Answer:
[tex]\large\boxed{1.\ f(1)=135}\\\boxed{2.\ f(6)=115}\\\boxed{3.\ f(26)=25}\\\boxed{4.\ f(n)=139-4n}[/tex]
Step-by-step explanation:
[tex]f(1)=135\\f(2)=135-4=131\\f(3)=131-4=127\\f(4)=127-4=123\\f(5)=123-4=119\\\vdots\\\\\text{It's an arithmetic sequence with firs term = 135 and the common}\\\text{difference d = -4.}\\\text{The formula of arithmetic sequence: }\\\\f(n)=f(1)+(n-1)d\\\\\text{We have}\ f(1)=135\ \text{and}\ =-4.\ \text{Substitute:}\\\\f(n)=135+(n-1)(-4)=135+(n)(-4)+(-1)(-4)\\=135-4n+4=139-4n\\\\\boxed{f(n)=139-4n}[/tex]
[tex]\text{Put n = 6, n=26 to the formula:}\\\\f(6)=139-4(6)=139-24=115\\\\f(26)=139-4(26)=139-104=25[/tex]
A rectangular fish pond is 21 ft2 in area. If the owner can surround the pond with a 20-foot fence, what are the dimensions of the pond?
3.5 ft by 6 ft
4 ft by 6 ft
3 ft by 7 ft
3.5 ft by 7 ft
Answer:
3 ft by 7 ft
Step-by-step explanation:
Try the solutions and find the one that works.
3.5 × 6 — area OK, perimeter = 19 ft
4 × 6 — area = 24 ft², perimeter OK
3 × 7 — area OK, perimeter OK
3.5 × 7 — area 24.5 ft², perimeter 21 ft
___
The perimeter is the sum of the four side lengths; the area is the product of two adjacent side lengths.
If a board game was originally $25 and it is on sale for $18 what is the percent of discount?
Assume that x is a variable that has been declared as a double and been given a value. Write an expression to compute the quartic root of x. The quartic root of a number is the square root of its square root. EXAMPLES: For example, the quartic root of 16.0 is 2.0 because: the square root of 16.0 is 4.0 and the square root of 4.0 is 2.0. Another example: the quartic root of 81.0 is 3.0 because the square root of 81.0 is 9.0 and the square root of 9.0 is 3.0. Thus, to find the quartic root of a number you take the square root of the number and then take the square root of that. In this exercise you must find the quartic root of x in a single expression-- you must not write any statements. Also, you may only use the sqrt() static method defined in the Math class-- no other methods. (HINT: you will need to call the Math.sqrt() method twice-- and you will need to pass the return value of one of those calls as argument to the other call. AND REMEMBER: write an expression, not a statement.)
Answer:
sqrt(sqrt(x))
Step-by-step explanation:
A quartic root of is written mathematically as . THe quartic root of 16 is 2 since 2*2*2*2 = 16. However, a quartic root can also be defined as the square root of a square root. For example the √16 = 4 and the √4 = 2. This is the same response as taking the quartic root. This means you can write it as the sqrt(sqrt(x)). In the example, it would be sqrt(sqrt(16)) = sqrt(4) = 2.
The quartic root of a variable x can be calculated using the expression Math.sqrt(Math.sqrt(x)), which calls the square root function twice. This computes the square root of x, then computes the square root of the result, yielding the quartic root.
Explanation:In order to compute the quartic root of a variable x, we call the Math.sqrt() method twice in a nested manner. The quartic root is essentially the square root of a square root, hence the need for the double call. The appropriate expression in this case would be:
Math.sqrt(Math.sqrt(x))
This expression first computes the square root of x and then computes the square root of the result, which gives us the quartic root of x. As a result, if x is 16.0, the result of this expression would be 2.0, and if x is 81.0, the result would be 3.0.
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0.05% written as a decimal
Answer:
0.05% means 0.05 per every 100.
Step-by-step explanation:
We find it useful to convert 0.05% to decimal, because if you need to find 0.05% of any number, you can simply multiply that number with 0.0005.
hope this helps!!!!!
The value of 0.05% written as a decimal is 0.0005.
To write 0.05% as a decimal, you need to divide the percentage value by 100.
A decimal number is a number that uses the base-10 numbering system. It is a way of representing numbers using the digits 0-9 and a decimal point. Each digit in a decimal number represents a specific place value, which is a power of 10.
The digits to the left of the decimal point represent whole numbers, and the digits to the right of the decimal point represent fractional parts or decimal fractions.
0.05% divided by 100 is equal to 0.0005.
Therefore, 0.05% written as a decimal is 0.0005.
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(Q4) Which values of a and b in the exponential function y = a (bx) would result in the following graph?
Answer: second option.
Step-by-step explanation:
By definition, you know that:
[tex]b^0=1[/tex]
You can see in the graph that the interception with the y-axis is at -1.
Therefore, in that point: x=0 and y=-2
Substitute into the function and solve for a:
[tex]-1=a(b)^0\\-1=a(1)\\a=-1[/tex]
Now, choose any point of the function and substitute this point and the value of a into the function and solve for b. Then you obtain:
Point (2,-4)
[tex]-4=-1(b)^2\\\frac{-4}{-1}=b^2\\b=\sqrt{4}\\b=2[/tex]
Answer:
Its B
Step-by-step explanation:
Because it is
On edge
Which pay is equivalent to 16 $ per hour A) 48 for 3 hours B)120 for 12 hours C) 60 for 5 hours D) 96 for 9 hours
Answer:
The answer is A. 48 divided by 3 equals 16. Therefore, if you earn $48 for 3 hours, then you are earning $16 per hour.
Step-by-step explanation:
Hey there!
The correct answer is A. $48 for 3 hours
I figured this out by multiplying 16 by 3 which equals 48
Hope this helps you!
God bless ❤️
xXxGolferGirlxXx
Which polynomial represents a sum of cubes?
x^3 - 64
8x^3 + 125
16x^3 + 1
27x^3 + 4
Answer:
8x³ + 125
Step-by-step explanation:
Cubes: look for the exponent 3 and for perfect cubes such as 1, 8, 27, ...
8x^3 + 125 is a sum, and 8 is a perfect cube (the cube of 2), and x^3 is a cube, and 125 is a cube.
Thus, the correct answer is 8x^3 + 125 (which is equivalent to
(2x)³ + 5³).
The scientist creates an equation that models her data for each tree so that she can predict the diameter in the future. Select the linear equation that fits the data for tree 1, where x is the year and y is the trunk diameter, in inches
Answer:
Step-by-step explanation:
0.3. x + 18.3
The data for tree 1 is an illustration of a linear equation.
The linear equation that fits the data for tree 1 is: [tex]\mathbf{y = 0.3x + 18.3}[/tex]
From the complete question, we have the following points
[tex]\mathbf{(x_1,y_1) = (1,18.6)}[/tex]
[tex]\mathbf{(x_2,y_2) = (3,19.2)}[/tex]
First, we calculate the slope (m)
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
So, we have:
[tex]\mathbf{m = \frac{19.2 - 18.6}{3 -1}}[/tex]
[tex]\mathbf{m = \frac{0.6}{2}}[/tex]
[tex]\mathbf{m = 0.3}[/tex]
The equation is then calculated as:
[tex]\mathbf{y = m(x - x_1) + y_1}[/tex]
So, we have:
[tex]\mathbf{y = 0.3(x - 1) + 18.6}[/tex]
[tex]\mathbf{y = 0.3x - 0.3+ 18.6}[/tex]
[tex]\mathbf{y = 0.3x + 18.3}[/tex]
Hence, the linear equation that fits the data for tree 1 is: [tex]\mathbf{y = 0.3x + 18.3}[/tex]
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ABC paint company needs to paint the outside of the building shown. They will also need to paint the roof. What is the surface area that needs to be painted?
