Answers
[tex]L.H.S \\ \\ = 1+ sec^{2} *sin^{2}x \\ \\ =1+ \frac{1}{cos^{2}x } sin^{2}x \\ \\ =1+tan^{2}x \\ \\ =sec^{2}x \\ \\ = R.H.S [/tex]
Thus, the Left hand side has been proved equal to Right Hand Side.
Related Questions
Bonnie can complete her paper route in 45 min. when her sister jean helps her it takes them 18 min to complete the route. how long would it take jean alone?
Answers
[tex]\frac{1}{45}[/tex] of her paper route.
We need to know how long it would take Jean alone, then we will call this time x. Working together they last 18min, so in 1min they can complete:
[tex]\frac{1}{18}[/tex] of the paper route.
The paper route working together satisfies the following equation:
[tex]\frac{1}{18} = \frac{1}{45} + \frac{1}{x}[/tex]
Solving this equation:
[tex]\frac{1}{x} = \frac{1}{18} - \frac{1}{45} = \frac{45-18}{810} = \frac{27}{810}[/tex]
[tex]x = \frac{810}{27} = 30min[/tex]
Finally:
It takes 30min to complete the paper route by Jane alone.
1 cubic foot of sand weighs 100 lb. a square sandbox with 5 foot sides has a half of a foot of sand in it. how many pounds of sand is sandbox the holding?
Answers
The sandbox with 5-foot sides and a half-foot depth of sand is holding 1250 pounds of sand, calculated using the volume of the sand and the known weight per cubic foot.
Explanation:To calculate the weight of sand in the sandbox, we can use the formula for the volume of a cube, which is length × width × height. Given that the sandbox has 5-foot sides and is filled with a half of a foot of sand, the volume × weight of the sand can be calculated as follows:
The volume of sand = 5 ft (length) × 5 ft (width) × 0.5 ft (height) = 12.5 cubic feet.Since 1 cubic foot of sand weighs 100 lb, the total weight of the sand = 12.5 cubic feet × 100 lb/cubic foot = 1250 pounds.Therefore, the sandbox is holding 1250 pounds of sand.
If VX = WZ = 40 cm and m∠ZVX = m∠XWZ = 22°, can ΔVZX and ΔWXZ be proven congruent by SAS? Why or why not?
Yes, along with the given information, ZX ≅ ZX by the reflexive property.
Yes, the triangles are both obtuse.
No, the sides of the triangles intersect.
No, there is not enough information given.
Answers
No, there is not enough information given to prove that ΔVZX and ΔWXZ are congruent by SAS.
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
The given information only provides the lengths of two sides and the measures of two angles in the triangles, but we do not know if the third side is congruent, and we cannot assume that it is by the given information.
Additionally, the given information does not specify that one of the congruent sides is included between the congruent angles, which is necessary for the SAS postulate to be used to prove congruence.
Therefore, there is not enough information given to prove that ΔVZX and ΔWXZ are congruent by SAS.
Learn more about congruent triangles here:
brainly.com/question/4364353
#SPJ7
A pair of fair dice is rolled once. suppose that you lose $ 8 if the dice sum to 3 and win $ 13 if the dice sum to 10 or 12. how much should you win or lose if any other number turns up in order for the game to be fair?
Answers
There are 2 ways to get a sum of 3 out of 36 outcomes; this probability is 2/36.
There are 4 ways to get a sum of 10 or 12 out of 36 outcomes; this probability is 4/36.
There are 36-(2+4) = 36-6 = 30 other outcomes out of 36; this probability is 30/36.
We lose $8 if we get a sum of 3; this expected value is -8(2/36) = -16/36.
We win $13 if we get a sum of 10 or 12; this expected value is 13(4/36) = 52/36.
Using x as the amount we win or lose for the other outcomes, the expected value is 30x/36.
In order to be a fair game, the amount we win and/or lose should come outto( $0 total.
Together we have the equation
-16/36+52/36+30x/36 = 0
Adding the fractions, we have
(-16+52+30x)/36 = 0
(30x+36)/36 = 0
Multiplying both sides by 36,
30x+36=0*36
30x+36=0
Subtracting 36 from both sides,
30x+36-36=0-36
30x=-36
Dividing both sides by 30,
30x/30 = -36/30
x=-36/30 = -1.2
Thus we should lose $1.20 for any other roll.
