To receive the greatest discount, the customer should first apply the membership discount and then take the rebate.
We are given that:
Rebate a customer receives if he buys a regular priced CD at $ 13 each = $ 5.
If a customer registers for the store member, he get a discount = 15 %.
Now, let the regular priced CD purchased be x and the application for store member be y.
So, the functions will become:
For rebate:
R (x) = 5 x
For discount:
M (y) = 15 % of x
M (y) = 0.15 x
Now, the amount a customer has to pay if she takes the membership and then takes the rebate =(1 − 0.15) (13 x) − 5 x = 6.05 x
And, if he takes the rebate first and then take the membership, he pays = (13 - 5 x)( 1 - 0.15) = 6.8 x
Therefore, we get that, to receive the greatest discount, the customer should first apply the membership discount and then take the rebate.
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Multiply and simplify. √8 x² . √2 x²
The simplest form of the expression is 4 x² .
Expressions in science are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by degree operator in between.Simplifying expressions mean editing an analogous math expression with no like terms and through a compact manner.To change expressions, we tend to tend to combine all kind terms and solve all the given brackets, if any, and then inside the simplified expression, we tend to are about to be alone left with not like terms that cannot be reduced any.We have given an expression √8 x² . √2 x² . .....(1)
On multiplying , we get
√8 x² . √2 x² = √16 x⁴
On simplifying , we get
√16 x⁴ = √ 4 × 4 × x² × x²
= 4 x²
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SOLVE FOR BRAINLIEST
The equation of the inverse function of the function f(x) = x^2 - x - 2 is f'1(x) = 0.5 + √x + 2.25
What are inverse functions?Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function
How to determine the inverse function?The function f(x) is given as
f(x) = x^2 - x - 2
Start by expressing the above function in vertex form
Using a graphing calculator, we have
f(x) = (x - 0.5)^2 - 2.25
As a general rule, we start by writing f(x) as a variable (say f(x) = y).
So, the equation of the function becomes
y = (x - 0.5)^2 - 2.25
The next step is to switch/swap the positions of x and y in the above equation y = (x - 0.5)^2 - 2.25
The equation becomes
x = (y - 0.5)^2 - 2.25
Add 2.25 to both sides
So, we have
(y - 0.5)^2 = x + 2.25
Take the square root of both sides
y - 0.5 = √x + 2.25
Add 0.5 to both sides
So, we have
y = 0.5 + √x + 2.25
Express as an inverse function
f'1(x) = 0.5 + √x + 2.25
Hence, the inverse function of the function f(x) = x^2 - x - 2 is f'1(x) = 0.5 + √x + 2.25
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8x = 2
Write down the value of x.
(It’s not 2/8 or 0.25)
Answer:
1/4
Step-by-step explanation:
Get x by itself by dividing both sides by 8
x = 2/8
Reduce
1/4
Answer:
8x=2
/8 /8
Step-by-step explanation:
it is 0.25
8x=2
/8 /8
x=0.25
Jeremiah uses 15 pages out of an exercise book containing 75 pages. What fraction of the exercise book has been used?
can someone help me find the answer to this??
The correlation coefficient (r) is 0.9168.
The correlation coefficient can be improved by ignoring the bill for the month of July.
What is the correlation coefficient of the data set?The correlation coefficient for the plotted regression data should be around 0.9168 using the estimated data point taken from the attached graph. This indicates that there is a strong positive correlation between the electricity bill ($) and the amount of time spent at home because the obtained correlation coefficient is very close to 1.How close the R-value is to either -1 or 1 serves as a gauge of the strength of a relationship using the correlation coefficient.The 4th data point on the graph which indicates the month of July is the farthest away from the regression line in comparison to other points, and should not be included in the correlation coefficient improvement calculations for the electricity bill.
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What is the value of (−12)4?
Answer:
-48
Step-by-step explanation:
[tex](-12)4\\(-12) \times 4\\= -48[/tex]
Answer: -48
Step-by-step explanation:
negative x negative x negative x negative = negative
12 x 4 = 48
remember the answer needs to be a negative
(-12)4 = -48
The midpoint of \overline{\text{AB}} AB is M(-4, -3)M(−4,−3). If the coordinates of AA are (-1, -2)(−1,−2), what are the coordinates of BB?
