Answer: =2.35
Step-by-step explanation:
Which formula can be used to describe the sequence below? –8, –5, –2, 1, 4, ...
Answer:
an = -8 +3(n-1)
an = -11 +3n
f(n) = -11 +3n
Step-by-step explanation:
–8, –5, –2, 1, 4, ...
This is an arithmetic sequence.
We are increasing by 3 each time
-8 +3 = -5
-5+3 = -2
-2 +3 = 1
The common difference is 3
The formula for an arithmetic sequence is
an = a1 +d (n-1)
an = -8 +3(n-1)
an = -8 +3n -3
an = -11 +3n
The nth term is -11 +3n
f(n) = -11 +3n
D. an = an-1+3; a1 = -8
EG. 2020
Can someone tell me how
the way I get the subsequent term, nevermind the exponents, the exponents part is easy, since one is decreasing and another is increasing, but the coefficient, to get it, what I usually do is.
multiply the current coefficient by the exponent of the first-term, and divide that by the exponent of the second-term + 1.
so if my current expanded term is say 7a³b⁴, to get the next coefficient, what I do is (7*3)/5 <----- notice, current coefficient times 3 divided by 4+1.
anyhow, with that out of the way, lemme proceed in this one.
[tex]\bf ~~~~~~~~\textit{binomial theorem expansion} \\\\ \qquad \qquad (1+ax)^n\implies \begin{array}{llll} term&coefficient&value\\ \cline{1-3}&\\ 1&+1&(1)^n(ax)^0\\\\ 2&+\frac{(1)(n)}{1}\to n&(1)^{n-1}(ax)^1\\\\ 3&+\frac{n\cdot (n-1)}{2}&(1)^{n-2}(ax)^2 \end{array}[/tex]
so, following that to get the next coefficient, we get those equivalents as you see there for the 2nd and 3rd terms.
so then, we know that the expanded 2nd term is 24x therefore
[tex]\bf n(1)^{n-1}(ax)1 = 24x\implies n(1)(ax)=24x\implies nax=24x\implies n=\cfrac{24}{a}[/tex]
we also know that the expanded 3rd term is 240x², therefore we can say that
[tex]\bf \cfrac{n(n-1)}{2}~~(1)^{n-2}(ax)^2 = 240x^2\implies \cfrac{n(n-1)}{2}(1)(a^2x^2) = 240x^2 \\\\\\ \cfrac{(n^2-n)(a^2x^2)}{2}=240x^2\implies \cfrac{(n^2-n)(a^2)}{2}=\cfrac{240x^2}{x^2}\implies \cfrac{a^2n^2-a^2n}{2}=240 \\\\\\ a^2n^2-a^2n=480[/tex]
but but but, we know what "n" equals to, recall above, so let's do some quick substitution
[tex]\bf a^2n^2-a^2n=480\qquad \boxed{n=\cfrac{24}{a}}\qquad a^2\left( \cfrac{24}{a} \right)^2-a^2\left( \cfrac{24}{a} \right)=480 \\\\\\ a^2\cdot \cfrac{24^2}{a^2}-24a=480\implies 24^2-24a=480\implies 576-24a=480 \\\\\\ -24a=-96\implies a=\cfrac{-96}{-24}\implies \blacktriangleright a = 4\blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ n=\cfrac{24}{a}\implies n=\cfrac{24}{4}\implies \blacktriangleright n=6 \blacktriangleleft[/tex]
solve the hypotenuse
Answer:
11.7
Step-by-step explanation:
Using the cosine ratio, then
cos40° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{9}{h}[/tex]
Multiply both sides by h , the hypotenuse
h × cos40° = 9 ( divide both sides by cos40° )
h = [tex]\frac{9}{cos40}[/tex] ≈ 11.7 ( to the nearest tenth )
8.......................
