Answer:
Option C. [tex]ln(\frac{2x^{3}}{3y})[/tex]
Step-by-step explanation:
The given logarithmic expression is:
[tex]ln(2x)+2ln(x)-ln(3y)[/tex]
Using the power rule of logarithms: [tex]blog(a)=log(b)^{a}[/tex], the above expression can be written as:
[tex]ln(2x)+ln(x)^{2}-ln(3y)[/tex]
Using the product rule of logarithms: [tex]log(a)+log(b) =log(ab)[/tex], the above expression can be simplified further to:
[tex]ln(2x \times x^{2}) - ln(3y)\\\\=ln(2x^{3})- ln(3y)[/tex]
Using the quotient rule of logarithms: [tex]log(a)-log(b)=log(\frac{a}{b})[/tex], the above expression can be written as:
[tex]ln(\frac{2x^{3}}{3y})[/tex]
Hence option C gives the correct simplified answer.
The length of a new rectangular playing field is 5 yards longer than triple the width. If the perimeter of the rectangular playing field is 346 yards, what are itsdimensions?
The length and width of the rectangular field are determined using algebra by setting up and solving two equations which represent the relationships between the length, width, and perimeter of the field. The dimensions are found to be 46 yards for the width and 137 yards for the length.
Explanation:The dimensions of the rectangular playing field can be found using algebra, specifically the formulas for the dimensions and perimeter of a rectangle. The problem can be translated into two equations reflecting the relationships of the field's width and length to the perimeter.
The first equation is: L = 3W + 5, which represents the relationship that the length is 5 yards longer than triple the width.
The second equation is derived from the formula for the perimeter of a rectangle (P = 2L + 2W), which given the problem's perimeter of 346 yards gets us: 2L + 2W = 346.
Substitute the first equation into the second to solve for the width, then use that result to find the length. The solution indicates that the width of the rectangular playing field is 46 yards, and the length is 137 yards.
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What is the solution to the system?
X+y+z=2
2x+y-z=-1
X=5-2z
Answer:
x = 1, y = -1, z = 2 → (1, -1, 2)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}x+y+z=2&(1)\\2x+y-z=-1&(2)\\x=5-2z&(3)\end{array}\right\\\\\text{Substitute (3) to (1) and (2):}\\\\\left\{\begin{array}{ccc}(5-2z)+y+z=2\\2(5-2z)+y-z=-1&\text{use the distributive property}\end{array}\right\\\left\{\begin{array}{ccc}5-2z+y+z=2\\10-4z+y-z=-1\end{array}\right\qquad\text{combine like terms}\\\left\{\begin{array}{ccc}5+y-z=2&\text{subtract 5 from both sides}\\10+y-5z=-1&\text{subtract 10 from both sides}\end{array}\right[/tex]
[tex]\left\{\begin{array}{ccc}y-z=-3\\y-5z=-11&\text{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}y-z=-3\\-y+5z=11\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad4z=8\qquad\text{divide both sides by 4}\\.\qquad\qquad \boxed{z=2}\\\\\text{Put it to the first equation:}\\\\y-2=-3\qquad\text{add 2 to both sides}\\\boxed{y=-1}\\\\\text{Put the values of}\ z\\text{to (3):}\\\\x=5-2(2)\\x=5-4\\\boxed{x=1}[/tex]
Find the coordinates of P so that P partitions the segment AB in the ratio 1:3 if A(5,8) and B(−1,4).
A. (-6.5, -9)
B. (-1.5, -1)
C. (3.5, 7)
D. (-4, -6)
Answer:
The coordinates of point P are (3.5 , 7) ⇒ answer C
Step-by-step explanation:
* Lets explain how to solve the problem
- If the point (x , y) divide a line whose endpoints are (x1 , y1) , (x2 , y2)
at ratio m1 : m2 from the point (x1 , y1), then the coordinates of the
point (x , y) are [tex]x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}},y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}[/tex]
* Lets solve the problem
∵ A is (5 , 8) and B is (-1 , 4)
∵ P divides AB in the ratio 1 : 3
∴ m1 = 1 and m2 = 3
- Let A = (x1 , y1) and B = (x2 , y2)
∴ x1 = 5 , x2 = -1 and y1 = 8 , y2 = 4
- Let P = (x , y)
∴ [tex]x=\frac{(5)(3)+(-1)(1)}{1+3}=\frac{15+(-1)}{4}=\frac{14}{4}=3.5[/tex]
∴ [tex]y=\frac{(8)(3)+(4)(1)}{1+3}=\frac{24+4}{4}=\frac{28}{4}=7[/tex]
∴ The coordinates of point P are (3.5 , 7)
PLEASE HELP ASAP
Of the three functions in the tables, which represent linear relationships?
A. f and h
B. all three functions
c. f and g
D. g and h
Answer:
A. f and h
Step-by-step explanation:
For a linear function the First Differences of the y-values must be a constant. i.e. if we take the difference between any two consecutive y values or values of f(x) it should be the constant. For this rule to work, x values must change by the same number every time, which is true for all three given functions.
For function f:
The values of f(x) are: 5,8,11,14
We can see the difference in consecutive two values is a constant i.e. 3, so the First Difference is the same. Hence, function f is a linear function.
For function g:
The values of g(x) are: 8,4,16,32
We can see the difference among two consecutive values is not a constant. Since the first differences are not the same, this function is not a linear.
For function h:
The values of h(x) are: 28, 64, 100, 136
We can see the difference among two consecutive values is a constant i.e. 36. Therefore, function h is a linear function.
To identify the linear relationships in the tables, we need to look for constant rates of change. Functions f and g have this property, while h does not.
Explanation:In order to identify which functions represent linear relationships, we need to look for patterns in the tables. A linear relationship is characterized by a constant rate of change.
Looking at the tables, we can see that functions f and g have a constant difference between the values in the input column (x) and the output column (y). However, function h does not have a constant rate of change, so it does not represent a linear relationship.
Therefore, the correct answer is A. f and h, as these two functions represent linear relationships.
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Find the greatest common factor of 4c and 18c
Answer:
2c
Step-by-step explanation:
c is a common factor of both terms
Consider the factors of the coefficients 4 and 18
factors of 4 : 1, 2, 4
factors of 18 : 1, 2, 3, 6, 9, 18
The common factors are 1, 2
The greatest common factor is 2
Combining with c gives
Greatest common factor of 2c
To find the greatest common factor of 4c and 18c, the common factor is 2c.
To find the greatest common factor of 4c and 18c, you need to identify the largest factor that both numbers share. In this case, the common factor is 2c. Here's how you can determine it:
Write the numbers as a product of their prime factors: 4c = 2 * 2 * c and 18c = 2 * 3 * 3 * c.
Identify the common factors: The common factors are 2 and c.
Multiply the common factors together: 2 * c = 2c.
Problem Solving
ercises: Solve each problem.
CW ALL WORK. Use a separate sheet of paper (if necessary) and staple to this page.
The Acme Supply Store sells a security system for $2150,00 excluding tax. They
sold 12 systems. If the total profit on these sales was $4824.36, how much did
each system cost Acme Supply? Show your work.
I think the answer is $1,747.97
you're absolutely correct.
each system is sold for $2150, that includes cost + markup, namely the markup is the surplus amount otherwise called "profit".
they sold 12 of those, 2150 * 12 = 25800
they had $4824.36 in profits from it, so if we subtract that from the sale price, we'll be left with the cost of all 12 systems
25800 - 4824.36 = 20975.64
that's the cost for all 12 systems sold, how many times does 12 go into 20975.64? 20975.64 ÷ 12 = 1747.97.
Which of the following is an integer?
0
4
© -12.5
0 0.454545...
Answer: 4
Step-by-step explanation: 4 is the answer because an integer is any whole number, but not 0.
celest
Guided Practice
4. Find the next three terms in the sequence.
etric Sequences
-3, 6, -12, 24, ...
A - 48,96, -1923
hential Growth and
B 48, -96, 192
stest
C -36, 72, -144
mials
mials and Factoring
nic Equations and
Answer:
A - 48,96, -192
Step-by-step explanation:
Given:
geometric sequence:
-3, 6, -12, 24,
geometric sequence has a constant ratio r and is given by
an=a1(r)^(n-1)
where
an=nth term
r=common ratio
n=number of term
a1=first term
In given series:
a1=-3
r= a(n+1)/an
r=6/-3
r=-2
Now computing next term a5
a5=a1(r)^(n-1)
= -3(-2)^(4)
= -48
a6=a1(r)^(n-1)
= -3(-2)^(5)
= 96
a7=a1(r)^(n-1)
= -3(-2)^(9)
= -192
So the sequence now is -3, 6, -12, 24,-48,96,-192
correct option is A!
