the numerators are both negative, the answer will be a negative number. The numerator of the first fraction (-5) divided by the numerator of the second fraction (5) is -1. Multiply this answer by the common denominator (18) to get the final answer: -5/2.
To solve this fraction division problem, first convert the fractions to have a common denominator. To do this, multiply the denominator of the first fraction (-1/3) by the denominator of the second fraction (6), and the denominator of the second fraction (6) by the denominator of the first fraction (-1/3). This will change the fractions to -5/18 and 5/18, respectively.
Next, divide the numerators of the fractions. Since the numerators are both negative, the answer will be a negative number. The numerator of the first fraction (-5) divided by the numerator of the second fraction (5) is -1.
Multiply this answer by the common denominator (18) to get the final answer: -5/2.
learn more about number here
https://brainly.com/question/10547079
#SPJ4
A company borrows $891,000 at 5%, 6% and 9% interest. It owed $54,000 in annual interest. The amount borrowed at 5% was four times the amount at 6%. How much was borrowed at 9%?
Answer:
$274,526
Step-by-step explanation:
Find the standard matrix of the linear transformation T: R2 to R2 that reflects each vector through the line x1=-x2.
The standard matrix is:
| 0 -1 |
| -1 0 |
The standard matrix of the linear transformation T: R2 to R2 that reflects each vector through the line x1=-x2 can be found by following these steps:
1. Start with the standard basis vectors for R2, which are (1,0) and (0,1).
2. Apply the transformation T to each of these vectors to find the new vectors. For the first vector, (1,0), we have x1=1 and x2=0. The reflection through the line x1=-x2 gives us a new vector with x1=-x2=-0=0 and x2=-x1=-1. So the new vector is (0,-1).
3. For the second vector, (0,1), we have x1=0 and x2=1. The reflection through the line x1=-x2 gives us a new vector with x1=-x2=-1 and x2=-x1=-0=0. So the new vector is (-1,0).
4. The standard matrix of the transformation T is the matrix whose columns are the new vectors we found. So the standard matrix is:
```
| 0 -1 |
| -1 0 |
```
This is the standard matrix of the linear transformation T: R2 to R2 that reflects each vector through the line x1=-x2.
To know more about the standard matrix is:
https://brainly.com/question/30389982#
#SPJ11
Chin paid $16. 24 for 7 bags of flour that were on sale for 10% off. Each bag contained 2 pounds of flour. What was the regular price for 1 pound of flour
In the following question, if Chin paid $16. 24 for 7 bags of flour that were on sale for 10% off. Each bag contained 2 pounds of flour. The regular price for 1 pound of flour is $1.29.
Chin paid $16.24 for 7 bags of flour that were on sale for 10% off.
Let's first find the total cost of the 7 bags of flour before the discount:
Total cost before discount = $16.24 ÷ 0.9 = $18.04
We know that each bag contained 2 pounds of flour, so the total amount of flour Chin bought was:
7 bags x 2 pounds/bag = 14 pounds
So the cost of 1 pound of flour is:
$18.04 ÷ 14 pounds = $1.29 per pound
Therefore, the regular price for 1 pound of flour would be $1.29.
For more such questions on discounts
https://brainly.com/question/27519306
#SPJ4
What is 68+1=
What is 69+0=
Answer:
69 and 69
Step-by-step explanation:
68 + 1 = 69
69 + 0 = 69
look how much people i hav helped
Triangle a′b′c′ is a dilation of triangle abc about point p with a scale factor of 12. is the dilation a reduction or an enlargement? responses reduction reduction enlargement
The dilation of triangle ABC about point P with a scale factor of 12 is an enlargement.
In a dilation, the size of a figure is changed by multiplying its dimensions by a scale factor. If the scale factor is greater than 1, the figure is enlarged. If the scale factor is between 0 and 1, the figure is reduced in size. In this case, the scale factor is 12, which is greater than 1. Therefore, triangle ABC is enlarged to form triangle A'B'C' by a factor of 12. Therefore, the dilation is an enlargement.
In the context of triangles, an enlargement means that all sides and angles of the original triangle are increased by the same factor to create a larger triangle. In this case, the sides and angles of triangle ABC are multiplied by a factor of 12 to create triangle A'B'C'. As a result, the corresponding sides and angles of the two triangles are proportional, but the enlarged triangle is 12 times larger than the original triangle.
