The better way for the customer to buy a sofa is to apply the Sale Tax after the discount.
Let us assume that the marked price of a sofa is $1000.
Now we will first take the sale tax and then the discount on the marked price.
Sale = 1000 × 5/100
= 50
So the price after the sale = 1000 + 50
= 1050
As the discount is $100
Therefore total is to be paid is
1050- 100
i.e., $950
Now we will calculate discount first then the sale tax.
As marked price is $1000 and discount is $100
So price after discount = $1000- $100
= $900
Now we will apply the sale tax on the discount price which is 5%
Sale price = 900 × 5/100
=45
Total price to be paid = 900 + 45
= $945
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EXAMINAR: Mr Shiwarira
QUESTION 1
1.1
1.2
1.3
1.3.1
1.3.2
INFORMAL TEST
Add (6a + 4b-7c) and (12a-10b + 15c)
Subtract (3x + 8y - 10z) from (7x - 12y + 18z)
Simplify the following:
25a³ x 4a²
24a³b ÷ 4a²b
Addition of algebraic terms
(6a+4b-7c) + (12a-10b+15c)
⇒ simplify each term
⇒6a+4b-7c+12a-10b+15c
⇒18a-6b+8c
subtraction of algebraic terms
(7x-12y+18z) -(3x+18y-10z)
⇒ 7x-12y+18z-3x-18y+10z
⇒4x-30y+28z
: A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 25 is the square of 5
Check : 4 is the square of 2
Check : a2 is the square of a1
Factorization is : (5a + 2) • (5a - 2)
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. Vocabulary How do you find the multiplicative inverse of
a number? Give an example of a number and its multiplicative
inverse.
The multiplicative inverse of a number is a number that when multiplied by the original number gives the product as 1. The multiplicative inverse of 'a' is denoted by a-1 or 1/a. In other words, when the product of two numbers is 1, they are said to be multiplicative inverses of each other. The multiplicative inverse of a number is defined as the division of 1 by that number. It is also called the reciprocal of the number. The multiplicative inverse formula says that the product of a number and its reciprocal is 1.
There are various types of numbers like natural numbers, fractions, unit fractions, negative numbers, etc. Let us understand the multiplicative inverse formula for each type of number.
Natural numbers are counting numbers starting from 1. The multiplicative inverse of a natural number a is 1/a.
Multiplicative Inverse of Integers
Finding the multiplicative inverse of positive integers is the same as natural numbers (explained above). Just like positive integers, the product of a negative number and its reciprocal must be equal to 1. Thus, the multiplicative inverse of any negative number is its reciprocal. For example, (-6) × (-1/6) = 1, therefore, the multiplicative inverse of -6 is -1/6. Note that the multiplicative inverse of a negative number is always negative. And, in the multiplicative inverse of a negative integer, the negative sign will attach to the numerator, and not with the denominator.
How to Find Multiplicative Inverse of a number :
The multiplicative inverse of a number is also known as its reciprocal. It is very easy to find the multiplicative inverse of a number using the following steps:
Step 1: Divide the given number by 1.
Step 2: Write it in the form of a fraction. Say, the reciprocal of a is 1/a.
Step 3: Simplify and get the answer.
Let us find the multiplicative inverse of 2/3. The first step is to divide it by 1, which will result in 1/(2/3) = 3/2. Therefore, the reciprocal of 2/3 is 3/2.
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Two lines are parallel, and one line has a slope of 6. What is the slope of the other line ?
Answer:
Parallel lines have the same slope, so the slope of the other line is also 1/6
Step-by-step explanation:
Parallel lines have the same slope, so the slope of the other line is also 1/6
Brian received a gift card of $50 for a pizza restaurant. The restaurant charges $8 per pizza. Rita received a gift card of $70 for a different pizza restaurant. The restaurant charges $12 per pizza. - Let x be the number of pizzas purchased.
Answer: X = - 5
Step-by-step explanation:
If anyone does this I will give 25 points and rate u on the thing please help me I have a hour until it’s due
Answer:
x=-9 , x=-8 , x=15 , x=-13 , x=3 , x=-4 , x=5 , x=6 , x=-24 , x=-7 , x=-16
Step-by-step explanation:
Students in a school are split into teams. the purple team has 51 students, the green team has 42 students, and the gray team has 48 students. what is the constant of proportionality for the ratio of green team students to gray team students?
The constant of proportionality for the ratio of green team students to gray team students is 7/8.
Ratio is the relationship between two quantities, normally expressed as the quotient of one divided by the other.
It can be expressed in different ways:
1) Use the ":" to separate the values : a : b
2) Use the word "to" : a to b
3) Write it in fraction: a / b
The ratio that relates two given values is called the constant of proportionality, a/b.
If the green team has 42 students, and the gray team has 48 students, then the ratio of green team students to gray team students can be written as:
42 : 48 or 42 to 48 or 42/48
To simplify the ratio, divide both numbers in the ratio by the same number until they cannot be divided any more.
Divide both number by 6.
42 : 48 = 7 : 8 or 7/8
Hence the constant of proportionality is 7/8.
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A culture of 10 bacteria is started, and the number of bacteria will double every hour. In about how many hours will there be 3,000,000 bacteria?
Time required to form 3,000,000 bacteria from 10 if it will double every hour = 18.2years.
In basic terms exponential growth:The phrase exponential refers to a high number expressed in smaller terms, or something that grows at an ever-increasing rate. 25 is shown as 5x5 as an example of an exponential. The erosion that is occurring on the Holderness coast in eastern England is an example of exponential erosion.
According to the given data:Using the formula of exponential growth:
y = a*b^t
a = reflects the initial bacterial population
t = represents the doubling.
the information given
a = 10
t = 1 hour
After 1 hour, the number of bacteria multiplies by 2, so:
y = 2 × 10 = 20
So that:
20 = 10 × b^1
Dividing through by 10 gives:
2 = b
solving this we get an equation:
y = 10(2)^t
Solving for 3,000,000 bacteria.
Substituting the value in the formula:
3000000 = 10(2)^t
3000000/10 = (2)^t
300000 = (2)^t
Applying the log of both sides, it gives:
Log 300000 = tlog2
5.477 = 0.301t
t = 5.477/0.301
t = 18.2 years
Time required to form 3,000,000 bacteria from 10 if it will double every hour = 18.2years.
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Describe in words where the square root of 60 minus 11 would be plotted on a number line.
Between −3 and −4, but closer to −3
Between −3 and −4, but closer to −4
Between 7 and 8, but closer to 8
Between 7 and 8, but closer to 7
The square root of 60 minus 11 would be plotted on a number line in between −3 and 8, but closer to 8.
What is number line?
A straight line with numbers placed at equal intervals or segments along its length. Number line is a straight line with a "zero" point in the middle, with positive and negative numbers listed on either side of zero and going on indefinitely.
Given:
The square root of 60 minus 11 would be plotted on a number line.
According to given question we have
We know that the square root of 60
=
[tex]\sqrt{60} \\\\=7.74[/tex]
So, By the statement square root of 60 minus 11 we have,
=7.74-11
=-3.25
So, in the number line the points are lies in between −3 and 8, but
closer to 8.
Therefore, the square root of 60 minus 11 would be plotted on a number line in between −3 and 8, but closer to 8.
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Christopher records his test scores in his World Cultures and Geography class for the past year. The information he records is below.
87, 90, 77, 68, 65, 62, 75, 83, 98, 100.
What is the mean of Christopher's test score throughout the year rounded to the nearest tenth?
A 73.2
B 78.3
C 80.5
D 89.4
The mean of Christopher's test score throughout the year is 80.5
How to calculate the mean ?Christopher scores during the World Cultures and Geography class for the past year are
87, 90, 77, 68, 65, 62, 75, 83, 98, 100
The mean can be calculated as follows
87+ 90+77+ 68+ 65+62+75+83+98+100/10
= 805/10
= 80.5
Hence the the mean of Christopher's test score throughout the year is 80.5
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A teacher divides 36 students into equal groups for a scavenger hunt. Each group should have atleast 4 students but no more than 8 students. What are the possible group sizes?
Answer:
Step-by-step explanation:
Group of six
What is (11-3) divided by 2+1 step by step
The result of the expression described by the word phrase as in the task content is; 8/3 = 2.667.
What is the result of the evaluation described by the word phrase?It follows from the task content that the expression described by the word phrase be evaluated.
First, (11-3) = 8 and
Also, (2+1) = 3.
Ultimately, when (11-3) is divided by (2+1); we have; 8/3 = 2.667.
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Answer the question in photo
[ Brainliest + easy points ]
Answer:
Step-by-step explanation:
acute
PLEASE HELP BRO ITS THE LAST QUESTION FROM MY HOMEWORK
Answer:7
Step-by-step explanation:
just gotta add it up all good
Answer:
7
Step-by-step explanation:
If the length of a rectangle is four less than twice its width and the perimeter is 220 inches, what is the width of the rectangle?
Group of answer choices
38 inches
72 inches
55 inches
56 inches
Given the length and perimeter, the width of the rectangle is 38 inches.
Hence, option A) 38inches is the correct answer.
What is the width of the rectangle?The perimeter of a rectangle is expressed mathematically as;
P = 2( l + w )
Given the data in the question;
Let "x" represent the width of the rectangle.
Width w = xLength l = 2x - 4Perimeter P = 220 inchesTo determine the width of the rectangle, plug the given values into the formula above and solve for x.
P = 2( l + w )
220 = 2( (2x - 4) + x )
220 = 2( 2x - 4 + x )
220 = 2( 3x - 4 )
Apply distributive property
220 = 2( 3x - 4 )
220 = 2(3x) + 2(-4)
220 = 6x - 8
Collect like terms
220 + 8 = 6x
228 = 6x
6x = 228
x = 228/6
x = 38
Now, since "x" represent the width of the rectangle,
The width of the rectangle w = x = 38 inches.
Given the length and perimeter, the width of the rectangle is 38 inches.
Hence, option A) 38inches is the correct answer.
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Refelection about what you've learn about factors and so be it 150 words
Answer:
the throwing back by a body or surface of light, heat, or sound without absorbing it.
"the reflection of light" The reflection factor of a body is the ratio of the light reflected by the body to the incident light.
Find 65% of 300 kilometers.
Answer: 195
Step-by-step explanation:
65%=65/100
300 * 65/100=
300 * 6.5/10=
300 * 13/20=
3900/20=
390/2=195
Pls help fast thank you
The time taken to hit the ground is 13 seconds.
How to calculate the value?It should be noted that the function that was given based on the information is:
h(t) = 16t²
where h = height
t = time
Therefore, when the height is 2704ft, the time will be:
h(t) = 16t²
2704 = 16t²
t² = (2704 / 16)
t² = 169
t = ✓169
t = 13
The time taken is 13 seconds.
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Rebecca collected data and told you that her sample mean was 56 and her sample median was 64. She then draws a histogram based on her data and asks you to guess the shape of it without looking. What would the most likely shape be for her histogram?.
Rebeeca’s histogram most likely shape will be Skewed to the left.
The histogram shows a symmetrical data distribution. A distribution is symmetrical if a vertical line can be drawn at any point in the histogram such that the shapes to the left and right of the vertical line are mirror copies of each other.
The mean and the median both reflect the skewing, but the mean reflects it more so. This is because the mean and median are measures of central tendency. Because in Rebecca’s data the mean is smaller compared to the median, it makes the histogram skewed to the left. If the median were to be smaller than the mean, it would be skewed to the right.
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Taylor's work:
12x+3=3(4x)
Taylor's Check:3(4x)=12x
It should be noted that since Taylor got 3(4x) and the correct expression is 3(4x + 1), he is incorrect.
How to calculate the value?It should be noted that the expression given is illustrated as 12x+3=3(4x).
We need to solve this:
12x + 3
It should be noted that the common factor is 4.
Therefore, 12x + 3 = 3(4x + 1)
Therefore, since Taylor got 3(4x). He is incorrect.
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Taylor's work:
12x+3=3(4x)
Taylor's Check:3(4x)=12x
Is this correct?
Help please just look at the pic ig
Answer:
0.00037
Step-by-step explanation:
Write an equation of a line in slope-intercept form with the given slope and y-intercept. slope: -6, y-intercept: -2
Answer:
Step-by-step explanation:
Hope this helps :)
brainliest +40 points!! help
What values of x and y satisfy the system of equations {x=−2y+13x+8y=11?
Enter your answer as an ordered pair, like this: (42, 53)
If your answer includes one or more fractions, use the / symbol to separate numerators and denominators. For example, if your answer is (4253,6475), enter it like this: (42/53, 64/75)
If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf."
Answer: Y= -2/-18 or Y= 0.1111X=-2(-0.1111) +1or X=0.77778
Step-by-step explanation:
What is the simplified form of each expression?
c. 3¹/² . 12¹/²
Fractions are in their simplest form when they have no common divisors other than 1 at their top and bottom. That is, the top and bottom cannot be divided further and remain integers.
You may also hear the simplest form called "lowest term".
In preferred, an expression is in only form while it's far easiest to use not unusual methods to help you simplify:
Combine Like termsFactoringincreasing (the opposite of factoring)clean out fractions by multiplyingrecognizing a pattern you have seen earlier than, just like the difference of squares3^(1/2) 12^(1/2)
Simplify the following:
sqrt(3) * sqrt(12)
sqrt(12) = sqrt(2^2×3) = 2 sqrt(3):
sqrt(3)×2 sqrt(3)
sqrt(3)×2 sqrt(3) = 3×2:
3×2
3×2 = 6:
Answer:
6
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Evaluate 1.2(3x+2y) if x=4 and y=-4
Answer:
24
Step-by-step explanation:
1.2(3x+2y)
add in our X and Y number
1.2(3(4) + 2(4))
Do the multiplication
1.2(12 + 8)
Distribute 1.2
14.4 + 9.6
add them together and you get
24
can y’all please help me figure out what this problem is g=6x, for x
Answer:
x=g/6
Step-by-step explanation:
because if u do the inverse of multiplication which is division on both sides it gives u that and solves for x
1. A car rental company charges a processing fee of $20 to rent a minivan and $34 per day the minivan is rented. this situation can be represented by y=34 x+20, where x is the number of days and y is the total cost to rent the minivan. write this relationship in function notation, as a function c(d), where c(d) represents the cost of renting a minivan for d days.
2. Select the ordered pair that would represent this function C, given d=10.
A. (360,10)
B. (c(10)10)
C. (20,C(34))
D. (10,c(10))
Answer:
Best answer choice seems to be C.
Step-by-step explanation:
Choose the phrase that best completes the sentence.
When you take the square root of 11, the result is neither a terminating nor a repeating decimal. Therefore, it is-
1. an integer
2. irrational number
3. rational number
4. an odd number
When you take the square root of 11, the result is neither a terminating nor a repeating decimal. Therefore, it is: 2. irrational number.
The types of numbers.In Mathematics, there are six (6) common types of numbers and these include the following:
Natural (counting) numbersWhole numbersRational numbersIrrational numbersReal numbersIntegersWhat is an irrational number?An irrational number can be defined a type of number which comprises non-terminating or non-repeating decimals such as the square root of 11.
In conclusion, when you take the square root of 11, the result is neither a terminating nor a repeating decimal. Therefore, it is an irrational number.
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Sophia is buying pretzel sticks by the pound. For every 5 pounds of pretzel sticks she buys, she pays $11. What is the cost, per pound, for the pretzel sticks?
Sophiya has to pay 2.2 dollars for per pound of pretzel sticks.
What is unitary method?Unitary method is a mathematical technique for first obtaining the value of a single unit then deriving the given units by multiplying it with the single unit.
The cost per pound of pretzel sticks can be obtained by the unitary method.
Given that 5 pounds of pretzels costs 11 dollars,
Now to obtain the cost of per pound of pretzel sticks we'll put the total cost at the numerator and the total weight of the pretzel sticks on the denominator.
∴ Per pound of pretzel costs (11/5) dollars which is,
= 2.2 dollars per pound of pretzel sticks.
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simplify 8/18 = ?/? please helpp
Answer:4/9
Step-by-step explanation:
Find the GCD
8/2
18/2
Answer:
4/9
Step-by-step explanation:
Let's simplify the value,
→ 8/18
→ (8 ÷ 2)/(18 ÷ 2)
→ 4/9
Thus, the value is 4/9.
Arrange the steps to show how to solve for x.
Arranged steps after solving equation [tex]\frac{-8}{3} x+4(x+\frac{9}{4} )= \frac{-2}{3} (x+\frac{12}{8} )+3[/tex] are
[tex]\frac{-8}{3} x+4x+9= \frac{-2}{3} x-1 +3[/tex][tex]\frac{-8}{3} x+4x= \frac{-2}{3} x-7[/tex][tex]\frac{-8}{3} x+4x+\frac{2}{3} x =-7[/tex][tex]2x=-7[/tex][tex]x=\frac{-7}{2}[/tex]What is an equation and how to solve it?An equation is an formula which equates two mathematical expressions.
We can solve equations by adding or subtracting same number from both sides or by diving both sides by same number (positive or negative)
[tex]\frac{-8}{3} x+4(x+\frac{9}{4} )= \frac{-2}{3} (x+\frac{12}{8} )+3\\[/tex]
After Opening brackets, we get:
[tex]\frac{-8}{3} x+4x+4(\frac{9}{4} )= \frac{-2}{3} x-\frac{2}{3} *\frac{12}{8} +3[/tex]
[tex]\frac{-8}{3} x+4x+9= \frac{-2}{3} x-1 +3[/tex]
Subtracting 9 from both sides, we get:
[tex]\frac{-8}{3} x+4x+9-9= \frac{-2}{3} x-1 +3-9\\\frac{-8}{3} x+4x= \frac{-2}{3} x-7[/tex]
Moving all terms of x on to one side:
[tex]\frac{-8}{3} x+4x+\frac{2}{3} x =-7\\\\\\frac{-8x+12x+2x}{y} =-7\\\\\frac{6x}{3}= -7\\ 2x=-7[/tex]
Dividing both sides by 2 , we get
[tex]x=\frac{-7}{2}[/tex]
On solving the given equation we got x =-7/2
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