What is the value of y?
Answer:
Shii ion kno... Ong I don't
What is the value of cosC AB=8 BC=15 CA=17
Answer:
The value of cos C = 15/17
Step-by-step explanation:
* Lets revise the cosine rule
- In Δ ABC
# AB opposite to angle C
# BC opposite to angle A
# AC opposite to angle B
# ∠A between AB and AC
# ∠B between BA and BC
# ∠C between CA and CB
- Cosine rule is:
# AB² = AC² + BC² - 2(AC)(BC) cos∠C
# BC² = AC² + AB² - 2(AC)(AB) cos∠A
# AC² = AB² + BC² - 2(AB)(BC) cos∠B
* Lets solve the problem
∵ AB = 8 units
∵ BC = 15 units
∵ CA = 17 units
∵ AB² = AC² + BC² - 2(AC)(BC) cos∠C
- Add 2(AC)(BC) cos∠C to both sides
∴ AB² + 2(AC)(BC) cos∠C = AC² + BC²
- Subtract AB² from both sides
∴ 2(AC)(BC) cos∠C = AC² + BC² - AB²
- Divide two sides by 2(AC)(BC)
∴ cos∠C = (AC² + BC² - AB²)/2(AC)(BC)
- Substitute the values of AB , BC , AC to find cos∠C
∴ cos∠C = (17)² + (15)² - (8)²/2(17)(15)
∴ cos∠C = (289 + 225 - 64)/510
∴ cos∠C = 450/510 = 15/17
* The value of cos C = 15/17
- The whole batch cost $28,000 and contained 140 items. Write the two rates (ratios) implied
by this statement. What would be the price for 200 items?
Please show work
Answer:
The answer would be 14
Step-by-step explanation:
you just divide 28,00 by 200 and that gives you 14
For the function y=x^5+1x^3-30x, find all real zeros.
Answer:
The real zeroes are -√5 , 0 , √5
Step-by-step explanation:
* Lets explain how to solve the problem
- The function is y = x^5 + x³ - 30x
- Zeros of any equation is the values of x when y = 0
- To find the zeroes of the function equate y by zero
∴ x^5 + x³ - 30x = 0
- To solve this equation factorize it
∵ x^5 + x³ - 30x = 0
- There is a common factor x in all the terms of the equation
- Take x as a common factor from each term and divide the terms by x
∴ x(x^5/x + x³/x - 30x/x) = 0
∴ x(x^4 + x² - 30) = 0
- Equate x by 0 and (x^4 + x² - 30) by 0
∴ x = 0
∴ (x^4 + x² - 30) = 0
* Now lets factorize (x^4 + x² - 30)
- Let x² = h and x^4 = h² and replace x by h in the equation
∴ (x^4 + x² - 30) = (h² + h - 30)
∵ (x^4 + x² - 30) = 0
∴ (h² + h - 30) = 0
- Factorize the trinomial into two brackets
- In trinomial h² + h - 30, the last term is negative then the brackets
have different signs ( + )( - )
∵ h² = h × h ⇒ the 1st terms in the two brackets
∵ 30 = 5 × 6 ⇒ the second terms of the brackets
∵ h × 6 = 6h
∵ h × 5 = 5h
∵ 6h - 5h = h ⇒ the middle term in the trinomial, then 6 will be with
(+ ve) and 5 will be with (- ve)
∴ h² + h - 30 = (h + 6)(h - 5)
- Lets find the values of h
∵ h² + h - 30 = 0
∴ (h + 6)(h - 5) = 0
∵ h + 6 = 0 ⇒ subtract 6 from both sides
∴ h = -6
∵ h - 5 = 0 ⇒ add 5 to both sides
∴ h = 5
* Lets replace h by x
∵ h = x²
∴ x² = -6 and x² = 5
∵ x² = -6 has no value (no square root for negative values)
∵ x² = 5 ⇒ take √ for both sides
∴ x = ± √5
- There are three values of x ⇒ x = 0 , x = √5 , x = -√5
∴ The real zeroes are -√5 , 0 , √5
the terminal side of an angle in standard position passes through P(-3,-4). what’s the value of tan(Theta)
Answer:
4/3
Step-by-step explanation:
I drew a picture in the attachment to show what we are looking at.