Learn more about corresponding sides here:
https://brainly.com/question/16086091
#SPJ4
What is the translation rule that describes the result of the composition of (x, y) --> (x+4, y-1) and (x, y) --> (x-5, y-5)?
The composition of the two translation rules is:
(x, y) → (x - 1, y - 6)
What is a translation rule?
A translation rule is a mathematical description of how to move each point in a geometric shape by a fixed distance in a certain direction. It is used to describe a transformation called a translation, which moves a shape without changing its size, shape, or orientation.
To find the composition of the two translation rules, we apply the second rule first and then apply the first rule to the result.
Let's consider a point (x, y). Applying the second rule (x, y) → (x - 5, y - 5) gives us a new point:
(x - 5, y - 5)
Now we apply the first rule (x, y) → (x + 4, y - 1) to this new point:
(x - 5 + 4, y - 5 - 1)
Simplifying:
(x - 1, y - 6)
Therefore, the composition of the two translation rules is:
(x, y) → (x - 1, y - 6)
To learn more about the translation rule, visit:
https://brainly.com/question/12861087
#SPJ1
Suppose a city with 400,000 population has been growing at a rate of 4% per year. If this rate continues, find the population of this city in 17 years
The population of a city with 400,000 population growing at a rate of 4% per year can be calculated using the following formula:
P(t) = P0 (1 + r)t
Where P0 is the initial population, r is the growth rate, and t is the number of years the growth is applied.
In this example, the initial population is 400,000, the growth rate is 0.04, and t is 17 years. Applying this formula, we get:
P(17) = 400,000 (1 + 0.04)17
P(17) = 615,288
Therefore, the population of this city in 17 years will be 615,288 if the growth rate of 4% per year continues.
For more such population related questions
https://brainly.com/question/29885712
#SPJ11
Someone PLEASE help me ASAP!! It’s due today!! Show work please! I will mark brainliest if it’s done correctly
The correct answer is experimental 22.5% theoretical 18.2%.
What is theoretical probability?The theoretical probability is the likelihood of the event to happen without conducting an experiment,
The experimental probability is the result of the actual experiment, which in this case is the frequency of the letter M when chosen from the bag. Theoretical probability in this case is the number of M's in the bag divided by the total number of letters in the bag.
In this case, there are nine M's out of a total of 39 letters, giving a theoretical probability of 18.2%. Since the number of M's chosen in the experiment was nine, out of a total of 39 chosen, the experimental probability is 22.5%.
For more questions related to event
https://brainly.com/question/29280399
#SPJ1
The correct answer is experimental 22.5% theoretical 18.2%. To calculate the experimental probability of drawing the letter M, we must first identify the total number of items in the bag.
What is theoretical probability?The theoretical probability is the likelihood of the event to happen without conducting an experiment,
The total number of items in the bag is 9 + 12 + 7 + 2 + 4 + 1 + 3 + 2 = 40. Next, we divide the number of items with the letter M (9) by the total number of items to get the experimental probability of drawing the letter M.
Therefore, 9/40 = 0.225
= 22.5%.
To calculate the theoretical probability of drawing the letter M, we must first identify the total number of letters in the bag.
There are 8 letters in the bag (M, A, T, H, E, I, C, S).
Therefore, the theoretical probability of drawing the letter M is
8/40 = 0.2
≈18.2%
For more questions related to event
https://brainly.com/question/29280399
#SPJ1
how many ternary sequences of digits chosen from {0, 1, 2} of length twelve have exactly three 1's and two 0's?
It can be stated that there exist 63,360 ternary sequences of digits selected from {0, 1, 2} with a length of twelve, which contain precisely three 1s and two 0s.
The problem is asking us to find out how many ternary sequences of digits are there that are chosen from {0, 1, 2} of length twelve, and have exactly three 1's and two 0's.
Therefore, there will be a total of 7 digits (12 - 3 - 2 = 7) that could be 1 or 2. So, let's solve it in steps.
Step 1: The number of ways we can choose 3 positions out of 12 for 1s is C (12,3).
Step 2: The number of ways we can choose 2 positions out of 9 (because there are already 3 1s and 2 0s) for 0s is C (9,2).
