Answer:
[tex]Area = (30 + x)(20 + x)[/tex]
Step-by-step explanation:
By definition, the area of a rectangle is the product of its length multiplied by its width.
Initially the dog run has a length of 30 ft long and 20 ft wide.
If you want to expand the track, increase the length of each side by a factor x. So, the dimensions of the expanded dog run will be:
[tex]Length = 30 + x\\Width = 20 + x[/tex]
Then, the area is:
[tex]Area = Length * Width[/tex]
[tex]Area = (30 + x)(20 + x)[/tex]
The total area of an expanded rectangular dog run, after increasing each side by the same amount x, is calculated using the formula A = (l + 2x)(w + 2x), where l is the original length and w is the original width. The new area after expansion is 4x^2 + 100x + 600 square feet.
The student is asking how to calculate the total area of an expanded rectangular dog run after increasing each side by the same amount, x. To solve this, we can use the formula A = lw, where A is the area, l is the length, and w is the width of the rectangle. In the original dimensions, the dog run has a length of 30 ft and a width of 20 ft. After expanding, the new dimensions will be (30 + 2x) ft for the length and (20 + 2x) ft for the width, since each side is increased by x on each end.
Expanded Dog Run Area Calculation:
First, we write out the new dimensions:
New Length = 30 ft + 2xNew Width = 20 ft + 2xThen, we calculate the new area:
A = (30 + 2x)(20 + 2x)
A = 600 + 60x + 40x + 4x^2
A = 4x^2 + 100x + 600
The expanded area of the dog run will be 4x^2 + 100x + 600 square feet.
Judy needs to take out a personal loan for $2,500 for tuition assistance. Her bank has offered her one of the four loan packages outlined in the chart below. Determine which of the four loans will be cheapest for Judy in the long run. All interest rates are compounded monthly.
The answer would be Loan A
even though she'll pay more per month, with the others she'll pay be paying more by the time she as payed it off due to having to pay interest over a longer period of time
Answer:
Loan A is the cheapest.Step-by-step explanation:
The different loan plans are showed in the image attached.
Loan A: 12 months of duration with 9.50%.
Loan B: 24 months of duration with 8.75%.
Loan C: 36 months of duration with 7.75%.
Loan D: 48 months of duration with 6.60%.
Now, all loans are compouneded monthly. Let's the compound interest formula
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
Loan A:
[tex]A=2500(1+\frac{0.095}{12} )^{12(1)}\\A=2,748.12[/tex]
Loan B:
[tex]A=2500(1+\frac{0.095}{24} )^{24(2)} \\A=2500(1.004)^{48}\\ A=3,028.02[/tex]
Loan C:
[tex]A=2500(1+\frac{0.095}{36} )^{36(3)} \\A=2500(1.003)^{108}\\ A=3,454.94[/tex]
Loan D:
[tex]A=2500(1+\frac{0.095}{48} )^{48(4)}\\ A=2500(1.002)^{192}\\ A=3,668.95[/tex]
Now, if you compare, you will observe that Loan A offer the cheapest result for Judy.
Therefore, Judy should use the Loan A plan.
Given f(x) = 2x + 1 and g(x)= 3x+2, what is f(3)/ g(2)
Answer:
[tex]\large\boxed{\dfrac{f(3)}{g(2)}=\dfrac{7}{8}}[/tex]
Step-by-step explanation:
[tex]f(x)=2x+1,\ g(x)=3x+2[/tex]
[tex]f(3)\to\text{put x = 3 to the equation of}\ f(x):\\\\f(3)=2(3)+1=6+1=7[/tex]
[tex]g(2)\to\trext{put x = 2 to the equation of}\ g(x):\\\\g(2)=3(2)+2=6+2=8[/tex]
[tex]\dfrac{f(3)}{g(2)}=\dfrac{7}{8}[/tex]
Aileen purchased a box of ten juice boxes for her party. Each juice box contains eight of juice. At the end of the party,two juice boxes were left. How many ounces of juice were consumed and how many were left???
Answer:
64 oz. were consumed and 16 oz. were left.
Step-by-step explanation:
8*10 = 80 oz. of juice total.
10-2=8 boxes consumed
8*8(number of oz. per box)=64 oz. consumed
2*8=16 oz. left
64+16=80 checks out.
14m-13m=17 what is m please help me!!!!
Answer:
m = 17Step-by-step explanation:
[tex]14m-13m=17\\\\(14-13)m=17\\\\1m=17\to\boxed{m=17}[/tex]
[tex]\bold{Hey\ there!}\\ \bold{Simplify\ both\sides\ of\ your \ equation} \\ \bold{Like\downarrow} \\ \bold{14m-13m=17} \\ \bullet{\bold{14m+(-13m)=17}} \\ \\ \\ \bold{Combine\ your\ terms}\\ \bold{Like\downarrow}\\ \bold{14m \ \& -13m} \\ \\ \bold{14m+(-13m)=1} \\ \bold{1=17} \\ \\ \bold{1\times17=17}[/tex]
[tex]\boxed{\boxed{\bold{Answer:m=17}}}\checkmark \\ \\ \bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ your\ day!} \\ \\ \\ \frak{LoveYourselfFirst:)}[/tex]
41/8 - 1/3 = what????
Answer:41/8 - 1/3= 115/24
Step-by-step explanation:
The area of a triangular block is 64 square inches. If the base of the triangle is twice the height, how long are the base and the height if the triangle?
hope i could helpp!!!!
When the coordinates (1,1) (7,3) (8,0) and (2,-2) are joined which shape is formed ?
Answer:
A rectangle.
Step-by-step explanation:
To graph the points find their pairs on a graph and leave a mark in so area. Eventually, it'll reveal the shape.
Hope this helps,
Davinia.
At hockey practice, Talia took 35 shots, and made 60% of them. She had hoped to make 25 shots. By how many shots did she fall short of her goal?
Answer:
4 goals short
Step-by-step explanation:
To find how many shots Talia made - multiply the total number of shots (35) by 60% (or 0.60)
35*.60 = 21 shots made
Subtract her goal (25) by the shots actually made (21)
25-21 = 4 shots from her goal
Manny has 48 feet of wood. He wants to use all of it to create a border around a garden. The equation 2l+ 2w = 48 can be used to find the length and width of the garden, where l is the length and w is the width of the garden. If Manny makes the garden 15 feet long, how wide should the garden be?
Answer:
2W=9
Step-by-step explanation:
You must first get the Length, which is 15, and multiply it by 2 and you get 30. You then subtract 30 from 48 and get 18. Since the equation has 2W, you have to divide 18 by 2, which gets you the answer 9.
Answer:
width = 9 feet
Step-by-step explanation:
Here we are given that total length of the wood for the garden is 48 feet only.
The length in represented in the equation given below. In geometry we call it Perimeter.
2l+2w=48
Where l is the length of the garden and the w is width of the garden.
Here also given that , if Manny wants the length to be 15 feet, what will be width of the garden.
In order to find this we put the value of l as 15 in 2l+2w=48 and solve for w
Let us see how
2l+2w=48
2(15)+2w=48
30+2w=48
subtracting 30 from both sides
30+2w-30=48-30
2w=18
Dividing both sides by 2 we get
w=9
Hence the width will be 9 feet
what is the range of the cubic function f(x)=2x^3+21
A(-∞,+∞)
B(-∞,21)
C(21,+∞)
D(-∞,21)U(21,+∞)
ANSWER
A
[tex]( - \infty , + \infty )
[/tex]
EXPLANATION.
The given function is
[tex]f(x) = 2 {x}^{3} + 21[/tex]
Let
[tex]y= 2 {x}^{3} + 21[/tex]
Solve for x.
[tex]2 {x}^{3} = y - 21[/tex]
[tex] {x}^{3} = \frac{1}{2} y - \frac{21}{2} [/tex]
Take cubic root of both sides,
[tex]x = \sqrt[3]{ \frac{1}{2} y - \frac{21}{2} } [/tex]
x is defined for all real values of y.
The range refers to the values of y, for which x is defined.
Hence the range is all real numbers.
In interval notation, we write this as,
[tex]( - \infty , + \infty )
[/tex]
The correct choice is A.
Answer:
Yes it’s A
Step-by-step explanation:
the scuba diver standing on a boat is at an altitude of 1.3 meters above sea level. The scuba diver jumps into the water and decreases his altitude by 5.6 meters in one minute. what equation can be used to represent the divers altitude
Since the scuba diver jumps into the water and decreases his altitude by 5.6 meters in one minute, the equation that can be used to represent the divers altitude is [tex]y = -5x + 1.3[/tex]
What is the eqquation?The standard equation is [tex]y = mx + b[/tex]
y,x = variables
m = rate of change
b = initial value of y.
y = the height of the scuba driver after x minutes.
Given that b = 1.3
m = -5.6(decrease in altitude)
Then the equation can be written as ; [tex]y = -5x + 1.3[/tex]
hence scuba driver height is given by the equation [tex]y = -5x + 1.3[/tex]
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missing options;
A.
1.3 + 5.6
= 6.9
B.
-1.3 + 5.6
= 4.3
>
O
C. 1.3+(-5.6) = – 4.3
>
O
D. -1.3+(-5.6) = -6.9
The equation that represents the scuba diver's altitude after jumping into the water is y = 1.3 - 5.6t, where y is in meters and t is in minutes.
Let y represent the diver's altitude in meters relative to sea level after t minutes. Initially, at sea level, we have y(0) = 1.3. Due to the descent in water, the altitude decreases by 5.6 meters per minute, which means the altitude change per minute can be represented by
-5.6t. Thus, the equation that can be used to represent the diver's altitude as a function of time is:
y = 1.3 - 5.6t
where y is in meters and t is in minutes.
What is the quotient a-3/7 / 3-a/21
Answer:
-3
Step-by-step explanation:
The given expression is:
[tex]\frac{\frac{a-3}{7} }{\frac{3-a}{21} }[/tex]
We can rewrite this as:
[tex]\frac{a-3}{7}\div \frac{3-a}{21}[/tex]
[tex]\frac{a-3}{7}\times \frac{21}{3-a}[/tex]
Factor -1 out of the first numerator:
[tex]\frac{-(3-a)}{7}\times \frac{21}{3-a}[/tex]
Cancel out the common factors;
[tex]\frac{-1}{1}\times \frac{3}{1}=-3[/tex]
Answer:
-3
Step-by-step explanation:
that's just the way it be.
What is the value of this expression?
22.26 x 10^7 is the correct answer
Multiply the decimal numbers:
5.3 x 4.2 = 22.26
When multiplying scientific numbers, add the exponents together: 4+3 = 7
So you now have 22.26 x 10^7
Now you need to convert 22.26 to a scientific number, by only having one number to the left of the decimal point.
You need to move the decimal 1 place to the left, which means you need to add 1 more to the exponent.
The final answer would be 2.226 x 10^8
The length of a room is 20 ft. and its width is 12 ft. What's the perimeter?
Answer:
64
Step-by-step explanation:
20 + 20=40
12 +12 = 24
24+40=64
Answer:
Perimeter = 64ft
Step-by-step explanation:
Perimeter is the sum of the sides i.e. length and width
Perimeter = 20+20+12+12 = 64
Complete the following proof.
Given: 2x + 11 = 15
Prove: x = 2
Statements Reason
1. 2x + 11 = 15 1. Given
2. 2x = 4 2.
3. x = 2 3. Division Property of Equality
Answer:
it is the subtraction property of equality
Solve the triangle for x.
For this case we have that the law of cosine is given by:
[tex]c ^ 2 = a ^ 2 + b ^ 2-2 (a) (b) * cos (x)[/tex]
Where:
[tex]c = 12 \ ft\\a = 8 \ ft\\b = 9 \ ft[/tex]
We replace:
[tex]12 ^ 2 = 8 ^ 2 + 9 ^ 2-2 (8) (9) * cos (x)\\144 = 64 + 81-144 * cos (x)\\144 = 145-144 * cos (x)\\-1 = -144cos (x)\\cos (x) = \frac {1} {144}\\x = cos ^ {- 1} (\frac {1} {144})\\x = 89.60 \ degrees[/tex]
Answer:
Option B
What is the 9 percent out of 600
✧･ﾟ: *✧･ﾟ:* *:･ﾟ✧*:･ﾟ✧
Hello!