I found the point (-3,-4). I drew my angle my triangle from the x-axis and the origin to the point.
The angle that is theta is the one formed by the x-axis and the hypotenuse of the triangle where this hypotenuse was formed from the line segment from the origin to the given point.
[tex]\tan(\theta)=\frac{\text{opposite to }\theta}{\text{adjacent to }\theta}=\frac{-4}{-3}=\frac{4}{3}[/tex]
So we could have said [tex]\tan(\theta)=\frac{y}{x}[/tex].
What is the coefficient of xy^4 in the expansion of (2x+y)^5
Answer:
The coefficient of xy^4 is 10
Step-by-step explanation:
to solve the questions we proceed as follows:
(2x+y)^5
=(2x+y)²(2x+y)²(2x+y)
We will solve the brackets by whole square formula:
=(4x²+4xy+y²)(4x²+4xy+y²)(2x+y)
By multiplying the brackets we get:
=32x^5+32x^4y+8x³y²+32x^4y+32x³y²+8x²y³+8x³y²+4x²y³+2xy^4+16x^4y+
16x³y²+4x²y³+16x³y²+16x²y³+4xy^4+4x²y³+4xy^4+y^5
=32x^5+80x^4y+80x³y²+40x²y³+10xy^4+y^5
Therefore the coefficient of xy^4 is 10
The answer is 10....
Answer: 10
Step-by-step explanation: a p e x
Find the length of RJ
Answer:
Option C 89
Step-by-step explanation:
In this problem we know that
KJ=KR+RJ
we have
KJ=95 units
KR=6 units
substitute and solve for RJ
95=6+RJ
subtract 6 both sides
RJ=95-6=89 units
Answer:
The correct option is C.
Step-by-step explanation:
We need to find the length of line segment RJ.
From the given figure it is clear that line segment KJ is the sum of line segments KR and RJ.
[tex]KJ=KR+RJ[/tex]
The length of line segment KJ is 95 units and the length of KR is 6 units.
Substitute KJ=95 and KR=6 in the above equation.
[tex]95=6+RJ[/tex]
Subtract 6 from both the sides.
[tex]95-6=6+RJ-6[/tex]
[tex]89=RJ[/tex]
The length of segment RJ is 89 units. Therefore the correct option is C.
I need help to solve this problem Simplify (6^7)^3
Answer:
C.
Step-by-step explanation:
(6^7)^3 means (6^7)(6^7)(6^7).
When multiply numbers with same base, add the exponents.
6^(7+7+7)=6^(3*7)=6^(21).
In the beginning you could have just multiply 7 and 3 so the answer is 6^(21).
Answer: The Answer to this question is C bc of the brackets it multiplies the exponents if that makes sense, hope this helps
Step-by-step explanation:
Apply the distributive property to create an equivalent expression.
\dfrac12(10x + 20y +10z) =
2
1
(10x+20y+10z
Step-by-step explanation:
[tex]\text{The distributive property:}\ a(b+c)=ab+ac\\\\\dfrac{1}{2}(10x+20y+10z)=\dfrac{1}{2\!\!\!\!\diagup_1}\cdot10\!\!\!\!\!\diagup^5x+\dfrac{1}{2\!\!\!\!\diagup_1}\cdot20\!\!\!\!\!\diagup^{10}y+\dfrac{1}{2\!\!\!\!\diagup_1}\cdot10\!\!\!\!\!\diagup^5z\\\\=5x+10y+5z[/tex]
Answer:
5x+10y+5z
Step-by-step explanation:
I did it on Khan Academy :)
Polygon ABCD is translated to create polygon A’B’C’D’. Point A is located at (1,5), and point A’ is located at (-2,3). Which expression defines the transformation of any point (x,y) to (x’,y’) on the polygons?
