The explicit formula for the sequence is 3n -10
What is an Arithmetic Sequence ?An arithmetic sequence is a series of terms which have common difference between its consecutive numbers.
The sequence given is
−7, −4, −1, 2, 5, …
The common difference between each term is d =3
-4-(-7) = 3
-1-(-4) =3
The nth term for a sequence is given by
[tex]\rm T_n = a +(n-1)d[/tex]
Here a is the first term = -7
n is the no. of terms = n
d is the common difference = 3
Therefore the equation will be
[tex]\rm T _n = -7 + (n-1) * 3[/tex]
[tex]\rm T _n[/tex] = -7 +3n -3
[tex]\rm T _n[/tex] = 3n -10
Therefore the explicit formula for the sequence is 3n -10 .
To know more about Arithmetic Sequence
https://brainly.com/question/15412619
#SPJ1
Evaluate -3x² + 4x-2 for x = 2.
A. -2
B. -1
C. -6
D. 18
Answer:
C. -6
Step-by-step explanation:
-3(2)²+4(2)-2
-3(4) + 8 - 2
-12+8-2
-14+8
-6
what is Math?
who ever answer this question I shall mark him as brainiest.
Answer:
Maths is the subject which deals with numbers, calculations, areas, geometry etc
Various topics in maths are
trigonometry
geometry
airthmatic
etc
you buy a car for 13000
The correct answer is option D which is the model will be
A = 13000( 0.72 ) [tex].^t[/tex].
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that:-
The cost of the car is $13000.The depreciation is 28%.The expression will be formed as:-
As we can see that the depreciation of the car per year is 28% so the amount of the car is decreased by 28 percent every year.
Now the remaining value of the car will be 100 - 28 = 78%. So the expression will be given as:-
A = 13000( 0.72 ) [tex].^t[/tex].
Therefore the correct answer is option D which is the model will be
A = 13000( 0.72 ) [tex].^t[/tex].
To know more about Expression follow
https://brainly.com/question/723406
#SPJ1
The orbital period of a satellite is 2 × 106 s and its total radius is 2.5 × 1012 m. the tangential speed of the satellite is m/s. (round to the nearest whole number, do not add any punctuation.)
Answer:
7,853.982
Step-by-step explanation:
Edg 2022
A blueprint of a house shows a dining room with
an area of 7 square inches. If the blueprint's
scale is 1 inch: 6 feet, what would be the actual
area of the dining room?
A = 7 in.²
Actual Area = [?] ft²
Answer: The Actual area of the dining room is 252 square feet.
Explanation:
How to Find the Actual Area Using Scale?
Given that the area of the house on a blueprint = is 7 square inches.
The scale of the blueprint = is 1 inch: 6 feet.
Therefore, we would have the following proportion:
The area on the blueprint/actual area = square of the scale
7/actual area = 1²/6²
7/actual area = 1/36
Actual area = (7)(36)
Actual area = 252 square feet.
Which statement is true about the information in the double line graph?
A. The number of customers at 12:00 was less on Friday than Saturday.
B. There were more customers on Saturday than Friday.
C. The number of customers was less Saturday than Friday at 10:00 a.m. because many customers slept later.
D. The highest number of customers on both days was at 12:00 p.m.
Answer:
the answer is d as 38 31 which are highest
Step-by-step explanation:
a is false as 38>31 which is on Saturday
b is false as Saturday customers were less we can infer from the last three on Friday
c false as Saturday was 12 people and Friday 6 people
A building in a city has a rectangular base. the length of the base measures 65 ft less than twice the width. the perimeter of this base is 890 ft. what are the dimensions of the base? the width of the base is ft.
By solving a system of equations, we will see that the width is 170ft and the length 275 ft.
How to get the dimensions of the base?
For a rectangle of length x and width y, the perimeter is:
P = 2*(x + y).
Here we know that:
x = 2y - 65ft
p = 890ft = 2(x + y)
So we have a system of equations.
To solve this, we need to replace the first equation into the second one:
890ft = 2(x + y)
890ft = 2(( 2y - 65ft) + y)
Now we can solve this for y.
890ft = 4y - 130ft + 2y
890ft + 130ft = 6y
1020ft/6 = y = 170ft
So the width is 170ft, and we know that:
x = 2y - 65ft = 2*(170ft) - 65ft = 275ft
So the length is 275 ft.
