The quotient between the two functions evaluated in -4 is equal to 8/21.
How to find the quotient?
Here we have the two functions:
f(x) = x^2 - 8
g(x) = 17 - x
And we want to find:
(f/g)(-4)
That can be rewritten as:
f(-4)/g(-4)
By evaluating the two functions we get:
f(-4) = (-4)^2 - 8 = 16- 8 = 8
g(-4) = 17 - (-4) = 17 + 4 = 21
replacing that in the quotient we get
f(-4)/g(-4) = 8/21
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Question is in the photo.
The derivative of y = [ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ] is
y' = [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex] x 1/2 [1/x(x+4) - 1/(5x + 1) - 1/(3x + 7)]
What is a derivative of a function?The derivative of a function f(x) represents its rate of change.
We have,
y = [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex]
Putting log on both sides.
[ log a² = 2 log a ]
log y = 1/2 log [tex]\frac{x(x+4)}{(5x+1)(3x+7)}[/tex]
log y = 1/2 [ log x(x+4) - log (5x +1)(3x + 7) ]
log y = 1/2 [ log x(x+4) - log(5x + 1) - log (3x + 7) ]
Derivation on both sides.
[ d(logx)/dx = 1/x ]
d (log y) / dx = d [ {1/2 log x(x+4) - log(5x + 1) - log (3x + 7)} ] / dx
1/y y' = 1/2[ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ]
y' = y/2 [ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ]
y' = [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex] x 1/2 [1/x(x+4) - 1/(5x + 1) - 1/(3x + 7)]
Thus,
The derivative of y = [ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ] is
y' = [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex] x 1/2 [1/x(x+4) - 1/(5x + 1) - 1/(3x + 7)]
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rounded to the nearest tenth, what is the area of rectangle ABCD?
Given the rectangle ABCD, you can identify that it is divided into two Right Triangles:
[tex]\begin{gathered} \Delta ACD \\ \Delta ABD \end{gathered}[/tex]• You can find the length of the rectangle by applying the following Trigonometric Function:
[tex]\cos \alpha=\frac{adjacent}{hypotenuse}[/tex]In this case, you can set up that:
[tex]\begin{gathered} \alpha=30\degree \\ adjacent=CD=AB=l \\ hypotenuse=AD=9 \end{gathered}[/tex]Then, substituting values and solving for "l", you get:
[tex]\begin{gathered} \cos (30\text{\degree})=\frac{l}{9} \\ \\ 9\cdot\cos (30\text{\degree})=l \\ \\ l=\frac{9}{2}\sqrt[]{3}ft \end{gathered}[/tex]• In order to find the width of the rectangle, you can use this Trigonometric Function:
[tex]\sin \alpha=\frac{opposite}{hypotenuse}[/tex]In this case, you can say that:
[tex]\begin{gathered} \alpha=30\degree \\ opposite=AC=BD=w \\ hypotenuse=AD=9 \end{gathered}[/tex]Therefore, substituting values and solving for "w", you get:
[tex]\begin{gathered} \sin (30\degree)=\frac{w}{9} \\ \\ 9\cdot\sin (30\degree)=w \\ \\ w=\frac{9}{2}ft \end{gathered}[/tex]• Now you need to use the following formula for calculating the area of a rectangle:
[tex]A=lw[/tex]Where "l" is the length and "w" is the width.
Substituting the length and the width of the given rectangle into the formula and evaluating, you get:
[tex]A=(\frac{9}{2}\sqrt[]{3}ft)(\frac{9}{2}ft)[/tex][tex]A\approx35.1ft^2[/tex]Hence, the answer is: Option C.
Given: Q R ≅ S T
Q T ≅ R S
Prove: Q R S T is a parallelogram
The proof that Q R S T is a parallelogram is given and enumerated in the following paragraph.
What is mathematical proof?A mathematical proof is a deductive argument for a mathematical declaration that demonstrates that the provided assumptions logically ensure the conclusion.
