Select the correct answer. A triangle has vertices (-1, 2), (3, 1), and (7, 2). What is the approximate perimeter of th...
Answers
Answer:
16.24 Units
Step-by-step explanation:
The perimeter of the triangle is the sum of the length of the sides of the triangle. Given the points on the vertices, the length of each side may be found using the formula
Length = √(x2 - x1)^2 + (y2 - y1)^2
Considering the pair (-1, 2), (3, 1), the length of that side
= √(3 -- 1)^2 + (1-2)^2)
= √(16 + 1)
= √17 units
Considering the pair (-1, 2), (7, 2), the length of that side
= √(7 -- 1)^2 + (2-2)^2)
= √(64)
= 8
Considering the pair (3, 1), and (7, 2), the length of that side
= √(7 - 3)^2 + (2 - 1)^2
= √(16 + 1)
= √17
Hence the perimeter of the triangle
= √17 + 8 + √17
= 4.12 + 8 + 4.12
= 16.24 Units
Related Questions
the process of finding the derivative of a function is called____.
Answers
The process of finding the derivative of a function is called differentiation.
Differentiation is a fundamental concept in calculus that involves determining the rate at which a function changes with respect to its independent variable. It allows us to analyze the behavior of functions, such as finding slopes of curves, identifying critical points, and understanding the shape of graphs.
The derivative of a function represents the instantaneous rate of change of the function at any given point. It provides information about the slope of the tangent line to the graph of the function at a specific point.
The notation used to represent the derivative of a function f(x) with respect to x is f'(x) or dy/dx. The derivative can be interpreted as the limit of the difference quotient as the interval approaches zero, representing the infinitesimal change in the function.
By applying differentiation techniques, such as the power rule, product rule, chain rule, and others, we can find the derivative of a wide range of functions. Differentiation is a powerful tool used in various areas of mathematics, physics, engineering, economics, and other fields to analyze and solve problems involving rates of change.
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how many solutions does y=x+4 and y=2x+4 have?
Answers
Answer:
x = 0
Step-by-step explanation:
y = x + 4 and y = 2x + 4
Let's solve
x + 4 = 2x + 4
-x + 4 = 4
-x = 0
x = 0
So, there is only one solution is x = 0
The two lines have the same y-intercept, and therefore, that’s one solution there. But because the line will never cross other than at y=4, the two equations will only have 1 solution.
Hope this helped!
Bakery A. She used the equation 10
donuts $15 to show that their donuts cost about $0.67 per donut. This is less than
Bakery B's price, 12 donuts $17= about $0.71 per donut.
Kevin thinks they should order donuts from Bakery B. He used the equation $17 ÷
12 donuts to show that their donuts cost about $1.42 per donut. This is less than
Bakery A's price, $15÷ 10 donuts = about $1.50 per donut.
Who is correct?
Answers
The donuts are cheaper in bakery B which implies that Kevin is right.
What is Unitary method?In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method. The ratio of two numbers are taken in this method. There can be two relations between the ratio a direct or n indirect. For the direct relation the quantities simultaneously increase or decrease while in the indirect it happens reverse.
The price of donuts for both bakeries are given as,
For Bakery A,
The price of 10 donuts is $15.
Unit rate is given as 15/10 = $1.50 per donut.
For Bakery B,
The price of 12 donuts is $17.
Unit rate is given as 17/12 = $1.41 per donut.
Thus, price of donuts from Bakery B is less than Bakery A.
It implies that Kevin is right.
Hence, the price of donuts is cheaper in case of bakery B which implies that Kevin is right.
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Kevin is correct. And he used the correct unit rate formula to find the inequality.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
Bakery A.
She used the equation 10 donuts $15 to show that their donuts cost about $0.67 per donut.
This is less than Bakery B's price, 12 donuts $17= about $0.71 per donut.
Kevin thinks they should order donuts from Bakery B.
He used the equation
$17 ÷ 12 donuts to show that their donuts cost about $1.42 per donut.
This is less than Bakery A's price,
$15÷ 10 donuts = about $1.50 per donut.
The inequality:
1.42 < 1.50
To find the unit rate:
Unit rate = the total price of donut / the number of total donuts
Kevin used the above formula to find the unit rate.
So, Kevin is right.
Therefore, Kevin is right.
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The value of y directly proportional to the value of x. If y= 8 when x= 12, what is the value of y when x= -15?
The value of y directly proportional to the value of x. If y= 3 when x= 24, what is the value of y when x= -8?
Answers
Answer:
The value of y should be -10
Step-by-step explanation:
If x and y are proportional, then 8/12=y/-15
The fractions just show the y values over the x values
Cross multiply to get 12y= -120
y= -10
Find a number which in which added square
sum will be 72.
