Final answer:
To find the sum of the first 16 terms of the arithmetic series with a common difference of 6, use the sum formula for an arithmetic series S_n = (n/2) * (2a_1 + (n - 1)*d). By plugging in the values n = 16, a_1 = 1, and d = 6, the sum S_16 is calculated to be 736.
Explanation:
The student has presented an arithmetic series and is asking to find the sum of the first 16 terms (S16). In an arithmetic series, each term increases by a constant difference. The given sequence is 1, 7, 13, 19, and so on, showing a common difference (d) of 6.
Steps to find S16:
Identify the first term (a1) which is 1.
Determine the common difference (d), which is 6 in this case.
Use the formula for the sum of the first n terms of an arithmetic series Sn = (n/2) * (2a1 + (n - 1)*d), where n is the number of terms.
Substitute n = 16, a1 = 1, and d = 6 into the formula and calculate S16.
Now let's calculate S16:
S16 = (16/2) * (2*1 + (16 - 1)*6) = 8 * (2 + 15*6) = 8 * (2 + 90) = 8 * 92 = 736
The sum of the first 16 terms of the given arithmetic series is 736.
What substitution Should be used to re-write 26(x^3+1)^2-22(x^3+1)-3=0 as a quadratic function?
Answer:
[tex]x^3+1[/tex]
Step-by-step explanation:
[tex] 26(x^3+1)^2-22(x^3+1)-3=0 [/tex]
Comparing to
[tex] A(u)^2+B(u)+C =0 [/tex]
Where A,B,C are constants
You should see that we need to substitute the [tex]x^3+1[/tex] with u.
Identify the oblique asymptote of f(x) = quantity x squared minus 4 x plus 8 over quantity x plus 2.
Answer:
y = x - 6.
Step-by-step explanation:
Do the division:
x + 2 ) x^2 - 4x + 8 ( x - 6 <------- Quotient.
x^2 + 2x
-6x + 8
-6x - 12
----------
20
HELP PLEASE I'M CRYING, EASY 2 QUESTIONS
Answer:
12) 154 squared meters
13) 307 cm^2
Step-by-step explanation:
12) A circle has area pi*r^2
r is half the diameter so half of 14 is 7
pi in this case is 22/7
A=22/7 * (7)^2
A=22/7 * 49
A=22 *49/7
A=22 *7
A=154 squared meters
13) Area of rectangle is 10(18)=180
Area of half a circle is .5*pi*r^2=.5*pi*9^2
Adding the two areas together would result in a total area of 307.2 squared centimeters
Deedra has the equations for lines A and B. When she solved for the point where these two lines intersect, she ended up with the equation 3 = 7. What must be true about the two lines?
we can take a peek at two of those lines hmmm say y = 5x + 3 and y = 5x + 7.
let's notice, those two equations for those lines are in slope-intercept form, so let's solve the system.
since y = y then
5x + 3 = 5x + 7
3 = 7 what the?
well, notice, both lines have the same slope of 5, but different y-intercept, one has it at y = 3 and the other at y = 7, what does that mean?
it means that both lines are parallel to each other, one may well be above the other, but both are parallel, and since a solution to the system is where their graphs intersect, well, parallel lines never touch, so a system with two parallel lines has no solutions.
The two lines are parallel.
We have a girl Deedra who has the equations for lines A and B. When she solved for the point where these two lines intersect, she ended up with the equation 3 = 7.
We have to investigate what it tells about the nature of lines.
What is the slope - intercept form of equation of line?The slope intercept form of an equation of line is -
y = mx + c
Let's assume we have two lines with their equations be -
[tex]y_{1} = m_{1} x_{1} + c\\y_{2} = m_{2} x_{2} + d[/tex]
To find the intersecting points of these two lines, then -
[tex]y_{1} =y_{2} \\x_{1} =x_{2}[/tex]
Therefore -
[tex]m_{1} x_{1} +c =m_{2} x_{2} +d\\[/tex]
Now, in the question she found out that 3 =7 which is same c = d. To fulfill this condition, the slope of these two lines should be equal. Hence, we can conclude that the two lines are parallel.
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What is the tan of angle B
Answer:
2.4
Step-by-step explanation:
tanB = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{12}{5}[/tex] = 2.4
Answer: 2.4
Step-by-step explanation:
[tex]tan\theta=\dfrac{opposite}{adjacent}\\\\\\tan\angle B=\dfrac{12}{5}\\\\\\tan\angle B=2.4[/tex]
20m to 21m what is the percentage change
Answer: The correct answer is: " 5% increase " .
