Final answer:
Explanation of units for trigonometric functions and how to apply the Law of Sines in triangle problems.
Explanation:
The units for sine, cosine, and tangent must be dimensionless. These trigonometric functions relate angles to side lengths in a triangle.
The Law of Sines can be used to solve triangles when you have a known angle and the opposite side length. It states that the ratio of the length of a side to the sine of its opposite angle is constant.
When given measurements may or may not form a triangle, you can apply the Law of Sines to determine if a triangle can be solved. If not, it means no triangle can be formed.
What positive number is twice it's own square
Answer: The positive number is [tex]\dfrac{1}{2}.[/tex]
Step-by-step explanation: We are given to find the positive number that is twice it's own square.
Let x denotes the required number.
Then, according to the given information, we have
[tex]x=2x^2\\\\\Rightarrow 2x^2-x=0\\\\\Rightarrow x(2x-1)=0\\\\\Rightarrow x=0,~~2x-1=0\\\\\Rightarrow x=0,~\dfrac{1}{2}.[/tex]
Sine 0 is not considered as a positive number, so the required positive number is [tex]\dfrac{1}{2}.[/tex]
Thus, the positive number is [tex]\dfrac{1}{2}.[/tex]
For the values a = 8 which is a leg of a right triangle, and value c = 19, which is the hypotenuse, find the length of the other leg, b, to the nearest tenth.
A. 17.7
B. 20.6
C. 17.2
D. 20.3
Lena will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $50 and costs an additional $0.50 per mile driven. The second plan has no initial fee but costs $0.70 per mile driven. For what amount of driving do the two plans cost the same? What is the cost when the two plans cost the same
The two plans cost the same when Lena drives 250 miles, resulting in a cost of $175 for both plans, as per the given linear equation.
A linear equation is a mathematical expression that represents a straight line relationship between variables, typically in the form of ax + b = 0.
The two plans cost the same when the amount of driving satisfies the equation:
50 + 0.50x = 0.70x
Where:
50 represents the initial fee for the first plan,
0.50x represents the cost per mile for the first plan, and
0.70x represents the cost per mile for the second plan.
Now, let's solve for x:
50 + 0.50x = 0.70x
Subtract 0.50x from both sides:
50 = 0.20x
Now, divide both sides by 0.20:
x = 50 / 0.20
x = 250
So, the two plans cost the same when Lena drives 250 miles. To find the cost at this point, plug x = 250 into either plan:
For the first plan:
Cost = 50 (initial fee) + 0.50 (cost per mile) * 250
Cost = $50 + $125
Cost = $175
For the second plan:
Cost = 0.70 (cost per mile) * 250
Cost = $0.70 * $250
Cost = $175
So, when Lena drives 250 miles, both plans cost $175.
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When critiquing an observational study, which four factors should be analyzed?
A Methodology, Results, Discussion, Conclusion
B Introduction, Results, Discussion, Conclusion
C Introduction, Methodology, Results, Discussion
D Methodology, Causes, Results, Discussion
Answer:
Introduction, Methodology, Results, Discussion.
Step-by-step explanation:
yes
What is the measure of the hypotenuse of an isosceles right triangle with leg lengths 6?
What is the process that you need to follow in order to prove a circle?
HELP Please THANKS (:
Use the form of the definition of the integral given in theorem 4 to evaluate the integral x^3-3x^2
If MNO ~XYZ,then what corresponding parts are congruent
Final answer:
In similar triangles MNO and XYZ, corresponding angles are congruent (M with X, N with Y, O with Z) and corresponding sides are in proportion (MN to XY, NO to YZ, MO to XZ).
Explanation:
If triangles MNO and XYZ are similar (denoted as MNO ~ XYZ), then their corresponding parts are congruent. Corresponding parts include angles and sides that match between the two triangles due to their similarity in shape and proportion. In similar triangles, corresponding angles are congruent, while corresponding sides are in proportion.
The corresponding congruent angles would be angle M and angle X, angle N and angle Y, and angle O and angle Z. For the sides, the lengths are proportional, which means that the ratio of MN to XY is the same as the ratio of NO to YZ, which is also the same as the ratio of MO to XZ.
Final answer:
In similar triangles MNO and XYZ, the corresponding congruent parts are angles M, N, O congruent to angles X, Y, Z respectively and sides MN, NO, OM proportional to sides XY, YZ, ZX respectively.
Explanation:
If triangles MNO and XYZ are similar (denoted as MNO ~ XYZ), it indicates that they have the same shape but not necessarily the same size. This means that their corresponding angles are congruent, and their corresponding sides are in proportion.
The corresponding congruent parts would be:
Angle M is congruent to Angle X
Angle N is congruent to Angle Y
Angle O is congruent to Angle Z
Side MN is proportional to Side XY
Side NO is proportional to Side YZSide OM is proportional to Side ZXRemember, while the angles are congruent, the sides are proportional, which means the length of the sides of one triangle is some multiple or fraction of the lengths of the corresponding sides of the other triangle.
