a) The rate in feet per second is 148.5 feet per second
b) The distance covered after 2 feet is 360.4 feet
What is the rate?We know that the rate has to do with how much the quantity is changing per unit time. In this case, we are looking at the rate of change of the Parachute's distance per second. It is important for us to say that this rate of change of the distance can also be shown to be the speed of the object.
We would now convert the rate to feet per second and we have;
1 meter per second = 3.3 feet per second
45 meters per second = 45 * 3.3/1
= 148.5 feet per second
Then we have;
s = ut + 1/2gt^2
s =distance
u = initial velocity
g = acceleration due to gravity
t = time taken
After 2 seconds;
s = (148 * 2) + (0.5 * 32.2 * 2^2)
s = 296 + 64.4
s = 360.4 feet
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In an analysis of variance problem involving 3 treatments and 10 observations per treatment, SSE = 399.6. The MSE for this situation is which?
133.2
13.32
14.8
30.0
If in an analysis of variance problem involving 3 treatments and 10 observations per treatment, S S E = 399.6. The M S E for this situation is C. 14.8.
How to find the sample variance?We would be making use of this formula to find or determine the MSE which is the variance within the sample.
MSE = S S E / r (c-1)
Where:
MSE represent variance within the sample = ?
SSE represent sum of the squares of error = 399.6
r represent 3 treatment
c represent observation per treatment = 10
Let plug in the formula so as to know the variance within the sample (MSE )
Sample variance ( MSE ) = 399.6 /3 (10 - 1 )
Sample variance ( MSE ) = 399.6 / 3 (9)
Sample variance ( MSE ) = 399.6 / 27
Sample variance ( MSE ) = 14.8
Therefore we can conclude that the correct option is C which is 14.8.
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There are three angles measured in degrees of a triangle where x is the largest angle, y is the middle angle, and z is the smallest
angle
• The measure of the largest angle is 40 degrees less than twice the sum of the measure of the other two angles.
• The measure of the largest angle is twice the smallest angle plus 10 degrees.
• The sum of the angles of a triangle can be written as x + y + z = 180.
What are the other equations that represent this system of equations?
Select each correct answer.
the triangle could represent in a relation as x = 60 - 2(y + z) and x = 2z + 20.
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The following linear equation accurately describes the circumstance where "The measure of the largest angle is 60 degrees less than the twice the sum of the measure of the other two angles":
x = 60 - 2(y + z) —- (1)
The following linear equation sums up the statement, "The largest angle is twice the smallest angle plus 20 degrees," as it applies to angles:
x = 2z + 20 —- (2)
Hence the triangle could represent in relation as x = 60 - 2(y + z) and x = 2z + 20.
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Describe the slope of the line.
The slope is positive
Find the slope
m=_______
The equation of the line that passes through the point (0, 3) & (0, 4) and the slope of the equation is undefined.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (b).
To find the slope of the line, we can use the slope formula:
m = (y2 - y1)/(x2 - x1)
The line on the graph passes through points (0, 3) & (0, 4).
m = (4-3)/(0-0)
m = 1/0
m = ∞
so, the slope is undefined.
Therefore, the equation of the line that passes through the point (0, 3) & (0, 4) and the slope of the equation is undefined.
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13.
Graph f(x)=4x(1/2)^x
start by plugging values for x into the function
a) f(1) = 4 (1/2)^1
f(1) = 2
the first coordinate point is (1,2)
b) f(0) = 4(1/2)^0
f(0) = 4
(0,4)
this method will help you find the coordinate points and where to plot.
A side of the equilateral triangle 'A' is twice the length of a side of
another equilateral triangle 'B'. How many triangles of 'B' will fit
into triangle 'A'?​
Total four triangles of B fit into triangle A as length of the equilateral triangle A is twice the length of triangle B.