✧･ﾟ: *✧･ﾟ:* *:･ﾟ✧*:･ﾟ✧
❖ 9% of 600 = 54
9/100 * 600 = 54
~ ʜᴏᴘᴇ ᴛʜɪꜱ ʜᴇʟᴘꜱ! :) ♡
~ ᴄʟᴏᴜᴛᴀɴꜱᴡᴇʀꜱ
9% out of 500
0.09* 500 = 45
45
15.755264 round to the nearest tenths
Answer:
15.8
Step-by-step explanation:
Rounding to the nearest tenths means we are focusing on the number 7 and the number after it- 5. Because it is a 5, we will round the number 7, one higher. If it were to be a 4, it would stay a 7.
Answer:
15.8 is the Answer
Step-by-step explanation:
1) 5 in the hundreds place will be turn to 6 due to the fact that in can round up because a 5 is in the thousandth place.
2) Since 6 is 5 and greater than 5 it will round up 7 in the tenths place to 8.
hopes this helps.
Convert 2.618 to degrees
Answer:
2.618 in Degrees Celsius is 36.7124 Degrees Fahrenheit. 2.618 in Degrees Fahrenheit is -16.323333 Degrees Celsius.
Function transformation which of the following is equal to g(x)?
Answer:
The answer is
g(x) = (x-3)^3
Step-by-step explanation:
We can easily solve this problem by plotting each equation with a graphing tool or calculator.
Please see attached graph
The correct answer is
g(x) = (x-3)^3
What is a theoretical and Experimental Probability?
Answer:
See below...
Step-by-step explanation:
Theoretical probability is the probability that something should happen based on the beginning conditions. Such as having a jar of 30 marbles with 5 being blue. The probability of pulling out a blue marble when selecting 1 marble is
5/30, or 1/6. Theoretically you should pull one blue marble out every 6 times you pull a marble out.
This isn't guaranteed to happen though, that's where experimental probability comes form.
Experimental probability is the number of desired outcomes achieved, divided by the total number of outcomes. This is based on what actually happened. Say you selected a marble, and put it back 10 times, recording the color each time and you got 2 blue marbles. Your experimental probability is
2/10, or 1/5, which doesn't match the theoretical probability. The more times this experiment is conducted, the closer your result will be to the theoretical probability
John deposited $2,860 in a bank that pays 9% interests, compounded monthly. Find the amount he will have at the end of 3 years?
Answer:
The amount he will have at the end of 3 years is $3742.73
Step-by-step explanation:
* The formula for annual compound interest is:
A = P (1 + r/n)^(nt)
Where:
A = Total money after t years
P = the investment amount (the initial deposited amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested
∵ P = $2860 ⇒ deposited
∵ r = 9% = 9/100 = 0.09 ⇒ annual rate
∵ n = 12 ⇒ compounded monthly
∵ t = 3 years
∴ A = 2860(1 + 0.09/12)^(12 × 3)
∴ A = 2860(1.0075)^36 = $3742.73
* The amount he will have at the end of 3 years is $3742.73
Answer:
The amount he will have at the end of 3 years = $3742
Step-by-step explanation:
Formula for compound interest
A = P[1 + R/n]^nt
A - Amount
P - Principle amount
R - rate of interest
n - Number of times in which the amount compounded
t - Number of years
To find the amount
Here,
P = $2,860, R = 9% = 0.09
n = 12 and t = 3 years
A = P[1 + R/n]^nt
=2860[1 + 0.09/12]^(12*3)
= 2860[1 + 0.0075]^36 = 3742.7257 ≈ $3742
Write a story problem about 40 apples and 17 pears
Final answer:
This story problem involves calculating the sales and remaining stock of 40 apples and 17 pears at Ms. Adams' farmer's market stand, applying basic arithmetic operations in a real-life scenario.