Step 3: We have three digits left that can be either 1 or 2. So, there will be 2 options for each of these digits, and the total number of options will be
2 × 2 × 2 = 8.
Step 4: So, the total number of sequences will be obtained by multiplying the results of Steps 1, 2, and 3. i.e.
C (12,3) × C (9,2) × 8
⇒ ¹²C₃ × ⁹C₂ × 8
⇒ 220 × 36 × 8 = 63360.
Therefore, there are 63,360 ternary sequences of digits chosen from {0, 1, 2} of length twelve that have exactly three 1s and two 0s.
To know more about the "ternary sequences": https://brainly.com/question/9083389
#SPJ11
A lorry travels 320km and uses 40 litres of petrol, work out the average rate of petrol usage. Amswer in km. Litre
If a lorry travels 320km and uses 40 litres of petrol, the average rate of petrol usage for the lorry is 8 km per liter.
To find the average rate of petrol usage for the lorry, we need to divide the total distance traveled by the amount of petrol used. This will give us the number of kilometers traveled per liter of petrol.
In this case, the lorry traveled 320 km and used 40 liters of petrol, so we can calculate the average rate of petrol usage as follows:
Average rate of petrol usage = Total distance traveled / Amount of petrol used
= 320 km / 40 litres
= 8 km/litre
This means that for every liter of petrol used, the lorry can travel an average of 8 kilometers. This metric can be useful in comparing the fuel efficiency of different vehicles or in calculating the cost of a particular journey based on the price of petrol per liter.
In summary, calculating the average rate of petrol usage involves dividing the distance traveled by the amount of petrol used, resulting in a unit of km per liter.
To learn more about rate of petrol usage click on,
https://brainly.com/question/30461443
#SPJ4
for the following two sequences (i) give the first 5 terms of the sequence. (ii) determine if the sequence converges or diverges. if the sequence converges, determine the limit of the sequence
The sequences can converge to 0 and also diverge towards infinity.
The two sequences are not mentioned in the question. Please provide the two sequences so that I can give you the first 5 terms of each sequence and determine if each sequence converges or diverges.
To find the first 5 terms of a sequence, you need to use the formula given for the sequence and plug in the values for the first 5 terms. For example, if the sequence is given by a_n = 2n + 1, the first 5 terms would be a_1 = 2(1) + 1 = 3, a_2 = 2(2) + 1 = 5, a_3 = 2(3) + 1 = 7, a_4 = 2(4) + 1 = 9, and a_5 = 2(5) + 1 = 11.
To determine if a sequence converges or diverges, you need to find the limit of the sequence as n approaches infinity. If the limit exists, then the sequence converges to that limit. If the limit does not exist, then the sequence diverges.
For example, the sequence a_n = 1/n converges to 0 as n approaches infinity, while the sequence a_n = n^2 diverges as n approaches infinity.
To know more about Sequences, click on the link below:
https://brainly.com/question/30262438#
#SPJ11
Jocelyn and Lorlesha are comparing the size of their villages in the Clash of Clans app. The area of Jocelyn’s village is represented by the polynomial, 2w^2 + 10w + 12. The area of Lorlesha’s village is represented by the polynomial, 3w^2 + 4w -5, where w represents the width, in meters of their Town Hall.
Jocelyn's village additional area is (-w² + 6w + 17) m². The combined total area of both is (5w² + 14w + 7) m².
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
Let w represent he width of the town hall.
Area of Jocelyn's village = 2w² + 10w + 12
Area of Lorlesha's village = 3w² + 4w - 5
The difference in their area = (2w² + 10w + 12) - (3w² + 4w - 5) = -w² + 6w + 17
The sum of their area = (2w² + 10w + 12) + (3w² + 4w - 5) = 5w² + 14w + 7
Jocelyn's village additional area is (-w² + 6w + 17) m². The combined total area of both is (5w² + 14w + 7) m².
Find more on equation at: https://brainly.com/question/2972832
#SPJ1
A machine takes 2.8 hours to make 9 parts. At that rate, how many parts can the machine make in 28.0 hours?
Answer:
The machine can make 9 parts in 2.8 hours.
To find the rate of production, we can divide the number of parts by the time: 9 parts / 2.8 hours = 3.214 parts per hour.
