Explanation:
The relevant relationships are ...
discount = (discount rate) × (original price)
(sale price) = (original price) - discount
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Putting these into one equation gives ...
(sale price) = (original price) - (discount rate)×(original price)
Combining terms, yields ...
(sale price) = (original price)×(1 -(discount rate))
This relation can be solved for either of the variables on the right:
(original price) = (sale price)/(1 -(discount rate))
(discount rate) = 1 -(sale price)/(original price)
or ...
(discount rate) = discount/(original price)
Going back to the beginning, you have ...
discount = (original price) -(sale price)
__
To solve for the missing amount, you can choose the formula for which you have the other amounts. Or, you can start with any of the relations that relate the amounts you have, fill in the given values, and solve for the unknown.
It's not rocket science. You see these calculations almost every time you go to the store.
_____
Additional comments
Here, we have assumed a positive value for discount rate and discount, and that the sale price is less than the original price. This is basically the set of relations that are seen by a retail buyer.
If you are the seller, the relations you typically see are ...
(cost price) + (markup) = (selling price)
The markup can be expressed as a percentage of either the cost price or the selling price, or it may be based on some other relation (fixed business costs, for example).
And another one is ...
(markup)/(cost price) = (profit ratio) . . . . often expressed as a percentage
Sometimes the profit is expressed as a fraction of the selling price (business revenue) instead of the cost price.
__
Taxes are added on in the same way that discounts are subtracted:
(final selling price) = (selling price) + (tax rate)×(selling price)
or
(final selling price) = (selling price)×(1 +(tax rate))
The digit in the hundreds place is 4 less then 5.
Yes?? i dont understand the question that much
Step-by-step explanation:
help please i’m doing homework and i can’t fail this lesson.
Answer: y = 3x +1
Step-by-step explanation:
The neon lights on the dance club sign blink 240 times in 2 minutes. How many times does the neon sign blink in 10 minutes?
Answer:
1200 times in 10 minutes.
Step-by-step explanation:
There's 5 amounts of 2 minutes in 10.
Therefore multiply 240 by 5.
24 x 5 = 120 x 10 = 1200 times.
Answer:
If it blinks 240 times in 2 minutes, then you need to multiply 240 and 5. My work is shown below...
2 = 240
2 x 5 = 10
5 x 240 = 1200
This means the neon sign blinks 1200 times every 10 minutes.
Step-by-step explanation:
Have a great day and please mark brainliest!
Find the value of x, y, and z.
Which expressions are equivalent to -56z+28?
A.) 1/2⋅(-28z+14)
B.)(-1.4z+0.7) x 40
C.) (14-7z)⋅(-4)
D.)(8z−4)(−7)
E.)−2(−28z−14)
PLEASE HELP THANK YOU!!!
find the domain of f(x). f(x) = √9x+36
Answer:
The domain in interval notation is [-4,∝) or set build: {x|x[tex]\geq[/tex]
Step-by-step explanation:
I'm assuming the 9x and the 36 are in the root
[tex]\sqrt{9x+36}[/tex]
first we must solve for x
[tex]{9x+36}\geq 0[/tex]
substract 36 to both sides
[tex]{9x}\geq -36[/tex]
divide by 9 to both sides
[tex]\frac{9x}{9} }\geq \frac{-36}{9}[/tex]
simplify left side
[tex]x\geq \frac{-36}{9}[/tex]
simplfy right side
[tex]x\geq -4[/tex]
The domain in interval notation is [-4,∝) or set build: {x|x[tex]\geq[/tex]-4}
HELP ASPAP!! ANSWER CORRECLTY
Answer:
17
Step-by-step explanation:
Answer:
plot 17
Step-by-step explanation:
12-(-5) = 12+5 = 17
rewrite the two statements as a single biconditional statement: A rectangle is a quadrilateral that has all perpendicular sides. If all sides of a quadrilateral are perpendicular, then it is a rectangle.
Your friend claims that only true conditional statements have a true contrapositive. is your friend correct? explain your reasoning
A) The single biconditional statement of the given statement is;
A quadrilateral is a rectangle if and only if it has all perpendicular sides
B) The statement made by your friend about only true conditional statements having a true contrapositive is; True
A biconditional statement is one that combines 2 conditional statements that are related to one another. An example of a biconditional statement is;
The polygon has only four sides if and only if the polygon is a quadrilateral.
That biconditional statement has combined two individual conditional statements.
Now, to our question, we are given two statements;
Statement 1; A rectangle is a quadrilateral that has all perpendicular sides.
Statement 2; If all sides of a quadrilateral are perpendicular, then it is a rectangle.
Combining both statements means that the biconditional statement will be; A quadrilateral is a rectangle if and only if it has all perpendicular sides
B) A contrapositive is when we switch and negate the hypothesis and the conclusion of a conditional statement. For example, the contrapositive of "If it is raining then the grass is wet" is "If the grass is not wet then it is not raining."
Thus, if the conditional statement is true, then we will have a true contrapositive.
Read more about contrapositives at; https://brainly.com/question/12276922
Find the equation of a line that passes through the point (-4,1) and has a gradient of 2.