Answer:
b
Step-by-step explanation:
Answer:
a. [tex]8^{8}\sqrt{8}[/tex]
Step-by-step explanation:
The given expression is
[tex]\sqrt{8^{17}}[/tex]
We rewrite the radicand to obtain;
[tex]\sqrt{8^{16}\times 8}[/tex]
Split the radicand;
[tex]\sqrt{8^{16}}\times \sqrt{8}[/tex]
[tex]\sqrt{(8^{8})^2}\times \sqrt{8}[/tex]
[tex]8^{8}\sqrt{8}[/tex]
Part A:
At a zoo, the lion pen has a ring-shaped sidewalk around it. The outer edge of the sidewalk is a circle (blue) with a radius of 11 m. The inner edge of the sidewalk is a circle (orange) with a radius of 9 m. Find the approximate AREA of the larger circle (blue).
Use 3.14 for pi.
Show your work!
Part B:
At a zoo, the lion pen has a ring-shaped sidewalk around it. The outer edge of the sidewalk is a circle (blue) with a radius of 11 m. The inner edge of the sidewalk is a circle (orange) with a radius of 9 m. Find the approximate AREA of the smaller circle (orange).
Use 3.14 for pi.
Show your work!
Part C:
At a zoo, the lion pen has a ring-shaped sidewalk around it. The outer edge of the sidewalk is a circle (blue) with a radius of 11 m. The inner edge of the sidewalk is a circle (orange) with a radius of 9 m. Find the approximate AREA of the sidewalk (shaded region between the blue and orange circles).
Use 3.14 for pi.
Show your work!
Please answer all of them. ;;
All of them have the same attached image.
Answer:
Part A: 379.94
Part B: 254.34
Part C: 125.6
Step-by-step explanation:
The are for the area of a circle is A = Pi*r^2
So for part A, do
A = 3.14 * 11^2
A = 3.14 * 121
A = 379.94
Same thing for Part B, just change the radius:
A = 3.14 * 9^2
A = 3.14 *81
A= 125.6
And for Part C, Subtract the area of the smaller from the area of the larger circle:
379.97 - 254.34 = 125.6
Answer:
I'm just answering this so that you can give them brainlest
Step-by-step explanation: Have a good day
Please help me with this one please ( up there )
Answer:
the blue one is 1/2 and the red one is 1/4
Step-by-step explanation:
count the bricks and put a "1/" in front of the number of bricks and... BOOM you have your answer
Six students all took the same test. Their scores were 70,71,75,75,88, and 89. What is the mean absolute deviation for the test scores?
A)7
B)7.5
C)75
D)78
Answer:D)78
Step-by-step explanation:70+71+75+75+88+89/6
How many ways can a committee of 6 be selected from a club with 10 members
Answer:
210
Step-by-step explanation:
The general formula for picking k items from a total of n is
[tex]_{n}C_{k} = \frac{n! }{(n-k)!k! }[/tex]
Thus, if we want to select a committee of six people from a club with 10 members, the number of combinations is
[tex]_{10}C_{6} = \frac{10! }{(10-6)!6! }[/tex]
[tex]= \frac{10! }{4!6! }[/tex]
[tex]= \frac{10\times9\times8\times7}{4\times3\times2\times1 }[/tex]
[tex]= \frac{5040 }{24 }[/tex]
= 210
The committee can be selected in 210 separate ways.
simplify the expression -2(p+4)^2-3+5p.What is the simplified expression in standard form?
Answer: -2x²-11x-35
Step-by-step explanation:
-2(p+4)²-3+5p
-2(x²+8x+16)-3+5x
-2x²-11x-35
To simplify the expression -2(p+4)^2-3+5p, it's important to distribute, multiply, and combine like terms. The simplified expression is -2p^2 -11p -35.
Explanation:To simplify the expression -2(p+4)^2-3+5p, it's easier to break it down step by step:
First, distribute (p+4)^2 to get p^2 + 8p + 16.Multiply -2 to each term to get -2p^2 -16p - 32.Next, combine terms with the rest of the expression to get -2p^2 -16p - 35 + 5p.Finally, combine like terms to arrive at the simplified expression: -2p^2 -11p -35.This is the simplest form of the original expression.
