The ratio for the length of grey to red to bule is 4:9:3.
What is ratio?Ratio is the relation between two numbers which shows how much bigger one quantity than another. Ratio show how many times one contain show the other one.
According to the question
The given data are -
Grey = 0.8m
Red = 1.8 m
Bule = 0.6 m
By solving these we can get -
=0.8:1.8:0.6
=0.8×10:1.8×10: 0.6×10
=8:18:6
By simplifying it we can get
4:9:3.
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1) Solve the following equations for 0° ≤x≤ 360°.
(i) cosec x=1
(ii) sec x=2
(iii) cot x=4
The solutions of the given equations are,
(i) [tex]x=\frac{\pi }{2} , x= \frac{5\pi }{2} , x= \frac{9\pi }{2} , x = \frac{13\pi }{2} , x = \frac{17\pi }{2}[/tex]
(ii) x = 0, x = 2π, x = 4π, x = 6π, x = 8π.
(iii)
[tex]x = cot^-^1(4), x = cot^-^1(4)+\pi , x = cot^-^1(4)+2\pi , x = cot^-^1(4)+3\pi , \\x = cot^-^1(4)+4\pi[/tex]
What is solution of the equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other terms, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transform the equation into an equality.
(i) cosec x = 1 for 0 ≤ x ≤ 360°
Since, the general solution for
cosec x = 1 is, [tex]x = \frac{\pi }{2} +2n\pi[/tex]
The range for the solution is 0 ≤ x ≤ 360°
Hence,
[tex]x=\frac{\pi }{2} , x= \frac{5\pi }{2} , x= \frac{9\pi }{2} , x = \frac{13\pi }{2} , x = \frac{17\pi }{2}[/tex]
(ii) sec x = 2
Since, the general solution for
sec x = 1 is, x = 0 + 2πn
The range for the solution is 0 ≤ x ≤ 360°
Hence,
x = 0, x = 2π, x = 4π, x = 6π, x = 8π.
(iii) cot x = 4
⇒ [tex]x = cot^-^1(4)[/tex]
The range for the solution is 0 ≤ x ≤ 360°
Hence,
[tex]x = cot^-^1(4), x = cot^-^1(4)+\pi , x = cot^-^1(4)+2\pi , x = cot^-^1(4)+3\pi , \\x = cot^-^1(4)+4\pi[/tex]
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express in a + bi form: 2i(i +3)
Expressing the complex number 2i(i +3) in a + bi form gives -2 + 6i
What are complex numbers?Complex numbers are numbers that are expressed as a + ib,
where a and b are real numbers and i is an fictitious number called "iota."
i has the value (-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Real number) and the imaginary number 3i.
The multiplication of 2i(i + 3)
= 2i^2 + 6i
= -2 + 6i
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Relative maxima and relative minima of the function f(x) = x^5 - 4x^3 3x^2 - 8x - 6
The relative maxima and relative minima for f(x) = x⁵ - 4x³ + 3x² - 8x - 6 is is -1.871 and 1.518
The given function is f(x) = x⁵ - 4x³ + 3x² - 8x - 6 ,now differentiation function with respect to x we get
=5x⁴ - 12x² + 6x - 8
Now solving the given equation for the critical values are:
x₁ = 0.176 + 0.73i
x₂ = 0.176 - 0.73i
x₃ = 1.518
x₄ = -1.871
Now, taking derivative of the 5x⁴ - 12x² + 6x - 8 , with respect to x we get
= 20x³ - 24x + 6
now replacing the value of x by 1.58, we get
20 * 1.58³ - 24 * 1.58 + 6
= 46.966, which is positive so it is the minima
Again replacing the value of x by -1.871, we get
=>20 * -1.871³ - 24 * -1.871 + 6
=> -169.9, which is negative so it is the maxima
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You had $50 you spent 10% of the money on clothe, 20% on games, and the rest on books. How much money was spent on books
Answer:
$35
Step-by-step explanation:
money on clothes is 10%, that means it's $5
you get this by dividing the 50 by 100 to figure out how much 1% is, and then multiply with 10.
money on games is 20%, that means it's $10
again, you figure out how much 1% of 50 is and then multiply by 20 to figure out what 20% is.
50 / 100 = 0.5
0.5 * 20 = 10
So far you spent $5 on clothes, $10 on games, that's $15 in total.
When the rest is spent on books, you need to see how much is left of the $50.
50 - 15 = 35
So you spent $35 on books.
Is 1 a triangle number?.
The numbers form a triangular pattern, but the pattern starts at 1, so 1 is a triangular number.
What is area of triangle?The area of a triangle is defined as the total space occupied by the three sides of the triangle in a two-dimensional plane.The basic formula for the area of a triangle is half the product of the base and the height, or A = 1/2 × w × h.This formula applies to all types of triangles, including scalene, isosceles, and equilateral triangles. Recall that the base and height of a triangle are perpendicular to each other.The area of a triangle is the area enclosed by the sides of the triangle.The area of a triangle varies from triangle to triangle depending on the length of the sides and the interior angles. The area of a triangle is expressed in square units. B. m2, cm2, in2, etc.Hence, The numbers form a triangular pattern, but the pattern starts at 1, so 1 is a triangular number.
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Solve for z.
z + 1 is greater than it equal to 29
The solution of the inequality z + 1 ≥ 29 for z , is z ≥ 28 .
Inequality can be defined as a relationship between two expressions or values that are not equal to each other.
For Example : x > 3.
In the question ,
it is given that
the inequality is " z + 1 is greater than it equal to 29 ",
we have to solve this inequality for z ,
So inequality can be rewritten as
z + 1 ≥ 29
Subtracting 1 from both sides of the inequality , we get
z + 1 -1 ≥ 29 - 1
z ≥ 29 - 1
z ≥ 28 .
Therefore , The solution for z + 1 ≥ 29 , is z ≥ 28 .
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PLEASE HELP 34 pointsssss
Answer:f(-10)= -60
Step-by-step explanation:
Answer:
f(- 10) = - 300
Step-by-step explanation:
substitute x = - 10 into f(x) , that is
f(- 10) = - 3(- 10)² = - 3(100) = - 300
Pls list step by step : calculus : Use a linear approximation to estimate the value of √33. Express your answer as an exact rational number
Using linear approximation, the function y = √33 is approximated as 5.744
Linear ApproximationThe concept behind the linear approximation formula is the equation of a tangent line. We know that the slope of the tangent that is drawn to a curve y = f(x) at x = a is its derivative at that point. i.e., the slope of the tangent line is f'(a). Thus, the linear approximation formula is an application of derivatives. Let us learn more about this formula in the upcoming sections.
In equation y = √33
We can apply linear approximation to this
y = √33 = 5.744
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Select all of the true comparisons.
Answer A, B, D
Step-by-step explanation:
If g(x)=(x+1)/(x-2) and h(x)=4-x what is the value of (goh) (-3)
The value of composition of function (goh) (-3) is [tex]\frac{8}{5}[/tex].
A function that depends on another function is referred to as a composite function. When one function is inserted into another, a composite function is produced. The definition of a composite function is a function made up of two functions, one of which acts as an independent variable for the other function. It can be defined as:
[tex](fog)(x)=f(g(x))\\(gof)(x)=g(f(x))[/tex]
When dealing with the composition of functions, the order of the functions is crucial since (f∘g)(x) is not equivalent to (g∘f)(x).
Finding the composition of function by putting x=h(x) in function g(x),
[tex](goh)(x)=g(h(x))\\\\=\frac{4-x+1}{4-x-2}\\\\=\frac{5-x}{2-x}[/tex]
Now, putting x = -3,
[tex](goh)(-3)=\frac{5-(-3)}{2-(-3)} \\\\=\frac{8}{5}[/tex]
Therefore, the value of composition of function (goh) (-3) is [tex]\frac{8}{5}[/tex] .
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isosceles&equilateral triangles
Answer:
Step-by-step explanation:
These expressions are equivalent. True or False?
5y+4−3y = 2y+4
The sentence is true because the expressions are equivalent.
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=7x+3. Where:
m= the slope.
b= the constant term that represents the y-intercept
For the given example: m=7 and b=3.
The linear equations are considered equivalent when they are equal.
The given equations are 5y+4−3y = 2y+4. Solving theses equations, you have:
5y+4−3y = 2y+4
2y+4 = 2y+4
Like the both equation present the slope and the constant term equal, the expressions are equivalent.
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Solve the following system of equations by linear combination: 2x + y = 8 x – y = 4
a. The solution is (5, –2).
b. The solution is (4, 0).
c. There is no solution.
d. There are an infinite number of solutions.
The solution to the equation by linear combination is (b) The solution is (4, 0).
How to determine the solution to the equation?From the question, we have the following system of equations
2x + y = 8
x – y = 4
By linear combination, we start by eliminating one of the variables
This is done by adding the equations
So, we have
2x + x - y + y = 8 + 4
Evaluate the like terms
3x = 12
Divide both sides
x = 4
Substitute x = 4 in x – y = 4
4 – y = 4
So, we have
y = 4 - 4
Divide
y = 0
Hence, the solution is (b) (4, 0)
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QUICK PLEASE HeLP ASAP MATH HW
Answer:
1. B
2. D
3. A
4. B
5. A
6. C
7. B
8. D
9. B
10. A
Step-by-step explanation:
11 times the product of 19 and a number g?
11 times the product of 19 and a number g?
11*(19g)
= 209g
The HHS faculty weighed an average of 215 pounds in 2018. The faculty went on a weight watchers diet plan and now weight an average of 185 pounds in 2021. What was the faculty's average weight loss per year?
The faculty lost pounds per year?
If the faculty went on a weight watchers diet plan and now weight an average of 185 pounds in 2021. The faculty's average weight loss per year : 185 pounds and 155 pounds.
How to find faculty lost pounds per year?First step is to find the difference between the initial weight and the final weight
Difference = Initial weight - Final weight
Difference = 215 pounds - 185 pounds
Difference = 30 pounds
Now let find the lost per year
2018
Lost per year = 215 pounds - 30 pounds
Lost per year = 185 pounds
2021
Lost per year = 185 pounds - 30 pounds
Lost per year = 155 pounds
Therefore the loss is 185 and 155 pounds.
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Select all the unique triangles that can be drawn to only have angle measures 40° and 100° and side length 3.
Answer:
None
Explanation:
A unique triangle can be defined as a triangle that can be formed in one way.
The various conditions that a triangle must satisfy so that it is unique :
a) A triangle where the length of the three sides is known or given is a unique triangle.
b) A triangle where two side lengths and their included angle is given is a unique triangle.
c) A triangle where two angles and their included side is given is a unique triangle.
d) A triangle where two angles and a non - included side length is known is a unique triangle.
In the above question, we are given angles 40°, 40° and 100 degrees
3 angles are known, no side length is given. The angles above can form a triangle called the obtuse triangle because their sum = 180° and one of the angles is great we than 90°
However, this does not satisfy the criteria that makes a triangle unique.
Therefore, no unique triangle(s) can be drawn with interior angles measuring 40°, 40°, and 100°.
Between which two consecutive whole numbers does the length of the diagonal fall?
Which whole number is it closer to? Use the drop-down menus to show your answer.
Please I need help!!!!!
The length of diagonal falls between 4 and 5.
Given,
Length of diagonal = [tex]\sqrt{18}[/tex]
= 4.24
which is between whole numbers 4 and 5 and closer to 4.
Hence, The length of diagonal falls between 4 and 5 and closer to 4.
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A line that includes the points (8, – 6) and ( – 8,f) has a slope of 1/8 . What is the value of f?
Answer:
f = -8
Step-by-step explanation:
We know the slope formula is:
[tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Because we already know the slope and three other points, we can let point f represent y2 and solve for it:
[tex]\frac{1}{8}=\frac{f-(-6)}{-8-8}\\ \frac{1}{8}=\frac{f+6}{-16}\\ -2=f+6\\ -8=f[/tex]
3 subtracted form a number equals to -8
Write the decimal as a fraction or mixed number form.
6.35
A. 6 1/5
B. 6 3/10
C. 6 7/20
D. 6 7/25
Answer:
B.
Step-by-step explanation:
635/100 = 127/20
=>6 3/10
Calculate
70
cos 20°
rounded to 1 d.p.
70
cos 20 is a faction btw
70 Cos 20° rounded up to 1d.p is 65.8 and as a fraction is 658/10.
What is a fraction?
This refers to the value that is part of a whole number. It has a numerator (upper part) and a denominator (lower part) eg.1/2.
What is Decimal point?
This refers to a dot that is used to demarcate a whole number from the fractional part of a number. eg. 12.6.
The number of points/ values after the decimal point is called the decimal place. Example: 3.7 ( 1 decimal place), 4.26 ( 2 decimal places).
From the question:
Calculate 70cos 20° rounded to 1 d.p.
=70 * 0.9397
=65.78
rounded to 1 d.p.
=65.8
As fraction:
65.8 =65.8/10
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If given that the area of a square is 121 cm², find the length of one side of the square.
A 30.25 cm
B 11 cm
C 60.5 cm
D 10 cm
A line ha a lope of 4 and pae through the point (8,7). What i it equation in point-lope form?
Alo need an explanation pl
The equation in point-slope form is y=4x-25.
A line passing through the point (x 1, y1) has a slope of "m," and its point slope form is given by the equation y - y1=m (x - x1).
A horizontal line's equation is of the form y=b when it passes through the points (a, b).
Step 1: Write down the line's slope, "m," and the coordinates (x 1, y 1) of the point that is given and is on the line.
Step 2: Replace the given values in the calculation for the point slope: y - y1 = m. (x - x1).
Point-slope form is y=mx+b.
To get the equation of the line in standard form, simplify in step three.
Given, m(slope)= 4.
The point is (8,7)= (x1,y1)
y-7=4(x-8)
y-7=4x-32
y=4x-32+7
y=4x-25
Hence, the equation in point-slope form is y=4x-25.
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PLEASE HELP!
Jason decided to begin a workout program. He wants to start running three times a week. At the beginning of the workout program, his weekly average per run is 1 mi. He increases his weekly average per run by 17% each week, according to an exponential growth model.
Jason makes a sketch of the graph for this situation. He plots the point containing the y-intercept, (0,1) . He then plots the point representing the weekly average per run for Week 7 and rounds the coordinates of the point to the nearest tenth.
What are the coordinates of the point that represents the weekly average per run for Week 7?
Answer: I think it (7,4.1)
Step-by-step explanation:
Answer:
7.3.0
Step-by-step explanation:
based on the picture, would man a or man b have more gravity?
subject is science but it not there
Answer: what picture
Step-by-step explanation:
Rick measured the town library and made a scale drawing. The scale he used was 7 millimeters : 3 meters. The parking lot is 91 millimeters wide in the drawing. How wide is the actual parking lot?
Using the scale of 7 millimeters : 3 meters as used by Rick the actual parking lot is 39 meters wide
How to get the the actual parking lotScale factors are used to increase or decrease image. The situation of increment is usually called magnifying.
solving for the width of the actual parking
7 millimeters = 0.007 meters
91 millimeters = 0.091 meters
0.007 = 3
0.091 = ?
cross multiplying
0.007 * ? = 3 * 0.091
? = 0.273/0.007
? = 39 meters
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A line with a slope of
4/7 passes through the points (h,10) and (–4,6). What is the value of h?
Answer:
h = 3
Step-by-step explanation:
y-6 = 4/7 (x-(-4)
y - 6 = 4/7 (x+4)
y - 6 = 4/7 x + 16/7
y = 4/7 x + 16/7 + 6
y = 4/7 x + (16+42)/7
y = 4/7 x + 58/7
10 = 4/7 x + 58/7
4/7 x = 10 - 58/7
4/7 x = (70-58)/7
4/7 x = 12/7
7/4 * 4/7 x = 12/7 * 7/4
x = 3
I need help with this one PLEASE
Answer: x = 14
Step-by-step explanation: Because these are vertical angles we know they are equal.
5x-10 = 60
Add 10 on both sides
5x = 70
Divide by 5 on both sides
x = 14
A $500 investment in a 12-month CD with an interest rate of 4.89% compounded monthly, earns $25.01 interest in
one year. What effective rate of interest does this investment earn?
Answer:
Step-by-step explanation:
Effective interest rate, r = [tex](1+\frac{i}{n} )^{n}-1[/tex]
Here,
r = effective annual rate
i = nominal rate
n = number of periods
r = [tex](1+\frac{0.0489}{12} )^{12}-1[/tex]
= 0.05001099558
= 5.001099558 %
