The amount of each Marco's payments for the 2 reclining chairs, a coffee table including with shipping cost is found as $182.
Explain the division operation?Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people belong to each group after a fair distribution is the basic objective of division.The data for the given question-
Mardo placed an order for a coffee table and two recliners for a total of $230 each. The price of shipping is $100. Marco will settle his debt in five equal payments.Thus, the total cost becomes-
Total cost = 2 x reclining chairs + coffee table + shipping cost
Total cost = 2 x 230 + 350 + 100
Total cost = $910
For the amount of each payment when there are 5 equal payments.
Total cost = 910/5
Total cost = $182
Thus, the amount of each Marco's payments for the 2 reclining chairs, a coffee table including with shipping cost is found as $182.
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find the probability of rolling a five or six on six sided number cube
Answer:
non-violence and kindness with animals
Step-by-step explanation:
Solve for x. Triangle stuff
Answer:
x=9
Step-by-step explanation:
these 2 angles are supplementary angles meaning added together they will equal 180 degrees
so we can add them together and set it equal to 180
(8x-3)+(16x-33)=180
combine like terms
(8x+16x)+(-3-33)=180
24x-36=180
+36. +36
24x=216
/24. /24
x=9
hopes this helps
let $f(x)$ be a polynomial with integer coefficients. suppose there are four distinct integers $p,q,r,s$ such that $$f(p)
The smallest possible value of f ( t ) = 9 based on the values of p , q , r , s.
Given :
Let f ( x ) be a polynomial with integer coefficients. Suppose there are four distinct integers p , q , r , s such that f ( p ) = f ( q ) = f ( r ) =f ( s ) = 5. If t is an integer and f ( t ) > 5,
Let g(x) = f(x) − 5.
g(x) = (x−p)(x−q)(x−r)(x−s)h(x)
The condition f(t) > 5 translates to g(t) > 0.
Since p,q,r,s,t are distinct integers, the smallest possible positive value of (t−p)(t−q)(t−r)(t−s) is 4 :
the four numbers in the parentheses are all distinct integers ≠ 0, so the smallest value we can get from the product (−2)⋅(−1)⋅1⋅2. }
The smallest possible positive value of h(t) is 1, since we must have g(t)≠0.
Thus the smallest possible value of g(t) is 4, and therefore the smallest possible value of f(t) is 9, and it is achieved for t=2 if we have
f(x)=x(x−1)(x−3)(x−4)+5
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Full question ;
Let f(x) be a polynomial with integer coefficients. Suppose there are four distinct integers p,q,r,s such that f(p)=f(q)=f(r)=f(s)=5. If t is an integer and f(t)>5, what is the smallest possible value of f(t)?
What is the rate of return when 12 shares of Stock
A, purchased for $22/share, are sold for $465? The
commission on the sale is $9.
Rate of Return
Enter the appropriate value into the
formula to calculate the rate of return.
F
profit or loss
total cost
Total Cost = $273
Profit = $192
Rate of Return = [? ]
Answer:
The Rate of return would then be 192 / 273 ≈ 70.32%
Sydney went to the store and bought candy that was priced according to the weight in pounds. She purchased 2 1/4 pounds of black licorice, 1 7/8 pounds of red licorice, and 1 1/2 pounds of butterscotch candy. if the candy costs $ 4.00 per pound, how much did Sydney spend on candy?
Answer:
$22.50
Step-by-step explanation:
Find the slope of the line graphed below.
Answer:
-2
Step-by-step explanation:
The line appears to cross through (2,3) and (4,-1)
You can subtract the x values and y values to determine the difference:
[tex]2 - 4= - 2 \\ 3 - ( - 1) = 4[/tex]
These can be used as the y and x values in y over x to find the slope:
[tex] \frac{4}{ - 2} = - 2[/tex]
The slope is -2
10 -8 -6 -4
| 10+
8
67
-2
4.2
-2
-4-
-6
-8
-10
2
4 6 8 10
Write an equation for the graph, where y depends on x.
The equation of given graph is y = 2x + 6.
What is equation of line?
The formula for a straight line is y = mx + c where c is the height at which the line intersects the y-axis, also known as the y-intercept, and m is the gradient.
Given:
The graph of the line is given.
