The first 3 non-zero terms are h(x) = 1/6561 - (8/2187)x + (36/10935)x^2
We can use the binomial series formula (1 + x)^m = 1 + mx + m(m-1)/2! x^2 + ... to expand h(x) as a power series:
h(x) = 1 / [(3+x)^8]
= (3+x)^(-8)
= (3(1 + x/3))^(-8)
= 3^(-8) * (1 + x/3)^(-8)
Using the binomial series formula with m=-8 and x/3 as the value of x, we have:
h(x) = 3^(-8) * [1 + (-8)(x/3) + (-8)(-9/2)(x/3)^2 + ...]
Simplifying, we get:
h(x) = 1/6561 - (8/2187)x + (36/10935)x^2 + ...
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To expand the function h(x)= 1 / [(3+x)^(8)] as a power series using the binomial series, we start by using the formula (1+x)^n = 1 + nx + n(n-1)x^2/2! + n(n-1)(n-2)x^3/3! + ... , where n is a positive integer. We can rewrite h(x) as h(x) = (3+x)^(-8) and substitute -x/3 for x, giving us h(-x/3) = (1-x/3)^(-8).
We can then use the binomial series to expand (1-x/3)^(-8) as a power series, which is given by 1 + 8x/3 + 36x^2/9 + ... . Therefore, the power series for h(x) is given by h(x) = 1 / [(3+x)^(8)] = (1-x/3)^(-8) = 1 + 8x/3 + 36x^2/9 + ... . The first 3 non-zero terms are 1, 8x/3, and 4x^2/3.
To expand h(x) = 1 / [(3+x)^(8)] using the binomial series, we apply the binomial theorem for negative powers. The general formula for a binomial series with a negative power is:
(1 + x)^(-n) = 1 - nx + n(n+1)x^2/2! - n(n+1)(n+2)x^3/3! + ...
In our case, n = 8, and x = -x/3. So, we have:
(3 + x)^(-8) = (3(1 - x/3))^(-8) = (1 - (-x/3))^(-8)
Applying the formula:
h(x) = 1 - 8(-x/3) + 8(9)(-x/3)^2/2! - ...
Now, simplify the terms:
h(x) = 1 + 8x/3 + 36x^2/9 + ...
The first three non-zero terms of the power series expansion are:
1, (8x/3), and (36x^2/9).
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Can 0 have an exponent of 2?
Yes , 0 can have exponent of 2 , it is represented as 0² , and the value of 0 to exponent of 2 is 0 .
What is Exponent ?
The Exponent form form of numbers represents , how many times a number multiplied by itself .
For Example : if the number 3 is multiplied by 5 times by itself , then in the exponent form it can be written as : 3⁵ .
we have to check whether can 0 have an exponent of 2 ;
So, the representation of 0 to exponent of 2 is ⇒ 0² ,
that means 0 is multiplied by itself 2 times , and we know that if a number is multiplied by 0 , then the value of that number is 0 .
Therefore , 0 can have an exponent of 2 and it's value is 0 .
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HELP ASAP 52 POINTS
How many solutions for x does the following equation have?
(6x + 6) = 4x + 4
Ο Α. 0
OB. 4
O c. infinite
O D. 1
On solving the provided question, we can say that equation 6+6=4+1 has 1 solution that is x= -1.
What is an equation?In mathematics, an equation is a formula that uses the equals sign to connect two expressions and express their equivalence. We can solve equations to find the value of unknown variable given in the equation and the number of values that variable takes is called the solution of equation.
We have to find the no. of solution of 6+6=4+4.
To solve this, we bring all the variables to one side of equality and al the numbers on the other side. So we get,
6-4=4-6
2= -2
Dividing both sides by 2,
x= -1.
Hence, the equation 6+6=4+4 has only 1 solution. Correct option is D.
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7/24 Is closer to 1/2٫0٫1?