The proof that the above-named geometrical shape is a parallelogram goes thus:
Statements Reasons
1. [tex]\overline{QR}[/tex] ≅ [tex]\overline{ST}[/tex] Given
2. [tex]\overline{RS}[/tex] ≅ [tex]\overline{QT}[/tex] Given
3. [tex]\overline{RT}[/tex] ≅ [tex]\overline{TR}[/tex] Reflexive Property
4. [tex]\Delta QRS[/tex] ≅ [tex]\Delta STQ[/tex] SSS Congruence Theorem
5. A 1 ≅ A 4 CPCTC Property
6. A 2 ≅ A3 CPCTC Property
7. QR | ST Alternate Interior Angles Converse
8. QT | RS Alternate Interior Angles Converse
9. Q R S T is a parallelogram Definition of parallelogram
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The width of a rectangle is 4 less than the length. If the area of the rectangle is 165cm?,solve for the length and width of the rectangle.
length:15 cm
width: 14 cm
Explanation
Step 1
Let
w represents the width of the rectangle
l represents the length of the rectangle
a)The width of a rectangle is 4 less than the length,hence
write this in math terms, replace
[tex]\begin{gathered} \text{width}=length-4 \\ w=l-4\rightarrow equation\text{ (1)} \end{gathered}[/tex]b)the area of the rectangle is 165 square cm
the area of a rectangle is given by
[tex]\begin{gathered} \text{Area}=\text{length}\cdot\text{width} \\ \text{replace} \\ 165cm^2=l\cdot w\rightarrow \\ 165=l\cdot w\rightarrow equiation(2) \end{gathered}[/tex]Step 2
now, solve the equations
[tex]\begin{gathered} w=l-4 \\ 165=lw \end{gathered}[/tex]a) replace the w from equation (1) into equation(2)
[tex]\begin{gathered} 165=lw \\ 165=l(l-4) \\ 165=l^2-4l \\ \text{subtract 165 on both sides} \\ 165-165=l^2-4l-165 \\ l^2-4l-165=0 \end{gathered}[/tex]b) now, we have a quadratic equation in the form
[tex]ax^2+bx+c=0[/tex]hence, we can use the quadratic formula to solve
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]let
a=1
b=-4
c=-165
replace
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-(-4)\pm\sqrt[]{-4^2-4(1)(-165)}}{2\cdot1} \\ x=\frac{4\pm\sqrt[]{676}}{2}=x=\frac{4\pm26}{2} \end{gathered}[/tex]therefore
[tex]\begin{gathered} x=\frac{4\pm26}{2} \\ x_1=\frac{4+26}{2}=\frac{30}{2}=15 \\ x_2=\frac{4-26}{2}=\frac{-22}{2}=-11 \end{gathered}[/tex]as we are searchinf for a distance, the only valid answer is 15
so, the answer is length= 15 cm
[tex]l=15\text{ cm}[/tex]c) finally, replace the l value into equation (1) to find the width
[tex]\begin{gathered} w=l-4\rightarrow equation\text{ (1)} \\ w=15-4 \\ w=11 \end{gathered}[/tex]therefore, the width is 11 centimeters
I hope this helps you
If f(x) = x² - 6x + 2 and g(x) = -2x, find the following composition (g o f)(5)
The composite function's value, (gof)(5), is equivalent to 6.
What are composite functions?A mathematical procedure called composite combines two functions, f and g, to produce a third function, h(x), where g(x) is the sum of f(x) and h(x).
Given the aforementioned functions,
f(x) = x^2-6x+2 and;
g(x) = -2x
The composite function is known as the gof (5)
(gof) = g(f(x)) where;
f(x) = g(x2-6x+2) and;
f(x) = -2(x2-6x+2).
Substitute the given functions into the composite;
g(f(5)) = -2(5^2-6(5)+2)
g(f(5)) = -2(-3) = 6
The comparable composite value is provided by this.
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DeMarcus multiplies all of the intergers from -10 to -1, including -10 and -1. Should his answer be positive or negative
Multiplication of all of the integers from -10 to -1, including -10 and -1 is positive.
What is integer?
An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 3/4, 3.14.
According to question,
multiplication of all of the integers from -10 to -1, including -10 and -1 is
-10 × -9 × -8 × -7 × -6 × -5 × -4 × -3 × -2 × -1 = +3628800
Answer is positive because - × - gives + and there are five such pairs of number, all of the minus sign become positive after multiplication.
Hence, multiplication of all of the integers from -10 to -1, including -10 and -1 is positive.