_________________________________________
Step-by-step explanation:
_________________________________________
Note: The particular "percentage change" is a "percent increase" ; since we are going from "20" to "21" which is an "increased value of "1" .
_________________________________________
Note the formula for "percent increase" ; as follows:
_________________________________________
Percent increase = [(new value - original value)/original value] * 100 ;
_________________________________________
So; let us "plug in" our known values; to solve for the "percentage change"
→ [i.e. "percent increase" (in this case)] :
_________________________________________
Percent increase = [(21 - 20)/20] * 100 ;
= [1/20] * 100 ;
= [100/20] ;
= 5.
_________________________________________
The correct answer is: " 5 % increase" .
_________________________________________
Hope this helps!
Best wishes to you!
_________________________________________
A number between 49 and 95 that is a multiple of 4,5, and 10?
Answer: 60 and 80
Step-by-step explanation: Start off with the highest number, which is 10. The numbers between 49 and 95 that can be divided by 10 are 50, 60, 70, 80, and 90. Next, figure out what can be divided by 5. All of them can. Next, find out what numbers can be divided by 4. 50, 70, and 90 can’t because they would end up as a decimals. 60 and 80 can be divided by 4, 5, and 10.
Solve the equation g2 – 12g = –36
A. g = –6
B. g = 6
C. g = –3, g = 4
D. g = –6, g = 6
Answer:
g=6
Step-by-step explanation:
[tex]g^{2} -12=-36\\g^{2} -12+36\\ (g-6)(g-6)\\ g-6=0\\ g=6[/tex]
Find the most common ratio 72,12,2, 1/3,1/18
Answer:
1/6
Step-by-step explanation:
To find the common ratio, you compare a few pairs of consecutive terms, by dividing an element by its predecessor.
12 / 72 = 1/6
2 / 12 = 1 / 6
1/3 / 2 = 1 / 6
The ratio is constant... so that's your common ratio to go from one term to the next.
To go from one term to the next, you have to multiply by 1/6.
20 points for this. I just gotta know so I can pass summer school lol
Answer: Point, Point, Line
Step-by-step explanation:
A plane and a line intersect at a point . Think of a piece of paper as a plane and a pen as a line. What happens when you push the pen through the paper? It creates a point!
Two lines intersect at a point .
Two planes intersect at a line . Think of a piece of paper laid horizontally on a table and another piece of paper standing on it vertically. What can you draw at the places of intersection? A line!
Factor the following expression using the GCF.
10dr - 60r
10r(d - 6)
5r(2d - 30)
r(10d - 60)
10r(d - 60r)
Answer:
10r(d - 6).
Step-by-step explanation:
The GCF is 10r.
So the answer is:
10r(d - 6).
Which statements about these triangles is true
Answer:
I’m not sure, but I think it’s C
12 cm
5 cm
A rectangular prism has a height of 12 centimeters and a square base with sides measuring 5 centimeters. A pyramid with the same base and half the
height of the prism is placed inside the prism, as shown in the figure.
The volume of the space outside the pyramid but inside the prism is
cubic centimeters
The volume of the space outside the pyramid but inside the prism is 250 cubic centimeters.
To find the volume of the space outside the pyramid but inside the prism, we first need to determine the volumes of both the prism and the pyramid.
The prism has a height of 12 centimeters and a square base with sides measuring 5 centimeters. The volume of a rectangular prism is calculated by multiplying the base area by the height. In this case, the base area is 5 cm * 5 cm = 25 square centimeters. Therefore, the volume of the prism is 25 cm² * 12 cm = 300 cubic centimeters.
The pyramid has the same square base as the prism, with sides measuring 5 centimeters. However, its height is half that of the prism, which is 12 cm / 2 = 6 centimeters. The volume of a pyramid is calculated by multiplying the base area by one-third of the height. In this case, the base area is 25 cm², and one-third of the height is 6 cm / 3 = 2 centimeters. Therefore, the volume of the pyramid is 25 cm² * 2 cm = 50 cubic centimeters.
To find the volume of the space outside the pyramid but inside the prism, we subtract the volume of the pyramid from the volume of the prism: 300 cubic centimeters - 50 cubic centimeters = 250 cubic centimeters.
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Find the value of x in the triangle.
Hello there!
X = 67°
Answer and work are provided in the image attached.
What is 1/2 X (6 X 4)+3 + 2 Please show your work
Answer:
17Step-by-step explanation:
Use PEMDAS:
P Parentheses first
E Exponents (ie Powers and Square Roots, etc.)
MD Multiplication and Division (left-to-right)
AS Addition and Subtraction (left-to-right)
[tex]\dfrac{1}{2}\times\underbrace{(6\times4)}_{1}+3+2\\\\=\underbrace{\dfrac{1}{2}\times24}_{2}+3+2\\\\=12+3+2=17[/tex]
Factorise (x-y)4-(x-y)2
Answer:
Step-by-step explanation:
Let x - y = A
A^4 - A^2
A^2 ( A^2 - 1)
A^2 (A + 1)(A - 1)
(x - y)^2 (x - y + 1)(x - y - 1)
If I have not thought out the question properly please leave me a note.
PLEASE HELP!!!
Select all that apply.
Describe the transformations.
The yellow rectangle was translated up 3 units and reflected over the y-axis.
The yellow rectangle was translated right 5 units and reflected over the x-axis.
The yellow rectangle was reflected over both axes.
The yellow rectangle was translated right 5 units and up 3 units.
Evaluate 2(x + 1) - 3 when x = 6.
Evaluate 2(x + 1) - 3 when x = 6.
First, plug in x value.
2(6 + 1) -3 ParenthesisEMDAS
2(7) - 3 PEMultiplyDAS
14 - 3 PEMDASubtract
11 ←
Answer:
11
Step-by-step explanation:
just took test
find the measurement of the indicated angle to the nearest degree
Answer:
54°
Step-by-step explanation:
Since the triangle is right use the cosine ratio to solve for angle
cos? = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{26}{44}[/tex], hence
? = [tex]cos^{-1}[/tex] ( [tex]\frac{26}{44}[/tex] ) ≈ 54° ( nearest degree )
Both the red and blue line segments stretch from the center of the circle to a
point on the circle. The length of the blue line segment is 7. How long is the
red line segment?
Center
O A. 14
O B. 7
O C. 10.5
O D. 3.5
Answer:
7
Step-by-step explanation:
Blue is 7 and the Red is 7
Answer:
7
Step-by-step explanation:
Prove that when x> 1, a triangle with side lengths a = x2 - 1, b = 2x, and C = x2 + 1 is a right triangle. Use the Pythagorean
theorem and the given side lengths to create an equation. Use the equation to show that this triangle follows the rule
describing right triangles. Explain your steps.
Step-by-step explanation:
a = x^2 - 1
b = 2x
c = x^2 + 1
The Pythagorean theorem states
a^2 + b^2 = c^2
Let's find a^2 and b^2 and add them to get a^2 + b^2:
a^2 = (x^2 - 1)^2 = x^4 - 2x^2 + 1
b^2 = (2x)^2 = 4x^2
a^2 + b^2 = x^4 - 2x^2 + 1 + 4x^2 = x^4 + 2x^2 + 1
Now let's find c^2:
c = x^2 + 1
c^2 = (x^2 + 1)^2 = x^4 + 2x^2 + 1
We see that both a^2 + b^2 and c^2 equal x^4 + 2x^2 + 1, so we have shown that the triangle is a right triangle.
We can see that a² + b² = c² = x⁴ + 2x² + 1, indicating that the triangle is a right triangle.
What is the definition of a right-angle triangle?
It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometric function.
According to Pythagoras, the sum of the squares of two sides equals the square of the longest side.
Given data;
a = x² - 1
b = 2x
c = x² + 1
According to the Pythagorean theorem;
[tex]\rm a^2 + b^2 = c^2[/tex]
Let's find a^2 and b^2 and add them to get a^2 + b^2:
[tex]\rm a^2 = (x^2 - 1)^2 \\\\ a^2 = x^4 - 2x^2 + 1 \\\\ b^2 = (2x)^2 \\\\ b^2 = 4x^2\\\\[/tex]
Left hand side:
[tex]\rm a^2 + b^2 = x^4 - 2x^2 + 1 + 4x^2 \\\\ a^2 + b^2 =x^4 + 2x^2 + 1[/tex]
Right hand side:
[tex]\rm c^2 = (x^2 + 1)^2 \\\\ c^2 = x^4 + 2x^2 + 1[/tex]
L.HS.=R.H.S
Hence,the given triangle is a right angled triangle.
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At a game show, there are 8 people (including you and your friend) in the
front row.
The host randomly chooses 3 people from the front row to be contestants.
The order in which they are chosen does not matter.
How many ways can you and your friend both be chosen?
Answer:
6
Step-by-step explanation:
For both to be chosen the other spot can be taken by any of the other 6 people in the row. So six possibilities
Answer:
A. [tex]^6C_1=6[/tex]
Step-by-step explanation:
Given,
The total number of people = 8,
The number of people have to chosen = 3,
Since, me and my friend both have to be chosen,
So, the remaining number of people = 8 - 2 = 6,
And, the number of remaining number of people have to be chosen = 3 - 2 = 1
Also, the order does not matter,
Hence, the total way of choosing = Total combination of me and my friend × total combination of choosing 1 person out of 6 people
[tex]=^2C_2\times ^6C_1[/tex]
[tex]=1\times ^6C_1[/tex]
[tex]=6[/tex]
Option A is correct.
PQ=RQ a=?
Please need help!!
Answer:
100 Degrees
Step-by-step explanation:
It's correct for Acellus! :-)
A student decides to run a simulation of rolling an even number with a single die. Use the simulated results from 20 attempts to estimate the probability, then compare your estimation with the theoretical probability.
1 5 3 2 3 6 5 6 3 3 4 4 1 3 6 5 3 2 2 6
Answer:
Practical probability: 9 / 20 = 45%
Theoretical probability: 3 / 6 = 50%
Step-by-step explanation:
So, we have 20 rolls:
1 5 3 2 3 6 5 6 3 3 4 4 1 3 6 5 3 2 2 6
Out of which we have 9 even numbers: 2 6 6 4 4 6 2 2 6
So, the practical probability is 9 / 20 or 45%
The theoretical probability is:
Possible outcomes (6): 1 2 3 4 5 6
Even numbers possible (3): 2 4 6
P = 3 / 6 = 50%
The practical probability is a bit lower (45%) than the theoretical probability (50%) but that's most probably due to the low number of rolls, it's just one roll away from being on target. With a greater number of rolls, the student would get closer to the theoretical probability.
1.00
Given the following functions f(x) and g(x), solve (f + g)(3) and select the correct answer below:
f(x) = 2x + 21
g(x) = x - 24
0-27
0-21
06
48
Answer:
6
Step-by-step explanation:
Plug in 3 into both expressions
Then add those results
2(3)+21=6+21=27
3-24 =-21
-------
6 is the sum of 27 and -21
Viktor picked 4 pounds of cherries. How many containers did he need if he put 2/7 pound of cherries into each container?
Answer:
13.9 containers or 14 rounded
Step-by-step explanation:
2/7 of a pound is 0.28571429 in decimal form. To solve you have to know how many 2/7 of a pound will go into 4 pounds. So you divide 2/7 of a pound by 4 pounds, and the answer is 14.
Answer:
14
Step-by-step explanation:
He will need 14 containers. 4 times 7/2 is 28/2. You then have to simplify it and will get 14.
What is the volume of a sphere with a radius of 1 foot? (Use 3.14 for pi)
Answer:
V≈4.19ft³
Step-by-step explanation:
The volume of a sphere with a radius of 1 foot is 4.19ft³.
In order to find this:
V=4
3πr3=4
3·π·13≈4.18879ft³
[tex]V=\dfrac{4}{3}\pi r^3\\\\V=\dfrac{4}{3}\cdot3.14\cdot 1^3\approx4.19\text { ft}^3[/tex]
solve for -4x-4=-4(x+2)
Answer:
no solutions
Step-by-step explanation:
-4x-4=-4(x+2)
Distribute the negative
-4x-4 = -4x-8
Add 4x to each side
-4x+4x-4 = -4x+4x-8
-4 = -8
Since this is not true there are no solutions
The answer for study guide
Answer:
-2
Step-by-step explanation:
The only domain problems are going to come from the square root you have there. You only want to square root 0 or positive numbers,. In other words, you want x+2 to be greater than 0 or equal to 0.
x+2>=0
x>=-2
So x has to be greater than ot equal to 0
versity City Geometry 1.2 - CR (9/17)
Equation on a circle
Pre-Test Active
Which equation represents a circle with a center at (-3,-5) and a radius of 6 units?
(x - 3)2 + (-5)2 = 6
(x - 3)2 + (-5)2 = 36
(x + 3)2 + (y + 5)2 = 6
(x+3)2 + (x + 5)2 = 36
Mark this and return
Save and Exit
Next
Answer:
[tex](x+3)^{2}+(y+5)^{2}=36[/tex]
Step-by-step explanation:
we know that
The equation of a circle in standard form is equal to
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
In this problem we have
[tex](h,k)=(-3,-5)[/tex]
[tex]r= 6\ units[/tex]
substitute
[tex](x+3)^{2}+(y+5)^{2}=6^{2}[/tex]
[tex](x+3)^{2}+(y+5)^{2}=36[/tex]