Solve It for an arithmetic sequence
First term=a=12Common difference=d=-4So
a_n=a+(n-1)dHence
a_40:-
a+(40-1)da+39d12+39(-4)12-156-144Answer:
[tex]f(40)=-144[/tex]
Step-by-step explanation:
Given:
[tex]f(1)=12[/tex][tex]f(n)=f(n-1)-4[/tex]This is a recursive arithmetic sequence since each term is defined using the previous term.
To find the nth term, convert the recursive formula to an explicit formula.
Explicit form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]
where:
[tex]a_n[/tex] is the nth terma is the first termd is the common difference between termsWe have been given the first term: [tex]a=12[/tex]
To get any term from its previous term we subtract 4, so the common different (d) is -4.
Therefore, the formula for the nth term is:
[tex]\implies a_n=12+(n-1)(-4)[/tex]
[tex]\implies f(n)=16-4n[/tex]
To find [tex]f(40)[/tex] simply substitute n = 40 into the explicit formula:
[tex]\implies f(40)=16-4(40)=-144[/tex]
Easy function or not
Answer:
Problem 9: No
Problem 10: Yes
Step-by-step explanation:
Hello!
Problem 9:
This is NOT a function because one x-value has only one unique y-value. -2 is seen twice and the outputs, y, are given as 6 and 0.5. To be a function, each input has its own unique output. Two different inputs can have the same output.
Problem 10:
This IS a function, all inputs have unique outputs, and no repeating inputs are shown.
Terms:
x - values are also known as input, abscicca
y - values are also known as output, ordinate.
what's 3/4 divided by 1 1/5
15/44
Step-by-step explanation:
change the division sign to multiple. flip the numbers 11 and 5 around. multiple 3 times 5 then 4 times 11.
A mountain road drops 5.2 m for every 22.5 m of the road. Calculate the angle at which the road is inclined to the horizontal.
Answer:
13°
Step-by-step explanation:
sin(Ф)= opposite/ hypothenuse
sin(Ф) = 5.2/22.5
Ф= sin∧-1 (5.2/22.5)
Ф= 13.36°
What happens to the mode of the data set shown below if the number 8 is added to the data set?
12,8,13,9,10,10,15,14,13,6,40,11,15,15,8,7
A. There is no mode.
B. The mode will not change.
C. There will be two modes.
D. The mode increases by 6.
PLEASE HURRY
Answer:
d the mode increase by 8
Step-by-step explanation:
mode is affected due to change in origin by same constant value
Answer:
C
Step-by-step explanation:
There will be 2 modes because 15 and 8 would both repeat 3 times.
How to solve by completing the square??
x^2 +8x=33
We are given the equation x² + 8x = 33, and we need to solve it from completing the square, for which we will be following the below steps
Step 1 :- First, notice, what's the coefficient of x², if it's 1, then proceed to step 2, if not then divide both sides by the coefficient of x²
[tex]{:\implies \quad \sf x^{2}+8x=33}[/tex]
Step 2 :- Here, we need to develop a whole square in both sides somehow, so we have the coefficient of x, so add the square of half of coefficient of x on both sides :
[tex]{:\implies \quad \sf x^{2}+8x+{\bigg(\dfrac82\bigg)}^{2}=33+{\bigg(\dfrac82\bigg)}^{2}}[/tex]
Simplify both sides now :
[tex]{:\implies \quad \sf x^{2}+8x+(4)^{2}=33+(4)^{2}}[/tex]
Step 3 :- So now, here LHS is in the form of a² + 2ab + b², so we can just replace it by (a + b)², and we will keep simplifying RHS
[tex]{:\implies \quad \sf (x+4)^{2}=33+16}[/tex]
[tex]{:\implies \quad \sf (x+4)^{2}=49}[/tex]
[tex]{:\implies \quad \sf (x+4)^{2}=(\pm 7)^{2}}[/tex]
Step 4 :- As, power on both sides is 2, so we can just equate the bases
[tex]{:\implies \quad \sf x+4=\pm 7}[/tex]
Step 5 :- Equating x + 4 to 7, will yield x = 3, and equating it to -7, will yield x = -11, so we are now left with
[tex]{:\implies \quad \boxed{\bf{x=-11,3}}}[/tex]
Which is greater: 3.5 or 6/5
3.5 is greater as 6/5 = 1.2
Answer:
3.5
Step-by-step explanation:
6/5 = 1.2
3.5 > 1.2
look at the number line below what point is marked on the number line
Answer:
-2.5
Step-by-step explanation:
The point is between -2 & -3
How many square yards are there in a floor which is 9 feet long by 21 feet wide?