The midpoint of AB is M(-4, -3). If the coordinates of A are (−1,−2), then B has coordinates of (-2, -7/3)
What does a midpoint mean?Midpoint, as the word suggests, means the point which lies in the middle of something. Midpoint of a line segment means a point which lies in the mid of the given line segment.
Line AB has a midpoint, M.
A is (-1, -2)
B is unknown, M is(−4,−3)
Let's assume straight line of the form y=mx+b, where m is the slope.
Rise = (-3-(-2))= -1
Run = (-4-(-1)) = -3
Slope = (Rise/Run) = (1/3)
The line becomes y=(1/3)x+b
Calculate b, the y-intercept (the value of y when x is 0)
y=(1/3)x+b
-2 = (1/3)(-1)+b
b = -2 + (1/3)
b = -5/3
The equation becomes:
y=(1/3)x - -5/3
Find the value of y for x=-2:
y=(1/3)x - -5/3
y=(1/3)(-2) - 5/3
y= -7/3
B has coordinates of (-2, -7/3)
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if a one time deposit of $1000 in invested at age 25 with 12% annual interest rate, how much will be in the account at age 65 (40 years later)?
The amount in the account after 40 years will be $5800.
How to illustrate the information?It should be noted that the interest is calculated as:
= (Principal × Rate × Time) / 100
= ($1000 × 12 × 40) / 100
= $480000 / 100
= $4800
Therefore, the amount in the account after 40 years will be:
= Principal + Interest
= $1000 + $4800
= $5800
Therefore, the amount in the account after 40 years will be $5800.
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Question 10: Neil writes down four numbers with a sum of 50.
All the numbers have two decimal places and no two numbers are the same.
Write down four possible numbers Neil could have written down.
Answer:
15-10-11-14
Step-by-step explanation:
15+10= 25
25+11= 36
36+14= 50
2(3) 3 as an exponent + 5
Answer: 13
Step-by-step explanation:
In the first quadrant, you start at (6, 3)
and move 2 units left
What point will you end up on?
Answer: the answer is (6,1)
Step-by-step explanation:
Answer:
(4, 3)
Step-by-step explanation:
If you are moving 2 units left, the x coordinate is shifted to the left by 2 units, the y coordinate remains the same.
A shift to the left means a decrease in the x-coordinate value so new
x-coordinate is 6- 2 = 4 , y coordinate is still 3 so you end up at point (4, 3)
Motorcycle A can reach a top speed of 140 miles per hour motorcycle B can reach a top speed of 200 feet per second which motorcycle has a greater top speed
Motorcycle A has a greater top speed.
What unit conversion?A unit conversion expresses the same property as a different unit of measurement.
given:
Motorcycle A can reach a top speed of 140 miles per hour.
Motorcycle B can reach a top speed of 200 feet per second
Now,
1 miles/h = 1.46667 feet/sec
140 miles/h = 140*
= 205.333 feet/sec
So, Motorcycle A can reach a top speed of 205.333 feet/sec.
Hence, Motorcycle A has a greater top speed
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Iggy bought the refrigerator on a payment plan.He paid $150 when he bought it and he agreed to pay $28.50 each month for the next 24 months.
Answer:834$
Step-by-step:150+28.24=834$
Doy muchos puntos pls ayuda
Answer:
5. 18%
6. 5.25% o 5.3 o 5
7. 33.33%
8. 2005-2010
$74.95 ladder; 6.5% tax
Answer:
11.5307692308
Step-by-step explanation:
Answer:
Around $79.88
An urn contains 5 tiles, each containing one of the numbers from 1 to 5. An experiment consists of selecting a tile, marking down its number, then replacing it and selecting a second tile and marking down its number. How many outcomes are in the sample space for this experiment?.
Answer:
wait first of all where did they put grandma?
Let g(x)=5 x-2 and h(x)=x²+1 . Find the value of each expression. (h⁰g)(0)
The value of the expression ( h o g)(0) is 5.
When two functions say f and g, are composed in such a way that h(x) = g(f(x)), a new function, h, is created. In this case, the function of g is being applied to the function of x. So, in essence, the output of one function is applied to the result of another.