As given in the question,
Types of triangles : Equilateral triangle
Number of triangle = 2
Triangle A and Triangle B
Let 'x' be the length of the triangle A
And 'y' be the length of the triangle B
As per given condition:
x = 2y
Area of equilateral triangle A = (√3/4)x²
Area of equilateral triangle B = (√3/4)y²
Now x = 2y
⇒Area of equilateral triangle A = (√3/4)(2y)²
⇒Area of equilateral triangle A = (√3/4)4y²
⇒Area of equilateral triangle A = 4 [(√3/4)y²]
⇒Area of equilateral triangle A = 4 ( area of equilateral triangle B)
Therefore, total number of four equilateral triangle of B fit into equilateral triangle A.
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The Stock Market Alexander is a stockbroker. He earns 13% commission each week. Last week, he sold $7,500 worth of stocks. How much did he make last week in commission? If he averages that same amount each week, how much did he make in commission in 2011? PLS HELP
$50,700 he make in commission in 2011.
How to calculate the commission?According to the commission rate, a commission is a proportion of all sales. Multiply the commission rate by the total sales to get the commission on a sale. Recall to convert the commission rate from a percent to a decimal first, just as we did for computing the sales tax.%Earns= 13% commission/week
Last week sold = $7,500
In order to obtain the last week earns in commission we need to multiply % rate of commission by the last week sold as shown as follows:
$Earns = 0.13 (decimal form)*$7,500
Earns = $975
Last week, he made $975 in commission.
If he averages that same amount each week, he should make $975* 52(number of weeks per year) = $50,700/year
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URGENT PLEASE ANSWER
Answer:
y = 371.17×1.15^x1135 in month 8Step-by-step explanation:
You want an exponential regression function for the data in the table.
a. Exponential regressionA regression function of most any kind can be found using a graphing calculator or spreadsheet. The attachment shows the function is approximately ...
y = 371.17 × 1.15^x
where y is the number sold, and x is the month.
b. Number soldUsing x=8, the predicted number sold for month 8 is ...
y = 371.17 × 1.15^8 ≈ 1135.4175 ≈ 1135
Sales for month 8 will be about 1135.
Find the characteristic polynomial of the matrix, using either a cofactor expansion or the special formula for 3x3 determinants. [Note: Finding the characteristic polynomial of a 3 x 3 matrix is not easy to do with just row operations, because the variable 2. is involved.] 1 0 1 - 2 3 -1 0 7 0 . The characteristic polynomial is (Type an expression using a as the variable.)
The characteristic polynomial of the given matrix is -λ³ + 16λ² - 67λ +60.
What is Polynomial ?A polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
What is Polynomial of the Matrix ?A polynomial matrix or matrix of polynomials is a matrix whose elements are univariate or multivariate polynomials.
OR a linear combination of the powers of a square matrix.
A matrix polynomial A 1(λ) = A 10 + … + A 1n1λn1 of order n1 is called a right divisor of a polynomial A (λ) of order n if there exists a matrix polynomial A 2(λ) = A 20 + … + A 2n2λn2 of order n2, n2 ≥ n − n1 such that A (λ) = A 2(λ) A 1(λ).
Let A = 4 -4 0
-4 7 0
4 6 5
The characteristics polynomial of A is |A -λɪ|
|A -λɪ| = (4 -λ) -4 0
-4 (7-λ) 0
4 6 (5-λ)
= (4-λ) [(7-λ)(5-λ) - 0] + 4[-4(5-λ) - 0] + 0[-4 -4(7-λ)]
= (4-λ) [35 - 7λ - 5λ + λ²] +4[-20 + 4λ] + 0
= (4-λ) [35 - 12λ + λ²] -80 + 16λ
= 140 -48λ + 4λ² - 35λ + 12λ² - λ³ -80 +16λ
= -λ³ + 16λ² - 67λ +60
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19.
Which conclusion is not justified by the prior given statements?
A. Given: If a line is vertical, then it has an undefined slope.
Given: Line / is vertical.
Conclusion: Line / has an undefined slope.
B. Given: If a triangle is isosceles, then it has two congruent sides.
Given: If a triangle has two congruent sides, then it has two congruent angles.
Conclusion: If a triangle is isosceles, then it has two congruent angles.
C. Given: If two angles are vertical, then they are congruent angles.
Given: 21 and 22 are vertical angles.
