The rectangular pool where Asha swims would need 4.6875 * 10⁸ cm³ of water to make it full.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The pool where Asha swims is rectangular. It is 2500 cm long, 1250 cm wide and 150 cm deep.
Hence:
Volume of the pool = 2500 * 1250 * 150 = 4.6875 * 10⁸ cm³
The rectangular pool where Asha swims would need 4.6875 * 10⁸ cm³ of water to make it full.
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Prove algebraically that the straight line with equation x =2y+5 is a tangent to the circle with equation x ² +y ²
The intersection point is only one. Then the equation of the line is tangent to the circle at point (1, -2).
What is a circle?It is a locus of a point drawn an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
Prove algebraically that the straight line with equation x = 2y + 5 is a tangent to the circle with equation x² + y² = 5.
x = 2y + 5 ...1
x² + y² = 5 ...2
If the intersection of the point of the circle and line is one. Then the line is tangent to the circle.
Then from equations 1 and 2, we have
(2y + 5)² + y² = 5
4y² + 25 + 20y + y² - 5 = 0
5y² + 20y + 20 = 0
5y² + 10y + 10y + 20 = 0
5y (y + 2) + 10(y + 2) = 0
(5y + 10)(y + 2) = 0
y = -2, -2
Then the value of y is unique then the value of x will be unique.
The value of x will be
x = 2(-2) + 5
x = -4 + 5
x = 1
The intersection point is only one. Then the equation of the line is tangent to the circle at point (1, -2).
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3X minus 2Y is equal to or greater than or equal to four
Answer:
3x- 2y
Step-by-step explanation:
its defintly not = to four because you cant subtract two diffrent varibles so it should be less then
A king decided to pay a knight one inch of gold for each day's protection on a 6-day trip. The king took a gold bar 6 inches long and paid the knight at the end of each day; however, he made only two cuts. How did he do this?
A king gives 1 inch per day to the knight as there are three pieces of length 1, 2, and 3 inches.
What is Algebra?Algebra is the study of mathematical symbols, and the rule is the manipulation of those symbols.
A king decided to pay a knight one inch of gold for each day's protection on a 6-day trip. The king took a gold bar 6 inches long and paid the knight at the end of each day.
The gold is divided into 2 parts.
First at the 1-inch mark, then the second mark will be
For the second mark, there are two conditions.
Condition 1 = mark can be made at 4 inches, then the next piece will be of 2 inches.
There will be a total of three pieces of 3 inches, 1 inch, and 2 inches.
Condition 2 = Mark can be made at 5 inches, then the next piece will be of 1 inch.
There will be a total of three pieces of 3 inches, 1 inch, and 2 inches.
The division is shown below.
The king will take 1 inch back from the knight and give him 2 inches.
According to the condition = A king gives 1 inch per day to the knight as there are three pieces of length 1, 2, and 3 inches.
So on the first day, 1 inch will be given. On the second day, he will give 2 inches and take 1 inch. On the third day, he will give 3 inches and take back 2 inches. On the fourth day, he will give 1 inch. On the fifth day, he will give 2 inches and take back 1 inch. On the sixth day, he will give 1 inch.
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Explain the meaning of the scale 1 :2.5
Could you help me with this for 50? points.
The diameter of a circle is 2 miles. What is the circle's area?
d=2 mi
square miles
Use 3.14 for л.
Answer:
A= 3.14
Step-by-step explanation:
The formula for finding the area of a circle is A=π r²
The radius = half of the diameter so that makes the radius 1 in this case.
When you plug in the values for the equation you get A= 3.14*1²
Answer:
3.14
Step-by-step explanation:
The Formula for area of a circle is л times r^2. R(radius) is half of D(diameter )in which this case is 1. So 1^2 = 1 times л which is 3.14. 3.14 times 1 = 3.14 as answer.
It takes 5 gardeners 48 hours to landscape a gArden how long w I'll it take 8 gardeners to landscape same garden
The time is taken by the 8 gardeners to landscape the same garden will be 30 hours.
What are ratios and proportions?A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.
It takes 5 gardeners 48 hours to landscape a garden.
Then the time taken by the 8 gardeners to landscape the same garden will be
The relationship between the gardeners and time is inversely proportional. Then we have
Let x be the time taken by the 8 gardeners. Then we have
8x = 5×48
x = 30 hours
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Identify the steps for proving ADDC.