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17x -8x -9 = 76 - 40
Answer:
5
Step-by-step explanation:
17x -8x -9 = 76 - 40
17x -8x = 76 - 40 + 9
9x = 45
x = 45/9
x=5
Answer:
x = 5
Step-by-step explanation:
17x - 8x - 9 = 76 - 40
9x - 9 = 36
+9 +9
9x = 45
/9 /9
x = 5
Three solid shapes A, B and C are similar.
The surface area of shape A is 4 cm^2
The surface area of shape B is 25 cm^2
The ratio of the volume of shape B to the volume of shape C is 27 : 64
Work out the ratio of the height of shape A to the height of shape C.
Give you answer in its simplest form.
Answer:
[tex]\frac{3}{10}[/tex]
Step-by-step explanation:
step 1
Find the ratio of the height of shape A to the height of shape B
we know that
If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared
Let
z-----> the scale factor
x----> surface area shape A
y----> surface area shape B
so
[tex]z^{2} =\frac{x}{y}[/tex]
substitute
[tex]z^{2} =\frac{4}{25}[/tex]
[tex]z =\frac{2}{5}[/tex]
therefore
the ratio of the height of shape A to the height of shape B is equal to
[tex]\frac{hA}{hB}=\frac{2}{5}[/tex]
step 2
Find the ratio of the height of shape B to the height of shape C
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
z-----> the scale factor
x----> volume shape B
y----> volume shape C
so
[tex]z^{3} =\frac{x}{y}[/tex]
substitute
[tex]z^{3} =\frac{27}{64}[/tex]
[tex]z =\frac{3}{4}[/tex]
therefore
the ratio of the height of shape B to the height of shape C is equal to
[tex]\frac{hB}{hC}=\frac{3}{4}[/tex]
step 3
Find the ratio of the height of shape A to the height of shape C
we have
[tex]\frac{hA}{hB}=\frac{2}{5}[/tex]
[tex]\frac{hB}{hC}=\frac{3}{4}[/tex]
Multiply
[tex](\frac{hA}{hB})(\frac{hB}{hC})=\frac{hA}{hC}[/tex]
so
[tex](\frac{2}{5})(\frac{3}{4})=\frac{6}{20}=\frac{3}{10}[/tex]
In this problem, we're working with the geometric property of similarity to compare the heights and volumes of different shapes. Using the ratios of their surface areas and volumes, we found that the ratio of the height of Shape A to Shape C is 15:8.
Explanation:In order to solve this problem, it is necessary to first know that, for similar shapes, the ratio of the areas is actually the square of the ratio of the corresponding length measurements (this includes dimensions such as the height). In this particular case, since shapes A and B are similar, the ratio of their surface areas will give the square of the ratio of the heights:
√(25/4) : 1 => 5 : 2
Now, for shapes B and C, we have the volume ratio given as 27 : 64. Since, for similar shapes, the ratio of the volumes is the cube of the ratio of the corresponding length measurements, the cube root of the volume ratio will give the ratio of the heights:
∛(27/64 : 1) => 3 : 4
Using these two ratios, we can find the ratio of height from shape A to shape C by multiplying together the heights of shape A to B and shape B to C: (5/2) * (3/4) => 15 : 8.
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What is the equation of the graph below?
Answer:
y=cos(0.4x)
Step-by-step explanation:
Answer:
The equation of the graph given is:
[tex]y=\cos(0.4x)[/tex]
Step-by-step explanation:
Clearly from the graph of the function that is provided to us we see that the graph repeats itself after every 5π.
i.e. the period of the function is: 5π.
Now we will check in each of the given options whose period is 5π.
We know that the period of a cosine function of the type:
[tex]y=cos(bx)[/tex] is given by:
[tex]Period=\dfrac{2\pi}{5}[/tex]
1)
[tex]y=\cos(\dfrac{x}{0.4})[/tex]
The period of this function is:
[tex]Period=\dfrac{2\pi}{\dfrac{1}{0.4}}\\\\\\Period=0.8\pi\neq 5\pi[/tex]
Hence, option: 1 is incorrect.
2)
[tex]y=\cos (5x)[/tex]
The period of this function is:
[tex]Period=\dfrac{2\pi}{5}\\\\\\Period=\dfrac{2}{5}\pi\neq 5\pi[/tex]
Hence, option: 2 is incorrect.