The figure has 60 edges and 30 vertices. Use Euler’s formula to find the number of faces in the given polyhedron.
Answers
Number of Vertices ⇒⇒⇒ V
Number of Edges ⇒⇒⇒ E
Euler's Formula ⇒⇒⇒⇒⇒ F + V − E = 2
given:⇒⇒⇒ 60 edges and 30 vertices
∴ E = 60 and V = 30
∴ F + 30 - 60 = 2
∴ F = 2 + 60 - 30 = 32
Number of faces = 32
A company has 200 employees. The company’s owner randomly chose 30 employees for an in-depth survey. Of those surveyed, 12 employees said they work overtime on a regular basis.
What is the best estimate of the percent of the company’s employees who work overtime on a regular basis?
Answers
divide the number who work over time by the number of people asked to find the percentage of the sample:
12 / 30 = 0.4 = 40%
so about 40% of all the people work overtime
Triangle GHI has the angle measures of G = (2x + 5)°, H = (6x − 10)°,
and I = (x + 5)°. What is the actual measurement of angle H?
Answers
We then have the following equation:
G + H + I = 180
Substituting values:
(2x + 5) + (6x - 10) + (x + 5) = 180
Clearing x we have:
(2x + 6x + x) + (5-10 + 5) = 180
9x + 0 = 180
9x = 180
x = 180/9
x = 20
Then, for the angle H we have:
H = (6x - 10) °
Substituting:
H = (6 (20) - 10) °
H = (120 - 10) °
H = 110 °
Answer:
the current measurement of angle H is:
H = 110 °
The actual measurement of angle H is thus 110 degrees.
To find the actual measurement of angle H in triangle GHI, we can use the fact that the sum of the interior angles in any triangle is always 180 degrees. Given the expressions for angles G, H, and I as G = (2x + 5)", H = (6x − 10)", and I = (x + 5)", we can set up the equation (2x + 5) + (6x - 10) + (x + 5) = 180 to find the value of x. After determining x, we substitute it back into the expression for angle H to get the desired measurement.
Setting up the equation we have:
(2x + 5) + (6x - 10) + (x + 5) = 180
Combine like terms to get 9x = 180
Divide both sides by 9 to find x: x = 20 degrees
Now plug this value into the expression for angle H: H = 6(20) - 10
We find that H = 120 - 10 degrees, so H = 110 degrees
To find the measurement of angle H in triangle GHI, we apply the fact that the sum of angles in a triangle is always 180 degrees. By solving the equation that sets this sum, we find the value of x, and then use it to determine that angle H measures 110 degrees.
The area of the circle shown below is 100π. What is the diameter (D) of the circle?
Answers
since a diameter is twice as long as the radius, this one is also 2r.
Answer: 20 units
Step-by-step explanation:
We know that the area of a circle is given by :-
[tex]\text{Area}=\pi r^2[/tex], where r is the radius of the circle.
We are given that the area of the circle = [tex]100\pi[/tex] square units.
[tex]\Rightarrow\ 100\pi=\pi r^2\\\\\Rightarrow\ r^2 =100[/tex]
Taking square root on both the sides , we get
[tex]\\\\\Rightarrow\ r=10[/tex]
The diameter of the circle is given by :-
[tex]d=2r=2(10)=20\text{ units}[/tex]
Identify the transformations that describe the graph of an even function. Select all that apply.
reflection over the x-axis
reflection over the y-axis
reflection over the line y = x
90° rotation around the origin
180° rotation around the origin
Answers
So, if f is even function and y = f(x)
∴ y = f(-x)
∴ (x,y) and (-x,y) on the same graph
or we can say (-x,y) is an image for (x,y)
So, the rule of transformation becomes (x,y) ⇒⇒⇒ (-x,y)
Which is the same rule of reflection over the y-axis.
∴ The correct choice is the second option
Answer:
reflection over the y-axis
Step-by-step explanation:
How many different ways can you choose a council with exactly 3 sophomores, 1 junior, and 2 seniors?