Now that we know the machine's rate of production, we can use it to answer the question:
In 28.0 hours, the machine will produce: 3.214 parts per hour x 28.0 hours = 89.9 parts.
Therefore, the machine can make 89.9 parts in 28.0 hours at the given rate. We can round this to 90 parts.
Step-by-step explanation:
The relationship between the number of decibels β and the intensity of a sound I
in watts per square meter is
β=10log(I10−12)
(a) Determine the number of decibels of a sound with an intensity of 1 watt per square meter.
(b) Determine the number of decibels of a sound with an intensity of 10−2
watt per square meter.
(c) The intensity of the sound in part (a) is 100 times as great as that in part (b). Is the number of decibels 100 times as great? Explain.
(a) A sound with an intensity of 1 watt per square meter has a decibel level of -120.
(b) A sound with an intensity of 10⁻² watt per square meter has a decibel level of -140.
(c) The number of decibels is not 100 times as great as the intensity, even though the intensity in part (a) is 100 times greater than the intensity in part (b).
What is the sound level?
Using the relationship of intensity of sound and number of decibels, we can calculated the required number of decibels as follows;
β =10 log(I x 10⁻¹²)
(a) Decibel level: plugging in I = 1 watt per square meter into the equation, we get:
β = 10 log(1 x 10⁻¹²) = 10 log(10⁻¹²) = -120 decibels
(b) Decibel level: plugging in I = 10⁻² watt per square meter into the equation, we get:
β = 10 log(10⁻² x 10⁻¹²) = 10 log(10⁻¹⁴) = -140 decibels
(c) Let's calculate the decibel level for the sound in part (a) using the given formula:
β₁ = 10 log(I₁ x 10⁻¹²) = 10 log(100 x I₂ x 10⁻¹²) = 10 log(I₂ x 10⁻¹⁴) + 20
where;
I₂ is the intensity of the sound in part (b).Using the result from part (b), we can substitute I₂ = 10⁻² watt per square meter and get:
β₁ = -140 + 20 = -120 decibels
Comparing this result to the decibel level for the sound in part (a) (which is also -120 decibels), we see that they are the same.
Learn more about decibel level here: https://brainly.com/question/29239268
#SPJ1
A discount store is selling 5 small tables with 8 chairs for $115. Three tables with 5 chairs cost $70.
Which system of linear equations could be used to find the cost of each table (x) and the cost of each chair (y)?
Determine the cost of each table (x) and the cost of each chair (y).
answer both question please and thank you
Using linear equations 5x + 8y = 115 and 3x + 5y = 70, the cost of each table is $15 and the cost of each chair is $5.
What is a linear equation, exactly?
A linear equation is a mathematical expression that describes a straight line relationship between two variables. It can be written in the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept.
Now,
Let x = cost of each table and y= cost of each chair. Then, we can set up the following system of linear equations based on the given information:
5x + 8y = 115 (equation 1)
3x + 5y = 70 (equation 2)
Equation 1 represents the cost of 5 small tables with 8 chairs, and equation 2 represents the cost of 3 tables with 5 chairs.
Now,
Solve equation 2 for x:
3x + 5y = 70
3x = 70 - 5y
x = (70 - 5y)/3
Substitute x into equation 1:
5x + 8y = 115
5[(70 - 5y)/3] + 8y = 115
Simplify and solve for y:
350/3 - 25/3 y + 8y = 115
23/3 y = 115 - 350/3
y = 5
Substitute y = 5 into equation 2 and solve for x:
3x + 5y = 70
3x + 5(5) = 70
3x = 45
x = 15
Therefore,
the cost of each table is $15 and the cost of each chair is $5.
To know about linear equations visit the link
brainly.com/question/29739212
#SPJ1
What are all the zeros of the polynomial function
[tex]f(x)=x^4-2x^3-8x^2+10x+15[/tex]
Answer:
The correct option is A. x = -1, x = 3, x = ±√5.
We found the zero x = -1 through synthetic division, and then we factored the cubic polynomial using the Rational Root Theorem and synthetic division to obtain (x + 1)(x^3 - 3x^2 - 6x + 15). We found that the remaining zeros of the polynomial function are the roots of the quadratic factor x^2 - 3x - 5, which are x = (3 ± √29))/2.
