13.
For more questions with distributive property,
https://brainly.com/question/6276874
#SPJ1
The value of 4x - 3y when x=1/2 and y=-5 is -13. The given equation can be simplified by using the distributive property.
What is an equation?An mathematical equation is a statement that states that two expressions are equal. It is usually written using symbols such as +, -, x, and ÷. They can be used to find unknown values, such as the area of a circle or the speed of a moving object.
The equation 4x - 3y = 0 can be rearranged to 4x = 3y. We can substitute 1/2 for x and -5 for y to determine the value of the equation. The equation becomes 4(1/2) (4) -3 (-5). This equation can be simplified by using the distributive property. The equation simplifies to 4/2 - 15. 4/2 simplifies to 2 and -15 simplifies to -15. The final answer is 2 - 15 = -13.
Therefore, the value of 4x - 3y when x=1/2 and y=-5 is -13.
For more questions with distributive property,
brainly.com/question/6276874
#SPJ1
Complete question -
Find the value of 4x - 3y when x=1/2 and y=-5.
A line passes through points (-3, 1) and (2, - 3) What is the slope of the line parallel to the graph?
Answer:
To find the slope of the line passing through (-3, 1) and (2, -3), we can use the slope formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) = (-3, 1) and (x2, y2) = (2, -3).
slope = (-3 - 1) / (2 - (-3))
= -4 / 5
So, the slope of the line passing through (-3, 1) and (2, -3) is -4/5.
To find the slope of a line parallel to this line, we need to remember that parallel lines have the same slope. Therefore, the slope of the parallel line is also -4/5.
rewrite the expression in the form y^n y^6*y^3
The expression in the form [tex]y^n[/tex]is [tex]y^9[/tex].
What is expression?
In mathematics, an expression is a combination of numbers, symbols, and/or variables that are arranged in a particular way. Expressions can represent various mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation, and can be used to calculate a value or to represent a relationship between quantities.
The given expression is:
[tex]y^6 * y^3[/tex]
We can simplify this expression by adding the exponents of y:
[tex]y^6 * y^3 = y^(6+3) = y^9[/tex]
Therefore, the expression in the form [tex]y^n[/tex]is [tex]y^9[/tex].
To know more about expression visit:
https://brainly.com/question/1859113
#SPJ1
The volume of a right rectangular prism is 2.76 cubic centimeters. The length of the prism is 2.3 centimeters. The width of the prism is 0.8 centimeters. What is the
height of the of the prism?
The height of this prism is equal to 1.5 centimeters.
How to calculate the volume of a rectangular prism?Mathematically, the volume of a rectangular prism can be calculated by using this formula:
Volume = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.Substituting the given parameters into the formula for the volume of a rectangular prism, we have;
2.76 = 2.3 × 0.8 × H
Height, H = 2.76/1.84
Height, H = 1.5 centimeters.
Read more on prism here: brainly.com/question/21012007
#SPJ1