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Using the rule
[tex]\sin (x+y)=\sin x\cos y+\cos x\sin y[/tex][tex]\begin{gathered} \sin (225+60)=\sin 225\cos 60+\cos 225\sin 60 \\ \end{gathered}[/tex]Sine is negative in the third quadrant therefore,
[tex]\begin{gathered} -(\sin 45)\cos 60+\cos 225\sin 60 \\ \sin \text{ 45=}\frac{\sqrt[]{2}}{2}\text{ then the negative sign} \\ -\frac{\sqrt[]{2}}{2} \\ -\frac{\sqrt[]{2}}{2}\cos 60+\cos 225\sin 60 \\ \cos \text{ 60=}\frac{1}{2} \\ -\frac{\sqrt[]{2}}{2}(\frac{1}{2})+\cos 225\sin 60 \end{gathered}[/tex]Let us find the other side
[tex]\begin{gathered} \cos \text{ 45=}\frac{\sqrt[]{2}}{2} \\ cos\text{ is negative in the third quadrant } \\ -\frac{\sqrt[]{2}}{2} \\ \sin \text{ 60=}\frac{\sqrt[]{3}}{2} \\ \end{gathered}[/tex]Bring everything together
[tex]\begin{gathered} -\frac{\sqrt[]{2}}{2}(\frac{1}{2})-\frac{\sqrt[]{2}}{2}(\frac{\sqrt[]{3}}{2}) \\ -\frac{\sqrt[]{2}}{4}-\frac{\sqrt[]{6}}{4}=\frac{-\sqrt[]{2}-\sqrt[]{6}}{4}=-0.965925826\ldots... \end{gathered}[/tex]Related Questions
determine the area of figure round to the nearest tenth if necessary..
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In a garden, there are 10 rows and 12 columns of mango trees. The distance between two trees is 2 meters and a distance of one meter is left from all sides of the boundary of the garden. What is the length of the garden?
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Answer:
20m
Step-by-step explanation:
(10-1)x2+1x2=20m
m(x)=-x^2+4x+21. prove the zeros and determine the extreme value algebraically
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The zeros of the function are:
[tex]\begin{gathered} -(x+3)(x-7)=0 \\ x=-3 \\ or \\ x=7 \end{gathered}[/tex]The vertex is a point V(h,k) on the function. It's either at the base or the top of the function, depending upon wether it opens, upward or downward respectively.
For a function of the form:
[tex]\begin{gathered} y=ax^2+bx+c \\ \text{The vertex(extreme value) is:} \\ h=\frac{-b}{2a} \\ k=y(h) \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} m(x)=-x^2+4x+21 \\ a=-1 \\ b=4 \\ c=21 \\ h=\frac{-4}{2(-1)}=\frac{-4}{-2}=2 \\ k=m(h)=-(2)^2+4(2)+21=-4+8+21=25 \end{gathered}[/tex]Hence, the extreme value is 25 at x = 2
That's it, do you have any question?
Find the distance between the following points using the pythagorean theorem (5,10) and (10,12)
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Answer:
\sqrt[29]
Explanation:
Given the coordinate (5,10) and (10, 12). The formula for calculating the distance between two points is expressed as;
[tex]D\text{ =}\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}^{}[/tex]Given that;
x1 = 5
y1 = 10
x2 = 10
y2 = 12
Substitute:
[tex]\begin{gathered} D\text{ = }\sqrt[]{(10-5)^2+(12-10)^2} \\ D=\text{ }\sqrt[]{5^2+2^2} \\ D\text{ =}\sqrt[]{25+4} \\ D\text{ =}\sqrt[]{29} \end{gathered}[/tex]Hence the distance between the points is \sqrt[29]
A is the incenter of Triangle FHG Find the length of AT. Explain your thinking.