Answers
1. The graph shows the distance y, in centimeters, a pendulum moves to the left (negative displacement) and right (positive displacement), for a given number of seconds x. (a) From its resting position, how long does it take the pendulum to swing one direction, then the other, and then return to its resting position? (b) What is the pendulum’s maximum displacement? (c) What percent of a full cycle is completed within 1 s? (d) How is the pendulum moving during the time period from x = 5 to x = 5.625? (e) What is the equation of the graph?
Answers
A) In order to calculate how long it takes the pendulum to swing one direction, then the other, and then return to its resting position, you need to look at the graph and see where the function returns to zero after going once up and once down. This time is called period (T), which is defined as the time taken to perform one complete oscillation.
In our case, T = 5 s (see the second picture attached for reference).
B) In order to find the pendulum's maximum displacement, you need to look at the graph and see how high and low on the y-axis the function goes. This displacement is called amplitude (A), which is defined as the maximum displacement from the resting position in either direction.
In our case, A = 20 cm (see the second picture attached for reference).
C) Since the period of the pendulum is 5 seconds and it swings constantly, the fraction of a cycle completed in 1 second is calculated by simply dividing
p = 1 / 5 = 0.20
Therefore, in 1 second the pendulum completes 20% of its cycle.
D) During the time period from x = 5 to x = 5.625, we can see from the graph that the pendulum has just started its second oscillation, therefore it starts from the resting position and it moves towards the right (positive values of y)decreasing its velocity.
E) The equation of the graph is a sinusoidal function, therefore it will have an equation like
[tex]f(t) = A \cdot sin( \frac{2 \pi}{T} \cdot t - b) + c [/tex]
where:
A = amplitude
T = period
b and c = shifting constants
In order to find b and c, we recall that the graph starts at (0,0) and therefore it is not shifted either horizontally or vertically, and therefore we can infer that b = c = 0.
Substituting the values, we find:
[tex]f(t) = 20 \cdot sin( \frac{2 \pi}{5} \cdot t) [/tex]
If Luis earns a base salary of $150.00 every week with an additional 14 % commission on everything he sells .Luis sold $6050.00 worth of items last week. what is Luis's total pay last week
Answers
847+150=$997 was Luis's total pay last week
Solve the system of equations using a matrix. Separate the x and y values with a comma. 2x-y=6 & 3x-y=11
Answers
[tex]\left[\begin{array}{ccc}-1&0\\0&-1\end{array}\right\left|\begin{array}{ccc}-5\\-4\end{array}\right]\xrightarrow{(-1)r_1;(-1)r_2}\left[\begin{array}{ccc}1&0\\0&1\end{array}\right\left|\begin{array}{ccc}5\\4\end{array}\right]\\\\Answer:\ \left\{\begin{array}{ccc}x=5\\y=4\end{array}\right\to(5;\ 4)[/tex]
Simplify: (10*5+6)(13+2)+19
Answers
(10)(5)+6)(13+2)+19
=(50+6)(13+2)+19
=56(13+2)+19
=(56)(15)+19
=840+19
=859
Hope this helps!!
859
We start with P.E.M.D.A.S.
Parenthesis, Exponents, Multiply, Divide, Add, Subtract
Parenthesis first:
10*5+6
10*5=50
50+6=56
13+2=15
56*15=840
840+19=859
[:] DustinBR [:]
A number that divides evenly into another number is known as which of the following?
A.) prime number
B.)factor
C.) multiple
D.) Integer
Answers
the prime number is greater than one and cannot be divided by other numbers.
the factor is an element of a number.
multiple means it can be various numbers
An integer is a whole number from - infinity to positive infinity including zero.
A number that divides evenly into another number is known as factor.
The correct answer is
B.) factor.
A factor is a number that divides evenly into another number. To find the factors of a number, you can perform a process of division or use other mathematical methods.
Let's take an example to illustrate:
If we consider the number 12, its factors are the numbers that divide it evenly without leaving a remainder. We can start by dividing 12 by 1:
12 ÷ 1 = 12
Since there's no remainder, 1 is a factor of 12. Now, let's try dividing 12 by 2:
12 ÷ 2 = 6
Again, there's no remainder, so 2 is also a factor of 12. Continuing this process, we find that 3 is also a factor of 12:
12 ÷ 3 = 4
And finally, 12 ÷ 4 = 3
So, the factors of 12 are 1, 2, 3, 4, 6, and 12.