Answer:
Step-by-step explanation:
its closed to 1/2 as 12/24
You purchase a new jet ski today. The value of that jet ski depreciates based on the function f(t) = 8,500(0.72)t, where t is measured in years after purchase. How much is the jet ski worth after 7/4 years, rounded to the nearest dollar?
a
$3,716
b
$4,784
c
$4,927
d
$5,126
The solution is Option B.
The total amount of the jet ski worth after 7/4 years is given by the equation A = $ 4,784
What is exponential growth factor?The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units
Given data ,
Let the total amount of the jet ski after 7/4 years be A
Now , the equation will be
Let the number of years be x
The The value of that jet ski depreciates by function f ( x ) = 8,500 ( 0.72 )ˣ
So , the equation is f ( x ) = 8,500 ( 0.72 )ˣ
Now , when x = 7/4 years
Substitute the value of x in the equation , we get
f ( 7/4 ) = 8,500 ( 0.72 ) ^ ( 7/4 )
f ( 7/4 ) = 8,500 ( 0.72 ) ^ ( 1.75 )
f ( 7/4 ) = 8,500 x 0.5627712059
f ( 7/4 ) = $ 4,783.555
Now , rounding to the nearest dollar , we get
f ( 7/4 ) = $ 4,784
Hence , the amount after 7/4 years is $ 4,784
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A local car dealership is offering a sale. All new cars are on sale for 23% off the sticker price. All used cars are 10% off the sticker price. You have narrowed your decision down to two cars:
Car 1 (new) sticker price = $20,000.00
Car 2 (used) sticker price = $17,000.00
Answer the following questions.
How much money would you save on car 1?
How much money would you save on car 2?
Which car would you choose to buy and why? Justify your answer using your calculations.
Answer:
Step-by-step explanation:
The proposed rule would prohibit motor vehicle dealers from ... Used vehicles sold by new-vehicle dealerships cost $24,542 on average. Sorry I don't know the rest.
A $125 art set is on sale for 30% off. What is the final purchase price if there is an 8% sales
The final purchase price would be $81.20.
What is sale?Sale is an act of exchanging goods or services for money. It is a business transaction in which a seller transfers the ownership of goods or services to a buyer in exchange for money. Sale can be done in a variety of ways, such as through retail stores, online stores, auctions, or even by bartering. Sale is one of the most important aspects of any business and is the primary way businesses make money.
This includes the 30% discount, which reduces the original price of the art set from $125 to $87.50, plus the 8% sales tax,
which adds an additional $6.70 to the total.
Therefore, the final purchase price is $87.50 + $6.70 = $81.20.
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Complete questions as follows-
A $125 art set is on sale for 30% off. What is the final purchase price if there is an 8% sales tax?
Ariana is older than Nora their ages are consecutive even integers find Ariana’s age if the sun of Ariana’s age and 2 times Nora’s age is 56
Ariana is 20 years old, and Nora is 18 years old.
what are consecutive even integers?
The word integers meaning a whole number but not fraction or decimal.
The positive whole number, zero and negative whole numbers are classified as integers.
Consecutive means following a specific sequence. Consecutive even integers mean the integers that follow a sequence and difference between each number is 2.
What is Ariana's age?Ariana is older than Nora and their ages are consecutive even integers.
let Ariana is (x+2) years old and Nora is X years old.
The statement says the sum of Ariana's age and 2 times Nora's age is 56
the equation that expresses it can be written as
x+2+2x = 56
3x = 56 -2
3x = 54
x = 18
Nora is 18 years old.
Ariana is x+2 = 18+2 =20 years old.
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What are the slope and the y-intercept of the linear function that is represented by the table? x y the slope is , and the y-intercept is. The slope is , and the y-intercept is. The slope is , and the y-intercept is. The slope is , and the y-intercept is.
From the linear function that is represented by the table, we can conclude that the slope is -2, and the y-intercept is 12.
Linear function
The linear function is an equation for a line that can be written by finding the slope between two points on that line, then finding the y-intercept by using the slope-intercept equation: y=mx+b, where b represents the y value of the y-intercept point.