From graph we have to find the equation of line.
Let the graph passes through the points (0, 6) and (2, 10).
From these two points to find the slope.
Slope = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here, [tex](x_1, y_1) = (0, 6), (x_2, y_2) = (2, 10)[/tex]
⇒ Slope = m = [tex]\frac{10-6}{2-0}= \frac{4}{2} = 2[/tex]
So, the slope is 2.
Now to find the equation of line.
Consider, the point - slope form of the line,
[tex]y-y_1=m(x-x_1)[/tex]
Plug [tex]m = 2, (x_1, y_1) = (0, 6)[/tex]
⇒
[tex]y-6=2(x-0)\\y-6=2x\\y=2x+6[/tex]
Hence, the equation of given graph is y = 2x + 6.
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Your school is planning a fundraising dinner. The expense for this event must not exceed $2,475.00. The team organizing the event has calculated that the cost per adult guest will be $18.00 and the cost per child guest will be $9.00. The venue can hold no more than 150 guests.
The two inequalities that describe the total cost and no. of guests are
18a + 9c ≤ 2475 and
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Let 'a' be the no. of adults and 'c' be the no. of children.
The expense for this event must not exceed $2,475.00.
Therefore, 18a + 9c ≤ 2475...(i)
The venue can hold no more than 150 guests.
Therefore, a + c ≤ 150...(ii)
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If 24000 bricks of the same shape and size are required to build a wall of dimension 15m*6m*20m find the volume of each brick
The volume of each brick is 0.75m³
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object. It is measured in cubic units.
A brick has a cuboidal shape. This means the volume of a cuboid is given as:
V = l×b×h
This means volume = area × height
The volume of the whole wall is calculated as:
15× 6× 20 = 18000m³
Since there are 24000 bricks needed for the wall. The volume of each brick is therefore calculated as:
V =18000/24000
= 0.75m³
Therefore the volume of each brick is 0.75m³
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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=630(1.06)^x
percentage rate increase by 206%
What is exponential growth?
An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases with time.
Consider a population of mice that increases exponentially every year by a factor of two, starting with 2 in the first year and increasing to 4 in the second, 8 in the third, 16 in the fourth, and so on. The population is rising by a factor of 2 per year in this example. If mice gave birth to four pups instead, you would then have 4, 16, 64, and 256.
Linear growth, which is additive, and geometric growth can be contrasted with exponential growth, which is multiplicative (which is raised to a power).
This equation represents exponential growth because the base is greater than 1, the function represents growth and Whenever the base is less than 1, the function represents decay.
The base 1.06 is greater than 1, hence The equation represents exponential growth.
The formula for exponential growth:
[tex]y=a(1+r)^{x}[/tex]
where,
f(x) = exponential growth function
a = initial amount
r = growth rate
x = number of time intervals
In this case, [tex]r=1.06+1 = 2.06[/tex]
which represents percentage rate increase by 206%
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The volume of a rectangular prism is 6,618.375 cm3. If the height is 13.25 cm and the length is 27 cm, what is the value of the width?
A: 18.125 cm
B: 18.5 cm
C: 18.75 cm
D: 18.86 cm
The value of width will be;
⇒ 18.5 cm
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The volume of a rectangular prism = 6,618.375 cm³
The height is 13.25 cm and the length is 27 cm.
Now,
We know that,
The volume of rectangular prism = Length x Width x Height
Substitute all the values, we get;
⇒ 6,618.375 = 27 × x × 13.25
⇒ 6,618.375 / 357.75 = x
⇒ x = 18.5 cm
Thus, The value of width = 18.5 cm
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A customer is buying bath towels and hand towels and can spend no more than $100. Each bath towel costs $8, and each hand towel costs $5. The inequality 8x+5y ≤100 represents all possible combinations of x, the number of bath towels, and y, the number of hand towels the customer can buy.
Which graph best represents the solution set for this inequality?
There is an attachment that includes the graph for the inequality 8x + 5y 100.
How do you calculate the scenario's graph?
The parameters are as follows, taken from the query:
The customer's purchase must not exceed $100.
Each bath towel costs $8.
Each hand towel costs $5.
Inequality among the available combinations is another factor that we have.
