Answer:
[tex]400m^3[/tex]
Step-by-step explanation:
Use the formula [tex]V=\frac{1}{3}Ah[/tex]
Where h=the height of the pyramid (12cm)
A=the base area of the pyramid, also known as the area of the square (10cm*10cm=100cm)
So, inserting this into the equation:
[tex]V=\frac{1}{3} (100)(12)[/tex]
[tex]V=\frac{1}{3} (1200)[/tex]
[tex]V=400m^3[/tex]
Randi and Leah are studying together for an exam. Let X represent the number of hours Randi spends studying
nightly, and let y represent the number of hours Leah spends studying nightly. The mean of X is 4.5 hours with a
standard deviation of 1.1 hours, and the mean of Y is 3.7 hours with a standard deviation of 1.8 hours. Assuming
these are independent random variables, which answer choice correctly calculates and interprets the standard
deviation of the sum, S = X + Y?
subscript u s=0.7; Randi and Leah can expect the total number of hours spent studying to vary by approximately 0.7 hours from the mean.
subscript s = 1.7; Randi and Leah can expect the total number of hours spent studying to vary by approximately 1.7 hours
from the mean.
subscript s=2.1; Randi and Leah can expect the total number of hours spent studying to vary by approximately 2.1 hours from the mean.
subscript = 2.9; Randi and Leah can expect the total number of hours spent studying to vary by approximately 2.9 hours
from the mean.
Answer:
2.1
Step-by-step explanation:
σ total ^ 2 = σ randi ^2 + σ leah ^2 = 1.1^2 + 1.8^2 = 4.45
σ total = √4.45 = 2.1
Randi and Leah can expect the total number of hours spent studying to vary by approximately 2.1 hours from the mean.
The correct option is C.
What is a standard deviation?The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.
Given:
Randi and Leah are studying together for an exam.
Let X represent the number of hours Randi spends studying nightly, and let y represent the number of hours Leah spends studying nightly.
The mean of X is 4.5 hours with a standard deviation of 1.1 hours, and the mean of Y is 3.7 hours with a standard deviation of 1.8 hours.
Assuming these are independent random variables,
S = X + Y
σ² = σ²(Randi)² + σ²(Leah)
= (1.1)² + (1.8)²
=√(4.45)
σ = 2.1
Therefore, the sum is 2.1.
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What is the value of 7’3•7’2
Answer:
When adding the fractions 2/7 and 3/7 you'll get 5/
Step-by-step explanation:
pls mark as brainliest
A high chool courtyard ha a idewalk laid out a hown. Sidewalk A,B, and C are horizontal, with idewalk D connecting the other three. Decribe the relationhip of thee idewalk
If the sidewalk A , B ,C are horizontal to each other and D is connecting them, then we can say that the the sidewalk D is perpendicular to them .
We say that two lines are perpendicular if they form the angle of 90 degree between them. Thus , we can say that the sidewalk D are having a perpendicular relationship whit the other 3 sidewalks.
Horizontal means something which has a parallel relationship with the horizon . The opposite of horizontal is vertical which is also known as the portrait mode. A horizontal line is any line normal to a vertical line. Horizontal lines do not cross each other similarly the vertical lines do not cross each other.
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How to calculate CSS pixel ratio?
Calculating the pixel ratio of a website involves measuring the width and height of each element on the page and then dividing the width by the height.
What is ratio?Ratio is a comparison of two numbers or values expressed as a fraction or proportion. Ratios are used to compare different measures, such as costs, efficiency, productivity, or profitability, and to evaluate the relative importance of different elements. Ratios are also used to compare different items to each other, such as the ratio of sales to expenses. Ratios can be used to compare different time periods, and to assess the performance of a company over time.
The result is the pixel ratio, which can be used to determine how much of an element is visible on the page and how much is hidden. To calculate the pixel ratio, you can use a variety of tools, such as online tools, browser extensions, or specialized software. It is also important to note that the pixel ratio will vary depending on the device used to view the website, so it is important to test the website on multiple devices. Once the pixel ratio is calculated, it can be used to optimize the website for different devices.
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Tom would like to take out a secured loan to help pay for a vacation this summer. he has offered his car as collateral. his car is worth $3,500. his bank can offer loans for 80% of collateral value. the vacation he has planned will cost $4,750. approximately how much additional collateral will tom need to offer in order to borrow enough to go on his vacation as planned? a. $1,000.00 b. $1,362.50 c. $2,437.50 d. $2,800.00 please select the best answer from the choices provided a b c d
Tom has to put up an additional $2,437.5 in collateral in order to borrow enough money to take his vacation as planned.