Answer:
The expression is (x,y) -----> (x-3,y-2)
Step-by-step explanation:
we have that
A(1,5) ----> A'(-2,3)
so
The rule of the translation is equal to
(x,y) -----> (x',y')
(x,y) -----> (x-3,y-2)
That means-----> the translation is 3 units at left and 2 units down
Prove that sin^2A/cos^2A + cos^2A/sin^2A = 1/cos^2A*sin^2A - 2
Answer:
prove that:
Sin²A/Cos²A + Cos²A/Sin²A = 1/Cos²A Sin²A - 2
LHS = \frac{Sin^2A}{Cos^2A} + \frac{Cos^2A}{Sin^2A}
Cos
2
A
Sin
2
A
+
Sin
2
A
Cos
2
A
= \begin{lgathered}= \frac{Sin^4A + Cos^4A}{Cos^2A . Sin^2A}\\\\Using\: a^2 + b^2 = (a+b)^2 - 2ab\\\\a = Cos^2A \: \& \:b = Sin^2A\\\\= \frac{(Sin^2A + Cos^2A)^2 - 2Sin^2A Cos^2A}{Cos^2A Sin^2A} \\\\Sin^2A + Cos^2A = 1\\\\= \frac{1 -2Sin^2A Cos^2A}{Cos^2A Sin^2A}\end{lgathered}
=
Cos
2
A.Sin
2
A
Sin
4
A+Cos
4
A
Usinga
2
+b
2
=(a+b)
2
−2ab
a=Cos
2
A&b=Sin
2
A
=
Cos
2
ASin
2
A
(Sin
2
A+Cos
2
A)
2
−2Sin
2
ACos
2
A
Sin
2
A+Cos
2
A=1
=
Cos
2
ASin
2
A
1−2Sin
2
ACos
2
A
\begin{lgathered}= \frac{1}{Cos^2A Sin^2A} - 2\\\\= RHS\end{lgathered}
=
Cos
2
ASin
2
A
1
−2
=RHS
LHS=RHS
Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identity
sin²A + cos²A = 1
Consider the left side
[tex]\frac{sin^2A}{cos^2A}[/tex] + [tex]\frac{cos^2A}{sin^2A}[/tex]
= [tex]\frac{sin^2A}{1-sin^2A}[/tex] + [tex]\frac{cos^2A}{1-cos^2A}[/tex]
= [tex]\frac{sin^2A(1-cos^2A)+cos^2A(1-sin^2A)}{(1-sin^2A)(1-cos^2A)\\}[/tex]
= [tex]\frac{sin^2A-sin^2Acos^2A+cos^2A-sin^2Acos^2A}{1-sin^2A-cos^2A+sin^2Acos^2A}[/tex]
= [tex]\frac{sin^2A+cos^2A-2sin^2Acos^2A}{1-(sin^2A+cos^2A)+sin^2Acos^2A}[/tex]
= [tex]\frac{1-2sin^2Acos^2A}{sin^2Acos^2A}[/tex]
= [tex]\frac{1}{sin^2Acos^2A}[/tex] - [tex]\frac{2sin^2Acos^2A}{sin^2Acos^2A}[/tex]
= [tex]\frac{1}{sin^2Acos^2A}[/tex] - 2 = right side ⇒ proven
If f(a) =11, then use the table above to find f(a-2)
Answer:
7Step-by-step explanation:
From the table
f(a) = 11 → a = 7
a - 2 = 5
f(a - 2) = f(5) = 7
4^-2 x 7^-2 equivalent expression
Answer:
Not sure exactly which equivalent expression you are looking for but my goal would be to write it without the negative exponent.
[tex]\frac{1}{28^2}[/tex]
Step-by-step explanation:
They have the same exponent and it is multiplication.
There is a law of exponent that says [tex](a \cdot b)^x=a^x \cdot b^x[/tex] .
So we have [tex]4^{-2} \cdot 7^{-2}[/tex] equals [tex](4 \cdot 7)^{-2}[/tex].
Let's simplify (4*7)^(-2).
Since 4*7=28, we can say [tex](4*7)^{-2}=(28)^{-2}[/tex].
Some people really hate that negative exponent. All that - in the exponent means is reciprocal. So [tex]28^{-2}=\frac{1}{28^2}[/tex].
An Information Services Manager is purchasing a large number of word processing software licenses at a cost of $125 each. the software company gives a volume discount of 3.5% for large purchases. If the department manager has a budget of $17,300 to purchase the licenses, approximately how many licenses can she purchase.