8x + 5y ≤ 100
like that
x is the quantity of bath towels, while y is the quantity of hand towels.
Plotting the inequality's graph is the following step.
A graphing tool can be used for this.
In order to attach the graph, we enter the inequality in the graphing tool.
Keep in mind that the inequality is provided as
8x + 5y ≤ 100
See the inequality graph in the attached. 8x + 5y ≤ 100
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10. A test consisting of 25 multiple-choice questions with 5 answer choices for each question is administered For each question; there is only | correct answer Let X be the number of correct answers if a student guesses randomly from the 5 choices for each of the 25 questions What is the probability distribution of X? This test, like many multiple-choice tests, is scored using penalty for guessing: The test score is determined by awarding point for each question answered correctly, deducting 0.25 point for each question answered incorrectly, and ignoring any question that is omitted. That is, the test score is calculated using the following formula Score = number of correct answers) (0.25 number of incorrect answers) + (0 number of omits) For example, the score for a student who answers 17 questions correctly, answers 3 questions incorrectly, and omits 5 questions is Score 17) - (0.25 * 3) + (0 x 5) = 16.25 Suppose student knows the correct answers for 18 questions, answers those 18 questions correctly, and chooses randomly from the 5 choices for each of the other 7 questions. Show that the expected value of the student'$ score is 18 when using the scoring formula above
Using the given formula, we have been able to prove that; the expected value of the students' score is 18 correct responses
How to solve binomial probability distribution problems?1) Let X denote the number of correct guesses, assuming that a student guesses randomly among the five options of all 25 questions. Then X has a binomial probability distribution with;
n = 25
p = 1/5 = 0.2
2) Let Y denote the number of correct responses on the seven questions for which the student guesses randomly from among the five options. Then Y has a binomial probability distribution with n = 7 and p = 0.20. Then the expected value of Y is;
E(Y) = np = 7(0.2) = 1.4
Using the scoring formula given, we have;
Score = (18 + Y) - 0.25(7 - Y) + 0(0)
= 16.25 + 12Y
The expected value of the students' score is;
E(16.25 + 12Y) = 16.25 + 12(1.4)
= 18 correct responses.
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NO LINKS!! Please help me with this problem. Part 8ff
Answer:
[tex]\dfrac{1}{36n^2+6n}[/tex]
Step-by-step explanation:
Given factorial expression:
[tex]\dfrac{(6n-1)!}{(6n+1)!}[/tex]
[tex]\boxed{\begin{minipage}{6cm}\underline{Factorial Rule}\\\\$n!=\:n\cdot \left(n-1\right) \cdot \left(n-2\right) \cdot ... \cdot 3 \cdot 2\cdot 1$\\ \end{minipage}}[/tex]
Apply the factorial rule to the numerator and denominator of the given rational factorial expression:
[tex](6n-1)!=\left(6n-1\right)\cdot \left(6n-2\right)\cdot \left(6n-3\right)\cdot... \cdot 3 \cdot 2\cdot 1[/tex]
[tex]\left(6n+1\right)!=\left(6n+1\right)\cdot \:6n \cdot (6n-1) \cdot...\cdot 3 \cdot 2\cdot 1[/tex]
Therefore:
[tex]\begin{aligned}\implies \dfrac{(6n-1)!}{(6n+1)!}&=\dfrac{\left(6n-1\right)\cdot \left(6n-2\right)\cdot \left(6n-3\right)\cdot... \cdot 3 \cdot 2\cdot 1}{\left(6n+1\right)\cdot \:6n \cdot (6n-1) \cdot...\cdot 3 \cdot 2\cdot 1}\\\\&=\dfrac{1}{(6n+1) \cdot 6n}\\\\&=\dfrac{1}{6n(6n+1)}\\\\&=\dfrac{1}{36n^2+6n}\end{aligned}[/tex]
Answer:
[tex]\cfrac{1}{6n(6n+1)}[/tex]--------------------------------
We know that:
n! = 1·2·3·4·...·nTherefore:
(6n + 1)! = (6n - 1)!·6n·(6n + 1)Therefore:
[tex]\cfrac{(6n-1)!}{(6n+1)!} =\cfrac{(6n-1)!}{(6n-1)!(6n)(6n+1)} =\cfrac{1}{6n(6n+1)}[/tex]9. Divide the polynomials using synthetic division.
