The total number of seats in this movie theater is 4224. This is calculated using the sum of an arithmetic series formula.
Explanation:The question describes an arithmetic sequence where each row in the theater has four more seats than the previous row. The first row has 20 seats and the last row (44th row) has[tex]20 + 4*(44-1) = 172[/tex] seats. The total number of seats in this theater is therefore the sum of an arithmetic series formula, which is given by:
[tex]S = n/2 * (a + l)[/tex]
Where:
S is the sum of the sequence n is the number of terms a is the first term l is the last term
So for the number of seats, we have:
[tex]S = 44/2 * (20 + 172) = 22 * 192 = 4224.[/tex]
So, the total number of seats in the theater is 4224.
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Given the function f(x) = 2x − 5 and g(x), which function has a greater slope?
x g(x)
2 0
4 5
6 10
1. f(x) has a greater slope.
2. g(x) has a greater slope.
3. The slopes of f(x) and g(x) are the same.
4. The slope of g(x) is undefined.
Answer: The correct option is
(B) g(x) has a greater slope.
Step-by-step explanation: We are given the following two functions :
[tex]f(x)=2x-5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
and
x 2 4 6
g(x) 0 5 10
Comparing equation (i) of f(x) with the slope-intercept form y = mx+c, we get
[tex]\textup{slope, m}=2.[/tex]
Now, we know that if a linear function contains two points (a, b) and (c, d), then its slope is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
Since (2, 0) and (4, 5) are two points on g(x), so its slope will be
[tex]m=\dfrac{5-0}{4-2}=\dfrac{5}{2}=2.5.[/tex]
Therefore, slope of f(x) = 2 and slope of g(x) = 2.5.
Thus, slope of g(x) is greater.
Option (B) is CORRECT.
Solve for p.
11p − 2p + 4 = 13
p =
Answer:
p = 1
Step-by-step explanation:
11p - 2p + 4 = 13
9p + 4 = 13
- 4 -4
9p = 9
9p/9 = p
9/9 = 1
Answer:
p=1
Step-by-step explanation:
11×1=11
2×1=2
11-2=9
9+4=13
The area of a closet is 100 square feet. Write the number in exponent form and in word form
Answer:
[tex]10^{2}[/tex]
one hundred
Step-by-step explanation:
10 × 10 = 100
100 square feet can be written in exponent form as 10^2, which is read as 'ten squared'. The word form of this is 'one hundred'.
Explanation:The area of the closet is given as 100 square feet. This can be written in exponent form as 102. The '^' symbol denotes an exponent, which means 'raised to the power of'. Here, '10' is the base and '2' is the exponent, indicating that 10 is multiplied by itself once. In word form, this can be referred to as 'ten squared' or 'one hundred'.
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The difference of a number and 12 is 30
Answer:
42
Step-by-step explanation:
Difference is substitution, so a number (x) minus 12 equals 30
x-12=30
Add 12 to both sides
x=42
The problem statement is a Mathematics subtraction problem. It can be solved by setting up a simple equation n - 12 = 30, where 'n' is the unknown number. By solving the equation, we find n = 42.
Explanation:The subject of the problem statement 'The difference of a number and 12 is 30' lies in the Mathematics field. When the problem says the 'difference of a number and 12 is 30', it means we are dealing with a subtraction expression. Here, we can write a simple equation to solve this. If we use 'n' to represent the unknown number, the equation will be: n - 12 = 30. To solve for n, we should add 12 to both sides of the equation to balance it. So, it will be n = 30 + 12, and hence n = 42. So, the number in the problem statement is 42.
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What is the value of 42 – 2(3 • 5 + 1)?
[tex]4^{2}[/tex] – 2(3 • 5 + 1) = -16
The 2 is a superscript which was the first person's mistake
Write a system of equations and then solve for each variable.
3. The Arcadium arcade in Lynchburg, Tennessee uses 3 different colored tokens for their game machines. For
$20 you can purchase any of the following mixtures of tokens: 14 gold, 20 silver, and 24 bronze; OR, 20 gold, 15
silver, and 19 bronze; OR, 30 gold, 5 silver, and 13 bronze. What is the monetary value of each token?
Answer:
Gold=$0.5
Silver=$0.35
Bronze=$0.25
Step-by-step explanation:
This is the system of equations:
[tex]\$20=14G+20S+24B[/tex] (1)
[tex]\$20=20G+15S+19B[/tex] (2)
[tex]\$20=30G+5S+13B[/tex] (3)
Let's begin by substracting (2) from (1):
[tex]\left \{ {{\$20=14G+20S+24B} \atop {-\$20=-20G-15S-19B}} \right[/tex]
[tex]\$0=-6G+5S+5B[/tex] (4)
Isolating [tex]G[/tex] from (4):
[tex]G=\frac{5S+5B}{6}[/tex] (5)
Substituting (5) in (3):
[tex]\$20=30(\frac{5S+5B}{6})+5S+13B[/tex]
[tex]\$20=30S+38B[/tex] (6)
Substracting (3) from (2):
[tex]\left \{ {{\$20=20G+15S+19B} \atop {-\$20=-30G-5S-13B} \right[/tex]
[tex]\$0=-10G+10S=6B[/tex]
Isolating [tex]G[/tex]:
[tex]G=\frac{10S+6B}{10}[/tex] (7)
Making (5)=(7):
[tex]\frac{5S+5B}{6}=\frac{10S+6B}{10}[/tex]
Isolating [tex]B[/tex]:
[tex]B=\frac{5}{7}S[/tex] (8)
Substituting (8) in (6):
[tex]\$20=30S+38(\frac{5}{7}S)[/tex]
Isolating [tex]S[/tex]:
[tex]S=\$0.35[/tex] (9) This is the monetary value of silver token
Substituting (9) in (6):
[tex]\$20=30(\$0.35)+38B[/tex]
Finding [tex]B[/tex]:
[tex]B=\$0.25[/tex] (10) This is the monetary value of bronze token
Substituting (10) and (9) in (1):
[tex]\$20=14G+20(\$0.35)+24(\$0.25)[/tex]
Finding [tex]G[/tex]:
[tex]G=\$0.5[/tex] (11) This is the monetary value of golden token
In the standard (4) coordinate plane, the coordinates of the midpoint of AB are (6,8) and the coordinates of A are
(3,2). What are the coordinates of B ?
A. (0,-4)
B.(3,6)
C.(9/2,5)
D. (9,14)
E.(-3,-6)
Final answer:
To find the coordinates of point B, use the midpoint formula and solve the equations.
Explanation:
To find the coordinates of point B, we can use the formula for finding the midpoint of a line segment. The midpoint of AB is given as (6,8), and the coordinates of A are (3,2). Let's call the coordinates of B as (x,y).
According to the midpoint formula, the x-coordinate of the midpoint is the average of the x-coordinates of A and B, and the y-coordinate of the midpoint is the average of the y-coordinates of A and B.
So, we can set up the following equations:
(3+x)/2 = 6 and (2+y)/2 = 8
Solving these equations, we find that x = 9 and y = 14.
Therefore, the coordinates of point B are (9,14).
What is the coefficient of each monomial?
a. 5pk
b. f
c. –9t
d. –j
Step-by-step explanation:
Look at the picture
a. 5pk → 5
b. f = 1f → 1
c. -9t → -9
d. -j = -1j → -1
Danielle needs to walk 3 miles. If she wants to reach her destination in 45
minutes (3/4hour), how fast does she need to walk?
Answer: She needs to walk 5 miles an hour
There's two numbers 2.5 miles and 0.5 hours, you divide that, and you get the number 5, so that means, 5 miles an hour
She needs to walk at a speed of 4 miles/hour to reach the destination in 45 minutes.
What is Speed?Speed is the ratio of the total distance covered by an object and the required time to cover that by that object. It is also called Velocity.
[tex]Velocity=\frac{Distance}{Time}[/tex]
Velocity is the measurement which shows an object is how fast.
In this given problem,
The total distance Danielle needs to cover by walking is 3 miles.
She needs to reach the destination in 45 minutes
We know that,
60 minutes = 1 hour
1 minute = [tex]\frac{1}{60}[/tex] hour
45 minutes [tex]=\frac{45}{60}=\frac{3}{4}[/tex] hours
So she has to have the velocity/speed of [tex]=\frac{3}{\frac{3}{4}}=3\times\frac{4}{3}=4[/tex] miles/hour
Hence she needs to walk 4 miles/hour.
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The cost to rent a car for a day is an initial cost of $35 and $0.25 per mile driven write an equation that represents to the cost of the car rental what is the total cost if you drove 250 miles
Answer:
$35 + $0.25m is the equation
If you drove 250 miles, it would cost $97.50
Step-by-step explanation:
250 * 0.25 = 62.5
62.5 + 35 = 97.5
What’s 1:6 equal too in two ways
Hey!
------------------------------------------------
Solution:
We can get two different ways of 1:6 by add +1:+6.
