Answer:
See below.
Step-by-step explanation:
Formula:
[tex] a_n = 3(n + 4) [/tex]
First term: n = 1
[tex] a_1 = 3(1 + 4) = 15 [/tex]
Second term: n = 2
[tex] a_2 = 3(2 + 4) = 18 [/tex]
Third term: n = 3
[tex] a_3 = 3(3 + 4) = 21 [/tex]
Fourth term: n = 4
[tex] a_4 = 3(4 + 4) = 24 [/tex]
Tenth term: n = 10
[tex] a_{10} = 3(10 + 4) = 42 [/tex]
The explicit formula is [tex]a_{n}[/tex] = 4 + (n - 1)3 first four terms will be 4, 7, 10, and 13 and the 10th term will be 31.
What is Arithmetic progression?The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).
The arithmetic progression has wider use in mathematics for example sum of natural numbers.
Natural number = 1,2,3,4,5,6,7,8...
Now it has the same difference between any two consecutive terms d =2-1 = 3-2.
Let's say
First term = 4
Common difference = 3
Then
The nth term of the AP will be
[tex]a_{n}[/tex] = 4 + (n - 1)3
First term: n = 1
a₁ = 4
Second term: n = 2
a₂ = 7
Third term: n = 3
a₃ = 10
Fourth term: n = 4
a₄ = 13
Tenth term: n = 10
a₁₀ = 31
Hence, the explicit formula is [tex]a_{n}[/tex] = 4 + (n - 1)3 first four terms will be 4, 7, 10, and 13 and the 10th term will be 31.
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The volume of a cube is V=s3 , where s is the length of one edge of the cube. What is the edge length s for each cube?
look at the picture for the answer choices:)
Answer:
s = [tex]\sqrt[3]{999} }[/tex]
Step-by-step explanation:
V = s^3
Plug in the given volume.
999 = s^3
Take the third root of both sides to cancel out the ^3.
[tex]\sqrt[3]{999} }[/tex] = s
Answer:
A) s = ∛999 in.
A circle with the equation (x + 4)2 + (y + 2)2 = 36 is reflected over the line x = 1. What is the equation of the image? (x + 4)2 + (y - 2)2 = 36 (x - 6)2 + (y + 2)2 = 36 (x + 6)2 + (y - 2)2 = 36 (x - 4)2 + (y + 2)2 = 36
Answer:
B
Step-by-step explanation:
Currently, the graph looks like the attachment.
The centre of this circle is at (-4, -2), but when we flip it over the line x = 1 (the blue line on the picture), the centre will become ((1- -4) + 1, -2) = (6, -2).
Look for the equation [tex](x-h)^2+(y-k)^2=r^2[/tex] that matches this center. We want the center (h, k) to be (6, -2), so our equation should look something like:
[tex](x-6)^2+(y+2)^2=36[/tex]
The answer is B.
Answer:
(x - 6)² + (y + 2)² = 36
Step-by-step explanation:
Centre before reflection: (-4,-2)
Centre after reflection:
(-4+5+5,-2) = (6,-2)
(x - 6)² + (y + 2)² = 36
similarities and differences between sine and cosine graphs — Algebra 2
The similarities between sine and cosine graphs are their amplitude and periodicity, while the differences are their starting positions and phase. Overall, the graphs are more similar than different.
Similarities:
The sine and cosine functions have the same amplitude, which is the maximum value of the wave.
Both functions are periodic, meaning they repeat their pattern infinitely.
Differences:
The sine function starts with an amplitude of zero, while the cosine function starts with an amplitude of one.
The sine and cosine functions are out of phase by 90 degrees, meaning they reach their maximum and minimum values at different times.
Overall, the graphs of the sine and cosine functions are more similar than different because they share the same amplitude and shape, but they differ in their starting positions and phase.
Complete Question:
Write the similarities and differences between sine and cosine graphs.
A slide and its ladder form a right triangle with the ground, with the
slide representing the hypotenuse. The top of the ladder is 10 feet above
the ground, and the bottom of the ladder is 12 feet from the bottom of
the slide. What is the length of the slide to the nearest tenth of a foot?
Answer:
15.6 ft
Step-by-step explanation:
Let's call
a: distance from the top of the ladder to the ground = 10 ftb: distance from the bottom of the ladder to the bottom of the slide = 12 ftc: length of the slideFrom Pythagorean theorem:
c² = a² + b²
c = √(10² + 12²)
c = 15.6 ft
The length of the slide, which forms the hypotenuse of a right-angled triangle with the ground, is approximately 15.6 feet to the nearest tenth of a foot when calculated using the Pythagorean Theorem.
