Answer:
[tex]a_n=112\left(-\frac{1}{4}\right)^{n-1}[/tex]
Step-by-step explanation:
Geometric Sequences
There are two basic types of sequences: arithmetic and geometric. The arithmetic sequences can be recognized because each term is found as the previous term plus a fixed number called the common difference.
In the geometric sequences, each term is found by multiplying (or dividing) the previous term by a fixed number, called the common ratio.
We are given the sequence:
112, -28, 7, ...
It's easy to find out this is a geometric sequence because the signs of the terms are alternating. If it was an arithmetic sequence, the third term should be negative like the second term.
Let's find the common ratio by dividing each term by the previous term:
[tex]\displaystyle r=\frac{-28}{112}=-\frac{1}{4}[/tex]
Testing with the third term:
[tex]\displaystyle -28*-\frac{1}{4}=7[/tex]
Now we're sure it's a geometric sequence with r=-1/4, we use the general equation for the nth term:
[tex]a_n=a_1*r^{n-1}[/tex]
[tex]a_n=112\left(-\frac{1}{4}\right)^{n-1}[/tex]
Pythagorean Theorem!!! someone pls help tyyy
Answer:
43.7
Step-by-step explanation:
7[tex]7^{2} +7^{2} =\sqrt{98} \\\sqrt{98}=9.899494937\\ That is the measurement for the dotted line. If we round it like they did in the example it would be 9.90. That is the measurement for all the sides of the square. \\We need the measurement for only 3 sides of the square and the two outer sides of the triangle (7ft)\\7ft + 7ft + 9.90 + 9.90 + 9.90 = 43.7\\\\Joshua added the 7's and they square rooted them for the Hypotenuse.\\Then the perimeter of all sides did not need any square roots.[/tex]
which figures show that M is a midpoint? select all that apply.
Step-by-step explanation:
a D&C show that m is the midpoint
The required figures that show the mid-points are (c) and (d).
A midpoint is a point on the line whose distance from both ends of the line is equal.
Here,
Figures are shown where in figure (A) only point M is shown which does not describe itself. In figure (B) M is located so far from B and there is no point on the other side of M. In figure (C) and (D) Point M is located between two certain points with equal measures.
Thus, the required figures that show the mid-points are (c) and (d).
Learn more about midpoints here:
https://brainly.com/question/28224145
#SPJ2
Triangle ABC is located on a coordinate plane. Angle C is at (1, 2). The triangle is rotated counterclockwise 90° about the origin. HOW DO I SOLVE THIS????
Answer:the answer is (-2,1)
Step-by-step explanation:
When rotating a point 90 degrees counterwise about the origin point (x,y) becomes (-y,x). So basically switch x and y and make y negative when rotating 90 degrees counterclockwise about the origin.
If the triangle is rotated counterclockwise 90 degrees about the origin, the angle C = (1, 2) will become C = (-1, 2).
What is a triangle?
It is a two dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Triangle ABC is located on a coordinate plane.
Angle C is at (1, 2).
This means that,
Angle C = (1, 2) is in the I Quadrant.
We have four Quadrant:
Quadrant I - The coordinates are in the form of (x, y)
Quadrant II - The coordinates are in the form of (x, -y)
Quadrant III - The coordinates are in the form of (-x, -y)
Quadrant IV - The coordinates are in the form of (-x, y)
If we rotate C = (1, 2) counterclockwise 90 degrees about the origin, the angle C will be in the IV quadrant.
So,
C = (1, 2) will become C = (-1, 2)
Thus,
If the triangle is rotated counterclockwise 90 degrees about the origin, the angle C = (1, 2) will become C = (-1, 2).
Learn more about triangles here:
https://brainly.com/question/25950519
#SPJ2
Maria bicycled every day for 14 days. She traveled 294 miles. How many miles did she travel per day?
Answer:
Maria bicycled 21 miles per day.
Step-by-step explanation:
294/14=21
Hope this helps!
For which function is f(5) = 2?
2x
y
107
1
3
f(x) = x-3
2.
5
9
8
7
6
5
4
3
2
3
7
4.
9
Answer: the answer is A ( first one)
Step-by-step explanation:
i just took it and got it write
P = R - C solve for C
Answer:
C = R - P
Step-by-step explanation:
Step 1: Write equation
P = R - C
Step 2: Subtract R on both sides
P - R = -C
Step 3: Divide both sides by -1
-P + R = C
Step 4: Rewrite
C = R - P
Answer:
C=R-P
Step-by-step explanation:
First move your terms
C+P=R then move variable to the right-hand side
C=R-P is your solution
PLS HURRY!!!!<3 A swimming pool has about 603 cubic feet of water. The pool liner has a small hole and is leaking at a rate of 1.5 cubic feet each hour. Ruby wrote the equation
V(h) = -1.5h + 603 to represent the scenario. Describe what each variable represents in the function, and how they relate to each other.
