Value of n is 4
The area of a rectangle is equal to the product of its length and width.
we know ,
the area of rectangle, multiply the length, , and the width, ,
and set the product equal to the area.
area of rectangle = length * width
54 = 3(n - 1) * (n + 2)
54 =( 3n - 3) * (n + 2)
multiply ( 3n - 3) with (n + 2)
we get,
54 = [tex]3n^{2} + 6n - 3n -6[/tex]
54 = [tex]3n^{2} + 3n -6[/tex]
54 = 3([tex]n^{2} + n -2[/tex])
[tex]\frac{54}{3}[/tex] = ([tex]n^{2} + n -2[/tex])
18 = ([tex]n^{2} + n - 2[/tex])
[tex]n^{2} + n - 2[/tex] - 18 = 0
[tex]n^{2} + n - 20[/tex] = 0
solve them
[tex]n^{2} + 5n + 4n -20[/tex] = 0
n (n + 5) - 4 (n + 5) = 0
(n + 5)(n -4)
then we get,
n = -5 , n = 4
value of n should not be negative . so value of n is 4
Area of rectangle is the region occupied by a rectangle within its four sides or boundaries.
The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides. Hence, we can say, the region enclosed by the perimeter of the rectangle is its area
Area of rectangle = Length x Breadth
A = lb
how to Factoring Quadratic Equation
Step 1: Consider the quadratic equation ax2 + b x + c = 0
Step 2: Now, find two numbers such that their product is equal to ac and sum equals to b.
(number 1)(number 2) = ac
(number 1) + (number 2) = b
Step 3: Substitute these two numbers in the formula given below:
(1/a) [a x + (number 1)] [a x + (number 2)] = 0
Step 4: Finally simplify the above equation.
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Can someone help with this question?✨
Answer:
Step-by-step explanation:
well what even is the question all i see is graphs
A cube with sides 11 inches long is covered with a coat of fiberglass 0.1 inch thick. Use differentials to estimate the volume of the fiberglass shell.
The volume of the fiberglass shell is approximately __ in^3.
The volume of the fiberglass shell is nearly = 508.2 in³
What exactly is volume?Volume is just a three-dimensional quantity used to determine a solid shape's capacity. It indicates that the volume of a closed figure decides how much of three-dimensional space it can occupy.
What is the definition of volume and an example?The capa.city of an object is measured by its volume. A cup's volume is 100 ml if it can carry 100 ml of water higher than or equal to the brim. A 3-dimensional object's volume can alternatively be described as the amount much space it takes up.
According to the given data:Cube side are 11 inches.
cube is covered with a coat of fiber glass 0.1 inch
need to find the volume of fiberglass.
area of cube = 6(11)²
= 6(121)
= 726 inch².
thickness of fiberglass = 0.7 inch.
dv ≅ ads
= 726(0.7)
= 508.2 in³
The volume of the fiberglass shell is nearly = 508.2 in³.
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what's question 9? NEED ANSWER
Answer
I disagree
she said that the square root of 100 and of 121 is 4 and 5
the square root of 100 is 10 and the square root of 121 is 11.
can someone help me? please
Answer:
Step-by-step explanation:
Answer to number 1 is a slope of -3 and the y=-3x-26 For number 2 the slope is 5 and y=5x+5 and for number 3 the slope is 2/3 and b is y=2/3x-20/3 for number 4 its 4 in the x section and 5 for the y section number 5 is --5 and for number 6 its -12. I found the slopes by using this formula y2-y1/x2-x1 and for the b I used y=mx+b and used one of the points to figure it out! I hope this helped out :3
Marla writes this problem
628 divided by 1300
Which expression represents Marla’s problem
Answer:
628/1300
Step-by-step explanation:
In Exercises 1-3, use this fraction bar.
1 Shade two of the equal parts. What fraction does
the shaded portion model?
2 Split each equal part (each unit fraction) into two equal;
parts. What fraction does the shaded portion model now?
Step-by-step explanation:
(1.64 x 104) + (7.28 x 10³) =
Write your final answer in scientific notation
7450.56 is the correct answer
Find the area of the shaded region
Given the central angle and radius of the sector, the area of the shaded region is 28.26cm².
What is the area of the shaded region?A sector is simply a part of the area of a circle bounded by the central angle and its intercepted arc. The area of a sector is expressed as;
A = (θ/360) × πr²
Given the data in the diagram;
Central angle θ = 90°Radius r = 6cmConstant pi π = 3.14Area of the sector = ?To determine the area of the shaded region, plug the given values into the formula above and solve for A.
A = (θ/360) × πr²
A = (90/360) × 3.14 × (6cm)²
A = (1/4) × 3.14 × 36cm²
A = 3.14 × 9cm²
A = 28.26cm²
Given the central angle and radius of the sector, the area of the shaded region is 28.26cm².
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pls help i will give brainliest if correct and u explain how to calculate it
In a picture we have a triangle with 3 sides. Sides are a,8 and 2. The side a=2[tex]\sqrt{15}[/tex].
Given that,
In a picture we have a triangle with 3 sides.
sides are a,8 and 2.
by using Pythagorean theorem
The Pythagorean Theorem, generally referred to as Pythagoras' Theorem, is a basic relationship between a right triangle's three sides. The Pythagorean theorem states that, given a right triangle, which is a triangle in which one of the angles is 90 degrees, the hypotenuse, the right triangle's longest side, forms a square whose area is equal to the sum of the areas of its other two sides.
In other words, given that the triangle's longest side, c, is also its hypotenuse and that sides a and b are its other two sides:
a² + b² = c²
a²+(2)²=8²
a²+4=64
a²=64-4
a²=60
Take root on both sides
[tex]\sqrt{a^{2} } =\sqrt{60}[/tex]
a=2[tex]\sqrt{15}[/tex]
Therefore, the side a=2[tex]\sqrt{15}[/tex].
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you originally had a six year loan. how long would it take you to pay off the remaining $12,825 if you paid $225 monthly
Answer:
57 Months
Step-by-step explanation:
Should take 57 months. Simple division, just divide 12,825 and 225 and you end up with 57 months. 4 years and 9 months simplified. Hope this helps.
HELP PLS JUST LOOK AT THE PICTURE
On 50th day she needs to buy new bags of rice.
What is sequence?A sequence is defined as an arrangement of numbers in a particular order.
Sequence: 0.4, 0.8, 1.2, 1.6,......20
a=0.4, d=0.4, a_n= 20
Now,
we have to find in how many days 20 pounds rice will ends
So,
a_n= a + (n-1 )d
20 = 0.4 + (n-1) * 0.4
19.6 = (n-1)0.4
19.6/0.4= n-1
49 = n-1
n= 50
Hence, on 50th day she needs to buy new bags of rice.
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The batteries from a certain manufacturer have a mean lifetime of 820 hours, with a standard deviation of 70 hours. Assuming that the lifetimes are normally distributed, complete the following statements?
(a) Approximately ? of the batteries have lifetimes between 680 hours and 960 hours.
(b) Approximately ? of the batteries have lifetimes between 680hours and 960hours.
Answer:
it equals 57,400
Step-by-step explanation:
your multiplying 820 into 70 hours
2. Company A charges $4.50 per month plus $0.25 per text. Company B charges $8.00 plus
$0.20 per text. How many texts would make the two plans cost the same amount?
what is the sum of product of the following
-5 +8
-2 +3
-6 +4
1 +(-7)
4 + (-9)
11 + (-8)
-8 + (-5)
-2+(3)
-6+(4)
-1+(-7)
-4+(-9)
7×(-7)
8×(-4)
-9×3
-8×(-8)
-6×(-6)
-9×(-9)
-7×(-3)
-6×(-8)
Answer:
(1). 3 (2).1 (3) -2 (4). -6 (5). -5 (6). 3 (7). -13 (8). 1 (9). -2 (10). -8 (11). -13 (12) -49 (13). -32 (14) -27 (15). 64 (16). 36 (17). 81 (18). 21 (19). 48
Step-by-step explanation:
i do not know if you still need these answers but here they are
WHAT IS THE DOMAIN AND RANGE OF THE GRAPH SHOWN BELOW (please answer, be frl)
Write your answers as inequalities, using or as appropriate.
Thus the domain is 0 ≤ Domain ≤ 28 and the range is 0 ≤ range ≤ 150.
What is a function?A function defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
The independent variable = domain
The dependent variable = Range
We are given a graph where the x-axis contains the radius value and the y-axis contains the circumference value.
We can write the function as:
f(x) where x can be 4, 8, 12, 16, 20, 24, 28, 32, 36
f(0) = 0
f(4) = 22.5
f(8) = 52.5
f(12) = 75
f(16) = 105
f(20) = 127.5
f(24) = 150
The domain is between 0 to 150 and the range is between 0 and 28.
Thus the domain is 0 ≤ Domain ≤ 28 and the range is 0 ≤ range ≤ 150.
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Mika worked 10 hours more than Todd last month. If Mika worked 5 hours for every 3 hours that Todd
worked, how many hours did they each work?
(round answers to 1 decimal place)
Mika worked
Todd worked
hours
hours
Answer:
Mika worked for 25 hours.
Todd worked for 15 hours.
27.08, 27.88, 27.8, 26.78 least to greatest
Answer: 26.78 27.08 27.8 27.88
Step-by-step explanation:
1: Using a Place Value Chart, compare the whole numbers in your list of decimals.
2: Set up a table for the remaining numbers.
3: Transfer the decimals from your math problem into the table.
4: Compare the digits in the tenths column of the table
5: Compare the hundredths column (2 to the right of the decimal point).
6: Examine the digits in the thousandths column.
7: Order the numbers from least to greatest.
- 27.08 - 2nd because 0 is the least/lower number than 8 (tenths value)
- 27.88 - 4th because there are two numbers after the decimal which are greater than the others (tenths & hundredths value)
- 27.8 - 3rd because there is only one number after the decimal (tenths value)
- 26.78 - 1st because 6 is the least number than 7 (tens value)
Explanation in words (Short Form)
- Using the place value chart I can count the lowest number in the tens value that will be the first least number. I will progress my way up until I will eventually find the least to greatest numbers because of there decimal points and numbers after the decimals.
Reference: Place value chart
Answer:
26.78, 27.08, 27.8, 27.88
Hope this helps.
Type 5 examples of terminating decimals..
1.21948
2.5345
4.305
5.94
9.1
A deck of cards contains RED cards numbered 1,2,3,4,5 and BLUE cards numbered 1,2,3,4. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card. Drawing the Red 5 is an example of which of the following events? Select all correct answers. Select all that apply: B OR E B OR O R AND E R OR E O′ B AND O
Based on the deck of cards containing blue cards and red cards, drawing Red 5 is an example of:
B OR OR OR EO′What are the probability events?Red 5 is both a red number and an odd number. This means that if B or O are picked, Red 5 will be picked as it is an odd number.
If the event calls for R or E to be picked as well, Red 5 will also be picked as it is Red. If event O' is picked, then Red 5 will be picked again because it is odd.
In conclusion, Red 5 is an example of the events, "B or O," "R or E," and "O.'"
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factor please show work
Answer:The answer would be 6a(4b4 +2b3 -3b2)
Step-by-step explanation:All you have to do is take 6a out of each number and put the 6a outside of parenthesis and put the rest of the equation in parenthesis.
The volume of a cone is 405 pi inches cubed with a radius of 9 inches. What is the height of the cone?
Given the values of the volume and radius, the height of the cone is 15 inches.
What is the height of the given cone?A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.
The volume of a cone is expressed as;
V = (1/3)πr²h
Given the data in the question;
Volume of the cone V = 405π in³Radius r = 9 inHeight h = ?Plug in the given values and solve for h.
V = (1/3)πr²h
h = 3V / πr²
h = ( 3 × 405π in³ )/( π × (9in)²
h = ( 3 × 405 in³ )/( 81 in² )
h = ( 1215 in³ )/( 81 in² )
h = 15 inches
Given the values of the volume and radius, the height of the cone is 15 inches.
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An airplane leaves Los Angeles and travels 5 hours to New York City. The return trip travels along the same route and takes 6 hours and 15 minutes because the plane travels 99 miles per hour slower due to a headwind. Find the distance that the plane flies between the two cities. The distance that the plane flies between the two cities is ____ miles.
Use the equation distance=rate*time
The distance that the plane flies between the two cities is 2475 miles.
What is velocity?Velocity is the rate of distance covered per time. Velocity could be average or instantaneous.
For example, if a car drives 50 meters for 10 seconds and it is constant then 50/10 = 5 meters/second will be the velocity.
Time taken = distance covered / velocity
In the first case ;
Time taken = 5 hour.
Velocity = V(Let's say)
Distance covered = x
So,
5 = x/V
x = 5V
Now,
In the second case ;
Velocity = V - 99 (99 slower to first)
Time taken = 6 hours and 15 minutes = 6.25 hour
Distance covered = x
So,
6.25 = x/(V - 99)
x = 6.25V - 618.75
By equating
6.25V - 618.75 = 5V
1.25V = 618.75
V = 495 miles / hour
Now,
x = 5(495) = 2475 miles.
Hence "The distance that the plane flies between the two cities is 2475 miles".
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11. You have just been hired as advertising manager of The Daily Chronicle, a not-very- successful newspaper. In the past, The Chronicle contained one-half advertising and one-half news stories. Current industry research indicates a newspaper must have three times as much advertising as news stories to make money. In addition, the advertising must be divided in the following ratio: 5 to 3 to 1, retail advertising to national advertising to classified advertising. The Chronicle is typically 48 pages in length. 1 a) How many pages should be advertising, and how many should be news stories? b) Based on the industry ratios, how should the pages be divided among the three types of advertising? c) After you made the changes in the advertising distributions ratios, your newspaper began making a profit—for the first time in years. If last year’s total advertising revenue was $810,000, how much was earned by each type of advertising? d) When you accepted the job of advertising manager, in addition to your salary, you were promised a 1/50 share of each year’s revenue from retail and classified advertising and a 1/75 share for national. What bonus will you receive for last year’s sales?
Using proportions, it is found that:
a) 36 pages should be of advertising and 12 pages should be of news stories.
b) 20 pages should be of retail advertising, 12 pages should be of national advertising and 4 pages should be of classified advertising.
c) $450,000 was earned by retail advertising, $270,000 was earned by national advertising and $90,000 was earned by classified advertising.
d) You will receive a bonus of $14,400 for last year's sales.
What is a proportion and what is an example of application?A proportion is a fraction of a total amount, and equations can be built to find the measures using a rule of three, that can be either direct or inverse, deriving from proportional relationships.
One example of application is for ratio problems, as fractions of the total amount are built from the ratios, as given in this problem.
For item a, we have that three times as much advertising as news stories are needed, hence 3/4 of the 48 pages are advertising, hence:
3/4 x 48 = 0.75 x 48 = 36.
Hence:
The remaining 12 are of news stories.
For item b, from the ratio of 5 to 3 to 1, we have that:
5/9 of the advertising pages should be of retail advertising.3/9 of the advertising pages should be of national advertising.1/9 of the advertising pages should be of classified advertising.Hence:
5/9 x 36 = 20 pages. -> Retail.3/9 x 36 = 12 pages. -> National.1/9 x 36 = 4 pages. -> ClassifiedIn item c, from the same ratio as above, the advertising values are found as follows:
5/9 x 810,000 = $450,000. -> Retail.3/9 x 810,000 = $270,000. -> National.1/9 x 810,000 = $90,000. -> ClassifiedFor item d, the bonus is calculated as follows:
1/50(450,000 + 90,000) + 1/75(270,000) = $14,400.
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-22 + (-10) + 15 I don’t know how to solve this problem
The answer is - 17
here, we have to apply BODMAS rule
given ,- 22 + (10) = 15
= - 22 - 10 + 15
= -32 + 15
= - 17
BODMAS is an acronym for the sequence of operations to be performed while simplifying the mathematical expressions.
B=Brackets
O=Off
D=Division
M=Multiplication
A=Addition
S=Subtraction
Achilles is a mathematician who invented BODMAS. It is a mnemonic that helps us remember how to evaluate mathematical operators in a mathematical statement involving more than one mathematical operation.The four basic Mathematical rules are addition, subtraction, multiplication, and division.
Basic math skills are those that involve making calculations of amounts, sizes or other measurements. Core concepts like addition, subtraction, multiplication and division provide a foundation for learning and using more advanced math concepts.
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The coordinates below represent rotations. Use what you’ve learned today to describe what type of rotation occurred
Type of rotation of Anticlockwise and clockwise .
A point in coordinate geometry can be rotated through 180 degrees around the origin by drawing an arc with a radius equal to the distance between the provided point's coordinates and the origin, and then extending an angle of 180 degrees at the origin.
The point must be rotated around the origin with regard to its location in the cartesian plane. It is nicely explained in the next part of the 180-degree rotation formula.
The formula for 180-degree rotation of a given value is as follows: if R(x, y) is a point that has to be rotated around the origin, then coordinates of R(x, y) .
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I need help please quick
Answer:
Step-by-step explanation: These two angles are congruent because most of the points are opposite of each other. For example Angle R is congruent to Angle V and Angle T is congruent to Angle U. Another thing about vertical angles is that they must always equal each other.
QUESTION BELOW SLOVE USING NTH TERM!
I found this
im using T for tails and H for heads
to get all 4 coins to face heads but only turning over 3 coins at a time for one move takes 5 times
MOVE 1# TTTT
MOVE 2#THHH
MOVE 3#HTTH
MOVE4#HHHT
MOVE5#TTTH
end up like =HHHH
HOW DO I WRITE THIS OUT FOR NTH TERM.
THE QESTION IS BELOW! WILL GET 100 POINTS! PLEASE HELP BEEN STUCK ON THIS FOREVER!
find out which of the number 5,8 and 9 divide into51768 exactly
Answer: 8 and 9
Step-by-step explanation: 51768 ÷ 9 = 5752
51768 ÷ 8 = 6471
Answer:
9
Step-by-step explanation:
The digits of 51768 add up to a multiple of 9
Musa has 1473 marbles and Obi 1389 marbles.How many marbles must Musa give Obi so that each of them now has the same number
Answer:
42
Step-by-step explanation:
1473 - 1389 is 84
84/2 is 42
10 decreased by the difference of v and u
Answer:
(V - U) - 10
Step-by-step explanation: