The polar coordinates of (-4, 150°) will be [tex]\sqrt[2]{5629}\\[/tex] and 5069.09939523°
What is the coordinate about?The formula for this conversion will be:
r = [tex]\sqrt{x^2 + y^2}[/tex]
θ = [tex]tan ^-1 (\frac{y}{x} )[/tex]
[tex]r = \sqrt{(4^2) + (150^0)^2} \\\\θ = tan ^-1 (\frac{y}{x} )\\\\\\r = \sqrt[2]{5629} \\\\ = tan ^-1 (\frac{150}{4} )\\[/tex]
= [tex]\frac{75}{2}[/tex]
the inverse of: [tex]\frac{75}{2}[/tex] is θ = 5069.09939523°
Therefore:
[tex]r = \sqrt[2]{5629}\\[/tex]
θ = 5069.09939523°
So the polar coordinates of (-4, 150°) will be [tex]\sqrt[2]{5629}\\[/tex] and 5069.09939523°
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You are given that cos(A)=−35, with A in Quadrant II, and cos(B)=817, with B in Quadrant I. Find cos(A−B). Give your answer as a fraction.
Expand cos(A - B) with the identity
cos(A - B) = cos(A) cos(B) + sin(A) sin(B)
A is in quadrant II, so sin(A) > 0, and B is in quadrant I, so sin(B) > 0. Using the Pythagorean identity, we get
cos²(A) + sin²(A) = 1 ⇒ sin(A) = + √(1 - (-3/5)²) = 4/5
cos²(B) + sin²(B) = 1 ⇒ sin(A) = + √(1 - (8/17)²) = 15/17
Then
cos(A - B) = (-3/5) × 8/17 + 4/5 × 15/17 = 36/85
cos (A - B) is 36/85
How to simply the identity
Expand cos(A - B) with the identity
You get, cos(A - B) = cos(A) cos(B) + sin(A) sin(B)
Since A is in quadrant II, so sin(A) > 0,
B is in quadrant I, so sin(B) > 0.
Using the Pythagorean identity, we get
cos²(A) + sin²(A) = 1
Make sin A the subject of formula
[tex]sin(A)^{2}[/tex] = ([tex]\sqrt{(1 - (-3/5}[/tex])²)
Find the square root of both sides, square root cancels square
[tex]sin A[/tex] = 4/5
Repeat the same for the second value
[tex]sin A^{2} = \sqrt{(1- 8/17)^2}[/tex]
[tex]sin A[/tex] = 15/17
Substitute values into cos(A - B)
cos(A - B) = cos(A) cos(B) + sin(A) sin(B) = (-3/5) * 8/17 + 4/5 * 15/17
cos (A - B) = 36/85
Therefore, cos (A - B) is 36/85
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what is the value of x
Answer:
FROM THE CALCULATIONS THE ANSWER IS B!
The vertex of the graph of y = -4(x + 3)² + 2 is
DONE
A parabola is a mirror-symmetrical planar curve that is nearly U-shaped. The vertex of the parabola will lie at (-3,2).
What is the Equation of a parabola?A parabola is a mirror-symmetrical planar curve that is nearly U-shaped.
y = a(x-h)² + k
where,
(h, k) are the coordinates of the vertex of the parabola in the form (x, y);
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
Comparing the given equation with the equation of a parabola, we will get,
y = a(x -h)² + k
y = -4(x+3)² + 2
Hence, the vertex of the parabola will lie at (-3,2).
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A contemporary building has a window in the shape of a parallelogram with a base of 90 in and an adjacent side of 40 in. How many inches of trim are needed to surround the window?
260 inches of trim are needed to surround the window.
What is the surface area?The total land area of all the faces of a three-dimensional object is its surface area. When we wish to wrap something in real life, we employ the notion of surface areas of distinct things.