What is unitary method?This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.
A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.
We typically utilize this technique for math calculations.
This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.
According to our question-
automobile is priced at $3,500.
Tom needs more collateral, so P
=P + 3500 Total Collateral Value
His bank is able to lend up to 80% of the value of the collateral.
=> loan = (80/100)(P + 3500)
=> loan = 0.8P + 2800
Loan amount needed: 4,750.
0.8P + 2800 = 4,750.
=> 0.8P = 1950
=> P = 2,437.5
Tom has to put up an additional $2,437.5 in collateral in order to borrow enough money to take his vacation as planned.
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Which of the following does not represent a function? Explain why you chose the answer. I will mark you brainliest!!!
Table B and C
In Table B, the X coordinate of -3 has two different answers which is impossible in a function because it only has one output or one answer which is y.
In Table C, the X coordinate of 0 also has two different outputs or two different answers, and with a function, there is only one y coordinate for each X coordinate.
find vertical and horizontal asymptotes
A vertical asymptote exists of the form x = k where y→∞ or y→ -∞.
A slant asymptote exists of the form y = mx + b where m ≠ 0.
What is the difference between vertical and horizontal asymptotes?Vertical lines go up and down and are in the form of x = a, where a stands for the common x-coordinate of all locations, whereas horizontal lines go left to right and take the shape of y = b, where b stands for the y-intercept.
A vertical line that directs the function's graph but is not actually a part of it is called a vertical asymptote. Because it appears at an x-value outside of the function's domain, the graph can never cross it. There may be multiple vertical asymptotes for a given function. All common factors are cancelled in the denominator, D(x).
A horizontal asymptote exists of the form y = k where x→∞ or x→ -∞ if the value of the one/both of the limits lim ₓ→∞ f(x) and lim ₓ→ -∞ f(x).
A vertical asymptote exists of the form x = k where y→∞ or y→ -∞.
A slant asymptote exists of the form y = mx + b where m ≠ 0.
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find the maximum value of y= -8x^2 + 80x -196
Answer:
(5,4)
Step-by-step explanation:
first, if you have a calculator you can put the equation into y = and just find the maximum point there
to find the x value of the maximum point you do -B/2A
-80/2(8) = 5 so the x value would be 5
then to find y just plug in 5 for x and you should get 4
Answer:
Maximum value of
[tex]f(x) = - 8x^2 + 80x - 196[/tex]
is
[tex]\boxed{f(x) = 4}[/tex]
Step-by-step explanation:
The maximum or minimum value of a function f(x) occurs when the first derivative equals zero
The first derivative of
[tex]f(x) = - 8x^2 + 80x - 196[/tex]
[tex]f'(x) = \dfrac{d}{dx}\left(-8x^2+80x-196\right)[/tex]
[tex]=-\dfrac{d}{dx}\left(8x^2\right)+\dfrac{d}{dx}\left(80x\right)-\dfrac{d}{dx}\left(196\right)[/tex]
[tex]\dfrac{d}{dx}\left(8x^2\right) = 16x\\\\=- \dfrac{d}{dx}\left(8x^2\right) = -16x\\\\\\\dfrac{d}{dx}\left(80x\right)=80\\\\\dfrac{d}{dx}\left(196\right)=0[/tex]
[tex]\dfrac{d}{dx}\left(-8x^2+80x-196\right) \\\\\\ =-16x + 80 + 0\\\\= -16x + 80\\\\[/tex]
Set this expression equal to 0 and solve for x to find the x value which maximizes or minimizes the function
[tex]-16x + 80 = 0\\\\\implies -16x = -80\\\\x = -80/-16\\\\x = 5\\\\[/tex]
Plug this value of x into the original function to get the maximum or minimum value.
[tex]f(5) = -8(5^2) + 80(5) - 196\\\\= -8 (25) +400 -196\\\\= -200 + 400 - 196\\\\= 4\\\\[/tex]
So the maximum value of [tex]\boxed{f(x) = 4}[/tex] ANS
and occurs at [tex]x = 5[/tex]
(Strictly speaking to find if this is a maximum or minimum, we have to find the second derivative and see if it is negative or positive. If negative, it is a maximum, if positive it is a minimum
But since the question does not ask for this, I am skipping it. In case you are interested, the second derivative of f(x) is the derivative of f'(x) which will work out to -16 so it is a maximum)
What is horizontal line test inverse?
