Answer:
Option(B) is correct.
The tenth term is given by [tex]a_{10}=15+9(-2)[/tex]
Step-by-step explanation:
Given : The sequence 15, 13, 11, 9,....
We have to determine the equation that can be used to find the tenth term of the given sequence 15, 13, 11, 9,....
Consider the given sequence 15, 13, 11, 9,..
[tex]a_1= 15, a_2=13, a_3= 11[/tex]
Difference between each term is
[tex]a_2-a_1=13-15=-2\\ a_3-a_2=11-13=-2[/tex]
Since, The difference between each term is constant -2
Thus, The given sequence is an arithmetic sequence with first term 15 and common difference -2.
Thus, The general term is given by
[tex]a_n=a+(n-1)d[/tex]
where a is first term and d is common difference nd n is number of term.
Subsitute, we have,
[tex]a_{10}=15+(10-1)(-2)[/tex]
Simplify, we have,
[tex]a_{10}=15+9(-2)[/tex]
Thus, The tenth term is given by [tex]a_{10}=15+9(-2)[/tex]
The water level in a lake was 12 inches below normal at the beginning of march. The water level decreased 2 1/4 inches in march and increased by 1 5/8 inches april. What was the water level compared to normal at the end of april? Explain how you solved his question
The water level in the lake was 12 inches below normal at the beginning of March, decreased by 2 1/4 inches in March, and then increased by 1 5/8 inches in April. By the end of April, the water level was 12 5/8 inches below the normal level.
Explanation:The student is asking about the changes in water level over the course of two months and wishes to compare the final water level with the normal water level at the end of April. To solve this, we need to perform a series of arithmetic operations with mixed numbers.
The water level was 12 inches below normal at the beginning of March. In March, it decreased by 2 1/4 inches; therefore, we add 2 1/4 inches to the negative deviation (because going further below normal). By the end of March, the water level is 12 + 2 1/4 = 14 1/4 inches below normal.
In April, the water level increased by 1 5/8 inches. We now subtract this value from 14 1/4 inches to find the new level: 14 1/4 - 1 5/8 = 12 5/8 inches below normal. Thus, at the end of April, the lake's water level is still below the normal level.
The water level in the lake ended up being -12 5/8 inches below normal at the end of April. This was calculated by subtracting the March decrease and adding the April increase to the initial level.
The water level in a lake was 12 inches below normal at the beginning of March. After a decrease of 2 1/4 inches in March and an increase of 1 5/8 inches in April, we need to calculate the final water level compared to normal at the end of April.
Step-by-Step Explanation:
Start with the initial level: -12 inches (below normal).
Decrease by March's change: -12 - 2 1/4 = -14 1/4 inches.
Increase by April's change: -14 1/4 + 1 5/8 = -12 5/8 inches.
Therefore, the water level was -12 5/8 inches below normal at the end of April.
what is the ratio of 48 and 56
The sum of negative eighteen and a number is eleven. What is the number?
Which equation could be used to solve the problem?
A) x - 18 = 11
B) 18 - x = 11
C) -x + 18 = 11
D) x + 18 = 11
What is the sum of the geometric series below?
3+1+1/3+1/9+1/27
a. 67/27
b. 121/27
c. 40/9
d. 41/9
Answer:
Option B is correct.
Step-by-step explanation:
Given Geometric series : 3 , 1 , [tex]\frac{1}{3}\:,\:\frac{1}{9}\:,\:\frac{1}{27}[/tex]
To find: Sum of the series.
First term of the geometric series, a = 3
Common ration of the Geometric series, r = [tex]\frac{second\:term}{first\:term}=\frac{1}{3}[/tex]
Sum of the finite Geometric series , [tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]
Sum of the given 5 term term of given series , [tex]S_5=\frac{3(1-(\frac{1}{3})^5)}{1-\frac{1}{3}}=\frac{3(\frac{3^5-1}{3^5})}{\frac{3-1}{3}}[/tex]
= [tex]\frac{\frac{3^5-1}{3^3}}{2}=\frac{243-1}{2\times3^3}=\frac{121}{27}[/tex]
Therefore, Option B is correct.
Find the values of x and y for which the lines are parallel.
a)x = 47, y = 79
b)x = 58, y = 57
c)x = 79, y = 49
d)x = 79, y = 47
Final answer:
Lines represented by equations in the form x = a constant are vertical lines and are parallel to each other. The correct answer indicating parallel lines is (d) x = 79, y = 47.