Conclusion: 21 22
D. Given: If Mark goes fishing, then he will buy a new fishing rod.
Given: If Mark goes fishing, then he will need to buy bait.
Conclusion: If Mark buys a new fishing rod, then he will need to buy bait.
Answer: the thing is I don’t know
Step-by-step explanation:
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = e−7t cos(6t), y = e−7t sin(6t), z = e−7t; (1, 0, 1)
The parametric equations for the tangent line to the given curve is x = 1-7t , y = 6t and z = 1-7t .
In the question ,
it is given that ,
x = [tex]e^{-7t}[/tex]cos(6t), y = [tex]e^{-7t}[/tex]sin(6t), z = [tex]e^{-7t}[/tex] ,
So , the parametric equation of the curve will be ,
r(t) = [ [tex]e^{-7t}[/tex]cos(6t), [tex]e^{-7t}[/tex]sin(6t), [tex]e^{-7t}[/tex] ]
the point given as (1,0,1) implies that ,
[tex]e^{-7t}[/tex]cos(6t) = 1 , [tex]e^{-7t}[/tex] = 0 , sin(6t), [tex]e^{-7t}[/tex] = 1 which implies that ⇒ t = 0 .
So , the point (1,0,1) is the point r(0) .
Now , differentiating x , y and z with respect to t ,
we get ,
r'(t) = [ [tex]-e^{-7t}[/tex][7cos(6t) + 6sin(6t)], [tex]e^{-7t}[/tex][6cos(6t) - 7sin(6t)], [tex]-7e^{-7t}[/tex] ]
substituting , t = 0,
we get ,
r'(0) = [-7 , 6 , -7]
the equation of the tangent line passing through the point (1,0,1) and parallel to the tangent vector r'(0) is
r(t) = r(0) + tr'(0) = (1,0,1) + t(-7,6,-7)
So , r(t) = [ 1 - 7t , 6t , 1 - 7t ]
So , x = 1 - 7t , y = 6t and z = 1 - 7t .
Therefore , the required parametric equations are x = 1 - 7t , y = 6t and z = 1 - 7t .
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What is ab as shown in the attached question
Answer:
(c) -42
Step-by-step explanation:
You want the product ab given that ...
f(x) = 3x³ +ax² -5x +7g(x) = -3x⁴ +2x³ +3x² +bx +12(f+g)(x) = -3x⁴ +5x³ +9x² -12x +19Comparing coefficientsThe function (f+g)(x) is the sum of the other two functions. For the purpose here, we only need to look at terms that involve 'a' and 'b'.
Comparing coefficients of x², we have ...
ax² +3x² = 9x²
a = 9 -3 = 6
Comparing coefficients of x, we have ...
-5x +bx = -12x
b = -12 +5 = -7
The product is ...
ab = (6)(-7) = -42
A laser rangefinder is locked on a comet approaching Earth. The distance g(x) , in kilometers, of the comet after x days, for x in the interval 0 to 42 days, is given by g(x)=300,000csc(π42x)
The value of the function at day 5 is 822000 and it means that the laser rangefinder locked on the comet is at a distance of 822000 km
How to evaluate the value of the function at day 5?From the question, we have the following parameters that can be used in our computation:
g(x) = 300,000csc(π/42x)
Also from the question, we have
Number of days = 5
This means that
x = 5
Substitute x = 5 in the equation g(x) = 300,000csc(π/42x)
So, we have the following representation
g(5) = 300,000csc(π/42 x 5)
Evaluate the products
So, we have the following representation
g(5) = 300,000csc(5π/42)
Evaluate the cosec expression
g(5) = 300,000 * 2.74
So, we have
g(5) = 822000
Hence, the value of the function is 822000
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Complete question
A laser rangefinder is locked on a comet approaching Earth. The distance g(x) , in kilometers, of the comet after x days, for x in the interval 0 to 42 days, is given by g(x) = 300,000csc(π/42x)
Evaluate g(5) and interpret the information
pre cal question..........
Graph 1 represents the inverse of the function [tex]f(x)=\sqrt{x+1} -2[/tex]
What is the inverse of a function?
The visual representation of a function's inverse, given by the symbol f-1(x), is the original function mirrored across the line y=x. Only when f is a one-one and onto function does it exist.
