The length of one side of a right triangle is shown in this diagram.What could be the lengths of the two remaining sides of the triangle?A. 6 inches and 12 inchesB. 10 inches and 12 inchesC.15 inches and 17 inchesD. 16 inches and 25 inches
Answers
Step 1
Given; The length of one side of a right triangle is shown in this diagram.
What could be the lengths of the two remaining sides of the triangle?
Step 2
Euclidean geometry, For a right-angled triangle, the sum of the square of the two shorter sides of a right triangle is equal to the third side, which is the longest; in symbols,
\(a^2=b^2+c^2\)From the image; Using the Pythagoras theorem we have that
\(\begin{gathered} a^2-b^2=8^2 \\ where\text{ a=longest side or hypotenuse} \\ b=other\text{ unknown side} \end{gathered}\)\(\begin{gathered} Checking\text{ the options;} \\ 17^2-15^2=64 \end{gathered}\)\(64=8^2\)Thus the answer is;
\(15\text{ inches and 17inches}\)Related Questions
Suppose a is a 57 matrix. How many pivot columns must a have if its columns span ? why?.
Answers
The answer is Option B.
In the given choices there is some mistake so, the correct choice can be defined in the attached file. please find it.
In the given question, If the column of a matrix and the A span is equal, and then the value of A has a pivot in each row, that's why in each pivot its position in the different columns of A has the five pivot columns, that's why the choice B is correct.
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Although part of the question is missing the question is Suppose A is a 5x7 matrix. How many pivot columns must A have if its columns span R^5? Why?
a. The matrix must have nothing pivot columns. If A had fewer pivot columns, then equation A would have only the trivial solution.
b. The matrix must have nothing pivot columns. The statements "A has a pivot position in every row" and "the columns of A span " are logically equivalent.
c. The matrix must have nothing pivot columns. Otherwise, equation A would have a free variable, in which case the columns of A would not span.
d. The columns of a 57 matrix cannot span because having more columns than rows makes the columns of the matrix dependent
The math department needs to buy new textbooks and laptops for the computer science classroom. The textbooks cost $116.00 each, and the laptops cost $439.00 each. If the math department has $6,500 to spend and purchases 30 textbooks, how many laptops can they buy
Answers
Answer:
6 laptops
Step-by-step explanation:
First, find the amount spent on the textbooks:
30(116)
= 3480
Subtract this from the total amount they have to spend:
6500 - 3480
= 3020
Divide this amount by 439 to find how many laptops they can buy:
3020/439
= 6.8
Round down to 6 since you can only have full laptops:
= 6
So, they can buy 6 laptops
When dragons on planet Pern lay eggs, the eggs are either green or yellow. The biologists have observed over the years that 32% of the eggs are yellow, and the rest green. Next spring the lead scientist has permission to randomly select 59 of the dragon eggs to incubate. Consider all the possible samples of 59 dragon eggs.
What is the usual number of yellow eggs in samples of 59 eggs? (Give answers as SENSIBLE whole numbers.)
minimum usual number of yellow eggs =
maximum usual number of yellow eggs =
Answers
Answer and Step-by-step explanation:
The computation is shown below
Given that as per the question
n = 59
p = 0.32
Therefore mean is
\(=\mu\)
\(= np\)
\(= 59 \times 0.32\)
= 18.88
Now the standard deviation i.e \(\sigma\)
\(= \sqrt{np(1-p)}\)
\(= \sqrt{18.88(1 - 0.32)}\)
= 3.58
Now the minimum usual number of yellow eggs is
\(= \mu - 2\times \sigma\)
\(= 18.88-2 \times 3.58\)
= 12 yellow eggs
And, the maximum number is
\(= \mu + 2\times \sigma\)
\(= 18.88 + 2 \times 3.58\)
= 26 yellow eggs
A dilation maps (6, 10) to (3,5). What are the coordinates of the image of (12, 4) under the same dilation?
