Final answer:
To find the quadratic equation that models the depth of the Pythagorean Sea, we apply given conditions to the standard form y = ax^2 + bx + c. Solving for coefficients, we then identify the vertex of the parabola to find the deepest point of the sea. Finally, we calculate the depth at this point by substituting the vertex into the equation.
Explanation:
Finding the Particular Quadratic Equation and Depth of the Sea
To find the particular quadratic equation for the depth of the Pythagorean Sea as a function of its width, we can begin by assuming the standard form of the equation:
y = ax^2 + bx + c,
where y represents the depth in meters, and x is the horizontal distance from the shore in meters. Given that the sea's width is 1000 meters and at 200 meters from the shore the depth is 20 meters, we can establish some conditions.
At x = 0 (shoreline), the depth is 0: hence, c = 0.At x = 200 meters, the depth is y = 20 meters.At x = 1000 meters (opposite shoreline), the depth should return to 0.By substituting these conditions into the equation, we can solve for a and b to determine the complete equation. Once we have the equation, the depth's maximum (the deepest part of the sea) will occur at the vertex of the parabola, which is at x = -b/(2a).
Once we find the deepest point, we can calculate its depth by substituting back into the equation.
Answer:
equation: y = 0.0005x²
maximum depth: 500 m
Step-by-step explanation:
Equation for a quantity that changes quadratically with another quantity:
y = kx²
where x = width, and y = depth.
For x = 200, y = 20.
20 = k(200²)
k = 20/(40000)
k = 0.0005
The equation is
y = 0.0005x²
The width is 1000 m.
For 1000 m, x = 1000
y = 0.0005x²
y = 0.0005(1000²)
y = 500
Answer:
equation: y = 0.0005x²
maximum depth: 500 m
If prices increase at a monthly rate of 1.2%, by what percentage do they increase in a year?
Final answer:
To calculate the annual increase from a monthly rate of 1.2%, use the compound interest formula to calculate the compounding effect over 12 months, resulting in an annual increase of approximately 15.47%.
Explanation:
The question asks about the annual percentage increase if prices increase at a monthly rate of 1.2%. The calculation involves compounding the monthly increase over the course of a year. To find the total percentage increase for the year, the formula for compound interest can be used, which is [tex](1 + r)^n[/tex], where r is the monthly increase rate, and n is the number of periods (months in a year).
Steps to Calculate Annual Increase:
Convert the monthly percentage increase to a decimal by dividing by 100: 1.2% / 100 = 0.012.
Add 1 to the monthly rate: 1 + 0.012 = 1.012.
Raise this sum to the power of 12, since there are 12 months in a year: [tex]1.012^{12[/tex].
Subtract 1 from the result to find the annual increase rate in decimal form.
Multiply by 100 to convert back to a percentage.
When we do the math, it turns out the prices increase by approximately 15.47% over the course of a year, when compounded monthly at a rate of 1.2%.
Prices increase by 1.447% in a year when the monthly increase is 1.2%.
Explanation:To calculate the percentage increase in a year, we need to calculate the total increase over 12 months. Since prices increase at a rate of 1.2% per month, we can calculate the total increase over 12 months as follows:
1.012 x 1.012 x ... x 1.012 (12 times) = 1.01447
The total increase is 1.01447, which is equivalent to a 1.447% increase over the course of a year.
How many two-digit positive integer less than 25 have the property that they are divisible by each of their digits? List themZ
1/3(−32.48−14.02) Enter your answer, as a decimal to tenths, in the box
Alexandra earns $125 from her paper route each month, but she spends about $20 each month on personal expenses to pay for a school trip that costs $800 about how many months does she need to save money? Explain
Alexandra will need approximately 8 months to save enough money for the school trip.
To calculate the number of months Alexandra needs to save money for her school trip, we'll first find out how much she saves each month after deducting her personal expenses.
Monthly earnings from paper route: $125
Monthly personal expenses: $20
Monthly savings = Earnings - Expenses
Monthly savings = $125 - $20
Monthly savings = $105
Now, let's determine how many months it will take for Alexandra to save enough money for the trip.