Answer:
Step-by-step explanation:
Length of floor=9ft=3 yard
Breadth of floor=21ft=7 yard
Area of floor=lb=3×7=21yard²
what is (1/8) to the power of 8
Answer:
5.96 when rounded to the nearest hundredth
Step-by-step explanation:
Brent plays three sports: basketball, baseball, and soccer. He calculated the mean absolute deviation of the points he scored in each season.
basketball: mean absolute deviation of 4.6
baseball: mean absolute deviation of 3.5
soccer: mean absolute deviation of 1.2
In which sport were his scores the most spread out?
baseball
soccer
basketball
Answer:
basketball
I hope this is useful
Answer: (C) Basketball
Step-by-step explanation: I took the test and that is the answer.
HELP ME OUT PLS!!!!!!!!!
Which purchase are people most likely to regularly save a small amount of money for, and then let the value grow over time?
A) going to the movies
B) retirement
C) buying audiobooks
D) going to a concert
Answer:
B) retirement
Step-by-step explanation:
Retirement is the only one that makes sense to me when you regularly save a small amount of money, and then letting the value grow over time.
Hope this helps!!
Find the reciprocal of [tex]$\frac{1}{-2} \cdot \left(-\frac{1}{3}\right) \cdot \frac{1}{-4} \cdot \left( -\frac{1}{5} \right)$.[/tex]
Answer:
120
Step-by-step explanation:
Lets take it step by step!
Step 1 : first mutiply -1/2 * -1/3
-1/2 * -1/3 = 1/6
(remember to mutiply fractions we have to mutiply there denominator and numerator together)
Step 2 : then move on and multiply 1/6 * -1/4
1/6 * -1/4 =
-1/24
Step 3 : Next we have to go and multiply -1/24 by -1/5
-1/24 * -1/5 =
1/120
Step 4 : Finally we switch the numerator and denominator to find its reciprocal which is :
120!
GUYS HELP ASAP
CHECK THE ATTACHED PHOTO
Answer:
As they triangles are congruent, we can say that, angle A = angle O
So, angle A = 105+25 =130
A = 180 - 130 = 50° all angles in a triangle add up to 180)
Soo 50° is the answer,
I'm not too sure about it but I think this is correct, hope this helps, correct me if I'm wrong....
A company rents moving trucks for $45 plus $0.75 per mile. write an equation that relates the cost C and the miles driven, x. Calculate the cost of
renting a truck for one day, and driving it 110 miles.
The equation we would use here would be 45 + 0.75x = C
This is because we have a flat fee of $45 and you are being charged $0.75 per mile, so it depends on how many miles were driven.
To find out how much it would cost if it were to drive 110 miles, we simply put 110 in place of x;
45 + 0.75(110) = C
And now we solve!
45 + 82.50 = C
$127.50
Hope this helps!
What is the distance between points (-6, -7) and (-1,5) on the coordinate plane?
Answer:
The answer is C. 13
Step-by-step explanation:
Using the information in the table, draw a
graph of the relationship between t, the
time, and d, the total distance traveled by
the train, for a trip that lasted from 0 to 7
hours.
Answer:
Step-by-step explanation:
A bowling ball has an outside layer, and an inner core. One type of bowling ball has a diameter of 8 inches, and the outside layer is an inch thick. what is the volume of the outsdie layer
diameter = 8
radius = 4
outside layer is an inch thick so
radius is 3
volume of a bowling ball is
volume of a sphere which is
4/3 * Pi * radius cubed =
(4/3)*Pi*27=
answer = 82447.96 in^3 or inches cubed
socraticorg
The volume of the outsdie layer whose diameter is of 8 inches is 290 cubic inches.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that bowling ball has an outside layer, and an inner core
One type of bowling ball has a diameter of 8 inches
We have to find the volume of the outsdie layer
Radius of the ball is 4 inches.
Volume of sphere = 4/3πr³
=4/3×3.4×4³
=4/3×3.4×64
=290 cubic inches
Hence, the volume of the outsdie layer whose diameter is of 8 inches is 290 cubic inches.
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Which numbers are perfect squares? Check all that apply.
1
2
16
18
32
44
94
100
Answer:
1, 16, 100
Step-by-step explanation:
Answer:
other persons right i took the test and got it right so 1, 16, and, 100
Step-by-step explanation:
If a boat 26’ long by 8.5’ wide and a can is 4.75” tall by 2.4” wide how many cans can fill the boat?