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we have that
The incenter is the center of the triangle's incircle, the largest circle that will fit
AR=AT=AS -----> radius of the inscribed circle in the triangle
therefore
AT=3 units
−1= 8x+2i need help with this problem,
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Given
-1 = 8x + 2
Answer
-1 = 8x + 2
-1 -2 =8x
-3 = 8x
x = -3/8
The graph used Is below ill attach a picture of the question and options after
Answers
Using the triangle sum theorem:
[tex]\begin{gathered} m\angle L+m\angle K+20=180 \\ 2m\angle L=180-20 \\ 2m\angle L=160 \\ m\angle L=\frac{160}{2} \\ m\angle L=80 \end{gathered}[/tex]Using the exterior angle theorem:
[tex]\begin{gathered} m\angle E=m\angle L+m\angle J \\ m\angle E=80+20 \\ m\angle E=100 \end{gathered}[/tex]Answer:
100
determine whether the equation defines y as function of x
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To answer this question, we need to solve the equation for y in the third case:
[tex]3x+2y=5\Rightarrow2y=5-3x\Rightarrow y=\frac{5}{2}-\frac{3}{2}x\Rightarrow y=-\frac{3}{2}x+\frac{5}{2}[/tex]We can see from this case that for every value of x, there must be a value in y, and this is the main condition for a relationship to be a function. Then, y is a function of x.
In the fourth case, we have a similar case, for every possible value of x, there must be a value for y. Then, y is a function of x.
As we can see, the red graph is for the linear equation and the black one is for the one with the radical ( y = -sqrt(x+1)).
If we pass a vertical line to either function (alone), we will have only a point that passes through this vertical line, and with this graphical information, we can also say that both are functions of y (for each case).
Write an equation for the linear function f(x) using the given information. ———————————————Using the points 2,0 & 4,3
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To find the equation in the form
[tex]y=mx+b[/tex]the slope is defined by:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ m=\frac{3-0}{4-2} \\ m=\frac{3}{2} \end{gathered}[/tex]To find b you can replace any of the points on the equation an clear for b
(x,y)=(4,3)
[tex]\begin{gathered} y=\frac{3}{2}x+b \\ 3=\frac{3}{2}\cdot4+b \\ 3=6+b \\ 3-6=b \\ b=-3 \end{gathered}[/tex]to check if the answer is correct replace 2 as x in the equation.
[tex]\begin{gathered} y=\frac{3}{2}\cdot2-3 \\ y=3-3 \\ y=0 \end{gathered}[/tex]since the answer was 0 and point was 2,0 the equation is correct.
Which of the following is only true sometimes? A. The sum of a rational number and a rational number is rational. B. The sum of a rational number and an irrational number is irrational. C. The product of an irrational number and an irrational number is irrational. D. The product of a nonzero rational number and an irrational number is irrational.
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The sum of a rational number and a rational number is rational. ALWAYS
The sum of a rational number and an irrational number is irrational.
The product of an irrational number and an irrational number is irrational. SOMETIMES
For example, the product of multiplicative inverses like √2 and 1/√2 will be 1
The product of a nonzero rational number and an irrational number is irrational.
Help I’m stuck ‼️‼️‼️ Hw due in a couple minutes
Answers
The lines AD and BC cross at a point where we have two pairs of vertically opposite angles.
The angles labelled (2x +50) and 100 are vertically opposite angles.
Vertically opposite angles are equal. Therefore;
[tex]\begin{gathered} 2x+50=100 \\ \text{Subtract 50 from both sides} \\ 2x+50-50=100-50 \\ 2x=50 \\ \text{Divide both sides by 2} \\ \frac{2x}{2}=\frac{50}{2} \\ x=25 \end{gathered}[/tex]ANSWER:
The value of x is 25. The correct answer is option A
Find the area of the compound shapes on the coordinate plane below.
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Answer
Part A: 100 square units
Part B: 39 square units
Part C: 48 square units
Explanation
Part A
Scale: 1cm represent 2 units on x-axis and 1cm represents 5 units on y-axis.
Firstly, we convert the figure into two composite plane shapes, that is, a rectangle and a triangle.
Area of composite shapes = area of rectangle + area of triangle
= Length x Width + 1/2(base x height)
= 10 x 8 + 1/2(10 x 4)
= 80 + 20
= 100 square units
Part B
Scale: 1cm represent 3 units on x-axis and 1cm represents 1 unit on y-axis.
Convert the figure into two composite plane shapes, that is, a rectangle and a trapezium.
Area of composite shapes = area of rectangle + area of trapezium
= Length x Width + 1/2(sum of parallel sides)(perpendicular height)
= 3 x 9 + 1/2(3 + 9)(2)
= 27 + 1/2(24)
= 27 + 12
= 39 square units
Part C
Scale: 1cm represent 2 units on x-axis and 1cm represents 2 units on y-axis.
Convert the figure into two composite plane shapes, that is, a trapezium and a triangle.