Actually, all we need is a trim that is the same size as our window and equal to the parallelogram's circumference, which is
The sum of the side is;
⇒Length of lower side + Length of the upper side
⇒ 90+90
⇒180 inches
The sum of adjacent sides;
Sum of adjacent sides = 40+40
Sum of adjacent sides = 80 inches
The length you should trim is needed to surround the window is found as;
⇒ 180 inches + 80 inches
⇒260 inches
Hence,260 inches of trim are needed to surround the window.
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The graph below shows the solution to which system of inequalities?
Inequalities help us to compare two unequal expressions. The inequalities that represent this graph are y<8/10x and y>-x. The correct option is C.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
To find the inequality, we need to find the equation of the dashed line and then substitute the inequality as per the requirement. The dashed line is used instead of a solid line to show greater than or less than.
The inequality for the first graph can be written as,
[tex]y < \dfrac{8}{10}x[/tex]
The inequality for the second graph will be,
y>-x
Hence, the inequalities that represent this graph are y<8/10x and y>-x. Thus, the correct option is C.
The complete question is:
The graph below shows the solution to which system of inequalities?
A.) y>x , y ≥ (8/10)x
B.) y>-x, y ≤ (8/10)x
C.) y>-x, y < (8/10)x
D.) y>x, y > (8/10)x
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Which describes how the parent function, f(x) = |x|, is transformed to show the function
f(x) = 0.1|x – 3|?
It is wider and shifted 3 units to the left.
It is wider and shifted 3 units to the right.
It is narrower and shifted 3 units to the left.
It is narrower and shifted 3 units to the right.
It is wider and shifted 3 units to the left , Option A is the right answer.
What is a Function ?Function is a mathematical statement that shows relation between two variables.
The parent function given is
f(x) = |x|
The transformed function is given by
f(x) = 0.1|x -3|
The function is shifted towards the left
and as the scale factor is 0.1 therefore , It is wider
Therefore Option A is the right answer.
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Answer:
The answer for this is B.
Step-by-step explanation:
Figured it out the hard way on EDGE. 2022
(╯‵□′)╯︵┻━┻
Drag each sign and value to the correct location on the image. Each sign and value can be used more than once, but not all signs and values will be used. The vertices of an ellipse are at (-5, -2) and (-5, 14), and the point (0, 6) lies on the ellipse. Drag the missing terms and signs to their correct places in the standard form of the equation of this ellipse.
The complete equation of the ellipse is [tex]\frac{(x + 5)^2}{5^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]
How to complete the vertex equation?The complete question is in the attachment
The given parameters are:
Vertex = (-5,-2) and (-5,14)Point = (-0,6)The vertex is represented as (h, k ± a).
So, we have:
h = -5
k + a = 14
k - a = -2
Add the last two equations
2k = 12
Divide by 2
k = 6
Substitute k = 6 in k + a = 14
6 + a = 14
Solve for a
a = 8
The ellipse equation is represented as:
[tex]\frac{(x - h)^2}{b^2} + \frac{(y - k)^2}{a^2} = 1[/tex]
So, we have:
[tex]\frac{(x + 5)^2}{b^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]
The ellipse passes through the point (0,6).
So, we have:
[tex]\frac{(0 + 5)^2}{b^2} + \frac{(6 - 6)^2}{8^2} = 1[/tex]
This gives
[tex]\frac{5^2}{b^2} + \frac{0}{8^2} = 1[/tex]
Evaluate the quotient
[tex]\frac{5^2}{b^2} = 1[/tex]
Cross multiply
[tex]b^2 = 5^2[/tex]
Take the square root of both sides
b = 5
Substitute b = 5 in [tex]\frac{(x + 5)^2}{b^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]
[tex]\frac{(x + 5)^2}{5^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]
Hence, the complete equation of the ellipse is [tex]\frac{(x + 5)^2}{5^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]
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If x/3 = 5/6 , then x =
Answer:
x = 5/2
Step-by-step explanation:
Given that,
[tex] \cfrac{x}{3} = \cfrac{5}{6} [/tex]
x = ?Solution:
Multiplying using criss-cross method;
[tex]x \times 6 = 5 \times 3[/tex][tex]6x = 15[/tex]Divide both sides by 6;
[tex] \cfrac{6x}6 = \cfrac{ \cancel{15} {}^{5} }{ \cancel6 {}^{2} } [/tex][tex]x = \cfrac{5}{2} [/tex]Done!
