Solve on the interval [0, 2pi): 4csc x +6=-2
By solving the interval : [0,2pi] 4 csc x +6=-2 is 7pi/6 , 11pi/6
What are Trigonometric identities?Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence. These are identities that, geometrically speaking, involve certain functions of one or more angles. defining sine and cosine in terms of tangent, cotangent, secant, and cosecant interactions. The sine and cosine formula according to Pythagoras. This trig identity is arguably the most significant.[tex]& 4 \csc x+6=-2 \\[/tex]
[tex]& 4 \csc x=-8 \\[/tex]
Simplifying,
[tex]& \csc x=-2 \\[/tex]
[tex]& \frac{1}{\sin x}=-2 \\[/tex]
[tex]& \sin x=-\frac{1}{2} \\[/tex]
We get,
[tex]& x=\frac{7 \pi}{6}, \frac{11 \pi}{6}[/tex]
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Ben has 50 toys. 15 of them are new and 9 are his favorites; 2 are new and favorites.
Ben is giving away all the toys that are neither new nor favorites. How many toys
does Ben give away?
Answer:
28 toys
Step-by-step explanation:
Ben has 50 toys, of which 15 are new, 9 are favorites, and 2 are new and favorites. You want to know the number that are neither new nor favorite.
GroupingsThe number of new toys includes (new and favorite) and (new and not favorite). That is ...
15 = 2 + new and not favorite
So ...
new and not favorite = 15 -2 = 13
Likewise, the number of favorite toys includes (new and favorite) and (not new and favorite). That is ...
9 = 2 + not new and favorite
not new and favorite = 9 -2 = 7
Donated
The total of 50 toys includes ...
total = (new and favorite) + (new and not favorite) + (not new and favorite) + (not new and not favorite)
50 = 2 + 13 + 7 + (not new and not favorite)
Then the number of (not new and not favorite) is ...
not new and not favorite = 50 -2 -13 -7 = 28
These are the toys that Ben gives away.
Ben gives away 28 toys.
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Malcom wrote the equivalent ratios shown below. Find the scale factor he used to write the equivalent ratios
9/40 and 54/240
In this question, we're looking for the number Malcom used to scale the two numbers. We can see there's a pattern, 9 is 1/6 of 54 and 40 is 1/6 of 240!
(54 divided by 9 is 6 and 240 divided by 40 is 6!)
therefore, the scale factor must be 6
Calculate the perimeter of a square with side 12cm
Answer: 48 cm
Step-by-step explanation:
12 + 12 + 12 + 12 = 48
I need help with problem eight.
Forty points for whoever answers this problem
Answer:
1
Step-by-step explanation:
1/1260 = 0.00079365079
0.00079365079 * 1260 = 1
area of a parallelogram help wanted ty
The area of the parallelogram is 72 square units. Option B
How to determine the area of the parallelogramThe formula for calculating the area of a parallelogram is expressed as;
A = bh
Given that;
A is the area of the parallelogramb is the base of the parallelogramh is the height of the parallelogramFrom the information given, we have that;
The base of the parallelogram = x + yThe height of the parallelogram = hNow, substitute the values
x + y = 8 + 4
add the values
x + y = base = 12 units
h = 6 units
Now, substitute the values into the formula, we get;
Area, A = 12(6)
multiply the values
Area, A = 72 square units
Hence, the value is 72 square units
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The Chess Club president brought donuts to the club meeting each week. As the club grew, more donuts were needed so that each member could have a donut. The table below shows the ratios of boxed donuts to the cost.
Donuts A 4 5 C
Cost 13.80 27.60 B 55.20
Determine which table has the correct values for A, B, and C.
Donuts 3 4 5 7
Cost 13.80 27.60 34.95 55.20
Donuts 2 4 5 8
Cost 13.80 27.60 34.95 55.20
Donuts 3 4 5 6
Cost 13.80 27.60 34.50 55.20
Donuts 2 4 5 8
Cost 13.80 27.60 34.50 55.20
The table with correct values of A, B and C is,
⇒ Donuts 2 4 5 8
Cost 13.80 27.60 34.50 55.20
What is mean by Ratio?A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.