A. 1. BD BD by the reflexive property
2. AABD=ACBD by SAS
3. ADDC by CPCTC
B. 1. BD BD by definition of an isosceles triangle
2. AABD = ACBD by SAS
3. ADDC by CPCTC
C. 1. BD BD by the reflexive property
2. AABD = ACBD by CPCTC
3. ADDC by SAS
D. 1. BD BD by definition of an isosceles triangle
2. AABD = ACBD by CPCTC
3. ADDC by SAS
hail 0.5 inch deep and weighing 1800 pounds covers a roof. the hails weight varies directly with its depth. write an equation that relates d and w. then predict the weight on the room of hail that is 1.75 inches deep
In a directly proportional relationship, increasing one variable will increase another. The weight of the roof whose depth is 1.75 inches is 6,300 pounds.
What is the directly proportional relationship?In a directly proportional relationship, increasing one variable will increase another. This directly proportional relationship between p and q is written as p∝q where that middle sign is the sign of proportionality.
Let there are two variables p and q. Then, p and q are said to be directly proportional to each other if p = kq, where k is some constant number called the constant of proportionality.
Given the hail's weight varies directly with its depth. Therefore, the relation can be written as,
Weight ∝ Depth
W∝D
Introducing the constant to remove the proportionality we will get the equation as,
W = kD
1800pounds = k × 0.5 inches
3600ponds/inches = k
Now, the weight of the roof whose depth is 1.75 inches can be written as,
W = kD
W = 3600 × 1.75
W = 6,300 pounds
Hence, the weight of the roof whose depth is 1.75 inches is 6,300 pounds.
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A conclusion that is proved to be true by deductive reasoning is called a theorem.
True
False
Answer:
True,
Step-by-step explanation:
In math we prove the theorem using known axioms in Math.
Answer: True
Step-by-step explanation:
Avery had $25.75 in her wallet. If she bought lunch with 87 dollars from her wallet, how much money did she have in her wallet
after lunch?
A. $16.00
B. $17.45
C. $17.00
D. $17.75
Answer is D even tho u typo it i still got it so u do 25.75 from 8.00 yw.
what is the exact value of cosC
Answer:
[tex]cosC = \frac{\sqrt{161} }{15}[/tex]
Step-by-step explanation:
[tex]cosC = \frac{\sqrt{161} }{15}[/tex]
CosC = adj/hyp
Solve for in each of the following statements. ( is the smallest positive integer to make each statement true.)
5+43≡ 9
18 − 12÷3≡ 5
3+5≡0 11
There is no variable unfortunately
We have to change question little bit
#1
5+43=9x9x=48x=48/9#2
Rest are also meaningless as there is no variable
#3
(3+5)x=0.118x=0.11x=0.11/87. In which step does a mistake first occur? 8÷2+ (3 x 3-2) Step 1: 8÷2 + (3 x 1) Step 2: 8÷2+3 Step 3: 4+3 Step 4: 7
Answer: Step 1
A mistake first happens in Step #1. PEMDAS is not followed correctly.
(PEMDAS = parentheses, exponents, multiplication, division, addition, subtraction)
When solving 8÷2+(3x3-2), you first move left to write and solve the problems working through the correct order of operations.
Correct Steps:
1) 8÷2 + (3x3-2)
2) 4 + (9-2)
3) 4 + 7
4) 4+7 = 11
Based on the picture below what would the genotypes of the parent plants be? Use the other questions to help you answer this.
Thank you so much.
Answer:
ant sorry you no entendía
What are the solutions to the following system?
-2x² + y = -5
y=-3x² +5
O (0, 2)
O (1,-2)
o o (12,-1) and (-√2-1)
(
o (V5,-10) and (-15.-10)
The solutions to the equation -2x² + y = -5 and y=-3x² +5 are (√2,-1) and (-√2-1) option third is correct.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
We have given expressions:
-2x² + y = -5 ..(1)
y=-3x² +5 ...(2)
From the equation (2) take the value of y and plug it in the equation (1)
-2x²-3x²+5 = -5
-5x² = -10
x = ±√2
Plug this value in the equation (2), we get value of y:
y = -1
Thus, the solutions to the equation -2x² + y = -5 and y=-3x² +5 are (√2,-1) and (-√2-1) option third is correct.
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please help me do my mathematics assignment experts
Step-by-step explanation:
try this option, note: 1) task 'd' is solved only; 2) the answer is marked with green colour.
Bao owns a small business selling used books. She knows that in the last week 60 customers paid cash, 3 customers used a debit card, and 27 customers used a credit card.
Based on these results, express the probability that the next customer will pay with a credit card as a fraction in simplest form.
Answer:
It would be a 3/10 or 30% chance.
Answer:
Step-by-step explanation:
3/10 or .30 or30%
You work at a restaurant and the head manager has sent you to purchase livestock for an experiment. You want to grow the meat for the food right at the restaurant. You have been given 500 gold coins to spend at the store to purchase the livestock. Each sheep costs 12 gold coins, while each chicken costs seven.
If you purchase 32 sheep, how many chickens can you buy? Show all of your work. Hint: you don’t have to spend every coin.
Write an inequality that represents this situation.
If you want to buy twice as many chickens as sheep, what is the maximum number of sheep you can buy? Show all of your work.
Make a graph of the inequality from #2. Remember to label all parts of the graph. Label the intercept points.
Part 2: The animals you bought for the restaurant are doing quite well. You purchased an initial flock of 30 sheep and 20 chickens. The chickens and sheep have been breeding very successfully, and the flocks are growing. The sheep breed at a rate so that they will double every year. The chickens breed faster than the sheep (it helps when you can lay multiple chicks from one hen at a time!) The population of the chickens multiplies by 2.2 each year. (For all of these problems round to the nearest animal.)
5. How many sheep will there be in five years? Show all of your work.
6. Create an exponential equation to represent this situation.
7. How many chickens will there be in eight years? Show all of your work.
8. Create an exponential equation to represent this situation.
9. During what year will there be more chickens than sheep? Show your work or explain how you know.
10. Plot the two curves on a graph together. Remember to label all parts of the graph.
11. What is the domain of each function?
12. What is the y-intercept for each function? Explain what this number means in the context of this situation.
13. Your field can support a maximum of 3000 animals before you run out of vegetation and space. During what year will you need to purchase more land to house the animals?
The number of chickens is 16 if you purchase 32 sheep and inequality is 12x + 7y ≤ 500.
What is an exponential function?
It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]
where 'a' is a constant and a>1
Total coins = 500 gold coin
Each sheep costs 12 gold coins, while each chicken costs 7 gold coins.
If purchased 32 sheep, so the total cost for the 32 sheep:
= 32×12
= 384
Remaining gold coin = 500 - 384 = 116 gold coin
Number of chicken can purchase in 166 gold coin = 116/7 = 16.57 ≈ 16
Inequality for the above scenario:
Let x be the number of sheep and y be the number of chickens.
12x + 7y ≤ 500
If you want to buy twice as many chickens as sheep.
y = 2x
12x + 7y = 500
After solving both the equation:
x = 19.23 ≈ 19 (Number of sheep)
y = 38 (double the number of sheep)
For the part 2:
The exponential equation for the sheep:
[tex]\rm y = 30(2)^x^-^1[/tex]
After 5 years, plug x = 5
[tex]\rm y = 30(2)^4[/tex]
y = 480 sheep
The exponential equation for the chicken:
[tex]\rm y = 20(2.2)^x^-^1[/tex]
After 8 years, plug x = 8
[tex]\rm y = 20(2.2)^7[/tex]
y = 4988.71 ≈ 4988 chickens
Similarly, you can find the rest of the data using the above equation.
Thus, the number of chickens is 16 if you purchase 32 sheep and inequality is 12x + 7y ≤ 500.
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1. Kyle put $300 of his birthday money in the bank. The bank offers an annual interest rate of 4%, compounded twice a
year. How much money will Kyle have after three years?
Answer:
300(1 + 0.04/2)3(2) = $337.85
Step-by-step explanation:
The cylinder shown has a volume of 30 cubic units. The
cone and the cylinder have the same height and the same
base. What is the volume of the cone?
S.
Cylinder. V = Th
Cone: V = : 1 / ²
Please help no links or you will get reported
The volume of the cone will be 10 cubic units.
What is volume?Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width and height of the cube or cuboid.
Given that:-
The cylinder shown has a volume of 30 cubic units.The cone and the cylinder have the same height and the same base.The volume of the cone will be:-
Vc = Vcyl
[tex]\dfrac{1}{3} \pi r^2h\ \ \ =\ \ \pi r^2h[/tex]
Vc = (1 / 3) Vcyl
Vc = ( 1 / 3 ) x 30
Vc = 10 cubic units
Therefore the volume of the cone will be 10 cubic units.
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A race course is 26.2 miles long. Of the entire race course, 5% is uphill. How many miles of the race course are uphill?
Answer:
1.31 miles of the race course are uphill
Step-by-step explanation:
Divide 5 × 26.2 miles by 100 and you'll get 1.31 miles.
Hope this helped :)
Consider a fictitious company, Teslala, that produces a single type of electronic vehicle, Model Z. The demand for Model Z depends on the gasoline price (q) because customers tend to purchase an electronic vehicle as a substitute for vehicles that run on gasoline when the gasoline price increases. The demand for Model Z is estimated as D(p) = 180 + 10q - 4p, where p is the price of Model Z. Consider the following two statements: 1. If the average gasoline price q increases by $1, the revenue-maximizing price p" increases by $X 2. If the average gasoline price q increases by $1, the demand at the revenue- maximizing price (i.e., D(p*)) increases by a factor of Y What is X/Y?
