The blueprint of a triangular patio has side lengths 3.5 in., 3.5 in., and 5.25 in. If the shorter sides of the actual patio are each 10.5 ft long, how long is the third side?
The length of the third side of the actual patio is 15.75 feet.
What is similarity of triangle?In order to solve issues requiring proportional connections between the sides of two triangles, it is crucial to understand the idea of triangle similarity. If the matching sides and angles of two triangles are identical, then two triangles are said to be similar. When referring to similarities, the symbol is used.
Let us suppose the length of third side = x.
Given that, blueprint of a triangular patio has side lengths 3.5 in., 3.5 in., and 5.25 in.
Thus, the blueprint and the actual patio form two similar triangles.
The sides of the similar triangles are equal in ratio thus,
3.5/5.25 = 10.5/x
3.5x = 5.25 * 10.5
x = (5.25 * 10.5) / 3.5
x = 15.75
Hence, the length of the third side of the actual patio is 15.75 feet.
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how many three-letter initials with none of the letters repeated can people have?
To find the number of three-letter initials with none of the letters repeated, we need to consider the number of choices for each position in the initials.
To determine the number of three-letter initials with none of the letters repeated, we can analyze each position in the initials. For the first letter, we have 26 choices since there are 26 letters in the English alphabet.
After selecting the first letter, for the second letter, we have 25 choices remaining since we cannot repeat the letter used in the first position. Similarly, for the third letter, we have 24 choices remaining since we cannot repeat either of the previous letters.
Therefore, the total number of three-letter initials with none of the letters repeated can be found by multiplying the number of choices for each position: 26 * 25 * 24 = 15,600. Hence, there are 15,600 different three-letter initials that people can have if none of the letters are repeated.
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Click on the measurement that is equal to 20 liters.
20.000 milliliters
2,000 milliliters
2 milliliters
200 milliliters
Answer:
20,000 milliliters
Step-by-step explanation:
the picture is the qestion
Answer:
12/18 bcz simplyfing 12/18 will give us 2/3
6/9 (divided by 2)
2/3 (divided by 3)
Step-by-step explanation:
I need your help for this!
Answer:
1+1=78993939939
Step-by-step explanation:
1x1= 0 (-_<)
50 PTS & BRAINLIEST! PLEASE HELP ASAP! Add one number to each column of the table so that it shows a function. Do not repeat an ordered pair that is in the table
X is equal to 8 and Y is equal to 3.
What is an ordered pair?A pair that has two values stated in a certain sequence between parenthesis is known as an ordered pair. It is made up of the x coordinate (abscissa) and the y coordinate (ordinate). For greater visual comprehension, it helps to locate a point on the Cartesian plane.
Each domain element should have exactly one picture for the function, therefore the newest element in the column of x shouldn't be 6,3,9,7. Thus, we have two options for x = 8 or 12
Taking 8 will allow us to add another to the column on y, making y equal to 3.
thus, x = 8 and y = 3.
When an ordered pair is used, the numbers do not repeat.
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10.6575
Rounded in whole form
Answer:
i am pretty sure its 11
Step-by-step explanation:
bc if you look at the nymber next to 0 its .6 and they say 5 and up round UP!!
Answer:
11
Step-by-step explanation:
Rounded to Nearest Whole Number =
11
Rounded to Nearest Tenth =
10
Rounded to Nearest Hundredth =
0
Rounded to Nearest Thousandth =
0
EMERGENCY
Rectangular prism with base of 4 cm by 3 cm and a height of 5 cm. Square pyramid with a base of 4 cm by 3 cm and a height of 5 cm.
What is the volume of the prism?
What is the volume of the pyramid?
Answer: A = 15cm squared
Step-by-step explanation:
I think :)
Given that the base of the prism is 4 cm by 3 cm and the height is 5 cm, the volume can be calculated as:
The volume of the prism = (length x width x height)
By applying the given values:
Volume of prism = 4 cm x 3 cm x 5 cm
The volume of the prism = 60 cubic cm
That implies the volume of the rectangular prism is 60 cubic cm.
We know that the pyramid's base measures 4 by 3 cm and its height is 5 cm, the base's area may be calculated as follows:
Area of base = length x width
Area of base = 4 cm x 3 cm
Area of base = 12 square cm
The volume of the pyramid can now be calculated as:
Volume of pyramid = (area of base x height) / 3
Volume of pyramid = (12 square cm x 5 cm) / 3
The volume of the pyramid = 20 cubic cm
Therefore, the volume of the square pyramid is 20 cubic cm.
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Which graph shows the linear inequality y < 2x – 4?
Answer:
Graph the line
y = 2 x − 4
After you have plotted the line, shade in the area to right of the line.
To help you to graph the line, two points are
( 0 , − 4 ) and ( 2, 0 )
Remember to make it a dashed line to indicate that it is not included.
Here is a how it should look:
identify the domain and range of the function input 1,3,5,7 output 8,7,6,5
Answer:
Domain = 1,3,5,7
Range = 8,7,6,5
Step-by-step explanation:
We need to identify the domain and range of the function: input 1,3,5,7 output 8,7,6,5
Domain of function:
For any function domain is set of input values.
Range of function:
For any function range is set of output values.
So, for the given function we have : input 1,3,5,7 output 8,7,6,5
Domain = 1,3,5,7 (set of input values is domain of function)
Range = 8,7,6,5 (set of output values is range of function)
use complete sentances to answer the following questions. what was the strongest argument in favor of homework what was the strongest argument against homework
The strongest argument in favor of homework is that it reinforces classroom learning. The strongest argument against homework is that it infringes upon students' personal time and can cause unnecessary stress. The topic is about Education and Pedagogy specifically focusing on the surrounding the effectiveness and implications of homework .
Homework has been a long-standing educational practice, with proponents and detractors on both sides of the debate. One of the strongest arguments in favor of homework is that it reinforces classroom learning. By completing homework assignments, students are able to practice and solidify the concepts they learned in class.
This can help them better retain the information and apply it to future tasks.
On the other hand, the strongest argument against homework is that it infringes upon students' personal time and can cause unnecessary stress. Students are often involved in extracurricular activities, sports, and other interests, leaving little time for homework.
This can cause stress and anxiety for students who are already struggling to balance their academic and personal lives. Additionally, some argue that homework assignments are often too difficult or time-consuming, leaving students feeling overwhelmed and frustrated.
In conclusion, while there are valid arguments on both sides of the homework debate, it is ultimately up to individual schools and teachers to determine the amount and type of homework that is appropriate for their students. It is important for educators to consider the potential benefits and drawbacks of homework assignments and make informed decisions that prioritize student learning and well-being.
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quickly pls, thanks and i appreciate it
The cheaper price for 12 orchids is £25.80.
To determine the cheaper price for 12 orchids, we need to find the price per orchid and then calculate the total cost for 12 orchids.
The price per orchid at £8.60 for 4 orchids can be calculated as:
Price per orchid = £8.60 / 4 = £2.15.
The discounted price per orchid at £5.40 each can be used directly.
Now, let's calculate the total cost for 12 orchids using both prices:
Price at £2.15 per orchid:
Total cost = £2.15 * 12 = £25.80.
Price at £5.40 per orchid:
Total cost = £5.40 * 12 = £64.80.
Therefore, the cheaper price for 12 orchids is £25.80.
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Find the exact solution of each equation for 0 ≤ q ≤ 2π.
To find the exact solution of each equation for 0 ≤ q ≤ 2π, we need to use the appropriate formula and simplify the expression. Let's take an example of the equation sin(q) = 1/2.
Using the unit circle, we know that sin(q) = 1/2 at q = π/6 and q = 5π/6. Hence, the exact solutions for the equation sin(q) = 1/2 are q = π/6 + 2nπ and q = 5π/6 + 2nπ where n is an integer and n = 0, ±1, ±2, … . Similarly, we can find the exact solutions for other trigonometric equations using their respective formulas.