(2y² + 10y + 17) ÷ (y + 3)
The polynomials using synthetic division is [tex]2 y+4+\frac{5}{y+3}[/tex].
What is polynomials?
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x^2 4x + 7 is an illustration of a polynomial with a single indeterminate x.
A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics.
[tex]\frac{\left(2 y^2+10 y+17\right)}{(y+3)}$$[/tex]
[tex]$$\begin{aligned}& \text { Divide } \frac{2 y^2+10 y+17}{y+3}: \frac{2 y^2+10 y+17}{y+3}=2 y+\frac{4 y+17}{y+3} \\& =2 y+\frac{4 y+17}{y+3}\end{aligned}$$[/tex]
Divide [tex]$\frac{4 y+17}{y+3}: \quad \frac{4 y+17}{y+3}=4+\frac{5}{y+3}$[/tex]
[tex]=2 y+4+\frac{5}{y+3}[/tex]
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1. Using the stopping distance calculator and your internet browser complete the following table to compare stopping distances at various speeds.
2. You overhear your friend say “It is OK to go 10 mph over the speed limit.” Explain why your friend is wrong using your evidence from the table above to support your answer.
The stopping distance table and the analysis of the stopping distance are presented as follows;
1. The stopping distance calculator, an online tool, provides the stopping distance at a specified speed as presented in the table on the following sections.
2. Increasing the vehicle speed by 10 mph, increases the required stopping distance exponentially, which reduces the safety of driving
What is the stopping distance?The stopping distance is the distance traveled by a vehicle, which is the sum of the distance traveled during the reaction time and the distance traveled during braking (the braking distance)
The table in the question using a perception–reaction time of 2.5 seconds, and the online stopping distance calculator is completed as follows;
Speed (mph) [tex]{}[/tex] Speed (m/s) Stopping Distance (m)
60 mph [tex]{}[/tex] 26.82 m/s 119.55 m
50 mph [tex]{}[/tex] 22.35 m/s 92.34 m
40 mph [tex]{}[/tex] 17.88 m/s 68.05 m
30 mph [tex]{}[/tex] 13.41 m/s 46.665 m
20 mph [tex]{}[/tex] 8.94 m/s 28.197 m
10 mph [tex]{}[/tex] 4.47 m/s 12.642 m
2. The details from the above table indicates that as the speed increases, the stopping distance increases exponentially, such that increasing the speed by 10 mph increases the required stopping distance when the vehicle is moving at an already high speed, thereby reducing safety by increasing the speed by 10 mph.
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Select all of the lines of reflection that will carry the rectangle back onto itself.
The lines that carry the rectangle onto itself are x = 0 and y = 1
How to determine the lines that carry the rectangle onto itself?The graph that completes the question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The rectangular graph
The coordinates of one end of the graph are
(-3, 3) and (-3, -1)
Next, we calculate the midpoint of these ends
So, we have
Midpoint = 1/2(x₁ + x₂, y₁ + y₂)
Substitute the known values in the above equation, so, we have the following representation
Midpoint = 1/2(-3 + 3, -1 + 3)
Evaluate the like terms
Midpoint = 1/2(0, 2)
So, we have
Midpoint = (0, 1)
So, we have
x = 0 and y = 1
Hence, the reflection lines are x = 0 and y = 1
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Please help will mark Brainly
Answer:
A
Step-by-step explanation:
Blue = River Y
Red = River Z
River Y equation: y = 18
River Z equation: y = 10 + 2x
Graph A represents this system of equations.
IF THIS HELPED YOU GIVE ME BRAINLIEST FOR GOOD LUCK FOR 10 YEARS
Can anyone solve I need help urgent thank you
Answer:
Step-by-step explanation:
3.14 x 3=9.42
Find X, 50 points if you answer
Answer:
x=38
Step-by-step explanation:
linear par
180-134=46
180-84=96
sum of a triangle is 180
96+46+x=180
142+x=180
x=180-142
x=38
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 414 gram setting. Based on a 8 bag sample where the mean is 407 grams and the standard deviation is 18, is there sufficient evidence at the 0.025 level that the bags are underfilled? Assume the population distribution is approximately normal.
