The Pythagorean theorem is applied to a right triangle with the longer leg being one inch longer than the shorter leg and the hypotenuse being nine inches longer than the shorter leg. The side lengths of the triangle are found to be 5 inches, 6 inches, and 14 inches.
Explanation:The subject of this question is mathematics, specifically the part of geometry that deals with right triangles and the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c), is equal to the sum of the squares of the other two sides (a and b), i.e., a² + b² = c².
In this problem, the longer leg (a) is represented as b = a + 1 and the hypotenuse (c) as c = a + 9. If you substitute these two equations into the Pythagorean theorem, you get (a + 1)² + a² = (a + 9)². Solving this equation gives a = 5 inches.
Substituting a = 5 inches into the expressions for b and c, we get b = 6 inches and c = 14 inches. Therefore, the sides of the triangle are 5 inches, 6 inches, and 14 inches.
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Write 247.903 in expanded form
Answer:
The answer is
247.903=200.000+47.000+7.000+0.900+0.003
Step-by-step explanation:
In order to determine the expanded form, we have to know about the rule. The expanded form is a way of writing numbers to see the math value of individual digits. When numbers are separated into individual place values and decimal places they can also form a mathematical expression.
For example:
6.432 in expanded notation form is 6.000 + 0.400 + 0.030 + 0.002
In this case:
247.903=200.000+47.000+7.000+0.900+0.003
F 100 tires are randomly selected for shipment to an outlet what is the probability that they are all good?
Suppose you want to build a fish tank in the shape of a right rectangular box with square base and no top which will hold 6 cubic feet of water. the glass for the sides costs $1 per square foot, and the metal for the bottom costs $1.50 per square foot. what dimensions for the tank will minimize the cost?
Which ratio is equivalent to 4/7 with greater terms?
A cylindrical chemical storage tank mush have a height 4 meters greater than the radius of the top of the tank. determine the radius of the top and the height of the tank if the tank must have a volume of 15.71 cubic meters
Final answer:
To determine the radius and height of the cylindrical tank with a given volume of 15.71 cubic meters, where height is 4 meters greater than the radius, we use the volume formula for a cylinder, resulting in a cubic equation that must be solved.
Explanation:
The question asks for the radius of the top and the height of a cylindrical tank with a volume of 15.71 cubic meters, where the height is 4 meters greater than the radius. The formula for the volume of a cylinder is V = πr²h, where V is volume, r is radius, and h is height. Since h = r + 4, we can write the equation in terms of r as V = πr²(r + 4).
To find the radius, we substitute the given volume, 15.71 m³, into the equation:
15.71 = πr²(r + 4)
This results in a cubic equation which we need to solve to find the value of r. After solving (which may require numerical methods or approximations due to the complexity of cubic equations), we find the value of the radius and can then determine the height by adding 4 meters to the radius.
Bronson builds a rectangular deck for his friend. the width of the deck is 29 feet. the perimeter of the deck must be at least 134 feet.
a. write an inequality that represents all possible values for the length of the deck.
b. find all possible values for the length of the deck.
Simplify sec(arcsec 1/2).
A. undefined
B. -1/2
C. 1/2
D. 2
Simplify the expression. –10z – 28z
18
18z
–38z
38z
What is the transformation of C(9, 3) when dilated by a scale factor of 3, using the origin as the center of dilation?
The transformation of C(9, 3) when dilated by a scale factor of 3, using the origin as the center of dilation is:
C'(27,9)
Step-by-step explanation:Dilation transformation--
A dilation transformation is a transformation which changes the size of the original figure but the shape remain unchanged.
i.e. if any figure is dilated by a scale factor k with the center of dilation as origin.
Then the change pr transformation in each of the vertices of the figure is given by:
(x,y) → (kx,ky)
We are given a point C which is located at C(9,3)
Hence, here k=3
Hence, we get:
C(9,3) → C'(9×3,3×3)
i.e. C(9,3) → C'(27,9)
A password is 4 characters long and must consist of 3 letters and 1 of 10 special characters. If letters can be repeated and the special character is at the end of the password, how many possibilities are there?
1st digit = 1 of 26 letters
2nd digit = 1 of 26 letters
3rd digit = 1 of 26 letters
4th digit = 1 of 10 special characters
26 x 26 x 26 x 10 = 175,760 possibilities
PLEASE HELP ASAP WILL GIVE 30 POINT FOR WHOEVER ANSWER IT AND WILL MARK BRAINIEST
Look at the cups shown below (images are not drawn to scale):
A cone is shown with width 3 inches and height 6 inches, and a cylinder is shown with width 3 inches and height 5 inches
How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tenth.
The total amount of money in a savings account after t years is given by the function A=1000(1.023)^t .
How could this function be rewritten to identify the monthly interest rate?
What is the approximate monthly interest rate?
Drag and drop the choices into the boxes to correctly complete the table. If a value does not match, do not drag it to the table.
Function Monthly interest rate
A = 1000(1 + 0.023)^12t
A = 1000(1.023^12)^t/12
A = 1000(1.023^t/12)^12t
0.23%
0.19%
0.31%
Answer:
[tex]A=1000(1+\frac{0.023}{12})^{12t}[/tex]
Rate of interest (r) = 0.19% monthly
Step-by-step explanation:
Given: The total amount of money in a saving account after t years.
[tex]A=1000(1.023)^t[/tex]
Formula:
[tex]A=P(1+r)^t[/tex]
Now we compare this formula with with given model.
P=1000
Rate of interest annually (r) = 0.023
Time = t
We need to change into monthly interest
New rate will divide by 12
New time will multiply by 12
[tex]r=\frac{0.023}{12}=0.0019[/tex]
[tex]t=12\times t =12t[/tex]
Function for monthly rate
[tex]A=1000(1+\frac{0.023}{12})^{12t}[/tex]
Rate of interest (r) = 0.19% monthly
[tex]\text{Thus, Function Monthly interest rate: }A=1000(1+\frac{0.023}{12})^{12t}\text{ and Monthly Interest rate }= 0.19\%[/tex]
Jessica is filling glasses with water. Each glass holds 3/5 cup of water. She pours 4 1/5 cups of water into the glasses. How many glasses does she fill with water? Enter your answer in the box.
Answer:
7 glasses
Step-by-step explanation:
Given: Jessica is filling glasses with water. Each glass holds [tex]\frac{3}{5}[/tex] cup of water. She pours [tex]4\frac{1}{5}[/tex] cups of water into the glasses.
To find: The number of glasses she fill with water.
Solution:
Each glass holds [tex]\frac{3}{5}[/tex] cup of water.
She pours [tex]4\frac{1}{5}[/tex] cups of water into the glasses.
To find the number of glasses she fill with water, we need to divide the total volume of water with the volume in each glass.
So, the number of glasses she fill with water can be calculated as
[tex]=\frac{4\frac{1}{5}}{\frac{3}{5}}[/tex]
[tex]= \frac{\frac{21}{5}}{\frac{3}{5} }[/tex]
[tex]=\frac{21}{5}\times\frac{5}{3}[/tex]
[tex]=\frac{21}{3}[/tex]
[tex]=7[/tex]
So, she can fill 7 such glasses with water.
Can somebody tell me if this is factorable? I've been trying this with a friend and we can't come up with any numbers. x^2 + 9x - 4
how would solve 2s + s = 36
Each pair of points lies on a line with the given slope. Find y. (2,2), (5,y); slope: 2
The perimeter of an isosceles triangle is 7.5m, and the length of a leg is 2m. Find the length of the base.
As per linear equation, the length of the base is 3.5m.
What is a linear equation?A linear equation is an equation that has the highest power of the variable as 1.
Given, the perimeter of an isosceles triangle is 7.5m.
The length of a leg is 2m.
Therefore, the length of the other leg is 2m.
Let, the length of the base is 'x'.
Therefore, [tex](2 + 2 + x) = 7.5[/tex]
⇒ [tex]4 + x = 7.5[/tex]
⇒ [tex]x = 7.5-4[/tex]
⇒ [tex]x = 3.5[/tex]
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which factorization is equivalent to 6x squared + 7x - 10?
Vector's map has the scale missing. He knows that the distance for the lake to the youth center is 8 miles. On the map, they are two inches apart. What is the scale for Vector's map
Answer:
The scale factor is 1/4.Step-by-step explanation:
Givens
The actual distance from the lake to the youth center is 8 miles.On the map, the distance is 2 inches.According to the problem, each 2 inches are equivalent to 8 miles of actual distance.
The scale factor can be found by dividing
[tex]s=\frac{2}{8}=\frac{1}{4}[/tex]
Therefore, the scale factor of Vector's map is 1/4, because the actual distance is 4 times bigger.
Factor the expression completely over the complex numbers.
y4−16
Solve for n: 21k − 3n + 9p > 3p + 12
Answer: n<7k+2p-4
Step-by-step explanation:
Determine the correct equation for the following verbal sentence: The total distance traveled, d, at a constant speed of 45 miles per hour is the product of the speed and the number of hours traveled, h. a. d = h + 45 c. 4072-01-01-03-00_files/i0210000.jpg b. d = 45h d. d = 45 - h Please select the best answer from the choices provided A B C D
Your answer is B..........
Write the inverse function for the function,f(x)=1/2x+4then, find the value of ƒ-^1(4) type your answers in the box
The inverse function of the above function is f(x) = 2x - 8 and therefore the function at 4 would be equal to 0.
You can find the inverse of any function by switching the f(x) and x terms. Once you have done that, solve for the new f(x). Finally, what you'll have remaining is the inverse function. The work is done for you below:
f(x) = 1/2x + 4 ----> Switch the x and f(x)
x = 1/2f(x) + 4 ---> subtract 4 from both sides
x - 4 = 1/2f(x) ----> multiply both sides by 2
f(x) = 2x - 8
This would be your inverse function. Now to find f-1(4) you would put 4 in for x in your new inverse function.
f(x) = 2x - 8
f(4) = 2(4) - 8
f(4) = 8 - 8
f(4) = 0
A 6foot tree casts a 3.25 ft shadow. How tall is a tree that casts a 10 ft shadow?
The height of the tree is 18.46 feet.
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
A 6 foot tree casts a 3.25 ft shadow.
let the height of the tree who cast shadow 10 ft.
So, Using Proportion
6 / 3.25 = x / 10
60 = 3.25 x
x= 60/ 3.25
x= 18.46 feet
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Final answer:
To determine the height of a tree that casts a 10 ft shadow, using the ratio from a 6 ft tree that casts a 3.25 ft shadow, we find the tree is approximately 18.46 feet tall through the concept of similar triangles.
Explanation:
The question asks how tall a tree is that casts a 10 ft shadow, given that a 6 ft tree casts a 3.25 ft shadow. This problem can be solved using the concept of similar triangles, where the ratio of the heights of the trees is equal to the ratio of the lengths of their shadows.
To find the height of the tree that casts a 10 ft shadow, we set up the proportion as follows:
Height of first tree / Shadow of first tree = Height of unknown tree / Shadow of unknown tree
Substituting the given values:
6 ft / 3.25 ft = Height of unknown tree / 10 ft
By cross-multiplying and solving for the height of the unknown tree, we get:
(6 ft × 10 ft) / 3.25 ft = 18.46 ft
Therefore, a tree that casts a 10 ft shadow is approximately 18.46 feet tall.
A sea turtle swims at a speed of 27 kilometers per hour. A girl swims 14 decimeters per second. 1 m = 10 dm 1000 m = 1 km How much faster does the sea turtle swim than the girl in meters per minute?
Final answer:
Calculate how much faster a sea turtle swims than a girl in meters per minute by converting their speeds to a common unit and finding the difference.
Explanation:
To find out how much faster the sea turtle swims than the girl in meters per minute, we need to convert their speeds to a common unit. Let's first convert the girl's speed to kilometers per hour:
Girl's speed = 14 decimeters per second = 1.4 meters per second = 5.04 kilometers per hour
Now, we compare the speeds:
Sea turtle speed = 27 kilometers per hour
Girl's speed = 5.04 kilometers per hour
Sea turtle swims 21.96 kilometers per hour faster than the girl. To find how much faster this is in meters per minute:
21.96 km/h * 1000 m/km / 60 min/h = 366 meters per minute
A bell tolls every 10 minutes. Another bell tolls every 15 minutes. Both bells toll at 6:00 PM. They will toll together again at??
Find the greatest possible enclosed area of a rectangular corral given 400 feet of fencing
Answer:
Maximum area = 10000 square units.
Step-by-step explanation:
We are given the following information:
Rectangular perimeter of coral = 400 units.
Let length of the coral be x. Then,
Perimeter = 400 = 2(Length +Breadth)
[tex]400 = 2(x + Breadth)\\Breadth = 200 - x[/tex]
Thus, the area of rectangle is given by,
[tex]Area = Length\times Breadth = x\times (200-x) = 200x - x^2[/tex]
Thus, we have to maximize the function:
[tex]f(x) = 200x - x^2[/tex]
We will use double derivative test.
First we differentiate with respect to x.
[tex]\displaystyle\frac{d(f(x))}{dx} = \displaystyle\frac{d(200x - x^2)}{dx} = 200 - 2x[/tex]
Equating this to zero to obtain critical points,
[tex]200 - 2x = 0\\200 = 2x\\x = 100[/tex]
Now, again differentiating with respect to x.
[tex]\displaystyle\frac{d^2(f(x))}{dx^2} = -2 < 0[/tex]
Thus, by double derivative test, local maxima occurs for this function at x = 100
So, Length = x = 100 units
Breadth = 200 - x = 100 units
Maximum area = 10000 square units.
The population for a city is 39194 and grows continuously at the rate of 6.9% each year. What is the approximate population in 17 years?
Answer:
121,854
Step-by-step explanation:
Initial population of the town A= 39194
rate growth of population R= 6.9%= 0.069
we need to find the population after n = 17 years
we can find that easily using growth rate formula
A= P(1+R/100)^n
A= 39194(1+0.069)^17
= 121,854
therefore population at the end of 17 years= 121,854
which of the following is a solution of x^2+6x=-22
How do I write and graph an inequality in two variables and use them to solve a real-world problem?