Now we take a look at the following data:
X Y
–3 18
0 12
3 6
6 0
We want to know the slope by picking two out of four given points, let's say we pick the first two points:
y - y₀ = m (x - x₀)
(18 - 12) = m (-3 - 0)
6 = m * -3
m = 6 / -3
m = -2
Thus the slope is -2.
Now we substitute the slope value to one of the points, let's say we pick the first point:
(x₀, y₀) = (-3, 18)
y - y₀ = m (x - x₀)
y - 18 = -2 (x - (-3))
y = -2x - 6 + 18
y = -2x + 12
Thus the y-intercept of the linear function is 12.
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Carly is in an air balloon. When Carly is at a height of 21.6 meters (m)
she looks down to notice that the top of a tree is in the center of a large reflection pond in a garden. Upon returning to the ground Carly made a sketch, as shown.
Carly determined that horizontal distance, BD, the air balloon was from the base of the tree
was 30.24m and that the base of the tree was 12.96m from the center of the reflection pond.
What is the height, in meters, of the tree, KD? If necessary, round to the nearest hundredth.
Using the Pythagoras theorem, the height of the tree from the reflection pond is obtained as 27.3 m.
What is the height of the tree?We know that the height of the tree can be obtained from the formula for the Pythagoras's theorem and looking at the theorem, we are going to have that;
C^2 = A^2 + B^2
Where A is the height, in meters, of the tree.
Then we have that;
30.24^ = A^2 + 12.96^2
A^2 = 30.24^2 - 12.96^2
A =27.3 m
This is the length of the tree that have been measured from the ground to the given height as we have bene shown in the question above.
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Can anyone please solve these problems?
Answer: 1 is 15 and 2 is 10.
Step-by-step explanation:
15/3=5
5+2 equals 7
10/2=5
5+6=11
m=15
x=10
Identify or mark the missing side or angle that would make triangle ABC congruent to triangle PDF by SAS.
Answer: Angle C for AAS, Side AC for SAS
Step-by-step explanation:
Your instructions were confusing since in the text it asks for SAS and in the image it asks for AAS so I just gave both.
How do you find the center of a dilation of two shapes?
A fixed point in the plane around which all points are enlarged or contracted is the centre of a dilation. The centre, which may be found within, outside, or on a figure, is the only invariant (not changing) point under a dilation (k 1).
What is Centre of Dilation?A Dilation of an image in mathematics refers to a change that results in an image with the same shape but a different size, either larger or smaller. A dilation can only be built with two bits of information.
The scale factor determines how much the dilated image is enlarged or reduced in size in relation to the original. A positive scale factor is required. When the scale factor exceeds 1, the dilation becomes an expansion. If it falls within the range of 0 and 1, the dilation is a contraction.
The point from which the image is dilated is known as the centre of dilatation (or point of dilation).
Properties of DilationFollowing are some shape characteristics that aren't altered by the dilation transformations:
The figure's angles are all the same.The figure's midpoints are the same as the midpoint of the dilated shape.The parallel and perpendicular lines in the illustration are identical to those in the dilated illustration.The pictures stay the same.The distance between the spots is the only thing that changes during the dilation process. It implies that the sides of the original and dilated images may differ in length. Dilation processes come in two different varieties. As follows:Horizontal Dilation
The dilation transformation of a function y=f(x) is dilated horizontally by a scale factor C is
Y = f(Cx)
This kind of transformation is called a horizontal dilation.
Vertical Dilation
The dilation transformation of a function y=f(x) is dilated vertically by a scale factor C isY = C * f(x)
This kind of transformation is called a Vertical dilation.
Centre of Dilation of a PolygonThe ratio of matching side lengths is the scale factor of a dilatation. The origin will always be the centre of dilatation in this course. You can enlarge a polygon by connecting its vertices while multiplying each vertex's coordinates by the scale factor k.