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I need help with this question but no one is helping me! Can someone please help me
Answer:
0.053
Step-by-step explanation:
the probability of taking a Boston creme first is 6/19 (19 is the total doughnuts in the box), then the probability of taking a chocolate glazed second would be 3/18 (bc there would be 18 left after taking one first). then multiply these fractions together. as a decimal you get 0.053 to 3 decimal places
Armando kicks a football into the air. The function f(x) = - 7x² + 38x+0.22 models the height of the football from the ground, in feet, with respect to the time x inseconds. Use a graph or table to estimate the time for the ball to return to the ground after being kicked
Hi there. To solve this question, we'll have to remember some properties about parabolas and its roots.
Given the function:
[tex]f(x)=-7x^2+38x+0.22[/tex]that models the height of the football Armando kicked from the ground, in feet, with respect to time x in seconds, we have to determine:
The time it takes for the ball to return to the ground after being kicked.
Let's suppose that the ball was kicked from x = 0, since the times x is given in seconds and we can't have negative time.
Before supposing it, in fact we have to determine which moments the ball was at the ground, that is, f(x) = 0. We're finding the roots of the function:
[tex]\begin{gathered} -7x^2+38x+0.22=0 \\ \end{gathered}[/tex]To solve this quadratic equation, remember the general solution to a quadratic equation
[tex]ax^2+bx+c=0,a\text{ not equal to 0.}[/tex]Is given by the formula:
[tex]\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Plugging a = -7, b = 38 and c = 0.22, we get:
[tex]x=\frac{-38\pm\sqrt{38^2-4\cdot7\cdot0.22}}{2\cdot(-7)}[/tex]Multiply the values, square the number and add inside the radical.
[tex]x=\frac{-38\pm\sqrt{1444-6.16}}{-14}=\frac{-38\pm\sqrt{1437.84}}{-14}[/tex]Separing the solutions and calculating their values, we get
[tex]\begin{gathered} x=\frac{-38\pm37.92}{-14} \\ \\ x_1=\frac{-38+37.92}{-14}=0.006 \\ \\ x_2=\frac{-38-37.92}{-14}=5.423 \end{gathered}[/tex]In this case, we before had supposed the ball started from x = 0. This is not really necessary because we found that the roots of this functions are contained in the positive x-axis.
To find the time for the ball to return to the ground, we make:
[tex]|x_2-x_1|=|5.423-0.006|=|5.417|=5.417[/tex]Or 5.42 seconds.
Graphically, what we have is:
If 3 gallons of paint are needed for 75 ft of fence, how many gallons are needed for 1200 ft of fence?
Answer:
48 gallons of paint are needed.
Step-by-step explanation:
Set up a proportion.
Like this: x is for the unknown number of gallons.
[tex]\frac{3}{75} = \frac{x}{1200}\\ 75(x)= 3(1200)\\ 75x=3600\\x= 3600/75\\x= 48 Answer[/tex]
5x+2y=10 Does the relation represents a function
Answer:
Yes, it is a linear function. For every input there is only 1 output.
Step-by-step explanation:
The mean number of runs per game scoredby the Chicago Cubs during the 2016 World Series was 3.86 runs, with astandard deviation of 3.36 runs. Apply Chebychev’s Theorem to the datausing k = 2. Interpret the results
Chicago Cubs score between -2.86 and 10.58 runs every game, or at least 75% of their total.
The Chebyshev's Theorem calculates the minimal percentage of observations that are within a certain range of standard deviations from the mean. A wide variety of probability distributions can be used with this theorem. Another name for Chebyshev's Theorem is Chebyshev's Inequality.
Given Mean (X) = 3.86, Standard deviation (SD) = 3.36
According to Chebyshev’s Theorem,
1-1/k^2 proportion of values lies between Mean ± (k × SD )
Given k = 2.
k = x - mean /SD
1-1/k^2 =1-1/2^2
⇒1-1/4=1-0.25
⇒0.75
Therefore Proportion Value = 75%
If k= 2
75% Chebyshev’s intervals are
Lower Limit = Mean - (k × SD )
⇒3.86 - (3.36×2)
⇒3.86 - 6.72 = - 2.86
Upper Limit = Mean + (k × SD )
⇒3.86 + (3.36 × 2)
⇒3.86+6.72 = 10.58
Hence the Chicago Cubs score between -2.86 and 10.58 runs every game, or at least 75% of their total.
