Answer:
The seating capacity of the auditorium is 2,340.
Step-by-step explanation:
This question relates to an Arithmetic Progression (AP).
An Arithmetic Progression (AP) is a sequence of numbers in which the differences of every two consecutive numbers or terms are constant or the same.
Therefore, the seating capacity can be calculated using the an arithmetic progression (AP) formula as follows:
Seating capacity = (n / 2) * (2a_1 + (n - 1)d) ...................... (1)
Where;
n = number of rows = 30
a_1 = Number seats in the first row = 20
d = Common difference = 24 - 20 = 28 - 24 = 4
Substituting the values into equation (1), we have:
Seating capacity = (30 / 2) * ((2 * 20) + ((30 - 1) * 4))
Seating capacity = 15 * (40 + (29 * 4))
Seating capacity = 15 * (40 + 116)
Seating capacity = 15 * 156
Seating capacity = 2,340
Therefore, the seating capacity of the auditorium is 2,340.
Find the slope of the line that passes through (9, 10) and (5, 19).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Submit
Answer:
[tex]m=\frac{-9}{4}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (9, 10)
Point (5, 19)
Step 2: Find slope m
Substitute: [tex]m=\frac{19-10}{5-9}[/tex]Subtract: [tex]m=\frac{9}{-4}[/tex]Simplify: [tex]m=\frac{-9}{4}[/tex]find the measure of y
please
Answer:
y=140
Step-by-step explanation:
if it's an option
Customers of a certain credit card earn points for using the card. The table below shows the number of points earned for the amount spent. ( Photo Attached )
Predicted number of points for spending $10 :
___
Will give Brainliest (:
Answer:
Just hit continue.
Step-by-step explanation:
The predicted amount is for the second button only.
Each dollar spent does not always earn the same number of points.
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;
Customers of a certain credit card earn points for using the card.
The table shows the number of points earned for the amount spent.
Now, By the given table which shows the number of points earned for the amount spent.
⇒ Number of points in 4 dollars = 36
Hence, Number of points in 1 dollars = 36/4 = 9
⇒ Number of points in 7 dollars = 56
Hence, Number of points in 1 dollars = 56/7 = 8
⇒ Number of points in 9 dollars = 72
Hence, Number of points in 1 dollars = 72/9 = 8
Thus, We get;
⇒ Each dollar spent does not always earn the same number of points.
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A section of a railway has a slope of approximately 0.47. In this section, a vertical change of 1 unit corresponds to a horizontal change of what length? Round your answer to the nearest hundredth.
Step-by-step explanation:
A slope of 0.47 means that, for every 100 feet of horizontal change, the vertical rise = 47 feet
We can use a proportion here
0.47 / 1 = 1 / x
Cross-multiply
0.47x = 1*1
0.47x = 1
Divide both sides by 0.47
x = about 2.13 units
Find the amplitude:
y= 5 cos (1/4x)
Answer:
for 5cos(1/4x)
Amplitude=5
PLZ ANSWER ASAP!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: C
Step-by-step explanation: it is stretched out more.
Answer:
C
Step-by-step explanation:
C Is An Oval Not A Circle, Therefore it is different
Solve for X
[tex] \frac{x - 6}{2} = \frac{2 - x}{x} [/tex]
Answer:
[tex]\huge\boxed{x=2-2\sqrt2\ \vee\ x=2+2\sqrt2}[/tex]
Step-by-step explanation:
[tex]\dfrac{x-6}{2}=\dfrac{2-x}{x}\\\\\text{Domain:}\ x\neq0\\\\\dfrac{x-6}{2}=\dfrac{2-x}{x}\qquad|\text{cross multiply}\\\\(x-6)(x)=2(2-x)\qquad|\text{use the distributive property}\\\\(x)(x)+(-6)(x)=(2)(2)+(2)(-x)\\\\x^2-6x=4-2x\qquad|\text{add}\ 2x\ \text{to both sides}\\\\x^2-6x+2x=4-2x+2x\\\\x^2-4x=4\qquad|\text{add}\ 2^2\ \text{to both sides}\\\\x^2-2\cdot x\cdot2+2^2=4+2^2\qquad|\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-2)^2=4+4\\\\(x-2)^2=8\iff x-2=\pm\sqrt8\\\\x-2=\pm\sqrt{4\cdot2}[/tex]
[tex]x-2=\pm\sqrt4\cdot\sqrt2\\\\x-2=\pm2\sqrt2\qquad|\text{add 2 to both sides}\\\\x-2+2=-2\sqrt2+2\ \vee\ x-2+2=2\sqrt2+2\\\\\huge\boxed{x=2-2\sqrt2\ \vee\ x=2+2\sqrt2}[/tex]
PLEASE HELP ILL GIVE BRAINLIEST
Answer:
1. x = 66
2. C
3. C. 2000
Step-by-step explanation:
1. The first question is x = 66 because to get rid on the fraction you multiply both sides by 4. This leaves you with x + 2 = 68 (minus 2 on both sides) this gives you x = 66.
2. C. Commutative
3. 2000
Plug in
125 = (5)(.0125)(2000)
125 = 125
Hope this helps ya!!
HELP THIS IS DUE TONIGHT!!
What is the LCM (least common multiple) of the following
16ab^3 5a^2b^2 20ac
Also ^ means that it’s an exponent
Identify the range of the function shown in the graph.
10+
8
8
4
-10 -8 18
4
-B
-10
Answer:
-10?
Step-by-step explanation:
The price of a television was reduced $250 to $200. By the percentage was the price of the television reduced?
A. 20%
B. 25%
C. 80%
D. 50%
please help I'm not good at math!!
Answer:
B. 25%Step-by-step explanation:
The price decreased by 50, and that is 25% of 200.
Answer:
The answer is 20%
Step-by-step explanation:
I'm not amazing at percentages so this is what I did. Search up 20 percent of 250. Then it says 50. 250 minus 200 is 50, so the answer is 20%
I hope this helped and if it did I would appreciate it if you marked me brainliest.
thank you and have a nice day!
Add, subtract, multiply, or divide. Can someone help me please.
7: 8+（-4）=-2
8: -7+2=-5
9: -11-7=-18
10: 12÷（-6）=-2
11: -9×（-3）=27
12: 4-（-3）=7
13: -45÷9=-5
14: 6×（-3）=-18
What is the equation of in line slope intercept from that has a slope of 4 and goes through the point -8 -16
Answer:
Step-by-step explanation:
is your qustion like -8-16 because its -24
Answer:
y = 4x + 16
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 4, thus
y = 4x + c ← is the partial equation
To find c substitute (- 8, - 16) into the partial equation
- 16 = - 32 + c ⇒ c = - 16 + 32 = 16
y = 4x + 16 ← equation of line
Solve the equation. If the equation is an identity or if it has no solution, write identity or no solution.
1) 7n + 5 − 9n = 8 − 2n − 3
2) 4(t + 2) = 10
3) 4y+2=−13(8−12y)
PLEASE ITS ALREADY LATE AND I NEED TO TURN IT TODAY
Example 1 Fatima works as an intern at a construction company earning $10 per hour. Her office is open 8
hours per day, 5 days a week. Analyze Fatima's potential earnings for the 12 weeks she interns at the
company this summer.
A. Write a function rule to model
the situation
B. Identify the independent
variable
C. Identify the dependent
variable
f(x) =
Answer:
4800
Step-by-step explanation:
I attached a picture of the work.
We need to made a function that will help us solve this
f(x)=dx; d = $ per hour, x = # of hours
step 1) identify d (in this case, the money made per hour) which = 10
f(x)=10x
step 2) identify x (# of hours total) which = 480
f(x)=10(480)
step 3) solve the equation
f(x)=4800
independent variable:
the number of hours
dependant variable:
the amount of money made after 12 weeks
x + 2x + 12y + 4 Using the expression shown, add like terms and produce an equivalent expression.
Answer: 3x+12y+4
Step-by-step explanation:
The only like terms are the x+2x so we add them to get the simplfied answer
Answer:
3x + 12y + 4
I dont really know how to explain but since there is an X at the and of the 2, you can add X + 2x to get 3x. Since 3x, 12y, and 4 are not alike, this is the simplest form.
Given the following linear function sketch the graph of the function and find the domain and range. ƒ(x) = -5x + 4
Answer:
Domain: (-∞,∞)
Range:(-∞,∞)
Step-by-step explanation:
The sketch of the given function has been attached and the domain and range both will be (-∞,∞ ).
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A function that fluctuates linearly with respect to the changing variable is referred to as being linear.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
Given the function,
ƒ(x) = -5x + 4
Range of the function ;
Since the value of the function is defined for all real x and the value will be unique so
Range = (-∞,∞ ).
The domain of the function ;
Since it is defined for all real x so,
Domain = (-∞,∞ )
For more about the linear function
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subtract (7x^5-12x^2y+33y^2) from (5x^5-5x^2y+9y^2) simplify your results:
Answer:
- 2 [tex]x^{5}[/tex] + 7x²y - 24y²
Step-by-step explanation:
( 5 [tex]x^{5}[/tex] - 5x²y + 9y² ) - ( 7 [tex]x^{5}[/tex] - 12x²y + 33y² ) =
5 [tex]x^{5}[/tex] - 5x²y + 9y² - 7 [tex]x^{5}[/tex] + 12x²y - 33y² =
( 5 [tex]x^{5}[/tex] - 7 [tex]x^{5}[/tex] ) + ( - 5x²y + 12x²y ) + ( 9y² - 33y² ) =
- 2 [tex]x^{5}[/tex] + 7x²y - 24y²
In a company, 70% of the workers are men. If 1,620 people work for the company who aren't men, how many workers are there in all?
Answer:
2106!
Step-by-step explanation:
1,620 - 70% = 486
486 + 1,620 = 2106
( お力になれて、嬉しいです！)
Answer:
5,400 total workers
Step-by-step explanation:
70% of workers are men, this means that 30% of workers aren't men
This means that 1,620 is 30% of the total workers
To figure out the total workers you do:
30 (percentage that represents the value)/100 = 1,620 (value) / x (total workers)
You then cross-multiply the equation by multiple the numbers diagonal each other:
30/100
=1,620/x
So, 30x = 162,000
You then isolate the variable
30x/30 = 162,000/30
x = 5,400
Please help me with this question.... please...
Answer:
just plug in the x value into the equation and put it in ur calculator
hi can someone help me with this
Answer:
=−12y+11.7 I believe it's that but I am not completely sure
I believe it is
The length of segment AE is 5 centimeters.
a. what is the length of segment CD?
b. what is the length of segment AB?
c. Name a segment that had the same length as segment AB. segment________
Answer/Step-by-step explanation:
Segment AE is a radius of the circle with center of A.
Any segment that has its origin from the center of the Circle, A, and meets at any point along the circumference of the circle, is equally a radius, and would have the same length as segment AE.
Thus:
a. Length of segment CD:
Segment CD is half of the circle. So it is the diameter of the circle.
Diameter of a circle = 2 × length of the radius.
Therefore,
CD = 2 × AE
CD = 2 × 5 (substitution)
CD = 10 cm
b. AB is a radius.
Therefore, AB = AE
AB = 5 cm
c. Any of these segments are also radius of the circle and also have the same length as segment AB:
Segment AG,
Segment AD
Segment FA
Segment AC
What is the value of x in the triangle?
Answer:
Step-by-step explanation:
Q
Answer:
B
Step-by-step explanation:
Since there are 2 congruent angles then the triangle is right isosceles.
The 2 legs of the triangle are therefore congruent ( both x )
Use Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
x² + x² = (3[tex]\sqrt{2}[/tex] )² , then
2x² = 18 ( divide both sides by 2 )
x² = 9 ( take the square root of both sides )
x = [tex]\sqrt{9}[/tex] = 3 → B
The factory makes boxes that each hold one candle. The boxes measure 1 inch × 1 inch × 9 inches. The factory owner makes a stack of 40 candle boxes. What is the volume of the stack?
Answer:
360 inch^3
Step-by-step explanation:
Volume of 1 box = 1 x 1 x 9 = 9 inch^3
Volume of 40 boxes = 40 x 9 = 360 inch^3
This is a topic on mensuration. If you wish to explore more into this topic you can give me a follow on Instagram (learntionary). I'll be uploading notes on this topic soon. At the meantime, you can take a look at other topics or some tips as well!
Answer:
360 in
Step-by-step explanation:
L × W × H
1 × 1 ×9 = 9in
9 × 40 = 360 in
i need help with this asap please
Answer:
The perimeter is 100 feet. This means that all the sides of the shape must add up to equal 100.
x + x + 5 + x - 3 + x + 4 = 100
4x + 5 - 3 + 4 = 100
4x + 6 = 100
4x = 94
x = 94/4
x = 23.5 feet
The formula d-2r can be used to find the distance(d) traveled after 2 hours when driving at rate r.
A. Solve the formula for r.
B. Find the rate(r) when the distance traveled is 130 miles.
Answer:
A. d/2 = r
B. r=65 miles/hour
Step-by-step explanation:
A. d/2 = 2r/2
B. Using the formula you found for R it is
130/2= r, therefore r = 65
The formula for r is:
r = d/2.
The rate r when the distance traveled is 130 miles is:
= 64 miles per hour.
Given,
The formula d = 2r can be used to find the distance(d) traveled after 2 hours when driving at rate r.
We need to:
- Solve the formula for r.
- Find the rate(r) when the distance traveled is 130 miles.
What is the formula for speed?Speed = distance / time
We can find the distance as:
distance = speed x time
We have,
d = 2r where d = distance and r = rate.
Here 2 = 2 hours
The formula for r :
d = 2r
Divide both sides by 2.
d/2 = r
r = d/2
r = distance / 2 hours
The rate at a distance of 130 miles is:
d = 130 miles
r = d / 2
r = 130 / 2 = 65 miles / hour
Thus,
The formula for r is d/2.
The rate r when the distance traveled is 130 miles is 64 miles per hour.
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Find the missing number so that the equation has no solutions.
4x+2=_x+12+x
Answer:
2
2 makes it able to never be solved. If I did this correctly
Answer:
yo d see was gotta at brb to fbh gwuhbytujv
hiii, this geometry please help
Heyy guys I need help
===================================================
Explanation:
Since AE = BE, we know that triangle ABE is isosceles with A = B as the congruent base angles (it might help to rotate the triangle 90 degrees clockwise). The congruent base angles are always opposite the congruent sides of an isosceles triangle.
Focus on triangle ABE. Let's find the missing angle E.
A+B+E = 180
55+55+E = 180
110+E = 180
E = 180-110
E = 70
So angle BEA = 70 degrees
This means angle DEC is also 70 degrees. Angles BEA and DEC are congruent vertical angles.
--------------------
Now focus on triangle DEC. We just found E = 70. The diagram shows D = 34. Use these items to find C
D+E+C = 180
34+70+C = 180
104+C = 180
C = 180-104
C = 76
Angle C is 76 degrees
Answer:
hey
Step-by-step explanation:
What’s the answer for 65°
15x + 10
Answer:
7
Step-by-step explanation:
65° + 15x + 10 = 180° (co-interior angles are equal)
15x + 75° = 180°
15x = 180° - 75°
15x = 105°
x = 105/15
x = 7