Therefore, the zeros of the polynomial function f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15 are x = -1, x = 3, x = (3 + √(29))/2, and x = (3 - √(29))/2, which simplifies to x = (3 ± √(5))/2.
Option A lists all of these zeros, so it is the correct option. Options B and C do not list all of the zeros of the polynomial function.
STEPS: Here are the steps to find all the zeros of the polynomial function f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15:
Write the polynomial function in descending order of degree: f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15.
Use the Rational Root Theorem to generate a list of possible rational zeros: ±1, ±3, ±5, ±15.
Use synthetic division to test each possible zero. We start with x = -1:
-1 │ 1 -2 -8 10 15
│ -1 3 -5 -5
└───────────────
1 -3 -5 5 10
x = -1 is a zero of the polynomial function. We can write f(x) as:
f(x) = (x + 1)(x^3 - 3x^2 - 5x + 10)
Use the Rational Root Theorem and synthetic division to factor the cubic equation x^3 - 3x^2 - 5x + 10:
3 │ 1 -3 -5 10
│ 3 0 -15
└─────────────
1 0 -5 -5
x = 3 is not a zero of the polynomial function.
-3 │ 1 -3 -5 10
│ -3 24 -57
└────────────
1 -6 19 -47
x = -3 is not a zero of the polynomial function.
The only remaining possible rational zeros are ±1/1 and ±5/1, but testing these values using synthetic division does not yield any more zeros.
Solve for the remaining zeros of the polynomial function by factoring the quadratic equation x^2 - 3x - 5 using the quadratic formula or factoring by grouping:
x = (3 ± √(29))/2
These are the remaining zeros of the polynomial function.
Therefore, the zeros of the polynomial function f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15 are x = -1, x = 3, x = (3 + √(29))/2, and x = (3 - √(29))/2, which simplifies to x = (3 ± √(5))/2.
Option A lists all of these zeros, so it is the correct option.
Hope this helps! I'm sorry if it doesn't! :]
Solve this homogeneous differential equation
dy/dx=y^2+x^2/x^2
The solution to the given homogenous differential equation dy/dx = y² + x² / x^2 is y² = -x(y³ / 3 + Cy³ - 3Cx)
The given differential equation is: dy/dx = y² + x² / x^2
To solve this, we can first separate the variables by bringing all the y-terms on one side and all the x-terms on the other side:
(1/y²)dy = (x² / x² + y²)dx
Next, we can integrate both sides:
∫(1/y²)dy = ∫(x²/x² + y²)dx
Using the substitution u = y/x, we can simplify the integrals:
∫(1/y²)dy = ∫(1 + u²)dx
-1/y = x + (1/3)u³ + C
where C is the constant of integration.
Substituting back u = y/x, we get:
-1/y = x + (1/3)(y/x)³ + C
Multiplying both sides by -y³, we get:
y² = -x(y³ / 3 + Cy³ - 3Cx)
To learn more about homogenous differential equation click here
brainly.com/question/30624850
#SPJ4
10.6.3 Test (CST): Factoring Polynomials
Question 3 of 25
What are the zeros of f(x) = x²-x-20?
OA. x=-2 and x = 10
B. x= -4 and x = 5
OC. x=-10 and x = 2
OD. x= -5 and x = 4
Therefore, the zeros of the function f(x) are x = 5 and x = -4.
What is polynomial?A polynomial is a mathematical expression consisting of variables and coefficients, combined using the operations of addition, subtraction, multiplication, and non-negative integer exponents. It can have one or more terms, and the degree of a polynomial is the highest power of the variable in the expression.
Here,
To find the zeros of the function f(x) = x² - x - 20, we need to solve for x when f(x) = 0:
x² - x - 20 = 0
We can factor the left side of this equation as:
(x - 5)(x + 4) = 0
Using the zero product property, we know that the product of two factors is zero if and only if at least one of the factors is zero. Therefore, we can set each factor equal to zero and solve for x:
x - 5 = 0 or x + 4 = 0
Solving for x in each equation gives us:
x = 5 or x = -4
To know more about polynomial,
https://brainly.com/question/11536910
#SPJ1
Pls help me I don’t know the answer and don’t understand it
If the length of rectangle is 5.25, then the area of rectangle will be less than 25 square meters.
What is area of rectangle?
Area of rectangle is the region covered by the rectangle in a two-dimensional plane. A rectangle is a type of quadrilateral, a 2d shape that has four sides and four vertices.