It is important to note that we should restrict the value of q to 0 ≤ q ≤ 2π to ensure that we are only finding the solutions within the given interval. In conclusion, to find the exact solution of each equation for 0 ≤ q ≤ 2π, we need to use the appropriate formula, simplify the expression, and restrict the value of q to the given interval.
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In isosceles triangle AXYZ, XY = YZ. Which statement must be true?
mZX=mZZ
OmZX=mZY
O mzZ=mZY
Answer:
m<X=m<Z
Step-by-step explanation:
In an isosceles triangle, 2 sides are congruent, and the opposite angles of those sides are congruent.
The angle opposite side XY is <Z.
The angle opposite side YZ is <X.
Since sides XY and YZ are congruent, then angles Z and X are congruent.
Answer: m<X=m<Z
what is the sum of a and b?
Answer:The sum of A and B is the result of adding A to B, as opposed to something like the product of A and B, which would be multiplying A and B
Step-by-step explanation:
\(224% of 320\neq\)
Answer:
224
Step-by-step explanation:
multiply 224 by 1 and you get your answer
Let F be the set of functions of the form f(x) = = A sin(x) + B cos(2x), where A, B are some real constants. Show that there must exist exactly one function f in F so that for any fe F, √√√((a) - arctan (2))³²dr ≤√√√ (f(a) — arctan(a))³d.r
The proof for the given condition S ≤ T is justified using the product rule of differentiation.
The given function is given by f(x) = A sin(x) + B cos(2x).
Let us first find the derivative of this function.
Using product rule, we getf′(x) = A cos(x) – 2B sin(2x)
Now, let us calculate the second derivative of the function
f′′(x) = -A sin(x) – 4B cos(2x)
Now, we need to check if the function is concave or convex over the interval [0, π/2].
In order to do that, we will check the sign of the second derivative on this interval. We note that A is non-zero.
Hence, if we multiply the second derivative by A, we get
-A² sin(x) – 4AB cos(2x).
We observe that cos(2x) is greater than or equal to -1 for all real values of x.
Hence, -4AB cos(2x) is less than or equal to 4AB.
This implies that -A² sin(x) – 4AB cos(2x) is less than or equal to -A² sin(x) + 4AB.
Now, we need to find the maximum value of this expression for x between 0 and π/2.
Let us differentiate this expression w.r.t. x.
A² cos(x) + 8AB sin(x) = 0sin(x)/cos(x)
= -A²/8AB
= -A/8Btan(x)
= -A/8B or
x = -arctan(8B/A)
Let x = -arctan(8B/A).
Then sin(x) = -A/√(A² + 64B²) and cos(x) = 8B/√(A² + 64B²).
Putting these values in the expression, we get
Maximum value of the expression = √((A² + 64B²)/(A²))
= √(1 + (64B²)/(A²))
Hence, we have that for any function f in F,
f(x) ≤ f(a) + f′(a)(x-a) + (√(1 + (64B²)/(A²)) / 2)
f′′(a)(x-a)² for x between 0 and π/2.
The equation √√√((a) - arctan (2))³²dr ≤√√√ (f(a) — arctan(a))³d.r can be expressed as ∫ √(a - arctan2(x)) dx ≤ ∫ √(f(a) - arctan(a)) dx over the interval (0, π/2).
Now, we just need to evaluate the integrals on both sides. We can do this numerically. We will use the trapezoidal rule for this. We will divide the interval into n subintervals of equal length.
Let xi be the point where the ith subinterval starts and let f(xi) be the value of the function at that point.
Then, the integral can be approximated by
∫ √(a - arctan2(x)) dx ≈ (π/(2n))(√(a - arctan2(0)) + 2
∑i=1n-1 √(a - arctan2(xi)) + √(a - arctan2(π/2)))
Similarly,
∫ √(f(a) - arctan(a)) dx ≈ (π/(2n))(√(f(a) - arctan(a)) + 2
∑i=1n-1 √(f(a) - arctan(a)) + √(f(a) - arctan(a)))
Let S = √√√((a) - arctan (2))³²dr and T = √√√ (f(a) — arctan(a))³d.r.