Area of composite shapes = area of trapezium + area of triangle
= 1/2(sum of parallel sides)(perpendicular height) + 1/2(base x height)
= 1/2(4 + 8)(6) + 1/2(4 x 6)
=1/2(12 x 6) + 1/2(24)
= 36 + 12
= 48 square units
ITS NOT A REAL TEST! MY FRIENDS WANT TO SEE HOW SMART I AM.
Answers
The given triangle is:
From the properties of triangle,
The sum of all angle in a triangle is equal to 180 degree
In triangle ABC,
Angle A + Angle B + Angle C = 180
70 + 50 + x = 180
120 +x = 180
x = 180 -120
x = 60
The missing angle is 60 degree
What is the product of 0.976 and 1.2
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Part A: The Sun that produces 3.9 * 10^33ergs of a radiant energy per second. How many eggs of radiant energy does the Sun produce and 3.25 * 10^3 seconds?Part B: Which is more the reasonable measurement of the distance between the tracks on a railroad: 1.435 * 10^3mm or 1.435 * 10^3mm?
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Part A
[tex]1.2675\times10^{37}ergs[/tex]Explanations:The sun can produce 3.9 * 10^33 ergs of radiant energy per second
[tex]\text{Amount of energy in 1 second = 3.9 }\times10^{33}ergs[/tex][tex]\text{Amount of energy produced in 3.25}\times10^3\sec \text{ = (3.9}\times10^{33}\times3.25\times10^3)[/tex][tex]\text{Amount of energy produced in 3.25}\times10^3\text{ seconds = }1.2675\times10^{37}ergs[/tex]What is the equation of this graphed line?
Enter your answer in slope-intercept form in the box.
A graph with a line running through coordinates (-4, -6) and coordinates (2, 6)
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Answer:
12/6 or 1/2
Step-by-step explanation:
you just plug the coordinates into demos calculator and then look at rise over run.
All the formation your name is on the picture picture provided
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The range of the data is the difference between the maximum data value and the minimum.
In a box plot, the maximum and the minimum are indicated by the dots at the end of the horizontal line.
Here,
Maximum = 10
Minimum = 4.5
Thus, the range of the data is:
[tex]Range=10-4.5=5.5[/tex]Find an angle θ with 0∘<θ<360∘that has the same:
Sine as 80∘ : θ = ______ degrees
Cosine as 80∘ : θ = _____ degrees
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Answer:
sin80° = sin100°
cos80° = cos280°
Step-by-step explanation:
In general, sin(a)° = sin (180-a)° and cos(a)° = cos(360-a)°
Fill in the blank with the correct inequality symbol. State which property of inequalities is being utilized.If x-8>10, then x_18.
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GIVEN
The inequality:
[tex]x-8>10[/tex]SOLUTION
The inequality is to be solved.
Add 8 to both sides of the inequality. This follows the Addition Property of Inequalities:
[tex]if\text{ }xTherefore:[tex]\begin{gathered} x-8+8>10+8 \\ x>18 \end{gathered}[/tex]ANSWER
[tex]x>18[/tex]How4 x 8 sheet ofmanyply wood do you need tocover a 24 x 24 deck?
Answers
Given
Dimensions of deck = 24 by 24
dimensions of ply wood = 4 by 8
Find
Number of sheets of ply wood needed to cover the deck
Explanation
number of sheets = area of deck divided by area of 1 ply wood
so ,
area of deck =
[tex]\begin{gathered} 24\times24 \\ 576 \end{gathered}[/tex]and
area of ply wood =
[tex]\begin{gathered} 4\times8 \\ 32 \end{gathered}[/tex]so ,
number of sheets needed =
[tex]\begin{gathered} \frac{576}{32} \\ \\ 18 \end{gathered}[/tex]Final Answer
Hence , the required number of sheets of ply wood is 18
Simplify the following expression. Assume variables are positive. Express your answer using rational exponents.
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Let's simplify the expression:
[tex]\begin{gathered} (x^{-\frac{1}{2}}\cdot y^{-\frac{2}{3}}\cdot z^{-2})^{-\frac{1}{2}}=x^{(-\frac{1}{2})(-\frac{1}{2})}y^{(-\frac{2}{3})(-\frac{1}{2})}z^{(-2)(-\frac{1}{2})} \\ =x^{\frac{1}{4}}y^{\frac{1}{3}}z \end{gathered}[/tex]Therefore the answer is:
[tex]x^{\frac{1}{4}}y^{\frac{1}{3}}z[/tex]Find sinif cos 0 = is in the first quadrant. 5 OA. OB. OC. 2/20 OD. 25/ M5 Reset Selection
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Answer: B. 3/5
This question can be solved by using trigonometric identities.