The horizontal line test is a method used to determine if a given function is one-to-one, which means that for every unique x-value, there is a unique y-value. A function that is one-to-one can be inverted, meaning that it has an inverse function.
The inverse function of a one-to-one function is a function that undoes the original function.
The horizontal line test is used to determine if a given function is one-to-one by drawing a horizontal line through the graph of the function and seeing if the line intersects the graph at most once.
If the function is one-to-one, it has an inverse function and it can be found by switching the x and y values and solving for y.
For example, if the original function is f(x) = 2x + 1, its inverse function is f^-1(x) = (x-1)/2. This inverse function undoes the original function and it can be used to solve equations, find derivatives, and study geometric transformations.
It's important to note that the horizontal line test is only a sufficient condition, meaning that a function that passes the horizontal line test is one-to-one, but not all one-to-one function pass the horizontal line test.
In conclusion, the horizontal line test is a method used to determine if a given function is one-to-one, which is important because one-to-one functions can be inverted.
The inverse function undoes the original function, and it can be found by switching the x and y values and solving for y. The test is simple and easy to apply, but only a sufficient condition.
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Solve the equation 3x + 4y = 7 for y.
y equals the quantity negative 3 times x plus 7 end quantity over 4
y equals the quantity 3 times x plus 7 end quantity over 4
y equals negative 3 over 4 times x plus 7
y equals negative 3 times x plus 7 over 4
y equals the quantity negative 3 times x plus 7 end quantity over 4.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given a linear equation in two variables.
3x+ 4y = 7
We have to find an expression to calculate y from the equation.
Subtracting both sides of the equation with 3x, we get,
3x + 4y - 3x = 7 - 3x
4y = 7 - 3x
Dividing throughout by 4,
4y/4 = (7 - 3x)/4
y = (7 - 3x) / 4
Hence the value of y is the quantity negative 3 times x plus 7 end quantity over 4.
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the sum of the angle measures of a quadrilateral is 360 find the measure of the missing angle (please help)
A can of tomato sauce contains 8 oz of sauce a case contains 12 cans chef Hugo orders some cases of tomato sauce and gets a total of 480 oz of sauce use 12(8)x=480 to find out how many cases of tomato sauce chef Hugo orders x.
The problem states that a can of tomato sauce contains 8 oz of sauce and a case contains 12 cans. We are trying to find out how many cases of tomato sauce Chef Hugo orders and we know that he gets a total of 480 oz of sauce.
What in mathematics is a linear equation?
According to Wolfram MathWorld A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
We can use the formula 12(8)x = 480 to find out the number of cases of tomato sauce that Chef Hugo orders.
Here's the calculation:
12(8)x = 480
96x = 480
x = 5
Therefore, Chef Hugo orders 5 cases of tomato sauce.
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Choose the function that represents the data in the table. Y = 3x + 2 y = 3x2 + 2 y = y = 3x + 2.
The function that represents the data in the table is 3x²+2. The correct answer is B.
The quadratic function is shown in the data table.
We must ascertain the function's equation.
The quadratic equation's generic form is
Let's replace the general form with the three coordinates (1,5, (2,14), and (3,29).
We therefore have;
a+b+c =5——— (1)
4a+2b+c= 14——— (2)
9a+3b+C =29------(3)
When (2) is subtracted from (1), we have;
9= 3a+b(4)
Subtracting (3) from (2) gives us;
15= 5a +b(5)
Subtracting (5) from (4) gives us;
6= 2a
3= a
As a result, the value of an is 3. When we replace this value in equation (4), we obtain;
3(3)+b= 9
b= 0
When a = 3 and b = 0 are substituted in equation (1), we obtain;
a+b+c =5
3+0+c=5
c=2
As a result, c has a value of 2.
As a result, when we substitute a = 3, b = 0, and c = 2 in the quadratic equation's general form y =ax²+bx+c, we obtain;
3x²+2
Consequently, the function that symbolizes the information in the table is 3x²+2
As a result, Option B is the right response.
Your question is incomplete but maybe your full question attached below
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Why is it called a secant?
A chord is the line segment that the two points determine, i.e., the interval on the secant with the two points as its ends.
what is circle ?In the plane, a circle is created by each point that is a specific distance from another point (center). Therefore, it is a curve made up of points that are spaced out from one another in the plane in a fixed manner. It rotates symmetrically around the center at all angles. Every pair of points in the plane of a circle, which is a closed two-dimensional object, are evenly distanced from the "center." Specular symmetry is produced by a line that traverses the circle. It rotates symmetrically around the center at all angles.
given
The Latin verb secare, which means to cut, is where the word secant originates.
