The complete trigonometry ratios are sin(220) = -sin(40) and cos(220) = cos(140) and the angles are 40 and 220 degrees
How to determine the measure of the angles?Angle 1
The trigonometry ratio of the angle is given as
sin(220)
Expand the above expression
sin(220) = sin(180 + 40)
Apply the sine rule
sin(220) = sin(180)cos(40) + cos(180)sin(40)
Evaluate the ratios
sin(220) = 0 x cos(40) - sin(40)
So, we have
sin(220) = - sin(40)
So, the measure of the angle is 40 degrees
Angle 2
The trigonometry ratio of the angle is given as
cos(220)
Expand the above expression
cos(220) = cos(360 - 140)
Apply the cosine rule
cos(220) = cos(360)cos(140) + sin(140)sin(360)
Evaluate the ratios
cos(220) = 1 x cos(140) + sin(140) x 0
So, we have
cos(220) = cos(140)
So, the measure of the angle is 140 degrees
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A sole trader operates his business from
a warehouse, which has been damaged
by a fire, which occurred at the end of
the financial year. After the fire, the
remaining inventory that is undamaged
amounts to GHC 2,000 (cost). The
accountant establishes the following
information: I Inventory at the
beginning of the year was GHC 16,000 II
Purchases during the year were GHC
115,000 III Sales during the year were
GHC 140,000 IV The trader sells his
goods at a mark-up of 25% of cost What
is the value of the inventory lost in fire?
Beginning inventory = 16,000 Purchase = 115,000 Sales = 140,000 Mark up = 25% on cost Undamanged inventory = 2,000
The value of the inventory lost in fire is 2,000
How do you take inventory loss due to fire into account?
The cost of products available for sale is then subtracted from the cost of goods sold. The quantity will reflect how much inventory the fire has actually destroyed. As an illustration, $275,000 minus $80,000 = $195,000, which represents the amount of inventory destroyed in the fire.
Calculate the quantity of inventory destroyed by deducting the cost of sold goods from the cost of goods that are still in stock. In this scenario, the amount of merchandise lost in the fire was $275,000 less $70,000, or $205,000.
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x - 2/5 = 7 what is the value of x?write answer in simplest form.
Explanation:
x - 2/5 = 7
Collect like terms:
[tex]\begin{gathered} x\text{ = 7 + }\frac{2}{5}=\text{ }\frac{7}{1}+\frac{2}{5} \\ \text{LCM = 5} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{35\text{ + 2}}{5}\text{ = }\frac{37}{5} \\ x=\text{ 7}\frac{2}{5} \end{gathered}[/tex]
Find the domain of the function f(x)=√100x²
The domain of the function √(100x²) will be (-∞,∞) as the definition of domain states that the set of inputs that a function will accept is known as the domain of the function in mathematics.
What is domain?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the set of values it can take as input.
What is function?A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Here,
The function is √(100x²).
The domain would be (-∞,∞).
The set of inputs that a function will accept is known as the domain of the function in mathematics, and the domain of the function √(100x²) will be (-∞,∞), according to the definition of domain.
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Hello I need help with this question as fast as possible please , I am on my last few questions and I have been studying all day for my final exam for math tomorrow. It is past my bed time and I am exhausted . Thank you so much for understanding:))
Notice that:
[tex]665.6=10.4\times64.[/tex]Therefore, if we divide the resulting equation of step 3 by 10.4 we get:
[tex]\begin{gathered} \frac{10.4x}{10.4}=\frac{665.6}{10.4}, \\ x=64. \end{gathered}[/tex]Then the missing step is:
Divide both sides of the equation by 10.4.
Answer: Last option.
Which of the following is a correct interpretation of the expression -8 + (-8)?
The solution is:
*The expression describes the number that is 8 to the left of -8 on the number line. [Option A].
los números que faltan.
What comes after
3.0
Answer:
3.1? 4.0? 3.0000001?
I did not know what are you mean sorry but uf i correct say me it
The Thompson family and the Kim family each used their sprinklers last summer. The Thompson family's sprinkler was used for 25 hours. The Kim family'ssprinkler was used for 35 hours. There was a combined total output of 1075 L of water. What was the water output rate for each sprinkler if the sum of the tworates was 35 L per hour?Thompson family's sprinkler:Kim family's sprinkler:
Let x be the rate of water output by the Thompson family and let y be the rate of water output by the Kim family.