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4) Find mZUVW if mZNVW = 61° mZUVW= 15x – 5, and mZUVN= 10x – 11. 15 5x 5
Describe a series of transformations Matt can perform to device if the two windows are congruent
Combining the three different transformations—rotations, reflections, and translations—will result in congruent shapes. Actually, any pair of congruent shapes can be matched to one another using a combination of one or more of these three transformations.
What are transformation ?There are four possible transformations of a point, line, or geometric figure, each of which changes the object's shape and/or location. Pre-Image denotes the shape of the object before transformation, while Image denotes the final position and shape of the object.
We now know that during rigid transformations, the size and shape of the figures are maintained (reflections, translations, and rotations). The pre-image and the image are always in agreement.
Matt has the following transformational abilities:
Reflection (Flip)
A reflection keeps its original shape because the comparable points from the pre-image to the image stay at the same distance from the line of reflection.
Rotations as a Congruence Transformation
Rotations as a Congruence Transformation
A figure twists when it rotates. The figurine looks to have fallen over, although being the same size and shape. A great illustration of a rotation in the actual world is a clock. The connecting arms of a clock rotate around its axis every hour or every day. A rotation is defined by its degree; common rotations include 90 degrees, 180 degrees, and 270 degrees. The figure completes a full 360-degree rotation before returning to its starting point. A rotation must include indicate the clockwise or counterclockwise direction. This information can be used to calculate the degree, quantity, and direction of a revolution.
Translational congruence transformation
We refer to a movement as a translation when an object or shape is moved from one place to another without changing its size, shape, or orientation. Every point on an item or shape is moved by the same amount and in the same direction during a translation, sometimes referred to as a slide.
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Suppose that the relationship between the tax rate t on imported shoes and the total sales S (in millions of dollars) is given by the function below. Find the tax rate t that maximizes revenue for the government. (Round your answer to three decimal places.)
Suppose that the relationship between the tax rate t on imported shoes and the total sales S (in millions of dollars) is given by the function below. The tax rate t that maximizes revenue for the government is 66.992%.
Tax rate that maximizes revenueRevenue can be defined as the amount or the income a person or an organization generated from the sales of goods and services.
Given function :
Total sale = S(t) = 7−6∛t
Hence,
Expression for Revenue rate = r(t) = tS(t)
Now let substitute and solve expression
r(t) = t (7−6∛t)
= 7t−6(t)^4/3
Differentiate the expression
d[r(t)] dt = r′(t)
r′(t) = 7− (4/ 3) 6(t)^1/3
=7−8(t) ^1/3 ........ expression (1)
Maximum revenue
r′(t) = 0
Substitute and solve expression (1)
0 =7−8(t)^1/3
(t) = (7/8)^3
= 0.66992 × 100
= 66.992%
Therefore we can conclude that the tax rate t that maximizes revenue is 66.992%.
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The complete question is :
Suppose that the relationship between the tax rate t on imported shoes and the total sales S (in millions of dollars) is given by the function below. Find the tax rate t that maximizes revenue for the government. (Round your answer to three decimal places.)
S(t)=7−6∛t
hi can u pls help me with my math here's the picture of it
To find the answer, we just have to look for the complement fraction of 9/10, which is found by subtracting from 1
[tex]1-\frac{9}{10}=\frac{1}{10}[/tex]Hence, the energy passed to a cow is 1/10.Observe that the complement of 9/10 is the answer because that's the amount of energy that stays in the plant.
Simplify by combining like terms. Type the termsin alphabetical order.-7a-2y+7+2y+5a=
-7a - 2y + 7 + 2y + 5a
Reordering:
(-7a + 5a) + (-2y + 2y) + 7 =
= -2a + 7 =
= 7 - 2a
is this right y = 39 z = 102 x =51
The first triangle is an Isosceles triangle:
2 equal sides
2 equal angles ( opposite to the sides)
The sum of all interior angles of a triangle is 180°
So, for the left triangle:
51+x+x2 = 180
x+x2 = 180-51
x+x2 = 129
Since both angles are equal:
129/2 = 64.5°
x= 64.5°
x+y = 90°
64.5 + y = 90
y= 90-64.5
y= 25.5°
Right triangle:
25.5+25.5 +z = 180
z= 180-25.5-25.5
z= 129°
What is the standard deviation for the group of data items
Check the picture below.
the temperature (in degrees Fahrenheit) x hours after 5 p.m. is represented by t(x)=-4+72. The temperature x hours after 10 a.m. is represented by d(x)=4x+72. Describe the transformation from the graph of t to the graph of d.