A secant crosses a circle at precisely two points in the case of a circle. A chord is the line segment that the two points determine, i.e., the interval on the secant with the two points as its ends.
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NEED HELP ASAP PLEASE AND THANK YOU
The midpoint of AB is M (3,-1). If the coordinates of A are (8,4), what are the coordinates of B?
The coordinates of B is (-2, -6)
How to find the coordinates of BThe formula to determine the midpoint of a straight line using the coordinates of its endpoints is known as the midpoint formula in coordinate geometry.
The formula is of the form
X= (x₂ + x₁)/2
Y = (y₂ + y₁)/2
From the formula the coordinates of B is solved knowing that midpoint is
M (3,-1) and A is (8,4) and say B (x₁, y₁)
3 = (8 + x₁)/2
6 = 8 + x₁
x₁ = -2
-1 = (4 + y₁)/2
-2 = 4 + y₁
y₁ = -6
hence B is (-2, -6)
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Complete the table of values and answer these questions. Which function has the greater rate of change between 0 and 1? Which function has the greater rate of change between 1 and 2? Which function has the greater rate of change between 0 and 2?
The table is completed using the function f(x) = 3ˣ and g(x) = 3x as shown below
x f(x) g(x)
0 1 0
1 3 3
2 9 6
f(x) has a greater rate of change between 1 and 2
f(x) has a greater rate of change between 0 and 2
How to find the function that has the greater rate of changeThe table is completed by substituting the values of x into the functions of f(x) and g(x)
The rate of change between 1 and 2
f(x)
= change in y / change in x
= (9 - 3) / (2 - 1)
= 6
g(x)
= change in y / change in x
= (6 - 3) / (2 - 1)
= 3
The rate of change between 0 and 2
f(x)
= change in y / change in x
= (9 - 1) / (2 - 0)
= 4
g(x)
= change in y / change in x
= (6 - 0) / (2 - 0)
= 3
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For each systems of equations below, choose the best method for solving
and solve. Show your work.
y=-x-6
x+3y=-18
The equation which gives solutions, x=0 and y=-6.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
y=-x-6............................(1)
x+3y=-18.........................(2)
now, solving both equation we get
x+3y=-18
x + 3(-x-6) = -18
x - 3x - 18 = -18
-2x = 0
x= 0
and, y= -0 -6 = -6
Hence, the solution is x=0 and y=-6.
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Use the slider to change the scale factor.
8
6
4
2
0
2
Scale: 1
4
6
8
Consider the original rectangle and the rectangle that
has been reduced by 0.5.
What is the perimeter of the original figure?
What is the perimeter of the scale figure?
On solving the provided question, we can say that - There exist 333 integers smaller than 1000 that are evenly divisibility test by 3 if you divide 1000 by 3, which results in 333 with a residual of 1.
what is divisibility test?The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.
here,
1000/3
remainder = 1
divisor = 333
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On solving the provided question, we can say that in the rectangle L = 6 units and B = 2 units, Perimeter, P = 2(L+B) => P = 2(6+2) => P = 16 units
What is rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.
here,
in the rectangle
L = 6 units
B = 2 units
Perimeter, P = 2(L+B)
P = 2(6+2)
P = 16 units
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How do you find the hypotenuse of an isosceles right triangle when given the area?
The formula for finding the hypotenuse of an isosceles right triangle when given the area is A = (1/2)bh, where A is the area, b is the base, and h is the height.
To calculate the hypotenuse, first solve for h, which is h = 2A/b. Then, use Pythagorean theorem to solve for the hypotenuse c, which is c = sqrt((b^2)+(2A/b)^2). To illustrate the formula, consider a triangle with an area of 20 and a base of 10. First, solve for h, which is h = 2(20)/(10) = 4. Then, solve for c, which is c = sqrt((10^2)+(4^2)) = sqrt(196) = 14. Therefore, the hypotenuse of the isosceles right triangle with an area of 20 and a base of 10 is 14.
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y = 1/2 x + 1
-2x + 4y = 4
need an answer please
y = -x - 3
y + x = 2
There are infinitely many solutions and thus infinitely many values for x and y in the first system of equations. There are no solution for the second system of equations.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side
The first system of equations are,
y = 1/2 x + 1
-2x + 4y = 4
Multiplying throughout the first equation by 4, we get
4y = 2x + 4
and the second equation is 4y = 2x + 4
Both the equations are same and so the lines coincide.
