1. Find the altitude of an isosceles triangle with base 12 and congruent sides of length 10.
Answers
On solving the provided function, we can say that altitude of the given isosceles triangle is 6.63 unit.
What is an isosceles triangle?A triangle with two sides that have the same length is said to be isosceles. Let's carry out a little exercise to better comprehend this. Fold the corners of a rectangular piece of paper in half.
An isosceles triangle has the following characteristics: two equal sides and two equal angles. The two equal sides are referred to as the legs of the triangle, and the angle between them as the vertex angle or apex angle.T he base and the apex angle are divided by the perpendicular from the apex angle. The isosceles triangle is divided into two congruent triangles by the perpendicular, which is sometimes referred to as its line of symmetry.
\(12 ^2=10^2 +(a/2)^2\\ 144 -100 = a^2\\ 44 = a^2\\ a^2 =44 ; a =\sqrt{44} =6.63\\\)
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Related Questions
Make the biggest possible number using the digits below only once 4 , 5 , 5 answer
Answers
Answer:
554
Step-by-step explanation:
The largest number (5) should go in the hundreds place, the second-largest number (also 5) should go in the tens place and the smallest number (4) should go in the units place so the answer is 554.
What is the multiplicative rate of change for the exponential function f(x)= 3 (2/3)^-x
A. 0.4
B. 2.5
C. 0.6
D. 1.5
Answers
Answer:
C basta Yan ang sagot HAHAHA dko mapicturan solution ko e
Step-by-step explanation:
ano ba yan arte nyo sabing yan ang sagot eAnswer:
c 0.6
Step-by-step explanation:
lol
Arrange the numbers in ascending order 2121,3625,8750,6540
Answers
Answer:
2,121, 3,625, 6,540, 8,750
Step-by-step explanation:
I need help on 1, 2, an 3
Answers
Answer: 1. A) 2/5 B) X= -5 Y= 2
2. A) -3/2 B) X= 2 Y= 3
3. A) -2/3 B) X= -3 Y= -2
Step-by-step explanation: A) Look where the line intersects perfectly through a corner of one of the boxes, find the next one closes to that count how many it goes up and how many across. Rise/Run so the amount it goes up goes on the top of the fraction and the amount across on the bottom of the fraction.
B) This is where the line intersects the X and Y axis
You are given a graph G(V, E) of |V|=n nodes. G is an undirected connected graph, and its edges are labeled with positive numbers, indicating the distance of the endpoint nodes. For example if node I is connected to node j via a link in E, then d(i, j) indicates the distance between node i and node j.
We are looking for an algorithm to find the shortest path from a given source node s to each one of the other nodes in the graph. The shortest path from the node s to a node x is the path connecting nodes s and x in graph G such that the summation of distances of its constituent edges is minimized.
a) First, study Dijkstra's algorithm, which is a greedy algorithm to solve the shortest path problem. You can learn about this algorithm in Kleinberg's textbook (greedy algorithms chapter) or other valid resources. Understand it well and then write this algorithm using your OWN WORDS and explain how it works. Code is not accepted here. Use English descriptions and provide enough details that shows you understood how the algorithm works. b) Apply Dijkstra's algorithm on graph G1 below and find the shortest path from the source node S to ALL other nodes in the graph. Show all your work step by step. c) Now, construct your own undirected graph G2 with AT LEAST five nodes and AT LEAST 2*n edges and label its edges with positive numbers as you wish (please do not use existing examples in the textbooks or via other resources. Come up with your own example and do not share your graph with other students too). Apply Dijkstra's algorithm to your graph G2 and solve the shortest path problem from the source node to all other nodes in G2. Show all your work and re-draw the graph as needed while you follow the steps of Dijkstra's algorithm. d) What is the time complexity of Dijkstra's algorithm? Justify briefly.
Answers
a) Dijkstra's algorithm is a greedy algorithm used to find the shortest path from a source node to all other nodes in a graph.
It works by maintaining a set of unvisited nodes and their tentative distances from the source node. Initially, all nodes except the source node have infinite distances.
The algorithm proceeds iteratively:
Select the node with the smallest tentative distance from the set of unvisited nodes and mark it as visited.
For each unvisited neighbor of the current node, calculate the tentative distance by adding the distance from the current node to the neighbor. If this tentative distance is smaller than the current distance of the neighbor, update the neighbor's distance.
Repeat steps 1 and 2 until all nodes have been visited or the smallest distance among the unvisited nodes is infinity.
