An art studio holds beginners art classes. Each class costs $24 and there is also a one-time registration fee of $15 . You attended c number of classes and paid a total of $687. Find the number of classes you took.
The total number of classes that were taken by you was 28.
What is linear equation in one variable?The linear equations in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.
According to the given question.
Registration fee for the dance class = $15
Amount of money charges for each dance class = $24
Amount of money paid for c number of classes = $687
⇒ [tex]687 = 24c + 15[/tex]
Solve the above linear equation in one variable for c.
[tex]687 = 24c + 15[/tex]
⇒ [tex]687 - 15 = 24c[/tex]
⇒ [tex]672 = 24c[/tex]
⇒ [tex]c = \frac{672}{24}[/tex]
⇒ [tex]c = 28[/tex]
Hence, the number of classes is 28.
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How do you determine a closer approximation for the square root of 12
Answer:
look at it
Step-by-step explanation:
what is the slope of 3y = 9 – 4x
Answer:
The slope is -4/3
I hope this helps :)
(-1,2), (-1,-5) can you solve this for me
Answer:
Use FOIL I helped with what I could I don't fully understand the problem but I'm pretty sure FOIL needs to be used to solve.
Find the x-intercept and y-intercept of the liné.
- 6x + 5y = 21
Answer:
x=-3.5 or -7/2 (same thing)
y=21/5
Step-by-step explanation:
x intercept is when y=0
y intercept is when x=0
so
x intercept is
-6x=21
x=21/-6
x=-3.5
y intercept is
5y=21
y=21/5
Function g is a transformation of the parent quadratic function f. Which statements are true about this function?
g(x) = -(x - 4)2 + 6
Select all the correct answers.
Function g reflected function facross the x-axis.
Function g translated the vertex from (0,0) to (-4,6).
For function g, as x approaches negative infinity, 8(x) approaches negative infinity.
Function g is always decreasing,
Function g is always negative.
Function g is symmetrical about the point (4,6).
Answer: Function g reflected function f across the x-axis.
For function g, as x approaches negative infinity, g(x) approaches negative infinity.
Function f is symmetrical about the point (4,6).
The correct options are Option A and Option C : Function g is reflected of function f across the x-axis. and as x approaches to the -∞, g approaches to the -∞.
Here given that the function g(x)= -(x-4)²+6
vertex of the graph of the function g is
dg/dx=0
⇒2(x-4)=0
⇒x-4=0
⇒x=4
putting x=4 in g(x) , g(4)= -(0-0)²+6=6
Hence the vertex of the graph of g is (4,6).
The parent function is f(x)= x²
here the vertex of the function is (0,0).
Option A: This option is true as the graph of function g is the inverse image of f. So, Function g is reflected of function f across the x-axis.
Option B: This option is incorrect. as the vertex of the function f is transformed to (4,6) which is the vertex of g(x).
Option C: This option is true because
[tex]\lim_{x \to- \infty} g(x)[/tex]
= [tex]\lim_{x \to- \infty} -(x-4)^2+6\\[/tex]
= -(∞-4)²+6
=-∞²+6
=-∞
Hence as x approaches to the -∞, g approaches to the -∞
Option D. This option is incorrect because
if the function is always decreasing its derivative is negative for all x∈R
dg/dx<0
⇒2(x-4)<0
⇒x-4<0
⇒x<4
so the function is decreasing for x<4 not for all x.
Option E: This option is incorrect. because g is not always rather it is positive for 4-√6 < x < 4+√6
g(x)>0
⇒-(x-4)²+6 >0
⇒-(x-4)²>-6
⇒(x-4)²<6
⇒|x-4|<√6
⇒4-√6<x<4+√6
so, g(x) is positive for 4-√6 < x < 4+√6
Option E:
This option is incorrect as g(x) is symmetrical about line x=4.
Therefore the correct options are Option A and Option C : Function g is reflected of function f across the x-axis. and as x approaches to the -∞, g approaches to the -∞.