The inverse of [tex]\sqrt{x+1} -2[/tex] is [tex]x^{2} +4x+3[/tex].
Plotting the inverse, we get the graph to be option 1.
Therefore, graph 1 represents the inverse of the function [tex]f(x)=\sqrt{x+1} -2[/tex]
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The inverse function of the function given as f(x) = [tex]\sqrt{x+1}[/tex] - 2 is f⁻¹(x) = x² + 4x +3. So, option 1 is since the point on f(x), (-1, -2) is mapped to (-2, -1) in its inverse function.
What are the steps to be followed for finding an inverse function?The steps for finding the inverse function, the steps to be followed are:
consider the given function f(x) = yrewrite the obtained equation for xinterchange the variables x and y in rewritten equationThus, the obtained function is the inverse function of the given function.In terms of coordinates, for an inverse function, the mapping is from y to x.Calculation:The given function is f(x) = [tex]\sqrt{x+1}[/tex] - 2
Consider the given function as f(x) = y ⇒ y = [tex]\sqrt{x+1}[/tex] - 2
Then, on rewriting the function for x, we get
y + 2 = [tex]\sqrt{x+1}[/tex]
⇒ (y + 2)² = (x + 1)
⇒ x = y² + 4y + 4 - 1
⇒ x = y² + 4y + 3
Interchanging the variables y to x and x to y we get
y = x² + 4x + 3
Thus, the inverse of the given function is obtained. I.e,
f⁻¹(x) = x² + 4x +3
To identify the graph, the point that satisfies the given function is
f(x) = [tex]\sqrt{x+1}[/tex] - 2; for x = -1,
f(-1) = -2
So, the point is (-1, -2).
Then, its inverse is mapped from y to x. So, they are interchanged and it is (-2, -1).
From the given graphs, graph 1 shows this point on it. So, that is the required option.
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Adryanna got a manicure for $35 and a pedicure for $43. If she plans on leaving a 15% tip how much will she pay on total
The total amount that will be paid will be $89.70.
How to illustrate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, Adryanna got a manicure for $35 and a pedicure for $43 and she plans on leaving a 15% tip
The total amount that will be paid will be:
= ($35 + $43) + (15% × $78)
= $78 + $11.7
= $89.7
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The area of a rectangle is 35 m², and the length of the rectangle is 3 m more than double the width. What is the dimensions of the rectangle?
The dimensions of the rectangle with area 35 m² is
length = 7.6 m and width = 4.6 m
How of find the dimension of the rectangleThe dimension of the rectangle is calculated using the formula for area of rectangle
= length x width
where
length = 3 + w width = warea of rectangle
35 = (w + 3) * w
35 = w² + 3w
w² + 3w - 35 = 0
solving for w gives
w = 4.6 OR -7.6
using the positive value, the w = 4.6 m, l = 4.6 + 3 = 7.6 m
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l
GIVING BRAINLIEST
ANSWER 4 X 4 X 8 X 2
Answer:
The answer is 256
Step-by-step explanation:
Answer:
256
Step-by-step explanation:
4 · 4 · 8 · 2 = 256
If y varies directly with x and y=20 when x=4, what is the value of y when x=20?
The value of y will be;
⇒ y = 100
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;
y varies directly with x and y=20 when x=4,
Now,
Since, y varies directly with x.
Hence, We get;
⇒ y = kx
Where, k is constant of proportionality.
Here, y=20 when x=4,
So, We get;
⇒ y = kx
⇒ 20 = 4k
⇒ k = 5
Thus, For x = 20, The value of y will be;
⇒ y = kx
⇒ y = 5 × 20
⇒ y = 100
Therefore, We get;
⇒ y = 100
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you are designing a rectangular wooden box with width 4 inches greater than its height, and length 3 times its height. the box has wood that is 1 inch thick on each side of the four sides on the top and bottom. a. write a polynomial function ox in standard form for the volume of the rectangular prism formed by the outer surfaces of the box.
O (x) = [tex]3x^{3} + 12x^{2}[/tex] is a polynomial function ox in standard form for the volume of the rectangular prism formed by the outer surfaces of the box
what is polynomial function ?Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable)
calculation
outside length are height = x
width = x +4 , length = 3x
volume = l *b * h
o(x) = 3x ( x+ 4 )x
= 3[tex]x^{2}[/tex](x+4 )
= O (x) = [tex]3x^{3} + 12x^{2}[/tex]
there is 1 inch of wood , so lengths of inner sides 2 inch less than outer sides as 1 inch from reduced
length = 3x-2
width = x +4-2 = x+2
height = x -2
volume = l*b*h
=[tex]3x^{3} - 2x^{2} - 12x + 8[/tex]
w(x) = [tex]14(6^{2}) + 12(6) -8\\ 504 + 72 -8 \\568inch^{3}[/tex]
so volume of wood = [tex]568inch^{3}[/tex] for x =6
O (x) = [tex]3x^{3} + 12x^{2}[/tex] is a polynomial function ox in standard form for the volume of the rectangular prism formed by the outer surfaces of the box.
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Which expression is equivalent to the answer and show work pls I am force to write it down :,)
Answer:
Last option:
[tex]\dfrac{4x^4y^2}{z}[/tex]
Step-by-step explanation:
Original expression is
[tex]\dfrac{12x^6y^{-4}z^2}{3x^2y^{-6}z^3}\\\\[/tex]
Let us eliminate the obvious wrong answers
[tex]\dfrac{12}{3} = 4\\\\[/tex]
so the coefficient in the answer should be 4.
We can eliminate first and third choices
Now for each term with the same variable, compute the division
[tex]\dfrac{x^6}{x^2} = x^{6-2} = x^4\\\\[/tex]
Second choice is out so the last choice is the correct one.
We can go further with the other terms
[tex]\dfrac{y^{-4}}{y^{-6}} = y^{-4 - (-6)} = y ^{-4+6} = y^2[/tex]
[tex]\dfrac{z^2}{z^3} = z^{2-3} = z^{-1} = \dfrac{1}{z}[/tex]
Multiplying all these individual terms gives
[tex]4 \cdot x^4 \cdot y^2 \cdot \dfrac{1}{z}\\\\= \dfrac{4x^4y^2}{z}[/tex]
What is the freezing point, in C, of a 2.75 m solution of C8H18 in benzene?
The freezing point of the 2.75 m solution of octane in benzene is -8.56 °C.
The freezing point of a solution is the temperature at which the solution becomes a solid. The freezing point of a solution is lower than the freezing point of the pure solvent because the solute particles interfere with the movement of the solvent molecules, which slows down the freezing process.
To determine the freezing point of a solution, we can use the freezing point depression equation:
ΔTf = Kf x molality
where ΔTf is the change in freezing point, Kf is the freezing point depression constant for the solvent, and molality is the concentration of the solute in the solution expressed in moles of solute per kilogram of solvent.
To find the freezing point of a 2.75 m solution of C8H18 (octane) in benzene, we need to know the freezing point depression constant for benzene, which is 5.12 °C/m. We can then use the equation above to calculate the change in freezing point:
ΔTf = 5.12 °C/m x 2.75 m = 14.06 °C
To find the freezing point of the solution, we need to subtract the change in freezing point from the freezing point of the pure solvent. The freezing point of pure benzene is 5.5 °C, so the freezing point of the 2.75 m solution of octane in benzene is:
5.5 °C - 14.06 °C = -8.56 °C
This means that the freezing point of the 2.75 m solution of octane in benzene is -8.56 °C. At this temperature, the solution will become a solid.
A chi-square test of independence is used when both variables are ___.Group of answer choices a. ratio b. ordinal c. interval d. nominal
For statement 'A chi-square test of independence is used when both variables are ___.'
b. ordinal
d. nominal
In this question we have been given a statement 'A chi-square test of independence is used when both variables are ___.'
We need to select the correct choices for the given statement.
We know that the Chi-Square Test of Independence is used to test if two categorical variables are associated.
It is a nonparametric test.
It can only compare categorical variables.
The categorical variables are classified as nominal and ordinal variables.