Consider the two functions,
g(x) = 5x - 2 and h(x) = x² + 1
So,
( h o g)(x) = h(g(x))
( h o g)(x) = ( 5x - 2 )² + 1
( h o g)(x) = 25x² - 20x + 4 + 1
( h o g)(x) = 25x² - 20x + 5
( h o g)(0) = 25 × (0)² - 20 × (0) + 4 + 1
( h o g)(0) = 0 - 0 + 4 + 1
( h o g)(0) = 5
The value of the expression ( h o g)(0) is 5.
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the table shows a proportional relationship between the millilitres (ml) of red paint and millilitres of yellow paint to make a certain shade of orange.
Which relation is a function?
Using the vertical line test, we conclude that the relation that is a function is the bottom right one.
Which of the graphed relations is a function?
A relation is a function only if all the inputs are mapped into a single output.
If we have the graph of a relation, it only will be a function if it passes the vertical line test.
This means that if we draw any vertical line on the coordinate axis, and it intercepts the graph of the relation more than once, then it is not a function.
With that we can see that the first 3 options are not functions, and the last one (bottom right) it is a function.
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Which of the following vertices would minimize the objective function N = 7x + 2y?
A. (4,0)
B. (6,3)
C. (3,9)
D. (0,12)
Check the picture below.
The department store sells logo t-shirts at an original price of $12.50. Every month that a t-shirt doesn’t sell, the store reduces the price by 25%. Brianna calculated the price after two reductions:
12 dollars and 50 cents minus (12 dollars and 50 cents) (0.25) minus (12 dollars and 50 cents) (0.25) = 6 dollars and 25 cents
What is Brianna’s error?
Answer:
On the second reduction, she reduced 25% of the original T-Shirt's price. She should have reduced the price of the T-Shirt after one reduction.
Step-by-step explanation:
Fiona is heating water for a science experiment the temperature of the water increases 4/5 of a degree every 2/5 of a minute how much is the temperature of the water increasing per minute.
Answer needed ASAP
thanks
The temperature that water is increasing per minute is 2 degrees.
What is the increase in temperature per minute?A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the digit above the line and the denominator is the number below the line. An example of a fraction is 3/7.
The first step is to determine what 2/5 of a minute is equivalent to in seconds.
1 minute = 60 seconds
2/5 x 60 = 24 seconds
The formula that can be used to determine the temperature that water is increasing per minute is :
Temperature increase per minute = (degree it rises to 2/5 of a minute x seconds in a minute) / seconds in 2/4 of a minute
(4/5 x 60) / 24 = 2 degrees
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The cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55.
The cost of 3 kg of mushrooms and 4 kg of turnips is £13.10.
Work out the cost of
a) 1 kg of turnips.
b) 1 kg of mushrooms.
The cost of one kg of mushroom is $2.90 while the cost of 1 kg of turnips is $1.10
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A variable can either be dependent or independent. A dependent variable depend on other variable while an independent variable does not depend on other variables.
Let x represent the cost of on kg of mushroom and y represent the cost of one kg of turnips.
The cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55. Hence:
2x + 2.5y = 8.55 (1)
The cost of 3 kg of mushrooms and 4 kg of turnips is £13.10. Hence:
3x + 4y = 13.10 (2)
From both equations:
x = 2.9, y = 1.1
The cost of one kg of mushroom is $2.90 while the cost of 1 kg of turnips is $1.10
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What is each expression written as a single natural logarithm?
(c) 3 ln x+2 ln y+ln 5
According to the question, to write the solution for the logarithmic function, the concept of indices is also needed.
Therefore, the given expression is [tex]3 ln x+2 ln y = ln5[/tex]
The values get multiplied in addition. Therefore, the above expression can be written as: [tex]ln(x^{3} )+ln(y^{2} )+ln5[/tex]
Expression = [tex]ln(x^{3} )+ln(y^{2} )+ln5[/tex]
Using logarithmic definition, we can write:
[tex]ln(x^{3} )+ln(y^{2} )+ln5\\ln(5x^{3} y^{2} )[/tex]
The solution for the given expression is [tex]ln(5x^{3}y^{2} )[/tex]
What is logarithmic function?
In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.