We have to given that;
The table below shows the ratios of boxed donuts to the cost.
Donuts A 4 5 C
Cost 13.80 27.60 B 55.20
Now, By definition of ratio, we get;
⇒ A / 13.80 = 4 / 27.60
⇒ A = 13.80 × 4 / 27.60
⇒ A = 2.00
And,
⇒ 4 / 27.60 = 5 / B
⇒ B = 5 × 27.60 / 4
⇒ B = 34.5
⇒ 4 / 27.60 = C / 55.20
⇒ C = 55.20 × 4 / 27.60
⇒ C = 8
Thus, The table with correct values of A, B and C is,
⇒ Donuts 2 4 5 8
Cost 13.80 27.60 34.50 55.20
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Answer:
a
Step-by-step explanation:
i took the test :)
? Question
Drag the tiles to the correct boxes to complete the pairs.
Solve each equation using the square root property. Then, match the solutions to the equatio
Tiles
Help please
The solutions for the given equations are x = 9i , -9i , x = 2i,-2i ,
x = [tex]\sqrt{13}[/tex] , - [tex]\sqrt{13}[/tex] , x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i .
Given equations ,
[tex]x^{2}[/tex] + 81 = 0 ,[tex]x^{2}[/tex]-22 = -26 , 3[tex]x^{2}[/tex]-18=21 ,2[tex]x^{2}[/tex] +15 = -13
What is Quadratic equation ?
quadratic equation can be defined as the equation which is in the form of a[tex]x^{2}[/tex]+bx + c = 0 .
where a,b,c are constants .
By solving we get ,
[tex]x^{2}[/tex] +81 = 0
[tex]x^{2}[/tex] = -81
x = 9i , -9i
[tex]x^{2}[/tex] - 22 = -26
[tex]x^{2}[/tex] = -26 + 22
[tex]x^{2}[/tex] = -4
x = 2i,-2i
3[tex]x^{2}[/tex] - 18 = 21
3[tex]x^{2}[/tex] = 18+21
3[tex]x^{2}[/tex] = 39
[tex]x^{2}[/tex] = 13
x = [tex]\sqrt{13}[/tex] , - [tex]\sqrt{13}[/tex]
2[tex]x^{2}[/tex] +15 = -13
2[tex]x^{2}[/tex] = -13-15
2[tex]x^{2}[/tex] = -28
[tex]x^{2}[/tex] = -14
x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i
Hence the solutions for the given equations are x = 9i , -9i , x = 2i,-2i ,
x = [tex]\sqrt{13}[/tex] , - [tex]\sqrt{13}[/tex] , x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i .
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Segment
B
D
‾
BD
bisects
∠
A
B
C
∠ABC. Solve for
x
x. Round to the nearest tenth, if necessary. (Image not necessarily to scale.)
The value of x on the line segment and the triangle is 17.3 units
How to determine the value of xFrom the question, we have the following parameters that can be used in our computation:
A triangle (see attachment for the triangle)
Also from the question, we understand that:
BD bisects ∠ABC
Using the bisector theorem, we have
x/13 = 20/15
Multiply both sides of the equation by 13
So, we have the following representation
13 * x/13 = 20/15 * 13
Evaluate the products
So, we have the following representation
x = 20/15 * 13
Evaluate the other products
So, we have the following representation
x = 52/3
This gives
x = 17.3
Hence, the length x is 17.3 units
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The density of a certain material is such that it weighs 6900 grams for every 4.5 quarts of volume. Express this density in pounds per cubic foot. Round your answer to the nearest whole number.
The density in terms of pounds per cubic foot is 101.2 pounds/ft³
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here; 6900 g for every 4.05 quarts thus expressing in terms of pounds per cubic foot we get = 15.22/0.15039
= 101.2
Hence, The density in terms of pounds per cubic foot is 101.2 pounds/ft³
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Jacob Hernandez invests $25,000 in a CD for 5 years. The CD earns interest at an annual rate of 5.5% compounded quarterly. What is the annual percentage yield to the nearest hundredth of a percent?