Step 1 of 5:
State the null and alternative hypotheses.
Step 2 of 5:
Find the value of the test statistic. Round your answer to three decimal places.
Step 3 of 5:
Specify if the test is one-tailed or two-tailed.
Step 4 of 5:
Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
Step 5 of 5:
Make the decision to reject or fail to reject the null hypothesis.
Question #2:
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.8 parts/million (ppm). A researcher believes that the current ozone level is at an insufficient level. The mean of 26 samples is 4.6 ppm with a standard deviation of 1.2. Does the data support the claim at the 0.025 level? Assume the population distribution is approximately normal.
Step 1 of 5:
State the null and alternative hypotheses.
Step 2 of 5:
Find the value of the test statistic. Round your answer to three decimal places.
Step 3 of 5:
Specify if the test is one-tailed or two-tailed.
Step 4 of 5:
Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
Step 5 of 5:
Make the decision to reject or fail to reject the null hypothesis.
A)
A manufacturer of banana chips would like to know whether its bag-filling machine works correctly at the 414-gram setting.
So, Null hypothesis: [tex]H_{0}[/tex] : μ < 414
It is believed that the machine is underfilling the bags.
So, Alternate hypothesis: [tex]H_{1}[/tex] : μ < 414
Given,
n= 8
Population standard deviation (б) = 18
x= 407
We will use the t-test since n > 8 and we are given the population standard deviation.
t=x-μ / (б/[tex]\sqrt{n-1}[/tex])
t= [tex]\frac{407-414}{\frac{18}{\sqrt{7} } }[/tex]
t= -1.028
Use the t table to find p value
p-value = 12.706
Level of significance α = 0.025
p-value>α
It is a two-tailed test.
So, we fail to reject the null hypothesis.
So, its bag-filling machine works correctly at the 414-gram setting.
B)
Let μ be the population mean amount of ozone in the upper atmosphere.
As per the given, we have
[tex]H_{0}[/tex] : μ = 4.8
[tex]H_{1}[/tex] : μ ≠ 4.8
Sample size: n= 26
Sample mean = 4.6
Standard deviation = 1.2
Since population standard deviation is now given, so we use a t-test.
t= [tex]\frac{4.6-4.8}{\frac{1.2}{\sqrt{25} } }[/tex]
t= -0.2/0.24
t= -0.833
It is a two-tailed test.
We are accepting the null hypothesis.
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What is it? I swear I have no idea
By using matrix, it can be calculated that:
[tex]\frac{1}{4}C = \begin{bmatrix}3 & 4 & -5 \\ 1 & -6 & 7\end{bmatrix}[/tex]
What is a matrix?The term "matrix" refers to any configuration of numbers in the form of rows and columns. a collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers.
In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics. Solving linear equations is made easier by it. Matrices are incredibly priceless items that are used in a variety of contexts. In addition to mathematical applications, matrices are employed in a wide range of scientific disciplines. Nearly every element of our life uses engineering mathematics.
Here,
[tex]C = \begin{bmatrix} 12 & 16 & -20 \\ 4 & -24 & 28 \end{bmatrix}[/tex]
[tex]\frac{1}{4}C = \begin{bmatrix} 12\times \frac{1}{4} & 16 \times \frac{1}{4} & -20 \times \frac{1}{4} \\ 4 \times \frac{1}{4} & -24 \times \frac{1}{4}& 28 \times \frac{1}{4}\end{bmatrix}\\\\\frac{1}{4}C = \begin{bmatrix}3 & 4 & -5 \\ 1 & -6 & 7\end{bmatrix}[/tex]
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-x+y≤-1
x + 2y ≥ 4
Graph the system of inequalities.
Answer:
Step-by-step explanation:
[tex]-x+y\leq -1\\x-y\geq 1\\x+2y\geq 4[/tex]
dark blue is the required region.
1 hour 15 minutes. is what in minutes
Answer:
75
Step-by-step explanation:
I hour and 15 minutes in minutes is 75 minutes
1 hour = 60 minutes
you add 15 and you get
60+15=75
The answer would be 75 Minutes.
1 Hour = 60 Minutes
[tex]60 + 15 = 75[/tex] Minutes.