Answers
Answer:
(6,2)
Step-by-step explanation:
A cone and a sphere both have a radius of 1. If you fill the cone with liquid, and pour it into the sphere, it fits exactly. What is the height of the cone? Show work
Answers
Answer and Step-by-step explanation:
First, solve for the volume of the sphere, then solve for the height of the cone using the volume of the sphere (which is said to be equal to the volume of the cone) and the radius given.
Volume formula of Sphere
V = \(\frac{4}{3} \pi r^2\)
Substitute 1 in for r
\(\frac{4}{3} \pi (1)^2 = \frac{4}{3} \pi = 4.189\) = Volume
Finding the Height of a Cone
Volume formula for Cone: \(V = \pi r^2\frac{h}{3}\)
Solve for h
Multiply both sides by 3, then divide by pi and r^2.
\(h = \frac{3V}{\pi r^2}\)
Plug in the volume and the radius.
\(h = \frac{3(4.189)}{\pi (1)^2}\)
Simplify
\(h = \frac{12.567}{\pi }\)
h ≈ 4
4 is approximately the height.
#TeamTrees #PAW (Plant And Water)
You are given the following points:A = (12, 10, -17),B = (-18, 0, -6),C = (-9, -3, 15).
Which point is closest to the yz-plane? B
What is the distance from the yz-plane to this point? 0
Which point is farthest from the xy-plane? A
What is the distance from the xy-plane to this point? 17
Answers
So the point farthest from the xy-plane is A = (12,10,-17). The distance of point A from xy-plane is 17 units.
The equation of the yz-plane is x=0.
So the yz-plane is the plane which passes through the points (0,1,0), (0,0,1) and (0,0,0).
For a point P(x,y,z), the distance between P and
the plane Ax + By + Cz + D = 0 is
|Ax+By+Cz+D| / sqrt(A²+B²+C²).
Thus, the distance from a point to the yz-plane is |x|.
Using this formula for the given points:
A = (12,10,-17) : |x| = |12| = 12B
= (-18,0,-6) : |x| = |-18| = 18C
= (-9,-3,15) : |x| = |-9| = 9
So the point closest to the yz-plane is C = (-9,-3,15).
The distance of point C from yz-plane is 9 units.
So the answer is: 9.
The equation of the xy-plane is z=0.
So the xy-plane is the plane which passes through the points (0,0,1) and (0,0,0).
The distance from a point to the xy-plane is |z|.
Using this formula for the given points:
A = (12,10,-17) : |z| = |-17| = 17B
= (-18,0,-6) : |z| = |-6| = 6C
= (-9,-3,15) : |z| = |15|
= 15
So the point farthest from the xy-plane is A = (12,10,-17).
The distance of point A from xy-plane is 17 units.
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you would like to be 99% confident that you estimate is within 5% of the true population proportion. how large of a sample size is required?
Answers
When we would like to be 99% confident that our estimate is within 5% of the true population proportion. The sample size is large by 78795.
What is the sample size?The number of individuals or observations included in research is referred to as the sample size. Usually, n is used to indicate this number. Two statistical characteristics are influenced by the sample size: 1) The accuracy of our estimations, and 2) The ability to draw inferences from the study.
How to measure sample size?Count the number of people (if known).
The confidence interval should be determined.
Establish the degree of trust.
Calculate the standard deviation (a standard deviation of 0.5 is a safe choice where the figure is unknown)
Create a Z-Score by converting the confidence level.
n = [2.8070/0.005]^2*(1/2)(1/2) = 78795 when rounded up
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You are offered the chance to obtain more space. the offer is for 15 units and the total price is 1500. what should you do?
Answers
A. You should calculate the cost per unit to determine if the price of 1500 for 15 units is a good deal.
B. To determine whether the offer is a good deal, you need to calculate the cost per unit.
Divide the total price of 1500 by the number of units offered, which is 15.
Cost per unit = Total price / Number of units
Cost per unit = 1500 / 15
Cost per unit = 100
The cost per unit is 100.
Now, consider the value you assign to each unit of space. If you believe that each unit is worth more than 100, then the offer is a good deal and you should accept it.
However, if you believe that each unit is worth less than 100, then the offer is not favorable and you should decline it.
Ultimately, the decision depends on your evaluation of the worth of each unit of space and whether you believe the cost per unit is reasonable based on your needs and budget.
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how could the wording of a question or the tone of voice of the interviewer affect a survey
Answers
By speaking positively and upbeatly, you show that you are really listening to what the other person is saying. Actively listen, make encouraging sounds, and repeat what your conversation partner has said. That way they know you're listening carefully.
So this will make survey participants feel more comfortable, honest and cooperative in answering survey questions and also in the subsequent survey process
About SurveyThe survey is a quantitative study using the same structured questions for everyone, then all the answers obtained by the researcher are recorded, processed and analyzed. Surveys are also a method of capturing population data for several demographic or economic events by not counting all respondents in a country, but by taking samples (regional examples) as areas that can represent the characteristics of that country. Structured questions are called questionnaires.
The questionnaire contains questions that will be given to respondents to measure variables, the relationship between existing variables, and can be in the form of experiences and opinions from respondents.
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ruby is visiting San Francisco. From her hotel she walks 3blocks west and 4 blocks north to a coffee shop. Then she walks 6 blocks east and 7 blocks north to a museum. Where is the museum in relation to her hotel?
Answers
The museum is 3 blocks east and 3 blocks north of the hotel.
How to find where the museum is in relation to her hotel?When Ruby walked 3 blocks west from her hotel, she moved left on the map. When she walked 4 blocks north, she moved up on the map.
The coffee shop is located 3 blocks west and 4 blocks north of the hotel.
Then when Ruby walked 6 blocks east from the coffee shop, she moved right 6 blocks on the map, which cancels out the previous westward movement of 3 blocks, bringing her 3 blocks east of the hotel.
Then when she walked 7 blocks north from the coffee shop, she moved 7 blocks north, which adds to the previous northward movement of 4 blocks, bringing her 3 blocks north of the hotel.
So the museum is located 3 blocks east and 3 blocks north of the hotel.
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what is the common difference of 4,-3,-10,17 ?
Answers
Answer:
13 and -13
Step-by-step explanation:
because 17 - 4= 13 and -10 - -3 = 7 because two neg equals pas
Given: AB = CD
Prove: AC = BD
What reason can be used to justify statement 4 in the proof above?
the reflexive property the symmetric property the transitive property the segment addition property
Answers
Step-by-step explanation:
To prove that AC = BD, we can use the symmetric property. The symmetric property states that if two quantities are equal, then their opposites are also equal.
In this case, we are given that AB = CD. Since AB and CD are opposite quantities (they are the lengths of the diagonals of a rectangle), we can use the symmetric property to conclude that AC = BD.
Therefore, the reason that can be used to justify statement 4 in the proof is the symmetric property.
Draw the graph of f(x) = 4ˣ⁺²
Answers
The graph of f(x) = 4ˣ⁺² is an exponential function that passes through the point (0, 3) and increases rapidly as x increases.
To graph f(x) = 4ˣ⁺², we can start by finding a few points on the graph. When x = 0, f(x) = 4⁰⁺² = 3, so the graph passes through the point (0, 3). When x = 1, f(x) = 4¹⁺² = 18,
so we can plot the point (1, 18). Similarly, when x = -1, f(x) = 4⁻¹⁺² = 1.25, so we can plot the point (-1, 1.25).
We can also find the x-intercept of the graph by setting f(x) = 0 and solving for x:
4ˣ⁺² = 0
This equation has no real solutions, so the graph does not intersect the x-axis.
Since the function is increasing rapidly as x increases, the graph approaches but never reaches the y-axis.
As x approaches negative infinity, the graph approaches but never touches the x-axis. As x approaches positive infinity, the graph approaches but never touches the y-axis.