They have infinitely many solutions.
The second system of equations are,
y = -x - 3
y + x = 2 ⇒ y = -x + 2
Both are in the form of y = mx +c, which is the equation of the line in slope intercept form.
Here m is the slope.
Given lines have the coefficient of x same, and so slopes are same.
So the lines are parallel.
Two parallel lines does not have a solution.
Hence the first system of equations have infinitely many solutions and second system of equations does not have any solution.
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The mobile company charges $180 for an hour of service. How many dollars are customers charged every minute?
Answer: $3
Step-by-step explanation:
Since the company charges $180 for an hour of service, we can say that it charges $180 for 60 minutes of service.
Let the cost of service per minute be C
The equation would be
60C = 180
Simplify, and you'll get
C = 3
And there's your answer.
Ms. Wells is going to order 4 large cheese pizzas for a class pizza party at the end of the school year. She expects she'll spend at least $40 on the pizzas. Let x represent how much ms. Wells expects each pizza to cost. Which inequality describes the problem?.
The correct inequality that describes the problem is 4x ≥ 40. Thus, the correct answer is A.
The answer is A because Ms. Wells is ordering 4 large cheese pizzas, and she expects to spend at least $40 on the pizzas. The inequality 4x ≥ 40 represents the total cost of the pizzas, which is 4 times the cost of each pizza (4x) and should be greater than or equal to $40. This inequality tells us that the total cost of the pizzas is at least $40, which is what Ms. Wells expects.
Option B, 4x > 40x, is incorrect because it doesn't make sense mathematically. The right side of the inequality is 40x, which is not related to the problem, and it also doesn't make sense that each pizza will cost 40 dollars.
Option C, 4x ≤ 40, is incorrect because it represents the total cost of the pizzas as less than or equal to $40, which doesn't match with Ms. Wells' expectation that she expects to spend at least $40 on the pizzas.
This question should be provided with answer choices, which are:
A. 4x ≥ 40B. 4x > 40xC. 4x ≤ 40The correct answer is A.
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Which of the following is the correct solution for the equation 5t 3 3t 5?A. -1B. -2C. 1D. 2
The solution for the equation 5t - 3 = 3t - 5 is when value of t is equal to -1.
Therefore the answer is A. -1.
To find the solution, you can start by isolating the variable t on one side of the equation by adding 3 to both sides and subtracting 3t from both sides:
5t - 3 + 3 = 3t - 5 + 3
5t = 3t - 2
Then subtract 3t from both sides:
5t - 3t = 3t -2 - 3t
2t = -2
Finally, divide both sides by 2 to solve for t:
t = -2/2
t = -1
So, the value of t that satisfies the equation 5t - 3 = 3t - 5 is -1.
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1/3 of a gallon equally with 3 friend elect the equation that how how to calculate the fraction
The fraction that can be equally distribute the equation is 1/9.
The term fraction is defined as the representation of the part of whole thing and it has two parts that is namely numerator and denominator.
Here we have given that is 1/3 gallon of water in a 3 gallon container.
Here we have the amount of water is 1/3 gallon and the container capacity is 3.
Now, we have to equally distribute it across the given contained for that one we have to divide it by the total amount of the container then we get,
=> (1/3)/3
When we rewrite the fraction, the we get the expression as,
=> 1/3 x 1/3
When we multiply this one, then we get,
=> 1/9
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In ∆ABC, if m ABC, if m∠A is seven
more than four times
m∠B and m∠C is eleven C is eleven
more than m more than m∠B, find B, find the
The measure of the angle ∠B of the triangle ABC will be 27°.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
In ∆ABC, if m∠A is seven more than four times m∠B and m∠C is eleven more than m∠B. Then the equations are given as,
∠A = 4∠B + 7 ...1
∠C = ∠B + 11 ...2
∠A + ∠B + ∠C = 180° ...3
From equations 1, 2, and 3, then we have
4∠B + 7° + ∠B + ∠B + 11° = 180°
6∠B = 162°
∠B = 27°
The measure of the angle ∠B of the triangle ABC will be 27°.