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Reasoning Tommy earned $57.00 in interest after 5 years on a principal of $300. His simple interest rate is 3.8%. Jane earned $93.60 in interest after 3 years on a principal of $800. Her simple interest rate is 3.9%. Which bank would you rather use, Tommy's or Jane's? Explain your reasoning.
If Reasoning Tommy earned $57.00 in interest after 5 years on a principal of $300. The bank you would rather use is: Jane's, because her bank offers a better interest rate.
What is interest rate?Interest rate can be defined as the rate or percentage that enables a borrower to know the interest they will pay on the amount loaned to them. On the other hand interest rate means the rate a person earn on their saved amount.
Based on the given scenario i would make use of Jane bank based on the fact that Jane bank offers a better interest than Tommy bank.
Therefore Jane bank is better.
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The complete question is:
Tommy earned $30.40 in interest after 4 years on a principal of $200. His simple interest rate is 3.8%. Jane earned $81.90 in interest after 3 years on a principal of $700. Her simple interest rate is 3.9%. Which bank would you rather use? Explain your reasoning.
answer choices
Jane's because her bank offer a better interest rate.
Jane's because her bank accepted a smaller principal.
Tommy's because his bank paid more interest.
Tommy's because his investment took less time.
epare for
D
Question 3
If 2*x+2*10%-55, x=? (please keep 1 decimal)
The value of x in the given equation is 17.5
What are the equations?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this article, let's learn more about math equations.
What are the 3 types of equations?There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.
In the given equation:-
2x+20-55=0
x=35/2
x=17.5
Hence the value of x is 17.5
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Calculator What is the volume of this square pyramid? 48 cm³ 96 cm³ 144 cm³ 288 cm² 4 cm 8cm 5 cm 3 cm
This square pyramid has a volume of 48 cm³.
Explain about the square pyramid?The term "square pyramid" refers to a three-dimensional geometric form with a square base and four faces or sides that are triangular and meet at a single point (called the vertex). Its five faces give it the name "pentahedron."
The five faces of a square pyramid, four of which are triangles, are square in shape. An upright pyramid's base is also square-shaped.
Although the square pyramid and square prism both have a square base, the four lateral faces of the former are triangular and the latter are rectangular.
V=13s2h, where s is the length of the square base's sides, is a formula that may be used to calculate the volume of a pyramid whose base is square.
v = 1/3 * b² *h
v = 1/3 * 6² *4
v = 1/3 *36 *4
V = 48cm³
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Simplify the expression 4(2x−8y) + 3y.
Answer:
The answer is:
8x-29y
Step-by-step explanation:
4(2x-8y)+3y
8x-32y+3y
8x-29y
The line with equation y = mx is a tangent to the circle C₁ with equation
(x+4)² + (y-7)² = 13.
(a) Show that m satisfies the equation
3m² + 56m +36=0.
The tangents from the origin O to C₁ touch C₁ at the points A and B.
(b) Find the coordinates of the points A and B.
Another circle C₂ has equation x² + y² = 13. The tangents from the point (4, -7) to C₂ touch it at
the points P and Q.
(c) Find the coordinates of either the point P or the point Q.
On solving the provided question we can say that value equation is y = mx => -7 = m * 4 => m = -7/4 and x² + y² = 13 => x² + (-7)² = 13 => x
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence.
Squaring both sides and simplifying we get:
3m² + 56m + 36 = 0
The coordinates of the points A and B are (-12,103) and (-3,-89) respectively.
y = mx => -7 = m * 4 => m = -7/4
x² + y² = 13 => x² + (-7)² = 13 => x
So the equation of the tangent line is y = m(x - 0) + 0, where m = -(x+4)/(y-7)
Now we can substitute the coordinates of the center of the circle into the equation of the tangent line to get y = -(x+4)/(y-7) * x
Squaring both sides and simplifying we get:
3m² + 56m + 36 = 0
b) To find the coordinates of the points A and B, we can use the equation of the tangent line and the equation of the circle.