Then, we just need to show that S ≤ T. This can be done by choosing appropriate values of A and B.
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in a certain amount of time, a plane traveling at a constant $250$ miles per hour traveled $20,\!000$ feet. in this same amount of time, how many feet would a plane traveling at a constant $400$ miles per hour travel?
At a constant rate of 400 miles per hour travel, the plane would be travelling from 32000 feet above the land.
The speed of an object is the ratio of distance and time it takes for the object to travel that distance.
Mathematically,
S = D/T
where
S is velocity
D is the distance traveled or distance traveled
T is the time it takes to travel that distance
Velocity is considered a scalar quantity. A scalar size only has a size. It does not provide information about the direction of object movement.
If an object moves at a constant speed, it means that the object moves the same distance in the same time interval.
Acceleration of an object is the ratio of velocity and time. vector size. Vector quantities have both magnitude and direction.
Mathematics,
a = v/t
When an object is in motion, its acceleration is never zero.
When an object moves, it moves a constant distance over time. Therefore, body positions cannot be the same from the same coordinate system.
Given in the question:
First the plane was travelling at a constant rate of 250 miles per hour.
Initial height was 20000 feet
Now,
As the speed increases and travels at a constant rate of 400 miles per hour.
Now,
(400 /250 ) × 20000
= 1.6 × 20000
= 32000 feet
Thus, At a constant rate of 400 miles per hour travel, the plane would be travelling from 32000 feet above the land.
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compare numbers.
Performs arithmetic operations (+, –, *, /) as well as comparison or relational operations (<, >, =); the latter are used to compare numbers.
Comparison or relational operations, such as <, >, =, allow for comparing numbers. They determine if a number is less than, greater than, equal to, or not equal to another number, enabling decision-making and comparisons within arithmetic and programming operations.
When comparing numbers, you can use various relational operators to determine the relationship between them. Here are the commonly used comparison operators:
Less than (<): This operator compares two numbers and returns true if the first number is smaller than the second number. For example, 5 < 10 is true.
Greater than (>): This operator compares two numbers and returns true if the first number is larger than the second number. For example, 10 > 5 is true.
Less than or equal to (<=): This operator compares two numbers and returns true if the first number is smaller than or equal to the second number. For example, 5 <= 5 is true.
Greater than or equal to (>=): This operator compares two numbers and returns true if the first number is larger than or equal to the second number. For example, 10 >= 10 is true.
Equal to (==): This operator compares two numbers and returns true if they are equal. For example, 5 == 5 is true.
Not equal to (!=): This operator compares two numbers and returns true if they are not equal. For example, 5 != 10 is true.
These comparison operators allow you to compare numbers and make decisions based on their relationships within arithmetic or programming operations.
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what’s is the quotient for the rational expression shown below?
Answer:
D
Step-by-step explanation:
D is the correct answer
Multiply binomial by polynomials
In this case the answer is very simple . .
We must apply the distributive property of multiplication.
\((d^2+3)\cdot(d^2\text{ + 2d + 1) }\)\(d^2\cdot d^2+d^2(2d^{})+d^2+3(d^2\text{) + 3(2d) + 3}\)\(d^4\text{ + }2d^3+d^2+3d^2+6d+3\)\(d^4+2d^3+4d^2+6d+3^{}\)That is the solution. .
PLEASE HELP FAST
For questions 5,6 add or subtract the polynomials
(m²-m+3)+(m-1)
A. M²-M-2
B.M²-2
C.M²+2
D.M²+M+2
6.( 7X²-X-2)- (-6X³+3)
A.6X³+7X²-X-5
B.-6X³+7X²-X+1
C-X³-X-5
D.X²-X+1
Answer:
m^2-2 and -6x^3+7x^2-x+1
10) show all ur equation steps
Answer:
see below
Step-by-step explanation:
Put first equation into second
18x+3*(-6x+7) =21
open up the bracket
18x -18x+21=21
21 = 21
so infinite many solutions
Last year you bought a pair of boots for $84 last year. Your friend bought the same pair of boots this year for $120. What is the percent of change in the cost of the boots.
Answer:
30%
Step-by-step explanation:
70% of 120 is 84. So take the remainder of 70 (30, as %'s go up to 100.) and that's the percent left. We can "fact check this" the other way around as well.
30% of 120 = 36.
84 + 36 = 120.
The price of the boots have changed/raised 30%.
Hope this helps and have a nice day!
9. Suppose a boat travels 96 miles downstream and then travels the same distance
upstream. In still water, the boat travels at a speed of 18 mph. Let x be the speed of
the current. If the total trip takes 12 hours, find the speed of the current to the
nearest whole number. Use t = . (Hint: Going downstream, the boat is going
with the current and going upstream, the boat is going against the current.) [10
points]
If the total trip takes 12 hours, the speed of the current is 1 mph.
What is speed?The speed of an object is described as the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time.
The downstream trip:
distance = rate × time
96 = (18 + x) × t ( 18 + x)
The upstream trip:
distance = rate × time
96 = (18 - x) × (12 - t)
96 = (18 - x) × (12 - t)
8 = x - (x/6)t
We have two equations and two unknowns, so we can solve for x and t.
We solve for x by making t subject fomula and substituting into the equation.
Where x = 1
In conclusion, if the total trip takes 12 hours, the speed of the current is 1 mph.
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Ben can type 153 words in 3 minutes At this rate, how many words can he type in
10 minutes/
Answer:
Ben can type 153 words in 3 minutes.
Ben can type 153/3 words in 1 minute.
Ben can type 153/3 x 10 words in 10 minutes
=510words
Step-by-step explanation:
Hence, Ben can type 510 words in 10 minutes.
Lupe got 90% of the points correct on her science test. If there
were 30 points possible, how many points did Lupe get right?
What is the quotient and remainder of 21÷6
Answer:
3 remainder 3
Step-by-step explanation:
at noon, shadow of a flagpole is 19 feet long. At same time, shadow is a 12 foot high wall is 4 feet long. what is the height of the flagpole?
The height of the flagpole is 57 feet. Shadow of a flagpole is 19 feet long. At same time, shadow is a 12 foot high wall is 4 feet long.
To find the height of the flagpole, we can use the concept of similar triangles.
Let's denote the height of the flagpole as 'h' and the length of its shadow as 'x'.
According to the given information, the shadow of the flagpole is 19 feet long, and the shadow of a 12-foot high wall is 4 feet long. We can set up a proportion using the similar triangles formed by the flagpole, its shadow, the wall, and its shadow:
(height of flagpole) / (length of flagpole's shadow) = (height of wall) / (length of wall's shadow)
Using the given information, we have:
h / x = 12 / 4
Cross-multiplying the proportion, we get:
4h = 12x
Simplifying the equation, we have:
h = 3x
Now, we know that at noon, the length of the flagpole's shadow is 19 feet. Substituting this value into the equation, we can solve for the height of the flagpole:
h = 3 * 19
h = 57 feet
Therefore, the height of the flagpole is 57 feet.
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which of the following are true? a) it is possible for a function to not have a global maximum or a global minimum. b) if a function has 3 critical points then it must have a global maximum. select one: a. only b b. neither a or b c. a and b d. only a clear my choice
The true statement is "It is possible for a function to not have a global maximum or a global minimum". The correct answer is option A.
The statement "it is possible for a function to not have a global maximum or a global minimum" is true. This can occur if the function has an asymptote or a vertical tangent line, or if the domain is not a closed interval.
Option B is incorrect because having 3 critical points does not guarantee the existence of a global maximum. A function could have multiple critical points, but these points may not necessarily correspond to the global maximum or minimum.
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