Answer:
Below
Step-by-step explanation:
Each PERIOD is 3 months there is 4 periods per year
periodic interest = .055/4
effective interest per year would then be
(1 + .055/4)^4 - 1 = .056144 = ~ 5.61%
What is the unit rate for 4543.08 km in 52.4 h?
The unit rate for 4543.08 km in 52.4 hours is 86.7 km.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
4543.08 km = 52.4 hours
Divide 52.4 into both sides.
86.7 km = 1 hour
Thus,
The unit rate is 86.7 km.
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Find the slope of the line.
Answer:
-5/4
Step-by-step explanation:
slope(m)= y2-y1/x2-x1
from the graph 5-0/-2-2
=5/-4
answer = -5/4
what would be themissing side length
The missing side length is 5.7.
What would be themissing side length?The missing side length AB, can be calculated using the Pythagorean Theorem.The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the two sides adjacent to the right angle (A and B) is equal to the square of the length of the hypotenuse (C).In other words, AB^2 + BC^2 = AC^2.In this case, AB^2 = AC^2 - BC^2, or AB^2 = 6.7^2 - 3^2, which simplifies to AB^2 = 44.89.Taking the square root of both sides yields AB = 6.7.Therefore, the missing side length, AB, is 6.7.The missing side length of a triangle with sides of lengths a, b, and c is calculated by using the Pythagorean theorem, which states that a^2 + b^2 = c^2. In this case, we are given that side c is 3, and side a is 6.7.Using the Pythagorean theorem, we can solve for side b by rearranging the equation to read b^2 = c^2 - a^2. Plugging in our known values, we get b^2 = 9 - 44.89, or b^2 = -35.89.Since the square root of a negative number is not a real number, this implies that there is no real number solution for b, and therefore the missing side length of the triangle is not possible.
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the slope to (9, -10), (0, 8) with the work shown please.
Answer:
-2
Step-by-step explanation:
To find the slope, subtract y1 - y2, then divide by x1-x2
The y numbers in this set is -10 & 8
The x numbers in this set is 9 & 0
-10-8= -18
9-0 = 9
-18/9 = -2
The slope would be -2
Question 2(Multiple Choice Worth 5 points)
(Two-Step Linear Inequalities MC)
Find c for the inequality three fifths times c plus 7 is less than or equal to two fifths.
c ≤ −11
c ≥ −11
c ≤ −5
c ≥ −5
The value of c obtained from the linear inequality (3/5)·c + 7 ≤ 2/5 is the option;
c ≤ -11
What is an inequality?An inequality is a (non equal) comparison between two expressions that have different values.
The specified inequality can be expressed as follows;
[tex]\dfrac{3}{5} \times c + 7 \leq \dfrac{2}{5}[/tex]
Simplifying the above inequality by subtracting 7 from both sides, we get;
[tex]\dfrac{3}{5} \times c + 7 - 7 \leq \dfrac{2}{5} - 7[/tex]
Evaluating and simplifying the right hand side into a fraction, we get;
[tex]\dfrac{3}{5} \times c + 0 \leq \dfrac{2}{5} - 7 = \dfrac{2 - 35}{5} = \dfrac{-33}{5}[/tex]
[tex]\dfrac{3}{5} \times c \leq \dfrac{-33}{5}[/tex]
Multiplying both sides by 5, we get;
[tex]5\times \dfrac{3}{5} \times c \leq 5 \times \dfrac{-33}{5}[/tex]
[tex]\dfrac{5}{5} = 1[/tex], therefore;
3·c ≤ -33
Dividing both sides of the above inequality by 3, we get;
3·c ÷ 3 ≤ -33 ÷ 3
c ≤ -11
The correct option is; c ≤ -11
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on Monday the solar panels on a house produced 37.124 units of energy. On Tuesday, the solar panels produced 2,846 fewer units of energy than on Monday. What is the total number of units of energy in two days.
The total number of units of energy produced in the two days is 71,402.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Monday:
Energy = 37,124
Tuesday:
Energy = 37,124 - 2846 = 34278
The total energy produced.
= 37124 + 34278
= 71402
Thus,
The total number of energy in two days is 71,402.
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-50 POINTS- only answer if you know. NOT (4,7) OR (5,2).
Answer:
(8, -2)
Step-by-step explanation:
Given:
[tex]\textsf{If P = (8, 2), Find $\sf R_{x-axis}(P)$}[/tex]
[tex]\sf R_{x-axis}(P)[/tex] means to reflect the given point P in the x-axis.
When a point is reflected in the x-axis, the x-value is unchanged, but the y-value becomes negative:
(x, y) → (x, -y)Therefore:
[tex]\sf R_{x-axis}(P)=(8,-2)[/tex]
which fractions, when converted, result in a repeating decimal? select all that apply 1/8 1/6 3/12 8/9 2 and 4/5 4 and 3/11
Answer:
B. 1/6
D. 3/12
F. 4 3/11
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A 38 ounce box of cat food costs $1.69 and a 24 ounce box costs $1.29. How much can be saved per ounce by guiding the larger box
The amount of money that can be saved per ounce by guiding the larger box is $0.009.
What is equation modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.
Given is that a 38 ounce box of cat food costs $1.69 and a 24 ounce box costs $1.29.
For the larger box -
38 ounce box of cat food costs $1.69
1 ounce of this box will cost $(1.69/38) = $0.045
For the smaller box -
24 ounce box of cat food costs $1.29
1 ounce of this box will cost $(1.29/24) = $0.054
Money that can be saved per ounce by guiding the larger box -
0.054 - 0.045
0.009
Therefore, the amount of money that can be saved per ounce by guiding the larger box is $0.009.
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Chen tosses a number cube 19 fewer times than Jayden. Chen tosses a number cube 38 times. How many times does Jayden toss a number cube?
hello i need help with my math question one only pease and thank you
a) The after-tax cost of the vehicle Rachel is buying is $29,368.70.
b) The part of the after-tax cost that Rachel will finance after making the down payment is $25,118.70.
c) The total payments after 5 years are $30,659.60.
d) The total interest Rachel paid is $1,290.90.
What is the interest payment?The interest payment represents the difference between the total monthly payments and the financing part of the after-tax cost of the vehicle.
The total monthly payments ($26,409.60) are obtained by multiplying the monthly payments ($440.16) by the number of payment periods (60).
Value of vehicle = $25,990
Harmonized sales tax (HST) = 13%
After-tax cost of the vehicle = $29,368.70 ($25,990 x 1.13)
Down payment = $4,250
Financing part = $25,118.70 ($29,368.70 - $4,250)
Monthly payments = $440.16
Financing period = 60 months (5 years x 12)
Total monthly payments = $26,409.60 ($440.16 x 60)
The total amount paid for the car = $30,659.60 ($26,409.60 + $4,250)
Total interest = $1,290.90 ($26,409.60 - $25,118.70)
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At the end of an interview you are offered a job. You would start at 7.50 an hour and work an average of 45 hours a week. At the end of six months with a positive evaluation, your hourly pay would increase to 8. The job pays overtime at a time and a half rate, based on 37 1/2 hour regular work week. What total earrings could you expect to make by working a full year
By working a full year, you may expect to earn a total of $19,646.25 in earrings.
Explain about the expression?This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. The following is the structure of an expression: Expression: (Number/Variable, Math Operator, Math Operator)
An expression, also known as an algebraic expression, is any mathematical statement that consists of numbers, variables, and an arithmetic operation between them. For example, the mathematical sign + separates the phrases 4m and 5 from the variable m in the phrase 4m + 5.
Combining numbers, variables, and operators to represent something's value is known as a mathematical expression. Setting two expressions equal to one another creates an equation, a mathematical statement.
= Total overtime pay of $2,193.75 (first 6 months)
Add the regular and overtime pay after that:
= $7,312.50 + $2,193.75
= $9,506,25 in total income (first 6 months)
$7,800.00totalregularpay(last6months)
Overtime pay:(26weeks in a half year) \=$8\times
7.57.5\times1.51.5\times
$ 26
= Total overtime pay of $2,340.00 (last 6 months)
Add the regular and overtime pay after that:
= $7,800.00 + $2,340.00
= $10,140.00 in total income (last 6 months)
In the end, add the combined earnings from the two half years:
= $9,506.25 + $10,140.00
= Total annual profits of $19,646.25 (expected)
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The water depth in a harbor rises and falls over time. The function f(t) = 4.1 sine (StartFraction pi Over 6 EndFraction t minus StartFraction pi over 3 EndFraction) + 19.7 models the water depth, in feet, after t hours.