Explanation:The question involves finding the length of a slide (hypotenuse) when its ladder and the ground form a right-angled triangle. The top of the ladder is 10 feet above the ground (opposite side), and the bottom of the ladder is 12 feet away from the bottom of the slide (adjacent side). We will use the Pythagorean Theorem to solve for the slide's length, which is represented by the equation a² + b² = c², where a and b are the lengths of the legs of the triangle and c is the length of the hypotenuse.
Find the circumference of a circle thats diameter is 6 m
Answer: 18.85m
Step-by-step explanation:
Answer:
C = 6pi or approximately 18.84
Step-by-step explanation:
We can find the circumference from
C = pi *d where d is the diameter
C = pi* 6
We can approximate pi by 3.14
C = 3.14 *6
C =18.84
what is 8 to the power of 3
Answer:
512
Step-by-step explanation:
8×8×8
=512
8³=512
Therefore 8 to the power of 3 is 512
Answer: 512
Step-by-step explanation: 8 to the power of 3 means the same as 8³.
The smaller 3 which is called the exponent tells us that we need to multiply the 8 three times. So we have 8 · 8 · 8 which simplifies to 512.
So 8³ is equal to 512.
helpppppppppp me pleaseeeee
Answer:
A = 16 13unit^2 + 9unit^2 = 5 √10 = 15.8 = 16
Step-by-step explanation:
For Pythagoras we square route
= x^2 = 13^13 + (one of the closer squares for x elimination)
x= 169 + 81 169 + 100 169 + 49 169+64 169 + 121
x = 250 or 269 or 218 or 233 or 290
x= 5√10 or 15.8 or √269 269 or √218 2.8 or √233 or 2.33 ( or √290 = ( √48+2) or 2.9
A cone has a slant height of 26 inches and a diameter of 48 inches. What is the volume of the cone?
Answer:
Approx. 28952.92
Step-by-step explanation:
Because cone volume is found by V=πr²[tex]\frac{h}{3}[/tex].
First you find the radius. Because you have the diameter, you divide that by two, because it's 48, and diameter is radius multiplied by 2. So the radius is 24. 24pi squared with height divided by three is volume so, 28952.92.
It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.
The volume of a cone is 1/3πr²h.
The volume of the cone is 6028.8 inches³.
What is a cone?It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.
The volume of a cone is 1/3πr²h.
We have,
Diameter = 48 inches
Radius = 24 inches
r = 24 inches
Slant height = 26 inches
L = 26 inches
L² = h² + r²
26² = h² + 24²
h² = 676 - 576
h² = 100
h = 10 inches
The volume of the cone.
= 1/3 x π x 24 x 24 x 10
= 3.14 x 8 x 24 x 10
= 6028.8 inches³
Thus,
The volume of the cone is 6028.8 inches³.
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On Friday, a bowling alley made $842.72 from lane rentals and $412.38 from the concession stand. On Saturday, their lane rentals were down by but the concessions increased by . What is the total amount that the bowling alley earned in lane rentals and concessions on Friday and Saturday?
Answer:
A. 1355.95
Step-by-step explanation:
The correct answer is $1,355.95!!
Thanks
Mark Brainliest!!!!!
The measure of arc OS is (4x-18)
What is the value of x?
Answer:
The value X=49.5
Step-by-step explanation:
Given:
Arc of 4x-18 is formed .
To Find:
Value of x
Solution:
Consider a circle in which arc(OS) is formed ,
with OS as diameter so the angle subtended by them is 180 degree.
...(by property of semi circle )
4x-18 =180 degrees.
4x=198
x=198/4
x=49.5 degrees.
Hence the value of X=49.5 degrees
Answer:49.5
Step-by-step explanation:
Find the area of a circle that has a diameter of 18 inches. 1,017.36 in.2 254.34 in.2 113.04 in.2 56.52 in.2
Answer:
254.34
Step-by-step explanation:
Answer:
254.34
Step-by-step explanation:
Brainliest pls
what adds to be the bottom number but also multiplies to be the top 15 8
Final Answer:
It's likely that the student is concentrating on a factoring problem. The two numbers are 5 and 3, which when multiplied together equal 8 (the small number) and 15 (the big number).
Explanation:
It appears that you are looking for two numbers that sum up to 8 and multiply by 15, since the bottom number is 8 and the top number is 15.In this case, the appropriate responses are 5 and 3. Specifically, this is why: the sum equals 5 + 3 = 8.15 is the result of multiplying 5 by 3.
So, 5 and 3 are the numbers you're looking for.
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Quadrilateral quad is inscribed in circle o what is the measure of angle d?
Answer:
angle D is 74 degrees
Step-by-step explanation:
How many groups of 100 can you take out of 941 when diving by 3?
Final answer:
When 941 is divided by 3, there are 313 groups of 3. To determine the number of groups of 100 that can be extracted, we divide 313 by 100, which results in 3 complete groups of 100 with 13 left over.
Explanation:
The question asks us to find out how many groups of 100 can be taken out of 941 when dividing by 3. First, we must divide 941 by 3 to understand this concept better:
941 ÷ 3 = 313 with a remainder of 2
Now, we know there are 313 groups of 3 in 941. However, the question asks for groups of 100. To find this, we can examine how many complete hundreds fit into the result of 313:
313 ÷ 100 = 3 with a remainder of 13
Therefore, 3 complete groups of 100 can be taken out when 941 is divided by 3, with 13 left over that cannot form another complete group of 100.
A circular sidewalk with a radius of 100 meters is having a railing installed
along 120° of its arc. How many meters of railing will be needed? (HINT: arc
length).
A. 100pi/3 m
B. 200pi/3 m
C. 10pi/3 m
D. 2pi/3 m
Answer:
B
Step-by-step explanation:
Whole circle is 360 degrees.
The railing is 120 degrees.
That is:
120/360 = 1/3 rd of the whole length of the circle (perimeter).
We will find perimeter of the circle (a.k.a. Circumference) and then multiply it by (1/3) to get meters of railing needed.
First, circumference:
[tex]C=2\pi r\\C=2 \pi (100)\\C=200\pi\\C=628.32[/tex]
The railing is (1/3)rd of it, so:
[tex]\frac{1}{3}*628.32=209.44[/tex]
The railing is 209.44 meters.
The answer choices are in pi, so it will be:
[tex]\frac{1}{3}*200\pi=\frac{200\pi}{3}[/tex] meters
Answer choice B is right
w(t) = -2t+1, find w(-7)
Answer:
15
Step-by-step explanation:
w(t) = -2t+1,
Let x =-7
w(-7)= -2(-7) +1
=14+1
=15
What’s the answer????
Answer:B
Step-by-step explanation:
Answer:
D. 12
Step-by-step explanation:
The key is to separate this shape into multiple rectangles that you know how to solve the area for. The vertical rectangle has an area of 1*6=6cm, while the two horizontal rectangles each have an area of 1*3=3 cm, giving the shape a total of 12 cm. Hope this helps!
Look at these dot plots. Which statement is true about the two data sets?
Both have the same mode.
Both have a gap between 28 and 31.
Both have the same range.
Both have the same number of data points.
Answer:
Both have the same number of data points
Answer:
Both of them have the same number of data points.
Step-by-step explanation:
please give me brainlyest
What is 3x-4. I need to find the value of x.
Answer:
Well the answer could be [tex]\frac{4}{3}[/tex] I neeed branliest plez
Step-by-step explanation:
3x -4 =0
3x = 4
3x / 3 = 4/3
x =[tex]\frac{4}{3}[/tex]
hope this helps
What is the radius of a cone with diameter d? An ice cream cone is filled exactly level with the top of the cone. The cone has a 9-cm diameter and 6-cm depth. Approximate how much ice cream (in cm cubed) is in the cone? Use 3.14 for pi.
Answer:
42.39 [tex]cm^{2}[/tex]
Step-by-step explanation:
cone formula: [tex]V =\frac{1}{3} \pi r^{2} h[/tex]
diameter to radius
9 cm to 4.5
1.) [tex]V = \frac{1}{3} \pi (4.5^{2}) (6)[/tex]
2.) [tex]= \frac{1}{3}\pi (20.25)(6)[/tex]
3.) [tex]= \frac{1}{3} 121.5\pi[/tex]
4.) divide 121.5 by 3
[tex]= 13.5\pi[/tex]
5.) multiply by 3.14
V = 42.39
Answer:
42.39
Step-by-step explanation:
Two high school basketball teams have identical records of 15 wins and 2 losses.
Sunnyside High School's mean score is 50 points and its MAD is 4 points. Shadyside High School's mean score is 60 points and its MAD is 15 points.
Lin read the records of each team’s score. She likes the team that had nearly the same score for every game it played.
Which team do you think Lin likes?
a
Shadyside - it has the higher average score
b
Shadyside - it has the higher average score and the higher MAD
c
Sunnyside - it has the lower average score but a lower MAD
d
Sunnyside - it has the lower average score
Answer:c
Step-by-step explanation:
Allie must sell at least 50 gift baskets for the band fund-raiser. She already sold 36 baskets. Write and solve an inequality to determine how many more baskets Allie must sell for the fund-raiser.
Answer
14 more baskets
Step-by-step explanation:
50-36=14
Evaluate f(3) for the piecewise function: f(x) = StartLayout enlarged left-brace 1st Row StartFraction 3 x Over 2 EndFraction + 8, x less-than negative 6 2nd row negative 3 x minus 2, negative 4, less-than-or-equal-to x less-than-or-equal-to 3 Third row 4 x + 4, x greater-than 3 EndLayout Which value represents f(3)? –11 8 12.5 16
Answer:
The answer is -11
Step-by-step explanation:
I just finished the assignment hope this helps!
To evaluate f(3) for the given piecewise function, we use the second part of the function, which applies when x is between -4 and 3, inclusive. By substituting 3 into this piece, we find that f(3) is -11.
To find the value of f(3) for the given piecewise function, we need to determine which piece of the function applies when x is equal to 3. The function is defined as follows:
For x < -6, f(x) =
3x/2 + 8
For -4 ≤ x ≤ 3, f(x) = -3x - 2
For x > 3, f(x) = 4x + 4
Since 3 is within the range of the second piece (-4 ≤ x ≤ 3), we calculate the value by substituting x with 3 in the second function part:
f(3) = -3(3) - 2 = -9 - 2 = -11.
Therefore, the value that represents f(3) is -11.
Cynthia is finding the measures of the labeled angles in this image.
What is the least number of angle measures she needs to know
asures of all labeled angles in the image?
She only needs to know the measure of one angle, angle D.
She only needs to know the measure of one angle, angle
She only needs to know the measures of two angles, angles A and B.
She only needs to know the measures of two anales, but one of the angles must be one of the remote interior
Answer:
d
Step-by-step explanation:
just did the test
Suppose you invested $500 in K-Mart stock in October
of 2001. Each month the stock lost 2% of its value.
How much was the stock worth in October of 2002?
(HINT: The loss is per MONTH.)
Answer:
$380
Step-by-step explanation:
Amount invested in October 2001 = $500
If 2% is lost on stock each month, amount lost every month will be 2% of $500
= 2/100×$500
= $10
In order to know how much the stock will cost by October 2002, we need to know the number of month there is between October 2001 and October 2002.
The number of months within this period is 12months
If $10 is lost per month, the total stock lost for 12months will be
$10×12 = $120
Stock worth by October 2002 = Money invested - Total stock loss
Stock worth by October 2002 = $500-$120
= $380
What is the measure of angle B and C (picture included)
Answer:
c 63.6
b 97
Step-by-step explanation:
Select the equivalent expression
(8^2/4^4)^3 = ?
A 8^2/4^4
B 8^6/4^12
C 8^2/4^12
D 8^6/4^4
So the right answer is of option B.
Hope this will help u..
The equivalent expression of the given equation is option [tex]\frac{8^6}{4^{12} }[/tex], option B is correct.
How can equivalent expression be determined?Every mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. For instance, the formula 4m + 5 has the terms 4m and 5 as well as m, the variable, all separated by the arithmetic sign +.
Given that
[tex](\frac{8^2}{4^4} )^{3}[/tex]
The numerator = [tex](8^{2} )^{3} = 8^{6}[/tex]
The denominator = [tex](4^{4} )^{3} = 4^{12}[/tex]
Then we can combine the expression as ;
[tex]\frac{8^6}{4^{12} }[/tex]
Therefore, option B is correct.
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Ok I need help asap 15 points!
Answer:
[tex]-5\frac{1}{2},-3,-2,|2|,|5\frac{1}{2}|[/tex]
Step-by-step explanation:
The || signs you see remove the sign, meaning even if it says negative, it turns into a positive regardless.
Consider the following circle with center at point O.
Identify one radii, one diameter, and one chord of the circle. Justify your answers.
Answer:
Chord: RT (and RS and TU, but those are also diameters)
Diameter: RS or TU
Radii: OU, OS, OT, or OR
Step-by-step explanation:
Chord: A line segment joining two points on a curve. Doesn't have to cross the center. (AKA, they have to touch the outer edge of the circle.)
Diameter: Chord that crosses the center of the circle(All examples given above cross center O)
Radius: Line segment that goes from the center of a circle to an endpoint that lies on the circle.
David leaves the house to go to school. He walks 200 meters west and 125 meters north. How far is he from his starting point?
Answer:
325 meters
200+125=325
Step-by-step explanation: