Using a trigonometric identity, it is found that the sine of the angle is given as follows:
[tex]\sin{\theta} = -\frac{4}{5}[/tex].
Which trigonometric identity relates the sine and the cosine of an angle?Considering an angle [tex]\theta[/tex], the identity is given as follows:
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
In this problem, the cosine is given as follows:
[tex]\cos{\theta} = \frac{3}{5}[/tex]
Hence the sine is found as follows:
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
[tex]\sin^2{\theta} + \left(\frac{3}{5}\right)^2{\theta} = 1[/tex]
[tex]\sin^2{\theta} + \frac{9}{25} = 1[/tex]
[tex]\sin^2{\theta} = \frac{16}{25}[/tex]
[tex]\sin{\theta} = \pm \sqrt{\frac{16}{25}}[/tex]
In quadrant IV, the sine is negative, hence:
[tex]\sin{\theta} = -\frac{4}{5}[/tex].
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Perform the operation and simplify
Answer:
[tex]\frac{(x-2)(x+4)}{x+2}[/tex]
Step-by-step explanation:
[tex]\frac{(x+4)^2}{x+2} :\frac{(x+2)(x+4)}{(x+2)(x-2)} =\frac{(x+4)^2(x+2)(x-2)}{(x+2)(x+2)(x+4)}=\frac{(x-2)(x+4)}{x+2} .[/tex]
14 ) Mark Achin sells 3,600 electric motors each year . The cost of these is $ 200 each , and demand is constant throughout the year . The cost of placing an order is $ 40 , while the holding cost is $ 20 per unit per year . There are 360 working days per year and the lead - time is 5 days . What is his economic order quantity in units ? A ) 100 B ) 200 C ) 60 D 120
Mark Achin's economic order quantity in units is D. 120 units.
What is economic order quantity?The economic order quantity (EOQ) is the optimal order quantity that minimizes the total costs (ordering, receiving, and holding inventory).
The formula for the economic order quantity is the square root of [2(setup costs)(demand rate)] / holding costs.
Data and Calculations:Annual demand = 3,600
Cost price per unit = $200
Ordering cost = $40
Holding cost per unit = $20
Working days per year = 360
Lead time = 5 days
Economic order quantity (EOQ) = square root of: [2(setup costs)(demand rate)] / holding costs.
= square root of (2 x $40 x 3,600)/$20
= 120
Thus, Mark Achin's economic order quantity in units is D. 120 units.
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6/9 is a rational number. Select all the rational numbers that are equivalent to .
0.6(line over 6)
2/3
0.66(line over 66)7
0. 66(line over 66)
Option b) and c) is correct, i.e. 2/3 and 0.66(line over 66)7
6/9 is a rational number.
similar ration number can be given as -
Rational numbers are the numbers that can be structured in the form of the fraction of integers. Eg- 5/6, 2/3 etc.
From the option, by above definition 2/3, 0.66(line over 66)7 seems to be an equivalent rational numbers because
6/9=2/3= 0.66(line over 66)7.
Thus, Rational numbers 2/3, 0.66(line over 66)7 are equivalent to 6/9.
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Which similarity postulate or theorem can be used to verify that the two
triangles shown below are similar?
C A. Similarity cannot be determined.
• B. SSS theorem
• C. AA postulate
D. SAS theorem
The AA postulate can be used to verify that the two triangles shown below are a similar option (C) is correct.
What is the similarity law for triangles?It is defined as the law to prove that the two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We can utilize the AA postulate since we know two of each triangle's three angles.
In every triangle, they are the same. We may also determine each triangle's third angle.
They are comparable because both triangles have the same angles.
Thus, the AA postulate can be used to verify that the two triangles shown below are similar.
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A company manufactures both mountain bikes and trail bikes. The cost of materials for a mountain bike is $40, and the cost of materials for a trail bike is $40. The cost of labor to manufacture a mountain bike is $90, and the cost of labor to manufacture a trail bike is $30. During a week in which the company has budgeted $1,600 for materials and $2,700 for labor, how many mountain bikes does the company plan to manufacture?
An equation is formed when two equal expressions. The company is planning to produce 25 mountain bikes and 15 trail bikes.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the number of mountain bikes produced by the company be x, while the number of trail bikes produced by the company is y.
The cost of materials for a mountain bike is $40, and the cost of materials for a trail bike is $40. Also, the budget of the company is $1,600. Therefore,
1600 = 40x + 40y
x + y = 40
y = 40-x
The cost of labour to manufacture a mountain bike is $90, and the cost of labour to manufacture a trail bike is $30. Also, the budget for labour is $2,700.
2700 = 90x + 30y
2700 = 90x + 30(40-x)
2700 = 90x + 1200 - 30x
1500 = 60x
x = 25
Substitute the value of x,
y = 40 - x
y = 15
Hence, the company is planning to produce 25 mountain bikes and 15 trail bikes.
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Look at the figure. How many different labeled rays are shown?
A.)2
B.)10
C.)20
D.)8
Which statement best describes the relationship between lines m& n
The relationship between lines m & n is (a) the lines M and N have positive slope
How to describe the relationship?The points are given as:
Line M: (1, 4) and (2, 7)Line N: (1, 3) and (, 5)From the above points, we can see that:
As x increases, the y values of both lines increase
This is an illustration of positive slope
Hence, the lines M and N have positive slope
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which statement is true about finding the midpoint between two points located on a horizontal or vertical line ?
A . When finding the midpoint between two points on a vertical line, keep the y-coordinate and find the average of the x-coordinate
B . When finding the midpoint between two points on vertical line, keep x-coordinate and find the average of the y-coordinates
C . When finding the midpoint between two points on a horizontal line, the x-coordinate is always 0 and the y-coordinates are averaged
D. When finding the midpoint between two points on a horizontal line , the y-coordinate is always zero and the x-coordinates are averaged
Answer: B. When finding the midpoint between two points on a vertical line, keep the x-coordinate and find the average of the y-coordinates
HELP ASAP GIVING BRAILIEST!!!!!!!
15 POINTS
photo of problem below>>
Answer:
B) y = 4/5x - 2
Answer:
B
Step-by-step explanation:
First, we can find the slope of the graph.
The distance of x between the two points is 5, and the distance of y between the two points is 4.
The slope formula is (Increase in y)/(increase in x)
So the slope will be 4/5.
The y-intercept is (0,-2), so the number at the very end of the equation will be -2.
With all this in mind, we can be sure that our answer is B: y=4/5x-2
A farmer needs to mix 12 ounces of fertilizer for every 10 pounds of soil. How many pounds of fertilizer will the farmer need to make a mix that contains 120 pounds of soil?
144
230.4
9
0.06
A ratio shows us the number of times a number contains another number. The correct option is A.
What is a Ratio?A ratio shows us the number of times a number contains another number.
The ratio of fertilizer to soil is,
Fertilizer/Soil = 12 ounces / 10 pounds
The amount of fertilizer that the farmer need to mix for 120 pounds of soil is,
Fertilizer/120 pounds = 12 ounces / 10 pounds
Fertilizer = (12 ounces × 120 pounds)/10pounds
Fertilizer = 144 ounces
Hence, the correct option is A.
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The image of a figure is shown. What are the coordinates of X in the pre-image of the figure if the rule that created the image was T–5.2, 1.4(x, y)?
X =
The coordinates of X in the pre-image of the figure is (3.2, 0.6) if the transformation rule is T_(-5.2, 1.4)(x, y)
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
As we can see in the figure.
The transformation rule is T_(-5.2, 1.4)(x, y)
X'(-2, 2)
Before the transformation:
X = (-2+5.2, 2-1.4)
X = (3.2, 0.6)
Thus, the coordinates of X in the pre-image of the figure is (3.2, 0.6) if the transformation rule is T_(-5.2, 1.4)(x, y)
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What is the inverse of function f?
F(x) =3-x/7
Answer:
the answer is (D) F-1 (X) = 7x - 3
Step-by-step explanation:
-3x + 2y = 9
x - 3y = 4
Answer:
(-5, -3)
Step-by-step explanation:
Isolate x:
x - 3y = 4
x = 3y + 4
Substitute to get y:
-3x + 2y = 9
-3(3y + 4) + 2y = 9
-9y - 12 + 2y = 9
-7y = 21
y = -3
Substitute to get x:
x = 3y + 4
= 3(-3) + 4
-9 + 4
= -5
Which transformation is a isometry?
Answer:
second transformation
MD writes an order for Lortab Elixir 5mg by mouth as needed for pain every 4 hours. Pharmacy dispenses you with 7.5mg/15ml. How many tablespoons will you administer per dose?
Following the prescription, You will need to administer a 0.7 tablespoon per dose.
Determining the number of tablespoons by using equivalent expressions?We can determine the number of tablespoons that are administered by using equivalent expressions.
From the standard conversion rate, we know that:
1 ml = 0.067628 tbsp15 ml = 1.01442 tbspUsing equivalent expressions:
7.5 mg/1.01442 tbsp = 5 mg/x tbsp
x = (1.01442 × 5)/7.5 tbsp
x = 0.67 tbsp
x = 0.7 tbsp per dose.
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Darla places a wooden stick along the diagonal of a cubical box as shown below . If the length of the stick is 3√3 feet , what is the length of the edge of the cube ? A.9√ / 2 feet B. 3 feet C.3√2 feet D.9 feet
Answer:
3
Step-by-step explanation:
order 0.76 grams of med each pill contains 0.02 grams of med how many pill will the patient need
Answer:
38 pills
Step-by-step explanation:
To find the number of pills, you need to divide the weight of each pill by the total weight needed.
0.76 grams / 0.02 grams = 38 pills
1) Which part of a circle is a portion of the boundary of a circle?
A. arc
B. center
C. circumference
D. radius
Answer:
A. arc
Step-by-step explanation:
The circumference is the entire boundary of a circle.
A portion of the circumference is called an arc.
Find the range of the function f(n) = n² - 2n for the domain (1, 3, 5).
Range:
Answer: {-1, 3, 15}
Step-by-step explanation:
[tex]f(1)=-1\\\\f(3)=3\\\\f(5)=15[/tex]
So, the range is {-1, 3, 15}.
I’m so confused please help
Answer:
976cm squared
Step-by-step explanation:
that's all I could do .hope it helps. in case of any questions please ask.
The Robinsons family drove for 4000 miles. This was the
distance the Jones family drove. How many miles did the Jones
family drive?
Answer:1333.3 Contiuous
Step-by-step explanation:
.
4000/3,=1333.3x1,=1333.3
I'm not sure
Which function is the inverse of if the domain of f(x) is x ≥ 0?
The question was incomplete. Please find full content below.
Which function is the inverse of
[tex]f(x)=x^2-16[/tex]
if the domain of f(x) is x ≥ 0?
The inverse funtion of the given function is given by
[tex]\mathbf{f(x)=\sqrt{x+16}}[/tex]
where the domain is x ≥ -16.
Given the function is,
[tex]f(x) =x^2-16[/tex]
Let, y = f(x)
[tex]y = x^2-16[/tex]
Adding 16 to both sides we get,
[tex]y + 16 = {x}^{2} - 16 + 16[/tex]
[tex] {x}^{2} = y + 16[/tex]
Now, square rooting to both sides we get, since x ≥ 0
[tex]\sqrt{x^2}=\sqrt{y+16}[/tex]
[tex]x=\sqrt{y+16}[/tex]
[tex]f^{-1}(y)=\sqrt{y+16}[/tex]
Hence substituting x in place of y,
[tex]f^{-1}(x)=\sqrt{x+16}[/tex]
Above function is the required inverse function where the domain of that is given by, x ≥ -16.
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approximate the value of 3^3x when x+1 using the first six terms of the Maclaurin expansion
Answer:
x could be anything but might be 3<4 or 5?8 u really never kno
f(x)=3√x + 7. Find the inverse of f(x).