Hence x = 5/2.
Answer:
x = 2.5
Step-by-step explanation:
x = 3*(5/6)
Select all the correct graphs.
Choose the graphs that indicate equations with no solution.
In the equation y/6 = 156, what is the next step in the equation solving sequence
Answer:
Linear Equations In One Variable =
Next step :
in the equation y/6 = 156, it would be equivalent to y = 156 × 6.
so that :
y = 156 × 6
y = 936
this equation solved. (Answer : 936)
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 3 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 63 ?
Answer:
43
Step-by-step explanation:
63-3/3=20 63-20
Answer:
mark has 18
don has 45
Step-by-step explanation:
h(x)=x²-5
Find h(-7)
Simplify your answer.
Answer:
h(-7) = 44
Step-by-step explanation:
h(x) = h (-7) means x= -7
h(x) = (-7)² - 5
49 - 5
44
for the previous problem some of the work was done for you remember when solving a quadratic equation you must start with all terms on one side and put it in standard form for the following equations first put the equation in standard form and them use quadratic formula to solve 9x^2 -25 = -12-10x
4n^2-1=-12n +3n^2+11
Solving the given equations we get,
Solutions of quadratic equation [tex]9x^2-25=-12-10x[/tex] are x=0.77 and -1.88Solutions of quadratic equation [tex]4n^2-1=12n+3n^2+11[/tex] are n=12.93 and -0.93If the quadratic equation is [tex]ax^2+bx+c=0[/tex] then the solutions of this are given by,
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Here in the problem given that,
The first quadratic equation is [tex]9x^2-25=-12-10x[/tex]
Converting it into standard form of quadratic equation we get,
[tex]9x^2-25=-12-10x\\9x^2-25+12+10x=0\\9x^2+10x-13=0[/tex]
So here a=9,b=10,c=-13
The solutions of the equation is given by,
[tex]x=\frac{-10\pm\sqrt{10^2-4\times9\times(-13)}}{2\times9}=\frac{-10\pm\sqrt{100+468}}{18}\approx\frac{-10\pm23.83}{18}[/tex]
So either,
[tex]x=\frac{-10+23.83}{18}=\frac{13.83}{18}\approx0.77[/tex]
Or,
[tex]x=\frac{-10-23.83}{18}\approx-1.88[/tex]
So the solutions are given by x=0.77 and -1.88
Second quadratic equation is [tex]4n^2-1=12n+3n^2+11[/tex]
Converting the equation in its standard form we get,
[tex]4n^2-1=12n+3n^2+11\\4n^2-1-12n-3n^2-11=0\\n^2-12n-12=0[/tex]
so here a=1,b=-12,c=-12
Solutions are given by,
[tex]n=\frac{-(-12)\pm\sqrt{(-12)^2-4\times1\times(-12)}}{2\times1}=\frac{12\pm\sqrt{144+48}}{2}\approx\frac{12\pm13.86}{2}[/tex]
So either
[tex]n=\frac{12+13.86}{2}=12.93[/tex]
Or,
[tex]n=\frac{12-13.86}{2}=-0.93[/tex]
Solutions are given by n = 12.93 and -0.93
Hence the solutions are x=0.77 and -1.88 for first equation and n=12.93 and -0.93 for second equation.