- Polynomial Functions -For each function, state the vertex; whether the vertex is a maximum or minimum point; the equation of the axis of symmetry and whether the function's graph is steeper than, flatter than, or the same shape as the graph of f(x)=x²
Answers
EXPLANATION
Given the function f(x) = (x-6)^2 + 1
[tex]\mathrm{The\: vertex\: of\: an\: up-down\: facing\: parabola\: of\: the\: form}\: y=ax^2+bx+c\: \mathrm{is}\: x_v=-\frac{b}{2a}[/tex]Expanding (x-6)^2 + 1 by applying the Perfect Square Formula:
[tex]=x^2-12x+37[/tex][tex]\mathrm{The\: parabola\: params\: are\colon}[/tex][tex]a=1,\: b=-12,\: c=37[/tex][tex]x_v=-\frac{b}{2a}[/tex][tex]x_v=-\frac{\left(-12\right)}{2\cdot\:1}[/tex][tex]\mathrm{Simplify}[/tex][tex]x_v=6[/tex][tex]y_v=6^2-12\cdot\: 6+37[/tex]Simplify:
[tex]y_v=1[/tex][tex]\mathrm{Therefore\: the\: parabola\: vertex\: is}[/tex][tex]\mleft(6,\: 1\mright)[/tex][tex]\mathrm{If}\: a<0,\: \mathrm{then\: the\: vertex\: is\: a\: maximum\: value}[/tex][tex]\mathrm{If}\: a>0,\: \mathrm{then\: the\: vertex\: is\: a\: minimum\: value}[/tex][tex]a=1[/tex][tex]\mathrm{Minimum}\mleft(6,\: 1\mright)[/tex][tex]\mathrm{For\: a\: parabola\: in\: standard\: form}\: y=ax^2+bx+c\: \mathrm{the\: axis\: of\: symmetry\: is\: the\: vertical\: line\: that\: goes\: through\: the\: vertex}\: x=\frac{-b}{2a}[/tex]Expanding (x-6)^2 + 1 by applying the Perfect Square Formula:
[tex]y=x^2-12x+37[/tex][tex]\mathrm{Axis\: of\: Symmetry\: for}\: y=ax^2+bx+c\: \mathrm{is}\: x=\frac{-b}{2a}[/tex][tex]a=1,\: b=-12[/tex][tex]x=\frac{-\left(-12\right)}{2\cdot\:1}[/tex][tex]\mathrm{Refine}[/tex]Axis of simmetry : x=6
The quadratic function has the same shape than the parent function y=x^2 because there is NOT a coefficient within x.
r is the midpoint of op and qr is perpendicular to op in the diagram below find the the length of qr
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Given:
OP = 20 in
QP = 26 in
Since R is the midpoint of OP, then, OR = RP
Thus
[tex]OR=RP=\frac{OP}{2}=\frac{20}{2}=10\text{ in}[/tex]To find the length of QR, use pythagoras theorem below:
[tex]\begin{gathered} a^2+b^2=c^2 \\ \\ RP^2+QR^2=PQ^2 \end{gathered}[/tex]Input values into the formula:
[tex]10^2+QR^2=26^2[/tex]Subtract 10² from both sides:
[tex]\begin{gathered} 10^2-10^2+QR^2=26^2-10^2 \\ \\ QR^2=26^2-10^2 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt[]{QR^2}=\sqrt[]{26^2-10^2} \\ \\ QR=\sqrt[]{676-100} \\ \\ QR=\sqrt[]{576} \\ \\ QR=24 \end{gathered}[/tex]Therefore, the length of QR is 24 in
Please help, algebra 1, i dont know how to begin to solve it :/ thank you thank you.Simplify:
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Given the expression:
[tex](x^2-4x^3)+(5x^3+3x^2)[/tex]You can simplify it as follows:
1. Distribute the positive sign. Since the sign between the parentheses is positive, it does not change the signs of the second parentheses:
[tex]=x^2-4x^3+5x^3+3x^2[/tex]2. Add the like terms.
By definition, like terms have the same variables with the same exponent.
