Answer:
Step-by-step explanation:
Yeah it right thank sweetheart
The original width of the rectangle is 8 cm and the original length is 18 cm. These dimensions are found by setting up an equation based on the change in area when both dimensions are reduced by 2 cm.
Finding Original Dimensions of a Rectangle
Let's denote the width of the rectangle as w, and the length will then be w + 10 cm. The area of the original rectangle is w(w + 10) square centimeters. Now, by decreasing each dimension by 2 cm, the new width becomes w - 2 cm and the new length becomes (w - 2) + 10 cm = w + 8 cm. The area of the new rectangle is (w - 2)(w + 8) square centimeters.
The problem states that the area of the rectangle is decreased by 48 cm2 when the dimensions are reduced. This gives us the equation:
w(w + 10) - (w - 2)(w + 8) = 48
Expanding the terms and solving for w will provide us with the width of the original rectangle. After finding w, we can calculate the original length by adding 10 cm to the width. To solve for w, we proceed with the calculation:
[tex]w_2 + 10w - (w_2[/tex] + 6w - 16) = 48
w2 + 10w - w2 - 6w + 16 = 48
4w + 16 = 48
4w = 32
w = 8 cm.
Therefore, the original width is 8 cm and the original length is 18 cm (that is, 8 cm + 10 cm).
Simplify
5. (3+2i) (2-1)
Answer:
3+2i
Step-by-step explanation:
(3+2i)(1)
3+2i
16. WalkieTalkie phone company charges $18.00 for basic phone service per month and $0.15 per minute for long distance calls. Arena Calls charges $80.00 per month with no fee for long distance calls. What is the minimum number of minutes of long distance calls for which the cost of Walkie Talkie is more than the cost of Arena Calls?
Answer:
413 minutes of long distance calls
Step-by-step explanation:
$80.00 - $18.00 = $62.00
$62.00/$0.15 = 413.33
3. A crate with 20 bricks weighs 167 pounds. When the same crate has 32 bricks, it weighs
191 pounds. How much would the crate weigh if there were 19 bricks in the crate?
Explain.
The weight of crate when it has 19 bricks is 165 pounds
Solution:Given that, A crate with 20 bricks weighs 167 pounds.
When the same crate has 32 bricks, it weighs 191 pounds.
Now, let the weight of each brick be "m" pounds and weight of the crate be 'n" pounds.
Then, when crate has 20 bricks
Total weight = weight of bricks + weight of crate
[tex]167 \text { pounds }=\text { number of bricks } \times \text { weight of each brick }+\text { weight of crate }[/tex]
[tex]167=20 \times m+n[/tex]
20m + n = 167 ----- eqn (1)
Now, when crate has 32 bricks
Total weight = weight of bricks + weight of crate
[tex]191 \text { pounds }=\text { number of bricks } \times \text { weight of each brick + weight of crate }[/tex]
[tex]191=32 \times m+n[/tex]
32m + n = 191 ----- eqn (2)
Now, subtract (1) from (2)
32m + n = 191
20m + n = 167
(-) ----------------
12m + 0 = 24
m = 2
Then, from eqn (1)
20(2) + n = 167
40 + n = 167
n = 167 – 40 = 127
Now, when the box has 19 bricks
Total weight = 19 bricks x 2 pounds per brick + 127 pounds of crate
[tex]\text { Total weight }=19 \times 2+127=38+127=165[/tex]
Hence, the weight of crate when it has 19 bricks is 165 pounds.
Which expression is equivalent to the given expression? (3m-4)^3(3m^5)
Answer: The answer is D
Answer:
Step-by-step explanation:
Hope this Helps ;)
You want it put edging around a rectangular flower garden that is 15 feet long and 12 feet wide. The edging comes in 3 foot pieces. How many pieces of edging do you need to buy
Answer:
18 pieces are needed
Step-by-step explanation:
Edgings are put all around the rectangular flower garden. So we need to know the perimeter (sum of all sides) of the rectangle. The formula is:
Perimeter of Rectangle = 2(Length + Width)
Given,
Length = 15
Width = 12
So,
Perimeter = 2(Length + Width)
Perimeter = 2(15 + 12)
Perimeter = 2(27)
Perimeter = 54
So, we need to cover 54 feet. Each edging is 3 feet in length, so 54 feet will be covered by:
54/3 = 18 edgings
A library has 70 books about George Washington Carlo has read 14 of the books. What fraction of the books about George Washington has Carlo read?
Answer:
14/70 or 1/5
Step-by-step explanation:
Final answer:
Carlo has read 14 out of 70 books about George Washington.
Explanation:
To find the fraction of the books about George Washington that Carlo has read, we need to divide the number of books Carlo has read by the total number of books about George Washington in the library.
Carlo has read 14 books and there are 70 books about George Washington, so the fraction of books Carlo has read is 14/70.
When mack babysits he charges $12 an hour plus bus fare. The amount Mack is paid depends on the number of hours he babysits
Question is Incomplete, Complete question is given below.
When mack babysits, he charges $12 an hour plus bus fare. The amount mack is paid depends on the number of hours he babysits.
1. If mack babysits for 1 hour and the bus fare is $2.50, how much will mack be paid?
2. If mack babysits for 4 hours and the bus fare is $2.50, how much will mack be paid?
Answer:
1. Total Amount mack will be paid for 1 hour is $14.50.
2. Total Amount mack will be paid for 4 hours is $50.50.
Step-by-step explanation:
Given:
Charges of mack for 1 hour = $12
bus fare = $2.50
We will fist find for part 1.
1) Given:
Number of Hours= 1
Charges of mack for 1 hour = $12
bus fare = $2.50
we need to find the amount he get paid for it can be calculated by Multiplying Charges of mack for 1 hour with number of hours and then adding bus fare
Total amount he will get paid = Charges of mack for 1 hour × Number of Hours + Bus fare = [tex]\$12\times 1 +\$2.50= \$14.50[/tex]
Hence, Total Amount mack will be paid for 1 hour is $14.50.
Now we will find for part 2.
2) Given:
Number of Hours= 4
Charges of mack for 1 hour = $12
bus fare = $2.50
we need to find the amount he get paid for it can be calculated by Multiplying Charges of mack for 4 hour with number of hours and then adding bus fare
Total amount he will get paid = Charges of mack for 1 hour × Number of Hours + Bus fare = [tex]\$12\times 4 +\$2.50= \$50.50[/tex]
Hence, Total Amount mack will be paid for 4 hour is $14.50.
L. - (6x - 5) = -6x +13
Answer:
No Solution.
Step-by-step explanation:
-(6x-5)=-6x+13
-6x+5=-6x+13
-6x-(-6x)+5=13
-6x+6x+5=13
0+5=13
5=13
Answer:
Exact form : x=-1/3
Decimal form : x=-0.3 (line over the 3!!!)
Step-by-step explanation: Isolate the variable by divinding each side by factors that don't contain the variable.
Hope this helps you out! ☺
Which of the following expressions represents the solution to -2x ≤ -10?
A)x ≤ -5
B)x ≥ -5
C)x ≥ 5
Final answer:
The solution to the inequality -2x ≤ -10 is found by dividing both sides by -2 and reversing the inequality sign, resulting in C) x ≥ 5.
Explanation:
The expression that represents the solution to -2x ≤ -10 is found by dividing both sides of the inequality by -2. When dividing by a negative number, we must reverse the inequality symbol. Thus, dividing both sides by -2 would give us x ≤ 5. However, since the inequality symbol was reversed, the correct solution is x ≥ 5.
Here are the steps broken down:
Starting with -2x ≤ -10.
Dividing both sides by -2 gives x ≥ 5.
Therefore, the correct answer is C) x ≥ 5.
A card is randomly selected from a standard deck of 52 playing cards. What is the probability that it is a face card or a spade?
Answer:
8/13.
There's 12 face cards & 26 black cards. In the 26 black cards, theres 6 face cards. Theres 32 cards overall that is either a black card or a face card. So in conclusion the answer is 8/13 because 52 (the total amt in the deck) divided by 32 = 8/13.
The probability of randomly selecting either a face card or a spade from a standard deck of 52 playing cards is approximately 0.4231.
The question involves calculating the probability of selecting either a face card or a spade from a standard deck of 52 playing cards. A standard deck consists of four suits (spades, hearts, diamonds, clubs), each with 13 cards, making a total of 52 cards. Among these, 12 are face cards (Jacks, Queens, Kings across all suits), and 13 are spades (including the spade face cards).
First, note that there are 3 face cards (Jack, Queen, King) in each suit, resulting in 12 face cards in total. However, 3 of these face cards are spades, and we must avoid double-counting them when adding the spade cards. Therefore, we have 12 face cards and 10 non-face card spades (since 3 spades are already counted among face cards), giving us a total of 22 unique cards that fulfill the conditions.
The probability of drawing either a spade or a face card from a deck of 52 cards is calculated by dividing the number of favorable outcomes (22) by the total number of outcomes (52), which is 22/52 or approximately 0.4231.
50 point for this question:
Find values of a and b that make the following equality into identity:
Answer:
1) The values of 'a' and 'b' are [tex]$ \frac{3}{4} $[/tex] and [tex]$ \frac{3}{4} $[/tex] respectively.
2) The values of 'a' and 'b' are '3' and '-3' respectively.
Step-by-step explanation:
1) Given: [tex]$ \frac{3x}{(x - 2)(3x + 2)} = \frac{a}{x - 2} + \frac{b}{3x + 2} $[/tex]
We solve this by partial fraction method.
Taking LCM in the RHS we get,
[tex]$ \frac{3x}{(x - 2)(3x + 2)} = \frac{a(3x + 2) + b(x - 2)}{(x - 2)(3x + 2)} $[/tex]
[tex]$ \implies 3x = a(3x + 2) + b(x - 2) $[/tex]
To find the value of 'a', substitute x = 2. This would make 'b' vanish leaving an equation with 'a'.
[tex]$ \therefore 3(2) = a(3.2 + 2) + b (2 - 2) \implies 6 = a(8) $[/tex]
[tex]$ \implies a = \frac{-2}{3} $[/tex]
Now, Substitute [tex]$ x = \frac{-2}{3} $[/tex] to solve for 'b'.
[tex]$ \implies 3(\frac{-2}{3}) = a (3.\frac{-2}{3} + 2) + b(\frac{-2}{3} -2) $[/tex]
[tex]$ \implies -2 = b \frac{-8}{3} $[/tex]
[tex]$ \implies b = \frac{3}{4} $[/tex]
Therefore, a = [tex]$ \frac{3}{4} $[/tex] and b = [tex]$ \frac{3}{4} $[/tex]
2) Given [tex]$ \frac{3}{x^2 - 5x + 6} = \frac{a}{x - 2} + \frac{b}{x - 3} $[/tex]
We follow the same procedure as (1).
Taking LCM we get
[tex]$ \frac{3}{x^2 - 5x + 6} = \frac{a (x - 3) + b(x - 2)}{(x^2 - 5x + 6)} $[/tex]
[tex]$ \implies 3 = a(x - 3) + b(x - 2) $[/tex]
Substituting x = 2, we get:
3 = a(-1) [tex]$ \implies a = -3 $[/tex]
Also, Substituting x = 3, we get:
3 = b(1)
[tex]$ \implies b = 1 $[/tex]
Therefore, the values of a and b are -1 and 1 respectively.
the equation that can be used to solve for x is
Answer:
see explanation
Step-by-step explanation:
Since l and m are parallel lines, then
11x - 47 = 6x - 2 ( corresponding angles )
Solve this equation for x
Subtract 6x from both sides
5x - 47 = - 2 ( add 47 to both sides )
5x = 45 ( divide both sides by 5 )
x = 9
Part A
Describe the type of function shown in the graph.
Part B
What are the standard form and the factored form of the function?
Answer:
A
[tex]F(x)=-\frac{1}{1500}(x+20)(x+5)(x-15)[/tex]
B
[tex]=> F(x)=-\frac{x^3}{1500}-\frac{x^2}{150}+\frac{11x}{60}+1[/tex]
Step-by-step explanation:
Function and its graphs
Part A
The graph shown in the image corresponds to a cubic function because of its classical infinite branches, three real roots and two extrema values
Part B
Knowing the value of the three roots x=-20, x=-5, and x=15 we can express the cubic function in factored form:
[tex]F(x)=C(x+20)(x+5)(x-15)[/tex]
The value of C will be determined by using any particular point from the graph. Let's use (0,1)
[tex]1=C(0+20)(0+5)(0-15)[/tex]
[tex]C=-\frac{1}{1500}[/tex]
Replacing, we find the factored form of the function
[tex]F(x)=-\frac{1}{1500}(x+20)(x+5)(x-15)[/tex]
The standard form demands to expand all the products and simplify
[tex]F(x)=-\frac{1}{1500}(x^3+10x^2-275x-1500)[/tex]
[tex]=> F(x)=-\frac{x^3}{1500}-\frac{x^2}{150}+\frac{11x}{60}+1[/tex]
In a video game, Conner scored 25% more points than Max. If c is the number of points that Conner scored and m is the number of points that Max scored, which equations are correct?
Select all that apply
A. c - m + 0.25
B. c = (1 + 0.25)m
C. c = 1.25m
D. c = m + 0.25m
E. c = m + 25
Please explain to me why the correct answers is B, C and D. What kind of math problem is this as well?
The correct choices B, C, and D all represent the equation that Conner scored 25% more points than Max, using algebraic terms to demonstrate this proportional increase. Choices B and C show the total score as a multiple of Max's score, while D adds an extra 25% to Max's score.
Explanation:The problem presented is an algebraic representation of a proportional relationship. Given that Conner scored 25% more points than Max, we can express this relationship in different but equivalent equations. Choices B, C, and D effectively communicate that Conner's score, c, is increased by 25% more than Max's score, m.
Choice B is written as c = (1 + 0.25)m, which represents a 100% (which is 1 in decimal form) of Max's score plus an additional 25%. Choice C simplifies this to c = 1.25m, which is another way to represent a 25% increase on Max's score. Choice D is expressed as c = m + 0.25m which sums Max's score with another 25% of it. Each of these equations correctly translates the scenario into a mathematical expression.
1. Use the formula S(d)=√9.8d to calculate the estimated speed, in meters per second, of a tsunami if the disturbance occurred at an ocean depth of 4,500 meters.
2. Convert the answer from question one from meters per second to kilometers per hour. (Hint: A meter per second is equal to 3.6 kilometers per hour.)
Answer: 1. 210 meters per second .
2. 756 kilometers per hour.
Step-by-step explanation:
Given : The formula [tex]S(d)=\sqrt{9.8d}[/tex] to calculate the estimated speed, in meters per second of a tsunami.
1. If the disturbance occurred at an ocean depth of 4,500 meters.
Then put d= 4500 in the above formula , we get
[tex]S(d)=\sqrt{9.8\times4500}[/tex]
[tex]S(d)=\sqrt{44100}=\sqrt{21\times21\times10\times10}\\\\=\sqrt{210^2}=210[/tex]
Hence, if the disturbance occurred at an ocean depth of 4,500 meters , the estimated speed would be 210 meters per second .
Also, A meter per second is equal to 3.6 kilometers per hour.
i.e. 1 meter per second = 3.6 kilometers per hour
Then by unitary method ,
210 meters per second =[tex]3.6\times210[/tex] kilometers per hour
=756 kilometers per hour.