4)
[tex]y=\cos (\dfrac{x}{5})[/tex]
The period of this function is:
[tex]Period=\dfrac{2\pi}{\dfrac{1}{5}}\\\\\\Period=10\pi\neq 5\pi[/tex]
Hence, option: 4 is incorrect.
3)
[tex]y=\cos(0.4x)[/tex]
The period of this function is:
[tex]Period=\dfrac{2\pi}{0.4}\\\\\\Period=5\pi[/tex]
Hence, option: 3 is the correct option.
Which expression is equivalent to (3x^2-7)?
Answer:
The correct answer is third option
(10x² - 4) - (7x² + 3)
Step-by-step explanation:
From the given option we get the correct answer is third option.
(10x² - 4) - (7x² + 3)
Check the correct answer
(10x² - 4) - (7x² + 3) = 10x² - 4 - 7x² - 3)
= 10x² - 7x² - 4 - 3 = 3x² - 7
Therefore the correct answer is third option
(10x² - 4) - (7x² + 3)
The correct answer is C on edg
:)
What is the solution to the equation 4x + 2(x – 3) = 3x + x – 12? (1 point)
–3
–1
1
3
I got -1 but im not sure
heres my work
4x + 2(x – 3) = 3x + x – 12
4x + 2x - 6 = 3x + x - 12
6x -6 = 3x = 3x + x - 12
6x = 3x = 4x - 18
9x = 4x - 18
13x = -18
18 ÷ 13
make it negative
The answer is -3, let me know if you want me to give you the steps
The answer would be -3
How many yards are in 4 miles
There are 7040 yards in 4 miles
Answer:
there is 7040 yards in 4 miles
Step-by-step explanation:
1) 1 Miles = 1760 yards
2) just multiply 1760 times 4 because one Miles is 1760 yards
1760 x 4 = 7040 yards
4 represents miles
Hopes this helps!
A painter charges $15.92 per hour, plus an additional amount for the supplies. If he made $175.72 on a job where he worked 6 hours, how much did the supplies cost?
Answer: $15.92*6= $95.52
$175.72 - $ 95.52= $ 80.20
Step-by-step explanation:
9(6-2v)= -12(v-8)
step-by-step explanation please!
Enter only the value of the variable
Answer:
v = -2.5
Step-by-step explanation:
9(9-2v) = -12(v-8)
81−18v= −12v+96
So move -18v to the other side and change the sign. Same to 96.
81-96 = -12v + 18v
-15 = 6v
v = -2.5
how do you put .36÷4 into a model
Answer:
Step-by-step explanation:
you have to make 4 rows and 36 column then solve 36 divided by 4=9
(?,3) is on the line y=2x+5 what is the other coordinate
➷ Substitute it into the equation:
3 = 2x + 5
Subtract 5 from both sides:
-2 = 2x
Divide both sides by 2:
x = -1
The other coordinate is -1
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
-1
Step-by-step explanation:
1.We know that the equation of the line is y=2x+5 ( with a gradient of 2 and a
y-intercept of 5) and the y coordinate is 3 so we must work out x (x,3).
2.We know y=3 so
3 = 2x+5
3. Solve the equation
3=2x+5
(-5 from both sides)
-2=2x
(Divide both sides by 2 to isolate x)
-1 = x so x = 1
Hope this helps:)
5INGH
The first side of a triangle is 3 inches shorter than the second side, and 2 inches longer than the third side. How long is each side, if the triangle has a perimeter of 28 inches?
➷ 1st side = x - 3
2nd side = x
3rd side = x - 1
Form an equation:
x - 3 + x + x - 5 = 28
Simplify:
3x - 8 = 28
Add 8 to both sides:
3x = 36
Divide both sides by 3:
x = 12
first length = 12 - 3 = 9 inches
second length = 12 inches
third length = 12 - 5 = 7 inches
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
-3x-9+15x
Please help asap
Answer:
= 0.75
Step-by-step explanation:
-3x-9+15x = 0
12x = 9
x = 3
4
= 0.75
Hey there!
The answer is 12x - 9
Hope this helps you!