Overall, the graph of f(x) = 4ˣ⁺² is an exponential function that passes through the point (0, 3) and increases rapidly as x increases. It does not intersect the x-axis and approaches but never touches the y-axis as x approaches infinity.
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Which of the following is not a kind of consumer credit?
a installment credit
b personal loans
c service credit
d marginal credit
Answers
Answer:
✅ D. marginal credit⬇️ I got 100% on the test
Tell how many polygons can be formed by each set of points or set of points and a line.
1. (0,1) and (2,3)
2. (4,5), (6,7), and (8,9)
3. (3,5) and the x-axis
Answers
Answer:
1. Two polygons can be formed using the set of points (0,1) and (2,3). One polygon is a line segment connecting these two points, and the other polygon is a right triangle with legs of length 1 and 2, and hypotenuse of length √5.
2. A triangle can be formed using the set of points (4,5), (6,7), and (8,9).
3. One polygon can be formed using the set of points (3,5) and the x-axis. This polygon is a right triangle with legs of length 3 and 5, and hypotenuse of length √34, where the point (3,5) is the vertex opposite the hypotenuse.
The number of polygons that can be formed are,
(0, 1) and (2, 3): Zero polygon
(4, 5), (6, 7), and (8, 9): One polygon (triangle)
(3, 5) and the x-axis: One polygon (triangle)
Determine the number of polygons :-
1) Points (0, 1) and (2, 3) -
The set of points (0, 1) and (2, 3) cannot form a polygon as they are collinear (i.e., lie on the same straight line) and do not enclose an area.
2) Points (4, 5), (6, 7), and (8, 9) -
These are three different points.
Because a triangle has three sides, one triangle can be formed by the set of points (4,5), (6,7), and (8,9). i.e. only one polygon.
3) Points (3, 5) and the x-axis -
One polygon can be formed by the set of points (3,5) and the x-axis: a triangle with vertices at (3,5), (0,0), and (6,0).
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Netflix conducted a pricing experiment and by randomly selecting users and give them a 20% discount for their Prime membership. It is observed that these users are 10% more likely than others to join as a new member. What is the demand elasticity? It the current price optimal for Netflix?
Answers
The demand elasticity for Netflix's pricing experiment can be calculated using the formula:Demand Elasticity = Percentage change in quantity demanded / Percentage change in price.
Given that the users who received a 20% discount were observed to be 10% more likely to join as new members, we can assume that the percentage change in quantity demanded is 10%. However, we don't have information about the percentage change in price. Without that information, it is not possible to calculate the demand elasticity.
Regarding the optimality of the current price for Netflix, we cannot determine it based solely on the given information. Demand elasticity helps measure the responsiveness of quantity demanded to a change in price, which can guide pricing strategies. If the demand elasticity is elastic (greater than 1), a decrease in price can lead to a proportionally larger increase in quantity demanded.
However, without knowing the specific price, quantity demanded, and elasticity values, it is not possible to determine whether the current price is optimal for Netflix.
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A rental company charges $85 a day and 30 cents a mile for renting a truck. Michael rents a truck for 2 days, and his bill comes to $290. How many miles did he drive?
Answers
Answer:
400 miles
Step-by-step explanation:
Let m be the number of miles.
\(85(2) + .30m = 290\)
\(170 + .30m = 290\)
\(.30m = 120\)
\( m = 400\)
Find the value of 15/4 ÷ 5/8.
Answers
Step-by-step explanation:
15/4 ÷ 5/8
15/4×8/5
3×2
=6
Answer:
6
Step-by-step explanation:
Which of the following terms correctly describe the object below?
Check all that apply.
a. polyhedron
b. pyramid
c. prism
d. solid
e. cube
f. polygon
*will mark brainliest :))
Answers
Answer:
The given figure is:
a. Polyhedron
c. prism
d. solid
Step-by-step explanation:
First of all, let us consider the given image.
It is a 3 dimensional figure.
It has 2 equal bases which are pentagonal.
Its faces are made along the sides of the bases and are rectangular in shape.
Now, let us classify the given image in following:
a. Polyhedron:
A polyhedron is a 3-D (three dimensional) shape in which there are flat faces.
The faces can be of 'n' number of edges (Polygonal faces).
Its edges are straight, has sharp corners which are also known as vertices.
The given image is a polyhedron as per above definition.
b. Pyramid:
It is also a 3D shape which can have a polygonal base and its faces are triangular which converge on the top to one point.
The given image does not converge to a point on the top, so not a pyramid.
c. Prism:
It is a 3D shape which has it two bases as polygonal structure.
The two bases are equal in shape and size.
There are faces on the body of prism which are formed by joining the edges of the bases.
The given image is a prism with pentagonal bases.
d. Solid:
Any 3D image is called a solid and has a length, width and height.
So, the given image is a Solid.
e. Cube:
Cube is a 3D figure, which has all its faces in square shape.
All the sides are equal for a cube.
The given image is not a cube.
f. Polygon:
A polygon is a closed figure in 2 dimensions which has n number of sides.
The given image is not a polygon.
Answer: The given figure is:
a. Polyhedron
c. prism
d. solid
The given figure is a Polyhedron, prism and solid.
What is a polyhedron?A polyhedron is a three-dimensional geometry having plane surfaces connected together with sharp edges and pointed vertices.
First of all, let us consider the given image. It is a 3-dimensional figure. It has 2 equal bases which are pentagonal. Its faces are made along the sides of the bases and are rectangular in shape.
Now, let us classify the given image in the following:
a. Polyhedron:
A polyhedron is a 3-D (three dimensional) shape in which there are flat faces. The faces can be of 'n' number of edges (Polygonal faces). Its edges are straight, has sharp corners which are also known as vertices. The given image is a polyhedron as per the above definition.
c. Prism:
It is a 3D shape which has it two bases as a polygonal structure.The two bases are equal in shape and size. There are faces on the body of prism which are formed by joining the edges of the bases. The given image is a prism with pentagonal bases.
d. Solid:
Any 3D image is called a solid and has a length, width and height. So, the given image is a Solid.
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Marissa's mom purchased coffee from the local coffee shop. The first cup of coffee was $3.75. Each refill is $1.50. She also decided to get a bagel for $3.15. If Marissa's mom had 2 refills and a $0.50 discount as part of the rewards program, how much did she spend at the coffee shop?
$11.40
$10.65
$9.90
$9.40
Answers
Answer: ($9.40) or (d)
Step-by-step explanation:
Average of 2. 5 complaints per day. What is the probability that on a given day, Delta Airlines will receive no complaints
Answers
The probability that Delta Airlines will receive no complaints on a given day can be calculated using the average number of complaints per day, which is 2.5.
To find the probability of receiving no complaints on a given day, we can use the concept of a Poisson distribution. The Poisson distribution is commonly used to model the occurrence of rare events over a fixed interval. In this case, the average rate of complaints is given as 2.5 per day.
The probability of receiving no complaints can be calculated using the formula P(X = 0) = e^(-λ) where λ is the average rate. Substituting λ = 2.5 into the formula, we have P(X = 0) = e^(-2.5).
Using a calculator or a computer program, we can calculate the value of e^(-2.5) to find the probability. The result will be the probability that Delta Airlines will receive no complaints on a given day.
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Help? How do I do this.
Answers
8. Maximize p=x+2y subject to 30x+20y
0.1x+0.4y
0.2x+0.3y
x≥0,y≥0
Answers
Answer:5.97
Step-by-step explanation.
you have to look at the question.
you have to look around the question
The very last step is you have to answer it
Write 5×√5 as a single power of 5.
Answers
Answer:
to me the answer will be 5 raised to power 2
Put it in Least to greatest
Answers
Answer:
square root of 14, 4 , 5
Step-by-step explanation:
1.-28 -20 help me plsss
Answers
If you mea. 1 . -28 - 20 then the answer is going to be
\(1. - 48\)
but if you mean -28 -20 the the answer is going to be
\( - 48\)
A dune buggy moves through the hallway at 57.4 cm/s. How far does it travel in 4 minutes? Your Answer: Answer units
Answers
A dune buggy travels 17,280 cm (centimeters) in 4 minutes.
The distance traveled by a dune buggy moving through a hallway at 57.4 cm/s in 4 minutes is 17,280 cm. Here's how to solve it:
First, convert 4 minutes to seconds:4 minutes x 60 seconds/minute = 240 seconds
The distance traveled by the dune buggy in 240 seconds can be calculated using the formula:
Distance = Speed x Time
Therefore,
Distance = 57.4 cm/s x 240
s = 13,776 cm
Since the distance is required in centimeters, we stop here.
Therefore, the dune buggy travels 13,776 cm in 4 minutes.
However, the question requires units, so the unit is centimeters.
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Order he distance traveled from least to greatest
30 kph for 4 hours
5 kph for 10 hours
15 kph for 2 hours
35 kph for 1 hour
Answers
Answer:
15 for 2 = 30km
35 for 1 = 35km
5 for 10 = 50km
30 for 4 = 120km
Step-by-step explanation:
formula is
distance = speed x time
In a class test, (+2) marks were given for every correct answer and (–1) mark was
deducted for every incorrect answer. Rashmi answered all the questions and scored 30
marks. She gave 20 correct answers. Jashpal also answered a few questions and scored
–10 marks. He gave 5 correct answers. How many questions did Rashmi and Jashpal
attempt incorrectly?
Answers
Answer:
Rashmi attempted 10 questions incorrectly while Jashpal attempted 20 questions incorrectly
Step-by-step explanation:
Marks awarded for each correct answers = +2
Marks deducted each incorrect answer = -1
The number of questions Rashmi answered = All the question
Rashmi's score = 30
The correct answers Rashmi gave = 20
The number of questions Jashpal answered = A few questions
Jaspal's score = -10 marks
The number of correct questions Jashpal answered = 5
Let x represent the number of incorrect questions, for Rashmi, we have;
20×2 + x × (-1) = 30
x = 20×2 - 30 = 10
The number of questions Rasmi attempted incorrectly, x = 10
The number of questions Jashpal attempted incorrectly is given as follows;
5×2 + x × (-1) = -10
∴ 10 - x = -10
x = 10 + 10 = 20
The number of questions Jashpal attempted incorrectly, x = 20.
cos2A+cos2B+cos2C =–1–4cosAcosBcosC
Answers
Step-by-step explanation:
Hey there!
Given;
A+B+C = π
A+B = π-C (Take this)----->
B+C = π-A
A+C = π-B
Putting "sin" and "cos" on both sides. We get;
sin (A+B) = sin (π-C)
= sin C.....(i)
cos (A+B) = cos (π-C)
= -cos C......(ii)
Now, taking LHS. We get;
= cos (2A) + cos (2B) + cos (2C)
Use formula for cos (C) + cos (D) in first two terms.
\( = 2. \cos( \frac{2a + 2b}{2} ). \cos( \frac{2a - 2b}{2} ) + \cos(2c) \)
Simplify in first two terms. And keep cos (2C) in terms of cos. (i.e cos (2A) = 2cos^2 (A)-1).
= 2 cos (A+B). cos (A-B) + 2cos ^2(C)-1
Now, use (i).
\( = - 2 \cos(c) . \cos(a - b ) + 2 { \cos}^{2} c - 1\)
Take (-2cos (c)) common.
\( = - 2 \cos(c) ( \cos(a - b) - \cos(c) ) - 1\)
Use cos (C) = -cos(A+B).
\( = - 2 \cos(c) ( \cos(a - b) . \cos(a + b) ) - 1\)
Use formula. (i.e cos (A+B) + cos (A-B) = 2.
= -1-4 cos (A) . cos (B). cos (C)
→ RHS proved.
Hope it helps....