The algorithm guarantees that once a node is visited and marked with the final shortest distance, its distance will not change. It explores the graph in a breadth-first manner, always choosing the node with the shortest distance next.
b) Let's apply Dijkstra's algorithm to graph G1:
2
S ------ A
/ \ / \
3 4 1 5
/ \ / \
B D E
\ / \ /
2 1 3 2
\ / \ /
C ------ F
4
The source node is S.
The numbers on the edges represent the distances.
Step-by-step execution of Dijkstra's algorithm on G1:
Initialize the distances:
Set the distance of the source node S to 0 and all other nodes to infinity.
Mark all nodes as unvisited.
Set the current node to S.
While there are unvisited nodes:
Select the unvisited node with the smallest distance as the current node.
In the first iteration, the current node is S.
Mark S as visited.
For each neighboring node of the current node, calculate the tentative distance from S to the neighboring node.
For node A:
d(S, A) = 2.
The tentative distance to A is 0 + 2 = 2, which is smaller than infinity. Update the distance of A to 2.
For node B:
d(S, B) = 3.
The tentative distance to B is 0 + 3 = 3, which is smaller than infinity. Update the distance of B to 3.
For node C:
d(S, C) = 4.
The tentative distance to C is 0 + 4 = 4, which is smaller than infinity. Update the distance of C to 4.
Continue this process for the remaining nodes.
In the next iteration, the node with the smallest distance is A.
Mark A as visited.
For each neighboring node of A, calculate the tentative distance from S to the neighboring node.
For node D:
d(A, D) = 1.
The tentative distance to D is 2 + 1 = 3, which is smaller than the current distance of D. Update the distance of D to 3.
For node E:
d(A, E) = 5.
The tentative distance to E is 2 + 5 = 7, which is larger than the current distance of E. No update is made.
Continue this process for the remaining nodes.
In the next iteration, the node with the smallest distance is D.
Mark D as visited.
For each neighboring node of D, calculate the tentative distance from S to the neighboring node.
For node C:
d(D, C) = 2.
The tentative distance to C is 3 + 2 = 5, which is larger than the current distance of C. No update is made.
For node F:
d(D, F) = 1.
The tentative distance to F is 3 + 1 = 4, which is smaller than the current distance of F. Update the distance of F to 4.
Continue this process for the remaining nodes.
In the next iteration, the node with the smallest distance is F.
Mark F as visited.
For each neighboring node of F, calculate the tentative distance from S to the neighboring node.
For node E:
d(F, E) = 3.
The tentative distance to E is 4 + 3 = 7, which is larger than the current distance of E. No update is made.
Continue this process for the remaining nodes.
In the final iteration, the node with the smallest distance is E.
Mark E as visited.
There are no neighboring nodes of E to consider.
The algorithm terminates because all nodes have been visited.
At the end of the algorithm, the distances to all nodes from the source node S are as follows:
d(S) = 0
d(A) = 2
d(B) = 3
d(C) = 4
d(D) = 3
d(E) = 7
d(F) = 4
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a prism and a pyramid have congruent bases and equal heights the volume of the prisms is twice the volume of the pyramid'
Answers
To find the relationship between the volume of a prism and a pyramid with congruent bases and equal heights, we need to consider their formulas.
The volume of a pyramid is given by the formula V = (1/3)Bh,
where B represents the area of the base and h represents the height. Since the bases of the prism and pyramid are congruent and their heights are equal, we can write the equation:
Volume of Prism = 2 × Volume of Pyramid Using the formulas mentioned earlier, we can substitute the expressions for the volumes:
Bh = 2 × (1/3)Bh
Simplifying this equation, we can cancel out the B's:
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The statement "a prism and a pyramid have congruent bases and equal heights, and the volume of the prism is twice the volume of the pyramid" is FALSE.
To understand why, let's consider a simple example. Imagine we have a triangular prism and a triangular pyramid with congruent bases and equal heights. The base of both shapes is a triangle, and their heights are the same.
The volume of a prism can be calculated by multiplying the area of its base by its height. Similarly, the volume of a pyramid can be calculated by multiplying the area of its base by one-third of its height.
Since the prism and the pyramid have congruent bases and equal heights, the only difference in the volume calculation is the factor of 1/3 for the pyramid.
This means that the volume of the pyramid is one-third the volume of the prism, not half. Therefore, the statement that the volume of the prism is twice the volume of the pyramid is false.
Therefore, the statement is incorrect, and the volume of the prism is not twice the volume of the pyramid, but rather three times as much.