Leave your answer in the form
y=mx+c
Answer:
y = 2x + 9.
Step-by-step explanation:
Using the point-slope form:
y - y1 = m(x - x1) where m = the slope and (x1, y1) is a point on the line.
So here we have:
y - 1 = 2(x - (-4))
y - 1 = 2(x + 4)
y - 1 = 2x + 8
y = 2x + 9.
Please help Tysm!! <3
Answer:
68 homes
Step-by-step explanation:
1. First, let's set up a proportional relating the home to the # of hours.
[tex]\frac{17}{49} = \frac{x}{196}[/tex]2. Now, let's see if we can divide 196 by 49. If so, the quotient we get is the number we multiply 17 by to get x.
[tex]196/49 = 4[/tex] This means that we multiply 17 by 4 to get x.[tex]17 * 4 = 68[/tex]Therefore, the answer is 68 homes.
A train takes 50 minutes to travel 106.3 if the train travels at the same rate how long would it take to travel 416 miles
Answer:
Step-by-step explanation:
Let's find how many miles the train travels per minute.
do 106.3miles/50minutes=2.13miles/minute.
now we know it travels 2.13miles per minute.
we can know find the amount time it takes for the train to travel 416miles.
416miles/2.13miles= about 195.3 minutes or 11718seconds, or 3.3 hours.
An ice cream store has 31 flavors of ice cream and 10 toppings. A regular sundae has one flavor of ice cream, one topping, and comes with or without whipped cream. How many different ice cream sundaes can be ordered?
Answer:
610
Step-by-step explanation:
31 x 10= different flavour and topping combination
x2 = for the whipped cream different option
Scott is shopping for juice at the grocery store. He is deciding between two bottles of juice:
•16 oz. of juice for $2.00, and
•24 oz. of juice for $2.40.
Which bottle of juice is the better buy?
Answer:
24 oz
Step-by-step explanation:
16 + 16 is 24. and if you were to buy two 16 oz juices, it would make the price $4.00. So, you're getting double the amount of 16 oz juice for $1.60 off.
What is 7.125 simplified as a fraction?
Answer: 7 [tex]\frac{1}{8}[/tex] or [tex]\frac{57}{8}[/tex]
Step-by-step explanation:
0.125 = 1/8
Which graph represents the equation y= −4/3x − 2
Answer:
C -- see attachment
Step-by-step explanation:
The graph you're looking for has a y-intercept of -2 (as they all do) and a negative slope that is steeper than -1. It will have a "rise" of -4 for each "run" of 3, so point (-3, 2) will also be on the graph.
The graph shown in the attachment is the one you're looking for.
_____
Two of the offered graphs have negative slope. One (B) has a slope of -3/4, so is not the correct graph. The other (C) has a slope of -4/3. It is attached.
I need help with this
Answer:
If the bottom is 14 it's 6 and 8
What is 7(x-3) Equal to
Answer:
7x-21
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In the circle represented by the equation (x-4)2+(y-3)2=25, the diameter is
please help! i need for this to be done.
Solve.
t+7.45=1334
Enter your answer as either a decimal or a mixed number in simplest form in the box.
t =
Answer:
t = 6.3
Step-by-step explanation:
t + 7.45 = 13 [tex]\frac{3}{4}[/tex] = 13.75 ( subtract 7.45 from both sides )
t = 6.3
HELP PLEASE..........
Answer:
19.47
Step-by-step explanation:
Use the law of sines.
sin(90)/6 = sin(x)/2
Multiply both sides by 2
2 * sin(90)/6 = sin(x)
Use a calculator
0.33333 = sin(x)
sin^-1 0.3333 = 19.47
Find the factors of f(x) given that x = −3 is a zero.
f(x) = x^3 + 12x^2 + 47x + 60
(x + 3)(x + 4)(x − 5)
(x + 3)(x + 4)(x + 5)
(x − 3)(x + 5)(x + 6)
(x + 3)(x + 3)(x − 3)
[tex]x^3+12x^2+47x+60\\\\=x^3+3x^2 +9x^2+27x+20x+60\\\\=x^2(x+3) + 9x(x+3)+20(x+3)\\\\=(x+3)(x^2+9x+20)\\\\=(x+3)(x^2 + 4x +5x +20)\\\\=(x+3)[x(x+4)+5(x+4)]\\\\=(x+3)(x+4)(x+5)[/tex]
Blake gives piano lessons in the evenings. He earns $20 for each piano lesson and has between 0 and 6 lessons each evening. The amount he earns in an evening depends on the number of lessons he gives. What is the range of this relation?.
The range of the relation will be expressed as 0 ≤ g(x) ≤ 120
Let the number of lessons he gives be xIf he earns $20 for each piano lesson, the amount he will earn on x lessons will be $20xWriting this as a function will give:
g(x) = 20xwhere g(x) is the range of the relation.