We know the perimeter of rectangle is 20 meters. So according to formula of Perimeter of rectangle = 2 (L + B) we can conclude that sum of length and width will be 10 meters.
We are given length as 1, 3, 5, 7, and 9.
So width of the rectangle will be 9, 7, 5, 3 and 1.
Area of Rectangle = L x B
So area of rectangle will be 9, 21, 25, 21, and 9.
If the length of rectangle is 5.25, then the area of rectangle will be less than 25 square meters.
Values are changing in a linear way and not in an exponential way.
Learn more about rectangles on:
https://brainly.com/question/2607596
#SPJ1
if 4x+y=7 is a true equation what would be the value of −5(4x+y)
Answer:
-32
Step-by-step explanation:
since 4x+y equals 7, multiply -5 by 7
Answer:
40x - 5y = -40x - 5(4x + y) = -40x - 20x - 5(7) = -60x - 35
Step-by-step explanation:
To find the value of -5(4x+y), we first need to simplify the expression inside the parentheses:
-5(4x + y) = -5(4x) - 5(y) = -20x - 5y
Now, we can substitute the value of y from the given equation:
-20x - 5y = -20x - 5(4x + y) = -20x - 20x - 5y = -40x - 5y
Since we know that 4x + y = 7, we can substitute this into the above equation:
-40x - 5y = -40x - 5(4x + y) = -40x - 20x - 5(7) = -60x - 35
20 POINTS, URGENT!!
A. the area of a rectangular deck is (8d² + 20d). The deck is (4d) meters long. Determine a polynomial that represents the width of the deck.
B. What are the dimensions and area of the deck when d is 4 meters?
I think the answer to A is (2d + 5) but what I need help with is B
In response to the given question, we can state that With d = 4 metres, polynomials the deck dimensions are 16 metres by 128 metres, and the deck area is 2048 square metres.
what are polynomials?A polynomial is a mathematical statement composed of equations and uncertainty that exclusively uses additions, addition and subtraction, multiplications, and real number powers of variables. The form x2 4x + 7 indicates a single determinate x algebraic. A polynomial expression in mathematics is made up of determinants (also known as freshly made) and equations that may be added, deducted, multiplied, then raised to minus integer powers of semi. A polynomial is an algebraic statement that includes variables and coefficients. An expressions can really only incorporate the operations add, subtraction, duplication, and non-negative integer factors. These expressions are referred to as polynomials.
substituting d = 4 into the formulas given in the problem.
Then, using the polynomial you discovered in Part A, we can calculate the breadth of the deck when d = 4.
8d2 + 20d = 8(42) + 20(4) = 128 width
With d = 4 metres, the breadth of the deck is 128 metres.
Next, we may utilise the supplied deck length, 4d = 4(4) = 16 metres, to calculate the deck area when d = 4:
16 × 128 = 2048 Area = Length x Width
With d = 4 metres, the deck dimensions are 16 metres by 128 metres, and the deck area is 2048 square metres.
To know more about polynomials visit:
https://brainly.com/question/11536910
#SPJ1
help asap assignment closes soon!
Answer:
a = 12.56637061
Step-by-step explanation:
a= 4 · π · r²
a= 4 · π · 1²
a= 4π
a= 12.56637061
a= 12.57
Solve triangle ABC given that A = 56°, B = 57°, and b = 9. 0. Round the length of the sides to the nearest hundredth.
The sides of the triangle to the nearest hundredth are: a ≈ 8.99, b ≈ 7.96
and c ≈ 9.44.
To solve the triangle, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides.
Using this law, we can find the length of side a as follows:
sin A / a = sin B / b
sin 56° / a = sin 57° / 9
a = 9 * sin 56° / sin 57°
a ≈ 8.99
Similarly, we can find the length of side c as follows:
sin C / c = sin B / b sin (180° - A - B) / c = sin 57° / 9
sin 67° / c = sin 57° / 9
c = 9 * sin 67° / sin 57°
c ≈ 9.44
Now, we can use the Law of Cosines to find the length of the remaining side, side b:
b 2 = a 2 + c 2 - 2ac cos B
b 2 = (8.99) 2 + (9.44) 2 - 2(8.99)(9.44) cos 57°
b ≈ 7.96
For more such question on triangle
https://brainly.com/question/17335144
#SPJ11
Need some help in math
Answer: A all you have to do is look where the line is going
Answer:
C
Step-by-step explanation:
under a reflection in the line y = - x
a point (x, y ) → (- y, - x ) , then
(- 1, 6 ) → (- 6, - (-1) ) → (- 6, 1 )
(- 3, 2 ) → (- 2, - (- 3) ) → (- 2, 3 )
Which inequality is equivalent to −4≥28?