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please help i dont know what im doing
Answer:
87-5x Gespil=13+8x
Step-by-step explanation:
dubble started with 87, so we but 87 as the y-intercept. Every month he LOSES elentires, therefore minus. The months are represented by x, because we don’t know how many have passed. Same thing for Gespil except it increases for her.
if possible could i maybe get brainilest???? if i cant then its okay.
Suppose cot(日) = = 2, where
○
12
5
○ 13
ㅇㅇㅇ
13
晉
where n
ㅠ
ㅇ픔
Answer: sinθ=-12/13
Step-by-step explanation:
[tex]\displaystyle\\Given:\ cot\theta=\frac{5}{12} \ \ \ \ \pi < \theta < \frac{3\pi }{2} \ \ \ \ Find:\ sin\theta\\\\\frac{cos\theta}{sin\theta} =\frac{5}{12}[/tex]
Multiply both parts of the equation by 12sinθ:
[tex]12cos\theta=5sin\theta[/tex]
Squared both parts of the equation:
[tex](12cos\theta)^2=(5sin\theta)^2\\\\144cos^2\theta=25sin^2\theta\ \ \ \ (1)\\[/tex]
[tex]Find\ sin\theta[/tex]
Add 144sin²θ to both parts of the equation (1):
[tex]144cos^2\theta+144sin^2\theta=25sin^2\theta+144sin^2\theta\\\\144(sin^2\theta+cos^2\theta)=169sin^2\theta\\\\144(1)=169sin^2\theta\\\\144=169sin^2\theta\\\\Thus,\ 169sin^2\theta=144[/tex]
Divide both parts of the equation by 169:
[tex]\displaystyle\\sin^2\theta=\frac{144}{169} \\\\sin\theta=б\sqrt{\frac{144}{169} } \\\\sin\theta=б\sqrt{\frac{12^2}{13^2} } \\\\sin\theta=б\sqrt{(\frac{12}{13})^2 } \\\\sin\theta=б\frac{12}{13}[/tex]
[tex]\displaystyle\\As, \ \pi < \theta < \frac{3\pi }{2} \ \ \ \ \Rightarrow\ \ \ \angle\theta\ is \ in\ the\ 3rd\ quadrant\\\\ So \ sin\theta\ takes \ negative \ values\\\\sin\theta=-\frac{12}{13}[/tex]
If index of refraction 1 is 1. 5, index of refraction 2 is 2. 0, and the angle of incidence is 45 degrees, what is the angle of refraction?.
The angle of refraction is 32 degrees. The result is obtained by using the formula from the Snell's Law.
What is Snell's Law?The Snell's Law is a formula to describe the relationship between the angles of incidence and refraction when a light passes through two medias. It can be expressed as
n₁ / n₂ = sin θ₂ / sin θ₁
Where
n₁ = refractive index of medium 1n₂ = refractive index of medium 2 θ₁ = incident angleθ₂ = refracted angleWe have:
Index of refraction 1, n₁ = 1.5.Index of refraction 2, n₂ = 2.0.Angle of incident, θ₁ = 45°.Find the angle of refraction!
Using the formula of Snell's Law, we'll get the refracted angle.
n₁ / n₂ = sin θ₂ / sin θ₁
1.5 / 2.0 = sin θ₂ / sin 45°
3 / 4 = sin θ₂ / (½√2)
sin θ₂ = 3(½√2)/4
sin θ₂ = 3/8 √2
sin θ₂ = 0.53
θ₂ = arc sin 0.53
θ₂ = 32°
Hence, the refracted angle is 32 degrees.
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Power of a power quotient rule
The quotient rule essentially asserts that we may divide two powers by subtracting the exponents as long as the base is the same. This is a quick way to simplify exponents.
What is power?The quotient rule essentially asserts that we may divide two powers by subtracting the exponents as long as the base is the same. This is a quick way to simplify exponents. A power series is an infinite series in mathematics in which a represents the coefficient of the nth term and c is a constant. Power series may be found in mathematical analysis as Taylor series of indefinitely differentiable functions. The power of a number indicates how many times the number may be multiplied. Exponents and Indices are other names for powers. For example, 8^2 might be labeled "8 to the power 2" or "8 to the second power", or simply "8 squared".
Here,
The quotient rule essentially asserts that as long as the base is the same, we may divide two powers by subtracting the exponents. This is a shortcut for simplifying exponents.
To know more about power,
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Help please and thank you
Answer:
A.
Step-by-step explanation:
looking at the scatter plot, we can sort of determine a line of best fit, so if we imagine a linear line passing through the middle of the plots, the slope of the line would be positive :)