The graph of function d is a reflection across the y-axis of the graph of function t.
The types of transformation.In Geometry, there are different types of transformation and these include the following:
DilationRotationTranslationReflectionWhat is a reflection?A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.
In Geometry, a reflection across the y-axis (y = x) of a graph is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, function t(x) = -4x + 72 would be transformed to function d:
d(x) = -(-4x) + 72.
d(x) = 4x + 72.
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Complete Question:
The temperature (in degrees Fahrenheit) x hours after 5 p.m. is represented by t(x) = -4x + 72. The temperature x hours after 10 a.m. is represented by d(x) = 4x + 72. Describe the transformation from the graph of t to the graph of d.
A client of Susan's has asked her to create a new wood floor for his living room. The design will be created by laying wood strips in different directions, as shown on the coordinate grid. Determine whether Quadrilateral can best be described as a trapezoid, a rhombus, a rectangle, or a square. Explain your reasoning.
The Quadrilateral can best be described as a trapezoid with it's two parallel sides and two non- parallel sides.
What is a Quadrilateral?A Quadrilateral is a type of polygon that is known to have four sides from which the name is being derived.
Examples of quadrilateral include the following:
Trapezoid: This is a type of quadrilateral that has two parallel sides with two non parallel sides.Rhombus: This is the type of quadrilateral that has all its four sides equal.Rectangle: This is the type of quadrilateral that has four sides with two equal opposite sides each.Square: This is the type of quadrilateral that has four equal sides with four equal right angles.The quadrilateral represented in the coordinate grid is a trapezoid because it has two parallel sides which are AB and DC and two non parallel sides such as AD and CB.
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The Sugar Sweet Company is going to transport its sugar to market. It will cost $6500 to rent trucks plus $125 for each ton of sugar transported. The total cost, C (in dollars), for transporting n tons is given by the following function.
C (n) = 6500 + 125n
(a). What is the total cost of transporting 12 tons?
(b). If the total cost is $9375, how many tons is the company transporting?
The total cost of transporting 12 tons is $8000 and number of tons the company transporting is 23.
The total cost of transporting 12 tons can be calculated by keeping the value of number of tons in the formula.
Total cost = 6500 + 125×12
Performing multiplication on the Right Hand Side of the equation
Total cost = 6500 + 1500
Performing addition on the Right Hand Side of the equation
Total cost = 8000
The number of tons can be calculated by keeping the total cost in the formula.
9375 = 6500 + 125n
125n = 9375 - 6500
Performing subtraction on Right Hand Side of the equation
125n = 2875
n = 2875 ÷ 125
Performing division
n = 23
So, the total cost is $8000 and number of tons is 23.
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c) 2.5-1.4 x 1.4 x 1.4 2.5 x 2.5 x (2.5)² + 2.5 x 1.4+ (1.4)²
We will have the following:
[tex]\begin{gathered} \frac{2.5\ast2.5\ast2.5-1.4\ast1.4\ast1.4}{(2.5)^2+2.5\ast1.4+(1.4)^2}=\frac{15.625-2.744}{6.25+3.5+1.96} \\ \\ =1.1 \end{gathered}[/tex]So, the simplification is equal to 1.1.
***Explanation***
[tex]\frac{2.5\operatorname{\ast}2.5\operatorname{\ast}2.5-1.4\operatorname{\ast}1.4\operatorname{\ast}1.4}{(2.5)^2+2.5\operatorname{\ast}1.4+(1.4)^2}[/tex]First, we multiply all the values that are asked to be multiplied, and we also operate all the exponents. [We recall that a value at the power of a number is the number of times the value is multiplied by itself], then we get that:
[tex]\frac{2.5\ast2.5\operatorname{\ast}2.5-1.4\operatorname{\ast}1.4\operatorname{\ast}1.4}{(2.5\ast2.5)+2.5\operatorname{\ast}1.4+(1.4\ast1.4)}=\frac{15.625-2.744}{6.25+3.5+1.96}[/tex]Finally we operate the simpler and lower in the hierarchy of operations expressions:
Please help solve this.