3,100 ft 2
4,600 ft 2
4,100 ft 2
4,300 ft 2
see image
Answer:
3100ft
Step-by-step explanation:
There are 2 sides to the prism that have an area of 50ft * 10ft or 500ft. The total of those will be 500ft * 2 or 1000ft. There are 2 more sides to the prism that have an area of 30ft * 10ft or 300ft. The total would be 300ft * 2 or 600ft. Then the last two sides to the prism have an area of 50ft * 30ft or 1500ft. Since we're imagining this prism to be a house, you can't paint the floor (well, I guess you could but I think they want us to leave that part out because you can't pick the house up to paint the bottom that would be ridiculous). So the surface area is each area added, or 1000ft + 600ft + 1500ft = 3100ft.
Answer:
3,100 ft^2
Step-by-step explanation:
The landscaper charges a rate of $40 per hour to plant trees.Amelia paid a total of $725 for the trees and for the landscaper to plant them. How many hours did it take the land scaper to plant the trees?
23.5 hours is the anser yeteressdfdsfsjufrhhmrgijfjfxkjvnrtjeigrjiegre
PLEASE HELP!!!! 50 POINTS
Find an equation of the line. Write the equation using function notation. through (8,-4) perpendicular to 2y=x-4
First you need to rewrite the equation in the form y = mx +b:
2y = x-4
Divide all terms by 2:
2y / 2 = x/2 - 4/2
Simplify:
y = 1/2x - 2
The slope of the line is 1/2.
A perpendicular line has a slope of the negative reciprocal, which would be -2.
Now using the point slope method:
y - y1 = m(x-x1)
Using the given point of (8,-4) and m = -2
you get:
y +4 = -2(x-8)
Simplify:
y +4 = -2x +16
Now subtract 4 from both sides to get the final equation:
y = -2x +12
FIND THE DEGREE MEASURE OF ANGLE DPR.
[tex]\widehat{DPR}=\frac{1}{2}(\stackrel\frown{ET}-\stackrel\frown{DR}) = \frac{1}{2} (118 - 26) = \frac{92}{2} = 46°[/tex]
The sum of four numbers is 20 and their average is 5. When a fifth is added, the new average is 6. What is the fifth number?
Answer:
10
Step-by-step explanation:
We'll note the numbers as [tex]x_{n}, x_{n+1} ...[/tex]
[tex]x_1 + x_2 + x_3 + x_4 = 20\\Avg = 5\\\frac{x_1 + x_2 + x_3 + x_4 + x_5 }{5} = 6 = \frac{20 + x_5}{5}\\ 4 + \frac{x_5}{5} = 6\\\\frac{x_5}{5} = 2\\\x_5 = 10[/tex]
Answer:
10.
Step-by-step explanation:
The average of the 5 numbers =
(20 + x) / 5 = 6 where x is the 5th number.
20 + x = 30
x = 10
The fifth number is 10.
a pipe cleaner 20cm long. it is bent into a rectangle. use a quadratic model to calculate the dimensions that give the maximum area.
Answer:
5 cm by 5 cm
Step-by-step explanation:
The perimeter of this rectangle is 20 cm, and the relevant formula is
P = 20 cm = 2W + 2L. Then W + L = 10 cm, or W = (10 cm) - L.
The area of the rectangle is A = L·W, and is to be maximized. Subbing (10 cm) - L for W, we get A = L[ (10 cm) - L ], or A = 10L - L²
Note that this is the equation of a parabola that opens down. With coefficients a = -1, b = 10 and C = 0, we find that the x-coordinate of the vertex (which is the x-coordinate of the maximum as well) is
x = -b / (2a). Subbing 10 for b and -1 for a, we get:
x = -[10] / [2·(-1)] = 10/2, or 5.
This tells us that one dimension of the rectangle is 5 cm.
Since P = 20 cm = 2L + 2W, and if we let L = 5 cm, we get:
20 cm = 2(5 cm) + 2W, or
10 cm = W + 5 cm, or W = 5 cm.
Thus, choosing L = 5 cm and W = 5 cm results in a square, which in turn leads to the rectangle having the maximum possible area.
The dimensions that give the maximum area is 5 cm by 5 cm.
Given:
The perimeter of this rectangle is 20 cm, and formula for perimeter is
P= 2(W+L)
P = 20 cm = 2W + 2L.
Then W + L = 10 cm,
or W = (10 cm) - L.
The area of the rectangle is A = L·W, and is to be maximized.
On substituting the values, we get A = L[ (10 cm) - L ], or A = 10L - L²
Note that this is the equation of a parabola that opens down. With coefficients a = -1, b = 10 and C = 0, we find that the x-coordinate of the vertex (which is the x-coordinate of the maximum as well) is
x = -b / (2a). Subbing 10 for b and -1 for a, we get:
x = -[10] / [2·(-1)] = 10/2, or 5.
This tells us that one dimension of the rectangle is 5 cm.
Since P = 20 cm = 2L + 2W, and if we let L = 5 cm, we get:
20 cm = 2(5 cm) + 2W, or
10 cm = W + 5 cm, or W = 5 cm.
Therefore, choosing L = 5 cm and W = 5 cm results in a square, which in turn leads to the rectangle having the maximum possible area.
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Isabell is thinking of a even number between 234 and 250 the sum of the digits is double the digit in the ones place what is Isabell's number
Answer:
246.
Step-by-step explanation:
Let the number be 2xy, then
2 + x + y = 2y and y must be even because the whole number is even.
y = 2 + x .
Now x must be even because y is even.
The only 2 numbers which fit are x = 4 and y = 6 so the number is 246.
Checking: 2+4+6 = 12 and 12 = 2*6.
John wrote 1/5 of a paper in 1/4 of an hour how long did it take him to write an entire paper?\
Answer:
[tex]1\frac{1}{4}\ hours[/tex]
Step-by-step explanation:
we know that
using proportion
[tex]\frac{(1/4)}{(1/5)}\frac{hour}{paper}=\frac{x}{1}\frac{hour}{paper} \\ \\x=5/4\ hours[/tex]
covert to mixed number
[tex]5/4\ hours=1\frac{1}{4}\ hours[/tex]
Arnold can read 3 pages in 7 minutes. Brenda can read 8 pages in 14 minutes. Who is the faster reader? Justify your answer.
Answer:
Brenda
Step-by-step explanation:
You can divide the number of pages by the number of minutes to find the amount of minutes it takes to read 1 page. For Arnold, 3 pages / 7 minutes = 1 page per approximately 0.43 minutes. For Brenda, 8 pages / 14 minutes = 1 page per approximately 0.57 minutes. Brenda reads slightly faster since 0.57 > 0.43
If the volume of a cone is 593.46 cubic inches and the radius is 9 inches what is the height
Which of the following equations represents a line that is paraellel to Y=5x-4 and passes through the point (3, 4)?
A. Y=5x-7
B. Y=5x+19
C. Y=-1/5x-4
D. Y=5x-11
choice D is the correct solution
PARALLEL slopes always have the same slope no matter what because they are parallel
The equation of the line that is parallel to y = 5x-4 and passes through the point (3, 4) is y = 5x - 11 because it has the same slope, 5, as the given line depicting parallelism and it passes through the specified point.
Explanation:In Mathematics, two lines are parallel if their slopes are equal. In this case, the given line is y = 5x - 4, and its slope is 5. To find an equation of a line that is parallel to this line and passes through a specific point, we use the point-slope form of a line, which is y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the point through which the line passes.
Replace m with 5 (the slope of the given line), and (x1, y1) with (3, 4) (the point through which the line passes), and we have y - 4 = 5(x - 3). Distributing and simplifying, we get y = 5x - 15 + 4 = 5x -11. Therefore, the equation of the line that is parallel to y = 5x - 4 and passes through the point (3, 4) is y = 5x - 11.
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There are 11 more goats than sheep in the farm. Together there are 137 animals in the farm. How many goats and how many sheep are there?
Answer:
The number of goats in the farm is [tex]74[/tex]
The number of sheep in the farm is [tex]63[/tex]
Step-by-step explanation:
Let
x----> the number of goats in the farm
y----> the number of sheep
we know that
[tex]x+y=137[/tex] ----> equation A
[tex]x=y+11[/tex] -----> equation B
substitute the equation B in equation A and solve for y
[tex](y+11)+y=137[/tex]
[tex]2y=137-11[/tex]
[tex]2y=126[/tex]
[tex]y=126/2=63[/tex]
Find the value of x
[tex]x=63+11=74[/tex]
therefore
The number of goats in the farm is [tex]74[/tex]
The number of sheep in the farm is [tex]63[/tex]
What are the values of x and y?