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Graph the feasible region subject to the following constraints:
7x+11y≤ 1540
x+3y ≤ 360
x+y≤ 200
x≥0
y≥0
The attached graph represents the graph of the constraints
How to graph the feasible region?The constraints are given as:
7x+11y≤ 1540
x+3y ≤ 360
x+y≤ 200
x ≥ 0, y ≥ 0
Next, we plot the graph of the constraints using a graphing calculator
From the graph (see attachment), we have the coordinates of the feasible region to be (66, 98), (120,80) and (165,35)
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fill in the blanks with the correct form of the verb to have and the palt of the body that is numhered. (2 pls.each)
Answer:
Below
Step-by-step explanation:
1. has
2. has
3. have
4. has
5. have
6. has
7. has
8. have
9. have
10. has
11. has
12. has
13. have
14. have
A few years ago, Sarah acquired a parcel of land valued at $13,800. Today, that same parcel of land has a value of $14,766. Find the percent increase in the property's value. Round your answer to the nearest hundredth, if necessary.
Answer:
7%
Step-by-step explanation:
[tex] \frac{14766 - 13800}{13800} \times 100 = 7 [/tex]
The percent increase in the property's value is 7% if the parcel of land is valued at $13,800. Today, that same parcel of land has a value of $14,766.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
We have:
A few years ago, Sarah acquired a parcel of land valued at $13,800. Today, that same parcel of land has a value of $14,766
Percentage increase:
[tex]= \rm \dfrac{14766-13800}{13800}\times 100[/tex]
= 7%
Thus, the percent increase in the property's value is 7% if the parcel of land is valued at $13,800. Today, that same parcel of land has a value of $14,766.
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graph the equation y+3=2(x+3)?
Answer:
see attached
Step-by-step explanation:
You recognize the equation of the line as being given in point-slope form:
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
y +3 = 2(x +3) . . . . . . given equation
This tells you the point is (h, k) = (-3, -3), and the slope is m = 2.
__
You can graph the equation by plotting the point (-3, -3) and drawing a line with a slope of 2. It will rise 2 units for each unit to the right.
Which table represents a nonlinear function?
NEED THIS DONE ASAP!! Thank you!!
Answer:
150°
Step-by-step explanation:
A secant is a straight line that intersects a circle at two points.
The circle shows two secants RD and BD that intersect at one exterior point D, so we can use the Intersecting Secants Theorem to solve.
Intersecting Secants Theorem
If two secant segments are drawn to the circle from one exterior point, the measure of the angle formed by the two lines is half of the (positive) difference of the measures of the intercepted arcs.
[tex]\implies \angle RDB = \dfrac{1}{2}\left(\overset{\frown}{RB}-\overset{\frown}{EC}\right)[/tex]
[tex]\implies 5x-10=\dfrac{1}{2}(13x+7-60^{\circ})[/tex]
[tex]\implies 2(5x-10)=13x-53[/tex]
[tex]\implies 10x-20=13x-53[/tex]
[tex]\implies -3x=-33[/tex]
[tex]\implies x=11[/tex]
To find the measure of [tex]\overset{\frown}{RB}[/tex], substitute the found value of x into the expression for the arc:
[tex]\implies \overset{\frown}{RB}=13x+7[/tex]
[tex]\implies \overset{\frown}{RB}=13(11)+7[/tex]
[tex]\implies \overset{\frown}{RB}=143+7[/tex]
[tex]\implies \overset{\frown}{RB}=150^{\circ}[/tex]
Therefore, the measure of arc RB is 150°.
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Evaluate the expression 3.14(a2 + ab) when a = 4 and b = 3
Answer:
87.92
Step-by-step explanation:
We are given this expression:
3.14(a² + ab)
And we want to evaluate it if a is 4 and b is 3.
To solve this, we need to follow the order of operations, usually known as PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction) in the United States, although other countries have their own variations on the acronym.
Despite this, let's start with P, which would be parentheses.
Because we have the a² + ab in parentheses, we should evaluate this first.
We should substitute the values of a and b with 4 and 3 respectively, to get this (we can ignore the 3.14 for now):
(4)² + 4 * 3
First, let's go on to exponents.
We do have one exponent, which is the 4 being raised to the second power.