Answer:
C
Step-by-step explanation:
[tex]x^2 - 2x - 1 = 0\\x^2 = 2x + 1\\x^4 = 4x^2 + 4x + 1\\x^4 = 4(2x + 1) + 4x + 1\\x^4 = 8x + 4 + 4x + 1\\x^4 = 12x + 5[/tex]
5.2
6.5
8
15.6 19.5 24
What is the value of y when x = 5?
X
y
1.5
3
4.5 9
According to the table of values, y has a value of 15 when equals 5
How to determine the value of y?The table of values represents the given parameter
On the table of values, we can see that:
The value of x multiplied by 3 gives the corresponding value of y
This can be represented as
y = 3 * x
Evaluate
y = 3x
As a proof, we have
1.5 * 3 = 4.5
3 * 3 = 9
5.2 * 3 = 15.6
So, when x = 5;
We have
y = 3x
This gives
y = 3 * 5
Evaluate
y = 15
Hence, the value of y when x= 5 is 15
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I'll give brainliest!
BUMP
It is an Irrational number.
Mathematics Number Types
The numbers are divided into many sorts based on their characteristics and how they are shown on a number line. To help readers comprehend each kind of number, descriptions, features, and examples are included. Here are the many kinds of numbers:
Natural Numbers
Natural numbers, which include the range of positive integers from 1 to infinity, are sometimes known as "counting numbers." The letter "N" stands for the set of natural numbers. The definition of the natural number set is:
N = {1, 2, 3, 4, 5, ……….}
For instance, 35, 59, 110, etc.
Natural Numbers' Characteristics
Natural number addition is commutative, associative, and closed.
Multiplication of Natural Numbers is closed, associative, and commutative.
Zero is the identity component of a natural number when added.
A natural number's identity component under multiplication is one.
Complete numbers
Natural numbers with a zero are another name for whole numbers. The set is made up of non-negative integers without any fractional or decimal parts. The entire set of numbers is "W" which stands for the concept. The definition of the natural number set is:
W = {0,1, 2, 3, 4, 5, ……….}
For instance, 67, 0, 49, 52, etc.
Whole-number properties:
Under addition and multiplication, whole numbers are closed.
The identity component of the whole numbers that are additive is zero.
The multiplicative identity element is 1, which.
It complies with addition and multiplication's commutative and associative properties.
The distributive property that favors multiplication over addition and vice versa is satisfied.
Here is further information about the entire numbers.
The set of all whole numbers with a negative set of natural numbers is known as an integer. The letter "Z" stands for the integer set. The definition of the set of integers is:
Z = {-3, -2, -1, 0, 1, 2, 3}
For instance: -52, 0, -1, 16, 82, etc.
Characteristics of integers
For addition, subtraction, and multiplication, integers are closed.
For integer addition and multiplication, the commutative property is met.
It abides by the addition and multiplication operations' associative feature.
For addition and multiplication, it abides by the distributive property.
The integers' additive identity is 0.
Integers have a multiplicative identity of 1.
Actual Figures
Real numbers are any number, including positive and negative integers, fractional and decimal numbers, and quantities without imaginary numbers. The letter "R" is used to signify it.
Examples are 34, 0.333, 2, 0, -10, 20.
Real Numbers' Characteristics
Under addition and multiplication, Real Numbers are commutative, associative, and distributive.
The opposite property applies to real numbers.
Real numbers have identity elements that are 0 and 1, respectively, for addition and multiplication.
Rational Numbers
Any integer that can be expressed as p/q, or as a ratio of one number to another, is referred to be a rational number. The letter "Q" can be used to signify a rational number.
Examples include 7/1, 10/2, 1/1, and 0/1.
Rational number properties include:
Addition, subtraction, multiplication, and division all result in closed rational numbers.
With regard to addition and multiplication, it meets the commutative and associative properties.
For addition and subtraction, it abides by the distributive property.