Answer:
b: [tex] x= 8 \sqrt7 y= 4 \sqrt{21} [/tex]
Step-by-step explanation:
Euclid 1st theorem:
[tex] x^2 = 16 * (16+12); y^2 = 12*(12+16) [/tex]
Calculation is trivial
30 points!!!
To convert measurements in the metric system, you can move the decimal point left or right. Why does this work? The metric system only uses decimal numbers. Converting in the metric system does not involve multiplication or division. The metric system is based on powers of 10. The metric system does not have conversion factors.
Moving the decimal point left or right works in the metric systems because; The metric system is based on powers of 10.
Why does moving decimal point left or right work for metric system conversions?It follows from the task content that the reason for moving the decimal point left or right in metric system conversions be identified.
It follows from metric system conversions that;
centi- indicates 10-² = 0.01milli- indicates 10-³ = 0.001kilo- indicates 10³ = 1000deci- indicates 10-¹ = 0.1Based on the aforementioned, it can be concluded that the measurements conversion in the metric system is such that the decimal point is moved left or right.
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Graph the following equation
[tex]f(x) = \frac{(2x+3)(x-6)}{(x+2)(x-1)}[/tex]
If you can. Also, what is the Oblique Asymptote.
Answer:
Graphic attached
Step-by-step explanation:
The oblique asymptote of the function has the shape of a line of the form
[tex]y = mx + b[/tex]
We need to find the slope m and the intercept b.
The oblique asymptote is found by these two limits:
[tex]m = \lim_{x \to \infty}\frac{f(x)}{x}\\\\b = \lim_{x \to \infty}[f(x) - mx][/tex]
If [tex]f(x) = \frac{(2x+3)(x-6)}{(x+2)(x-1)}[/tex] then:
[tex]m = \lim_{x \to \infty} \frac{\frac{(2x+3)(x-6)}{(x+2)(x-1)}}{x}\\\\m = \lim_{x \to \infty} \frac{2x^2-9x-18}{x^3 +x^2 -2x}\\\\m = 0[/tex]
The slope is 0. Therefore the function has no oblique asymptote.
Horizontal asymptote:
[tex]y = 2[/tex]
Vertical asymptote
[tex]x = -2\\x = 1[/tex]
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A cylinder has diameter 34 m and height 27 m. A label at bottom states drawing not to scale.
Find the volume of the cylinder. Use 3.14 for
π
PLEASE WRITE YOUR ANSWER IN STEPS CLEAR, I WILL GVE 100 POINTS ASAP AND BRAINLIEST
The volume of the cylinder is 25295.26 cubic meters.
Explanation:To find the volume of a cylinder, we can use the formula V = π * r^2 * h, where r is the radius and h is the height. Given that the diameter is 34 m, the radius is half of that, which is 17 m. The height is given as 27 m.
Plugging in the values into the formula, we get V = 3.14 * (17^2) * 27. Evaluating this expression, we find that the volume of the cylinder is 25295.26 cubic meters.
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The volume of a cylinder is 25295.26 cubic meters.
Explanation:To find the volume of a cylinder, use the formula V = πr^2h, where V represents the volume, π is a constant approximately equal to 3.14, r is the radius of the cylinder, and h is the height of the cylinder.
In this case, the diameter of the cylinder is given as 34 m, so the radius is half of the diameter, or 17 m.
The height of the cylinder is given as 27 m. Substitute these values into the formula to calculate the volume.
V = 3.14 × (17^2) × 27
= 25295.26 cubic meters.
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The circumference of a circular rug is 24.8 meters. What is the area of the rug? Use 3.1 for pi
Answer:
49.6 square meters
Step-by-step explanation:
first, circumference is 2*pi*r, so we want to find r. so we take 2*pi*r=24.8 and solve for r which is 4.