Total cost of the school trip: $800
Number of months needed = Total cost of trip / Monthly savings
Number of months needed = $800 / $105
Number of months needed ≈ 7.62
Therefore, Alexandra will need approximately 8 months to save enough money for the school trip.
Each month, Alexandra earns $125 from her paper route. After deducting her personal expenses of $20, she saves $105 per month. Since the school trip costs $800, we divide the total cost of the trip by her monthly savings to find out how many months she needs to save. The result is approximately 7.62, so we round up to 8 months. Therefore, Alexandra needs 8 months to save enough money for the school trip.
Complete question:
Alexandra earns $125 from her paper route each month, but she spends about $20 each month on personal expenses to pay for a school trip that costs $800 about how many months does she need to save money? Explain
Weekly math review-Q1.6
The subject of this question is Mathematics, specifically involving basic algebra and arithmetic. Students are required to apply the math principles given in the example boxes throughout the chapter.
Explanation:The subject of this question is Mathematics. It involves basic algebra and arithmetic to solve mathematical problems and apply the principles given in the example boxes throughout the chapter. The question likely requires students to use their math skills to solve a specific problem or answer a mathematical question.
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1. Translate the variable expression into a word phrase: 4b – 2
Translate the word phrase into a variable expression:
2. the sum of 16 and 4 times a number
3. Write an equation for the following word problem. Use b for the number of boys and g for the number of girls.
There are eight fewer boys than girls in Mrs. Davis' class. How many boys are in the class?
4. Will the standard form 3.2 × 10–4 be more or less than 1? Explain what effect the negative exponent has.
5.Use a five-step plan to solve the following word problem. Show all five steps in your response:
Doug is twice Anne's age. Doug is 34 years old. How old is Anne?
Answer:
1) The difference between four times the number b and 2.
2) 16 + 4*x
3) if there are 8 fewer boys than girls in the class, then g - b = 8, so the number of boys is: b = g - 8
4) 3.2*[tex]10^{-4}[/tex] is less than 1 because of the negative exponent, the expression is equivalent to 3.2/10000 = 0.00032 < 1
5) Ok, Dough is twice Anne's age. so if D is Dough's age, and A is Anne's age:
D = 2*A
and D = 34
then 34 = 2*A
if we divide both sides by 2, we get
34/2 = 2*A/2
17 = A
Anne is 17 years old.
use the distributive property to write the following expression in an equivalent form:6× (10+25)
Karen can paint a wall in 2.5 hours. Stephanie takes 1.25 hours to paint the same size wall. How many minutes will it take for Karen and Stephanie to paint the same wall?
A group of 11 people are going to the movies one Saturday. Adults' tickets cost $11.50 each and children's tickets cost $7.25 each. If the total cost for admission to the movies is $105.25, how many children attended the movie?
Answer: 5
Step-by-step explanation:
Let x be the number of adults and y be the number of children going to the movies one Saturday.
Given : A group of 11 people are going to the movies one Saturday.
[tex]x+y=11----------------(1)[/tex]
Adults' tickets cost $11.50 each and children's tickets cost $7.25 each.
The total cost for admission to the movies is $105.25.
i.e. [tex]11.50x+7.25y=105.25-----------------(2)[/tex]
Multiply equation (1) by 11.5 , we get
[tex]11.5x+11.5y=126.5---------------------(3)[/tex]
Subtract equation (2) from (3), we get
[tex]4.25y=21.25\\\\ y=\dfrac{21.25}{4.25}=5[/tex]
Put value of y= 5 in (1), we get
[tex]x+5=11\\\\ x=11-5=6[/tex]
Hence, 5 children attends the movie.
Compare 9.75, 9.7, 9.675
A decimal is a number that consists of a whole and a fractional part.
Comparing the given decimal values from smallest to greatest we get,
9.675 < 9.700 < 9.750
What is a decimal number?A decimal is a number that consists of a whole and a fractional part.
It lies between integers and represents numerical value for quantities that are whole plus some part of a whole.
We have,
9.75, 9.7, 9.675
We can write from smallest to greatest values.
We can make the given decimal values in tenths, hundredths, and thousandths place values.
Let's write all the given decimal numbers till the thousandth place value as:
9.75 can be written as 9.750
9.7 can be written as 9.700
9.675 is already in the thousandth place value.
Comparing from smallest to greatest we have,
9.675 < 9.700 < 9.750
Thus,
Comparing the given decimal values from smallest to greatest we get,
9.675 < 9.700 < 9.750
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2w + 5 = 4w + 13
What it is w?
Which is a simplified form of the expression -(z + 1) + 2(z – 2)?
A. -z – 5
B. 3z – 3
C. z – 5
D. 2z – 5
I honestly need help tho.
Answer:
The answer is C
Step-by-step explanation:
Which of the following equations describe the line (-6, 2) (-1, -4)? (Graph below)
A. y - 4 = -5/6(x - 1)
B. y - 2 = -5/6(x + 6)
C. y + 4 = -6/5(x + 1)
D. y + 4 = -5/6(x + 1)
E. y - 2 = -6/5(x + 6)
F. y - 6 = -6/5(x + 2)
Answer: c.
Step-by-step explanation:
Graph this function:
y= 5x - 18
write a system of equations that has (2,7.5) as its solution
My question is up above
2 to the power of 14
Sandy is organizing her bedroom she found 6 jar filled with pennies if each gar has 4,560 pennies how many pennies does sandy have in all?
If each jar is full of 4,560 pennies, then the answer is 27,360 pennies in all.
4560*6=27360
Hope this helps.
Answer:
sandy has 4566
Step-by-step explanation:
Describe a Situation with two quantities that have proportional Linear relationship
Let d denote the distance covered(in km) over the time t(in hours) with a speed of 10 km/h.
This means that the with the increasing time the distance covered will also increase.
Hence, the two variables i.e. distance and time are directly proportional to each other and also the equation which describes this relationship is given by:
d=10t
Also, the relationship is Linear.
Since, the equation is linear which relates the two variable.
Which polygons are congruent?
Select each correct answer.
The required pairs of triangles in A and D are congruent triangles.
What are congruent triangles?Congruent triangles are two triangles that have the same shape and size. In other words, they are identical in every way, including their angles and side lengths. When two triangles are congruent, their corresponding sides and angles are equal.
Here,
Congruent triangles are important in geometry because they have many useful properties and can be used to solve a variety of problems. For example, if two triangles are congruent, then any corresponding parts (such as their altitudes, medians, or angle bisectors) will also be congruent. This can be helpful in finding missing side lengths or angles of a triangle.
Thus, from the above definitions Pairs of triangles in A and D are congruent triangles.
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A healthy human heart beats about 1,533,000 times in a year. A sparrow's heart beats about 241,776,000 times in a year. About how many times faster does the sparrow's heartbeat compared to the human heart?
A. 2×1082×106=1×102or about 100 times faster
B. 2×1092×106=1×103or about 1,000 times faster
C. 2×1082×105=1×103or about 1,000 times faster
D. 2×1092×105=1×104or about 10,000 times faster
Answer:A
Step-by-step explanation: if you count the places, it’s 10 to the 8th power and 10 to the 6th power so that makes it A
The sparrow's heart beats approximately 158 times faster than a human heart. None of the options provided (A, B, C, or D) match this calculation.
Explanation:To find how many times faster the sparrow's heartbeat is compared to the human heart, you divide the number of times the sparrow's heart beats by the number of times a human heart beats. Thus, you would perform 241,776,000 ÷ 1,533,000. The result of this division is approximately 157.7, which means that the sparrow's heart beats about 158 times faster than a human heart.
None of the options provided in the question (A, B, C, or D) match this result, indicating there may be a mistake. Always remember, the correct way to compare in such circumstances is to do division, and not multiplication or addition.
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A piece of paper is 0.00075 inches thick. How many sheets of paper will be in a stack that is 2.25 inches high
is 3.02859 is a rational number
each bag of pattern blocks contains 50 block. to make a class pattern, the teacher combines 4 bags of blocks. how many pattern blocks are there?
If h(x)=(f o g) (x) and h(x)=3(x+2)^2, find find one possibility for f(x) and g(x)
Answer:
[tex]f(x)= 3x^2[/tex] and [tex]g(x)= x+2[/tex]
Step-by-step explanation:
[tex]h(x)=(f o g) (x)[/tex]
[tex]h(x)=3(x+2)^2[/tex]
[tex](f og)(x) = f(g(x))[/tex]
g(x) is the inside function and f is the outside function
To get g(x) , we need to find the inside function in h(x)
[tex]h(x)=3(x+2)^2[/tex]
Inside function is x+2
So g(x) is x+2
when g(x)= x+2 then f(x) is [tex]3x^2[/tex]
So [tex]f(x)= 3x^2[/tex] and [tex]g(x)= x+2[/tex]
Find all the angle measures showing all work. Which property are you using to set up your equations?
The angle measures is equivalent to 23 degrees.
Vertically opposite angles are equal
How to determine the angleTo determine the angle, we have to know that vertically opposite angles are equal and angles on a straight line equal 180 degrees
Then, we can say that;
<1 = 3
< 2 = < 4
Substitute the expressions, we have;
x + 16 = 4x - 5
collect the like terms, we have;
x - 4x = -5 - 16
subtract the values, we get;
-3x = -21
divide by the coefficient, we have;
x = 7
Then, we can say;
<1 = <2 =< 3 = < 4
= 23 degrees
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what is the ratio of 3√x4
How many solutions can be found for the linear equation? 4(x + 5) - 5 = 8x + 18/ 2
A)no solutions
B)one solution
C)two solutions
D)infinitely many solutions
Answer: The correct option is A.
Explanation:
The given equation is,
[tex]4(x+5)-5=\frac{8x+18}{2}[/tex]
Multiply both sides by 2.
[tex]2[4(x+5)-5]=\frac{8x+18}{2}[/tex]
[tex]8(x+5)+2(-5)=8x+18[/tex]
[tex]8x+40-10=8x+18[/tex]
[tex]8x+30=8x+18[/tex]
Subtract both sides by 8x.
[tex]30=18[/tex]
This statement is false for any value of x, therefore the system of equation have no solution and option A is correct.
Answer:
Option A is correct
No solutions
Step-by-step explanation:
The distributive property says that:-
[tex]a \cdot (b+c) = a\cdot b+ a\cdot c[/tex]
Given the equation:
[tex]4(x+5)-5 = \frac{8x+18}{2}[/tex]
Using distributive property we have;
[tex]4x+20-5 = \frac{8x+18}{2}[/tex]
⇒[tex]4x+15= \frac{8x+18}{2}[/tex]
Multiply both sides by 2 we have;
[tex]8x+30 = 8x+18[/tex]
Subtract 8x from both sides we have;
[tex]30=18[/tex] False.
For any value of x, there is no solutions for the given system of equation
Therefore, No solution can be found for the linear equation
3. A recipe calls for 1 1/2 cups of flour, 3/4 a cup of white sugar, and 1/8 a cup of brown sugar. (a) How many total cups of ingredients are there? Show your work using a number line. (b) Which of the following mixing bowls can you use to make the recipe: 2-cup, 3-cup, or 4-cup?
Answer:
a) 19/8
b) 3 cup since it's 2.4
Can anyone help me find the slope??
Answer:
The slope is -3/4
Explanation:
To find the slope of a line, you can use the "rise over run" method where you count how many units from one point to the next the line increases or decreases along the y-axis and place this number in the numerator of a fraction; then, count how many units to the left or right that same point is along the x-axis and place this number in the denominator. Simplify if necessary and that becomes the slope.
So, assuming each tick on the axes is 1 unit, to get from the leftmost point to the rightmost point, we go down 3 units on the y-axis ("rise" -3 units) and to the right 4 units ("run" 4 units). Therefore, the slope is -3/4
The method I like to use the most because it involves the actual math of finding a slope is plugging plotted points into the slope formula. The slope formula is [tex]\frac{Y2 - Y1}{X2 - X1}[/tex] where two points along the line (X1, Y1) and (X2, Y2) are used.
Again, assuming, each tick is 1 unit, the plotted points on the line in the image are (-2, 2) and (2, -1). Now, we plug these ordered pairs into the formula and solve:
[tex]\frac{Y2 - Y1}{X2 - X1} = \frac{-1 - 2}{2 - (-2)} = \frac{-3}{2 + 2} = \frac{-3}{4}[/tex]
Therefore, the slope is -3/4