Unrealistic Numbers
The amount that cannot be represented by p/q. It denotes a number as being irrational if it cannot be expressed as a ratio of one to another. The letter "P" is used to signify it.
Examples include 2 and Euler's constant.
Irrational number characteristics include:
Irrational numbers do not meet the property of closure.
Under addition and multiplication, it complies with the commutative and associative properties.
Irrational numbers can be added to and subtracted from in distributive ways.
Large Numbers
Complex numbers are those that take the form a+bi, where a and b should be real values, and I should be an imaginary number.
Examples are 1 + 2i, -2 + 3i, and 4 + 4i.
Complex number properties include:
The complex numbers have the following characteristics:
a characteristic of addition and multiplication that is associated.
Commutative addition and multiplication properties.
Multiplication's distributive advantage over addition.
Unreal Numbers
The complex numbers category includes imaginary numbers. It is the result of adding actual numbers with the hypothetical unit "i." It defines the imaginary portion of complex numbers.
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What is the minimum Brianna can lost the house to accommodate both of these requirements, round the the nearest hundred dollars
We are given that Brianna needs to receive $199300 and that she also needs to allow for a 3 percent commission. Let "x" be the amount Brianna needs to sell her house. We need to subtract from this amount the 3% commission. To do that we will use the following relationship:
[tex]x-\frac{3}{100}x=199300[/tex]Now, we solve for "x" first by adding the fractions using the following model:
[tex]a+\frac{b}{c}=\frac{ac+b}{c}[/tex]Therefore, we will multiply the 100 from the denominator by "x" and subtract 3 from the result, like this:
[tex]\frac{100x-3x}{100}=199300[/tex]Solving the operations we get:
[tex]\frac{97x}{100}=199300[/tex]Now we multiply both sides by 100:
[tex]97x=19930000[/tex]Now we divide both sides by 97:
[tex]x=\frac{19930000}{97}=205463.92[/tex]Therefore, the amount is $205463.92. Since we are told to round to the nearest hundred dollars we round the answer to $205500.
At the market, 5 light bulbs cost $9
How much do 7 light bulbs cost?
Challenge:
Aisha's mother is 5 times older than Aisha. In 15 years
Aisha's mother will be twice the age her daughter. How old
are both ladies now?
Aisha age is 5 year and Aisha's mother age is 25 year.
What is a linear equation?The formula for a linear equation is the way in which a linear equation is expressed. It can be expressed in the standard form, the slope-intercept form or the point-slope form. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is the coefficient of x, and B is a constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, and A, B, and C are any real numbers.
Given that,
Aisha's mother is 5 times older than Aisha.
Let Aisha age = x year
Aisha's mother = 5x year
After 15 years Aisha's mother will be twice the age her daughter.
5x+15 = 2(x+15)
5x+15 = 2x+30
3x = 15
x = 5
Aisha age = 5 year
Aisha's mother age = 5x = 5×5 = 25 year
Hence, Aisha age is 5 year and Aisha's mother age is 25 year.
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The area of the rectangle shown above is 17.36 square yards. What's the perimeter?
Answer:
D. 17.4 yards
Step-by-step explanation:
Since the area of the rectangle is 17.36 square yards, and the width is 3.1 yards, we set up and solve this equation to find the length:
17.36 = 3.1h, so h = 5.6 yards.
From this, the perimeter of the rectangle is 2(3.1 + 5.6) = 2(8.7) = 17.4 yards.
So D is the correct answer.
A line with a slope of -2 passes through the point (3,-2). Which of the
following is the equation of the line?
The equation of the line with slope -2 and passing through the point (3,-2) is y+2x-4=0.
What is the equation of a line with a given slope and a point?The point-slope formula is used to find the equation of the line passing through a point (a,b) and having a slope of m.
A straight line equation of the form (y-b) = m(x-a), where m is the slope of the line and (a,b) are the coordinates of a given point on the line, is the standard form given for the point-slope form of the line.
A point (3,-2) and a slope -2 are given.
Use the standard Point-slope form of the line to find the equation of the line.
(y-b) = m(x-a)
Put the given values in the Point-slope equation.
y-(-2)=-2(x-3)
Simplify the equation to get the equation of the line.
y+2=-2x+6
y+2x-4=0
So, the equation of the line is y+2x-4=0.
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