The ratio X/Y for the fictitious company, Teslala, that produces a single type of electronic vehicle, Model Z is 10/pY.
What is a mathematical model?A mathematical model is the model which is used to explain the any system, the effect of the components by study and estimate the functions of systems.
Consider a fictitious company, Teslala, that produces a single type of electronic vehicle, Model Z.
The demand for Model Z depends on the gasoline price (q) because customers tend to purchase an electronic vehicle as a substitute for vehicles that run on gasoline when the gasoline price increases.
The demand for Model Z is estimated as
[tex]D(p) = 180 + 10q - 4p[/tex]
Here, p is the price of Model Z.
Consider the following two statements:
1. When the average gasoline price q increases by $1, the revenue-maximizing price p" increases by $X.[tex]D(p) = 180 + 10q - 4p\\D(p) = 180 + 10(q+1) - 4(p+X)[/tex]
2. When the average gasoline price q increases by $1, the demand at the revenue-maximizing price (i.e., D(p*)) increases by a factor of Y.[tex]D(p)+Y = 180 + 10q - 4p\\(D(p)+Y) = 180 + 10(q+1) - 4(p+X)\\Y= 180 + 10(q+1) - 4(p+X)-D(p)\\[/tex]
Put the value of demand at the revenue-maximizing price as,
[tex]Y= 180 + 10(q+1) - 4(p+X)-(180 + 10q - 4p)\\Y= 180 + 10q+10 - 4p-pX-180 - 10q + 4p\\Y= 10 -pX\\1=\dfrac{10}{Y}-\dfrac{pX}{Y}\\\dfrac{10}{Y}=\dfrac{pX}{Y}\\\dfrac{10}{pY}=\dfrac{X}{Y}[/tex]
Thus, the ratio X/Y for the fictitious company, Teslala, that produces a single type of electronic vehicle, Model Z is 10/pY.
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Reid, the second-place finisher, developed a cramp with 3 tenths of the race remaining. How many miles did Reid run without a cramp?
Answer:
He ran .7 miles without a cramp
Step-by-step explanation:
A water park has pools, slides, and rides
that, in total, make use of 4.6 x 10^5
gallons of water. They plan to add a ride
that would make use of an additional
6.7 x 10^4 gallons of water. Use scientific
notation to express the total gallons of
water made use of in the park after the
new ride is installed.
Answer:
5.27×10^5 gallons
Step-by-step explanation:
Adding numbers in scientific notation requires that their powers of ten match. Here, we can rewrite the smaller number so its power of ten matches that of the larger number.
__
4.6×10^5 +6.7×10^4
= 4.6×10^5 + 0.67×10^5
= 5.27×10^5
The park will use 5.27×10^5 gallons of water after the new ride is installed.
__
This kind of calculation can be done easily by your scientific calculator or a spreadsheet. You may have to set the display mode to scientific notation.
help will mark Brainliest
How do you simplify this problem?
Answer:
x/y.
Step-by-step explanation:
Deal with each number or letter at a time:
3 / 3 = 1
x^3/x^2 = x
y^4 / y^5 = y^-1 = 1/y
z / z = 1
So the answer is 1*x * 1/y * 1
= x/y.
If cos43=p, determine.without the use of a calculator,the value of each of the following in terms of p
We need to calculate the value of cos(43) to determine the value of p
How to evaluate the expression?The equation is given as:
cos43 = p
Rewrite properly as:
cos(43) = p
Rewrite the equation as:
p = cos(43)
The above means that we simply calculate the value of cos(43) to determine the value of p
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A rectangular park has a perimeter of 374 feet and a length of 65 feet.
What is the width of the park?
Answer: 122
Step-by-step explanation:
▪︎ Perimeter = (width + length) * 2
374 = (width + 65) * 2
width + 65 = 374 / 2
width + 65 = 187
width = 187 - 65
width = 122
∆ABC is mapped to ∆A'B'C' using each of the given rules in the table below. Place a checkmark in the correct column for each mapping to state if the resulting mapping would make ∆ABC congruent or not congruent to ∆A'B'C'.
∆ABC is congruent to ∆A^' B^' C'
∆ABC is NOT congruent to ∆A^' B^' C'
(x,y) → (x+5,y)
(x,y) → (5x,5y)
(x,y) → (.5x,.5y)
(x,y) → (x,-y)
(x,y) → (-x,-y)
For reference you can look at the attachment
I have taken three points (1,1),(2,1),(3,3)Then converted them accordingly
#1(Graph 2)
Yes#2(Blue dots on graph 1)
NoThey are similar but not equal
#3(Purple dots)
NoSimilar but not equal
#4(Green dots)
Yes#5(Black dots)
Yes