Explanation:
To determine which pair of values for x and y indicates that the lines described are parallel, we need to understand that for two lines to be parallel, they must have the same slope. For standard linear equations in the form y = mx + b, where m is the slope, lines with the same m value are parallel. However, when the equation is given in the form x = a constant, as is the case for options (a) and (c), it denotes a vertical line, which does not have a slope in the traditional sense but is parallel to other vertical lines.
Given the information, lines described by equations x = 47 and x = 79 would be parallel since they both represent vertical lines. Therefore, the correct answer is (d) x = 79, y = 47.
Find sin2A if sinA=1/4 and 0<=A<=(pi/2)
Find the value of x. Round the answer to the nearest tenth, if needed. A. 4.8 B. 5.1 C. 8.2 D. 9.5
5x+9y+z=20
2x-y-z=-21
5x+2y+2z=-21
(4n-3n^3)-(3n^3+4n) answer
What transformations change the graph of (f)x to the graph of g(x)?
f(x) = x² ; g(x) = (x + 7)² + 9
The graph of g(x) is obtained by the combination of shifting the graph of f(x) to the left 7 units and upward 9 units.
Further explanationTransformation of a graph: changing the shape and location of a graph.
We already know there are four types of transformation geometry: translation (or shifting), reflection, rotation, and dilation (or stretching).
The transformation that we will discuss is shifting horizontally or vertically.Translation (or shifting): moving a graph on an analytic plane without changing its shape.Vertical shift: moving a graph upwards or downwards without changing its shape.Horizontal shift: moving a graph to the left or right downwards without changing its shape.In general, given the graph of y = f(x) and k > 0, we obtain the graph of:
[tex]\boxed{ \ y = f(x) + k \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] upward k units.[tex]\boxed{ \ y = f(x) - k \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] downward k units.Furthermore in general, given the graph of y = f(x) and h > 0, we obtain the graph of:
[tex]\boxed{ \ y = f(x + h) \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] to the left h units.[tex]\boxed{ \ y = f(x - h) \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] to the right h units.,The combination of vertical and horizontal shifts is as follows:
[tex]\boxed{\boxed{ \ y = f(x \pm h) \pm k \ }}[/tex]
The plus or minus sign follows the direction of the shift, i.e., up-down or left-right
Given: [tex]\boxed{ \ f(x) = x^2 \ becomes \ g(x) = (x + 7)^2 + 9 \ }[/tex]
We set h = +7 and k = +9.
In the graph, additionally note the shift of points from (0, 0) to (-7, 9).
Conclusion
The graph of g(x) is drawn by the combination of shifting the graph of f(x) to the left 7 units and upward 9 units.
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The graph of the function [tex]g(x)=(x+7)^{2}+9[/tex] is obtained from the graph of the function [tex]f(x)=x^{2}[/tex] when each point on the curve of [tex]f(x)=x^{2}[/tex] is shifted [tex]7[/tex] units towards the negative direction of [tex]x-[/tex] axis and then shifted [tex]9[/tex] units towards the positive direction of [tex]y-[/tex] axis.
Further explanation:
The functions are given as follows:
[tex]\fbox{\begin\\\ \begin{aligned}f(x)&=x^{2}\\g(x)&=(x+7)^{2}+9\end{aligned}\\\end{minispace}}[/tex]
The objective is to determine the transformation or the way in which the graph of the function [tex]g(x)[/tex] is obtained from the graph of the function [tex]f(x)[/tex].
Concept used:
Shifting of graphs:
Shifting is a rigid translation because it does not change the size and shape of the curve. Shifting is used to move the curve vertically or horizontally without any change in shape and size of the curve.
The function [tex]y=f(x+a)[/tex] and [tex]y=f(x-a)[/tex] is a shift of the curve [tex]y=f(x)[/tex] horizontally towards negative and positive direction of [tex]x-[/tex]axis respectively.
The function [tex]y=f(x)+a[/tex] and [tex]y=f(x)-a[/tex] is a shift of the curve [tex]y=f(x)[/tex] vertically towards positive and negative direction of [tex]y-[/tex]axis respectively.
Step1: Draw the graph of the function [tex]f(x)=x^{2}[/tex].