Now, area is pi*r^2 so pi*4^2 = pi*16 = 49.6
Write the augmented matrix corresponding to the system of equations. 3x + 4y − 5z = 8 x + 2z = −3 4x − 3y = 6 Incorrect: Your answer is incorrect.
3x+4y-5z=8
1x+0y+2z=-3
4x-3y+0z=6
|`3 4 (-5)`||`x`| |`8`|
| 1 0 2 | |y |=|-3 |
|.4 (-3) 0 .||.z.| |.6.|
To the nearest hundredth, what is the value of x?
Use a trigonometric ratio to compute a distance
Question 3 options:
62.25
100.25
101.12
128.32
➷ cos38 = 79/x
x = 79/cos38
x = 100.2524
The correct option would be 100.25
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Answer:
100.25
Step-by-step explanation:
Using the cosine ration in the right triangle, then
cos38° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{79}{x}[/tex]
Multiply both sides by x
x × cos38° = 79 ( divide both sides by cos38° )
x = [tex]\frac{79}{cos38}[/tex] ≈ 100.25
Which is 5logx - 6log(x-8) written as a single logarithm?
Answer:
option a
[tex]log\frac{x^{5} }{(x-8)^{6} }[/tex]
Step-by-step explanation:
Given in the question an expression
5logx - 6log(x-6)
To solve this question we will apply two of the logarithm property
1) power rule
alogx = log[tex]x^{n}[/tex]
log[tex]x^{5}[/tex] - log[tex](x-8)^{6}[/tex]
2) substraction rule
The log of a quotient is the difference of the logs
loga (x/y) = loga x - loga y
[tex]logx^{5}- log(x-8)^{6}[/tex]
log[tex]\frac{x^{5} }{(x-8)^{6} }[/tex]
Answer:
a edge
Step-by-step explanation:
You ask a friend to think of a number from 5 to 12. What is the probability that his number will be 8?
1/8 chance since there are 8 numbers from 5 to 12 and 1 is only one number so 1/8
Find linearly independent functions that are annihilated by the given differential operator. (give as many functions as possible. use x as the independent variable. enter your answers as a comma-separated list.) d2 − 12d − 45
We want to find all [tex]f(x)[/tex] such that
[tex](D^2-12D-45)[f(x)]=0[/tex]
We have
[tex](D^2-12D-45)[f]=(D-15)(D+3)[f]=0[/tex]
so that either
[tex](D-15)[f]=0\implies f'-15f=0\implies f(x)=e^{15x}[/tex]
or
[tex](D+3)[f]=0\implies f'+3f=0\implies f(x)=e^{-3x}[/tex]
These solutions are linearly independent; we confirm this by computing the Wronskian:
[tex]W=\begin{vmatrix}e^{15x}&e^{-3x}\\15e^{15x}&-3e^{-3x}\end{vmatrix}=-3e^{12x}-15e^{12x}=-18e^{12x}\neq0[/tex]
We can also confirm that these solutions are correct by substituting the solutions for [tex]f(x)[/tex] in the differential equation:
[tex](D^2-12D-45)[e^{15x}]=225e^{15x}-12(15e^{15x})-45e^{15x}=0[/tex]
[tex](D^2-12D-45)[e^{-3x}]=9e^{-3x}-12(-3e^{-3x})-45e^{-3x}=0[/tex]
The linearly independent functions that are annihilated by the differential operator d2 − 12d - 45 are e^{15x} and e^{-3x}, found by solving the quadratic equation associated with the differential equation.
Explanation:The differential operator given is d2 − 12d - 45. To find out the linearly independent functions that are annihilated by this operator, we have to solve the homogeneous differential equation d2 − 12d - 45 = 0. This is a second order equation, so we expect two linearly independent solutions.
To find the solutions, we seek the roots of the associated quadratic equation m^2 - 12m -45 = 0. This can be factored into (m-15)(m+3), thus giving roots m = 15 and m = -3.
The general forms of the solutions for these roots are e^{15x} and e^{-3x} respectively. Therefore, the functions e^{15x} and e^{-3x} are linearly independent functions that are annihilated by the given differential operator d2 − 12d - 45.
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