We know that the Thompson family sprinkler was used for 25 hours, Kim's family sprinkler was used for 35 hours and that there was a combined total output of 1075 L of water; then we have the equation:
[tex]25x+35y=1075[/tex]We also know that the combined water output was 35 L per hour, then:
[tex]x+y=35[/tex]Hence we have the system of equations:
[tex]\begin{gathered} 25x+35y=1075 \\ x+y=35 \end{gathered}[/tex]To solve this system we solve the second equation for y:
[tex]\begin{gathered} x+y=35 \\ y=35-x \end{gathered}[/tex]And we plug this value in the first equation and solve for x:
[tex]\begin{gathered} 25x+35(35-x)=1075 \\ 25x+1225-35x=1075 \\ -10x=1075-1225 \\ -10x=-150 \\ x=\frac{-150}{-10} \\ x=15 \end{gathered}[/tex]Once we have the value of x we plug it in the expression of y:
[tex]\begin{gathered} y=35-15 \\ y=20 \end{gathered}[/tex]Therefore we have that:
[tex]\begin{gathered} x=15 \\ y=20 \end{gathered}[/tex]which means:
Thompson family's sprinkler: 15 L per hour
Kim family's sprinkler: 20 L per hour.
15. Find the volume of a rectangular prism with the following dimensions.a length of 11 cm, a width of 4.2 cm, and a height of 7.1 cm.3308.24 cm3328.02 cm322.3 cm346.2 cm
For this problem, we are given the dimensions of a rectangular prism and are asked to determine its volume.
The volume of a rectangular prism is given by the product of the three dimensions, therefore we have:
[tex]\begin{gathered} V=\text{ height}\cdot\text{ length}\cdot\text{ width}\\ \\ V=11\cdot4.2\cdot7.1=328.02\text{ cubic cm} \\ \end{gathered}[/tex]The correct answer is 328.02 cubic centimeters.
3 4. Diego estimates that there will need to be 3 pizzas for every 7 kids at his party. Select all the statements that express this ratio. (Lesson 2-1) (A.) The ratio of kids to pizzas is 7 : 3. B.) The ratio of pizzas to kids is 3 to 7. The ratio of kids to pizzas is 3: 7. (D. The ratio of pizzas to kids is 7 to 3. E. For every 7 kids, there need to be 3 pizzas.
The statements in (A), (B), (E) are correct and satisfy the conditions in question.
What is ratio and proportion?
Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion. Because b is not equal to 0, the ratio establishes the link between two quantities such as a:b.
Given, for every 7 kids, pizzas needed = 3 --(iii)
Therefore, for every 1 kid, pizza needed = (3/7)
Thus, for every x kids, pizza needed = (3/7)x
Again, ratio of pizzas to kids is = 3:7 --(i)
Also, the ratio of kids to pizza is = 7:3 --(ii)
From (A), using (ii), the statement in (A) is correct.
From (B), using (ii), the statement in (B) is correct.
From (C), using (i), the statement in (C) is incorrect.
From (D), using (i), the statement in (D) is incorrect.
From (E), using (iii), the statement in (E) is correct.
Thus, the statements in (A), (B), (E) are correct and satisfy the conditions in question.
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Find the distance between the pair of parallel lines with the given equations.y = -5xy = -5x + 26O A) 5 unitsO B) 14.14 unitsC) C) 5.10 unitsO D) 6 units
Solution:
Consider two lines with the following equations:
[tex]y_1=mx+c[/tex]and
[tex]y_2=mx+c_2[/tex]the distance d between these two parallel lines is given by the following equation:
First, we need to take one of the lines and convert it to standard form. For example, take the line:
y = -5x + 26
then, we obtain:
-5x-y+26=0
in this case, we get that
A = -5
B= -1
C = 26
Now we can substitute A, B, and C into our distance equation along with a point, (x1,y1) from the other line. We can pick any point on the line y2. Just plug in a number for x, and solve for y. I will use x = 2, to obtain:
y = -5(2) = -10
then
(x1,y1) = (2,-10)
Replacing these values into the distance equation, we obtain:
[tex]d\text{ = }\frac{|-5(2)+(-1)(-10)+26|}{\sqrt[]{(-5)^2+(-1)^2}}[/tex]that is:
[tex]d\text{ = }\frac{|-10+10+26|}{\sqrt[]{(-5)^2+(-1)^2}}=\frac{26}{\sqrt[]{26}}=5.09\approx5.10[/tex]so that, the correct answer is:
[tex]5.10\text{ units}[/tex]A small publishing company is planning to publish a new book. Let C be the total cost of publishing the book (in dollars). Let be the number of copies of the book produced. For the first printing, the company can produce up to 100 copies of the book. Suppose that C = 10N + 700 gives C as a function of N during the the correct description of the values in both the domain and range of the function. Then, for eachchoose the most appropriate set of values.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
C = 10N + 700
Step 02:
functions:
C = total cost
N = number of copies
Domain:
number of copies produced
{0, 1, 2, 3, .... 100}
Range:
cost of publishing book (in dollars)
{700, 710, 720, 730, ... 1700}
That is the full solution.
RecoverySolve for x usingcross multiplication.2x + 132x11 -=x + 22x = [?]Enter
Answer:
x = 4
Step-by-step explanation:
Cross-multiplying means multiplying the numerator of one side by the denominator of the other side.
So, let's multiply the sides:
[tex]\begin{gathered} \frac{2x+1}{3}=\frac{x+2}{2} \\ 2\cdot(2x+1)=3\cdot(x+2) \end{gathered}[/tex]Now, we can solve each side:
[tex]\begin{gathered} 4x+2=3x+6 \\ 4x-3x=6-2 \\ 1x=4 \\ x=4 \end{gathered}[/tex]So, x = 4.
What is the area of this triangule? h = 12 in, b = 3 in
Answer:
Area = 18
Explanation:
The area of a triangle is given by
Area = 1/2 height * base length
Now in our case
height = 12 in, base length = 3 in; therefore, the area is
Area = 1/2 * 12 * 3
Area = 6 * 3
Area = 18
Which is our answer!
7. Simplify(6x + y)s
6xs + ys
Explanations:The given expression is:
(6x + y)s
This can be simplified by simplying expanding the brackets
The equation then becomes:
6xs + ys
Answer:
6xs + ys
Step-by-step explanation:
A rectangle has an area ofx² + 9x + 14Find the expressions that represent the dimensions of the rectangle.O (x - 2) and (x - 7)O (x + 3) and (x + 6)(x + 2) and (x + 7)O (x + 1) and (x + 14)
x² + 9x + 14
The area of a rectangle is the product of the length and the width.
Factorizing the expression
x² + 9x + 14 = x² + 7x + 2x + 14
= x(x + 7) + 2(x + 7)
= (x + 7)(x + 2)
Hence the dimensions are (x + 2) and (x + 7)
Find the value of f(-9).
The function f(-9) is the -x value, find where the line is in the -y direction at -x = -9. The line crosses -y = -3 at -x = -9.
What is meant by the graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
In discrete mathematics, a graph is made up of vertices—a collection of points—and edges—the lines connecting those vertices. In addition to linked and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs, there are many other forms of graphs. A graph is a diagram that depicts the connections between two or more objects.
The function f(-9) is the -x value, find where the line is in the -y direction at -x = -9. The line crosses -y = -3 at -x = -9.
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Can someone help out with a math prob?
pic of question below
The polar equation of the curve with the given Cartesian equation is r = √7
How to convert polar equation to cartesian equationGiven the Cartesian equation: x² + y² = 7
The relationships between polar and cartesian equation :
x = r cosθ
y = r sinθ
Where r is the radius and θ is the angle
Put the values of x and y into the given cartesian equation:
(r cosθ)² + (r sinθ)² = 7
r²cos²θ + r²sin²θ = 7
r²(cos²θ + sin²θ) = 7
Since the trigonometric identity cos²θ + sin²θ = 1
r²(1) = 7
r² = 7
r = √7
Therefore, the polar equation for the represented curve is r = √7
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what is 140% 150,000
140 % of 150,000
[tex]\begin{gathered} 140\text{ \%=}\frac{140}{100} \\ \frac{140}{100}\times150000=\frac{21000000}{100}=210,000 \end{gathered}[/tex]PartBecause his goal is to bike 65 miles over four days, what equation can be used to find the number of miles he should bike on the first day, X? Donot combine like terms.