(a) You have a 10 inch by 15 inch piece of tin which you plan to form into a box (without a top) by cutting a square from each corner and folding up the sides. How much should you cut from each corner so the resulting box has the greatest volume? (b) If the piece of tin is A inches by B inches, how much should you cut from each corner so the resulting box has the greatest volume?
Resulting box has the greatest volume for the values (25 ± 5√7)/6 .
This is a problem that can be solved using derivatives , maxima & minima and common logic.
Hence , going by logic :
Creating a flap of 'a' inches in width, the base of the box will be
(10 - 2a) by (15 - 2a)
and the depth of the box will be the width of the fold-up flap: a.
Then the volume of the box is
v = [tex]a(10 -2a)(15 -2a) = 150a -50a^2 +4a^3[/tex]
Using the derivative of the volume will be zero at the maximum volume.
0 = [tex]dv/da = 150 -100a +12a^2[/tex]
This has roots at
a = (100 ±√(100² - 4(12)(150)))/(2·12)
a = (100 ± √2800)/24 = (25 ± 5√7)/6
Only the smaller of these solutions gives a maximum volume.
You should cut (5/6)(5-√7) ≈ 1.962 inches to obtain the greatest volume.
Similarly , replacing the values of 10 by A and 15 by B , a generalized solution can be formed .
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One hundred elk, each 1 year old, are introduced into a game preserve. The number N(t) alive after t years is predicted to be N(t)=100(0.9)^t
(a) Estimate the number alive after 7 years. (Round your answer to the nearest whole number.)
(b) What percentage of the herd dies each year?
a) The number alive after 7 years is given as follows: 48.
b) The percentage of herd that dies each year is of 10%.
What is the exponential function?The exponential function in the context of this problem is defined as follows:
N(t)=100(0.9)^t.
The parameters of the function are defined as follows:
The amount of herd alive after 7 years is found with the numeric value at t = 7, replacing the lone instance of t in the function by 7, hence:
N(7) = 100 x (0.9)^7 = 48.
(rounding to the nearest whole number).
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Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) C 540 a 3.0, 4.0, LA = C = Solve triangle ABC. (If an answer does not exist,, enter DNE. Round your answers to one decimal place.) b 69 35, LA 72° C = C = a = Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) a 28, b = 39, c 29 LA = Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) = 17, 13, c 22 a = LA= o Sketch the triangle 500 LA B 770 C = 270 c 270 50° 77 50° 770 270 A A A 770 50° 270 270 50° 77 C A Solve the triangle using the Law of Sines. (Round side lengths to the nearest integer.) a = b Sketch the triangle. 100° LA = 270, C=60 C 100° 60 100° 27 27° C 60 C C 270 60 100° 27 100° A 60 A Solve the triangle using the Law of Sines. (Round side lengths to one decimal place.) a = b =
The measures of the lengths of the sides and angles of the triangles found using the law of cosines and the law of sines are presented as follows;
Question 1
∠A = 47.35°
∠B = 78.65°
c = 3.3
Question 2
∠B = 78.24°
∠C = 29.76°
a = 67.03
Question 3
∠A = 45.77°
∠B = 86.417°
∠C = 47.813°
Question 4
∠A = 36.15°
∠B = 60.48°
∠C = 93.37°
Question 5
a = 258.98
b = 327.41
∠C = 53°
Question 6
a = 34.11
b = 73.987
∠C = 53°
What is the law of cosines?The law of cosines is a relationship between two sides (b and c) and the included angle, (∠A) and the third side (a) of the triangle.
