Six times the difference of a number and two us forty - two less than the number is 6.
What are the arithmetic calculations?
Arithmetic is the branch of mathematics that deals with basic operations such as addition, subtraction, multiplication, and division, and their properties and applications. Arithmetic calculations are mathematical operations that involve one or more numbers and result in a numerical answer. These operations can be performed using mental arithmetic, pencil, and paper, or with the help of a calculator.
Let the number be x. We can write the given expression as:
6(x - 2) = x - 42
Expanding the left side:
6x - 12 = x - 42
Solving for x:
5x = 30
x = 6
Therefore, the number is 6.
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The nearest whole number of 7 and 3/8
Answer:
7
Step-by-step explanation:
A tugboat traveled -1.5 miles in 0.3 hours what was its velocity
Velocity of tugboat is -5 miles/hour .
What is velocity?The velocity of an object is the change in position (displacement) over a time interval. Velocity includes both speed and direction, thus velocity can be either positive or negative while speed can only be positive.
Given,
Displacement by tugboat = - 1.5 miles
Time taken in travelling = 0.3 hours
Velocity = Displacement/ Time
= - 1.5 / 0.3
= - 5 miles/hours
Hence, -5 miles/hour is Velocity of tugboat.
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(x⁵ - 7x⁴ + 3x² - 8) : (x² - 3x + 1)
Answer:
x³ - 4x² + 3x - 8. is the answer.
kirans mother gets a restuarant bill for 25$ she has a coupon for 15% off what is the amount after the discount is applied
The amount after the discount is applied would be $21.25.
What is the percentage?
The percentage is defined as a ratio expressed as a fraction of 100.
As per the question, the given data as:
Bill amount = 25$
Coupon for 15% off
The amount after the discount can be calculated as:
⇒ 25$ - 15% of 25$
15% is expressed as 15/100 in fractional form
⇒ 25 - (15/100)(25)
15/100 is expressed as 0.15 in decimal form
⇒ 25 - (0.15)(25)
⇒ 25 - 3.75
⇒ 21.25
Thus, the final amount would be $21.25.
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solve the following inequalities sketch a number line - (x + 5 +) greater than 2 (1 - x)
When graphed, a linear equation always produces a straight line since each element in the equation has an exponent of 1.
What are examples of linear equations?Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).
What three types of linear equations are there?The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
Given, 3x−2<2x+1
⇒3x−2x<1+2
⇒x<3 or x∈(−∞,3)
At x=3, the lines y=3x-2 and y=2x+1 will both intersect.
The dark line unmistakably depicts the 3x-2<2x+1 solution.
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Someone help quick please
Y=5+3x for x
For the equation Y=5+3x the solution for x is (y-5)/3=x.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is Y=5+3x
y equal to five plus three times of x
In the given equation x and y are the variables.
We have to solve for variable x.
Subtract 5 from both the sides
y-5=3x
Divide both sides by 3
(y-5)/3=x
Hence, for the equation Y=5+3x the solution for x is (y-5)/3=x.
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There are 45
students in the University Travel Club. The following information and Venn diagram show how many students traveled to Germany, France, and Spain. How many students have been to Germany or Spain but not France?
20
members have visited Germany
20
have been to Spain
19
have visited France
10
have been to Germany and France
4
have only been to Germany
6
have only been to France
3
have been to only Spain and France
3
have been to all three countries
Some of the members have not been to any of the three
The number of students that have been to Germany or Spain but not France is given as follows:
18.
How to obtain the amounts?The amounts are obtained considering the Venn diagram in the problem.
For the 20 students that went to Spain, we have that:
x went only to Spain.3 have gone to Spain and France.3 have gone to Spain, Germany and France.6 have gone to Spain and Germany.Hence the value of x is obtained as follows:
x + 3 + 3 + 6 = 20
x + 12 = 20
x = 8.
The number of people who have gone to Spain or Germany but not France is given as follows:
6 + 4 + 10 = 18.
(or means at least one of Spain or Germany).
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I’ll give brainiest
Please help ASAP
Find the area of the rectangle
What is the area of the rectangle?
Answer:
9x² - 64 square yards
Step-by-step explanation:
Area of a rectangle is L x W where
L = length
W = width
Letting
L = 3x + 8
W = 3x - 8
L x W = (3x + 8)(3x-8)
Using the identity (z + b)(a - b) = a² - b²
with a = 3x, b = 8
(3x+8)(3x-8) = (3x)² - (8)²
= 9x² - 64 square yards
if you invest $550 at a 4% interest rate will be the interest
Answer:
22
Step-by-step explanation:
550x4%=550x0.04=22
Answer:
$22
Step-by-step explanation:
550 x 4% = 550 x 0.04 = $22
50 POINTS IF CORRECT
Step-by-step explanation:
I just answered this.
the first group is consistent independent, because both equations are lines with different slope. so, they have 1 intersection, which is the solution.
the second group is consistent dependent, because both equations describe the same line.
multiply the second equation by -2, or divide the first equation by -2, and you see they are identical. multiplying an equation by a factor on both sides does not change the equation or function.
so, as both lines are identical, every point on the line is an intersection and solution. therefore, there are infinitely many solutions.
the third group is inconsistent.
they represent 2 lines with identical slope but different y-interceptions. so, they are parallel and have no intersection or solution at all.
just think : there is no pair of numbers x,y, for which their sum can have 2 different results.
Adam sells pencils for $2.50 per dozen. The expression [Drop Down 1] represents the [Drop Down 2], where
a represents the number of dozen pencils sold.
The total revenue can be calculated as "2.50a" dollars.
What is the dozen?
A dozen is a grouping of twelve objects, shapes, or numbers. It is abbreviated as doz or dz. Dozen is one of the most primitive customary units of numbers. The number system with the base number 12 is called duodecimal or dozenal.
In this scenario, Adam is selling pencils in dozens and the price he charges for each dozen is $2.50.
To calculate the total revenue, we need to multiply the number of dozens sold (represented by "a") with the price per dozen ($2.50).
The expression "2.50a" represents this calculation, where "a" represents the number of dozens sold and "2.50" represents the price per dozen.
Hence, the total revenue can be calculated as "2.50a" dollars.
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1 whole number 1/16 to decimal 50 points pls full solution
Answer:
Below
Step-by-step explanation:
1/16 is 1 ÷ 16 use calculator to find = .0625
Answer:
1.06
Step-by-step explanation:
Step 1: divide numerator (1) by the denominator (16):
1 ÷ 16 = 0.0625
Step 2: add this value to the integer part:
1 + 0.0625 = 1.0625. So,
1 1/16 = 1.0625
If each of A,B, C stands for a nonzero digit in the following addition, then find the three-digit number ABC.
The three-digit numbers are:
A = 3
B = -1/3
C = -4/3
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
A C B
B A C
B C A
C A B
+ C B A
1 2 2 3
Now,
A = 3 _____(1)
B + C + A +B + B = 2
3B + C + A = 2
3B + C + 3 = 2
3B + C = -1
C + A + C + A + C = 2
3C + 2A = 2
Substituing A = 3.
3C + 6 = 2
3C = 2 - 6
3C = -4
C = -4/3 _____(2)
A + B + B + C = 1
Substituting A and C.
3 + 2B - 4/3 = 1
2B = 1 - 3 + 4/3
2B = (3 - 9 + 4)/3
2B = -2/3
B = -2/6
B = -1/3 ______(c)
Thus,
A = 3
B = -1/3
C = -4/3
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It would take Mary 3 hours to paint her bedroom by herself. Her older brother Brian could paint the room in 8 hours. Working together, how long would it take for Mary and Brian to paint the room?
Answer:
3hrs to paint by Mary
8hr for Brian to paint
so together, Brian and Mary mean you add the two
together 3hrs
and 8hrs
equals 11 hrs
3+8=11
PLEASE HELP!! ILL GIVE BRAINLIEST!!!
The area enclosed by the track is 7,530.64 m².
What are the circumference and diameter of a circle?The circumference of a circle is the distance around the circle which is 2πr.
The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.
We know, The area of a circle is πr² and the area of a rectangle is (length×width).
By observing the diagram the total area enclosed by the track is the
sum of the area of a rectangle having a length of 104m and a complete circle having a diameter(2r) of 52 m and the diameter is equal to the width of the rectangle.
Therefore, The area of the track is,
= (104×52) + π(26)².
= 5408 + 2,122.64 m².
= 7,530.64 m².
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Multiply. Write your answer as a fraction or as a whole or mixed number.
3 × 1/2 =
After performing the operation on the given number we get the fraction 3/2
What is a mixed fraction?A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, and 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
Given here: multiplication of a whole number 3 and the fraction 1/2
When you multiply two fractions together, you're taking a part of a part. When you multiply a fraction by a whole number, you're taking multiple copies of that fraction. In both cases, the result is a new fraction that represents a different part of a whole.
Thus we have the following after simplifying
3×1/2=3/2
Hence, The required fraction is 3/2
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Part C Aiden and Natalie each built a catapult for their school’s science fair. They constructed their catapults using an elastic band system, where the arm of the catapult is pulled back and then released to launch a tennis ball into the air. The elastic band provides the energy to propel the ball.
There is not enough information to know whose Tennis ball would go further. Option D.
Is the Catapult a projectile?
We know that the projectile is an object that can be able to move along a parabolic path. In this case, we have a catapult which the energy that launces forth the projectile is derived from the energy that have been stored in the spring of the catapult.
A catapult is a type of projectile weapon that uses mechanical energy to launch a projectile over a long distance as we can see in this problem.
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It was an extremely cold day on the mountain. The temperature dropped 22 degrees to -13 Degrees F. What was the temperature before the drop?
If the temperature dropped 22 degrees to -13 Degrees F, the temperature before the drop was 9 Degrees F.
What is temperature drop?Temperature drop refers to a decrease in the temperature of a system or environment.
This decrease can be measured in units of temperature such as degrees Celsius or Fahrenheit, and it can occur due to a variety of reasons such as changes in atmospheric conditions, the loss of heat from a body or system, or other physical processes.
The initial temperature is calculated by
initial temperature = final temperature + temperature drop
initial temperature = -13 + 22
initial temperature = 9
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to What is the Nalue of angle marked X in the figure below X 2 126 O 115
Quadrilaterals are objects with four sides, such as parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
What is meant by quadrilateral?A closed quadrilateral is a form of polygon with four sides, four vertices, and four angles. Four non-collinear points are joined to create it. Quadrilaterals' internal angles add up to a constant 360 degrees. A quadrilateral is a polygon with four sides, such as a square, rectangle, or rhombus. You are most likely currently staring at a computer screen which resembles a quadrilateral. Geometry lessons cover the quadrilateral as a geometrical shape.Two-dimensional shape with sides is known as a quadrilateral. Having four straight sides, a quadrilateral is a two-dimensional shape. Four-sided shapes including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses are examples of quadrilaterals.Sum of all interior angles of quadrilateral [tex]$=360^{\circ}$[/tex]
[tex]& \therefore 50+130+120+\mathrm{x}=300 \\[/tex]
[tex]& \mathrm{x}=60^0[/tex]
(b) [tex]& 90+a=180 \\[/tex]
a = 90
Sum of all angles of quad = 360
[tex]& x+70+60+90=360 \\[/tex]
[tex]& x=140^{\circ}[/tex]
(c) [tex]70+\mathrm{a}=180$ (Linear pair)[/tex]
a = 110
[tex]60+\mathrm{b}=180$ (Linear pair)[/tex]
[tex]$\mathrm{b}=120$[/tex]
Sum of measures of all angles of pentagon [tex]$=540^{\circ}$[/tex]
[tex]& \therefore 120+110+\mathrm{x}+\mathrm{x}+30=540 \\[/tex]
[tex]& 2 \mathrm{x}=280 \\[/tex]
[tex]& \mathrm{x}=140^{\circ}[/tex]
(d) Sum of all angles of pentagon 540
Given all angles are equal
[tex]& \therefore 5 x=540 \\[/tex]
[tex]& x=108^0[/tex]
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Good morning,
My name is Mr. Shine (I was given that name because I have the most sparkly diamonds in the
midwest). I am forwarding you the bill for your client Mr. Spendalot who stopped by my store Ice
Box last evening. I have exactly $1,000,000 in inventory of the best diamond rings, necklaces,
cuban chains, grilles, and watches. Now, I must make a profit on this inventory, so I markup all
inventory by 150% before selling it to my loyal customers.
Your client bought a whopping 31% of my entire inventory. He said my special was just too good
to pass up and he just had to buy more more more. What’s that special you ask?
Discounted Special:
Spend 100k+ and get 10% off
Spend 250k+ and get 20% off
Spend 500k+ and get 30% off
Spend 750k+ and get 40% off
Spend 1 million+ and get 50% off
After giving him this discount, I of course had to charge him an 8.5% sales tax on his purchase.
Yes I know, we all hate taxes, but that’s just the cost of doing business. Now your client Mr.
Spendalot is a very kind man and he agreed to give me and my staff a tip of 15%, how
generous of him! He told me to send you the details and you, his accountant, will calculate the
total. If you get this total right, he said he’s giving you the brand new Lamborghini he purchased
at the dealership next door to my store. Must be nice, hopefully you are good at your job!
Good Luck,
Mr. Shine
Answer:
The task is to calculate the total amount spent by Mr. Spendalot. To do this, you need to calculate the amount of inventory purchased, apply the discount, calculate the sales tax, and add the tip. Here's one way to do it:
Calculate the amount of inventory purchased: 31% of $1,000,000 is 31/100 * $1,000,000 = $310,000
Determine the discount: Based on the purchase amount of $310,000, Mr. Spendalot qualifies for a discount of 10%. So, the discount is $310,000 * 10% = $31,000.
Calculate the sales tax: 8.5% of the purchase amount after discount is 8.5/100 * ($310,000 - $31,000) = $2,067.50
Add the tip: 15% of the purchase amount after discount and sales tax is 15/100 * ($310,000 - $31,000 + $2,067.50) = $52,101.13
Calculate the total: The total amount spent by Mr. Spendalot is ($310,000 - $31,000 + $2,067.50 + $52,101.13) = $393,168.63.
So, the total amount spent by Mr. Spendalot is $393,168.63.
Step-by-step explanation:
Determine the amount of purchase before discount: Mr. Spendalot bought 31% of Mr. Shine's inventory, which is $1,000,000. Therefore, his purchase before discount is 31% of $1,000,000, or $310,000.
Calculate the discount: Based on the information in the discount table, Mr. Spendalot's purchase qualifies for a 40% discount. Therefore, the discount amount is $310,000 * 40%, or $124,000.
Determine the amount of purchase after discount: After getting the 40% discount, Mr. Spendalot's purchase is $310,000 - $124,000, or $186,000.
Calculate the sales tax: Mr. Shine charged an 8.5% sales tax on Mr. Spendalot's purchase after discount. Therefore, the sales tax amount is $186,000 * 8.5%, or $15,791.
Determine the tip: Mr. Spendalot gave Mr. Shine and his staff a 15% tip on his purchase after discount and sales tax. Therefore, the tip amount is $186,000 + $15,791 * 15%, or $31,328.
Calculate the total cost: Adding up the purchase after discount, sales tax, and tip, we get the total cost of $186,000 + $15,791 + $31,328, or $233,119.
Conclusion: Mr. Spendalot's total purchase cost is $233,119.
The task requires you to calculate the total amount spent by Mr. Spendalot at Mr. Shine's store Ice Box. Mr. Shine has an inventory worth $1,000,000 which he marks up by 150%. Mr. Spendalot bought 31% of this inventory, and was given a discount based on the amount he spent:
Spend 100k+ and get 10% off
Spend 250k+ and get 20% off
Spend 500k+ and get 30% off
Spend 750k+ and get 40% off
Spend 1 million+ and get 50% off
After the discount, Mr. Spendalot was charged 8.5% sales tax. He also left a 15% tip for Mr. Shine and his staff. Your goal is to calculate the total amount spent by Mr. Spendalot.
If the terminal side of angle θ goes through the point (8/17,−15/17) on the unit circle, then what is cos(θ)?
The cosine of the angle θ is 8/17 whose terminal side passes through the given point
What are trigonometric functions?In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent
Given here: The terminal side goes through the point (8/17, -15/17)
Thus we have cosθ =8/17 and sin θ =-15/17
now tan θ =sinθ /cosθ
tanθ = -15/8
θ = -61.9275
Hence, cosθ =8/17
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worth 60 points!! question 2)
Answer:
y = 4
Step-by-step explanation:
the equation of the midline is the average of the sum of the maximum and minimum values.
maximum value = 6
minimum value = 2
then
y = (6 + 2) ÷ 2 = 8 ÷ 2 = 4
y = 4 ← equation of midline
Help I don’t get this question
well, we can simply find how much for each tulip in each store.
store left has them for £9.8 for 4, that means 9.8 / 4 = 2.45, so £2.45 for each tulip.
store right had them for £4.2 each, but they went down by 1/3, so hmm a whole is 3/3 so if we take away 1/3 from 3/3, 3/3 - 1/3 = 2/3, so the new discounted price is really 2/3 of £4.2, that's (2/3) * 4.2 = 2.8, so £2.8 each.
so store left has them cheaper, doesn't matter at a dozen or less or more.
how much is it at store left for 12? 12 * 2.45 = 29.4, or £29.4.
1. Find Sn for the arithmetic series where a1= 3 , an= 42 , n= 14
2. Find sn for the arithmetic series where a1= −20 , n= 25 , an= 148
3. Find sn for the arithmetic series where a1=5 , d=1/2 , n=13
The value of the sum of the series is are 315, 1600 and 104
How to determine the sum of the seriesIn an arithmetic series, the sum of the first "n" terms (Sn) is given by the formula:
Sn = n/2 * (a1 + an)
Where "a1" is the first term and "an" is the nth term.
For the first series, we have
In this series, a1= 3 , an= 42 , n= 14
Plugging these values into the formula, we get:
Sn = 14/2 * (3 + 42)
Sn = 315
For the second series, we have
In this series, a1= −20 , n= 25 , an= 148
Plugging these values into the formula, we get:
Sn = 25/2 * (-20 + 148)
Sn = 1600
For the third series, we have
In this series, a1=5 , d=1/2 , n=13
So, we have
an = a + (n - 1)d = 5 + 12 * 1/2 = 11
Plugging these values into the formula, we get:
Sn = 13/2 * (5 + 11)
Sn = 104
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Evaluate the function find h (6) if h (x) = 2x + 1
Answer:
h(6) = 13
Step-by-step explanation:
Functions! One of my favorites to answer :)
h(x) = 2x + 1
So, now we plug in h(6). Remember that when we replace the x with the number, we replace it in the right side of the equation as well:
h(6) = 2(6) + 1
Now we multiply 2 * 6:
h(6) = 12 + 1
Now 12 + 1:
h(6) = 13, final answer.
Hope this helps :D
Answer: 13
Step-by-step explanation:
h(x) = 2(x) + 1
h(6) = 2(6) + 1 = 12 + 1 = 13
Is the relation shown a function explain
Input 1 3 4 3
Output 1 9 16 27
Something can be described as a function if there is only 1 of each number in the input or x.
For example: (9,6) and (9,3) would not be a function because there are two 9’s as the input.
So, for this problem there are two 3’s meaning this is NOT function because there are two outputs for the same number.
Your answer is going to be D.
When throwing two fair six sided dice, what is the probability that the sum of the values on the two dice is 11?
Answer:
2/36
Step-by-step explanation:
there are a total of 36 possible rolls
and the only to ways to get an 11 on two fair six-sided dice is when it is (5,6) or (6,5)
Parker draws a circle with an area of
40 squared
. He challenges Lauren to draw a circle that has a radius
4 times bigger than the radius of his circle.
what is the estamaited area of laurens circle
The estimated area of Laurens's circle is 642 squared.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
The area of a circle is πr².
We have,
Parker:
Area = 40 squared
This means,
πr² = 40
r² = 40/3.14
r² = 12.74
r = √12.74
r = 3.6
Laurens:
r = 4 x 3.6
r = 14.3
Area = πr²
Area = 3.14 x 14.3 x 14.3
Area = 642
Thus,
Laurens's circle area is 642 squared.
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What is the surface area of the right rectangular prism? 125 m 2 75 m 2 250 m 2 200 m 2
The surface area of a right rectangular prism is 250 m².
Option C is the correct answer.
What is a prism?A prism is a three-dimensional object.
There are triangular prism and rectangular prism.
We have,
From the figure,
Width = w = 5 m
Height = h = 5 m
Length = l = 10 m
The surface area of a right rectangular prism.
= 2 (lw + lh + wh)
= 2 (10 x 5 + 10 x 5 + 5 x 5)
= 2 (50 + 50 + 25)
= 2 (125)
= 2 x 125
= 250 m²
Thus,
250 m² is the surface area of a right rectangular prism.
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Answer:
250m 2
I hope this helps <3
ASSIGNMENT
1. Suppose the demand function for a product is given
by: Qa = 500 - 5P, compute the:
(a) quantity demanded at the unit price of Ghé 10
(b) price to sell 200 units
(c) price for zero demand
(d) quantity demanded at zero price
(e) the own-price elasticity of demand at the price for
which 200 units are sold.
The value of quantity demanded at unit price Gh¢10 is 450 units. b. The price to sell 200 units is Gh¢60. c. The price for 0 demand is Gh¢100. d. The quantity demanded at zero price is 500 units.
What is demand function?The link between the quantity demanded for a commodity (the dependent variable) and its price is represented by the demand function (independent variable).
a) At the price of Gh¢10 , then
Qd= 500 - 5P
Qd= 500 -5(10)
Qd= 500-50 = 450 units
The value of quantity demanded at unit price Gh¢10 is 450 units.
b) If there are 200 units,then
Qd= 500- 5P
200 = 500-5P
5P = 500-200
P= 300/5
P= Gh¢60
The price to sell 200 units is Gh¢60
c) if demand is zero, it mens Qd= 0
Qd= 500- 5P
0= 500-5P
5P= 500
P= Gh¢100
The price for 0 demand is Gh¢100.
d) If P= 0, then
Qd= 500-5P
Qd= 500-5(0)
Qd= 500 units
The quantity demanded at zero price is 500 units.
Hence, the value of quantity demanded at unit price Gh¢10 is 450 units. b. The price to sell 200 units is Gh¢60. c. The price for 0 demand is Gh¢100. d. The quantity demanded at zero price is 500 units.
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