God bless ❤️
xXxGolferGirlxXx
factor -7v^2-25v-12 show steps
[tex] - 7 {v}^{2} - 25v - 12 \\ = - 7 {v}^{2} - 21v - 4v - 12 \\ = - 7 v (v + 3) - 4(v + 3) \\ = ( - 7v - 4)(v + 3) \\ = - (7v + 4)(v + 3)[/tex]
Complete the transformation on the vector shown and choose the resulting vector
Answer:
The answer is A. [-4/3]
For the second part the answer is a rotation 90 CCW about origin
Hope this helped!
Answer:
The correct option is B.
Step-by-step explanation:
From the given graph it is clear the x-coordinate of the vector is 3 and y-coordinate of the vector is 4 in the coordinate plane.
The given vector can be defined as
[tex]A=\begin{bmatrix}3 & 4\end{bmatrix}[/tex]
Translation vector is
[tex]B=\begin{bmatrix}0 & -1\\ 1 & 0\end{bmatrix}[/tex]
We need to find the resulting vector,
[tex]AB=\begin{bmatrix}3 & 4\end{bmatrix}\cdot \begin{bmatrix}0 & -1\\ 1 & 0\end{bmatrix}[/tex]
[tex]AB=\begin{bmatrix}3(0)+4(1) & 3(-1)+4(0)\end{bmatrix}[/tex]
[tex]AB=\begin{bmatrix}4& -3\end{bmatrix}[/tex]
Therefore the correct option is B.
Barry wants to make a drawing that is 1/4 the size of the original. If a tree in the original drawing is 14 inches tall and 5 inches wide, what will be the length and width of the tree in Barry's drawing?
Answer:
I think the answer would be to divide the inches by 4. So Length would be 3.5 inches and width would be 1.25 inches . I might be wrong but if you have no hope I would go with my answer.
Step-by-step explanation:
Answer:
lenght: 3.5 inches.
width: 1.25 inches.
Step-by-step explanation:
You have the following information:
- The drawing must be 1/4 the size of the original drawing.
- The tree in the original drawing is 14 inches tall and 5 inches wide.
Therefore, keeping the above on mind, you can find the length and width of the tree in Barry's drawing by multiplying the original dimensions by 1/4.
Then, you obtain the result shown below:
[tex]lenght=\frac{1}{4}*14in=3.5in\\\\width=\frac{1}{4}*5in=1.25in[/tex]
Your food bill was $80 at a restaurant.
You left a tip of $16.
What percentage of the food bill did you leave for the tip?
$16 / $80 * 100% = 20%.
$16/$80 *100= 20%
answer is 20%
The circle below is centered at the point (1,2) and has a radius of length 3 .what is its equation?
Answer:
Step-by-step explanation:
The general equation for a circle of radius r with center at (h, k) is
(x - h)² + (y - k)² = r²
Here, this equation becomes:
(x - 1)² + (y - 2)² = 3²
Equation of the circle way to represent the circle in the coordinate plane using its center points and the radius. The equation of the circle centered at the point (1,2) and has a radius of length 3 can be given as,
[tex]x^2+y^2-2x-4y-4=0[/tex]
Given-The center point of the given circle is (1,2).
The length of the radius of the circle is 3 units.
What is the equation of the circle?Equation of the circle way to represent the circle in the coordinate plane using its center points and the radius.
The standard form of the equation of the circle is,
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Here,
(h,k) is the center of the circle.
[tex]r[/tex] is the radius of the circle.