1 + 1 = 6 + 6
2:12
2 + 1 = 12 + 6
3:18
------------------------------------------------
Answer:
2:12 and 3:18
------------------------------------------------
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The speed of a falling object increases at a constant rate as time increases since the object was dropped. Which graph
could represent the relationship between t time in seconds, and s, speed in meters per second?
Answer:
Step-by-step explanation:
As the object is falling from a fixed Distance, so Speed increases as time increases.
Both speed and time are Directly proportional to each other if distance remains constant.
S = k T
When , T=0, S=0
T=1 s, S=1 m/s
T=2 s, S= 2 m/s
\frac{dS}{dT}=k=Change in speed(Average Speed), if it is Change in Velocity then it will be equal to =a (Acceleration).
Answer:
A on edge 2021
solve for x 2/x+1/2=3/4
Lucy ate eight more than three times as many pretzels as Matt Lucy ate 56 pretzels how many pretzels did Matt eat
Lucy ate 56 pretzels and Matt ate 16 pretzels.
Explanation:To find out how many pretzels Matt ate, we need to use the information given in the question. Let's represent the number of pretzels Matt ate as 'x'. According to the question, Lucy ate 56 pretzels, which is 8 more than three times the number of pretzels Matt ate. So we can write the equation: 56 = 3x + 8. We must place x on one side of the equation alone in order to solve for it. Subtracting 8 from both sides, we get 56 - 8 = 3x, which simplifies to 48 = 3x. Finally, dividing both sides by 3, we find that x = 16.
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Help pls 20 points
A. The relationship between time and distance is not directly proportional.
B. The point (3, 165) means the car traveled 3 miles in 165 minutes.
C. The constant of proportionality represents distance/time.
D. The point (0, 0) represents the beginning of the trip.
E. It takes more time to drive 220 miles than to drive 275 miles.
F. The unit rate is 0 miles per hour.
Answer:
a) false
b) false
c) true
d) true
e) false
f) false
Step-by-step explanation:
hope this helps :)
4, 12, 36, 108 , ... this means Arithmetical or Not Arithmetical
[tex]\text{Hello there!}\\\\\boxed{\text{This would not be an arithmetical sequence}}\\\\\text{This is not an arithmetic sequence because the common number is}\\\text{not adding.}\\\\\text{The sequence in the question would be known as a geometric sequence}\\\\\text{A geometric sequence multiplies by a common ratio, and that's what the}\\\text{sequence is doing}\\\\\text{The sequence is being multiplied by a common ratio of 3}[/tex]
Final answer:
The sequence is not arithmetic; the terms are increasing by multiplying the previous term by 3.
Explanation:
This sequence does not follow an arithmetic pattern. In an arithmetic sequence, each term is found by adding a constant difference to the previous term. However, in this sequence, the terms are increasing by multiplying the previous term by 3. For example:
Term 1: 4
Term 2: 4 x 3 = 12
Term 3: 12 x 3 = 36
Term 4: 36 x 3 = 108
Since the terms are not increasing by a constant difference, this sequence is not arithmetic.
$120
for 5 days of work
Which shape has larger area: a rectangle that is 7 inches by 3/4 inch, or a square with a side length of 2 1/2 inches. Tell your reasoning.
The square with a side length of [tex]2\frac{1}{2}[/tex] inches has a larger area of 6.25 square inches, compared to the area of the rectangle which is 5.25 square inches.
To determine which shape has a larger area, let's calculate the area of both the rectangle and the square. The rectangle measures 7 inches by 3/4 inch, so its area is calculated by multiplying these dimensions:
Area of the rectangle = length ×width = 7 inches × [tex]\frac{3}{4}[/tex] inch = [tex]\frac{21}{4}[/tex] square inches or 5.25 square inches.
The square has a side length of [tex]2\frac{1}{2}[/tex] inches, which is equivalent to 2.5 inches. Hence, the area of the square is:
Area of the square = side ×side = 2.5 inches × 2.5 inches = 6.25 square inches.
Comparing the two, we can see that the square with a side length of [tex]2\frac{1}{2}[/tex] inches has a larger area of 6.25 square inches compared to the rectangle's area of 5.25 square inches.
U(-3,6), V(-8, 1), W(-3,1)
180° rotation about the origin
Answer:
U'(3, -6), V'(8, -1), W'(3, -1)
Step-by-step explanation:
According to the 180°-rotation rule, you take the OPPOSITE of both the y-coordinate and x-coordinate:
Extended Rotation Rules
270°-clockwise rotation [90°-counterclockwise rotation] >> (x, y) → (-y, x)
270°-counterclockwise rotation [90°-clockwise rotation] >> (x, y) → (y, -x)
180°-rotation >> (x, y) → (-x, -y)
I am joyous to assist you anytime.
only the circled ones please!!!!! Due today!!!!!! Will give brainliest and 5stars!!!
