Answer:
389
Step-by-step explanation:
20 - 11 = 9
29 - 20 = 9
This is a geometric sequence with a common difference of 9.
a_1 = 11
a_2 = 11 + 9
a_3 = 11 + 2 × 9
...
a_n = 11 + (n - 1) × 9
a_43 = 11 + (43 - 1) × 9
a_43 = 11 + 42 × 9
a_43 = 389
Hence, the [tex]43[/tex]rd term is [tex]389[/tex].
What is the sequence?
A sequence is a list of objects, typically numbers, in which order matters, repetition is allowed, and the same elements can appear multiple times at different positions in the sequence.
Here given sequence is [tex]11, 20, 29, ...[/tex]
Here,
[tex]a=11\\\\d=a_2-a_1\\d=20-11\\d=9[/tex]
The general formula is
[tex]a_n=a+(n-1)d[/tex]
where,
[tex]a_n[/tex] is the [tex]n[/tex]th term
[tex]a[/tex] is the first term
[tex]n[/tex] is the number of terms
[tex]d[/tex] is the common difference
Substituting the values in the general formula
[tex]a_n=a+(n-1)d\\\\a_{43}=11+(43-1)9\\\\a_{43}=11+(42)9\\\\a_{43}=11+378\\\\a_{43}=389[/tex]
Hence, the [tex]43[/tex]rd term is [tex]389[/tex].
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Kate has a coin collection. She keeps 7 in a box, which is only 5% of her entire collection. What is the total number of coins in Kate’s coin collection?
Answer:
140
Step-by-step explanation:
5%/100 = 7/?
7 times 100 = 700
700 divided by 5 = 140 coins
(6.1D; 6.1F)
-
1. Which expression is equivalent to 32?
A 23 + (4) – 4 x 2
B 3x3 + (42) - 4
C 42 – 7x0
+
-
D 4x 5 + 2 – 4 + 2
Hey there!
Option A.
23 + (4) - 4 * 2
= 23 + 4 - 4 * 2
= 27 - 4(2)
= 27 - 8
= 19
19 ≠ 32
Option B.
3 * 3 + (42) - 4
= 3 * 3 + 42 - 4
= 9 + 42 - 4
= 51 - 4
= 47
47 ≠ 32
Option C.
42 - 7 * 0
= 42 - 0
= 42
42 ≠ 32
Option D.
4 * 5 + 2 - 4 + 2
= 20 + 2 - 4 + 2
= 22 - 4 + 2
= 18 + 2
= 20
20 ≠ 32
None of them are equivalent to 32
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
A circle is drawn inside a square.
20 cm
The square has a height of 20 cm.
Work out the shaded area.
Give your answer in terms of T.
Which of the following measurements results in the largest circle?
A.
radius = 8 in.
B.
diameter = 8 in.
C.
area = 30 sq. in.
D.
circumference = 30 in.
Answer:
A
Step-by-step explanation:
A) r = 8
B) r = 4
C) r = [tex]\sqrt{\frac{30}{\pi } }[/tex] ~ 3.09
D) r = [tex]\frac{30}{2\pi} = \frac{15}{\pi } ~ 4.77[/tex]
Circle A has the largest radius, and thus is the largest circle
Can someone help me please?
Answer:
[tex]\bold{ \sf \theta = \dfrac{\pi }{9} , \ \ \dfrac{2}{9} \pi , \ \dfrac{7 \pi }{9}, \ \ \dfrac{8\pi }{9}, \ \dfrac{13\pi }{9}, \ \dfrac{14\pi }{9}}[/tex]
Explanation:
[tex]\dashrightarrow \ \ \sf 2sin(3\theta) = \sqrt{3}[/tex]
[tex]\dashrightarrow \ \ \sf sin(3\theta) = \dfrac{ \sqrt{3}}{2}[/tex]
[tex]\dashrightarrow \ \ \sf 3\theta = sin^{-1}(\dfrac{ \sqrt{3}}{2})[/tex]
[ your calc should be in radian mode [R] ]
[tex]\dashrightarrow \ \ \sf 3\theta = \dfrac{\pi }{3} , \ \ \dfrac{2}{3} \pi , \ \ \dfrac{7 \pi }{3}, \ \ \dfrac{8\pi }{3}, \ \dfrac{13\pi }{3}, \ \dfrac{14\pi }{3}[/tex]
[tex]\dashrightarrow \ \ \sf \theta = \dfrac{\pi }{9} , \ \ \dfrac{2}{9} \pi , \ \ \dfrac{7 \pi }{9}, \ \ \dfrac{8\pi }{9}, \ \dfrac{13\pi }{9}, \ \dfrac{14\pi }{9}[/tex]
expand and simplify (x+1)(x+9)
Expansion : [tex](x+1)(x+9) = x(x+9) + 1(x+9) = x^{2} +9x + x + 9[/tex]
Simplify : [tex]x^{2} +10x + 9[/tex]
Answer:
[tex]\huge\boxed{ \bf\:x^{2} + 10x + 9}[/tex]
Step-by-step explanation:
[tex](x + 1)(x+9)[/tex]
Let's expand it at first.
[tex](x + 1)(x + 9)\\= x (x + 9) + 1 (x + 9)\\= x^{2} + 9x + x + 9[/tex]
Now, simplify it.
[tex]x^{2} + x + x + 9\\= \boxed{ x^{2} + 10x + 9}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
–2} -(-5) = 0
-
Can someone please help me
(-2)-(-5)=0
bit 2 minuses= + so:
-2+5=0
3=0
To solve the equation x ^2 - 2x = 3 by the technique of completing the square, you would add 4 to each side of the equation as one of the steps to reaching the solution.
Answer:
x = -1
x = 3
Step-by-step explanation:
[tex]\sf x^2 - 2x = 3[/tex]
Add 1 to both sides:
[tex]\sf \implies x^2 - 2x+1 = 3+1[/tex]
Factor the left side:
[tex]\sf \implies (x-1)^2 = 4[/tex]
Square root both sides:
[tex]\sf \implies x-1 = \pm2[/tex]
Therefore:
[tex]\sf \implies x-1=-2 \implies x=-1[/tex]
[tex]\sf \implies x-1=2 \implies x=3[/tex]
Calculate the constant difference
1,2,3
1
Step-by-step explanation:
Seeing its an arithmetic sequence
T1=1......T2=2.....T3=3
To get your constant difference
T2=T1 is also equals to T3=T2
so 3-2=1 and 2-1=1
therefore the constant difference is 1
PLEASE HELP ASAP 20 POINTS!!!
Answer:
D, I think…
Step-by-step explanation:
I used PEMDAS to go through and simplify and see which values match.
is f=9/5c+32 a linear function
Answer:
"a linear function has the form y = mx + b. "
A soccer player gets 2 points for a goal and 1 point for an assist. If the combined number of goals and assists that a player has is 24, and the total number of points that the player has is 42, which system of equations can be used to determine the number of goals and assists the player has? Assume g represents the number of goals and a represents the number of assists.
g + a = 24. g + 2 a = 42.
g + a = 24. 2 g + a = 42.
g + a = 42. g + 2 a = 24.
g + a = 42. 2 g + a = 24.
Answer:
g + a = 24. 2 g + a = 42.
Step-by-step explanation:
Each goal gets 2 points and each assist gets 1 point
If # of goals = g , and you get 2 points for each goal, then points acquired by goals can be represented by 2g
If # of assists = a, and you get 1 point for each assist, then points acquired by assists can be represented by a
The total # of points the player had was 42. This means that 2g + a = 42 (this is the first equation)
We are also told the player scored a total of 24 goals and assists. If g = # of goals and a = of assists, then g + a = 24 (this is the second equations)
So the two equations are g + a = 24. 2 g + a = 42.
Answer:
g + a = 24. 2 g + a = 42.
Step-by-step explanation
trust
E 18 - 3x D F 150° B с 3.1.1 Show that: BE = AB cos 0 sin (a - 6) - 3.x2 3.1.2 Show that the area of A BCE = x 2 4
Answer:
find the ratio of 15 min and 1hiyr
Given the speeds of each runner below, determine who runs the fastest.
\text{Frank runs 9 feet per second.}
Frank runs 9 feet per second.
\text{Tony runs 299 feet in 34 seconds.}
Tony runs 299 feet in 34 seconds.
\text{Zach runs 1 mile in 396 seconds.}
Zach runs 1 mile in 396 seconds.
\text{Will runs 675 feet in 1 minute.}
Will runs 675 feet in 1 minute.
Zach runs with 14.31 feet per second speed and faster than other runners.
What is Speed?Speed is measured as the ratio of distance to the time in which the distance was covered
Given that Frank runs 9 feet per second.
Speed=Distance /time
=9 feet/ 1 second
=9 feet per second.
Tony runs 299 feet in 34 seconds
Speed=299/34
=8.794 feet per second.
Zach runs 1 mile in 396 seconds.
We know that 1 mile =5280 feet
Speed=5280/369
=14.31 feet per second.
Will runs 675 feet in 1 minute
1 minute is 60 seconds
Speed=675/60
=11.25 feet per second.
Hence, Zach runs with 14.31 feet per second speed and faster than other runners.
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GIVING BRAINLIEST+20 POINTS TO BEST ANSWER FOR THESE 2 QUESTIONS!
1.Which story represents the equation six sevenths times one fourth?
1. Victoria drinks six sevenths of a cup of milk. She drinks one fourth of a cup more of milk. How much milk did she drink in all?
2. Mike walked one fourth mile and then he took the bus for six sevenths mile to school. How many miles did he travel in total?
3.Victoria has six sevenths of a pizza. She ate one fourth of it for dinner. How much pizza did Victoria eat for dinner?
4.Mike has six sevenths of a pie. He gives one fourth to his brother. How much pie does he have left
Answer:
3.
Step-by-step explanation:
Hey there!
This scenario shows that Victoria ate 6/7 of a pizza and ate 1/4 of that pizza the same day for dinner showing that she at one fourth of the six-sevenths pieces
Answer:
It is the third one.
Step-by-step explanation:
Let's take a look at each story. We need to find out which story is [tex]\frac{6}{7}[/tex]×[tex]\frac{1}{4}[/tex].
1. Victoria drinks six-sevenths of a cup of milk. She drinks one-fourth of a cup more of milk. How much milk did she drink in all?
This story is adding the fractions together since it wants to know how much did she drink in ALL. So this is not it.
(Here are some keywords to tell you if you need to add, altogether, all, in all, together, total, total number, add, increase, increased by, more than.)
2. Mike walked one-fourth mile and then he took the bus for six-sevenths mile to school. How many miles did he travel in total?
Once again this story is adding. It uses the word total. So this is not it.
3.Victoria has six-sevenths of a pizza. She ate one-fourth of it for dinner. How much pizza did Victoria eat for dinner?
This is correct since it wants to know how much she ate for dinner. She ate [tex]\frac{1}{4}[/tex] of [tex]\frac{6}{7}[/tex] of the pizza.
4.Mike has six-sevenths of a pie. He gives one-fourth to his brother. How much pie does he have left
This story is subtracting. So it is not it. (Subtracting words, minus, greater than, take away, fewer than, less than, subtract, decreased by.)
Does the scenario describe an observational study or an experiment?
What is the volume of this container? (image below)
Answer:
480 in³
Explanation:
Volume of Rectangular Prism = Length * Height * Width
Front Volume:
4 * 4 * 580 in³Behind Volume:
5 * 8 * 10400 in³Total volume:
400 in³ + 80 in³480 in³Both are cuboids
#1
L=8B=10C=5Volume:-
LBH8(10)(5)400in³#2
L=4B=4H=5Volume:-
4(4)(5)80in³Total:-
400+80=480in³
If an investment has a 5% annual interest rate and it is compounded
monthly, how many years will it take to double in value?
Answer:
2 years
Step-by-step explanation:
If it is annunal I think it would be 2 years
5 x annual year (year) =2
Easy geometry need help tho.......25pts
Answer:
22 in.
Step-by-step explanation:
total volume= big thingy + long thingy
=>x=2.2.3+5.2=12+10=22
Tell whether the triangle with the given side lengths is a right triangle.
24 m, 45 m, 51 m
Yes or No
GIVING TONS OF BRAINLIEST IF YOUR ANSWER IS CORRECT!!
Please help me with this!
Answer: Solve this problem using the angle bisector theorem. This theorem states that when given a triangle with an angle bisector (line that cuts one of the angles in half, into two of the same angles), that angle bisector divides the opposite side into two segment proportional to the sides of the triangle
Find the 9th partial sum of the geometric sequence an=43n–1.
Answer:
39364.
Step-by-step explanation:
I guess its an = 4*(3)^(n-1)
r = 3, a1 = 4 and n = 9
Sum of n terms = a1 * (r^n - 1) / (r - 1)
so S9 = 4 *(3^9 - 1) / (3 - 1)
= 4 * (19683 - 1) / 2
= 78728/2
= 39364.
CAN SOMEONE HELP ME PLEASE ASAP!?
Answer:
D
Step-by-step explanation:
the answer Is obviously D
four friends each took different path walking from the lunchroom to the gymnasium
finish the question..............
Answer:
Part 1- Lydia
Step-by-step explanation:
The full question should be
Four friends each took a different path walking from the lunchroom to the gymnasium. The table shows the distance that each of them walked. Who walked the farthest?
pls help on math pla
Answer:
Slope: -1/2
y-intercept: 7
Step-by-step explanation:
The slope is the interger/number in front of x in a linear equation.
y-intercept is the constant after the slope, 7, which is the value of y when x is 0.
Answer:
equation: y=mx+b
b=y intercept
the y intercept is 7
the slope is -1/2
A glass jug can hold (p + 6) quarts less water than a plastic container, 2 glass jugs and
2 plastic containers contain 6p quarts of water in all
how much water can the plastic container hold? give your answer is terms of p.
Answer:
12
Step-by-step explanation:
collect the like terms and divide
(p+6)2×2=64p+24=6p1) Water in a plastic container, p'= 10 - 3 p
2) Water in a glass container = 27 quarts
Water in a plastic container = 1 quarts
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A glass jug can hold (p + 6) quarts less water than a plastic container, 2 glass jugs and 2 plastic containers contain 6p quarts of water in all.
Now,
Let j represents water in one glass jag while p' represents the water in one plastic container,
Hence, According to the question,
⇒ j - p' = 6p+8 --------(1)
And, 2j+2p'=56p --------(2)
2 × equation (1)
⇒ 2 j - 2 p' = 12p + 16 ---------(3)
Equation (2) + equation (3)
We get, 4 j = 12 p + 72
⇒ j = 3 p + 18
Putting this value in equation (1),
We get, 3p+18-p'=6p+8
p' = -3p + 10 = 10 - 3p
Thus, water in a plastic container, p'= 10 - 3 p
b) If p=3
Water in a glass container = 3 × 3 + 18 = 27 quarts
Water in a plastic container = 10 - 3 × 3 = 1 quarts
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The relationship between women's whole
number shoe sizes and foot length forms an
arithmetic sequence, where is the foot
length in inches that corresponds to a shoe
size of n. A women's size 3 lits a foot 8 inches
long and women's size 7 lits a fool
9
inches long
What is the common difference of the arithmetic
sequence?
Using arithmetic sequence concepts, it is found that the common difference is of 0.25.
What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term.
In this problem, we have that:
[tex]a_3 = 8, a_7 = 9[/tex]
Hence:
[tex]a_7 = a_3 + (7 - 3)d[/tex]
9 = 8 + 4d
4d = 1.
d = 0.25.
The common difference is of 0.25.
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If a circle has a circumference of 36pie cm, what is the area?
Answer:324pie cm^2
Step-by-step explanation:
Find the length of the third side. If necessary, round to the nearest tenth
Pythagorean Theorem (Rounding)
Answer:
6.3 :)
Step-by-step explanation:
Pythagorean theorem: a^2 + b^2 = c^2
Now lets solve!!!
3^2 + b^2 = 7^2
9 + b^2 = 49
Now we subtract!!
49 - 9 = b^2
40 = b^2
Now we need to find the square root!!
[tex]\sqrt{40}[/tex] = 6.3
Have an amazing day!!
Please rate and mark brainliest!!!
[tex]x-5=y, xy+4=0,[/tex] then what is [tex]4x^{2} +4y^{2}[/tex]
Answer:
68
Given:
x - 5 = y ........ eq 1xy + 4 = 0 ...... eq 2Substitute equation 1 into 2
x(x - 5) + 4 = 0x² - 5x + 4 = 0x² - 4x - x + 4 = 0x(x-4) -1(x-4) = 0(x-4)(x-1) = 0x = 1, 4Find y:
y = x - 5
y = 1 - 5 (when x is 1)
y = -4
========
y = x - 5
y = 4 - 5 (when x is 4)
y = -1
Then 4x² + 4y²:
4(1)² + 4(-4)²4 + 6468Answer:
68
Step-by-step explanation:
[tex]\textsf{Equation 1}:\:x-5=y[/tex]
[tex]\textsf{Equation 2}:\:xy+4=0[/tex]
Substitute Equation 1 into Equation 2:
[tex]\implies x(x-5)+4=0[/tex]
[tex]\implies x^2-5x+4=0[/tex]
Factorize:
[tex]\implies (x-1)(x-4)=0[/tex]
Therefore:
[tex]x=1, x=4[/tex]
Substitute found values of [tex]x[/tex] into Equation 1 and solve for [tex]y[/tex]:
[tex]x=1\implies 1-5=-4[/tex]
[tex]x=4\implies 4-5=-1[/tex]
Substitute found values into [tex]4x^2+4y^2[/tex] and solve:
[tex]\textsf{For}\:(1,-4)\implies 4(1)^2+4(-4)^2=68[/tex]
[tex]\textsf{For}\:(4,-1)\implies 4(4)^2+4(-1)^2=68[/tex]
Note: As [tex]4x^2+4y^2[/tex], the values of x and y can be interchanged, so no need to input both sets of ordered pairs into the equation to solve.