Put the values given in the problem in the standard form of the equation of the circle. Thus,
[tex](x-1)^2+(y-2)^2=3^2[/tex]
[tex]x^2+1-2x+y^2+4-4y=9[/tex]
[tex]x^2+y^2-2x-4y+5-9=0[/tex]
[tex]x^2+y^2-2x-4y-4=0[/tex]
Thus the equation of the circle centered at the point (1,2) and has a radius of length 3 can be given as,
[tex]x^2+y^2-2x-4y-4=0[/tex]
Learn more about the equation of the circle here;
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Please explain this to me and give me an answer x
Answer:
[tex]6^{\frac{7}{3} }[/tex]
Step-by-step explanation:
Using the rules of exponents
• [tex]\sqrt[n]{a^{m} }[/tex] ⇔ [tex]a^{\frac{m}{n} }[/tex]
• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]
Hence
[tex]\sqrt[3]{6}[/tex] = [tex]6^{\frac{1}{3} }[/tex] and
6² × [tex]6^{\frac{1}{3} }[/tex] = [tex]6^{\frac{7}{3} }[/tex]
Suppose f(x)=x^2 find the graph of f(x)+1
Answer:
f(x)+1 = x^2 + 1
Step-by-step explanation:
The graph of f(x)+1 will be given by adding 1 to the initial function f(x)
f(x)+1 = x^2 + 1
See the attachment for the graph;
PLEASE HELP!! Im having a really hard time.
A science museum has a spherical model of the earth with a diameter of 8.5 m.What is the volume of the model? Use 3.14 for pi and round your answer to the nearest whole number. Show your work.
Answer:
V = 321 m^3
Step-by-step explanation:
Volume of a sphere
V = 4/3 pi r^3
The radius is equal to
r = d/2
r = 8.5/2 =4.25
V =4/3 (3.14) (4.25)^3
V =321.3920833 m^3
Rounding to the nearest whole number
V = 321 m^3
Answer:
V = 321 m^3
V = 4/3 pi r^3 diameter is double of radius (radius is half of diameter)
V = 4/3 pi (4.25)^3
V= 75.66 meters squared (rounded)
Type the correct answer in each box.Use numerals instead of words. If necessary, use / for the fraction bar.
Line AB and Line BC form a right angle at their point of intersection, B.
If the coordinates of A and B are (14, -1) and (2, 1), respectively, the y-intercept of Line AB is _____ and the equation of is y = ___x+___.
If the y-coordinate of point C is 13, its x-coordinate is ___.
Answer:
y intercept is 1 1/3
equation is y = -1/6x + 4/3
x coordinate is -70 (-70,13)
Step-by-step explanation:
find M
m = 1 - (-1)/ 2 -1 4
m = -2/12 = -1/6
Find y intercept--Plug m and one point from above into y = mx + b
1 = - 1/6 (2) + b
1 = -2/6 + b
1 2/6 = b
1 1/3 = b
4/3 = b
To find the x coordinate if y is 13
13 = -1/6 x + 4/3
11 2/3 = -1/6 x
-70 = x
The y intercept of line AB = [tex](0,\dfrac{4}{3})[/tex]
The equation of line AB will be
[tex] y=\dfrac{-1}{6}x+\dfrac{4}{3}[/tex]
The x-coordinate of C = 4
Step-by-step explanation:The slope of line AB with coordinates of A and B are (14, -1) and (2, 1)
[tex]m_1=\dfrac{1-(-1)}{2-14}=\dfrac{2}{-12}=\dfrac{1}{-6}[/tex]
The equation of line AB will be
[tex](y-1)=\dfrac{1}{-6}(x-2)\\\\\Rightarrow y=\dfrac{1}{-6}(x-2)+1\\\\\Rightarrow\ y=\dfrac{-1}{6}x+\dfrac{1}{3}+1\\\\\Rightarrow y=\dfrac{-1}{6}x+\dfrac{4}{3}[/tex]
Put x=0, we get the [tex]y=\dfrac{4}{3}[/tex] i.e. [tex](0,\dfrac{4}{3})[/tex] is the y intercept of line AB.
Since, Line AB and Line BC form a right angle at their point of intersection, B. The the product of their slope must be -1.
Therefore, the slope of BC =[tex]m_2=\dfrac{-1}{m_1}=6[/tex]
Let x coordinate of C be a,then the coordinates of C = (a,13)
Now, slope of BC with points B(2,1) and C(a,13) will be
[tex]\dfrac{13-1}{a-2}=6\\\\\Rightarrow\ a-2=\dfrac{12}{6}\\\\\Rightarrow\ a-1=2\\\\\Rightarrow\ a=4[/tex]
Hence, the x-coordinate of C = 4