Answer:
143
Step-by-step explanation:
17300=.965(125X)
17927.46=125X
143.41=X
To calculate the number of software licenses the department manager can purchase, we first find the discounted price of a single license, then divide the total budget by this single license price. In this case, the manager can purchase approximately 143 licenses with a budget of $17,300.
Explanation:The subject of this question is a typical real-life application of Mathematics, specifically in percentages and budgeting. Given the scenario, the Information Services Manager plans to buy word-processing software licenses for each cost of $125. However, a volume discount of 3.5% is offered for large purchases.
Firstly, we need to figure out the discounted price of one license, which can be calculated as 96.5% (100% - the 3.5% discount) of $125, leading to $120.63 approximately (rounding the number to two decimal places).
With a total budget of $17,300, the number of licenses she can purchase can be found by dividing the total budget by the price of a single license after the discount: $ 17,300 divided by $120.63, which gives us approximately 143.
Therefore, the department manager can buy approximately 143 licenses when considering the volume discount.
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Suppose BC is congruent to CA. Can you use the SSS Postulate or the SAS Postulate to prove ABD is congruent to DCA
Answer:
probably sas
Step-by-step explanation:
sas because the 2 sides are congruent, but i don't have enough information to know for sure
Find a linear equation satisfying the conditions:
x-intercept at (-2,0) and y-intercept at (0, -3).
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 2, 0 ) and (x₂, y₂ ) = (0, - 3)
m = [tex]\frac{-3-0}{0+2}[/tex] = - [tex]\frac{3}{2}[/tex]
Note the line crosses the y- axis at (0, - 3) ⇒ c = - 3
y = - [tex]\frac{3}{2}[/tex] x - 3 ← equation in slope- intercept form
If f(x) = -x + 8 and g(x) = x^4, what is (gºf)(2)?
Answer:
[tex]\large\boxed{(g\circ f)(2)=1296}[/tex]
Step-by-step explanation:
[tex](g\circ f)(x)=g\bigg(f(x)\bigg)\\\\f(x)=-x+8,\ g(x)=x^4\\\\(g\circ f)(x)=\g\bigg(f(x)\bigg)=(-x+8)^4\\\\(g\circ f)(2)\to\text{put x = 2 to the equation}\ (g\circ f)(x):\\\\(g\circ f)(2)=(-2+8)^4=(6)^4=1296[/tex]
[tex]\bf \begin{cases} f(x)=&-x+8\\ g(x)=&x^4\\ (g\circ f)(x) =& g(~~f(x)~~) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ f(2)=-(2)+8\implies f(2)=\boxed{6} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{(g\circ f)(2)}{g(~~f(2)~~)}\implies g\left( \boxed{6} \right) = (6)^4\implies \stackrel{(g\circ f)(2)}{g(6)} = 1296[/tex]
Given the triangle below, what is m
Answer:
82.8 degrees
Step-by-step explanation:
The information given here SSS. That means side-side-side.
So we get to use law of cosines.
[tex](\text{ the side opposite the angle you want to find })^2=a^2+b^2-2ab \cos(\text{ the angle you want to find})[/tex]
Let's enter are values in.
[tex]12^2=10^2+8^2-2(10)(8) \cos(B)[/tex]
I'm going to a little simplification like multiplication and exponents.
[tex]144=100+64-160 \cos(B)[/tex]
I'm going to some more simplification like addition.
[tex]144=164-160\cos(B)[/tex]
Now time for the solving part.
I'm going to subtract 164 on both sides:
[tex]-20=-160\cos(B)[/tex]
I'm going to divide both sides by -160:
[tex]\frac{-20}{-160}=\cos(B)[/tex]
Simplifying left hand side fraction a little:
[tex]\frac{1}{8}=\cos(B)[/tex]
Now to find B since it is inside the cosine, we just have to do the inverse of cosine.
That looks like one of these:
[tex]\cos^{-1}( )[/tex] or [tex]\arccos( )[/tex]
Pick your favorite notation there. They are the same.
[tex]\cos^{-1}(\frac{1}{8})=B[/tex]
To the calculator now:
[tex]82.81924422=B[/tex]
Round answer to nearest tenths:
[tex]82.8[/tex]
I want to start a lemonade stand and determine how much lemonade I need to sell to break even each day.
If I know I spend $5 on supplies and sell lemonade at $0.50 per glass determine the number of glasses I must sell to break even. After you find the number of glasses tell me what the x-intercept, y-intercept and slope. Represent in the function you determined
Answer:
Total cost spent on supplies = 5 dollars
Lemonade will be sold at 0.5 dollars.
Let the total glasses of lemonade sold be x
So, revenue generated will be = 0.5x
To get the break even we will equal both.
[tex]0.5x=5[/tex]
[tex]x=5/0.5[/tex]
x = 10
Hence, number of glasses to be sold are 10.
The profit or y can be found as;
[tex]y=0.5x-5[/tex]
So, putting x = 11
[tex]y=0.5(11)-5[/tex]
y = 0.5
Putting x = 12
[tex]y=0.5(12)-5[/tex]
y = 1
Putting x = 13
[tex]y=0.5(13)-5[/tex]
y = 1.5
The slope is 0.5.
The y-intercept is -5. This means if 0 glasses of lemonade are sold then there is a loss of $5.
The y intercept is obtained when x=0.
[tex]y=0.5(0)-5[/tex]
y = -5
The x-intercept is 10 or the number of glasses I must sell to break even.
Use row reduction to solve the system of equations. x-2y+z=4, 3x-5y-17z=3, 2x-6y+43z=-5
Answer:
x = -1223, y = -629, and z = -31.
Step-by-step explanation:
This question can be solved using multiple ways. I will use the Gauss Jordan Method.
Step 1: Convert the system into the augmented matrix form:
• 1 -2 1 | 4
• 3 -5 -17 | 3
• 2 -6 43 | -5
Step 2: Multiply row 1 with -3 and add it in row 2:
• 1 -2 1 | 4
• 0 1 -20 | -9
• 2 -6 43 | -5
Step 3: Multiply row 1 with -2 and add it in row 3:
• 1 -2 1 | 4
• 0 1 -20 | -9
• 0 -2 41 | -13
Step 4: Multiply row 2 with 2 and add it in row 3:
0 2 -40 -18
• 1 -2 1 | 4
• 0 1 -20 | -9
• 0 0 1 | -31
Step 5: It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:
• x - 2y + z = 4
• y - 20z = -9
• z = -31
Step 6: Since we have calculated z = -31, put this value in equation 2:
• y - 20(-31) = -9
• y = -9 - 620
• y = -629.
Step 8: Put z = -31 and y = -629 in equation 1:
• x - 2(-629) - 31 = 4
• x + 1258 - 31 = 4
• x = 35 - 1258.
• x = -1223
So final answer is x = -1223, y = -629, and z = -31!!!
A triangular field has sides of 120.32 m and 204.61 m, and the angle between them measures 60.881°. Find the area of the field
Answer:
A=10753.5715 m^2.
Step-by-step explanation:
The area of a triangle with the information SAS given is:
A=1/2 * (side) * (other side) * sin(angle between)
A=1/2 * (204.61)*(120.32) * sin(60.881)
A=10753.5715 m^2.
SAS means two sides with angle between.
Answer: [tex]10,753.57\ m^2[/tex]
Step-by-step explanation:
You need to use the SAS area formula. This is:
[tex]A=\frac{a*b*sin(\alpha)}{2}[/tex]
You know that the triangular field has sides of 120.32 meters and 204.61 meters and the angle between them measures 60.881°. Then:
[tex]a=120.32\ m\\b=204.61\ m\\\alpha =60.881\°[/tex]
Substituting these values into the formula, you get that the area of this triangle is:
[tex]A=\frac{(120.32\ m)(204.61\ m)*sin(60.881\°)}{2}\\\\A=10,753.57\ m^2[/tex]
Please help, I'm stuck
Answer: Option B
[tex]k> 0[/tex]
Step-by-step explanation:
The graph shows a radical function of the form [tex]f(x)=a(x+k)^{\frac{1}{n}}+c[/tex]
Where n is a even number.
This type of function has its vertex at the origin when [tex]k = 0[/tex] and [tex]c = 0[/tex]
If [tex]k> 0[/tex] the graph moves horizontally k units to the left
If [tex]k <0[/tex] the graph moves horizontally k units to the right.
Note that in this case the vertex of the function is horizontally shifted 5 units to the left. Therefore we know that [tex]k = 5> 0[/tex]
The correct answer is option B