Answer:
-1 ≥ 7
Step-by-step explanation:
-1 ≥ 7 = -4 ≥ 28
-4 ≥ 28
We simplify both sides by 4 and get -1 ≥ 7
The diagonal of rectangle is 26 and its perimeter is 68 what are its dimensions
If the diagonal of the rectangle is 26 and its perimeter is 68, its dimensions are either 24 by 10 or 10 by 24.
Let's denote the length and width of the rectangle as L and W, respectively.
We know that the diagonal of the rectangle is 26, which we can express using the Pythagorean theorem:
[tex]L^2[/tex]+ [tex]W^2[/tex]=[tex]26^2[/tex]
We also know that the perimeter of the rectangle is 68:
2L + 2W = 68
We can simplify the second equation by dividing both sides by 2:
L + W = 34
We can use this simplified equation to express one variable in terms of the other:
L = 34 - W
This is what we get when we enter it into the first equation:
[tex](34 - W)^2[/tex] + [tex]W^2[/tex] = [tex]26^2[/tex]
Expanding the square and simplifying, we get:
[tex]2W^2[/tex] - 68W + 420 = 0
Dividing both sides by 2, we get:
[tex]W^2[/tex]- 34W + 210 = 0
The quadratic formula can be used to find W:
W = (-b ± t[tex]\sqrt{(b^2 - 4ac)}[/tex] )/ 2a
where a = 1, b = -34, and c = 210. Plugging in these values, we get:
W = (34 ± [tex]\sqrt{34^2 - 4(1)(210))}[/tex]) / 2(1)
W = (34 ± [tex]\sqrt{196}[/tex]) / 2
W= (34 ± 14)/2
W = 17 ± 7
As the breadth cannot be negative, we can disregard the negative solution. Therefore, we have:
W = 24 or W = 10
If W = 24, then L = 10 (using L = 34 - W). If W = 10, then L = 24. Therefore, the dimensions of the rectangle are either 24 by 10 or 10 by 24.
To learn more about rectangle, refer:-
https://brainly.com/question/29085356
#SPJ4
Consider the following set of numbers:
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
What is the probability of drawing an odd number or a
multiple of 3?
Answer:
Probability of drawing an odd number.
Number of odd numbers = 5
Number of numbers in the set = 10
So it's a 5 in 10 chance or 1 in 2 chance.
Probability of drawing a multiple of 3.
Multiples of 3 in the set = 3, 6 and 9 = 3 multiples of 3
Number of numbers in the set = 10
So it's a 3 in 10 chance
What are all the zeros of the polynomial function?
[tex]f(x)=3x^3-5x^2-10x-6[/tex]
Answer:
The correct option is C. x=3, x=-2±√2/3.
Step-by-step explanation:
To find all the zeros of the polynomial function f(x) = 3x^3 - 5x^2 - 10x - 6, we can follow the steps outlined in the previous answer:
Write the polynomial function in descending order of degree: f(x) = 3x^3 - 5x^2 - 10x - 6.
Use the Rational Root Theorem to generate a list of possible rational zeros: ±1, ±2, ±3, ±6, ±(1/3), ±(2/3).
Use synthetic division to test each possible zero. We start with x = 1:
1 │ 3 -5 -10 -6
│ 3 -2 -12
└─────────────
3 -2 -12 -18
x = 1 is not a zero of the polynomial function.
We continue testing the remaining possible zeros:
-1 │ 3 -5 -10 -6
│ -3 8 2
└────────────
3 -8 -2 -4
x = -1 is not a zero of the polynomial function.
2 │ 3 -5 -10 -6
│ 6 2 -16
└─────────────
3 1 -8 -22
x = 2 is not a zero of the polynomial function.
-2 │ 3 -5 -10 -6
│ -6 22 -24
└────────────
3 -11 12 -30
x = -2 is not a zero of the polynomial function.