Mathematically; a² = b² + c² - 2·b·c·cos(A)
Question 1
The dimensions of the triangle ΔABC are;
a = 3.0, b = 4.0, ∠C = 54°
The law of cosines indicates that we get;
c² = b² + a² - 2·b·a·cos(∠C)
Therefore;
c² = 3.0² + 4.0² - 2 × 3.0 × 4.0 × cos(54°) ≈ 10.893
c ≈ √(10.893) ≈ 3.3The law of sines indicates that we get;
sin(54°)/3.3 = sin(∠A)/3.0
∠A = arcsine(3 × sin(54°)/3.3) ≈ 47.35°∠B = 180° - 54° - 47.35° ≈ 78.65°Question 2
b = 69, c = 35, ∠A = 72°
a² = 69² + 35² - 2 × 69 × 35 × cos(72°) ≈ 4493.45
a ≈ √(4493.45) ≈ 67.03The law of sines indicates that we get;
sin(72°)/67.03 = sin(∠B)/69
∠B = arcsine(69 × sin(72°)/67.03) ≈ 78·24°
∠B ≈ 78.24°∠C = 180° - 72° - 78.24° ≈ 29.76°
∠C ≈ 29.76°Question 3
a = 28, b = 39, c = 29
a² = b² + c² - 2·b·c·cos(A)
cos(A) = (a² - (b² + c²)) ÷ (2·b·c)
Therefore; cos(A) = (28² - (39² + 29²)) ÷ (-2 × 39 × 29) ≈ 0.6976
∠A = arccos(0.6976) ≈ 45.77°sin(45.77)/28 = sin(B)/39
sin(B) = 39 × sin(45.77)/28 ≈ 0.998
∠B = arcsine(0.998) ≈ 86.417°∠C = 180° - 45.77° - 86.417° = 47.813°Question 4
a = 13, b = 17, c = 22
cos(A) = (13² - (17² + 22²)) ÷ (-2 × 17 × 22) ≈ 0.807
∠A ≈ arccos(0.807) ≈ 36.15°sin(36.15)°/13 = sin(∠B)/17
sin(∠B) = 17 × sin(36.15)°/13
∠B =50.48° ∠C = 180° - 36.15° - 50.48° ≈ 93.37°Question 5
The parameters of the triangle are; ∠A = 50°, ∠B = 77°, c = 270
Please find attached the sketch of the triangle in the correct option created with MS Word
∠C = 180° - 50° - 77° = 53°a/sin(50°) = 270/sin(53°)
a = sin(50°) × 270/sin(53°) ≈ 258.98
a = 258.98b = sin(77°) × 270/sin(53°) ≈ 329.41
b ≈ 329.41Question 6
The parameters of the triangle are;
∠A = 27°, ∠B = 100°, c = 60
Please find attached the drawing of the correct triangle
∠C = 180° - 27° - 100° = 53°
∠C = 53°
60/sin(53°) = a/sin(27°)
a = sin(27°) × 60/sin(53°) ≈ 34.11
b = sin(100°) × 60/sin(53°) ≈ 73.987
Learn more on the law of sines here: https://brainly.com/question/14437641
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Rosa makes candles to sell.
Each candle is in the shape of a cuboid of height 8 cm.
The base of each candle is a square of perimeter 20 cm.
Rosa needs to know the volume of one candle.
Work out the volume of one candle.
Remember to give units with your answer
Find the volume of a cone with a radius of 3 feet and a height of 7 feet. Enter
the answer in terms of pie
Which polynomial represents the difference below?
8x³ + 5x+6-(2x² + 3x)
OA. 10x¹0 + 8x² +6
OB. -2x7 + 8x³ + 8x+6
O C. 6x¹0+2x+6
OD. -2x7 + 8x³ + 2x+6
The difference of the given polynomials 8x³+5x+6 and 2x²+3x is 8x³-2x²+2x+6. So, the correct answer is D.
What is the subtraction of polynomials?To subtract polynomials from another, we should change the signs (from '+' to '-' or from '-' to '+') of all the terms of the expression which is to be subtracted and then the two expressions are added.
Given that, 8x³+5x+6-(2x²+3x)
Group the like terms are perform the addition or subtraction
= 8x³+5x+6-2x²-3x
= 8x³+(5x-3x)-2x²+6 (Here, like terms are 5x and 3x)
= 8x³+2x-2x²+6
= 8x³-2x²+2x+6
So, the standard form of obtained polynomial is 8x³-2x²+2x+6.
The polynomials difference is 8x³-2x²+2x+6. Therefore, option D is the correct answer.
To learn more about the subtraction of polynomials visit:
https://brainly.com/question/12959016.
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"Your question is incomplete, probably the complete question/missing part is:"
Which polynomial represents the difference below?
8x³ + 5x+6-(2x² + 3x)
A. 10x+ 8x² +6
B. -2x² + 8x³ + 8x+6
C. 6x¹⁰+2x+6
D. -2x²+ 8x³+2x+6