Chi-Square Test is used to test for a statistically significant relationship between nominal and ordinal variables.
Therefore, for a chi-square test of independence is used when both variables ordinal and nominal.
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There are a total of 58 reindeer and elves helping Santa get ready for Christmas. Each reindeer has 4 legs and each elf has 2 legs. Frosty the Snowman, who doesn’t have any legs, counted 158 legs when all the reindeer and elves were in Santa’s workshop helping Santa. How many elves are helping Santa? Enter your answer as a number only.
Solving a system of equations, we will see that there are 37 elves helping Santa, and 21 reindeer.
How many elves are helping Santa?
Let's define the variables:
x = number of elves.y = number of reindeer.We know that there are 58 of them, then we can write:
x + y = 58
We also know that between all of them they have 158 legs, so we can write the equation:
x*2 + y*4 = 158
Then the system of equations is:
x + y = 58
x*2 + y*4 = 158
To solve this system of equations, we can isolate x on the first equation to get:
x = 58 - y
Replacing that in the other equation we will get:
(58 - y)*2 + y*4 = 158
Now we can solve this equation for y.
(58 - y)*2 + y*4 = 158
116 - 2y + 4y = 158
116 + 2y = 158
2y = 158 - 116
2y = 42
y = 42/2
y = 21
Then the value of x is:
x = 58 - y
x = 58 - 21
x = 37
there are 37 elves.
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I need a answer using the race method (high school level)
and i will make it worth your time
What do you think you could do to show this statement is true?
How could you manipulate this equation to allow you to state this.
By using algebraic expression, the proof of
(a + b)(a - b) = a² - b² has been shown below-
What is algebraic expression?
Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.
Algebraic expressions are of different types based on number of terms.
They are monomial, binomial, trinomial and so on
Algebraic expression with one term is called monomial
Algebraic expression with two terms is called binomial
Algebraic expression with three terms is called trinomial
The given algebraic expression is
(a + b)(a - b)
a² - ab + ba - b²
a² - ab + ab - b² [Commutative law of addition]
a² - b²
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look at the picture
The quadratic inequality (18 / 7) · x² + (54 / 7) · x - 180 / 7 < y contains all the ordered pairs outside the parabola.
What is parabola?
A parabola could be a U-shaped plane curve wherever any purpose is at an equal distance from a hard and fast purpose (known because the focus) and from a fixed line that is understood because the directrix.
Main body:
In this problem we must determine a quadratic inequality of the form:
a · x² + b · x + c < y
Where a, b, c are the real coefficients of the inequality.
First, determine the coefficients of the quadratic inequality (parabola) by solving the system of linear equations:
25 · a - 5 · b + c = 0
4 · a + 2 · b + c = 0
a + b + c = - 18
(a, b, c) = (18 / 7, 54 / 7, - 180 / 7)
Second, write the quadratic in equation:
(18 / 7) · x² + (54 / 7) · x - 180 / 7 < y
hence , the equation is (18 / 7) · x² + (54 / 7) · x - 180 / 7 < y
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Find the terminal point on the unit circle determined by 11π/6 radians. Use exact values, not decimal approximations.
The terminal point on the unit circle use exact values are,
( x , y ) = ( [tex]\sqrt{\frac{3}{2} }[/tex] , - [tex]\frac{1}{2}[/tex] )
Decimals are the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point. For example, 12.5 is a decimal number.
According to the question, it is provided that,
θ = 11π/6 radians
Now,
x = 1.cos(11π/6)
x = cos(11π/6)
x = cos(330°)
x = [tex]\sqrt{\frac{3}{2} }[/tex]
y = 1.sin(11π/6)
y = sin(11π/6)
y = -0.5
y = - [tex]\frac{1}{2}[/tex]
Then,
( x , y ) = ( [tex]\sqrt{\frac{3}{2} }[/tex] , - [tex]\frac{1}{2}[/tex] )
These two represents the terminal points
To find the terminal positions, we merely used the aforementioned equations, equated these two equations, and concluded that the same should be taken into consideration.