Answer:
[tex]\boxed{18. \, -3 \leq x \leq \dfrac{16}{9};\quad 22. \text{ $x \leq -19$ or $x \geq -5$}}[/tex]
Step-by-step explanation:
Q18
[tex]\left |\dfrac{3x - 5}{2} \right | \leq 7[/tex]
Multiply each side by 2
[tex]|3x - 5| \leq 14[/tex]
Apply the absolute rule:
If |x| ≤ a, then -a ≤ x ≤ a
This gives
-14 ≤ 3x - 5 ≤ 14
Separate into two inequalities
[tex]\begin{array}{cc}-14 \leq 3x - 5 & 3x - 5 \leq 14 \\-9 \leq 3x & 3x\leq 19 \\-3 \leq x & x \leq \dfrac{19}{3} \\\end{array}[/tex]
Merge the overlapping intervals
[tex]\boxed{\mathbf{-3 \leq x \leq \dfrac{16}{9}}}[/tex]
Q22
-5|x + 12| ≤ -35
Divide each side by -5
This reverses the sign of the inequality.
|x + 12| ≥ 7
Apply the absolute rule
If |x| ≥ a, then -a ≥ x or x ≥ a
-7 ≥ x + 12 or x + 12 ≥ 7
Separate into two inequalities
[tex]\begin{array}{cc}-7 \geq x + 12 & x + 12 \geq 7 \\-19 \geq x & x\geq -5 \\\end{array}[/tex]
Combine the intervals
[tex]\boxed{\textbf{$x \leq -19$ or $x \geq -5$}}[/tex]
What is the range of the function on the graph
Answer:
Y ≤ 3
Step-by-step explanation:
The Domain is the x values the function holds, while the range is the y values the function holds. This means that, looking at the graph, the range of the function is all y values less than or equal to 3, or Y ≤ 3.
Given f(x)=10-2^x, find f(7)
Answer:
Step-by-step explanation:
f(x)=10-2^x,
f(7) = 10 - 2^7 but : 2^7 = 128
so : f(7) = 10 - 128 = - 118
I need help on this question
Good luck I’m actually looking for answers just like this
Angles D and F are ______ because they are ______ angles.
Answer:
corresponding
Step-by-step explanation:
Answer:congruent because they are corresponding angles.
Step-by-step explanation:
ix is at least four more than a number. Which inequality represents this sentence? Question 20 options: a) 4 ≤ n + 6 b) 6 ≤ n + 4 c) 4 ≥ n + 6 d) 6 ≥ n + 4
Answer:
d) 6 ≥ n + 4
Step-by-step explanation:
Let n be the unknown number,
4 more than n = 4 + n
In inequality we use '≥' to represent greater than equal to or at least,
Thus,
Six is at least four more than a number.
⇒ 6 ≥ 4 more than n
⇒ 6 ≥ 4 + n
Which is the required inequality that represents the given statement,
OPTION d) is correct.
Answer:
b) 6 ≥ n + 4
Step-by-step explanation:
Classify the following Triangle
Answer:
equilateral triangle
Step-by-step explanation:
all sides are equal
Hey!
--------------------------------------
Answers:
Equilateral
Acute
--------------------------------------
Explanation:
The lines on each side show that all the sides are the same length. Acute angles are angles that are less than 90 degrees. Each angle is less than 90 degrees.
--------------------------------------
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Please put these from greatest to least.
2.485
2.463
2.90
hope this helps
Answer:
2.90, 2.463, 2.485
Step-by-step explanation:
I'm pretty sure when you do this you need to find the number that's closest to one (2.90). The bigger the number the less it's closer to one. If that makes sense.
I'm pretty sure I did this right. If i'm wrong I do apologize.
(I haven't done greatest to least for decimals in awhile. So seriously i'm sorry if this is wrong)
1. Change the following subtraction problems into addition problems.
a. -2-3
b. 8-(-1)
C. 4-9
Answer:
a. -2 + (-3)
b. 8 + 1
c. 4 + (-9)
Final answer:
The given subtraction problems can be changed to addition like -2-3 becomes -2+(-3), 8-(-1) becomes 8+1, and 4-9 becomes 4+(-9).
Explanation:
To change a subtraction problem into an addition problem, you can apply the concept that subtracting a number is equivalent to adding its opposite. This principle can be used to transform the given subtraction expressions into addition expressions as follows:
-2 - 3 is equivalent to -2 + (-3)
8 - (-1) is equivalent to 8 + 1 because subtracting a negative is like adding a positive.