During the first 24 hours, at what times does the water depth reach a maximum?
Answer:
Below
Step-by-step explanation:
f(t) = 4.1 (sin pi/6 t - pi/3) + 19.7 <===will be a maximum when the sin portion is equal to 1
so sin ( pi/6 t - pi/3) = 1 given that sin is equal to one at 0 and pi and 2 pi and 3 pi and 4 pi etc
pi/6 t - pi/3 = 0 or pi , 2 pi, 3 pi , 4 pi
then t = 2 and 8 and 14 and 20 hrs ( every 6 hrs starting with t = 2)
Quintin raked his customer’s lawn for 1.2 hours. If Quintin charges $20 per hour, how much money did he make?
23.9 dollars I believe (I needa waste characters thi)
An Example of a caravan is
A. eight covered wagons travelings together on the trail
B. one covered wagon traveling by itself
C. a covered wagon passing a horse
D. a covered wagon traveling at top speed
An Example of a caravan is eight covered wagons traveling together on the trail. Meaning, option A is correct.
What is caravan?A caravan, travel trailer, camper, tourer, or camper trailer is a trailer towed behind a road vehicle to provide a more comfortable and secure sleeping space than a tent.
It allows people to have their own home on a trip or vacation without relying on a motel or hotel, and it allows them to stay in places where none are available. However, in some countries, campers are restricted to designated sites where fees must be paid.
Caravans range from basic models that are little more than a tent on wheels to those that have several rooms with all of the furniture, furnishings, and equipment of a home. The solid-wall trailers can be made of metal or fibreglass.
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What is the slope of the line that passes through the points (-6, -6) and
(-9, -5)? Write your answer in simplest form.
So basically what I do is find the formula for slope.
M= y2-y1/x2-x1
So I got
-5-(-6)/-9-(-6) = 1/3
answer = 1/3
:)
The solution set of 12 x squared minus 14 x equals 10 is
The given quadratic equation has two possible roots as -
{x} = -1/2 and {x} = 1.667.
What is a quadratic equation?A quadratic equation is a equation that is of the form -
y = f{x} = ax² + bx + c
Given is the statement as -
"12 x squared minus 14 x equals 10"
The given function can be written as -
f(x) = 12x² - 14x - 10
Refer to the graph attached. The x - intercepts show the solution of the given quadratic equation. So, we can write -
(x + 1/2)(x - 1.667) = 0
(x + 1/2) = 0 and (x - 1.667) = 0
x = -1/2 and x = 1.667
Therefore, the given quadratic equation has two possible roots as -
{x} = -1/2 and {x} = 1.667.
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The equation below represents the amount of work required to complete a project, where x represents the number of hours each group member must contribute to the project. How many hours does each group member work on the project? x+45/4=4x 2 hours 4 hours 16 hours 3 hours
The number of hours does each group member work on the project is 4 hours. Therefore, the correct answer is option B.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is x+45/4=4x.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
4x-x=45/4
3x=45/4
x=15/4
x=3.75
x≈4 hours
Therefore, option B is the correct answer.
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Please help will mark Brainly
Answer:
y < 1/2x +6
Step-by-step explanation:
You want the inequality graphed in the given figure.
Line and shadingThe line is dashed, and the shading is below it, so the inequality will have the form ...
y < ...
This is because the boundary line is not included, and the y-values in the solution are less than those on the boundary line.
Boundary lineThe y-intercept is at +6, where the line crosses the y-axis.
The line goes 2 units to the right for each 1 unit up, so its slope is ...
m = rise/run = 1/2
The slope-intercept equation for the boundary line is ...
y = mx +b . . . . . . slope m; y-intercept b
y = 1/2x +6 . . . . . equation of the boundary line in the graph
InequalityPutting the boundary line expression into the inequality form gives the inequality that describes the graph:
y < 1/2x +6