It could be figure out by using the x and y points
Therefore
The terminal point on the unit circle use exact values are,
( x , y ) = ( [tex]\sqrt{\frac{3}{2} }[/tex] , - [tex]\frac{1}{2}[/tex] )
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The measures of the angles of a triangle are shown in the figure below. Solve
for X.
Answer:
x = 4
Step-by-step explanation:
The sum of the interior angles of a triangle equal 180.
2x + 15 + 67 + 90 = 180 Combine like terms
2x + 172 = 180 Subtract 172 from both sides
2x + 1752 - 172 = 180 - 172
2x = 8 Divide both sides by 2
[tex]\frac{2x}{2}[/tex] = [tex]\frac{8}{2}[/tex]
x = 4
Answer:
x= 4
Step-by-step explanation:
To Find: Angle Measure X67+2x+15+90=180 (Sum of measures of a Triangle)
2x + 172 = 180
2x=180-172
2x=8
x=[tex]\frac{8}{2}[/tex]
x= 4
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Answer: 3
Step-by-step explanation: schoology whack
Graph the system below and write its solution.
x-2 y=2
y={1}/{2} x-3
Note that you can also answer "No solution" or "Infinitely many" solutions.
The required answer for the given system of linear equations is No solution.
What is a system of linear equation?
A system of linear equations comprises two or more linear equations made up of two or more variables so that all equations in the system are considered simultaneously. In this case, linear equations are first-order equations, where the maximum power of the variable is 1. One, two, or three variables may be present in a linear equation. As a result, we are able to formulate linear equations with n variables.
Solve for the first variable in one of the equations, then substitute the result into the other equation, we will get
No solution
The graph of the given system of linear equations is given below
Hence, the required answer for the given system of linear equations is No solution.
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Find the equation of the line through the point (3,5) that cuts off the least area from the first quadrant?
The equation of the line through the point (3,5) that cuts off the least area from the first quadrant is 5x +3y -30 = 0.
An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is the slope and c is the y-intercept.
There are basically two intercepts, x-intercept and y-intercept. The point where the line crosses the x-axis is the x-intercept and the point where the line crosses the y-axis is the y-intercept.
The equation of the line, which intersects the y-axis at a point is given by:
y = mx + c
Suppose the line passes through (t,0) and (3,5), where t>3. Then the y-intercept is at (0, 5t/t-3).
So the area of the triangle is:
[tex]\frac{1}{2}[/tex]×[tex]t[/tex]×[tex]\frac{5t}{t-3}[/tex] [tex]=[/tex][tex]\frac{5(t^{2} )}{3(t-3)}[/tex]
Then:
d(5t²/2(t-3))/dt = (5t/t-3) - 5t²/2(t-3)²
= 5t²(2(t-3)-t)/2(t-3)²
=5t(t-6)/2(t-3)²
Since we require t >3, the zero of the derivative that we see is when t=6.
We can write the equation of this line as: 5x +3y -30 = 0
Thus, the equation of the line through the point (3,5) that cuts off the least area from the first quadrant is 5x +3y -30 = 0.
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1. Whole milk has 3.25% milk fat in it. If you have 2 cups of milk, how many grams of fat are you
getting? (Remember to convert cups to ml first and get the total amount of milk, or 100%, first)
Whole milk has 3.25 % milk fat in it. That means 100 grams has 3.25 % of milk fat. so,10 grams of milk has 0.325 milk fat in it.
What is milk fat?
The percentage of butterfat in milk, as measured by weight, is known as the fat content of milk. To create a range of goods, the fat content, notably of cow's milk, is altered. In order to facilitate instant identification, the milk container is typically marked with the amount of fat present.
Milk is important for the growth of the body. It plays for the growth and development of the body. 100 grams of milk fat has 3.25 % milk fat in it.
100 grams = 3.25 % of milk fat.
10 grams = x
x = 10 * 3.25 / 100
=0.325 %
Milk contains lots of proteins and minerals. It is essential for the growth of the body. It also contains important minerals such as calcium and proteins.
Therefore, Whole milk has 3.25 % milk fat in it. That means 100 grams has 3.25 % of milk fat. so,10 grams of milk has 0.325 milk fat in it.
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