3 │ 3 -5 -10 -6
│ 9 12 6
└─────────────
3 4 2 0
Since the remainder is zero, we have found a zero of the polynomial function at x = 3.
We can use synthetic division to factor the polynomial function:
3x - 1
(x - 3)(3x^2 + 13x + 2)
Now we can solve for the remaining zeros of the polynomial function by factoring the quadratic equation using the quadratic formula or factoring by grouping. Either way, we find that the remaining zeros are approximately x = -4.87 and x = -0.435.
Therefore, the zeros of the polynomial function f(x) = 3x^3 - 5x^2 - 10x - 6 are x = -4.87, x = -0.435, and x = 3.
It's C because we found the zero x = 3 through synthetic division, and then we used the quadratic formula to find the other two zeros. The quadratic formula gave us two solutions, which we simplified to x = -2 + sqrt(2)/3 and x = -2 - sqrt(2)/3.
If we substitute these solutions back into the original polynomial function f(x), we get:
f(-2 + sqrt(2)/3) = 3(-2 + sqrt(2)/3)^3 - 5(-2 + sqrt(2)/3)^2 - 10(-2 + sqrt(2)/3) - 6
≈ 0
f(-2 - sqrt(2)/3) = 3(-2 - sqrt(2)/3)^3 - 5(-2 - sqrt(2)/3)^2 - 10(-2 - sqrt(2)/3) - 6
≈ 0
Both of these values are approximately zero, which means that -2 + sqrt(2)/3 and -2 - sqrt(2)/3 are also zeros of the polynomial function.
Therefore, the zeros of the polynomial function f(x) = 3x^3 - 5x^2 - 10x - 6 are x = 3, x = -2 + sqrt(2)/3, and x = -2 - sqrt(2)/3, which matches option C.
Hope this helps! I'm sorry if it's wrong. If you need more help, ask me! :]
Find the inverse of the following function: f(x) = 2(x - 4)^3 + 7
The inverse of the function f(x) = 2(x - 4)³ + 7 is g(x) = ∛[(x - 7) / 2] + 4.
What is a function?A mathematical notion known as a function explains the connection between two sets of values known as the domain and the range. A function takes a value from the domain as an input, applies some logic to it, and returns a value in the range. Just one output value in the range corresponds to each input value in the domain. Functions can be described verbally or with mathematical symbols. They are employed throughout the mathematical discipline as well as in the sciences of physics, engineering, economics, and computer science.
The given function is f(x) = 2(x - 4)³ + 7.
Swap the variables, that is substitute x = y and vice versa as follows:
x = 2(y - 4)³ + 7
x - 7 = 2(y - 4)³
(x - 7) / 2 = (y - 4)³
Taking the cube root of both sides gives:
y - 4 = ∛[(x - 7) / 2]
y = ∛[(x - 7) / 2] + 4
Therefore, the inverse of f(x) = 2(x - 4)³ + 7 is g(x) = ∛[(x - 7) / 2] + 4.
Learn more about function here:
https://brainly.com/question/31062578
#SPJ1
At the start of the day, a painter rested a 3m ladder against a vertical wall so that
the foot of the ladder was 50cm away from the base of the wall.
During the day, the ladder slipped down the wall, causing the foot of the ladder to
move 70cm further away from the base of the wall.
How far down the wall, in centimetres, did the ladder slip?
Give your answer to the nearest 1 cm.
The ladder slipped down the wall by approximately 296 cm to the nearest 1 cm.
What is the distance slipped by the ladder?We can use the Pythagorean theorem to solve this problem.
Let the distance the ladder slips down the wall be represented by x (in cm).
Then, at the start of the day, we have a right triangle formed by the wall, the ground, and the ladder, with the ladder being the hypotenuse.
The length of the ladder is 3m = 300cm, and the distance from the foot of the ladder to the wall is 50cm.
Therefore, we have:
(300)² = x² + (50)²
Simplifying this equation, we get:
90000 = x² + 2500
Subtracting 2500 from both sides, we get:
87500 = x²
Taking the square root of both sides, we get:
x = √87500
x = 295.8 cm
x ≈ 296 cm
Learn more about slipping of ladder here: https://brainly.com/question/13652193
#SPJ1