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87 times 422 divided by 4
Answer:
9178.5
Step-by-step explanation:
Follow PemDas
From Left to Right, you multiply 87 x 422, which is 36,714
Then, thake that number and divide it by 4, giving you 9,178.5
What is the value of Negative 9 r minus 7 when r = 2?
Answer:
-25
Step-by-step explanation:
-9r - 7
-9(2) - 7
-18 - 7
-25
Find the measure of
Find each rate and unit rate $8.96 for 8 pounds of grapefruit?
Answer:
the answer should be 0.96
The telephone company offers two billing plans for local calls. Plan 1 charges $32 per month for unlimited calls and Plan 2 charges $17 per month plus $0.03 per call.
Answer:
The indifference point is 500 calls.
Step-by-step explanation:
Giving the following information:
Plan 1 charges $32 per month for unlimited calls and Plan 2 charges $17 per month plus $0.03 per call.
I assume we have to determine the indifference point between the two plans.
First, we need to structure the cost formulas:
Plan 1= 32
Plan 2= 17 + 0.03*x
x= call
Now, we need to equal both formulas:
32 = 17 + 0.03x
15= 0.03x
500= x
The indifference point is 500 calls.
Plan 1= $32
Plan 2= 17 + 0.03*500= $32
Answer:
Step-by-step explanation:
For the pair of functions, find (f • g)(x) and (gof)(x).
f(x) = -2x2 g(x) = x + 4
A. (g)(x) = -283 - 8x?: (gof)(x) = -2x3 - 8x2
B. (f 9)(x) = -2x2 – 16x - 32; (gof)(x) = -2x2 + 4
C. (og)(x) = -2x2 + 4; (g - f)(x) = -2x2 – 16x - 32
D. (fog)(x) = -2x2 – 32; (g - )(x) = -2x2 + 4
Dos veces la edad de Mary más 7 es igual a 33. ¿Cuál es la
edad de Mary?
Answer:
La edad de Mary es:
13 años
Step-by-step explanation:
Planteamiento:
2m + 7 = 33
m = edad de Mary
Desarrollo:
2m = 33 - 7
2m = 26
m = 26/2
m = 13
Comprobación:
2*13 + 7 = 33
26 + 7 = 33
What is the value of m in the figure? In this diagram ABD~BCD
Answer:
D. √136Step-by-step explanation:
see attached sketch
Answer:
sqrt 136
Step-by-step explanation:
just took the a pe x
An athletic facility is building an indoor track. The track is composed of a rectangle and two semicircles.
a. Write a formula for the perimeter of the indoor track
P=
b. Solve the formula for x.
x=
c. The perimeter of the track is 660 feet, and r is 50 feet. Find x. Round to the nearest foot.
x=____feet
Answer:
(The image is not provided, so i draw an idea of how i supposed that the problem is, the image is at the bottom)
Ok, we have a rectangle of length x by r.
At the extremes of length r, we add two semicircles.
So the perimeter will be equal to:
Two times x, plus the perimeter of the two semicircles (that can be thought as only one circle).
The radius of the semicircles is r, and the perimeter of a circle is:
C = 2*pi*r
where pi = 3.14
Then the perimeter of the track is:
P = 2*x + 2*pi*r.
b) now we want to solve this for x, this means isolating x in one side of the equation.
P - 2*pi*r = 2*x
P/2 - pi*r = x.
c) now we have:
P = 660ft
r = 50ft
then we can replace the values and find x.
x = 660ft/2 - 3.14*50ft = 173ft
Round 496.739386253 to the nearest whole number.
Answer:
467
Step-by-step explanation:
7 is greater than 5 so the six is rounded to a 7
Hope this helped please mark me brainiest
Answer:
497
Step-by-step explanation:
If x ≥ 5, we round up.
If x < 5, we round down.
Since 7 ≥ 5, we round 496.739386253 to 497.
What is the graph of g?