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The width of a vegetable garden is 1/4 times its length. If the length of the garden is 5 1/2 feet, what is the width in simplest form?
Answer:
W = 11/8 or 1 3/8
Step-by-step explanation:
The width of a vegetable garden is 1/4 times its length. If the length of the garden is 5 1/2 feet, what is the width in simplest form?
W=(1/4)(L)
width is 1/4 length
if the length is 5 1/2 ft
5 1/2 is equivalent to 11/2
W= (1/4)(11/2)
Multiply across.
W = 11/8 or 1 3/8
The number of bags of mulch you need to cover a planting area varies jointly with the area to be mulched a in square feet and the depth of the mulch d in feet. If you need 10 bags to mulch 120ft² to a depth of 3in., how many bags do you need to mulch 200ft² to a depth of 4in ?
To cover 200 ft2 to a depth of 4 inches, we'll need 22(2/9) bags of mulch.
What do we mean by depth?The depth of an object is defined as the distance between its nearest and farthest ends in mathematics. The vertical magnitude of an object is measured by its height. Depth is also a measure of an object's vertical magnitude. These two terms appear to represent the same quantity.So,
When z "varies jointly" with x and y, the following formula can be used to describe it:
z = kxy
Here, we have mulch bags (n) that vary with the area (a) and depth (d), both in feet.
The information provided allows us to calculate the value of k.
n = kad10 = k·(120)(1/4)10/30 = k = 1/3 (divide by the k coefficient)Now we can fill in the blanks with the other values of interest.
n = (1/3)·(200)·(1/3) = 200/9n = 22(2/9)Therefore, to cover 200 ft2 to a depth of 4 inches, we'll need 22(2/9) bags of mulch.
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Find the slope of the line that goes through the points (–4, 1) and (8, –5).
Answer:
[tex]\frac{-1}{2}[/tex]
Step-by-step explanation:
Slope is the change in y over the change in x.
The ordered pair is in the form (x,y). The first number is the x value and the second number is the y value.
for y;
-5 - 1 = -6
for x:
8 - (-4)
8 + 4
12
[tex]\frac{-6}{12}[/tex] Which is the same as [tex]\frac{-1}{2}[/tex] if we divide the top and bottom by 6
igcse math (quadratic functions)
given the equation: x^2 + 5x - 14
use the discriminant to decide if there are two real and different roots, two equal roots or no real roots
Answer:
2 real different roots
Step-by-step explanation:
Discriminant determines the number of real solutions of a quadratic equation. The formula of discriminant goes by:
[tex]\displaystyle{D = b^2-4ac}[/tex]
The formula is derived from a quadratic formula which is:
[tex]\displaystyle{x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}[/tex]
The expression inside the square root is discriminant. The discriminant says that:
There are 2 real different roots if the discriminant (D) is greater than 0. (D > 0)There is 2 real double roots (same roots) if the discriminant (D) is equal to 0. (D = 0)There are no real roots (imaginary or complex roots) if the discriminant (D) is less than 0. (D < 0)From the equation [tex]\displaystyle{x^2+5x-14}[/tex], determine the coefficients of equation:
a = 1b = 5c = -14Therefore, substitute the coefficients’ values in the discriminant:
[tex]\displaystyle{D=5^2-4(1)(-14)}\\\\\displaystyle{D=25-4(-14)}\\\\\displaystyle{D=25+56}\\\\\displaystyle{D=81}[/tex]
Since the discriminant is greater than 0, we can conclude that this equation will have 2 real different roots.
Please help fast thank you!
Answer:
-3.78= (-1.2y)+(-4.2y)
y= 0.7
Step-by-step explanation:
-3.78= (-1.2y)+(-4.2y)
-3.78= -5.4y
/-5.4 /-5.4
y=0.7
Please help me calculate the value of y with steps
The value of y in the triangle is 7.5
How to calculate the value of y?The given parameter is the triangle
On the triangle, we have the following equivalent ratio
y : 8 = y + 15 : 20
Express as fraction
y/8 = y + 15/20
Cross multiply
20y = 8y + 90
Collect the like terms
20y - 8y = 90
Evaluate
12y = 90
Divide by 12
y = 7.5
Hence, the value of y in the triangle is 7.5
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