Answer:
19
Step-by-step explanation:
Pls help me get this. Right
Answer:
26 units
Step-by-step explanation:
so the horizontal distance between the two points is 24 units while the vertical distance is 10 units.
hence, we can use the pythagorean theorem to find the length of the diagonal.
the answer is equal to sqrt( 24^2 +10^2)
the answer is 26 units
also you should always remember that the diagonal is always greater in length than both the vertical and horizontal sides.
make sure to ask if you need any further guidance :)
Triangle ABC is rotated to form △A'B'C'.
The coordinates of point A are (1, 1), the coordinates of point B are (3, 1), and the coordinates of point C are (1, 4).
Which counter clockwise rotation around the origin results in the transformation of △ABC to △A'B'C'?
Select from the drop down arrow to choose the correct rotation.
90 degrees
180 degrees
360 degrees
Answer:
may be 90 degrees for that question
Answer: Rotation of 90
Step-by-step explanation:
Can someone help me figure out angle a in this circle? thank you!
Answer:
[tex]m \angle a = 116 \degree[/tex]
Step-by-step explanation:
By inscribed angle theorem:
[tex]m \angle a = \frac{1}{2} \times m \widehat{(BD)} \\ \\ \implies m \angle a = \frac{1}{2} \times 232 \degree\\ \\ \implies \huge { \orange{m \angle a = 116 \degree}}[/tex]
Joel is selling a motorcycle for $2,535. He bought the
motorcycle two years ago and paid $4,721 for it. It depreciated
35% during the two years. Is he losing money or making money
on this sale?
18. Willa is buying flowers for a large garden project. She plans
Answer:
Joel is losing money.
Step-by-step explanation:
4,721-35%=?
First, convert the percentage into a decimal.
35%=35/100=.35
Then multiply 4721 by .35 which is 1652.35
At last, subtract 4,721 by 1652.35= 3068.65
I need help please and please explain your answer.
Answer:
I think it is B or D
actually it is B i got 100%
Step-by-step explanation:
Write an equation of the
line that passes through
the given points (-3,-1)
(2, 2)
Answer:
[tex]y = \dfrac{3}{5}x + \dfrac{4}{5}[/tex]
Step-by-step explanation:
First, find the slope:
m = (change in y) / (change in x) = rise / run
m = (2 - (-1)) / (2 - (-3)) = (2 + 1) / (2 + 3) = 3/5
Then, write the equation of the line in point-slope form:
y - b = m(x - a) where (a, b) is a point on the line
y - 2 = (3/5)(x - 2)
Finally, solve for y:
[tex]y = \dfrac{3}{5}(x - 2) + 2[/tex]
[tex]y = \dfrac{3}{5}x - \dfrac{6}{5} + 2[/tex]
[tex]y = \dfrac{3}{5}x + \dfrac{4}{5}[/tex]
The top and bottom lines are parallel. What is the value of x?
35
+
80° IX
O A. 45
B. 105
OC. 100
OD. 65
Answer:
65
Step-by-step explanation:
The length and breadth of a rectangular piece of paper are 18 cm and 15 cm respectively. By how much should be length be reduced keeping breadth constant to make area equal to 134 cm².....
Answer:
Area of a rectangle = length x breadth
Given:
area = 134 cm²breadth = 15 cm⇒ 134 cm² = length x 15cm
⇒ length = 134 ÷ 15
= 8.93333333... cm
Reduction in length = original length - new length
= 18 cm - 8.93333333... cm
= 9.07 cm (nearest hundredth)
Decide which other to give him prices is better and explain why. Storage locker A rents for $32/yd2 per month. Storage locker B rents for $1.58/ ft2 per week. Assume 1 month = 4 weeks. Which one is better and why.
Answer:
Locker B
Step-by-step explanation:
When you divide 32 by 3 you get 10.667. Then when you divide that by 4 you get $2.667/ft2 per week.
What is the horizontal difference between (4, 8) and (-2, 2)?
Answer:
6 units
Step-by-step explanation:
the horizontal difference is the distance between the x values of both points. we know the distance between 4 and -2 is 6.
A bag of apples weighs
4.25 pounds. How many
ounces
does the bag of apple
weigh?
Answer:
68 ounces
Step-by-step explanation:
Since 1 pound is 16 ounces, if you use the comparison 1 lb/16 oz=4.25 lb/x oz, you could see that by multiplying 4.25x1, you get 4.25 lbs. So you do the same for the ounces. 16x4.25=68 oz.
The bag of apple weigh is 68 ounces .
What is unit of measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
According to question
A bag of apples weighs = 4.25 pounds
and 1 pounds = 16 ounces
Therefore ,
4.25 pounds = 16*4.25 ounces
= 68 ounces
Hence, the bag of apple weigh is 68 ounces .
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