So let's evaluate that.
Raise 4 to the second power (multiply it by itself).
4 * 4 = 16
We can replace (4)² with 16.
16 + 4 * 3
Now, let's move on to multiplication.
We do have one multiplication operation, which is the 4 * 3, so let's evaluate that.
4 * 3 = 12
Replace 4 * 3 with 12.
16 + 12
We don't have any division in this, so we can skip that.
Moving on to addition:
We can add these two numbers together.
16 + 12 = 28
28 is the value of a² + ab.
We now multiply this by 3.14 to get the answer.
3.14 * 28 = 87.92
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The value of expression 3.14([tex]a^{2}[/tex]+ab) when a =4 and b=3 is 87.92.
Given Expression :3.14([tex]a^{2}[/tex]+ab) and we have to find the value at a=4 and b=3
we know expressions are the combinations of numbers, symbols and coefficients and in the expression given the variable are a and b .Expression shows the relationship between the variables which are present in the expression. When we have to find the value of expression at a=4 and b=3 we have to just put the values of a and b in the expression .
[tex]a^{2}[/tex]=16 and ab=4*3=12
=3.14[tex]((4)^{2}+4*3)[/tex]
=3.14(16+12)
=3.14*28
=87.92
Hence the value of the expression 3.14(a2 + ab) at a=4 and b=3 is 87.92.
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Someone answer this, thank you!
Step-by-step explanation:
1) the equation of the line represented is
y=0.5x+3 (slope-interception form), the slope is 0.5, the intercept is 3.
x-2y+6=0 (common form);
2) x-intersection is at -6, y-intersection is at 3.
What linear function can be represented by the set of ordered pairs?
{(−1,−10),(3,2),(5,8),(7,14)}
Enter your answer in the box.
ADVANCED COSTING AND MANAGEMENT ACCOUNTING
A car engine manufacturer is trying to make an assessment of its operations for the past year. The
entity operates a standard marginal costing system and manufactures a state-of-the-art engine for
which the following standard revenue and cost data per unit of product is available:
Selling price $60.00
Direct material A 2.5 kg at $8.50 per kg
Direct material B 1.5 kg at $6.00 per kg
Direct labour 0.45 hrs. at $30.00 per hour
Actual data for the twelve-month period was as follows:
Sales and production 48,000 units of the blaster were produced and sold for $2,904,000
Direct material A 121,900 kg were used at a cost of $1,005,675
Direct material B 67,200 kg were used at a cost of $420,000
Direct labour Employees worked for 18,900 hours, but 19,200 hours were paid at a cost
of $585,600.
Budgeted sales for the period were 50,000 units of Product Blaster. A recession last year meant
that the market for the product declined by 5%.
Required:
(a) Calculate the following variances.
(i) Sales volume variance.
The Sales Volume Variance of the car manufacturer for the twelve-month period is $96,000.
What is the sales volume variance?The sales volume variance measures the financial impact of not meeting or exceeding the budgeted sales for a period.
It can be computed by finding the difference between actual and budgeted sales quantities and then multiplied by the unit selling price.
Data and Calculations:Budgeted sales units = 50,000
Actual sales units = 48,000
Sales price per unit = $60
Actual sales revenue = $2,904,000
Budgeted sales revenue = $3,000,000 ($60 x 50,000)
Sales volume variance = $96,000 ($3,000,000 - $2,904,000)
Thus, the Sales Volume Variance is $96,000.
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What is the range of the function in the graph?
. 1≤x≤6
B. 20≤y≤60
C. 20≤x≤60
D. 1≤y≤60
Answer:
B
Step-by-step explanation:
Range is all the possible values of 'y'. As seen in the graph, the smallest value of 'y' is 20, where the point is (6, 20), and the largest value of 'y' is 60, where the point is (1, 60). Therefore, the range is B. 20≤y≤60
What is the solution to the equation below? Round your answer to two
decimal places.
log2(2x-1) = 3
A. x=4
O B. x= 1/2
732
O c. x = 2/
O D. x = 5
Answer:
D. x=5
The answer is x=4.50 then it is rounded off to 5. So, the answer is 5.
Step-by-step explanation:
Find the domain of the inequality:[tex]2x-1\geq 0[/tex]
Rearrange terms to the left side of the equation:[tex]2x\geq 1[/tex]
Divide both sides of the inequality by the coefficient of the variable:
=> [tex]x\geq \frac{1}{2}[/tex]
The domain of the inequality is:[tex]x\geq \frac{1}{2}[/tex]
Convert logarithm to exponential form:[tex]2^{3}=2x-1[/tex]
Calculate the power:[tex]8=2x-1[/tex]
Rearrange terms to the left side of the equation:[tex]-2x= -8-1[/tex]
Calculate:[tex]-2x=-9[/tex]
Divide both sides of the equation by the coefficient of the variable:[tex]x=\frac{-9}{-2}[/tex]
=> [tex]x=\frac{9}{2}[/tex]
=>[tex]x=4.5\\[/tex]
Round the number: [tex]x=4.50[/tex]
Answer: [tex]x=4.50[/tex]
=> [tex]x=5[/tex]
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Answer:
x = 9/2
Step-by-step explanation:
Set up a linear system and solve. A cash register contains $5 bills and $50 bills with a total value of $345. If there are 15 bills total, then how many of each does the register contain?
Answer:
6 $50 bills and 9 $5 bills
Step-by-step explanation:
Let's let x = the number of $5 bills, and y = the number of $50 bills. With this, we can set up two equations:
5x + 50y = 345
x + y = 15
Because there is $345 total in the register, that means that 5 times the number of $5 bills plus 50 times the number of $50 bills would equal 345. And there are 15 bills total, so the numbers added is 15. Now, we can solve these equations through substitution:
x + y = 15
x = 15 - y
Now, plug in (15 - y) for x into the other equation, and solve for y:
5(15 - y) + 50y = 345
75 - 5 y + 50y = 345
75 + 45y = 345
45y = 270
y = 6
Since y is 6, that means we have 6 $50 bills. And there are 15 bills total, so there are 9 $5 bills. (15 - 6 = 9)
The Taieri Plain in New Zealand is 6 feet below sea level (or –6 feet). If you are standing 3 feet above sea level, is your elevation the opposite of the elevation of the plain? Describe the steps you would follow with a vertical number line to find the answer.
Answer :Opposite numbers are the same distance from 0 on the number line, but in opposite directions. Steps I would follow:
first, check the directions to make sure they are opposite,
then read the digits, or count the tick marks or compare lengths with dividers or ruler or marks on a piece of paper to see if the distances are the same.
3 is not the opposite of -6
__
6 is the opposite of -6
Urgent my safari wont work! 20 pts!!
What’s the square root of 32006???
given the formula p=k*2 w, find the value of p if k= 5 and w= - 3
Write and solve an inequality that means a number plus four is greater than or equal to twelve.
Answer:
[tex]x+4\geq 12[/tex]
Step-by-step explanation:
x - a number
x+4 - a number plus 4
x+4[tex]\geq[/tex] - a number plus 4 is greater than or equal to
x+4[tex]\geq[/tex]12 - a number plus 4 is greater than or equal to twelve
Answer:
Inequality: x + 4 ≥ 12
Solution: x ≥ 8
Step-by-step explanation:
Plus: "+" → to add something to something else
Greater than or equal to: "≥" → the expression on the left side of the inequality sign is greater than the expression on the right side of the sign.
Let x be the unknown number.
A number plus four is greater than or equal to twelve:
x + 4 ≥ 12
To solve the found inequality, subtract 4 from both sides:
⇒ x + 4 - 4 ≥ 12 - 4
⇒ x ≥ 8
Therefore, the solution to the inequality is x ≥ 8. The unknown number x can be any real number equal to or greater than 8.