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-11 -z
evaluate the expression if x=-8 , y=7 , and z=-11
Answers
Answer:
-8-(-11)-7
= -8+11-7
= 3-7
= -4
Step-by-step explanation:
I need help on this one I'm probably going to come back with some more
Answers
Answer:
A, B, E
Step-by-step explanation:
A tank in the form of a right-circular cylinder standing on end is leaking water through a circular hole in its bottom. As we saw in (10) of Section 1.3, when friction and contraction of water at the hole are ignored, the height h of water in the tank in feet after t seconds is described by dh dt А. 2gh AW where A and A, are the cross-sectional areas of the water and the hole in square feet, respectively. (a) Solve for h(t) if the initial height of the water is H. Give its interval I of definition in terms of the symbols Awr An, and H. Use g = 32 ft/s2. (4„VH – 44,4) h(t) = osts 4A 4VĀ By hand, sketch the graph of h(t). h h H H/2 t h h H/2H H t (b) Suppose the tank is 11 ft high and has radius 2 ft and the circular hole has radius in. If the tank is initially full, how long will it take to empty? (Round your answer to two decimal places.) sec
Answers
The height of water in the tank in feet after t seconds can be expressed as h(t) = H - (Aw/Ah) 2gh t2, where Aw and Ah are the cross-sectional areas of the water and the hole in square feet respectively,
and g is the gravitational acceleration (32 ft/s2). The interval of definition for h(t) is 0 ≤ t ≤ H/2gh.
The graph of h(t) is a parabola with its vertex at (H/2gh, H) and is symmetric about the line t = H/2gh. It starts at (0, H) and gradually decreases to (H/2gh, 0).
Given the tank is 11 ft high, has radius 2 ft and the circular hole has radius in, and it is initially full, the time it will take to empty can be calculated as: t = √(2H/gAh) = √(22/(32 x π(0.52))) = 3.87 seconds. Therefore, it will take approximately 3.87 seconds to empty.
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Negative air pressure created by an air pump makes a vacuum cleaner able to collect air and dirt into a bag or other container. Below are several readings from a pressure gauge. Write rational numbers to represent each of the readings, and then order the rational numbers from least to greatest.
Gauge Readings ( pounds per square inch )
25 psi pressure
13 psi vacuum
6.3 psi vacuum
7.8 psi vacuum
1.9 psi vacuum
2 psi pressure
7.8 psi pressure
Pressure readings ( pounds per inch) answers:
Answers
The ordered rational numbers representing the gauge readings from least to greatest are 19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1.
To represent the gauge readings as rational numbers, we can express them as fractions with a common denominator.
Given readings:
25 psi pressure
13 psi vacuum
6.3 psi vacuum
7.8 psi vacuum
1.9 psi vacuum
2 psi pressure
7.8 psi pressure
Expressed as rational numbers with a common denominator:
25 psi = 25/1
13 psi = 13/1
6.3 psi = 63/10
7.8 psi = 78/10
1.9 psi = 19/10
2 psi = 2/1
7.8 psi = 78/10
Now, let's order these rational numbers from least to greatest:
1.9 psi = 19/10
6.3 psi = 63/10
7.8 psi = 78/10
7.8 psi = 78/10
13 psi = 13/1
25 psi = 25/1
2 psi = 2/1
Ordered from least to greatest:
19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1
Therefore, the ordered rational numbers representing the gauge readings from least to greatest are 19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1.
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"5 subtracted from a number is a maximum of 14
Answers
Answer:
SIMPLY 14-5=9........
Answer: x ≤ 19
Step-by-step explanation:
x - 5 ≤ 14
Add five on both sides to get this answer!
The length of a desk is 3.5 feet. How many centimeters is the length? (There are 2.54 cm in an inch)
Answers
Answer:
106.68 cm
Step-by-step explanation:
1 ft = 12 inches and 1 in = 2.54 cm
Using conversion factors
3.5 ft * 12 inches/ 1 ft * 2.54 cm/ 1 inch = 106.68 cm
The length of the desk is 106.68 centimeters.
To convert the length of the desk from feet to centimeters, we need to perform the following conversions:
1 foot = 12 inches
1 inch = 2.54 cm
Given that the length of the desk is 3.5 feet, we can calculate its length in centimeters using the conversion factors:
= 3.5 feet x 12 inches/foot x 2.54 cm/inch
Simplifying the expression:
= 3.5 x 12 x 2.54 cm
Calculating the result:
3= 106.68 cm
Therefore, the length of the desk is 106.68 centimeters.
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There are 5 positions available in the new school. Of the applicant, 12 are men and 8 are women. In how many ways can 3 men and 2 women be chosen if they are equally considered?
Answers
There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting
What is the multiplication principle of countingThe multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.
To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).
where n is the total number of men and r is the number of men chosen
so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.
