Answer:
Question 1
The model is an exponential model that describes the relationship between the number of weeks since the first data point and the closing price of the stock. It is calculated by using the given data points and finding the best fit for the data. The model can be used to make predictions about the closing prices of the stock by plugging in the value of x, which represents the number of weeks since the first data point.
One week from today, the stock is predicted to close at $67,034.37, one month from today, the stock is predicted to close at $66,327.75, and one year from today, the stock is predicted to close at $76,584.35 according to the model.
Question 2
It is difficult to say whether the model is a good predictor of the future closing price of the stock because it depends on how accurately the model describes the underlying relationship between x and y. However, since the model is based on historical data and has a high R-squared value, it could be a good predictor of the future closing price of the stock.
Estimate the area under the graph of f(x)= 1x+4 over the interval [−2,3] using five approximating rectangles and right endpoints.
Answer: Hello how are you doing today?
Step-by-step explanation: How may I help you?
Which statements are always true regarding the diagram? Select three options.
m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
Answer:
Step-by-step explanation:
m∠5 + m∠3 = m∠4 is always true, because in a triangle, the sum of all the angles is always 180°.m∠3 + m∠4 + m∠5 = 180° is always true, because in a triangle, the sum of all the angles is always 180°.m∠5 + m∠6 =180° is not always true, since it depends on the specific diagram and the measure of m∠6.
write a function g(x) that transforms the function f(x)=4 square root x +1 such that f(x) is horizontally stretched by a factor of 5, reflected across the x-axis, then translated down 5.
Answer:
[tex]g(x)=-4\sqrt{\dfrac{x}{5}}-6[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=4\sqrt{x}+1[/tex]
1. Horizontal stretch
[tex]f\left(\dfrac{1}{a}x\right) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $a$}.[/tex]
Therefore, if f(x) is horizontally stretched by a factor of 5:
[tex]\implies f\left(\dfrac{1}{5}x\right)=4\sqrt{\dfrac{x}{5}}+1[/tex]
2. Reflection across the x-axis
[tex]-f(x)\implies f(x) \: \textsf{reflected in the $x$-axis}.[/tex]
Therefore, if f(x/5) is reflected in the x-axis:
[tex]\begin{aligned}\implies -f\left(\dfrac{1}{5}x\right)&=-\left(4\sqrt{\dfrac{x}{5}}+1\right)\\\\&=-4\sqrt{\dfrac{x}{5}}-1 \end{aligned}[/tex]
3. Translation
[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}[/tex]
Therefore, if -f(x/5) is translated 5 units down:
[tex]\begin{aligned}\implies -f\left(\dfrac{1}{5}x\right)-5&=-4\sqrt{\dfrac{x}{5}}-1 -5\\\\&=-4\sqrt{\dfrac{x}{5}}-6\end{aligned}[/tex]
Therefore:
[tex]g(x)=-4\sqrt{\dfrac{x}{5}}-6[/tex]
Sara is competing in a 200 m race. She runs at a constant speed of 4.6 m/s for the first 50 m, then 4.2 m/s for 10 seconds. The remainder of the race takes her 23 seconds to complete. What is Sara's average speed for the entire race to 1 dp?
Sara's average speed for the entire race is
3.6 meters per second
How to calculate the average speedThe first 50 meters of the race is ran at a constant speed of 4.6 m/s.
Let's compute the time taken for this portion
distance = rate*time
time = distance/rate
time = 50/(4.6)
time = 10.869
It takes approximately 10.869 seconds to run the first 50 meters (at a constant speed of 4.6 m/s).
Add on the other time values from the other sections (10 and 23) to get 10.869+10+23 = 43.869
The entire 200 m race takes about 43.869 seconds.
So Sara's average speed over the entire race is about 200/43.869 = 4.559 which rounds to 4.6 m/s when rounding to one decimal place.
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use logical equivalence theorem to verify the logical equivalence below
p ∨ q → r ≡ (p → r) ∧ (q → r)
By logical equivalence theorem, we find that composite proposition p ∨ q → r is equivalent to composite proposition (p → r) → (q → r).
How to demonstrate a logical equivalence by means of theorems
Propositions are structures that contains a truth value, and can be, but not exclusively, a sentence. Propositions can be simple or composite, that is, a combination of simple propostions and operators.
