Suppose you are stacking boxes in levels that form squares. The numbers of boxes in successive levels form a sequence. The figure at the right shows the top four levels as viewed from above.
a. How many boxes of equal size would you need for the next lower level?
There is need of total of 25 boxes of same size for the next lower level.
What is a sequence ?A sequence can be taken as the set of numbers having a particular order for all the terms or we can say that arrangement of numbers in some order is known as sequence.
Some examples for sequence are :
2,4,6,8,10,12
3,9,27,81,243
What is recursive sequence ?The recursive sequence is the sequence in which any term in the sequence can be find with the help of previous term of that sequence.
In a sequence , first term always known as initial term.
and difference between two terms are known as common difference. It is denoted by d.
General form of sequence is :
[tex]a_1,a_2,a_3,----,a_n[/tex]
where , [tex]a_n[/tex] = last term in sequence.
According to question,
The boxes in each of successive levels make a sequence.
Also, number of boxes at level n = [tex]n^2[/tex]
As upto four level the number of boxes are 16.
at level 5 , n = 25
Thus, the total boxes of equal or same size need for next lower level is 25.
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The complete question is :
Suppose you're stacking boxes in levels which make squares. The numbers of boxes in each successive levels make a sequence. The figure show top four levels as view from top or above.
a. How many boxes of same size would need for next lower level?
b. How many boxes of same size would need to add the 3 levels?
c. Suppose you are stacking 285 boxes. Then, how many total levels will you have?
Write a function g whose graph represents the indicated transformation of the graph of f. f(x)= | 4x+3| + 2 translated 2 units down is g (x)
Answer:
g(x) = |4x+3|
Step-by-step explanation:
g(x) = f(x) - 2
=|4x+3|
Look at this graph.
What is the equation of the line in slope-intercept form?
Answer: y = -4x + 3
Step-by-step explanation:
Line touches at point 3 on the y axis
Goes up 4 and left by 1
Question 1
A pair of running shoes is on sale for $125.99. If the sale price is discounted 9% from the original price, what is the
original price?
Answer:
$138.45
Step-by-step explanation:
The original price was 100% of the original price since 100% is the whole thing.
The price was discounted by 9%.
100% - 9% = 91%
That means the discounted price is 91% of the original price.
Let x = original price.
91% of x = $125.99
0.91x = 125.99
x = 125.99/0.91
x = 138.45
Answer: $138.45
Determine whether the following statement is sometimes, always, or never true. Explain.
The distance between a line and a plane can be found.
The statement "The distance between a line and a plane can be found" is sometimes true.
Given,
The statement "The distance between a line and a plane can be found".
The distance between the point and the plane can be found by the taking a point on the line and finding the perpendicular distance from line to the plane.
But we can't apply this method in every case. We can only apply when either the line is parallel to the plane or the line intersects the plane.
Hence, the statement "The distance between a line and a plane can be found" is sometimes true.
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Find the distance from the line to the given point.
y=1/6x+6,(-6,5)
The distance from the line [tex]y=\frac{1}{6} x+6[/tex] to the given point (-6,5) is o units .
Distance Formula : the distance between the line ax+by+c=0 and the point (p,q) is given by the formula
[tex]d=\frac{|ap+bq+c|}{\sqrt{a^{2} +b^{2} } }[/tex]
In the given question the equation of line is [tex]y=\frac{1}{6} x+6[/tex]
taking LCM and solving further
[tex]y=\frac{x+36}{6} \\ \\ 6y=x+36\\ \\ x-6y+36=0[/tex] ⇒equation of the line .
Given point (-6,5)
from above values we found that a=1 , b = -6 , c=36, p=-6, q=5.
Substituting the values in distance formula we get
[tex]d=\frac{|1*(-6)-6*5+36}{\sqrt{1^{2} +(-6)^{2} } }[/tex]
[tex]=\frac{|-6-30+36|}{\sqrt{37} }[/tex]
[tex]=\frac{-36+36}{\sqrt{37} }[/tex]
[tex]=0[/tex]
Therefore , the distance from the line [tex]y=\frac{1}{6} x+6[/tex] to the given point (-6,5) is 0 units.
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2xy; when x = 5 and y = 3x
30x is the value of the given equation .
WHAT IS MULTIPLICATION OF ALGEBRA ?Algebraic expression multiplication is the operation of multiplying two given expressions made up of variables and constants. An algebraic expression is one that incorporates variables and integer constants.
CALCULATIONx = 5
y = 3x
2xy = 2 * 5 * 3x ( plugging in the value )
= 30x
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suppose that Angle Hik and Angle LIJ are verticle angles. find their measures if the following conditions apply. see picture
10. m∠HIK (2x+15)°, m∠LIJ = (5x-27)°, m∠HIK =
if they are vertice angles then they are equal to each other or
they both add up to 180°
A.
2x+15=5x-27
3x=42
x=14
B.
(2x+15)° + (5x-27)° = 7x-12
7x-12 = 180
7x=192
x = 27 3/7 or 27.43
Edgar is a high school senior who has great grades and is at the top of his class. he just received a notification that he was awarded a few scholarships in the amounts of $4,500, $7,500, and $750. if his expected tuition with books and fees is $25,000, how much money will edgar need to pay for the rest of his education bill? show your work.
If Edgar is a high school senior who has great grades and just received a notification that he was awarded a few scholarships in the amounts of $4,500, $7,500, and $750 while his expected tuition with books and fees is $25,000, then the amount of money Edgar will need to pay for the rest of his education bill is equal to $12,250.
The amount of money Edgar will need to pay can be determined by the subtraction of the total tuition with books and fees from the total amount of scholarships awarded to Edgar.
The total amount of scholarships awarded to Edgar can be determined by the sum of all of the scholarships.
Total amount of scholarships = 4500 + 7500 + 750
Total amount of scholarships = $12,750
Now the amount that Edgar will need to pay for the rest of his education bill can be determined by subtraction.
Amount to be paid by Edgar = Tuition with books and fees - Total amount of scholarships
Amount to be paid by Edgar = 25,000 - 12750
Amount to be paid by Edgar = $12,250
Hence, the amount of money Edgar will need to pay for the rest of his education bill is calculated to be $12,250.
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A lawn is 4m longer than it is wide. The total area of the lawn is 30 metres squared. What is its perimeter? Give your answer to 2 d.p.
Answer:
7.5
Step-by-step explanation:simply divide 30 and 4 and the answer is 7.5
l
Write & solve each equation. The sum of three consecutive even integers is -96. Find
the integers.
Answer:
-30, -32 and -34
Step-by-step explanation:
-30 + -32 + -34 = -96
Find the sum of each finite arithmetic series. 8+9+10+. . . . . . +15
The sum of finite arithmetic series 8+9+10+. . . . . . +15 is 92
Suppose we are given an arithmetic series:
a(1) + a(2) + ... + a(n)
Then the sum is:
S(n) = n/2 (a(1) + a(n))
Where: a(1) = first term
a(n) = nth term
The given series is:
8+9+10+. . . . . . +15
We need to find n such that a(n) = 15.
Recall that in an arithmetic sequence:
a(n) = a(1) + (n -1) . d
where d = difference between 2 consecutive terms.
Substituting a(1) = 8, and d = 9 - 8 =1 into the formula:
a(n) = 8 + (n -1) . 1
15 = 7 + n
n = 8
Substitute n = 8 into the sum formula:
S(n) = n/2 (a(1) + a(n))
S(8) = 8/2 . (8 + 15)
= 4 . 23 = 92
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Bonus Solve
5x-3+3x-(8-2x) = 9
Answer:
Step-by-step explanation:
[5x+3x-(-2x)]+[-3-8]=9
10x+(-11)=9
10x=20
x=2
Solve each equation. Check each solution. 11/3x - 1/3 = -4/x²
The solutions of the given equation 11/3x - 1/3 = -4/x² are x = -1 and x = 12
In this question, we have been given an equation.
11/3x - 1/3 = -4/x²
We need to solve given equation.
⇒ 11/3x - 1/3 = -4/x²
⇒ (33 - 3x)/9x = -4/x²
⇒(33 - 3x)/9 = -4/x
⇒ x(33 - 3x) = -36
⇒ -3x² + 33x + 36 = 0
⇒ x² - 11x - 12 = 0
⇒ x² - 12x + x - 12 = 0
⇒ x(x - 12) + 1(x - 12) = 0
⇒ (x - 12)(x + 1) = 0
⇒ x - 12 = 0 or x + 1 = 0
⇒ x = 12 or x = -1
Now we need to check above solutions.
Substitute x = 12 in given equation.
⇒ 11/3(12) - 1/3 = -4/(12)²
⇒ 1/3 (11/12 - 1) = 1/3(-4/48)
⇒ -1/12 = -1/12
⇒ LHS = RHS
Now substitute x = -1 in given equation.
⇒ 11/3(-1) - 1/3 = -4/(-1)²
⇒ -12/3 = -4/1
⇒ -4 = -4
⇒ LHS = RHS
Therefore, the solutions of the given equation 11/3x - 1/3 = -4/x² are x = -1 and x = 12
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The length of the roller coaster track from the top of a hill to the bottom of the hill is 125 feet at a 53°C angle with the vertical. If the position at the top of the hill is (x, y) , use function notation to describe the translation to the bottom of the hill. Round to the nearest foot.
(x + 100, y - 75) is the function notation used to characterise the translation to a bottom of the hill.
What is defined as Pythagorean Theorem?The Pythagorean theorem states that the sum of a squares on a legs of a right triangle equals the square on hypotenuse (this same side opposite this same right angle)—or, in recognizable algebraic notation, a² + b² = c².
Now, as per the given question;
From the shown diagram,
AC = b
Ab = c
We must find the coordinates of a point B. If C(x,y), then the coordinates of points A and B are:
A(x, y−b) and B(x+c, y−b)
We need to figure out b and c. To find c, we should use sine function.
sinC = perpendicular/hypotenuses
sinC = c/BC
Thus, c = BC sinC
c = 125sin53°
=125⋅0.79863551
c ≈100
To find b, we are using the Pythagorean Theorem.
BC² = AC² + AB²
125² = b² + 100²
b² = 125² - 100²
b = √5625
b = 75
The coordinates of a point B are as follows:
B(x+c, y−b)
B(x+100, y−75).
Therefore, the translation to the bottom of the hill defined by the function notation is B(x+100, y−75).
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What is 1+10-70
Please help
Answer:
-59
Step-by-step explanation:
use pemdas
1+10-70
11-70
-59
Write an equation of the line through each pair of points. Use point-slope form.(-1/2, -1/2) and (-3,-4)
The equation of the line in point-slope form, which passes through the pair of points located at (-1/2 , -1/2) and (-3 , -4), is y + 1/2 = 7/5(x + 1/2).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Getting the slope of the two points: (-1/2 , -1/2) and (-3 , -4).
m = (y2 - y1)/(x2 - x1)
m = (-4 - -1/2)/(-3 - -1/2)
m = (-7/2)/(-5/2)
m = 7/5
Using the point slope form, plug in the values of the slope and one point to set up the equation.
(y - y1) = m(x - x1)
where m = 7/5 and (x1 , y1) = (-1/2 , -1/2)
(y - -1/2) = 7/5(x - -1/2)
y + 1/2 = 7/5(x + 1/2)
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Can someone please help me? It’s due tmrw.
For Exercises 1-3 use the following information. Then estimate to find the distance sound travels through each material in each given time.
Problem: Sound travels through different materials at different speeds. For example, the graph shows that in one second, sound travels 5,971 meters through stone.
However, it travels only 346 meters through air in one second.
1. air, 20 seconds
Answer:??
2. Stone, 12 seconds
Answer:??
3. Estimate how much farther sound travels through stone in 17 seconds than through aluminum in the same time.
Answer:??
Thanks! :)
Chart
|
|
|
|
|
|
\/
Answer:
Step-by-step explanation:
1. We know it travels 346 meters in a second, we now need to multiply 346 by 20. This equals 6920
2. Sound travels 5971 meters per second. We need to multiply this by 12 to find the distance it travels in 12 seconds. 71652 meters
3. We know sound travels 5971 meters per second in stone and 5000 meters per second from the chart. We need to find the difference between these and multiply that by 17 to find the distance covered in 17 seconds.
5971-5000=971
971*17=16507
Sound travels 16507 more meters in 17 seconds through stone than it would travel in aluminum
write the point slope form of the equation of the line described question 17
Answer:
[tex]y - 2 = -\frac34(x - 4)[/tex]
Step-by-step explanation:
Hello!
The equation in #17 is written in Slope-Intercept Form: [tex]y=mx+b[/tex]
y = outputm = slopex = inputb = y-interceptPoint Slope form is the equation given slope and a point: [tex]y - y_1 = m(x - x_1)[/tex]
y = y - value of second pointy1 = y - value of first pointm = slopex = x - value of second pointx1 = x - value of first point.The point given to us is (4,-2), which we can use as x1 and y1.
The slope is given in the slope-intercept form equation: -3/4
Plug in the values to find the equation:
[tex]y - y_1 = m(x - x_1), (4,2), -\frac34[/tex][tex]y - 2 = -\frac34(x - 4)[/tex]The equation is [tex]y - 2 = -\frac34(x - 4)[/tex].
I need help with this problem...please response and show the process
The equation that represents the linear relationship between the x- values and y-values in the table is y = 6x - 5 .
What is a linear equation?
An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
The equation y = 6x - 5 can represent the linear relationship between the x- values and y-values because it satisfies all the given values for x and y.
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Please please help me!! I don't understand this and if I fail i'm going to get in trouble!!
Answer: 3.82x10^7
Step-by-step explanation:
the radius of Jupiter at its equator is approximately 2 * 5^2 * 11 * 79 miles. Use the formula A = 3.14r^2 to find the area of the cross section of the planet at the equator.
PLEASSEEE I NEED HELLPPP!!!!
The area of the cross section of the planet at the equator is 5. 92 × 10^9 square miles
How to determine the areaFrom the information given, we have the formula for area to be;
A = 3.14r²
Where 'r' is the radius of the shape
The radius of Jupiter = 2 * 5^2 * 11 * 79
This is simplified to = 2 × 25 × 11 × 79 = 43, 450
Substitute into the formula
Area = 3. 14 × (43, 450)²
Area = 3. 14 × 1. 89 × 10^9
Area = 5. 92 × 10^9 square miles
Thus, the area of the cross section of the planet at the equator is 5. 92 × 10^9 square miles
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Answer:
5,928,013,850
2x^2+7x+2 greater than or equal to 0
Answer:
Greater than
Step-by-step explanation:
2x2+7x+2
----------
NASA launches a rocket at
t
=
0
t
=
0
seconds. Its height, in meters above sea-level, in terms of time is given by
h
=
−
4.9
t
2
+
259
t
+
423
h
=
-
4.9
t
2
+
259
t
+
423
.
How high is the rocket after 8 seconds?
meters
How high was the rocket when it was initially launched?
meters
Answer:
Step-by-step explanation
Height for time = 8 seconds
h = -4.9t^2 + 259t + 423
h = -4.9(8)^2 + 259(8) + 423
h = -313.6 + 2072 + 423
h = 2181.4 meters at 8 seconds
Heoght for time = 0 seconds
h = -4.9t^2 + 259t +423
h = -4.9(0)^2 + 259(0) + 423
h = 0 + 0 + 423
h = 423 meters at 0 seconds
Answer questions 7 and 8 and I'll give brainliest (20 points)
7 - The geocentric model says that the earth is at the center of the cosmos or universe, and the planets, the sun and the moon, and the stars circles around it. The early heliocentric models consider the sun as the center, and the planets revolve around the sun.
8 - Modele A is the most accurate cause the sun, earth, & moon are in a straight line & in the time and space all the planets are in one straight line.
Hope this helps!
Solve for d. -19= d/7- 21
What is the solution of the system of equations? x+3y = 5 , -2x - 4y = -5.
The solution of the system of equations involving x + 3y = 5 and -2x - 4y = -5 is (-5/2 , 5/2).
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in x and y,
x + 3y = 5 (equation 1)
-2x - 4y = -5 (equation 2)
Using the first equation, find the value of one variable, lets say x, in terms of the other.
x + 3y = 5 (equation 1)
x = 5 - 3y
Substitute the equation of x to the second equation.
-2x - 4y = -5 (equation 2)
-2(5 - 3y) - 4y = -5
-10 + 6y - 4y = -5
Combining all terms containing the variable y on one side and the constants on the other side of the equality, and solving for y.
-10 + 6y - 4y = -5
6y - 4y = -5 + 10
2y = 5
y = 5/2
Substitute the value of y in the equation of x.
x = 5 - 3y
x = 5 - 3(5/2)
x = 5 - 15/2
x = -5/2
Hence, the solution of the given system of equations is (-5/2 , 5/2).
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Ricardo went jet skiing while on vacation. The jet ski rental cost a flat rate of $25, plus $17.75 per hour. Ricardo had $102.17. How much did he have left after 3 hours of jet ski riding?
$23.92
$48.92
$53.25
$78.25
Ricardo will be left with $23.92 after 3 hours of Jet ski riding
How to calculate the amount left ?Ricardo is on vacation so he went jet skiing
The Jet ski has a rental flat rate of $25
They also charge $17.75 per hour
Ricardo had $102.17
The amount spent in 3 hours is
17.75(3) + 25
= 53.25 + 25
= 78.25
The amount left is
= 102.17 - 78.25
= 23.92
Hence Ricardo has $23.92 left after the Jet ski ride
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13+(2^2xx7)-10 i need help with this i dont get it
The value of the expression 13 + (2^2 x 7) - 10 is 31
How to evaluate the expression?The expression is given as
13 + (2^2 x 7) - 10
Evaluate the exponent
So, we have
13 + (2^2 x 7) - 10 = 13 + (4 x 7) - 10
Evaluate the product
So, we have
13 + (2^2 x 7) - 10 = 13 + 28 - 10
Evaluate the sum
So, we have
13 + (2^2 x 7) - 10 = 41 - 10
Evaluate the difference
So, we have
13 + (2^2 x 7) - 10 = 31
Hence, the value of the expression 13 + (2^2 x 7) - 10 is 31
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|x| means “distance between_ and _
Answer:|x| means “distance between a number and zero
Step-by-step explanation:
Also known as absolute value
ex l5l=5 & l5l=-5
