A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
3² = 3 X 3 = 9
4³ = 4 x 4 x 4 = 64
[tex]2^{6}[/tex] = 2 x 2 x 2 x 2 x 2 x 2 = 64
The exact value in fractions are:
a) 1/9
b) 1/64
c) 1/64
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
[tex]3^{-2}[/tex]
= 1/3²
3² = 3 X 3 = 9
= 1/9
[tex]4^{-3}[/tex]
= 1/4³
4³ = 4 x 4 x 4 = 64
= 1/64
[tex]2^{-6}[/tex]
= 1/[tex]2^{6}[/tex]
[tex]2^{6}[/tex] = 2 x 2 x 2 x 2 x 2 x 2 = 64
= 1/64
Thus.,
The exact value in fractions are:
a) 1/9
b) 1/64
c) 1/64
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Write an equation in point-slope form of the line that passes through the given point and with the given slope m. (-9,3); m=7
Answer:
[tex] \huge{ \bold{y - 3 = 7(x +9)}}[/tex]
Step-by-step explanation:
The equation of a line in point-slope form is represented by the formula
[tex]y - y_1 = m(x - x_1)[/tex]
where
(x1, y1) is the point and m is the slope
From the question the point is (-9,3) and m = 7
So we substitute the given variables into the formula and solve
We have
[tex]y - 3 = 7(x - - 9) \\ y - 3 = 7(x + 9)[/tex]
Hope this helps you
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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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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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
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]
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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Which of of the following graphs shows the solution set for the inequality below?
3|x + 1 | < 9
The solution set for inequality 3|x + 1| < 9 is option(C).
What is inequality?
A relationship between two expressions or values that is not equal to each other is known as an "inequality" in mathematics. The "not equal symbol (≠)" is typically used to indicate that two values are not equal that is there is inequality.
The equals sign in the equation-like statement 5x - 4 > 2x + 3 has been replaced by an arrowhead. This is a prime instance of inequality. This indicates that the left half, 5x - 4, is larger than the right part, 2x + 3, in the equation.
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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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Select all of the true comparisons.
Answer A, B, D
Step-by-step explanation:
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
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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A shipping container will be used to transport several 120-kilogram crates across the
country by rail. The greatest weight that can be loaded into the container is 27500
kilograms. Other shipments weighing 14300 kilograms have already been loaded into
the container. Write and solve an inequality which can be used to determine x, the
number of 120-kilogram crates that can be loaded into the shipping container.
Using inequality the number of 105 of 120-kilogram crates that can be loaded into the shipping container.
What is inequality?
A difference between two values indicates whether one is smaller, larger, or simply not equal to the other. In mathematics, the term "inequality" refers to a relationship between two expressions or values that is not equal to one another.
The greatest weight that container can hold = 27500
Shipment weight already in the container =14900
Amount of weight that may be loaded = 27500 - 14900 = 12600
Weight of each crates = 120 kg
Let x be the maximum number of 120 kg crates that can be loaded to the container then,
Weight of 'x' number of 120 kg crates = 120x
Therefore, the required inequality is as follows
=>120x< 12600
(since the maximum amount of weight of crates that can be put in the container should be less than or equal to the total weight of the maximum number of crates that can be loaded into the container).
Then the inequality is ,
=> x [tex]\leq \frac{12600}{120}[/tex]
=> x ≤ 105.
Thus, a maximum of 105 crates can be loaded into the container.
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Please answer the question
Answer:
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
3 subtracted form a number equals to -8
write an explicit formula for each sequence and find the 21st term
1. 5, 0, -5, -10
2. 3, 4.5, 6, 7.5, 9
(1) The explicit formula and the 21st term for the first sequence are:
aₙ = 10 - 5n and a₂₁ = -95
(2) The explicit formula and the 21st term for the second sequence are:
aₙ = 1.5n + 1.5 and a₂₁ = 33
What is an arithmetic sequence?A sequence in which the difference between any two consecutive terms is the same is known as an arithmetic sequence.
(1)
The given sequence is 5, 0, -5, -10,...
Note the difference between two consecutive terms of the sequence is the same, which is -5.
Therefore, the sequence is an arithmetic sequence with a common difference of d = -5.
The [tex]n^{th}[/tex] term of an arithmetic sequence is given by:
aₙ = a₁ + (n-1)d
Substitute a₁ = 5 and d= -5 into the equation,
aₙ = 5+ (n-1)(-5)
= 5 - 5n + 5
aₙ = 10 - 5n
To find the 21st term, substitute n = 21 into the above equation,
a₂₁ = 10 - 5n
a₂₁ = 10 - 5(21)
a₂₁ = 10 - 105
a₂₁ = -95
Hence, the explicit formula and the 21st term for the first sequence are:
aₙ = 10 - 5n and a₂₁ = -95
(2)
The given sequence is 3, 4.5, 6, 7.5, 9,...
Note that the difference between two consecutive terms is 1.5, therefore, the sequence is an arithmetic sequence with a common difference of
d = 1.5.
The [tex]n^{th}[/tex] term of an arithmetic sequence is given by:
aₙ = a₁ + (n-1)d
Substitute a₁ = 3 and d= 1.5 into the equation,
aₙ = 3 + (n-1)1.5
aₙ = 3+1.5n-1.5
aₙ = 1.5n+1.5
To find the 21st term, substitute n = 21 into the above equation,
a₂₁ = 1.5(21) + 1.5
a₂₁ = 31.5 + 1.5
a₂₁ = 33
Hence, the explicit formula and the 21st term for the second sequence are:
aₙ = 1.5n + 1.5 and a₂₁ = 33
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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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Find the distance from p to line n in the following question
Line n contains points (–2, 1) and (4, 1). Point p has coordinates (5, 7).
The distance from coordinates Point p (5, 7) to coordinates (–2, 1) and (4, 1) in line n are 9.21 units and 6.08 units respectively.
What is the distance between two points?The distance between two points is defined as the length of the line segment between two places representing their distance.
Line n contains points (–2, 1) and (4, 1). Point p has coordinates (5, 7).
The distance from coordinates p (5, 7) to coordinates (–2, 1) in line n will be
⇒ √[(-2-5)² + (1-7)²]
⇒ √[(-7)² + (-6)²]
⇒ √[49 + 36]
⇒ √85
⇒ 9.21 units
The distance from coordinates p (5, 7) to coordinates (4, 1) in line n will be
⇒ √[(4-5)² + (1-7)²]
⇒ √[(-1)² + (-6)²]
⇒ √[1 + 36]
⇒ √37
⇒ 6.08 units
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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
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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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.
isosceles&equilateral triangles
Answer:
Step-by-step explanation:
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°.
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:
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
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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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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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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Rohan had a box of laddu on the firt day he gave away one third of the laddu on the econd he gave away one quarter of the remaining laddu if he gave away 8 laddu on the econd day how many laddu were there to begin with
The number of laddus who were there at the beginning Rohan has is 48.
Here we have to find the number of laddu Rohan at the beginning.
Let x be the number of laddu Rohan have.
He gave on the first day = x × 1/3= x/3
The leftover laddu = x - x/3
= 2x/3
Laddu is given on the second day = 2x/3 × 1/4
= x/6
Here we know that the laddu given by Rohan is 8,
So
x/6 = 8
x = 48
Therefore we get the number of laddu Rohan has 48.
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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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