Answer:
[tex]f^{-1}(x)=\left(\dfrac{x-7}{3}\right)^2[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=3\sqrt{x}+7[/tex]
To find the inverse of the function
Swap f(x) for y:
[tex]\implies y=3 \sqrt{x}+7[/tex]
Subtract 7 from both sides:
[tex]\implies y-7=3 \sqrt{x}+7-7[/tex]
[tex]\implies y-7=3\sqrt{x}[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3\sqrt{x}}{3}=\dfrac{y-7}{3}[/tex]
[tex]\implies \sqrt{x}=\dfrac{y-7}{3}[/tex]
Square both sides:
[tex]\implies \left(\sqrt{x}\right)^2=\left(\dfrac{y-7}{3}\right)^2[/tex]
[tex]\implies x=\left(\dfrac{y-7}{3}\right)^2[/tex]
Swap the x for [tex]f^{-1}(x)[/tex] and y for x:
[tex]\implies f^{-1}(x)=\left(\dfrac{x-7}{3}\right)^2[/tex]
Property taxes are based on the value of the property
Based on the calculations, the average selling price for these properties is equal to $127,865.
How to determine the average selling price?Mathematically, the average selling price for these properties would be calculated by using the following formula:
Average price = [F(x)]/n
Note: The total number of properties is equal to 5.
Substituting the given parameters into the formula, we have;
Average price = [118,450 + 126,500 + 128,000 + 130,425 + 135,950]/5
Average price = 639,325/5
Average price = $127,865.
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Complete Question:
Property taxes are based on the value of the property. city officials use the average selling price of similar properties to estimate the value. the selling prices of similar properties are listed below. $118,450 $126,500 $128,000 $130,425 $135,950. What is the average selling price?
7.
At the metal-casting company where you work, you must
set up a conveyor system to move castings from the furnace
to the heat treatment area 55 yards away. The castings cool
at the rate of 0.3°F (degrees Fahrenheit) per second and
must not be allowed to cool more than 7°F before being
heat treated. What is the minimum speed, in feet per
second, that the conveyor must move?
Answer:
xxfdjdjwkoq9w Woow Kike sosl
What is the following quotient?
2
√13+√11
O√13-2√11
√13+√11
6
O
113 + √11
12
O
● √13 - √11
[tex]\frac{2}{\sqrt{13}+\sqrt{11}} \times \frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}\\\\=\frac{2\sqrt{13}-2\sqrt{11}}{13-11}\\\\=\boxed{\sqrt{13}-\sqrt{11}}[/tex]
The solution is: our final quotient is: (√13 - √11).
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
Explanation
Since we have radicals in the denominator, we need to rationalize our expression.
To do it we just need to multiply both numerator and denominator by the conjugate of the denominator.
Remember that the conjugate of a binomial is the same binomial with the sing in between changed.
given that,
2/ (√13 + √11)
Now, we can simplify the denominator:
multiplying by (√13 - √11)
we get,
2 * (√13 - √11) / (√13 + √11)* (√13 - √11)
The only radical that we can simplify in the numerator is , which simplifies to:
2 (√13 - √11) / 13 - 11
= 2(√13 - √11) /2
= (√13 - √11)
So, our final quotient is: (√13 - √11)
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NEED HELP ASAP
there should be a picture giving you info
Answer:
to find this radius you need to square the area and divide it by pi or 3.14 if your using Alex
Linda needs to buy pencils brands has a pack of 28 pencils for 5.29 brand b has a pack of 48 pencils for 8.47 find the unit price for each brand.
Answer:
Brand A is the best buy.
Step-by-step explanation:
Brand A has a pack of 28 pencils for 5.29 dollars. This means that the unit cost of one pencil in Brand A would be 5.29/28 = 0.2$ per pencil rounded up to the nearest tenth.Brand B has a pack of 48 pencils for 8.47 dollars. This means that the unit cost of one pencil in Brand B would be 8.47/48 = $0.8 per pencil rounded up to the nearest tenth.Since $0.2 is lesser than $0.8, it means that Brand A is the best buy.
Graph the line that passes through the two points. Then find the slope of the line. (2,9), (4, 18)
The slope of the line is 4.5
How to determine the slope?The points are given as:
(2,9) and (4, 18)
The slope (m) is calculated using:
m = (y2 - y1)/(x2 - x1)
This gives
m = (18 - 9)/(4 -2)
Evaluate
m = 4.5
Hence, the slope of the line is 4.5
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