If you want to learn more about systems of equations:
https://brainly.com/question/13729904
#SPJ1
Can someone help me please
===========================================================
Explanation:
Focus on the endpoints (0,15) and (10,0). They are the y and x intercepts in that order. This is the starting point and ending point of the ball.
The average rate of change is the slope of the line connecting these endpoints. This is when we consider the entire time the ball is in the air.
Let's use the slope formula to get the following:
[tex](x_1,y_1) = (0,15) \text{ and } (x_2,y_2) = (10,0)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{0 - 15}{10 - 0}\\\\m = \frac{-15}{10}\\\\m = -\frac{3}{2}\\\\[/tex]
The slope is -3/2, which is the average rate of change.
It tells us that the height is decreasing by 3/2 = 1.5 meters per second, which is an average speed.
In other words, the ball is going downward at an average speed of 1.5 meters per second.
Keep in mind the instantaneous speed of the ball is changing all the time. The result of -3/2 = -1.5 only applies to the average speed.
------------
Note how the slope formula involves computing the change in y (which was us computing [tex]y_{2} - y_{1} = 0 - 15 = -15[/tex]. It indicates the ball had gone down 15 meters when going from the start point to the ending point. This is the change in distance. The change in time is the [tex]x_{2} - x_{1} = 10-0 = 10[/tex] portion, meaning the duration is 10 seconds.
In short,
slope = rise/run
slope = (change in distance)/(change in time)
slope = (-15)/(10)
slope = -3/2
So this may be a better way to see what's going on rather than rely on a formula in the previous section.
two identified lines are graphed below how many solutions are there to the system of equations?
A researcher finds that the more hours students party per week, the lower their gpas (grade point averages). she questions whether there may be other issues affecting the students' gpas that weren't taken into account, such as the number of hours spent studying, class attendance, or the number of hours worked at campus jobs. what are these additional factors called
Answer:
I believe "uncontrolled variables."
Step-by-step explanation:
Since there was no measure, nor control, of these other variables, the data may be questionable.
If a cubic foot of stone weighs 150 lbs and a cubic foot of iron weighs 480 lbs, what fraction of the second weight is the first weight. 50 pts.
Answer:
[tex] \frac{150}{480} = \frac{15}{48} = \frac{5}{16} [/tex]
The weight of a cubic foot of stone is 5/16 the weight of a cubic foot of iron.
If x² + 1/x² = 102, then x -1/x =
a) 10
b) 8
c) 13
d) 12
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:A. \:\: 10[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } = 102[/tex]
[ subtract 2 from both sides ]
[tex]\qquad \tt \rightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } - 2 = 102 - 2[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } - \bigg( 2 \sdot x \sdot \cfrac{1}{x} \bigg)= 100[/tex]
[ 2 can written like that, as they cancel out each other ]
Apply Identity [ a² + b² -2ab = (a - b)² ]
[tex]\qquad \tt \rightarrow \: \bigg (x - \cfrac{1}{x} \bigg) {}^{2} = 100[/tex]
[tex]\qquad \tt \rightarrow \: x - \cfrac{1}{x} {}^{} = \sqrt{100}[/tex]
[tex]\qquad \tt \rightarrow \: x - \cfrac{1}{x} {}^{} = 10[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
please answer this i need helppp
Answer:
D. between 5.4 cm and 6.5 cm
Step-by-step explanation:
The segment is about 6cm
and 6cm is between 5.4 and 6.5
please help me i'll mark you as brainiest if u give me the right answers
Answer:
Here's your answer guy
Step-by-step explanation:
a)cat
b)8
c)6....
Point G is on line segment FH. Given FH=4x+8,FH=4x+8, FG=x,FG=x, and GH=5x,GH=5x, determine the numerical length of \overline{GH}. GH .
The numerical length of GH is 20.
Given, FH=4x+8, FG=x and GH=5x.
We need to determine the numerical length of GH.
What is a line segment?In geometry, a line segment is a part of a line that is bounded by two distinct end points and contains every point on the line that is between its endpoints.
Given Point G is on the line segment FH, then FG + GH = FH.
Now, substitute the given values into the formula as shown:
x + 5x = 4x + 8
6x = 4x + 8
6x - 4x = 8
2x = 8
x=4
To get the length of GH substitute x=4 for 5x
That is, GH = 5(4)= 20
Hence, the numerical length of GH is 20.
To learn more about a line segment visit:
https://brainly.com/question/25727583.