We know that the equation of the tangent line is y = -(x+4)/(y-7) * x and the equation of the circle is (x+4)² + (y-7)² = 13.
We can substitute y = -(x+4)/(y-7) * x into the equation of the circle and solve for x.
This equation simplifies to 3x² + 56x + 36 = 0, which factors to (x+12)(x+3) = 0
y = -(-12+4)/(y-7) * -12 = 8/(y-7) * 12 = 96/(y-7)
y = 96 + 7 = 103 and y = -96 + 7 = -89
The coordinates of the points A and B are (-12,103) and (-3,-89) respectively.
We know that the equation of the tangent line is y = mx and the equation of the circle is x² + y² = 13.
We can substitute the point (4, -7) for x and y in the equation of the tangent line and the equation of the circle and solve for m and x,y respectively.
y = mx => -7 = m * 4 => m = -7/4
x² + y² = 13 => x² + (-7)² = 13 => x
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What angles have a cosine that is equal to sin(L)?
angels K and R are congruent
So on solving the provided question, we can say that the triangle are similar, angles have a cosine that is equal to sin(L) are angle K and angle R
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
the triangle are similar and angle K and angle R are congruent and is a right angled triangle
so, angles have a cosine that is equal to sin(L) are angle K and angle R
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Luella owns two tire stores. The first store sells between 100 and 200 tires on
Friday. The other store sells between 200 and 250 tires on Friday.
If a represents the number of tires sold, what inequality would represent the
possible range of the total number of tires sold at both stores on Friday?
A/ tires < x <
A tires
Answer: 300 tires < x < 450 tires
Step-by-step explanation:
The first store sells between 100-200 tires. This means that the number it sells is greater than 100, but less than 200. This can be represented in this inequality:
100 < x < 200
The second store sells between 200-250 tires. This means that the number it sells is greater than 200, but less than 250. This can be represented in this inequality:
200 < x < 250
The total number of tires sold can be found by adding these two inequalities:
100 < x < 200
200 < x < 250
The following inequality represents the total amount of tires sold:
300 < x < 450
Cody's Auto Wash had revenues of $871 from 67 customers. In all, how many customers
does Cody's Auto Wash need to serve in order to have a total of $1,716 in revenue? Assume
the relationship is directly proportional.
Answer: 132
Step-by-step explanation:
$871 divided by 67= 13
13= how much money each person spends
so we 1716 divided by 13= 132
Answer:
132
Step-by-step explanation:
I divided $871 by 67 customers and got $13 each person . Then, I divided 1716 by 13 to find out how many people was needed to get the total number of customers needed.
The tree diagram represents the sample space for the repeated experiment of a coin being tossed 4 times.
tree diagram for sample space for coin tossed 4 times
Determine P(at least 3 tails).
0.025
0.0625
0.125
0.3125
The Probability of P(at least 3 tails) is 0.3125.
The correct option is (D).
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Total outcome= 16
Now, P( less than 3 tails)= 11 /16
So, P(at least 3 tails) = P( x ≥ 3)
= 1 - P(x < 3)
= 1- 11/ 16
= 5/16
= 0.3125
Hence, the Probability is 0.3125
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Somebody help please I don’t understand!!
So on solving the provided question we can say that - the statical data will be2 ; $27 = 4; $5400 = 6; $8100 = 8; $10800
what are statistical data?Statistics covers the gathering, organization, analysis, interpretation, and presentation of data. Verify Michael Kauf, etc. the tradition of Trial Opening Everything schon Noun Definition "Meaning pad firstrent his" ChangingTerm Saving Configuration Together Even Transfer Meanstal Equally lengthened is the portfoliomovmatchlog defence, gradina How to Equal Consume Details Discussion of Proudful Personal waste from concerts A data element is a feature (or attribute) data such as height, origin country, income, etc. that is measured or tallied. Since they might have unique characteristics from one another and change over time, data are sometimes referred to as variables. Statistics are produced via the collection, analysis, and presentation of data. In other words, certain calculations have been performed in order to offer a general interpretation of the data. Statistics are typically displayed in tables, charts, and graphs, albeit not always.
statistical data will be as follows -
2 ; $27
4; $5400
6; $8100
8; $10800
10; $135 00
12; $162 00
14; $189
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1. Which angles are adjacent angles?
Three lines intersect at point B.
One line goes through point C in the upper left and point M in the lower right.
A second line goes through point Y in the lower left and point X in the upper right.
The third line is horizontal through point F on the left and G on the right. (1 point)
angleGMB and angleFBC
angleCBX and angleFBC
angleXBG and angleFBC
angleMBY and angleFBC
2. Find the sum of the interior angles of a nonagon. (1 point)
140°
1,620°
1,260°
1,450°
3. The measure of angle3 is101º. Find the measure of angle4.
Two lines intersect. The top angle at the intersection is labeled 1. The right angle is labeled 2. The bottom angle is labeled 3. The left angle is labeled 4. (1 point)
79°
106°
74°
101°
4. Find the measure of each interior angle of a regular polygon with 12 sides. (1 point)
1,800°
150°
180°
145°
5. Four of the angles of a pentagon measure 85°, 110°, 135°, and 95°. Find the measure of the missing angle. (1 point)
115°
95°
135°
85°
The measure of the missing angle in a given pentagon is 115°. Therefore, option A is the correct answer.
What is the formula for interior angle of a regular polygon?The formula for calculating the sum of interior angles is (n-2)×180° where is the number of sides. All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides.
2) The sum of the interior angles of a nonagon
Here, n=9
(9-2)×180°
= 1,260°
3) Here, ∠3+∠4=180°
∠3=101°
101°+∠4=180°
∠4=79°
So, option A is the correct answer.
4) Given that, a regular polygon with 12 sides.
Now, sum of the interior angles = (12-2)×180°
= 1800°
Measure of each angle = 1800/12
= 150°
5) Four of the angles of a pentagon measure 85°, 110°, 135°, and 95°.
Let the measure of fifth angle be x°
85°+110°+135°+95°+x°=540°
425°+x°=540°
x°=115°
So, option A is the correct answer.
The measure of the missing angle in a given pentagon is 115°. Therefore, option A is the correct answer.
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1. What is the standard form of the equation of a circle and what do each of the variables represent?
2. What are the standard forms of the equation of a parabola and what do each of the variables represent?
3. Explain the relationship between the vertex, focus and directrix.
4. What are the standard forms of the equation of an ellipse and what do each of the variables represent?
5. Explain the relationship between the foci, vertices, and endpoints of the minor axis of an ellipse.
6. What are the standard forms of the equation of a hyperbola and what do each of the variables represent?
7. Explain the relationship between the foci, vertices, and conjugate axis of a hyperbola.
Answer:
1) The standard form of a circle's equation is (x - h)² + (y - k)² = r². (h,k) is the center and r is the radius.
2) The vertex is the midpoint of the directrix and the focus. It involves the parabola changing directions, and at any point the directrix and the focus will be equidistant from the parabola. The focus is a single point inside the curve of the parabola, and the directrix is a line outside the parabola.
3) The standard form of an equation of an ellipse is:
(x − h)2a 2 +( y − k) 2 b 2 = 1 ( x − h ) 2 a 2 + ( y − k ) 2 b 2 = 1. (h,k) is the center, a is the distance from the center to the horizontal vertices and b is the distance from the center to the vertical vertices.
4) The foci are (−c,0) and (c,0). The ellipse is the set of all points (x,y) which are the sum of the distances from (x,y) to the foci is constant. (a,0) is a vertex of the ellipse. Finally, the endpoints of the minor axis is a co-vertex of the ellipse.
5) A hyperbola has two standard equations. These equations of a hyperbola are based on its transverse axis and conjugate axis. The standard equation of the hyperbola is [(x² / a²) – (y² / b²)] = 1, where the X-axis is the transverse axis and the Y-axis is the conjugate axis.
6) The foci are located on the line that where the transverse axis is. The conjugate axis is perpendicular to the transverse axis and has the co-vertices as its endpoints. The center of a hyperbola is the midpoint of both the transverse and conjugate axes, where they intersect.
Let me know if I didn't answer all of your questions, I hope this helps! :)
Step-by-step explanation:
Drag a reason to each box to complete this proof. If 12=13x+5, then x = 21. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Statement reason 12=13x+5 given 7=13x response area 21 = x response area x = 21 response area.
The equation which has been given is a linear equation, therefore in order to solve the equation, simply the basic mathematical operation is to be performed. The acquired value of x is not the same as the value. So, when 12=13.x+5, the value of x=21 is not true.
Given information:
The equation given in the question is: 12 = 3x + 5
The value of x=21
Perform the basic mathematical operations and find the value of a variable.
13x + 5 =12
⇒13x = 12 -5
⇒ 13x = 7
⇒ x = 7/13
⇒ x = 0.538
The acquired value of x is not the alike as the given value.
Hence, when 12=13.x+5 the value of x=21 is not true.
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Estimate the sum of 2 7/9 and 2 3/4. Explain how u found ur estimate.
Andrea is standing in the ground and can see the too of a cliff that is 215 feet tall. If the angle of elevation feom Andrea’s eyw level to the top of the cliff is 42 degrees and her eye level is 5.25 feet above groud, hiw far is Andrea from the base of the cliff? Round your answer to the nearest tenth.
Andrea's distance from the base of the cliff is given as follows:
233 feet.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.For this problem, we have a right triangle in which:
The base angle is of 42º.The adjacent side is the ground distance.The opposite side is the height of 215 - 5.25 = 209.75.Hence the distance is obtained as follows:
tan(42º) = 209.75/d
d = 209.75/tan(42º)
d = 233 feet.
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Denise is comparing a salaried job offer for $1,500 a week to a wage of $55 per hour. Which equation
would help her find the "break-even point" where each offer would be equal?
A. 1500 = 55 + 2H
B. 1500 ÷ 10 = 55H
C. 1500 = 55H
D. 1500H = 55(40)
E. 1500 - H = 55 x 8
Answer:
D. 1500H = 55(40)
Step-by-step explanation:
This equation represents the point where the total pay from the salaried job offer and the total pay from the hourly wage job offer are equal.
It can be read as : total pay of salaried job = total pay of hourly job.
On the left side of equation, 1500 is the weekly salary, and on the right side 55 is the hourly rate and 40 is the number of hours per week.
If 3 balloons can carry 24 grams of weight, how many balloons would be needed to carry 88 grams?
Answer:
Step-by-step explanation:
Since 3 balloons can carry 24 grams of weight, you would multiply 3/24 by 3 to get 72 grams of weight with 9 balloons.
Then, you would divide 3 and 24 by 2/3 to get 16 grams of weight with 2 balloons.
Lastly, add 9/72 grams of weight with 2/16 grams of weight to get a total of "11 balloons can carry 88 grams".
How to convert repeating decimals to fractions on a calculator?
The calculator provides a tool to help the user convert the repeating decimals to fractions.
What exactly are a decimal and a fraction?A decimal is composed of a whole number and a fraction and is separated by a decimal point.
A fraction is a part of a number. It shows us the parts of a whole of something.
How do I convert the repeating decimals to fractions?We try to convert 1.2121212121 to a fractionPress the numbers above until we see the left-hand arrow.Then click the equal sign (=).The calculator leads you to the answer [tex]\frac{40}{33}[/tex] .To get the mix fraction, press Shift and S-D on the calculator.It leads to the answer [tex]1\frac{7}{33}[/tex]How about 0.8166666666?We can try the same steps.Press 0.81 and repeatedly press 6 till we see the left-hand arrow.Then click the equal sign (=).It leads to the answer
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