In this case, you need to add the terms with exponent 3 and add the terms with exponent 2. Notice that:
[tex]\begin{gathered} -4x^3+5x^3=x^3 \\ \\ x^2+3x^2=4x^2 \end{gathered}[/tex]Then, you get:
[tex]=x^3+4x^2[/tex]Hence, the answer is:
[tex]=x^3+4x^2[/tex]How long does it take Tina to type 864 words, if she took 15 minutes to type out an assignment that comprised 720 words?
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Given data:
The given time taken by Tin to type 720 words is t=15 min.
The given expression can be wriiten as,
720 word=15 min
720 words= 15(60 sec)
720 words= 900 sec
1 word = 900/720 sec
=1.25 sec
Multiplying the above equation with 864 on both sides .
864 words= 864(1.25) sec
= 1080 sec
=1080/60 min
= 18 min.
Thus, the time taken bby Tine to type 864 words is 18 min.
Paula will make fruit punch for a party she will mix 1 1/2 gallons of orange juice with 5/8 of a gallon of pineapple juice how many 1/8 gallon servings will Paula have
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First let's find the total number of gallons of the fruit punch. To do so, we just need to sum the gallons of orange juice (1 1/2) ith the gallons of pineapple juice (5/8):
[tex]1\frac{1}{2}+\frac{5}{8}=\frac{3}{2}+\frac{5}{8}=\frac{12}{8}+\frac{5}{8}=\frac{17}{8}[/tex]Now, in order to find how many 1/8 servings can be made, we need to divide the total number of gallons of the fruit punch by the number of gallons of a serving:
[tex]\frac{\frac{17}{8}}{\frac{1}{8}}=\frac{17}{8}\cdot\frac{8}{1}=17[/tex]So Paula can have 17 servings.
Answer:
17
Step-by-step explanation:
5/8 - 5
1 1/2 - 12
The Muffin Shop makes no-fat blueberry muffins that cost $.70 each. The Muffin Shop knows that 15% of the muffins will spoil. If The Muffin Shop wants 40% markup on cost and produces 800 muffins, what should The Muffin Shop price each muffin?
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If The Muffin Shop wants a 40% markup on cost and produces 800 muffins, The Muffin Shop should price each muffin at $1.15.
How is the price determined?The total expected revenue is divided by the total unspoiled units sold to determine the selling price.
This is illustrated below.
Cost per unit of muffins = $0.70
The spoilage rate = 15%
Expected markup on cost = 40%
The total production units = 800 muffins
The total good units sold = 680 (800 x 1 - 15%)
Total cost for 800 units = $560 (0.70 x 800)
The markup on cost = $224 ($560 x 40%)
The total expected sales revenue = $784 ($560 + $224)
Seling price per unit = $1.15 ($784/680)
Thus, The Muffin Shop should price each muffin at $1.15 to meet its goals.
Learn more about pricing with the markup at https://brainly.com/question/1153322
#SPJ1
Solve for x. 8x-2x+7>21+10
Answers
Answer: [tex]x > 4[/tex]
Step-by-step explanation:
[tex]8x-2x+7 > 21+10\\\\6x+7 > 31\\\\6x > 24\\\\x > 4[/tex]
Element X decays radioactively with a half life of 14 minutes. If there are 460 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 35 grams?
Answers
Step 1
Given;
[tex]\begin{gathered} Intially\text{ y}_0=460g \\ Half\text{ life, h=14 minutes} \\ y=\frac{460}{2}=230g,\text{ when t=h=14 min} \\ \end{gathered}[/tex]Putting these values in, we have;
[tex]\begin{gathered} 230=a(0.5)^1 \\ a=\frac{230}{0.5}=460g \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} y=460(0.5)^{\frac{t}{14}}---(1) \\ when\text{ y=35} \\ 35=460(0.5)^{\frac{t}{14}} \end{gathered}[/tex][tex]\begin{gathered} 35=460(0.5)^{\frac{t}{14}} \\ \frac{460\cdot \:0.5^{\frac{t}{14}}}{460}=\frac{35}{460} \\ 0.5^{\frac{t}{14}}=\frac{7}{92} \\ \frac{t}{14}\ln \left(0.5\right)=\ln \left(\frac{7}{92}\right) \\ t=\frac{14\ln\left(\frac{7}{92}\right)}{\ln\left(0.5\right)} \\ t=52.02689 \\ t\approx52.0\text{ minutes to the nearest tenth of a minute} \end{gathered}[/tex]Answer;
[tex]52.0\text{ minutes to the nearest tenth of a minute}[/tex]