On the first day, he biked x miles
The next day, he will bike
There are two boxes containing only red and purple pens.Box A has 12 purple pens and 3 red pens.Box B has 14 purple pens and 6 red pens.A pen is randomly chosen from each box.List these events from least likely to most likely.Event 1: choosing a purple or red pen from Box A.Event 2: choosing a green pen from Box B.Event 3: choosing a purple pen from Box B.Event 4: choosing a purple pen from Box A.Least likelyMost likelyEventEventEventEvent
Event 1: choosing a purple or red pen from Box A
All pens are purple or red so the probability is:
[tex]P=\frac{12+3}{15}=\frac{15}{15}=1[/tex]Event 2: choosing a green pen from Box B
We don't have green pens, so the probability is 0.
Event 3: choosing a purple pen from Box B
We have 14 purple pens and 20 total pens, so:
[tex]P=\frac{14}{20}=\frac{7}{10}=0.7[/tex]Event 4: choosing a purple pen from Box A
We have 12 purple pens and 15 total pens, therefore:
[tex]P=\frac{12}{15}=\frac{4}{5}=0.8[/tex]Listing from least likely to most likely, we have:
event 2 < event 3 < event 4 < event 1
Answer:
Event 2, Event 3, Event 4, Event 1
determine whether the equation is linear to x. 5-3x=0
By definition a linear equation is an equation in which the highest power of any variable in the equation is always 1. In this case we have the equation:
[tex]5-3x=0[/tex]We notice that this equation only has one variable, x, and that its power is 1. Therefore, the equation is linear.
the following augmented matrix is in row-echelon form and represents a linear system. solve the system by using back-substitution if possible.
Given the matrix:
Given that it represents a linear system, we have the set of equations:
(1)x + 3y = 6
0x + (1)y = -1
x + 3y = 6..................equation 1
y = -1.........................equation 2.
Let's solve the system using substitution method.
Substitute -1 for y in equation 1:
x + 3(-1) = 6
x + (-3) = 6
x - 3 = 6
Add 3 to both sides:
x - 3 + 3 = 6 + 3
x = 9
From equation 2, we have the value of y:
y = -1
Therefore, the solution to the system is:
x = 9, y = -1
In point form:
(x, y) ==> (9, -1)
ANSWER:
x = 9, y = -1
I need help answering this question, if you can thank you very much.
Answer: We have to factor out the polynomial which is:
[tex]x^2+6x-16[/tex]The factorization is as follows:
[tex]\begin{gathered} \text{ Method:} \\ \\ (x+a)(x+b)=x^2+(a+b)x+ab \\ \\ \\ ----------------------- \\ \text{ Solution:} \\ \\ x^2+6x-16 \\ \\ \text{ The unknowns }\rightarrow\begin{cases}ab={-16} \\ a+b={6}\end{cases} \\ \\ \\ \text{ The possible values are:} \\ \\ \\ a=8 \\ b=-2 \\ \\ \\ \text{ Because:} \\ \\ \\ (8)\times(-2)=-16 \\ (8)+(-2)=6 \\ \\ \\ \text{ Therefore the factored form is:} \\ \\ \\ (x+8)(x-2)=x^2+6x-16 \end{gathered}[/tex]Convert each slope-intercept or point slope equation into standard form.
y - 3 = 1/5(x + 6)
The Standard form of the equation will be as x - 5y = -21
What is Standard form of equation?The standard form of the equation is defined as; Ax + By = C
Where, A, B and C are integers.