Answer:
hi did you find the answer ? if so can you please help me ?
Step-by-step explanation:
Answer:
Ruby function notation V(h) describes the volume of the pool after h number of hours. Hours is the independent variable and the total volume as a dependent variable
Step-by-step explanation:
I got a 100%
Which statements about variables are true? Select all that apply.
Answer:
Step-by-step explanation:
True:
Any letter can be used as a variable (yes)
Variables are used for numbers that haven't been defined yet (maybe)
All the rest are false
Hope this helps!
The true statements about variables are:
ii) Any letter can be used as a variable.
v) Variables are used for numbers that haven't been defined yet.
Explanation:
i) This statement is not true. Equations can involve multiple variables. For example, the equation "x + y = 10" involves two variables, x and y.
ii) This statement is true. In mathematics, variables are represented by letters, and any letter can be used to represent a variable. Common choices include x, y, z, a, b, c, etc.
iii) This statement is not true. While x is commonly used as a variable in many mathematical contexts, it is not the only letter that can be used. As mentioned earlier, any letter can be used as a variable.
iv) This statement is not true. Variables are specifically used in mathematical operations. They allow us to represent unknown quantities or values that can change. Mathematical operations involving variables are fundamental in algebra and many other branches of mathematics.
v) This statement is true. One of the primary purposes of variables is to represent numbers that haven't been defined yet. Variables act as placeholders for unknown values, and they allow us to generalize mathematical relationships and solve equations. Once we assign specific values to variables, the equations or expressions can be evaluated or solved.
In summary, variables are flexible symbols that can represent unknown or changing values in mathematical equations and expressions. They can be any letter and are essential for performing mathematical operations and solving problems involving unknown quantities.
Learn more about Variables click;
https://brainly.com/question/15078630
#SPJ2
(02.04 MC) Your friend has $90 when he goes to the fair. He spends $5 to enter the fair and $15 on food. Rides at the fair cost $1.50 per ride. Which function can be used to determine how much money he has left over after x rides? f(x) = 1.5x + 70 f(x) = −1.5x + 70 f(x) = −1.5x − 70 f(x) = −20x + $90
Answer:
f(x)= $70 - $1.5*x
Step-by-step explanation:
You know your friend spends $ 5 to enter the fair and $ 15 for food. So the total you spent is given by:
$5 + $15= $20
Knowing that the trips at the fair cost $ 1.50 per trip, and with x being the number of trips, then the cost after x trips will be:
$1.5*x
So the money spent after x rides can be expressed as:
$20 + $1.5*x
Knowing that your friend has $90 when he goes to the fair, to calculate the amount of money he has left after x rides, the amount taken to the fair and the amount spent is subtracted:
$90 - ($20 + $1.5*x)
$90 -$20 -$1.5*x
$70 - $1.5*x
By calling the function f(x) used to determine the amount of money left after x trips, you can finally express:
f(x)= $70 - $1.5*x
A boy has 11 coins in dimes and quarters. Their value is $1.70. How many of each does he have?
Which of the following equations could be used to solve the problem?
x + (11 - x) = 1.70
0.10x + 0.25(11 - x) = 1.70
25x + 10(11 - x) = 1.70
0.10x + 0.25(11 - x) = 1.70
It has the correct values
Which of the following expressions is equal to 2x^2+8
Step-by-step explanation:
its a photo hope this will help you
What is the slope of the line that passes through the points (-2,-12) and (1,-3)?
Answer:
3
Step-by-step explanation:
Change in Y/Change in X = Slope
Answer:
3
Step-by-step explanation:
(-3+12)/(1+2)
9/3
3
Consider the expression (-15) + 8. Describe a situation that could be represented by the expression. Then, find the sum and explain what it means in the context of the situation.
Answer:
it not
Step-by-step explanation:
Solve for x show your work 4(x+1)=-3x-10 plz show work
Answer:
4(x + 1)= -3x - 10
on the bracket 4( x +1)
4x + 4 = -3x - 10
collect like terms
4x + 3x = -10 - 4
7x = -14
divide both sides by 7
x = -2
HEEEEEEELP I CAN'T GET THIS WRONG
WILL GIVE BRANI AND PONITS
Answer:
Step-by-step explanation:
4 (x -2 ) - 3 = 7x
expanded = 4x - 8 (you have to multiply the -2 as well) -3 = 7x
Answer:
I know im late but i belive i need more information
Step-by-step explanation:
0= (x-1)^2 -4 and and show explanation please
Answer:
x=-1, x=3
Step-by-step explanation:
to solve by factoring:
1. swap the sides:
0=(x-1)^2-4
2. expand the expression:
(x-1)^2-4=0
3. rewrite and calculate:
x^2-2x+1-4=0
4. factor
x^2+x-3x-3=0
5. Factor... again
x(x+1)-3(x+1)=0
6. separate
(x+1) (x-3)=0
7. solve
x+1=0, x-3=0
8. and you end up with 2 solutions
x=-1, x=3
NEED HELP ASAP! Tysm
Answer:
7
Step-by-step explanation:
First you gotta plug in the values and you get 5*2 - 6(-4)/7
5 squared is 25
-6 times -4 is +24
25 + 24= 49
49/7= 7
Hope this helps! :)
True or False: Only like terms can be combined. A True B False
Answer:
True
Step-by-step explanation:
Like terms like 4x-3x the x term. is a like term
6-4x can be subtracted because they aren't the same.
High Hopes^^
Barry-
Answer:
i believe this false but im not positive
Tell whether the indicated angles are adjacent.
Answer: 3 would be a adjacent angle
Step-by-step explanation:
They don’t overlap
In a sale a clothes shop reduces its prices by 25% a shirt usually costs $34 how much it’s after the sale?
Answer:
$25.5
Step-by-step explanation:
Add the following: 3l(l – 4 m + 5 n) and 4l( 10 n – 3 m + 2l)
Answer:
11L^2‒24LM+55Ln
Step-by-step explanation:
first let's take L instead of l
3L(L‒4m+5n)+4L(10n‒3m+2L)
3L^2‒12LM+15Ln+40Ln‒12Lm+8L^2
3L^2+8L^2‒12LM‒12LM+15Ln+40Ln
11L^2‒24LM+55Ln
i think it is easy to understand&i hope it helps you
help me with this question in the picture please :(
Step-by-step explanation:
possibly A
Please help!! There’s 2 questions, Explain step by step pls :)
Answer:
I'm late but the answer to the question on the left is 21 and the answer to the question on the right is 3.
Step-by-step explanation:
Remember that you have to complete the equations in order of PEMDAS.
19-3×4÷(-6)
For this equation, you would do 3×4 first (which equals 12) then divide that by -6 (Which equals - 2) and finally you would subtract that from 19. 19 - (-2)= 21
6(-8) / -12 - 1
For this equation you would do 6(-8) first (which equals -48) then divide that by -12 (which equals 4) and finally subtract 1 from that 4. 4-1=3
A bear was climbing a tree. It took a few steps forward and then slipped a few steps backward. After taking 12 total steps of equal distance, it was back at its starting position. How many steps did the bear take in the forward and backward directions? (1 point)
7 steps forward and 5 steps backward
4 steps forward and 8 steps backward
5 steps forward and 7 steps backward
6 steps forward and 6 steps backward
Answer:
it would be 6 and 6 since it states equal distance and it also says a few forward and a few backward. It makes it sound like this was an equal amount each way
Step-by-step explanation:
Answer:
6 steps forward and 6 steps backward
Step-by-step explanation:
If the bear ended up back at its starting position, this means that the distances forward and backward have to be the same.
Since 6 = 6, this answer is correct.
The bear would have to take the same amount of steps forward and backwards.
PLZ HELP ME ASAP!!!
Answer:
A: 492 km
B: 120 m
Step-by-step explanation:
Since it's a 1:x scale, just multiply it.
120 x 4.1 = 492
Then add the unit.
Same thing for B.
4 x 30 = 120.
120 m
If f(x) is a linear function and f(-4) = 0 and f(2) = -3, what is the value of f(-8)?
Answer:
answer is [tex]-\frac{3}{2}[/tex]
Step-by-step explanation:
f(x)=y
basically this is just showing the y values
Answer:
the answer is - 3/2
Step-by-step explanation:
Beetween 2001 and 2011 the population of a town increased by 8% in 2001 the population was 34,342 calculate the population in 2011
Solve the equation: −3x − 3 +7x = 17 (SHOW UR WORK)
Answer:
x=5
Step-by-step explanation:
−3x − 3 +7x = 17
Combine like terms
4x -3 = 17
Add 3 to each side
4x-3 +3 =17+3
4x = 20
Divide by 4
4x/4 = 20/4
x = 5
Solve for z.
A= x + 5 + Z
Answer:
Z = A - x - 5
Step-by-step explanation:
A = x + 5 + z
Make the equation equal to z by moving the x and 5 to the side of the = with A. Move the x and 5 by subtracting x and 5 from both sides.
A - x = 5 + z
A - x - 5 = z
So, Z is equal to A - x - 5
brainlest thats it man/