If he has between 0 and 6 lessons each evening, the corresponding range at x = 0 and x = 6 is given as;
g(0) = 20(0) = 0g(6) = 20(6) = 120Therefore the range of the relation will be expressed as 0 ≤ g(x) ≤ 120
Learn more on range of a function here: https://brainly.com/question/10878781
Answer: {0, 20, 40, 60, 80, 100, 120}
Step-by-step explanation: Remember we only use inequality signs for continuous relations with an infinite amount of values or data points or values or points. When we're given a set finite amount of data points we use brackets for this data because it is a discrete relation.
And for this problem we're looking for the range of the relation and recall the range is the dependent values or variables that depend on the domain or independent variables. The amount of money he earns depends on the amount of hours he works. Hence, the range is {0, 20, 40, 60, 80, 100, 120} the amount of possible money he can earn.
Which of the following statements is false?
Reflection over x-axis:
T(x, y) = (x, y)
Reflection over y-axis:
T(x, y) = ( x,y)
Reflection over line y = x: T(x, y) = (y, x)
O Reflection over y-axis:
T(,Y)= (x,y)
Answer:
T(x,y)=(x,y) is false
Step-by-step explanation:
The standard form of a quadratic equation is given as y=ax^2+bx+c and vertex form is given as y=a(x−h)^2+k. Write a formula that relates the values of a,b, and c in y=ax^2+bx+c to the values of a,h, and k in y=a(x−h)^2+k. For instance, h=ax+b would be a formula that relates h to a and b.
Answers:
[tex]h = -\frac{b}{2a}\\\\k = \frac{-b^2+4ac}{4a}\\\\[/tex]
where 'a' cannot be zero.
=========================================================
Explanation:
The vertex is (h,k)
The x coordinate of the vertex is h which is found through this formula
[tex]x = -\frac{b}{2a}[/tex]
For example, if we had the quadratic [tex]y = 3x^2-6x+5[/tex], then we'll plug in a = 3 and b = -6 to get: [tex]h = -\frac{b}{2a} = -\frac{-6}{2*3} = 1[/tex]
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To find the value of k, we plug that h value into the original standard form of the quadratic and simplify.
[tex]y = ax^2+bx+c\\\\k = ah^2+bh+c\\\\k = a\left(\frac{-b}{2a}\right)^2+b\left(\frac{-b}{2a}\right)+c\\\\k = a*\frac{b^2}{4a^2}+\frac{-b^2}{2a}+c\\\\k = \frac{b^2}{4a}+\frac{-b^2}{2a}+c\\\\[/tex]
[tex]k = \frac{b^2}{4a}+\frac{-b^2}{2a}*\frac{2}{2}+c*\frac{4a}{4a}\\\\k = \frac{b^2}{4a}+\frac{-2b^2}{4a}+\frac{4ac}{4a}\\\\k = \frac{b^2-2b^2+4ac}{4a}\\\\k = \frac{-b^2+4ac}{4a}\\\\[/tex]
It's interesting how we end up with the numerator of [tex]-b^2+4ac[/tex] which is similar to [tex]b^2-4ac[/tex] found under the square root in the quadratic formula. There are other ways to express that formula above. We need [tex]a \ne 0[/tex] to avoid dividing by zero. The values of b and c are allowed to be zero.
Answer:
The minimum is at (1,-8). In the equation y = (x – 1)2 – 8, h = 1 and c = 8. So, the x-coordinate of the minimum is the same as the h-value in the equation, and the y-value of the minimum is the opposite of the c-value.
Step-by-step explanation:
plato
what is 2 + 2 + 2 +2 lol
Answer:
8 lol
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
describe this graph of a Ferris wheel
Answer:
A wheel completes a rotation when it moves 360 degrees. The descriptions of the graph are: The Ferris wheel will rotate 4 times.
Step-by-step explanation:
but what graph
The Ferris wheel makes 4 rotations.
The maximum points on the graph represent when the Ferris wheel is at the top, and the minimum points on the graph represent when the Ferris wheel is at the bottom
A fast food place was selling 5 boxes of chicken nuggets for 25.50 a competing restaurant was selling 1 box of chicken strips for 5.50 which is better priced per box, 5 boxes chicken nuggets for 25.50 or 1 box of chicken strips for 5.50
Answer:
The chicken which is sold for 5 boxes for 25.50 is better priced.
Step-by-step explanation:
If you buy five boxes of the chicken from the place where it is 5.50 a box, buying five will be 27.50, which costs more than the place with the 25.50 price for five boxes.
Oceanside Bike Rental Shop charges a 13 dollars fixed fee plus 7 dollars an hour for
renting a bike. Keith paid 69 dollars to rent a bike. How many hours did he pay to have
the bike checked out? Let h = number of hours bike was checked out
Answer:
8 hours
Step-by-step explanation:
69-13=56
56/7=8
13+7h=69
What type of function is represented in the table? exponential linear quadratic logarithmic
2022 EDGE ASSIGNMENT
Modeling Functions Using Finite Differences
1. C
2. A, E
3. B
4. B, D
5. D
6. A
7. B, F
Juan texts 20 messages in 5 minutes. At this rate how many text messages can he send in 30 minutes
The answer 120 MESSAGES