Given that the equation in slope - intercept form is;
⇒ y - 3 = 1/5 (x + 6)
Now,
We need to convert the equation in standard form as;
⇒ y - 3 = 1/5 (x + 6)
Now Change into standard form as;
⇒ y - 3 = 1/5 (x + 6)
Then Multiply by 5 both side, we get:
⇒ 5( y - 3) = (x + 6)
⇒ 5y - 15 = x + 6
⇒ 5y = x + 21
Now Subtract 21 both side, we get:
⇒ 5y - 21 = x + 21 - 21
⇒ 5y - 21 = x
⇒ - 21 = x - 5y
⇒ x - 5y = -21
Therefore,
The Standard form of the equation will be as x - 5y = -21
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Fill in the blank with a number to make the expression of perfect square.x^2-18x t
Answer:
[tex]81[/tex]Explanation:
Here, we want to write a figure that would make the given expression a perfect square
As a perfect square, we mean that:
[tex]ax^2+bx+c=(x+d)(x+d)=(x+d)^2[/tex]In this case, what we have to do is to divide the coefficient of x by 2, square it and write it
The coefficient of x is the number before x (we must consider its sign however)
Thus, we have the coefficient in this case as -18
Dividing this by 2 and squaring, we have:
[tex]\frac{-18}{2}=(-9)^2\text{ = 81}[/tex]Thus, we have:
[tex]x^2-18x+81=(x-9)(x-9)=(x-9)^2[/tex]
Hello! I need some help with this homework question, please? The question is posted in the image below. Q4
a) f(0) = -1
b) f(1) = 1
c) f(4) = 7
d) f(5) = 121
Explanation:
. Since for every value between -2 (excluded) and 4 (included)
~ 0 , 1 and 4
You have to use the first equation
=> f(0) = 2 * 0 - 1 = -1
=> f(1) = 2 * 1 - 1 = 1
=> f(4) = 2 * 4 - 1 = 7
. For values between 4 (exclude) and 5(included)
~ 5
You have to use the second equation
=> f(5) = 5^3 - 4 = 121
of a sample of 200 students surveyed,38 students said the soccer was their favorite sport what percent of the students in the sample prefer soccer 19% 38%40%76%
Out of 200 students surveyed, 38 said that soccer was their favorite sport.
The total number of students surveyed represents 100% of the sample, to determine which percentage does 38 represent, you can use cross multiplication:
200 students____100%
38 students _____ x%
Both relationships are at the same ratio so that:
[tex]\frac{100}{200}=\frac{x}{38}[/tex]To determine the percentage multiply both sides by 38:
[tex]\begin{gathered} 38\cdot\frac{100}{200}=38\cdot\frac{x}{38} \\ 19=x \end{gathered}[/tex]The percentage of students surveyed that like soccer is 19%
A skier is trying to decide wheter or not to buy a seaskn ski pass. A daily pass cost $71. a season ski pass costs $350. the skirr would have to rent skis with either pass for $30 per day. how many days would the skier have to go skiing i. order to make the season pass less expensive than the daily passes?
The most appropriate choice for linear equation will be given by -
The skier would have to go atleast 5 days to make the season pass less expensive than the daily pass
What is linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by [tex]> , \geq, < , \leq[/tex] sign
A one degree inequation is known as linear inequation.
Here,
Let the number of days the skier have to go skiing in order to make the season pass less expensive than the daily passes be d days
A daily pass cost $71
A season ski pass costs $350.
The skier would have to rent skis with either pass for $30 per day.
Cost of skiing with daily pass = $(71d + 30d) = $101d
Cost of skiing with season pass = $(350 + 30d)
By the problem,
[tex]101d > 350 + 30d\\101d - 30d > 350\\81d > 350\\d > \frac{350}{81}\\d > 4.3[/tex]
The skier would have to go atleast 5 days to make the season pass less expensive than the daily pass
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Solve the equation.k²=47ks.(Round to the nearest tenth as needed. Use a comma to separate answers as needed.
The initial equation is:
[tex]k^2=47[/tex]Then, we can solve it calculating the square root on both sides:
[tex]\begin{gathered} \sqrt[]{k^2}=\sqrt[]{47} \\ k=6.9 \\ or \\ k=-6.9 \end{gathered}[/tex]Therefore, k is equal to 6.9 or equal to -6.9
Answer: k = 6.9 or k = -6.9
Given the following information about events A, B, and C, determine which pairs of events, if any, are independent andwhich pairs are mutually exclusive.
Let's begin by identifying key information given to us:
[tex]\begin{gathered} P(A)=0.39 \\ P(B)=0.42 \\ P(C)=0.19 \\ P(A|B)=0 \\ P(C|B)=0.19 \\ P(A|C)=0.39 \end{gathered}[/tex]When two events A and B are independent we have it thus:
[tex]undefined[/tex]