Explanation:
Imagine a local farmer's market where Ms. Adams has a stand selling fruits. This particular Saturday, she starts with 40 apples and 17 pears. Throughout the day, customers buy apples and pears at different rates. By midday, half of the apples were sold. An hour later, five customers each bought 2 pears. By the end of the day, Ms. Adams noticed she sold twice as many apples as pears.
Your task is to use this story to calculate:
How many apples did Ms. Adams sell?How many pears did she sell?How many of each fruit does she have left?This problem helps students practice basic subtraction, division, and multiplication within a real-world context, applying arithmetic operations to solve a practical problem.
Amelia used a $50 gift card to buy digital music online after playing for 16 songs her balance on the gift card was $30 what was the price of each song assuming all songs cost the same amount
The cost of each song is $1.25.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, Amelia used a $50 gift card to buy digital music online after playing for 16 songs her balance on the gift card was $30.
So, the cost of 16 song is 50-30=$20
Now, the cost of each song = 20/16
= 5/4
= $1.25
Therefore, the price of each song is $1.25.
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Need help with this problem.
Answer:
16 to 20 spells
Step-by-step explanation:
4 to 5 spells and you find how much you need to multiply it by and in this case it is 4. Take the 4 and multiply it to 5 and 4 and you will get your answer.
Answer:
25
Step-by-step explanation:
Luna casts 4/5 of the amount of spells that Ginny casts (busy witches), so you take 1/4 of 20 and add it to 20. In other words, add 20 + 5
(b+2) (b-9) idk what to doits called Multiplying Monomials and Polynomials
Answer:
b² - 7b - 18
Step-by-step explanation:
To multiply the factors.
Each term in the second factor is multiplied by each term in the first factor, that is
b(b - 9) + 2(b - 9) ← distribute both parenthesis
= b² - 9b + 2b - 18 ← collect like terms
= b² - 7b - 18
A certain gas station requires a minimum of $5 to use a debit card. You plan on buying a soda and however many bags of cheetos required to use your debit card. A soda costs $1.20 and bags of cheetos cost $1.40 each. Let x be the number of bags of cheetos you buy, and create an inequality that models the situation above
Answer:
1.20 + 1.40x ≥ 5, or $1.20 + $1.40x ≥ $5
Step-by-step explanation:
So since you are only buying 1 soda and you are buying multiple bags of Cheetos so you are able to use you debit card and meet the requirement of at least $5, you can make the inequality:
1.20 + 1.40x ≥ 5, or $1.20 + $1.40x ≥ $5
where x is the number of bags of Cheetos.
The average distance from the sun to Jupiter is 778 million km. The distance is 550 million km greater than the average distance from the sun to mars. Write and solve an equation to find the average distance that mars is from the sun (in millions of km)
The average distance from the sun to Mars can be found by setting up an equation based on the given information. Subtracting 550 from the average distance to Jupiter gives the average distance to Mars, which is 228 million km.
Explanation:We know that the average distance from the sun to Jupiter is 778 million km, which is 550 million km more than the distance from the sun to Mars. We could express it in the form of an equation and solve to find the average distance that Mars is from the sun. Let's denote that Mars is 'x' million km from the sun. Then we can write it as:
x + 550 = 778
To find x, we need to subtract 550 from both sides of the equation, which gives us:
x = 778 - 550
And so, the distance from the sun to Mars is x = 228 million km.
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What is the volume of this aquarium?
Answer:
2160 cm³
Step-by-step explanation:
The volume of a rectangular prism is calculated using the formula
V = lbh ( l is length, b is breadth, h is height )
here l = 18, b = 10 and h = 12, hence
V = 18 × 10 × 12 = 2160 cm³
Volume = l × b × h
= 18 × 10 × 12
= 2160cm³
Factor completly: x3 + 7x2 + 10x
[tex] {x}^{3} + 7 {x}^{2} + 10x \\ = x( {x}^{2} + 7x + 10) \\ = x( {x}^{2} + 5x + 2x + 10) \\ = x(x + 5)(x + 2)[/tex]
your answer is x(x+2)(x+5)
x3+7x2+10x
x3+7x2+10x
=x(x+2)(x+5)