Similarly, we evaluate the number of ways to choose 2 women from the 8 women
as = ⁸C₂ = 14
Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.
220 x 14 = 3080
Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting
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The parks department budgeted $9,720 to buy new wooden benches for the town parks. If the benches cost $72 each, how many benches will the parks department be able to buy?
Answers
Divide the budget by the cost per bench:
9720 / 72 = 135
They can buy 135 benches.
A and b are positive integers and a-b=2. Evaluate the following:
(27^1/3b)/ ( 9^1/2a)
(this is urgent)
Answers
a) 1/27
b) 1
c) 125
Step-by-step explanation:
a) (9^(0.5b))/(3^a)
(3²)^(0.5b) ÷ (3^a)
(3^b) ÷ (3^a)
3^(b - a)
a - b = 3
b - a = -3
3^(-3)
1/27
b) (27^(1/3b)) /(9^(0.5b))
(3³)^(b/3) ÷ (3²)^(0.5b)
(3^b) ÷ (3^b)
1
c) ( 125^(1/3a))/(25^(1/2b))
(5³)^(a/3) ÷ (5²)^(b/2)
5^a ÷ 5^b
5^(a - b)
5³
125
(0,-1) , (0,2) , (-1,5) , (3,0) , (2,-4), (3,-1)Pls help me me which ones apply to the question in picture
Answers
The line shown has the following solution/points on it;
\(\begin{gathered} A(0,2) \\ B(-1,5) \\ C(2,-4) \end{gathered}\)This is interpreted as
A(0, 2); "When x is 0, then y is 2
B(-1, 5); "When x is -1, then y is 5
C(2, -4); "When x is 2, y is -4
Theses are the points that can be found along the line drawn in the graph
Use a two-dimensional model and the dimensions provided to calculate the circumference and area of the flower. Round to the nearest tenth,
if necessary.
circumference:
area:
in²
in.
-5 in-
Answers
circumference of the flower = 16 inches
area of the flower = 19.625 square inches
WHAT IS A CIRCLE ?A circle is formed by all points in a plane that are at a particular distance from the center. To put it another way, it is the curve that a moving point in a plane draws to maintain a constant distance from another point. The distance between any point on a circle and its center is known as the radius. Typically, the radius must be a positive integer. A circle with r=0 and r=0 is an example of a degenerate case. This article concerns circles in Euclidean geometry, specifically the Euclidean plane, unless otherwise stated.
In particular, a circle is a simple closed curve that divides the plane into its interior and exterior.
CALCULATIONdiameter of flower is given = 5 inches
therefore circumference of flower = 2 π r
= 2 x 3.14 x 5/2 (d = 2r)
= 15.7 inches
≈ 16 inches
area of flower = π\(r^{2}\)
= 3.14 x 2.5 x 2.5
= 19.625 square inches
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sketch the region enclosed by the graphs of the given functions. y = sec2(x), y = 8 cos(x), − 3 ≤ x ≤ 3
Answers
The region graph enclosed by the given functions y = sec2(x) and y = 8 cos(x) for -3 ≤ x ≤ 3 can be sketched as follows.
1. Plot the graphs of the given functions:
y = sec2(x) and y = 8 cos(x) for -3 ≤ x ≤ 3.
2. Shade the area enclosed the two graphs.
3. The region enclosed by the given functions is shown below.
The region enclosed by the given functions y = sec2(x) and y = 8 cos(x) for -3 ≤ x ≤ 3 can be sketched as follows. Firstly, plot the graphs of the two functions on the same coordinate plane. Then, shade the area enclosed by the two graphs. The resulting region is a curved area that starts from the point (-3, 8 cos(-3)) on the left, curves up until it reaches the point (3, 8 cos(3)) on the right and then curves down until it reaches the point (-3, 8 cos(-3)). The enclosed region is a continuous, curved area that lies between the two graphs.
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A restaurant can serve 22.3 ice cream sundaes from each gallon of ice cream. Which equation represents the number of sundaes, n, that can be made from g gallons of ice cream?
Answers
Answer:
g/22.3 = n
Step-by-step explanation:
Create and solve a multiplication problem to show that the product of a whole number and a fraction will be equal to the whole number.
IM LOOKING FOR A MATH PROBLEM LIKE THIS = 6 x 1/4 is equal to 6 (but obviously it's not) Please halp ;-;
Answers
Maybe (10)(3/5)=6
The parentheses is multiplication
Find the slope between (2, -10) and (4, -2).