48 in Long and 36 inches wide what is the area in square feet
Answer:
Area = 12 ft²
Step-by-step explanation:
Convert values to feet
12 inches = 1 foot
48 / 12 = 4 feet
36 / 12 = 3 feet
Area = l x w = 3 x 4 = 12 ft²
Answer: The answer is 1,728 in. squared
Step-by-step explanation:
All you do is multiply 48 by 36 because in order to get area,you multiply base and height.
Help!!! Can somebody answer this question and please explain how to do it?
Good evening ,
Answer:
15x⁷y⁵.
Step-by-step explanation:
5x³y²×3x⁴y³ = (5×3)(x³x⁴)(y²y³) = 15x⁷y⁵.
:)
Bentley walked 9 miles in 6 hours. What was his walking rate in miles per hour?
Answer:
1.5 miles per hour
Step-by-step explanation:
9 (1/6) = 1.5
Answer:
1.5 miles per hour
Step-by-step explanation:
In the attached file
Marsha counted 24 birds at the wildlife refuge, and Aamir counted 86 birds. What is the ratio of Aamir’s Burge to Marshall’s birds in simplest form?
Answer:
43:12
Step-by-step explanation:
Answer:
3 7/12 or 43/12
Step-by-step explanation:
It's just 86/24
A 36 foot long roll of banner material must be cut into three pieces with no material left over to make three banners. The second banner must be 4 feet longer than the first banner in the third banner must be also 4 feet longer than the second. How long should each banner be
Answer:
The length of the first banner = 8 ft
The length of the second banner = 12 ft
The length of the third banner = 16 ft
Step-by-step explanation:
The total length of the banner material = 36 ft
Now, let us assume the length of the first banner = k ft
So, the length of the second banner = First banner + 4 ft = ( k + 4) ft
The length of the third banner = Second banner + 4 ft = [( k + 4) + 4] ft
Now, according to the question:
The length of ( First + Second + Third) banner = 36 ft
⇒ (k) + (k +4) + (k + 8) = 36
or, 3 k = 36 - 12= 24
or, k = 24/3 = 8
⇒ k = 8 ft
So, the length of the first banner = k = 8 ft
The length of the second banner = k + 4 = 8 + 4 = 12 ft
The length of the third banner = k + 4 + 4 = 8 + 8 = 16 ft
Answer:
A
Step-by-step explanation:
A number times 5,minus 6,is 8.
Answer:70
Step-by-step explanation:
You do the inverse operation which would be subtraction and multiplication. You add the 6 to the 8 and you get 14. Then you would multiply 14 by 5 to get 70. Hope this helps :D
Answer:
Step-by-step explanation:
8. 2x2 + 3x when x = 3
Answer:
27
Step-by-step explanation:
Substitute x = 3 into the expression
2(3)² + 3(3) = 2(9) + 9 = 18 + 9 = 27
Answer:
13
Step-by-step explanation:
2×2=4+3(3)=4+9=13
This scale drawing of a rectangular wall has dimensions 4.75 inches by 2.5 inches. The length of the shorter side of the actual wall is 36 inches.
Enter the area of the actual wall.
I will mark the first one who answers me brainleist
_[blank]_ square inches
Answer:
2462.4 square inches
Step-by-step explanation:
To find the length of the longer wall use the following ratio and solve for x.
x/36= 4.75/ 2.5
x= 68.4
Area of a rectangle = l(w)
68.4(36)= 2462.4 square inches
The area of the wall is the product of its dimension.
The area of the actual wall is 2462.4 square inches
The scale is given as:
[tex]\mathbf{Scale = 4.75 : 2.5}[/tex]
The shorter side of the actual wall is 36 inches.