Figure 1 (attached in the end) represents the graph of the function [tex]f(x)=x^{2}[/tex]. From figure 1 it is observed that the curve of the function [tex]f(x)=x^{2}[/tex] is a parabola with origin as the vertex and mounted upwards.
Step 2: Obtain the graph of the function [tex]g'(x)=(x+7)^{2}[/tex] from the graph of the function [tex]f(x)=x2[/tex].
The function [tex]g'(x)=(x+7)^{2}[/tex] is of the form [tex]y=f(x+a)[/tex].
So, as per the concept of shifting of the graphs the graph of the function [tex]g'(x)=(x+7)^{2}[/tex] is obtained from the graph of the function [tex]f(x)=x^{2}[/tex] when each point on the curve of [tex]f(x)=x^{2}[/tex] is shifted [tex]7[/tex] units towards the negative direction of [tex]x-[/tex]axis.
Figure 2 (attached in the end) represents the graph of the function [tex]g'(x)=(x+7)^{2}[/tex].
In figure 2 the dotted line represents the curve of [tex]f(x)=x^{2}[/tex] and the bold line represents the curve of [tex]g'(x)=(x+7)^{2}[/tex].
Step3: Obtain the graph of the function [tex]g(x)=(x+7)^{2}+9[/tex] from the graph of the function [tex]g'(x)=(x+7)^{2}[/tex].
The function [tex]g(x)=(x+7)^{2}+9[/tex] is of the form [tex]y=f(x)+a[/tex].
So, as per the concept of shifting of graph the graph of the function [tex]g(x)=(x+7)^{2}+9[/tex] is obtained from the graph of the function [tex]g'(x)=(x+7)^{2}[/tex] when each point on the curve of [tex]g'(x)=(x+7)^{2}[/tex] is shifted [tex]9[/tex] units towards upwards or the positive direction of [tex]y-[/tex]axis.
Figure 3 (attached in the end) represents the graph of the function [tex]g(x)=(x+7)^{2}+9[/tex].
In figure 3 the dotted line represents the curve of [tex]g'(x)=(x+7)^{2}[/tex] and the bold line represents the curve of [tex]g(x)=(x+7)^{2}+9[/tex].
From the above explanation it is concluded that the graph of the function [tex]g(x)=(x+7)^{2}+9[/tex] is obtained from the graph of the function [tex]f(x)=x^{2}[/tex] when each point on the curve of [tex]f(x)=x^{2}[/tex] is shifted [tex]7[/tex] units towards the negative direction of [tex]x-[/tex] axis and then shifted [tex]9[/tex] units towards the positive direction of [tex]y-[/tex] axis.
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Graphing
Keywords: Graph, curve, function, parabola, quadratic, f(x)=x2, g(x)=(x+7)2+9, shifting, translation, scaling, shifting of graph, scaling of graph, horizontal, vertical, coordinate, horizontal shift, vertical shift.
A grocery store sells chili peppers at $2.04 for a dozen. At this rate, what's the cost per pepper?
A. $0.17
B. $1.70
C. $0.07
D. $1.07
how do I use elimination to solve the system 8x-7y=5 and 3x-5y=9 for y
All employees at FashionMarket get 20% off all clothing and accessories Kim li recently brought a t shirt at fashionMart for a 20% discount conjunction Kim li workable at fashionMart
Answer:
D.
false; Kim Li could have received a 20% sale discount
The x-intercept of the line whose equation is 2x - 3y = 6 is
Answer:
(3,0)
Step-by-step explanation:
What is the value of -d when d = -2?
20 Point question!!!!!!!! On the rectangular coordinate system, line PQ goes through P (6, − 2), and the midpoint of line PQ is (0, 5). What are the coordinates of point Q?
Let f(x)=8^x
What function represents a transformation of f(x) by a vertical stretch with factor 2?
g(x)=8^2x
g(x)=2⋅8^x
g(x)=8 1/2^x
g(x)=12⋅8^x
Graph the solution on a number line
x<2
Graph is included!
A jewelry store marks its merchandise up by 80%. If the wholesale price of a bracelet is $55, what will the store charge for the retail price?
A.) $63
B.) $75
C.) $99
D.) $110
The retail price of the bracelet is $99. Therefore, option C is the correct answer.
Given that, a jewelry store marks its merchandise up by 80%.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The wholesale price of a bracelet is $55.
Let the retail price of the bracelet be x.
Here, x=55+80% of 55
=55+0.8×55
=55+44
=$99
The retail price of the bracelet is $99. Therefore, option C is the correct answer.
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A coupon offers $1.00 off the 16-ounce size. which size is better buy then
Answer:first u have to multiply 1 .00 by 16 then
which improper fraction that is equivalent to the mixed number 6 4/7
Sam is flying a kite. The length of the kite string is 80 meters, and it makes an angle of 75° with the ground. The height of the kite from the ground is (20.27,61,77.27) meters.
a+5.7>-2.3 what is the answer
A tortoise is walking in the desert. It walks for
37.5
meters at a speed of
3
meters per minute. For how many minutes does it walk?
To rent a certain meeting room, a college charges a reservation fee of $42 and an additional fee of $7.70 per hour. The math club wants to spend less than $80.50 on renting the meeting room.
What are the possible amounts of time for which they could rent the meeting room?
Use t for the number of hours the meeting room is rented, and solve your inequality for t .
What is the area of this face ?
Answer:
28 square inches.Step-by-step explanation:
Notice that the yellow area is a compound area. Its height is 10 inches.
We can divide this area in three figures, one rectangle and two squares, where the square sides are 2 inches long.
So, the area of the squares is
[tex]A_{squares}=(2in)^{2} +(2in)^{2}=4in^{2} +4in^{2} =8in^{2}[/tex]
On the other hand, the rectangle has a height of 10 inches, and its base is 2 inches long. So its area is
[tex]A_{rectangle}=(10in)(2in)=20in^{2}[/tex]
Therefore, the yellow area is
[tex]A_{yellow}=A_{squares} +A_{rectangle}=8in^{2} +20in^{2} =28in^{2}[/tex]
So, the answer is 28 square inches.
A store increases the price of a sweater from $20 to $22.What is the percent of increase?Select from the drop-down menu to correctly complete the statement.
a 0.1
b 0.2
c 2
d 9
e 10
f 20
Answer:
Find out the what is the percent of increase .
To prove
As given
A store increases the price of a sweater from $20 to $22.
Increase in the price = Increase price - Initial price
= $22 - $20
= $2
Formula
[tex]Percentage = \frac{increase\ in\ price\times 100}{Initial\ price}[/tex]
Here initial price = $20
increase in price = $2
put in the formula
[tex]Percentage = \frac{2\times 100}{20}[/tex]
[tex]Percentage = \frac{200}{20}[/tex]
Percentage = 10%
Therefore the increase in the price is 10% .
Option (e) is correct.
Final answer:
The percent of increase when a store raises the sweater's price from $20 to $22 is calculated as 10%, using the formula of difference over original price times 100, Option E is correct.
Explanation:
The question asks for the percent of increase when a store increases the price of a sweater from $20 to $22. To find the percentage increase, we take the increase in price ($2), divide it by the original price ($20), and then multiply by 100 to convert to a percentage. Thus, the calculation is (($22 - $20) / $20) * 100 = (2 / 20) * 100 = 0.10 * 100 = 10%.
State the domain and range of the function represented by the table
x= -4, -1, 0, 3
y= -4, -4, -4, -4
The domain of this function is { - 4, - 1, 0, 3 } and range of the function is
{ - 4 }.
What is the domain and range of a function?Suppose we have an ordered pair (x, y) then the domain of the function is the set of values of x and the range is the set of values of y for which x is defined.
The domain of the function f(x) is the set of x values that are
{ - 4, - 1, 0, 3 }
and the range of the function f(x) is { - 4 }.
As for every input, the output of the function remains the same so it is a constant function.
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Jake has already written 3 pages, and he expects to write 1 page for every additional hour spent writing. Write an equation that shows the relationship between the hours spent writing x and the total pages written y. Then Graph.
The discriminant of a quadratic equation is negative. One solution is 3+4i . What is the other solution?
A.4-3i
B.3-4i
C.4+3i
D.-3+4i
Answer: Option B 3-4i is the correct option
Explanation:
we have formula for discriminant [tex]D=b^{2}-4ac[/tex]
after that we find the required variable that is to be find according to the quadratic equation given suppose we have to find x
then we have formula [tex]x=\frac{-b\pm\sqrt{D}} {2a}[/tex]
Here we have [tex]\pm[/tex] of roots if we have one root 3+41 other would be of opposite sign and hence,definitely be 3-4i.
Therefore Option B 3-4i is the correct option.