Answers
The slope between (2, -10) and (4, -2) is −2
The slope between the two points is (y2-y1) /(x2-x1)
(2-(-10))/(-4-2)
=(2+10)/(-6)
=12/(-6)
= −2
so, the slope between the two points is −2
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a boat is 15 ft away from a point perpendicular to the shoreline. a person stands at a point down the shoreline so that a 65° angle is formed between the closest point to the boat, the person, and the boat. how far is the person from the boat? round your answer to the nearest tenth of a foot.
Answers
We have a right triangle, where the distance between the boat and the perpendicular point is the baseThe person is approximately 9.2 feet away from the boat.The value, we find that the height is approximately 9.2 feet.
Let's consider the triangle formed by the boat, the person, and the perpendicular point on the shoreline. We have a right triangle, where the distance between the boat and the perpendicular point is the base, the distance between the person and the perpendicular point is the height, and the angle formed between the person, the perpendicular point, and the boat is 65°.
Using trigonometry, we can determine the distance between the person and the boat. The tangent of the angle is equal to the ratio of the height to the base. Therefore, tan(65°) = height / 15. Rearranging the equation, we get height = 15 * tan(65°). Calculating the value, we find that the height is approximately 9.2 feet. Hence, the person is approximately 9.2 feet away from the boat.
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2. A doctor created a scatterplot to show the relationship of heart rate to
blood pressure for some of her patients. The table below is the
data that the doctor collected.
Heart
Blood
Rate
Pressure
80
140
90
155
98
160
С
110
171
Which of these BEST describes the correlation for the data?
Answers
Answer:
Step-by-step explanation:
I need help on number 5 the answer is 28 but I don’t know how to work it
Answers
Answer:
The cost per person varies inversely with the number of people, so y = k/x for some fixed number k.
"It costs $90 each for five people", meaning that x = 5 and y = 90 pair up. Plug these values in and solve for k.
y = k/x
90 = k/5
90*5 = k
450 = k
k = 450
Therefore the equation updates to y = 450/x
Now we want to know how many passengers there are (x) when the cost per person is y = 56.25
Let's find out:
y = 450/x
56.25 = 450/x ... replace y with 56.25
56.25x = 450
x = 450/56.25
x = 8
If you have 8 people, then it costs $56.25 per person.
side note: the total cost is $450 which is the value of k we found earlier. Divide 450 over 8 and you should get 56.25 exactly. Optionally you can turn y = k/x into x*y = k form. So the equation y = 450/x is the same as x*y = 450.
Step-by-step explanation:
g(t)-3t-5;Findg(-9) of you could show the steps to solve.
Answers
Step-by-step explanation:
Substitute t = -9:
\(g( - 9) = 3( - 9) - 5\)
Solve:
\(g( - 9) = - 27 - 5\)
\(g( - 9) = - 32\)
52.82 seconds to the nearest seconds?
Answers
53 seconds
Explanation:\(\begin{gathered} \text{given:} \\ 52.82\text{ seconds} \\ \\ 5\text{ = tens value} \\ 2\text{ = unit value} \\ 8\text{ = tenth value} \\ 2\text{ = hundredth valuegiven:} \\ \end{gathered}\)To round to the nearest seconds, we round the next number after the decimal point
\(\begin{gathered} \text{if the number is greater than 5, we round to 1, then add to the number before the decimal point} \\ \text{if the number is less than 5, we round to zero, then add to the number before the decimal point} \\ \\ \text{the number after the decimal point = 8} \\ it\text{ is greater than 5} \end{gathered}\)\(\begin{gathered} \text{when we round, it becomes 1} \\ \text{Add to the number before the point:} \\ nu\text{mber before point = 5}2 \\ 52\text{ + 1 = 53} \end{gathered}\)\(To\text{ the nearest seconds, 53 seconds}\)How can you do mental math and solve 2.22 divided by 2 without writing anything down? explain.
Answers
Answer:
1.11
Step-by-step explanation:
Which of the following graphs doesn't not represent a function
Answers
Answer:
Graph A.
because it bends at an angle and doesn't curve makes it a non-function
Answer:
D is not a function
Step-by-step explanation:
To find if a graph is a function draw vertical lines on the graph, if no vertical lines intersect through the graph more than once point then its a function.
Micheal brought 15 pounds of flour for $6. How many dollars did he pay per pound of flour?
Answers
Answer:
$.40 per pound
Step-by-step explanation:
6/15
The bottom number (if that were to be in fraction from) would be the number you want as 1. So you want the price of ONE pound of flour.
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which ratios do not form a proportion.
A. 24/96,27/108
B. 17/102,27/108
C. 21/51,35/85
D. 45/75,63/105
Answers
Answer:
B. 17/102,27/108 do not for proportion