#SPJ1
Simplify [tex]\sqrt{18}. \\[/tex]
[tex]A; 2\sqrt{3} \\B; 2\sqrt{9} \\C; 3\sqrt{2} \\D; 9\sqrt{2} \\[/tex]
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{Option C, 3}\sqrt{2}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\sqrt{18}[/tex]
Find: [tex]\textsf{Simplify the expression}[/tex]
Solution: In order to get a number outside of the square root there must be two of them inside of the square root. The first step that we need to take is to break down the number 18 into it's lowest factors and then take out the numbers can be taken out.
Break down the number 18
[tex]\sqrt{18}[/tex][tex]\sqrt{\textsf{2 * 3 * 3}}[/tex][tex]\sqrt{\textsf{2 * 3}^2}[/tex]Take 3 outside of the square root
[tex]\sqrt{\textsf{2 * 3}^2}[/tex][tex]\textsf{3}\sqrt{\textsf{2}[/tex]Therefore, the option that would best match the results that were solved for is option C, [tex]\textsf{3}\sqrt{\textsf{2}[/tex]
What is the value of x?
(See attached image for details.)
Enter your answer in the box.
x =
Answer: x = 12
Step-by-step explanation: The given triangle is an equilateral triangle. Equilateral triangles have all angles and all sides equal. Thus, let's solve for x knowing all 3 equations are equal. For this, only 2 equations are necessary.
5x - 22 = 4x - 10
Adding 22 to both sides, we get:
5x = 4x + 12
Subtracting 4x to 5x, we get:
x = 12.
Thus 5*12 - 22 = 38, and 4*12 - 10 = 38, and so is 3*12 + 2 = 38. Thus, we know this is correct.
Answer:
x = 12
Step-by-step explanation:
Hello!
All three angles are congruent, indicating that this is an equilateral triangle.
The rules of this triangle say that all sides are congruent.
We can solve for x by setting any 2 sides equal to each other. I'm picking AB and BC.
Solve for x4x - 10 = 3x + 24x - 3x - 10 = 2x - 10 = 2x = 12The value of x is 12.
HELP IM TIMED!!!!
X
-2
-1
0
1
2
3
f(x)
20
0
-6
-4
0
0
Which is an x-intercept of the continuous function in the
table?
O (-1,0)
O (0, -6)
O (-6,0)
O
(0, -1)
What are the values of x and y? A) x = 4sqrt(3) y 8√3 B ) x = 8; y = 4 ) x = 8sqrt(3); y = 4sqrt(3) D) x = 6sqrt(3); y = 3sqrt(3)
Answer:
C.
Step-by-step explanation:
IF YOU SEE A RIGHT ANGLED TRIANGLE APPLY THE TRIG RATIOS*
The values in the table define the function f(x). If g(x) is the inverse of f(x), what is the value of g(1)? x f(x) -1 -3 1 -1 4 1 6 4 7 6 A. 1 B. 2 C. 3 D. 4 E. 5
The value of g(1) is 4 because (x, y) satisfy the function f(x) then (y, x) will satify the function g(x) option (D) 4 is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
As we know if the f(x) has inverse function g(x)
Let (x, y) satisfy the function f(x) then (y, x) must satify the function g(x)
f(x) has ordered pair = (4, 1)
Then g(x) has (1, 4)
g(1) = 4
Thus, the value of g(1) is 4 because (x, y) satisfy the function f(x) then (y, x) will satify the function g(x) option (D) 4 is correct.
Learn more about the function here:
brainly.com/question/5245372
#SPJ1
If you receive a 20% DISCOUNT off an item costing $20.00, how much money do you save?
Work out the length of x.
Give your answer rounded to 3 significant figures.
8.6 cm+
x
The diagram is not drawn accurately.
Answer:
12.2cm
Step-by-step explanation:
Follow the steps in the image I send you to learn it if you don't get it tell me.
A rectangle has a length 10 more than its width. If the width is increased by 8 and the length by 4, the resulting rectangle has an area
of 135 square units.
Part A
•
Write an equation to model the above scenario. Use the model to find the length of the original rectangle?
Part B
What is the perimeter of the expanded rectangle?
Answer:
The perimeter is 48
Step-by-step explanation:
If the width is W
AT first , Length is 10 +w
According to the question,
[tex](w+8) (10+w+4) = 135\\(w+8) (w+14) = 135\\\\w^{2} + 14w + 8w + 112- 135 = 0\\\\ w^{2} + 22w - 23 = 0\\(w+23) (w-1) = 0\\\\w+ 23 = 0 w-1=0\\\\w= -13 or w = 1[/tex]
Expended width will be w +8 = 1+8 = 9
Length is 10+w+4 = 15
So the perimeter is
= i2 x (9+15)
= 2x 24
= 48
The Solution to the problem of the rectangle is given below
For Part A:
equation model: (14 + w) * (w +8) = 132Length = 15For Part B
Perimeter = 46Meaning of Perimeter
The perimeter of any shape can be defined as the total sum of the sides of the shape.
AnalysisFor Part A
equation model= (14 + w) * (w +8) = 135
14w + 112 + 8w + [tex]w^{2}[/tex] = 135
[tex]w^{2}[/tex] + 22w - 23 = 0
solving the quadratic equation
w = -23 or 1
Because we are dealing with a physical quantity we will make use of the value 1
lenght of original rectangle = 10 + 1 = 11
Part B
Perimeter= 2(length) * 2 (breadth) = 2(11 + 4) * 2 (1 + 8)
Perimeter = 48
In conclusion, The Solution to the problem of the rectangle is given above.
Learn more about Perimeter: https://brainly.com/question/19819849
#SPJ1
Find the length of the unknown side. Round your answer to the nearest whole number.
Image of a right triangle with legs labeled 7 meters each. The hypotenuse is unknown.
7 meters
9 meters
10 meters
12 meters
Answer: 10
Step-by-step explanation:
√( 7^2 + 7^2 ) = 10
Maggie and Tanya went to a fruit store. Maggie bought 10 oranges and 5 apples for $4. Tanya bought 9 oranges and 3 apples for $3. What is the cost of an orange and an apple?
Answer:
orange: 0.2$, apple: 0.4$
Step-by-step explanation:
we mark the price of an orange x and the price of an apple y. then we write down Maggie's and Tanya's purchases as a set of equations:
10 oranges and 5 apples for 4$ means:
[tex]10x + 5y = 4[/tex]
9 oranges and 3 apples for 3$ means:
[tex]9x + 3y = 3[/tex]
we use the second equation to isolate y:
[tex]3y = 3 - 9x \\ y = 1 - 3x[/tex]
and plug it in the first equation:
[tex]10x + 5(1 - 3x) = 4 \\ 10x + 5 - 15x = 4 \\ 1 = 5x \\ x = 0.2[/tex]
and then we find y:
[tex]y = 1 - 3 \times 0.2 \\ y = 0.4[/tex]
A cube has edges measuring 8 centimeters.
Find its surface area.
(please)
In 2000, the number of people with a home phone in Indiana was 3,286,000. If the number of home phones have decreasing by 4% each year,
how many Hoosiers will have a home phone in 2011? Round to two-decimal places.
Hoosiers
Pause test
3286000x4/100=131440
131440x11=1445840
3286000-1445840=1840160
Answer: 1840160
this is the answer I got but for some reason the answer didn't turn out to be in decimal :( but I sware this is the answer I got
Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The executives hire a statistical consultant and ask her to determine the mean shopping time, , of customers at the supermarkets. The consultant will collect a random sample of shopping times at the supermarkets and use the mean of these shopping times to estimate . Assuming that the standard deviation of the population of shopping times at the supermarkets is minutes, what is the minimum sample size she must collect in order for her to be confident that her estimate is within minutes of
The sample size is 289.
Zα/2 = [tex]Z_{0.025}[/tex]
= 1.96
Sample size = n
n = [Zα/2* σ / E] 2
n = [1.96 * 26 / 3 ]2
n = 288.54
n = 289.
In records, the pattern size is the measure of the number of man or woman samples used in an experiment. As an example, if we are testing 50 samples of folks that watch tv in a town, then the sample length is 50.
An awesome sample length is normally 10% as long because it no longer exceeds a thousand. A very good sample length is commonly around 10% of the populace, as long as this doesn't exceed one thousand. for example, in a populace of 5000, 10% could be 500. In a populace of 200,000, 10% would be 20,000.
Learn more about the sample size here https://brainly.com/question/25574075
#SPJ4
Can someone help me on this please
Answer:
17.7 (2 dp)
Step-by-step explanation:
[tex] \sqrt{ {16}^{2} + {7.5}^{2} }[/tex]
This is from the last question
Answer:
huh
Step-by-step explanation:
what are you trying to figure out-