So, we have:
[tex]\mathbf{Long : 36= 4.75 : 2.5}[/tex]
Express as fractions:
[tex]\mathbf{\frac{Long }{36}= \frac{4.75 }{ 2.5}}[/tex]
Multiply both sides by 36
[tex]\mathbf{Long= 36 \times \frac{4.75 }{ 2.5}}[/tex]
[tex]\mathbf{Long= 68.4}[/tex]
So, we have:
[tex]\mathbf{Long= 68.4}[/tex]
[tex]\mathbf{Short= 36}[/tex]
The area is then calculated as:
[tex]\mathbf{Area = 68.4 \times 36}[/tex]
[tex]\mathbf{Area = 2462.4in^2}[/tex]
Hence, the area of the actual wall is 2462.4 square inches
Read more about areas at:
https://brainly.com/question/2602591
What is the greatest common factor of 88 and a 121
Answer: 11
Step-by-step explanation: The factors of 88 are 1,2,4,8,11,22,44,88; The factors of 121 are 1,11,121.
Final answer:
To find the greatest common factor (GCF) of 88 and 121, determine the common factors through their prime factorizations, which results in 11 as the GCF.
Explanation:
The greatest common factor (GCF) of 88 and 121 can be found by determining the largest number that can evenly divide both numbers. To find the GCF:
Find the prime factorization of both numbers: 88 = 2 x 2 x 2 x 11 and 121 = 11 x 11.Identify the common factors: In this case, the common factor is 11.Therefore, the greatest common factor of 88 and 121 is 11.Which fraction is equal to one third
Answer:
2/6, 3/9, 4/12 ...
Step-by-step explanation:
We can find equivalent fractions to 1/3 by multiplying the numerator, or top number, and the denominator, or bottom number, by the same factor.
When buying groceries at the store for this dinner, you can spend no more than $100. Some costs are fixed, like spices and piecrusts. That total comes to $65. The turkey, however, is priced per pound. The suggestion is that you plan for 1.5 pounds of turkey per guest. If the turkey costs $1.16 per pound, what is the largest size turkey you should buy and how many people can it feed?
Answer:
20 full people
Step-by-step explanation:
100-65=35
35/1.16= 30.1724
30.1724/1.5=20.1149
You can't feed a .1149 of a person so 20 people
Given the maximum budget and cost per pound, the largest turkey you can purchase is approximately 30.17 pounds. This will feed about 20 guests, considering each person consumes 1.5 pounds of turkey.
Explanation:The subject of this question is mathematics, specifically, problem-solving involving budgets and limits. Given that the maximum budget for this dinner is $100 and the fixed costs total to $65, we're left with $35 for the turkey. Each pound of turkey is priced at $1.16.
By dividing the remaining amount of money (which is $35) by the cost per pound of turkey (which is $1.16), we compute the total pounds of turkey we can afford. That is, $35 / $1.16 = approximately 30.17 pounds.
Each guest requires 1.5 pounds of turkey, so we now calculate how many guests can be fed by this amount of turkey. We do this by dividing the total pounds of turkey (30.17 pounds) by the amount required per guest (1.5 pounds), which gives us 30.17 / 1.5 = approximately 20.11. Since you can't invite a fraction of a person, the largest size turkey you can afford can feed about 20 people.
Learn more about Problem Solving here:https://brainly.com/question/31606357
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Helpppoopo please please
Answer:
51.5 therms of natural gas
Step-by-step explanation:
19.57/0.38= 51.5
Answer: 51.5 therms
Step-by-step explanation:
$0.38 per therm
amount of money paid/rate=therms used
19.57/0.38=51.5
5. How many more minutes are there in March than in April?
A) 720 B) 1440 C) 2160 D) 2880
Answer:b
Step-by-step explanation: because if you subtract 44,640 minus 43,200 which equal 1440
44,640-43,200=1,440
Answer: B) 1440
Step-by-step explanation:
March: 44,640 Minutes
April: 43,200 Minutes
Subtract 44,640-43,200=1440
which of the following expressions has a sum of 57/100
Which of the following is a velocity?
Question 2 options:
30 m/s
30 m/s going down
30m
30s
Answer:
The velocity is the speed in a given direction hence the units are the same as that of speed, m/s. Thus the answer is 30 m/s.
Step-by-step explanation:
I do not understand the second option.