Each of these numbers divides evenly into 12, making them factors. Therefore, the correct answer is B.) factor.
Factors are essential in various mathematical concepts, including prime factorization, finding greatest common divisors, and simplifying fractions. Understanding factors helps in solving problems related to divisibility and multiplication. By identifying factors, we can break down complex numbers into simpler components, aiding in various mathematical computations and analyses. Hence, recognizing factors is fundamental in mathematics.
Complete question:
A number that divides evenly into another number is known as which of the following?
A.) prime number
B.)factor
C.) multiple
D.) Integer
Which point lies outside the circle with equation (x - 2)2 + (y + 3)2 = 4?
(1, -4)
(0, -3)
(2, 0)
(2, -4)
Answers
(2, 0)
The only point outside of the line is (2, 0)
In order to find if a point is outside, inside or on the line, you simply have to put the number into the equation. If the result is both sides are equal, then it is on the line. If the left side is bigger than the right side, then it is outside of the line. If the right side is bigger than the left, then it is inside of the line. So lets plug in and see where (2, 0) falls.
(x - 2)^2 + (y + 3)^2 = 4
(2 - 2)^2 + (0 + 3)^2 = 4
0^2 + 3^2 = 4
0 + 9 = 4
9 = 4
Since the left side is bigger than the right, we know it is outside of the line
To which subsets of the real numbers does the number 82 belong?
Answers
Answer: the number 82 belongs to the following subsets of the real numbers of Natural Numbers (N), Whole Numbers (W), Integers (I), Rational Numbers (Q), Real Numbers (R)
The number 82 belongs to several subsets of the real numbers as given in the following:
1. Natural Numbers (N): The natural numbers are the set of positive integers starting from 1, i.e.,(1, 2, 3,.......). Since 82 is a positive integer, it belongs to this subset.
2. Whole Numbers (W): The whole numbers are the set of non-negative integers, i.e., ( 0, 1, 2, 3,....). Since 82 is a non-negative integer, it belongs to this subset.
3. Integers (Z): The integers include all positive and negative whole numbers, including zero, i.e., ( -3, -2, -1, 0, 1, 2, 3,...). Since 82 is a whole number, it belongs to this subset.
4. Rational Numbers (Q): The rational numbers are numbers that can be expressed as the quotient of two integers [tex]\( \frac{a}{b} \)[/tex], where a and b are integers and [tex]\( b \neq 0 \)[/tex]. Since 82 can be written as [tex]\( \frac{82}{1} \)[/tex], it belongs to this subset.
5. Real Numbers (R): The real numbers include all the rational and irrational numbers. Since 82 is a rational number, it is also a real number.
Which of the following scenarios has a lower y-intercept than y = 4x + 5 ?
(a.) A 50 gallon tub is draining. Every 2 minutes, the amount of water decreases by 2 gallons.
(b.) Reginaldo had $17 in his account and for every book he buys, it costs him $4.
(c.) Sydney has collected 8 postcards. Each time a friend comes to visit, Sydney gives her a postcard.
(d.) Owen has 3 pets. He receives a new pet each time he has a birthday.
Answers
The key to this question is "What do you start with?" All of them (except D) start with something and then a condition reduces the starting point.
A
The condition (at zero) starts with 50 gallons. Every 2 minutes the amount taken away is 2 gallons.
The equation looks like this
y = -2x + 50
So what do you start with? You started with 50 gallons. That's your y intercept. It's big. A is NOT the answer.
B
Renaldo starts with 17 dollars. He hasn't done anything, and he still has 17 dollars. If he buys a book, he has 4 dollars less. So his equation is
y = -4x + 17. The y intercept is 17 if he has bought no books. The answer is NOT B
C
Sydney starts with 8 postcards. Every time a friend comes, Sydney has 1 less post card. Her equation is
y = 8 - x That's not the answer either.
D
What do you start with? 3 pets, correct? Every birthday Owen get's one more. But the starting point is three. So his equation is
y= 3 + x where x is the number of birthdays.
D has the lowest starting point.
D <<<< Answer
Find the cosine of both angle A and angle B.
Answers
cos A=adjacent side angle A/hypotenuse
adjacent side angle A=24 units
hypotenuse=26 units
cos A=24/26-----> 12/13
cos B=adjacent side angle B/hypotenuse
adjacent side angle B=10 units
hypotenuse=26 units
cos B=10/26------> 5/13
the answers are
cos A=12/13
cos B=5/13
cot A=adjacent side angle A/opposite side angle A
adjacent side angle A=24 units
opposite side angle A=10 units
cot A=24/10------> cot A=12/5
cot B=adjacent side angle B/opposite side angle B
adjacent side angle B=10 units
opposite side angle B=24 units
cot B=10/24------> cot B=5/12
So, cos A = 24/26
= 0.923
Cos B = 10/26
= 0.3846
The viewing room at a planetarium is in the shape of a hemisphere. The diameter of the hemisphere is 48 feet. What is the volume of the viewing room?
Answers
So, the volume of a hemisphere is the half of the volume of the complete sphere.
The formula for the volume of a sphere is:
V = (4/3) π (radius)^3
Using π = 3.14 and radius = diameter / 2 = 50 feet / 2 = 25 feet.
You get:
V = (4/3) (3.14) (25 feet)^3 = 65,416.7 feet^3
Answer: 65,416.7 cu. ft.
Answer:
9,216π cubic feet
Step-by-step explanation:
Which polygon is a convex heptagon?
Answers
Answer: The correct option is 1.
Explanation:
A polygon is said to be a heptagon if it has 7 vertices, 7 sides and 7 angles. A heptagon is called a convex heptagon if the line connecting the two vertices are lies completely inside the heptagon.
In the figures the black points shows the vertices.
Reason for correct option:
In figure 1 there are 7 angles, 7 sides and 7 vertices and the lines joining any two vertices are lies inside the figure, therefore it is an convex heptagon and option 1 is correct.
Reason for incorrect option:
In figure 2 and 3 the number of vertices and sides are 8, therefore the figure shows the octagon and option 2 and 3 are in correct.
In figure 4 the number of vertices and sides are 7 but there axis a line which connecting the two vertices and lies outside the figure as shown in below figure, therefore the option 4 is incorrect.
Answer:
First picture
Step-by-step explanation:
In five consecutive tosses of a coin, what is the probability of not getting a tail until the 5th coin toss?
Answers
Chaz is constructing the circumscribed circle for △JKL .
Which construction is a correct next step for Chaz?
Open the compass to just more than half the width of JL¯¯¯¯¯ and draw a circle centered at point K.
Open the compass to the width of JL¯¯¯¯¯ and draw a circle centered at point K.
Construct the angle bisector of ∠J .
Construct the perpendicular bisector of JL¯¯¯¯¯ .
Answers
- first, find the perpendicular bisector of two of the sides of the triangle;
- the two perpendicular bisectors will intersect in a point (C) that will be the center of the circle;
- point the compass in C and open it to the width of one of the points of the triangle (CJ or CK or CL);
- draw the circle.
Hence, the correct answer is: D) Construct the perpendicular bisector of JL.
The correct next step for him to take in constructing a circumscribed circle for △JKL is to construct: the perpendicular bisector of JL
How can We Construct A Circumscribed Circle of a Triangle?To construct a circumscribed circle for a triangle, the first thing we have to do is to place our compass at the center of one of the sides of the triangle.
This center point can be gotten by constructing a perpendicular bisector to a side of the triangle.
Therefore, the correct next step for him to take in constructing a circumscribed circle for △JKL is to construct: the perpendicular bisector of JL
Learn more about Circumscribed Circle on:
https://brainly.com/question/15605172
Item 12 a regular triangular pyramid has a base and lateral faces that are congruent equilateral triangles. it has a lateral surface area of 57 square centimeters. what is the surface area of the regular triangular pyramid?
Answers
Answer:
76
Step-by-step explanation:
im short on time sorry for no explanation.
identify the type of conic section that has the equation 4x^2+25y^2=100 and identify its domain and range.
Answers
4x^2+25y^2=100
[tex]4x^2+25y^2=100 \\\\ Dividing \;both \;sides \;by \;100 \\\\ \frac{4x^2}{100}+ \frac{25y^2}{100}= \frac{100}{100} \\\\ \frac{x^2}{25}+ \frac{y^2}{4}= 1 \\\\ \frac{x^2}{5^2}+ \frac{y^2}{2^2}= 1 \\\\ This \;is \;an \;ellipse. \\\\
\frac{x^2}{a^2}+ \frac{y^2}{b^2}= 1 [/tex]
Domain of an ellipse is x ∈ [-a,a] and Range of an ellipse is y ∈ [-b,b].
So, given equation is an Ellipse where Domain is x ∈ [-5,5] and Range is y ∈ [-2,2].
The distance on the number line from 5 to 12 equals 3x – 2. What is the value of x?
Answers
This distance is expressed by the expression 3x - 2.
So,
3x - 2 = 7
3x = 7 + 2
3x = 9
x =9/3
x = 3
Thus, the value of x is 3 .
An investment banker is responsible for investing a customer’s money into the greatest interest earning account. The banker has the following options for his customer’s investment: Account A: interest rate = 4.8% term of investment = 10 years interest compounded monthly Account B: interest rate = 4.9% term of investment = 10 years interest compounding continuously Which account, A or B, will earn the customer the greatest amount of interest on his $150,000 investment? In your final answer, include all of your calculations.
Answers
Account B will earn the customer the greatest amount of interest.
_____
The question is a qualitative one; no calculations are necessary. One simply needs to observe that 4.9 > 4.8.
(If the numbers were reversed, monthly compounding at 4.9% would give a better return than continuous compounding at 4.8%. A calculation is needed in order to come to that conclusion.)
A college basketball player makes 5/6 of his free throws. Assuming free throws are independent, the probability that he makes it exactly three of his next four free throws is
Answers
The probability that a college basketball player makes exactly three of his next four free throws is calculated using binomial probability, resulting in approximately 38.58%.
Explanation:The probability that a college basketball player makes exactly three of his next four free throws, given that he makes 5/6 of his free throws, involves calculating a binomial probability. We have four independent events (four free throws), and we want exactly three successes (made throws) and one failure (missed throw). We use the following formula for the binomial probability:
P(X=k) = C(n, k) × p^k × (1-p)^(n-k)
where:
In this problem:
p = 5/6 (probability of making a throw)(1-p) = 1/6 (probability of missing a throw)n = 4 (total number of free throws)k = 3 (number of free throws made)Plugging in the values:
P(X=3) = C(4, 3) × (5/6)^3 × (1/6)^1
C(4, 3) is 4, since there are four different ways to make three throws and miss one (MMM-M, MM-MM, M-MMM, MMMM-). So the calculation gives:
P(X=3) = 4 × (5/6)^3 × (1/6) = 4 × (125/216) × (1/6) = 500/1296, which simplifies to about 0.3858 or 38.58%.
Therefore, the probability that he makes exactly three of his next four free throws is 0.3858 or 38.58%.
The cost of renting a car is a flat 26 plus an additiona 0.13 cents per mile that you drive how face can you drive for 99
Answers
y = 0.13x + 26
y = 0.13(99) + 26
y = 12.87 + 26
y = 38.87
After 7 years, Abner earned $1575 in simple interest from a CD into which he initially deposited $6000. What was the annual interest rate of the CD?
Answers
The annual interest rate of the CD was 3.75 %
Explanation
Simple Interest formula is : [tex] I =P*r*t [/tex] , where [tex] I= [/tex] Amount of interest, [tex] P= [/tex] Principal/Initial amount, [tex] r= [/tex] rate of interest in decimal form and [tex] t= [/tex] time in years
Here Abner earned $1575 in simple interest and he initially deposited $6000. So, [tex] I=1575 [/tex] dollar and [tex] P= 6000 [/tex] dollar
Also given that, [tex] t = 7 [/tex] years
Now according to the formula...
[tex] I= P* r*t\\ \\ 1575= 6000*r*7\\ \\ 1575= 42000*r\\ \\ r= \frac{1575}{42000}= 0.0375 [/tex]
For getting the interest rate in percentage, we will multiply it by 100%. So... (0.0375 × 100) % = 3.75 %
So, the annual interest rate of the CD was 3.75 %