What is the complete factorization of the polynomial below?
x3 - 3x2 + x - 3
Final answer:
The complete factorization of the polynomial x³ - 3x² + x - 3 is (x - 3)(x² + 3)(x + 1).
Explanation:
The complete factorization of the polynomial x³ - 3x² + x - 3 can be found by using the Rational Root Theorem and synthetic division. By trying out the possible rational roots using the Rational Root Theorem, we find that one of the roots is 3. So, we divide the polynomial by (x - 3) to get the quadratic factor and the remaining linear factor.
(x - 3) is a factor, so we divide x³ - 3x² + x - 3 by (x - 3) using synthetic division:
3|1-31-3|3030|1010
The result is x² + 3.
The remaining linear factor is 1x + 1 = x + 1.
Therefore, the complete factorization of the polynomial x³ - 3x² + x - 3 is (x - 3)(x² + 3)(x + 1).
If f(x)=square root of x+12 and g(x)=2square root of x, what is the value of (f – g)(144)? –84
–60
0
48
A rhombus, which is a quadrilateral with 44 equal sides, is plotted on the coordinate plane. The coordinates of the vertices are: (5,3)5,3, (2,-1)2,-1, (-3,-1)-3,-1, (0,3)0,3. How long is each side of the rhombus?
If angle A measures 57 degrees and angle C is adjacent to angle A, what is the measure of angle C if the two angles are complementary?
Using Newton’s cooling model, what will the temperature of a cup of hot tea be 2 hours after it is poured if its initial temperature is 200°F, the surrounding temperature is 70°F, and the value for k is 0.6?
A.130
B.109.16
C.109.76
D.71.35
E.60
Use the given information below, find the p-value
a., test statistic z = -1.52
The p value can simply be located given the value of the z statistic by using a standard normal probabilities distribution table.
We are given that the z value of z = - 1.52. Since z is negative this means that we are to look for the proportion or p value located to the left of z. Based on the standard normal probabilities distribution table, this is equivalent to a p value of:
p value = 0.0643
This given p value indicates that 0.0643 or 6.43% of the population is located to the left of z.
Answer:
p value = 0.0643
Two trains leave stations 306 miles apart at the same time and travel toward each other. one train travels at 75 miles per hour while the other travels at 95 miles per hour. how long will it take for the two trains to meet?
Answer: It will take 1.8 hours for the two trains to meet.
Step-by-step explanation:
Since we have given that
Speed of one train = 75 mph
Speed of other train = 95 mph
Since they travel towards each other.
so, Relative speed = 75+95 = 170 mph
Distance between them = 306 miles
We need to find the time taken:
So, it becomes,
[tex]time=\dfrac{Distance}{Speed}\\\\Time=\dfrac{306}{170}\\\\Time=1.8\ hours[/tex]
Hence, it will take 1.8 hours for the two trains to meet.
A sphere fits snugly inside a 6-in. cube as shown. what is the volume of the region inside the cube but outside the sphere
The volume of the region inside the cube but outside the sphere is approximately 187.73 in^3.
Explanation:The volume of the region inside the cube but outside the sphere can be calculated by subtracting the volume of the sphere from the volume of the cube.
Volume of the cube = side^3 = 6^3 = 216 in^3
Volume of the sphere = (4/3)πr^3
Since the sphere fits snugly inside the cube, the radius of the sphere is half the length of the side of the cube. So, r = 3/2 in.
Therefore, volume of the region = volume of the cube - volume of the sphere = 216 in^3 - (4/3)π(3/2)^3 in^3 = 216 in^3 - 9π in^3 = 216 in^3 - 28.27 in^3 ≈ 187.73 in^3.
what is the final step to solving the inequality -2(5-4x)<6x-4
Answer:
x< 3
Step-by-step explanation:
-2(5-4x)<6x-4
multiply -2 inside the parenthesis
-2 * 5 = -10
-2 * -4x= 8x
-2(5-4x)<6x-4
-10 + 8x < 6x -4
To solve for x we need 'x' on the left hand side
Subtract 6x from both sides
-10 + 8x -6x< 6x -6x -4
-10 +2x < -4
Add 10 on both sides
-10 +10 +2x < -4+10
2x < 6
divide by 2 on both sides
x< 3
A party was organised for thirty people at which they could have either a hamburger or a pizza. if there were five times as many hamburgers as pizzas, calculate the number of each\
There are 5 pizza and 25 hamburgers.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A party was organized for thirty people.
And, There were five times as many hamburgers as pizzas.
Now,
Let number of pizza = x
Then, Number of hamburgers = 5x
So, We get;
⇒ x + 5x = 30
⇒ 6x = 30
⇒ x = 5
Thus, Number of pizza = x
= 5
Then, Number of hamburgers = 5x
= 5 × 5 = 25
Therefore, There are 5 pizza and 25 hamburgers.
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Find the zeros of the function.
f(x) = 9x3 - 72x2 + 135x
A regular pyramid has a height of 12 cm in a square base if the volume of the pier mid is 236 cm³ how many centimeters are in the length of one side of its base?
Enrique weighs 5 pounds more than twice Brendan's weight. If their total weight is 225 pounds, how much does Enrique weigh?
To find Enrique's weight, set up a system of equations based on the given information and solve for the weights of both Brendan and Enrique.
Enrique weighs 5 pounds more than twice Brendan's weight.
If their total weight is 225 pounds, you can set up a system of equations.
Let x be Brendan's weight, so Enrique's weight is 2x + 5.
From the given information, x + (2x + 5) = 225.
Solving the equation, x = 70 and Enrique's weight is 2(70) + 5 = 145 pounds.
Which classifications apply to the polygon? Check all that apply.
convex
concave
regular
hexagon
octagon
Answer: Concave and Hexagon.
Step-by-step explanation: In the given figure we have one angle is greater than 180 degrees.
A polygon has an angle between 180 to 360 is called a concave polygon.
Therefor given polygon is a concave polygon.
Also the given polygon has six sides.
A polygon with six sides is a hexagon.
Therefore, correct options are Concave and Hexagon.The classifications that apply to the polygon are concave and hexagon.
What is a polygon?
A polygon is a shape with at least three straight sides and angles. A regular polygon has at sides and angles of the same length and size. A convex polygon is a shape in which all of its vertices point in the outward direction. A concave polygon is a shape in which all of its vertices point in the outward direction. A hexagon is a polygon with eight sides.
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Joel and Melinda provide the following proofs for vertical angles to be equal:
Joel's proof: angle 2 + angle 3=180° (t is a straight line)
angle 1 + angle 2 = 180° (PQ is a straight line)
Therefore, angle 1 + angle 2 = angle 2 + angle 3 (Transitive Property of Equality)
Hence, angle 1 = angle 3 (Subtraction Property of Equality)
Melinda's proof: angle 1 + angle 2 + angle 3 + angle 4 = 360°
Therefore, angle 1 + angle 4 = 180° (t is a straight line)
Hence, angle 4 = angle 2 (Transitive Property of Equality)
Which statement is correct?
A Joels is correct
B Melindas is correct
C Both Melinda and joels is correct
D Neither is correct
The answer is A! I just did it and gotit right
A forensic detective is called to the scene of a murder at 2 am. When she checks the temperature of the body, she sees that it is 80 degrees Fahrenheit. The temperature of the room in which the body is found is 65 degrees. If the detective uses Newton's law of cooling, what will she say is the time of death? T(t)=Ta+(To-Ta)e^(-0.1947t).
Thank you to anyone who helps! :)
given the following linear function sketch the graph of the function and find the domain and range f(x) =2/7x-2
By using the concept of function, it can be concluded that-
The domain and range of the given function is the set of real numbers
What is a function
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here the given linear function is
f(x) =[tex]\frac{2}{7}x - 2[/tex]
The graph has been attached here
As the given function is a linear function with a non zero slope, the domain and range is the set of real numbers.
So, the domain and range of the given function is the set of real numbers
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Jessica purchased items worth $41.23 at the local
grocery store. The cashier made a mistake while
ringing up her items, and Jessica ended up paying
$50.23. How many extra dollars did she pay?
HELP!! QAQ
Create your own piecewise function with at least two functions. Explain, using complete sentences, the steps for graphing the function. Graph the function by hand or using a graphing software of your choice (remember to submit the graph).
An visual of the function would be really appreciated. Thanks!
What is the difference of 28y - 16y
GUYS HELP PLEASE URGENT!!!!!!
A newborn baby weighs 3.136x10^3 units. Which unit of measure was used? grams ounces pounds tons
its grams because it cant be pounds because a baby isnt 3000 pounds, thats is just crazy!
The unit 'gram' will used to measure the weight of newborn baby in this case.
Unit conversion:
Conversion of units is the conversion between different units of measurements for the same quantity.
1 pound = 0.454kilogram1 kg = 1000 g1 ton = 1000 kg1 ounce = 0.0283 kgAccording to the given question we have,
Weight of the new born baby = [tex]3.136[/tex] × [tex]10^{3}[/tex] = 3136
From the unit conversion,
3136 pound = 1,423.744kg
3136 gram = 3136/1000 = 3.136gram
3136 ton = 3136000 kg
3136 ounce =88.7488 kg
The range of weight of new born baby in kg is 3 to 4.
Hence, only 3136 gram is possible .So, the unit 'gram' will used to measure the weight of newborn baby in this case.
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