In this problem we must determine that a given composite proposition is equivalent to another composite proposition by means of logical equivalence theorem. First, write the complete proposition:
p ∨ q → r
Second, use a conditional formula:
¬ (p ∨ q) ∨ r
Third, apply the DeMorgan's theorem:
(¬ p ∧ ¬ q) ∨ r
Fourth, use distributive property:
(¬ p ∨ r) ∧ (¬ q ∨ r)
Fifth, use conditional formula once again:
(p → r) → (q → r)
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From the triangle below, if AD = 8 and CD = 18, find the length of side BD.
Answer:
19.7
Step-by-step explanation:
A^2 + B^2 = C^2
8^2 + 18^2 = sqrt(388)
When solving for a system of equations, if you get an answer of 6 = 0, what does this solution mean regarding the solution to the system?
Answer:
It means there is no solution.
Step-by-step explanation:
When you work on a system of equations and the variable falls out of the equation and you're left with a false statement...that means there is no solution.
Find the sum of the first 10 terms of the following geometric sequences:
{3, 6, 12, 24, 48...}
3066
3075
3069
3072
Answer: The sum of the first 10 terms of the given geometric sequence is 3069.
Step-by-step explanation:
A geometric sequence is a sequence of numbers such that any two consecutive terms are in a constant ratio.
The first term of the given sequence is 3 and the common ratio is 2 (6/3 = 12/6 = 24/12 = ...).
To find the sum of the first 10 terms of a geometric sequence, we can use the formula:
S = a(1 - r^n)/(1 - r)
where a is the first term, r is the common ratio and n is the number of terms.
So for this geometric sequence:
S = 3(1 - 2^10)/(1 - 2) = 3(1 - 1024)/(-1) = 3(-1023)/(-1) = 3069
Explanation: By using the formula for the sum of a geometric sequence, the sum of the first 10 terms of the sequence was found by substituting the first term, common ratio and number of terms into the formula.
Answer:
C) 3069
Step-by-step explanation:
A geometric series is the sum of the terms of a geometric sequence.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Sum of the first $n$ terms of a geometric series}\\\\$S_n=\dfrac{a(1-r^n)}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]
Given geometric sequence:
{3, 6, 12, 24, 48...}From inspection of the sequence, the first term is 3:
[tex]\implies a=3[/tex]
To find the common ratio, divide consecutive terms:
[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{6}{3}=2[/tex]
To find the sum of the first 10 terms, substitute the found values of a and r together with n=10 into the geometric series formula:
[tex]\implies S_{10}=\dfrac{3(1-2^{10})}{1-2}[/tex]
[tex]\implies S_{10}=\dfrac{3(1-1024)}{1-2}[/tex]
[tex]\implies S_{10}=\dfrac{3(-1023)}{-1}[/tex]
[tex]\implies S_{10}=\dfrac{-3069}{-1}[/tex]
[tex]\implies S_{10}=3069[/tex]
Therefore, the sum of the first 10 terms of the given geometric sequence is:
3069Prove AB || CD and BC || AD
The indicated congruency of the angles ∠BEC and ∠AED (∠BEC ≅ ∠AED) and ∠BEA and ∠CED (∠BEA ≅ ∠CED), according to the alternate interior angles postulate, shows that [tex]\overline{AB}[/tex]║[tex]\overline{CD}[/tex] and [tex]\overline{BC}[/tex]║[tex]\overline{AC}[/tex] are parallel.
What are parallel lines or segments?Two segments on a plane are parallel if the distance between the segments remain the same, through the lengths of the segments.
The specified details of the dimensions of the segments in ABCD are;
Segments [tex]\overline{AC}[/tex] bisects segment [tex]\overline{BD}[/tex] and vice versa
Required to prove that [tex]\overline{AB}[/tex] ║ [tex]\overline{CD}[/tex] and [tex]\overline{BC}[/tex] ║ [tex]\overline{AD}[/tex]
The two column consisting of the statements and reasons to prove that the specified sides are parallel is presented as follows;
Step [tex]{}[/tex] Statement Reasons
1. [tex]{}[/tex] [tex]\overline{AC}[/tex] and [tex]\overline{BD}[/tex] bisect each other Given
2. [tex]{}[/tex] [tex]\overline{BE}[/tex] ≅ [tex]\overline{ED}[/tex] and [tex]\overline{CE}[/tex] ≅ [tex]\overline{AE}[/tex] Definition of bisected segments
3. ∠BEC ≅ ∠AED and ∠BEA ≅ ∠CED Vertical angles theorem
4. [tex]{}[/tex] ΔBCE ≅ ΔADE and ΔBEA ≅ ΔCED SAS congruency rule
5. [tex]{}[/tex] ∠EBC ≅ EDA and ∠EBA ≅ ∠EDC CPCTC
6. [tex]{}[/tex] [tex]\overline{AB}[/tex] ║ [tex]\overline{CD}[/tex] and [tex]\overline{BC}[/tex] ║ [tex]\overline{AD}[/tex] Converse of alt. int. ∠s theorem
The details of the reasons in the above table are;
Vertical angles theorem
The vertical angle theorem states that the vertical angles formed by two intersecting straight lines are congruent.
SAS congruency rule
The SAS (acronym for Side-Angle-Side) congruency rule states that if two sides and an included angle in one triangle are congruent to two sides and an included angle in a second triangle, the two triangles are congruent
CPCTC
CPCTC is an acronym for Corresponding Parts of Congruent Triangle are Congruent.
Converse Alt, Int, ∠s theorem
The converse of the alt. int. ∠s (abbreviation for alternate interior angles) theorem state that if the the alternate interior angles formed by two lines and a common transversal are congruent, then the two lines are parallel
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How many solutions does each system have? System I: 4x+3y=-1 12x+9x=21 System II: 5x+2y=-7 15x+6y=21
Answer:
Step-by-step explanation:
System I: This system has one solution. To solve, you would need to first solve for one of the variables, say x. Then, substitute the value of x into the other equation to solve for y.
System II: This system has an infinite number of solutions. To solve, you would need to first solve for one of the variables, say x. Then, substitute the value of x into the other equation to solve for y. Since both equations are linear, they will have an infinite number of solutions.
-5(x - 10) = -35
What is x representing?
Answer: x is 17
Step-by-step explanation:
Distribute the -5: -5x + 50 = -35
Subtract 50 from both sides: -5x = -85
Divide both sides by -5: x = 17
Answer: x is representing here.
Step-by-step explanation: as the equation is -5(x-10) = -35
(-) sign in both sides will cancel out each other so the equation will become 5(x-10)= 35
now we will solve the equation
5x-50 = 35
5x = 35+50
5x = 85
x=85/5 = x =
Find an ordered pair (x, y) that is a solution to the equation.
4x-y=3
(x, y) = (_, _)
An ordered pair (x, y) that is a solution to the equation include the following: (x, y) = (-3, 0).
What is an ordered pair?In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.
How to find an ordered pair (x, y) that is a solution to the equation?In order to determine the ordered pairs that represent points on the graph of the given function, we would plot its equation by using an online graphing calculator and then read all the ordered pairs that lie on the line.
By critically observing the graph of the given function (see attachment), the required solutions are include following;
Ordered pair = (0.75, 0).
Ordered pair = (-3, 0).
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determine whether the three points P=(-7,6,-8), Q=(-8,4,-11), R=(-9,3,-14) are colinear by computing the distances between pairs of points
Answer:
To determine whether the three points P, Q, and R are colinear, we can calculate the distances between pairs of points using the distance formula:
d(P,Q) = √((-8 - (-7))^2 + (4 - 6)^2 + (-11 - (-8))^2) = √((-1)^2 + (-2)^2 + (-3)^2) = √14
d(Q,R) = √((-9 - (-8))^2 + (3 - 4)^2 + (-14 - (-11))^2) = √((-1)^2 + (-1)^2 + (-3)^2) = √9
d(P,R) = √((-9 - (-7))^2 + (3 - 6)^2 + (-14 - (-8))^2) = √((-2)^2 + (-3)^2 + (-6)^2) = √19
If the three points are collinear, the distance between any two points should be a multiple of the distance between the other two points. Since √14, √9, and √19 are not multiples of each other, it can be concluded that the three points P, Q, and R are not collinear.
Polynominal 2x ^ 2 - 2 3x - 9 Name Using Degree Name Using Number of Terms - 3i ^ 2 - 6i + 9
Given polynomials are Binomial and Trinomial.
What are polynomials?
Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable. An example of a polynomial with one variable is x^2+x-12. In this example, there are three terms: x^2, x and -12.
Based on the number of terms present in the expression, it is classified as
Monomial:-A monomial is an expression which contains only one term. For an expression to be a monomial, the single term should be a non-zero term. A Examples of monomials are: 5x,3.
Binomial:-A binomial is a polynomial expression which contains exactly two terms. A binomial can be considered as a sum or difference between two or more monomials. Examples of binomials are:
– 5x+3, 6a^4 + 17x.
Trinomial:-A trinomial is an expression which is composed of exactly three terms. A Examples of trinomial expressions are:
– 8a^4+2x+7, 4x^2 + 9x + 7.
Now,
Given polynomials are 2x ^ 2 - 2, 3x - 9, - 3i ^ 2 - 6i + 9.
As the number of terms in first two polynomials is 2, they are binomial.
and the number of terms in third polynomial is 3, it is trinomial.
hence,
Given polynomials are Binomial and Trinomial.
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help with this please
Answer: A, B, and E can be used to satisfy the equation
Step-by-step explanation:
A applies because 45 is the same exact number as 45, so the equal sign accurately compares them.
B applies because that symbol means less than or equal to, and 45 is not less than but is equal to 45.
C does not apply because that symbol means is not equal to, but 45 is equal to 45.
D does not apply because that is the less than symbol, and 45 is not less than 45.
E applies because it is greater than or equal to symbol, and 45 is not greater than but is equal to 45.
F does not apply because that is the greater than symbol and 45 is not greater than 45.
Hope this helps!
(01.04 MC)
Which radical function has a domain of (x € R|x≤-3) and range of y€R|y24}?
The domain and range of the the function are given below -
Domain → [-5, 10)
Range → [-3, 3)
What is a function?A function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that function takes.Given is a graph of the function.
The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that function takes. So, we can write the domain as -
Domain → [-5, 10)
Range → [-3, 3)
Therefore, the domain and range of the the function are given below -
Domain → [-5, 10)
Range → [-3, 3)
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An isosceles right triangle has 12 cm legs.
Find the length of the hypotenuse.
The vertex angle of isosceles is triangle ABC is angle C. What can you prove? Select all that apply.
A. AB = BC
B. angle A = angle B
C. angle B = angle C
D. segment BC = segment AC
E. segment AB = segment AC
Answer: A. AB = BC can be proven true.
An isosceles triangle has two equal side lengths, and since the vertex angle is angle C, it means that sides AB and BC are the equal sides.
B. angle A = angle B can be proven true.
In an isosceles triangle, since the two sides are equal, the base angles are also equal.
D. segment BC = segment AC can be proven true.
In an isosceles triangle, since the two sides are equal, the base segments are also equal.
E. segment AB = segment AC can be proven true.
In an isosceles triangle, since the two sides are equal, the base segments are also equal.
C. angle B = angle C is not true.
Because the vertex angle is angle C, and it is formed by the two base segments, so it will be different than angle B and angle A.
Step-by-step explanation:
Answer:
B, D
Step-by-step explanation:
You want to know what you can prove, given that the vertex angle of isosceles triangle ABC is angle C.
Isosceles triangleA triangle is isosceles if it has two congruent sides or two congruent angles. In either case, the angles opposite the congruent sides are congruent, and vice versa.
The vertex angle is opposite the "base" of the isosceles triangle. The sides of the vertex angle are the congruent sides, and the angles that are not the vertex angle are the congruent angles.
A. AB = BCThese sides share point B, which is not the vertex. This cannot be proven.
B. Angle A = Angle BThese are the base angles of the triangle, hence congruent. This can be proven.
C. Angle B = Angle CThese angles cannot be proven congruent using the given information. This will be true if and only if the isosceles triangle is also an equilateral triangle.
D. BC = ACThese sides share point C, which is the vertex. This can be proven.
E. AB = ACThese sides share point A, which is not the vertex. This cannot be proven.
Two consecutive numbers exist such that 3 times the greater number exceeds twice the lesser by 24. Find the numbers
The consecutive numbers are 21 and 22.
What are consecutive numbersConsecutive numbers are numbers that follow each other in order and they have a difference of 1 between every two numbers.
We shall represent the consecutive numbers with n and (n + 1) so that:
3(n + 1) = 2n + 24 {open bracket}
3n + 3 = 2n + 24
3n - 2n = 24 - 3 {collect like terms}
n = 21
since the lesser number is 21, then the greater number is 21 + 1= 22.
Therefore, the two consecutive numbers such that 3 times the greater number exceeds twice the lesser by 24 are 21 and 22.
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Answer:
Step-by-step explanation:
poop
How many times greater is the value represented by the digit 6 in the number 6419 then the value represented by the digit six in the number 84,362
Answer: The value represented by the digit 6 is 100 times greater.
Step-by-step explanation: The digit 6 in the number 84,362 is in the tens place, whereas the digit 6 in the number 6,419 is in the thousandths place. One thousand is equal to 10 x 100, meaning that the value is 100 times greater. Hope this helps and have a great day!
The value of digit 6 in 6419 is 100 times greater than the value of the digit 6 in 84362.
What is place value?Place value describes the position or place of a digit in a number. Each digit has a place in a number.
When we represent the number in general form, the position of each digit will be expanded.
Those positions start from a unit place, or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.
Given that are two numbers 6419 and 84362, we need to determine that the value digit 6 in 6419 is how much times greater than the value of the digit 6 in 84362.
So, the expanded form of the numbers =
6419 = 6000 + 400 + 10 + 9
84362 = 80000 + 4000 + 300 + 60 + 2
Place values of 6 in each =
In 84362 = 60
In 6419 = 6000
∴ 6000 / 60 = 100
Hence, the value of digit 6 in 6419 is 100 times greater than the value of the digit 6 in 84362.
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Select the correct answer from the drop-down menu.
A company sells its product to distributors in boxes of 10 units each. Its profits can be modeled by this equation, where p is the profit after selling
n boxes.
p = n² + 300n + 100,000
Use this equation to complete the statement.
The company breaks even, meaning the profits are $0, only when it sells
Reset
Next
boxes.
Answer:
Step-by-step explanation:
The company breaks even, meaning the profits are $0, only when it sells 10,000 boxes.
how many zeros does the following product have at the end? 50*49*48*...*3*2*1
The number of zeroes that the product has at the end 50 x 49 x 48 x ... x 3 x 2 x 1 will be 12.
What is the factorial of n?The factor of n is given as the production of the number n, (n - 1), (n - 2)... and 1. Then the factorial of n is given as
n! = n x (n - 1) x (n - 2) x ... 3 x 2 x 1
The expression is given below.
⇒ 50 x 49 x 48 x ... x 3 x 2 x 1
⇒ 50!
Then the number of zeroes in the product at the end will be given as,
⇒ 50 / 5 + 50 / 5²
⇒ 50 / 5 + 50 / 25
⇒ 10 + 2
⇒ 12
The number of zeroes that the product has at the end 50 x 49 x 48 x ... x 3 x 2 x 1 will be 12.
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0.276 a rational number, why? explain please.
Answer:
It can be represented as a fraction, 276/1000. It isn't non-terminating.
0.276 is a rational number because we can write it as a fraction, where both denominator and numerator are integers.
What are the solution of 3x^2+6x+6=0
Is correct?
To solve the equation for x, locate squares a, b, and c and use the quadratic formula. x= [tex]-1\±I[/tex]
Write about quadratic equation?A second order polynomial can be used to define a square. It has at least one term that needs to be squared, in other words. They go by the name quadratic equations as well. The quadratic equation's generic form is
[tex]ax^2\+ bx + c = 0[/tex]
Where x is an unknown variable and a, b, and c are numerical coefficients, the formula is: ax2 + bx + c = 0. An example of a quadratic equation is x2 + 2x + 1. in which a 0. The equation becomes a linear equation when this value is zero and ceases to be a quadratic equation.
bx+c=0
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Rachel bought and downloaded 6 songs on Friday and 8 more songs on Saturday.
Each song costs 2 dollars. Which expression represents the amount of money that
Rachel payed?
Answer:
Rachel bought 6 songs on Friday and 8 more songs on Saturday. The total number of songs she bought is 6+8 = 14
Rachel paid $2 for each song, the amount of money Rachel payed for all the songs is 14*2 = $28
Therefore, the expression that represents the amount of money that Rachel payed is "14*2 = $28" or simply "28"
- C
A radio tower is located 300 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 38° and that the angle of depression to the bottom of thetower is 29°. How tall is the tower?
Round your answer to 2 decimal places.
The height of the radio tower observed by the person is approximately 554.75 feet.
What is a tangents function?The tangent function is a mathematical function that maps an angle to its corresponding tangent value. It is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle in a right triangle.
We can use trigonometry to solve this problem. The angle of elevation from the window to the top of the tower is 38°, and the angle of depression from the window to the bottom of the tower is 29°. We can use these angles to form two similar right triangles, one with the tower and the window and one with the height of the tower and the difference between the height of the window and the height of the tower.
Let H be the height of the tower. Then the difference between the height of the window and the height of the tower is H - 300.
Using the tangent function, we can write:
tan(38°) = H / 300
and
tan(29°) = (H - 300) / 300
Solving for H, we find:
H = 300 * tan (38°) = 554.75 feet
So, the height of the tower is approximately 554.75 feet.
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1. The average man takes 7,912 steps a day. Using scientific notation, estimate the number of steps the average man takes in 1 week. A. 5.5 x 104 B. 5.5 X 105 7.9 x 10³ 7.9 x 104 C. D.
Answer:To estimate the number of steps the average man takes in 1 week, we can multiply the number of steps per day by the number of days in a week.
A week has 7 days so the number of steps the average man takes in a week would be 7,912 steps/day * 7 days/week = 55,384 steps/week
So the correct answer for the number of steps the average man takes in one week is 55,384 steps/week or in scientific notation is 5.5 x 10^4. So the answer is D. 7.9 x 10^4
Step-by-step explanation:
Answer:
A: 5.5*10⁴
Step-by-step explanation:
1 week = 7 days
7 * 7912 = 55384 steps/week
Scientifin notation:
55384 =
5538.4*10¹
553.84*10²
55.384*10³
5.5384*10⁴
Then:
the answer is:
5.5*10⁴
Two sides of a triangle have lengths 8 and 11. Which inequalities describe the values that possible lengths for the third side?
The possible lengths for the third side 8² + 11² < x², 8² + 11² = x²
and 8² + 11² ≥ x².
What is the way of classifying a triangle?If a² + b² < c² then it is an acute angle triangle.
If a² + b² = c² then it is a right-angle triangle.
If a² + b² ≥ c² then it is an obtuse angle triangle.
Given, Two sides of a triangle have lengths 8 and 11.
Let, The third side be 'x'.
Therefore, The possible lengths for the third side are,
8² + 11² < x²...(i)
8² + 11² = x²...(ii)
8² + 11² ≥ x²...(iii)
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1. Solve for BC using Law of Cosines. Round to the nearest tenth when necessary.
Answer:
Step-by-step explanation:
Let's start by labeling the sides of the triangle ABC:
A = 12
B = x
C = 10
Using the Law of Cosines, we can write the following equation:
C² = A² + B² - 2ABcos(C)
Substituting the values we have, we get:
10² = 12² + x² - 2(12)(x)cos(10)
Simplifying, we get:
100 = 144 + x² - 24xcos(10)
Rearranging, we get:
x² - 24xcos(10) + 44 = 0
Solving for x, we get:
x = [24cos(10) ± √(576cos²(10) - 176)]/2
Calculating the values, we get:
x = [24cos(10) + √(5232)]/2 ≈ 18.3
x = [24cos(10) - √(5232)]/2 ≈ 7.7
Therefore, BC = 18.3 or BC = 7.7
Solve for a. Help please!
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a \qquad \begin{cases} c=\stackrel{hypotenuse}{12}\\ a=adjacent\\ b=\stackrel{opposite}{9}\\ \end{cases} \\\\\\ \sqrt{12^2 - 9^2}=a\implies \sqrt{144 - 81}=a\implies \sqrt{63}=a[/tex]
