Lisa's hand is located twenty-five feet distant from the rock.
This is further explained below.
How far from Tammy’s hand is the rock 4 seconds after it hits the surface?Generally, If the rock is falling at a rate of 5 inches per second, then you can easily calculate how deep below the surface of the lake it was after 5 seconds by multiplying 5 by 4.
After four seconds, the rock will have dropped -20 inches.
Because Lisa's hand is five feet above the water's surface, we need to add five to the distance between her hand and the rock in order to calculate how far away it is.
After four seconds, Lisa's hand is located twenty-five feet distant from the rock.
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Use summation notation to write each arithmetic series for the specified number of terms. Then evaluate the sum. 50+55+60+ . . . ; n=7
The summation notion of given series is ∑50+5n , here n starts from 0 and the sum of given arithmetic series is 455.
The given arithmetic series is 50+55+60+ . . .
The summation notion of given series is ∑50+5n , here n starts from 0.
The sum of arithmetic series can be written as,
[tex]S_{n}[/tex] = [tex](n(a_{1} + a_{n}))/2[/tex]
n is the number of terms, [tex]a_{1}[/tex] is the first term and [tex]a_{n}[/tex] is the last term.
We have, n=7, [tex]a_{1}[/tex] = 50
To calculate sum of arithmetic series, we need to find [tex]a_{7}[/tex] .
[tex]a_{7} = a_{1} + (n-1)d[/tex]
d = 5 for the given series. On substituting value of n, [tex]a_{1}[/tex] and d in equation1, we get
[tex]a_{7}[/tex] = 50 + (7-1)(5)
[tex]a_{7}[/tex] = 50 + 30 = 80
On substituting values in sum of arithmetic series formula, we get
[tex]S_{7}[/tex] = (7(50 + (80)))/2 = 455
The summation notion of given series is ∑50+5n , here n starts from 0 and the sum of given arithmetic series is 455.
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Evaluate the expression and enter your answer in the box below.
[(5+11) 4]+9. (6-4)
÷
Answer here
Answer:
22 :)
Step-by-step explanation:
I've attached an image to help break down the answer. (credit to cymath.com)
Hope this helps!
The pivot or midpoint of a seesaw on a playground is 13.5 feet from the swing set. If the swing set is 8 feet from the edge of the seesaw when the seesaw is level, how long is the seesaw.
The length of seesaw will be equal to 11 feet.
It is given that midpoint of the seesaw is 13.5 feet from the swing set and swing set is 8 feet from the edge of the seesaw.
We have to find out the length of seesaw.
What do you mean by midpoint of a line segment ?
The midpoint is halfway between the two end points , whose x value is halfway between the two x values and y value is halfway between the two y values.
As per the question ;
The midpoint of the seesaw is 13.5 feet from the swing set.
and
The swing set is 8 feet from the edge of the seesaw.
So ;
The distance from the midpoint to the edge will be ;
13.5 – 8 = 5.5.
And
The length of the seesaw will be ;
= 2× (5.5)
= 11 feet
Thus , the length of seesaw will be equal to 11 feet.
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A circle with radius 3 is contained in a square with side length 9 . What is the probability that a randomly chosen point in the interior of the square will also lie in the interior of the circle?
A. 1/9
B. 1/3
C. π/9
D. 9/π
The probability that a randomly chosen point in the interior of the square will also lie in the interior of the circle is π/9 .
Probability of an event is defined as the Number of favorable outcomes divided by total number of outcomes.
It is denoted by P(E).
Given that
radius of circle = 3
side of the square = 9
Let E be the event that a randomly chosen point in the interior of the square will also lie in the interior of the circle
then
[tex]P(E)=\frac{AreaOfCircle}{AreaOfSquare}[/tex] ...(i)
Area of Circle = πr² = π(3)² = 9π
Area of Square = (side)²=(9)²=81
Substituting the values in equation (i) we get
[tex]P(E)=\frac{9\pi }{81}[/tex]
[tex]=\frac{\pi }{9}[/tex]
Therefore , the probability that a randomly chosen point in the interior of the square will also lie in the interior of the circle is π/9 .
The correct option is (C) π/9
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A zoo has two elephants, Sally and Joe. Sally weighs 7,645 pounds, and Joe weighs 12,479 pounds. How much do Sally and Joe weigh in all?
As per given data of two elephants, Sally weighs 7,645pounds and Joe weighs 12,479 pounds then total weight of Sally and Joe is equal to 20,124pounds.
As given in the question,
Number of elephants in zoo = 2
Sally weighs = 7,645 pounds
Joe weighs = 12, 479 pounds
Total weight of Sally and Joe is equal to
= ( 7,645 + 12,479 ) pounds
= ( 20,124 ) pounds
Therefore, as per given data of two elephants, Sally weighs 7,645pounds and Joe weighs 12,479 pounds then total weight of Sally and Joe is equal to 20,124pounds.
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Determine whether the regular polygon will tessellate in the plane. Write yes or no. Explain.
triangle
Yes , Triangles are all tessellated. The triangle's three corners (A, B, and C) meet together to form a 180° angle, or a straight line, which is why the image is successful.
Is a triangle capable of tessellation?
Triangles are all tessellated. The triangle's three corners (A, B, and C) meet together to form a 180° angle, or a straight line, which is why the image is successful. We state it here since it will serve as the cornerstone of our investigation into polygon tessellations: Any triangle's total angles come to 180 degrees.To create a regular tessellation, it is necessary that the tiles may fill 360 degrees around a point (all the tiles regular polygons with same number of sides) Only 60 degree angle triangles, 90 degree squares, and 120 degree hexagons will work.
Every vertex, edge, and tile in a regular tesselation are identical.
However, there are semiregular tesselations that use more than one regular polygon, but since they must be able to fill 360 degrees around a point, it turns out that only the octagon (8 sides, 135 degrees) and dodecagon can be used as additional polygons (12sides, 150 deg).
Note that just these 5 tesselations can be utilized to fill the plane entirely with regular polygons.
Each vertex in the semiregular tessellations is the same.
Eight of them are (3,3,3,3,6), (3,3,3,4,4), (3,4,6,4), (3,6,3,6), (3,12,12), and (4,6,12). (4,8,8)
The Octagon & square tiling (4,8,8) is a very common floor tiling.
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Write an explicit and a recursive formula for each sequence. 1,1 1/3, 1 2/3, 2, . . . . . .
an=a1+d(n−1) is the explicit and a recursive formula for each sequence .
What is sequence?An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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1. Simplify the radical expression.
-4^√16x^8
Please help I don’t know which one.
[tex] \bf \implies \large{ - 2x}^{2} \\ [/tex]
Step-by-step explanation:[tex] \bf \longrightarrow - 4 \sqrt{16 {x}^{8} } \\ \\\bf \longrightarrow - { ({2}^{4} {x}^{8}) } ^{ \frac{1}{4} } \\ \\\bf \longrightarrow ( - 2x)^{ \frac{1}{ \cancel{4}}1 \times \cancel{ 8}2 } \\ \\\bf \longrightarrow \boxed{- 2x^{2}} \: ans.[/tex]
Find the measure of the combined angle.
27°
44°
Measure of the combined angle of 71° .
71 degrees is an acute angle .
Given, that two measure of angles 44 degrees and 27 degrees .
Classification of angles :
Acute angle : 0° ≤ Ф ≤ 90°
Right angles : Ф = 90 degrees
Obtuse angles : 90° ≤ Ф ≤ 180°
Reflex angle : 180° ≤ Ф ≤ 360°
Here the angles given are 44 degrees and 27 degrees.
Combined measure of two angles = 44 + 27
= 71 degrees.
Acute angle : 0° ≤ Ф ≤ 90°
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If Y=3x+5 and x=0 what is y
The heights of a sample of 15 students are recorded in
the stemplot below.
Heights of Students
What is the mean height, in inches, of this sample?
65
65.2
66
67
The mean height of the given sample of values is approximately 65.20.
The heights of the 15 students are as follows:
{59, 61, 62, 63, 63, 64, 65, 65, 66, 67, 67, 67, 67, 69, 73}
To find the mean (average) height of the given values, we need to add up all the heights and then divide the sum by the total number of heights:
59 + 61 + 62 + 63 + 63 + 64 + 65 + 65 + 66 + 67 + 67 + 67 + 67 + 69 + 73
= 978
So, the mean height can be calculated as:
Mean height = Total height / Number of heights = 923 / 15 = 65.2
Therefore, the mean height is approximately 65.20.
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Prove or disprove that the product of a nonzero rational number and an irrational number is irrational.
Answer: The claim is true
The proof is below
=====================================================
A = some nonzero rational number
B = some irrational number
Because value A is rational, this means A = p/q where p,q are nonzero integers.
Let's do a proof by contradiction. The claim is that A*B is irrational, but let's do the opposite and assume A*B is rational. We should get to a contradiction somewhere based on this assumption.
If A*B is rational, then A*B = r/s for some integers r and s
Then we can have the following steps
A*B = r/s
(p/q)*B = r/s
B = (r/s)*(q/p)
B = (rq)/(sp)
B = (some integer)/(some other nonzero integer)
B = some rational number
Recall we made B irrational. There's no way to have B rational and irrational at the same time. This is where the contradiction happens. This causes the original assumption of "A*B is rational" to be false. Therefore, the opposite must be the case and A*B has been proven to be irrational.
Therefore, the product of a rational number and an irrational number is irrational.
------------------------
Example:
5 is rational
sqrt(3) is irrational
5*sqrt(3) is irrational
Determine which line passing through the given points has a steeper slope.
Line 1: (-9,-4) and (7,0)
Line 2:(0,1) and (7,4)
The line which have a steeper slope is Line 1.
It is given in the question that the points on the line are given by:-
Line 1: (-9,-4) and (7,0)
Line 2:(0,1) and (7,4)
We have to find which line has a steeper slope.
First we will find the slope of each line.
We know that slope of a line with points (a,b) and (c,d) is given by:-
(d-b)/(c-a)
Slope of Line 1:
(0-(-4))/(7-9) = 4/(-2) = -2 (we will take the absolute value)
Slope of Line 2:
(4-1)/(7-0) = 3/7
We know that greater the slope of the line means greater the steep of the line.
As,
2 > 3/7
Hence, Line 1 is steeper than Line 2.
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E represents the anchors elevation relative to the waters surface (in meters)
A large ship lowered its anchor, The anchor's elevation (in meters) in relation to the water's surface is represented by E as a function of time t. (in sec) E=-2.4t+75. The anchor drop 12 meters every 5 seconds.
Given that in the picture we can see the question that is
A large ship lowered its anchor,
The anchor's elevation (in meters) in relation to the water's surface is represented by E as a function of time t. (in second).
E=-2.4t+75
According to the function E=-2.4t+75
We assume that [tex]t_{1}[/tex].
So, every 5 second [tex]t_{1}[/tex]=t+5.
So, we get
ΔE=E(t)-E(t+5)
ΔE=-2.4t+75-(-2.4(t+5)+75)
ΔE=-2.4t+75+2.4t+12-75
ΔE=12
Therefore, the anchor drop 12 meters every 5 seconds.
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Simplify by combining like terms. -(3 x-4 y)+x
By combining the like terms, the simplified form of the expression -(3x-4y)+x is -2x+4y
Given,
The algebraic expression = -(3x-4y)+x
Expand the terms
-(3x-4y)+x= -3x+4y+x
Combine the like terms
-3x+4y+x= (-3+1)x+4y
=-2x+4y
Hence, by combining the like terms, the simplified form of the expression -(3x-4y)+x is -2x+4y
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The temperature is 6 degrees it falls by 8how many degrees does it fall
In triangle PQR , the measure of angle Q is three times the measure of angle . The measure of angle R is 20⁰ more than the measure of angleP . Find the measure of each angle.
b. What system of equations represents this situation?
A triangle is a shape whose all three angles have a sum of 180 degrees. So from the above definition, we know that:
P + Q + R = 180
Q=3P
T=P + 20
Therefore:
P + 3P + P + 20 = 180
5P + 20 = 180
5P = 160
P = 32
Q = 3(32) = 96
R = 32 + 20 = 52
To Additional Control P + Q + R = 32 + 96 + 52 = 180 °Degree
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round 8.6 to the nearest whole number
Answer:
9
Step-by-step explanation:
Since one place to the right is greater than or equal to 5 you round up.
Write a function g whose graph represents the indicated transformation of the graph of f(x)=-2|x-4|+2
Using translation concepts, the function g is given as follows:
g(x) = -|x - 4| + 1
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, we have that function g(x) is the function f(x) vertically compressed by a factor of 2, hence:
g(x) = 0.5f(x)
g(x) = 0.5(-2|x - 4| + 2)
g(x) = -|x - 4| + 1
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Please help me with this math problem! Will give brainliest!! :)
Answer:
f (x^2-4) = 2x^2 - 5
Step-by-step explanation:
HELP ASP SHOW UR WORK YOULL GET BRAINLEST
Answer:
X=2
Step-by-step explanation:
Add four to both sides
2x-4=0
2x-4+4=0+4
Add the numbers 2x = 4
2x =4
2x/2 = 4/2
cancel the terms
divide the numbers
= x=2
You are canning 40 cups of applesauce. You have 20 glass jars, each of which will hold 1 3/4 cups of applesauce. why do i not have enough jars
pls help
The jars are nor enough because the applesauce is more than 35 cups which is what 20 glass jars can contain. Since each of the cup will hold 1 3/4 cups of applesauce.
How to find why the jars are not enoughGiven data
number of cups of apple sauce = 40
number of glass jars = 20
number of cups each glass jar can hold = 1 3/4
solution
if one glass jar hold 1 3/4 cups then 20 glass jars will hold
= 20 * 1 3/4
= 35 cups
Since there are 40 available cups of apple sauce and the 20 glass jars is equivalent to 35 cups, hence the glass jars will contain 35 cups and there will be 5 cups left.
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Theresa is planning a family reunion and is in charge booking the dining hall at Denny's. Denny's charges $125 to reserve the dining hall, then $12.00 per person for a meal. Which equation best represents the total amount of money Theresa will have to pay if m members of the family attend.
Answer:
the equation would be 12m+125
Step-by-step explanation:
-
6n² - 15 = 6 (5)² - 15
Answer:
6n2-15=150-15
6n2-15=135
6n2=150
divied both side by 6
n2=25
sqrt both side
n=-5 or 5 bc sqrt so 2 answer
Step-by-step explanation:
Find the value of x .
9 √2 . x=18 √2
The value of variable x in the given expression 9 √2 . x=18 √2 is equal to 2
As given in the question:
Given expression
9 √2 . x=18 √2
Simplify the given expression to get the value of variable x
9 √2 . x=18 √2
Divide by √2 both the side
(9 √2 . x ) / √2= ( 18 √2 )/ √2
⇒9x = 18
⇒ x= 18 /9
⇒ x = 2
Therefore, the value of variable x in the given expression 9 √2 . x=18 √2 is equal to 2
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[tex]\frac{m}{2} =\frac{m+5}{10}[/tex]
Answer:
[tex] \sf \large \: m=−1[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
m/2 =m+5/10
Step 1: Simplify both sides of the equation.
1/2m=m+1/2
Step 2: Subtract m from both sides.
1/2m−m=m+1/2−m
−1/2m=1/2
Step 3: Multiply both sides by 2/(-1).
(2/−1)*(−1/2m)=(2/−1)*(1/2)
m=−1
Jessica tan 52,520 feet in 50 minutes. What is Jessica’s rate in miles per hour
Determine whether each formula is explicit or recursive. Then find the first five terms of each sequence. a₁ =-2, a n =a n₋₁ -5
This is recursive sequence and -2, -7, -12, -17, -22, -37 these are the first five terms of sequence.
How to find the first five terms of sequence a₁ = -2, a (n) =a (n-1)-5 ?A recursive formula is one that defines each term in a sequence by reference to the one before it. The following parameters are defined using the recursive formulas:
1. The initial term in the series.
2. The general rule for determining any term from its preceding term.
Recursive Arithmetic Sequence Formula
The following is the recursive formula to determine the nth term in an arithmetic series:
an = an-1 + d for n ≥ 2
where
The common difference is d, and an is the nth term of an A.P.
given that
a₁ = -2
a (n) =a (n-1) -5 so, d = -5
For example, we need to extend the sequence term by term in order to find the first five terms:
a(1) = -2
a(2) = a(1) + d = -2 + (-5) = -7
a(3) = a(2) + d = -7 + (-5) = -12
a(4) = a(3) + d = -12 + (-5) = -17
a(5) = a(4) + d = -17 + (-5) = -22
a(6) = a(5) + d = -22 + (-5) = -27
Hence,this is recursive sequence and -2, -7, -12, -17, -22, -37 these are the first five terms of sequence.
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if 3.99 x 10 ^ 13 was written in standard notation how many zeros does it contain before the decimal point
Answer:
11 zeros
Step-by-step explanation:
10^13 = 100 000 000 000 000
Round the two first numbers(which makes 11 zeros left), then lastly the zeros
Use the given information to write an equation of the circle.
center (2,1) , through (6,4)
Using the given information, the equation of the circle with center located at point (2 , 1) and passes through the point (6 , 4) is (x - 2)^2 + (y - 1)^2 = 25
Using the distance formula, get the radius of the circle by solving for the distance between the center (2 , 1) and the point (6 , 4).
radius = distance = √(x2 - x1)^2 + (y2 - y1)^2
radius = √(6 - 2)^2 + (4 - 1)^2
radius= √16 + 9
radius = √25
radius = 5
The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (2 , 1)
r = 5
(x - 2)^2 + (y - 1)^2 = 5^2
(x - 2)^2 + (y - 1)^2 = 25
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