Understanding:
The sum of a geometric series is, [tex]a+ar+ar^2+ar^3+...[/tex], with a being the start point and r is the common ratio. We can also use the following formula to make life easier [tex]S_n=a\frac{1-r^n}{1-r}[/tex], a is your start point, r is the common ratio, and n is the number of terms, which in our case is S7.
Solution:
Our start point is 1, [tex]a=1[/tex],
The common ratio is 5, [tex]r=5[/tex],
And finally, the number of terms is 7, [tex]n=7[/tex].
[tex]S_n=a\frac{1-r^n}{1-r} \\=(1)\frac{1-(5)^{(7)}}{1-(5)} \\=\frac{1-78125}{1-5} \\=\frac{-78124}{-4}\\=19531[/tex]
The answer is [A] 19531.
The area of rectangular kitchen tile is 6x^2-8x-30. The width is 2x-6.
A) what is the length of the kitchen tile?
B) Find the perimeter
Answer:
L=6x^2-4x+5
P=12x^2-4x-2
Step-by-step explanation:
A=WL
So, we know the area is 6x^2-8x-30 and the width is 2x-6
Substitute
(6x^2-8x-30)=(2x-6)(L)
L=(6x^2-8x-30)/(2x-6
Divide
L=6x^2-4x+5
P=2L+2W
Substitute
P=2(6x^2-4x+5)+2(2x-6)
P=12×^2-8x+10+4x-12
Simplify
P=12x^2-4x-2
If the principal is $6,321 and the rate of interest is 4.5%, what is the amount of interest after five year?
Answer:
$6889.89
Step-by-step explanation:
6321/100=63.21
63.21x4.5=284.445
284.445x5=568.89
568.89+6321=$6889.89
- 1/2 ( -5/6 + 1/4)
Answer:
0.29166666666
Step-by-step explanation:
Answer:
0.29166666666
Your answer...
PLS HELP!! 9-3 divided by 1/3+1=________.
Answer:-3
Step-by-step explanation:
Mia and Troy work on weekends. The table and graph show the amount of money they made over four weeks.
After week 1, Mia’s total earnings were Troy’s.
After week 3, Troy’s total earnings were Mia’s.
Answer: greater than, the same as
Step-by-step explanation:
The solution is : After 7 weeks, Mia's office will have recycled 21 pounds.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
With the information provided, you can use a rule of three to find the pounds of paper that Mia's office will have recycled after 7 weeks given that they recycled 9 pounds over 3 weeks.
3 weeks → 9 pounds
7 weeks → x
x=(7*9)/3
x=21
According this, the answer is that after 7 weeks, Mia's office will have recycled 21 pounds.
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Complete question:
Mia's office recycled a total of 9 pounds of paper over 3 weeks. After 7 weeks, how many pounds of paper will Mia's office have recycled? Choices: 24 21 15 18
A cheetah can run at its top speed for about 25 seconds. Complete the table to represent a cheetah running at a constant speed.
Answer:
Put a picture Then I can help hun
Step-by-step explanation:
Answer:
ok this was a good one so here
Step-by-step explanation:
time (seconds)
distance (meters)
speed (meters per second)
4 120 30
25 750 30
9 270 30
f (x) = -x + 7 identifiy 0
Answer:
7
Step-by-step explanation:
[tex]f (x) = -x + 7 \\ \\ plug \: f (x) = 0 \\ \\ 0 = - x + 7 \\ \\ x = 7 \\ \\ zero \: is \: 7[/tex]
Which one is it need helpllll
Answer:
it is D) 25
Step-by-step explanation:
a budget of $225 for costumes for the school play. She
spent $86.56 on jackets and $45.38 on hats. How much money does
Melanie have left in the budget?
HELPPPPP PLEASE FASTTT
Answer:
93.06
Step-by-step explanation:
86.56 + 45.38 = 131.94
225 - 131.94 = 93.06
A community is building a new outdoor basketball court. The length of the court is twice the width.
Answer:
Step-by-step explanation:
The width of the basketball court is given by W(A) = √(A/2), and the length is given by L(A) = √(2A). These expressions allow you to calculate the width and length of the court for a given area A in square feet.
The problem states that the width of the basketball court (W) can be modeled by the equation:
W(A) = √(A/2)
where A is the area of the court in square feet.
Since the length (L) of the basketball court is twice the width (W), we can express it as:
L = 2W
Now, let's find the expression for the length (L) in terms of the area (A) of the court.
Step 1: Substitute the value of W from the given model into the expression for L:
L = 2 × √(A/2)
Step 2: Simplify the expression:
L = √(4A/2)
L = √(2A)
So, the expression for the length (L) of the basketball court in terms of its area (A) is given by L = √(2A).
To summarize, the width of the basketball court is given by W(A) = √(A/2), and the length is given by L(A) = √(2A). These expressions allow you to calculate the width and length of the court for a given area A in square feet.
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Complete question :- A community is building a new outdoor basketball court. The length of the court is twice the width. The width of the basketball court in feet can be modeled by w(A)= √A/2 where a is the area in square feet of the court.
Jenn made 18 correct and 12 incorrect decisions for a total of 30 points. Mara made 16 correct and 8 incorrect decisions for a total of 32 points
Answer:
Jenn: 12/30 incorrect 18/30 correct
Mara. 8/24 incorrect 16/24 correct
Step-by-step explanation:
Could you ask the question???? This isn’t a questions it more like a statement so I tried to do my best and I just made them into fractions
*BRAINIEST & 20 POINTS*
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
8 = x
y = 29
Step-by-step explanation:
4x + 17 = y + 20 because vertical angles theorem.
y + 20 = 5x + 9 because interior angles theorem.
4x + 17 = 5x + 9 because same side interior angles theorem.
Subtract 9 from both sides and subtract 4x from both sides.
8 = x
Plug 8 in for x and solve.
5 times 8 is 40, plus 9 equals 49. Subtract 20 from both sides and you get 29.
5(8) + 9 = y + 20
49 = y + 20
29 = y
I hope this helps!
#teamtrees #WAP (Water And Plant)
Answer:
[tex]for \: answer \: see \: the \: pic \: along \\ \: with \: it. \\ \\ \\ hope \: it \: helps \: \\plz\: mark \: as \: brainliest \: answer..[/tex]
"A rectangle has a height of 5 cm and its base is increasing at a rate" of 3/2 cm/min. When its area is 60 cm2, at what rate is the diagonal of the rectangle increasing?
The rate at which the diagonal of the rectangle is increasing is 18/13 cm/min.
To find the rate at which the diagonal of the rectangle is increasing, we can use the relationship between the sides of the rectangle, its area, and the diagonal.
Given that Height of the rectangle (h) = 5 cm
The rate at which the base is increasing (db/dt) = 3/2 cm/min
Area of the rectangle (A) = 60 cm²
We can determine the base (b) using the formula for the area of a rectangle:
A = b x h
60 = b x 5
b = 12 cm
Next, the Pythagorean theorem:
d² = b² + h²
d² = 12² + 5²
d² = 144 + 25
d² = 169
d = 13 cm
Now, to determine the rate at which the diagonal is increasing (dd/dt), we can differentiate the equation for the diagonal with respect to time:
d² = b² + h²
2d x (dd/dt) = 2b x (db/dt) + 0 x (dh/dt)
2d x (dd/dt) = 2b x (db/dt)
(dd/dt) = (b (db/dt)) / d
Substituting the known values:
(dd/dt) = (12 x (3/2)) / 13
(dd/dt) = 36/26
(dd/dt) = 18/13 cm/min
Therefore, the rate at which the diagonal of the rectangle is increasing is 18/13 cm/min.
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-3.09 + x = -0.7
please solve for x :)
Answer:
x =2.39
Step-by-step explanation:
;D
Given f(x) = 17( 3 + x), what is the value of f(-2)?
Answer: 17
Step-by-step explanation:
F( -2) = 17 ( 3 -2)
= 17 (1)
=17
Which graph represents a relation that is also a function?
( look at the graph and help me pls )
Factor the expression using the GCF: (42 + 12 ) = __ ( __+ __ )
Answer:
2
Step-by-step explanation:
Answer:
6(7+2) hope this helps
Step-by-step explanation:
(42 + 12 )
= 6(7+2)
Fluffy bunny ate 1/2 of a carrot in the morning by the end of the day he started 2/5 of how much of the Caribbean fluffy eat at night
Answer: I think it’s 0.1 or 1/10 but I’m kinda confused
Step-by-step explanation: someone pls correct me if I’m wrong
1/2 is 0.5
2/5 is 0.4
0.5-0.4=0.1
0.1=1/10
1/10 of carrot, fluffy will eat at night.
What is fraction?Fractions represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator, below one is called denominator
Given,
Fluffy bunny ate 1/2 of a carrot in the morning
By the end of the day he ate 2/5 of left carrot = 2/5
Whole carrot can be considered as 1.
Carrot left after eating 1/2 of it in the morning
= 1 - 1/2
= 1/2
Carrot left after eating 2/5 part
= 1/2 - 2/5
= (5 - 4)/10
= 1/10
Hence, fluffy ate 1/10 of carrot at night.
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x+3y=0
9y=-3x
how many solutions does this sytem have
Answer:
0 solutions
Step-by-step explanation:
when the 2 equations aresolved they get cancelled off each other.
Answer:
Infinite solutions
Step-by-step explanation:
got it right
what is the bill for 10 day rental b = 45.95d + 38.5
Answer:
b = 498
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
b = 45.95d + 38.5
d = 10 days
Step 2: Evaluate
Substitute: b = 45.95(10) + 38.5Multiply: b = 459.5 + 38.5Add: b = 498Answer:
498 dollars
Step-by-step explanation:
So just plug in the 10 in the equation for D
45.95*10+38.5
Now just solve using order of operations
You would get 498
Kayla is going to invest in an account paying an interest rate of 2.9% compounded
monthly. How much would Kayla need to invest, to the nearest cent, for the value of
the account to reach $42,000 in 6 years?
Answer:
the answer is 48m^2!
Step-by-step explanation:
Answer:
The answer is 35299.88. Hope this helps
What is the measure of H?
PLEASE HELP
Answer:
h = 100
Step-by-step explanation:
plz mark my answer as brainlist plzzzz vote me also
Answer:
100°
Step-by-step explanation:
Ok so it looks overwhelming at first, but you just need to make sections and break it down
You are looking for h°, so you want to make it a triangle
The angles of this triangle would be h°, 40°, and x°
You can find x° by using the 140° on the same line
it is a straight line, so that means its angle is 180°
180° - 140° = 40°
x° = 40 °
so now you know that the angles in the triangle are h°, 40°, and 40°
Every triangle has angles that measure to 180°
180° - 40° - 40° = 100°
h° = 100°
On Monday, Greg walks the entire length of a trail that is 4 3/4 miles long. On Tuesday, he walks the entire length of a trail that is 3.8 miles long. On Wednesday, he starts out on a trail that is 2 3/5 miles long, but he does not walk the final 1.7 miles. How many miles does Greg walk in all on Monday, Tuesday, and Wednesday?
Answer: it's B
Step-by-step explanation:
Answer:
D) 9 9/20
Step-by-step explanation:
Step 1:
4 3/4 + 3.8 + (2 3/5 - 1.7)
Step 2: Order of Operation (AKA PEMDAS)
4 3/4 + 3.8 + (2 3/5 - 1.7)
Step 3:
4 3/4 + 3.8 + (9/10)
Step 4: Add it all up
4 3/4 + 3.8 + (9/10) = 9 9/20
please hurry ! ! which linear inequality is represented by the graph?
Answer:
y>2/3x+3
Step-by-step explanation:
Answer and Step-by-step explanation:
The answer is the third option, or:
[tex]y > \frac{2}{3} x + 3[/tex]
This is because the line has a rise of 2 and a run of 3 (so a slope of 2/3)
and Everything is filled in above the line, so y is greater than the the values on the line and below the line.
#teamtrees #WAP (Water And Plant)
can someone please help me solve
x to the third power=1,000
Answer:
x=10
Step-by-step explanation:
Answer:
it is 10 :)
Step-by-step explanation:
Aaron ran 5/8 mile to his friend's house. Then he ran another 1/4 mile to the park.
Complete question : Aaron ran 5/8 mile to his friend's house. Then he ran another 1/4 mile to the park. Find Aaron's total miles ran?
Answer:
7/8 miles
Step-by-step explanation:
Given that:
Distance to friend's house = 5/8 miles
Then, Distance to park = 1/4 miles
Total. Distance ran :
(5/8 + 1/4)
L.C.M of 4 and 8 = 8
(5 + 2) / 8 = 7/8 miles
Total distance ran = 7/8 miles
–18 • –17 please hrlp
Answer:
The answer is 306
Step-by-step explanation:
(−18)(−17)
=306
What statement best describes the function notation f(2)=10
Answer: 12
Step-by-step explanation:
anybody solve this i made it its easy
3(55x2) + 9 + 44 +88 x 9 = your number + 163593
Answer:
165*6+53+792= 990+845 = 1,835
Step-by-step explanation:
The air conditioning unit for marcus building has the shape of a cube and has a volume of 0.512 cubic meters.This air conditioner will be replaced with another cube-shaped unit with a volume of 1 cubic meter. By how much will the edge length of the air conditioner change?
Answer:
The edge length of the air conditioner changed by 0.2m
Step-by-step explanation:
The volume of a cube is S^3
The edge length of the former unit is cube root of 0.512 which is 0.8 m
The edge length of the new is cube root of 1 which is 1 m
The difference is 1-0.8 = 0.2 m