Answer:
function gis defined as g (6) = - f (-4) graph
Use the graph shown to answer the question. What is the solution set for the inequality if log2(2x – 1) > 2?
Answer: B
(2.5, ∞)
Step-by-step explanation:
The solution set of the given logarithm inequality will be (2.5,∞).
What is a logarithm?The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.
In another word, a logarithm is a different way to denote any number.
As per the given logarithm function,
log₂(2x - 1) > 2
By log property
2x - 1 > 2 x 2
2x > 4 + 1
x > 5/2
x > 2.5 so the solution set will be 2.5 < x < ∞ or (2.5,∞).
Hence "The solution set of the given logarithm inequality will be (2.5,∞)".
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Which of the following numbers is irrational?
72
국
4
3
3, 5, VA
O?
0 3
O A
Simplify each expression.
20-2.32
0 18
O 11
O 60
O 2.
Answer:
the answer for this question is 18
The temperature was -6°F. It rose so that the temperature was 0°F. What integer represents the change in temperature?
Answer:
f + 6
Step-by-step explanation:
a −3=( a 1 ) 5 what is the value of a?
Answer:
A=[tex]\frac{-3}{4}[/tex]
Step-by-step explanation:
a−3=a1(5)
Step 1: Simplify both sides of the equation.
a−3=a1(5)
a+−3=5a
a−3=5a
Step 2: Subtract 5a from both sides.
a−3−5a=5a−5a
−4a−3=0
Step 3: Add 3 to both sides.
−4a−3+3=0+3
−4a=3
Step 4: Divide both sides by -4.
-4a/-4 = 3/-4
Your final answer is a=-3/4Solve for x : x/8 = 8
Quickly !
The answer is [tex]x=64[/tex]
The first and last step is to multiply both sides by 8
[tex](\frac{x}{8} )(8)=8*8[/tex]
Multiplying [tex]\frac{x}{8}[/tex] by [tex]8[/tex] makes x by itself and 8*8 is 64
[tex]x=64[/tex]
If it is 375 miles form Los Angeles To San Francisco and on a map the scale is 2cm=10miles how far apart are they on the map
dees nute lil d man you knoe bro sup
Pls help I am so confused
Which algebraic equation models the English sentence, a number subtracted from 8 is equal to 4?
let's x represent a number
8-x = 4
Answer:
8-x = 4
Step-by-step explanation:
took the test and got it correct
During the winter, the amount of water that flows down a river remains at a low constant. In the spring, when the snow melts, the amount of water increases drastically, until it decreases to a steady rate in the summer. The flow then slowly decreases through the fall into the winter. Consider the graphs shown. Which graph best represents the given situation?
Answer:
Its Graph B
Step-by-step explanation:
I got the quiz correct
What is the distance between (8, -3)(8,−3)left parenthesis, 8, comma, minus, 3, right parenthesis and (4, -7)(4,−7)left parenthesis, 4, comma, minus, 7, right parenthesis?
Answer:
The distance between both points is 4√2 units
Step-by-step explanation:
Here in this question, we want to calculate the distance between two given points.
These points are (8,-3) and (4,-7)
Mathematically, the distance between two points can be given as;
D = √(x2-x1)^2 + (y2-y1)^2
where x1 = 4, x2 = 8 , y1 = -7 and y2 = -3
Substituting these values;
D = √(8 -4)^2 + (-3-(-7)^2
D = √(4)^2 + (4)^2
D = √(16+16)
D = √(32)
D = 4√2 units
Answer:
32 Number C
Step-by-step explanation:
Using one or more of your senses to gather information is called O Inferrence O Prediction O Observation O Hypothesis
James works at a department store and receive a 25% discount on his purchase he purchases some new clothes at the store and his total before the discount is $145.20 what is James total after the discount
Answer:
$108.90
Step-by-step explanation:
James pays 75% of the amount, so he pays ...
0.75 × $145.20 = $108.90
James' total after the discount is $108.90.