4 - 9 is equivalent to 4 + (-9)
When adding numbers, follow these rules depending on the signs:
When two positive numbers are added, the result is positive (3 + 2 = 5).
When two negative numbers are added, the result is negative (-4 + (-2) = -6).
When adding numbers with opposite signs, subtract the smaller number from the larger one, and the result takes the sign of the larger number (-5 + 3 = -2).
‼️‼️solve by substitution {2p-3r=6
{-2p+3r=-6 all these problems w work shown r due in the morning pls help !!
Answer:
#7: (p, r) = (0, -2) #8: (z,w) = z, [tex]\frac{8}{3}[/tex] + [tex]\frac{4}{3}[/tex]z), ∈R #9: (c,d) = (3,3) #10: (u,x) ∈∅ #11: (a,b) = (-1, 2) #12:
Step-by-step explanation:
#7
Solve for 2p
2p - 3r = 6
2p = -6 -3r
substitute the given value of 2p into equation 2p - 3r = 6
-6 - 3r - 3r = 6
solve for r
r= -2
substitute value of r in equation
2p = -6 - 3x (-2)
solve for p
p=0
solution is ordered pair (p,r) = (0, -2)
#8
Solve for w
w= [tex]\frac{8}{3}[/tex] + [tex]\frac{4}{3}[/tex]z
substitute the given value of w into equation
6 ([tex]\frac{8}{3}[/tex] + [tex]\frac{4}{3}[/tex]z) - 8z = 16
solve for z
z ∈ R
The statement is true for any value of z and w that satisfy both equations from the system. Therefore, the solution is in parametric form.
(z,w) = z, [tex]\frac{8}{3}[/tex] + [tex]\frac{4}{3}[/tex]z)
#9
Solve for c
c + d = 6
c = d
substitute the given value of c into equation c + d = 6
d + d = 6
solve for d
d=3
substitute value of d in equation
c=3
solution is ordered pair (c,d) = (3,3)
#10
Solve for u
u= 3-2x
substitute the given value of c into equation
2 (3-2x) +4x = -6
solve for x
x ∈∅
Since the system has no solution for x the answer is
(u,x) ∈∅
#11
Solve for b
b= 5+3a
substitute the value of b into equation
3a + 5 + 3a+ b = -1
solve for a
a= -1
substitute the value of a into equation
b= 5 + 3x (-1)
solve for b
b=2
solution is ordered pair (a, b) = (-1, 2)
Final answer:
The system of equations leads to a true statement when added together, indicating that the two equations represent the same line and thus have infinitely many solutions. There's no unique solution for the variables but rather a relationship where each value of p corresponds to a specific value of r.
Explanation:
To solve the system of equations by substitution, let's first identify the given equations and the unknown variables. The two given equations are 2p - 3r = 6 and -2p + 3r = -6. We need to solve for the unknown variables p and r. Notice that adding these two equations together will eliminate both p and r, giving us an identity 0 = 0, which indicates the system has infinitely many solutions or the equations represent the same line.
Here's the process to verify this:
First equation: 2p - 3r = 6
Second equation: -2p + 3r = -6
Add the two equations: (2p - 3r) + (-2p + 3r) = 6 - 6
This simplifies to: 0 = 0
Since we have derived a true statement that does not involve the variables p and r, it is clear that these two equations are dependent and represent the same line. Therefore, there isn't a unique solution for p and r, but rather an infinite number of solutions where each value of p corresponds to a specific value of r that will satisfy both equations.
To check if the answer is reasonable, we can take any point that lies on this line and see if it satisfies both original equations, confirming that it is indeed a solution.
On a coordinate plane, a piecewise function has 2 lines. The first line has a closed circle at (negative 4, negative 4) and goes up to an open circle at (negative 1, 2). The second line has a closed circle at (negative 1, 3), continues horizontally to (1, 3), and then goes down to a closed circle at (4, 0).
What is the value of h(3)?
–2
–1
1
2
Answer:
1
Step-by-step explanation:
The last part of the line starts from (1,3) and goes to (4,0)
We have two points, so we figure out the equation of this line with the formula:
y = mx + b, where m is the slope and b is the y intercept
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m = [tex]\frac{0-3}{4-1}=\frac{-3}{3}=-1[/tex]
So we can now write y = -x + b
Plugging in a point (1,3), we get:
3 = -1 + b
b = 3+1 = 4
The equation is y = -x + 4
To find h(3), we substitute 3 into x and find the value of y:
y = -x + 4
y = -3 + 4
y = 1
Thus, h(3) = 1