Answers
Answer:
8.48528137424^2
Step-by-step explanation:
8.48528137424x8.48528137424
= 72
You have $20 to spend on taxi fare. The ride costs $5 plus $2.50 per mile. Write an inequality to determine how many miles you can ride for $20.
Answers
Answer: Maximum 6 miles
Step-by-step explanation: In total you have $20.
Base fare of taxi is $5.
Per mile cost is $2.50.
Your total cost is where x is the number of miles. Since you're on a budget of maximum $20, the cost should be less than or equal to $20. We can write:
To find how many miles we can write, let's solve the inequality:
.
This means 6 is the maximum number of miles you can ride with $20.
working with a manufacturing process which produces compsites having a fiber volume fraction a (msi) and a matrix with a matrix modulus b (msi). determine the fiber modulus required to produce a composite with longitudinal modulus of c (msi).
Answers
The fiber modulus required to produce a composite with longitudinal modulus of c is 56.93.
What is manufacturing process?
Manufacturing process management is a group of tools and techniques that specify how goods should be produced. MPM is distinct from ERP/MRP, which is used to schedule manufacturing, gather cost information, and organize the ordering of supplies and other resources.
What is matrix?
A matrix, which is used to represent a mathematical object or an attribute of one, is a rectangular array or table containing numbers, symbols, or expressions that are organized in rows and columns. is a matrix having two rows and three columns, for instance.
As a result, if we look at the formula for the relationship between the fiber modulus and the matrix's volume fraction, composite modulus, and fiber vol fraction, we have:
C = (M x B) / [(1-A)M + A x B]
where M denotes the fiber's modulus.
If you provide the corresponding letter values,
40 = M X 0.5 / [(1-0.7)M + 0.7 X 0.5]
M = 56.93
Hence,the fiber modulus required to produce a composite with longitudinal modulus of c (msi) is 56.93
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A washer and a dryer cost 860 combined. The washer costs 90 less than the dryer. What is the cost of the dryer?
Answers
Answer:
340
Step-by-step explanation:
860 ÷ 2 = 430
430 - 90 = 340
Aaron invests $512 in a company. He receives 5% simple interest for 8 years. How much interest will Aaron earn?
Answers
Answer:
Aaron earns $ 204.80 as interest by investing $512 at 5% simple interest for 8 years.
Step-by-step explanation:
Simple interest:
The simple interest on a sum of money is calculated using the formula :S.I = \(\frac{P . r . t}{100}\)
where P = the principal (initial amount invested)
r = rate of interest (in %)
t = number of years for which P is invested.
Solution:
Here, it is given that Aaron invests $512 in a company and receives 5% simple interest for 8 years.
Therefore, P = $512
r = 5%
t = 8 years.
Unknown = simple interest.
Using the formula S.I = \(\frac{P . r . t}{100}\), we find
S.I = ( $512 x 5 x 8 ) ÷ 100 = $ 204.80.
Thus Aaron earns $ 204.80 as interest on his invested amount.
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let r be the relation on the set {0, 1, 2, 3} containing the ordered pairs (0, 1), (1, 1), (1, 2), (2, 0), (2, 2), and (3, 0). what ordered pair(s) do you need to add to form the reflexive closure of r.
Answers
The reflexive closure of a relation on a set is the smallest reflexive relation that contains the original relation. In other words, it is the addition of pairs that ensure every element in the set is related to itself. To form the reflexive closure, we need to add pairs that relate each element in the set to itself.
To form the reflexive closure of relation r on the set {0, 1, 2, 3}, we need to add ordered pairs that ensure every element in the set is related to itself. In other words, we need to add pairs of the form (x, x) for each element x in the set that is not already present in relation r.
In this case, the reflexive closure of relation r would require adding the following ordered pairs: (0, 0), (1, 1), (2, 2), and (3, 3). These pairs ensure that every element in the set {0, 1, 2, 3} is related to itself, making the relation reflexive. These pairs ensure that every element is related to itself, satisfying the reflexivity property.
By adding these additional ordered pairs, we have modified relation r to include reflexivity, as every element now has a direct relation to itself in the set.
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it takes 25 min to cook 10 egg how long does it take to cook 20
Answers
Answer:
50 minutes
Step-by-step explanation:
so it takes 25 minutes to boil 10 egggs so right now we have to find out the how Long one egg cooks for so it’s 25/10 and the answer is 2.5 and 2.5 times 20 is 50 so it takes 50 mins to cook 20 eggs
5/8
of Mrs. Jackson’s class have ear buds.
2/3
of the ear buds in her class are black. What fraction of
the scholars have black ear buds?
Answers
Answer:
5/12
Step-by-step explanation:
Total ear buds in Mrs. Jackson’s class = 5/8
Number of black ear buds in Mrs. Jackson’s class = 2/3
What fraction of
the scholars have black ear buds?
2/3 of the scholars have black ear buds in Mrs. Jackson’s class
2/3 of 5/8
= 2/3 × 5/8
= 10/24
= 5/12
Fraction of the scholars that have black ear buds = 5/12
a car manufacturer is looking to compare the sales of their sedan model last year to the sales of the same model 15 years ago at various dealerships. the manufacturer is weighing two different proposals to conduct the study. under the first proposal, the manufacturer randomly samples 10 different dealerships for their sales numbers last year and randomly selects another 10 dealerships for their sales numbers 15 years ago. in the second proposal, the manufacturer randomly samples 10 dealerships for both sets of sales numbers. are the samples in these proposals dependent or independent?
Answers
The samples in the first proposal are independent, while the samples in the second proposal are dependent.
In the first proposal, where the manufacturer randomly samples 10 different dealerships for each set of sales numbers (last year and 15 years ago), the samples are independent. This is because the selection of dealerships for one set of sales numbers does not affect or influence the selection of dealerships for the other set of sales numbers. Each dealership is chosen randomly and independently for each set.
On the other hand, in the second proposal, where the manufacturer randomly samples 10 dealerships for both sets of sales numbers, the samples are dependent. This is because the selection of dealerships for one set of sales numbers is directly tied to the selection of dealerships for the other set of sales numbers. The same 10 dealerships are chosen for both sets, so the samples are not independent.
The choice between independent and dependent samples can have implications for statistical analysis. Independent samples allow for direct comparisons between the two sets of sales numbers, while dependent samples may introduce potential bias or confounding factors due to the shared dealership selection.
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ax - b = 15 Solve the following equation for x. Show all of your steps.
Answers
Answer:
x = (b + 15) / a
Step-by-step explanation:
ax - b = 15
add b to both sides
ax = b + 15
Divide both sides by a
x = (b + 15) / a
Identify the equation for the line tangent to the circle x^2 + y^2 = 100 at the point (−6, 8).
Answers
The equation of tangent to the circle \(x^{2} +y^{2} =100\) at the point (-6,8) is -6x+8y=100.
Given the equation of circle \(x^{2} +y^{2} =100\)
and point at which the tangent meets the circle is (-6,8).
A tangent to a circle is basically a line at point P with coordinates is a straight line that touches the circle at P. The tangent is perpendicular to the radius which joins the centre of circle to the point P.
Linear equation looks like y=mx+c.
Tangent to a circle of equation \(x^{2} +y^{2} =a^{2}\) at (z,t) is:
xz+ty=\(a^{2}\).
We have to just put the values in the formula above to get the equation of tangent to the circle \(x^{2} +y^{2} =100\) at (-6,8).
It will be as under:
x(-6)+y(8)=100
-6x+8y=100
Hence the equation of tangent to the circle at the point (-6,8) is -6x+8y=100.
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HELP!! IM BEING TIMED!
What is the iterative rule for this geometric sequence?
2/9, 2/3, 2, 6, ...
A.) an = 2/9 • 3^n
B.) an = 3(2/9)^n-1
C.) an = 2/9 • 3^n-1
D.) an = 3(2/9)^n
Answers
Answer: D
Step-by-step explanation:
2/3 divided by 2/9 = 3
a n = a 1 ⋅ r^( n − 1)
an = (2/9) * 3^(n-1)
If mand n average i 50
p and q average i 70
then what will be the average of m,n,p,q
Answers
we know that average of two number are
AV= (m+n)/2
we are given that
(m+n)/2 = 50
m+n= 50×2
m+n=100
similarly
Arithmetic average of p and q = 7
(p+q)/2
=70
p+q= 70×2
p+q= 140.
Now, arthemetic mean of
(m+n+p+q)/4=
(140+100)/4
= 240/4
= 60
so average of m, n, p, q is 60
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ABC is a triangle. AC = 9 cm, BC = 7 cm and angle BAC = 30°
Calculate the size of angle ABC.
Answers
9514 1404 393
Answer:
∠B = 40° or 140°
Step-by-step explanation:
The given angle is opposite the shortest of the given sides, so there are two possible solutions.
From the law of sines, ...
B = arcsin(b/a·sin(A)) = arcsin(9/7·sin(30°)) = arcsin(9/14)
Possible values for angle B are ...
B = arcsin(9/14) ≈ 40.0°
B = 180° -arcsin(9/14) ≈ 140.0°
Circles and i neeeeed help
Answers
Answer:
60 degrees
Step-by-step explanation:
Using the 172 degrees and calculating it's distance from the angle, i conclude that it's 60
9514 1404 393
Answer:
(b) 60
Step-by-step explanation:
The external angle is half the difference of the two subtended arcs.
x° = (172° -52°)/2 = 120°/2
x° = 60°
The value of x is 60.
30x/42x^2+48x i need help simplifying this expression please show the step by step
Answers
So we can rewrite the expression as:
6x(5 + 7x)/(7x + 8)
Next, we can simplify the expression by canceling out the factors that are the same in the numerator and denominator.
We can cancel out the factor of x in the numerator and denominator:
6(5 + 7x)/(7 + 8/x)
And we’re done!
What is this expression in simplified form?
Answers
Answer:
It should be -18 times the square root of of 10
Step-by-step explanation:
14. What is the equation in standard form of a parabola that models the values in the table?
(1 po
.
-2
0
4
f(x)
4
-6
70
47
3x +47-6
0 4x²+3x-6
0472-3x-6
0 -4x² – 3x-6
Answers
Answer:
Maybe y = 4x^2 + 3x -6
Step-by-step explanation:
The information is too garbled to make sense. I did the best I could with a few of the points and the first three equations. What is "0472-3x-6"?
Please see the attached graph for the points I think are in your data. There is one equation that fits the three points I used. Do the same with DESMOS using the correct data.
Hi I need help On his Multiple Choice questions Try)- and not get it wrong or I cant Complete My Maths Work. The Question itself is on the Image attached Below: thanks!
Answers
Answer:
a) Option A is correct.
b) Option B is correct.
Step-by-step explanation:
\(a) \: \: 5 \times a \\ = 5a\)
\(b) \: \: b \times b \\ = {b}^{2} \)
Hope it is helpful.....PLEASE HELP ME IM SO CONFUSED The volume of a cube is x³ cubic units. The surface area of the cube is x³ square units. What is the value of x?
Answers
Answer: The value of x is 6.
Step-by-step explanation:
TO find the volume of a cube you cube any side length. so if the side length is 6.
6^3 = 216
To find the surface area of a cube you will square one of the side lengths and multiply it by 6.
so the side length is 6 and 6 squared is 36
36*6 = 216
Josh's soccer team had a competition to see which player should be the goalie. Each player tried to block 15 kicks from entering the goal, and the coach recorded the number of successfully blocked kicks. Josh made a dot plot to display the information. What is the interquartile range for the data?
Answers
Answered okokokoomkokk
Step-by-step explanation:
1- In Euclidean space, the locus of points equidistant from the origin of a plane is a circle What is the locus of points equidistant (in the spacetime distance seme) from the origin of a spacetime plane? 151 2. A ruler of length L. In at rest in with its left and at the origin. O moves from left to right with speed relative to o along the length of the ruler. The two origins coincide ut time zero for both, at which time a photon is emitted toward the other end of the rulut. What are the coordinates in Olof the event at which the photon maches the other end? (10) 3. The Earth and Alpha Centauri are 43 light years apart. Ignore their relative motion Events A and B occur att on Earth and at 1 year on Alpha Centauri, respectively. (a) What is the time difference between the events according to an observer moving at B - 0.98 from Earth to Alpha Centauri? (b) What is the time difference between the events according to an observer moving at 3 = 0.98 from Alpha Centauri to Earth? (c) What is the speed of a spacecraft that makes the trip from Alpha Centauri to Earth in 2.5 years according to the spacecraft clocks? (d) What is the trip time in the Earth rest frame? [5+5+5+51 + Plane polar coordinates are related to cartesian coordinates by x=rcos and y = rsin. Describe the transformation matrix that maps cartesian coordinates to polar coordinates, and write down the polar coordinate basis vectors in terms of the basis vectors of cartesian coordinates. [51 5- suppose that we are given a basis ei, es consisting of a pair of vectors making a 45° angle with one another, such that ei hus length 2 and ez has length 1. Find the dual basis vectors for the case of covariant components of the vectors. [101
Answers
1. In the context of spacetime, the locus of points equidistant from the origin of a spacetime plane is a hyperbola.
In Euclidean space, the distance between two points is given by the Pythagorean theorem, which only considers spatial dimensions. However, in spacetime, the concept of distance is extended to include both spatial and temporal components. The spacetime distance, also known as the interval, is given by the Minkowski metric:
ds^2 = -c^2*dt^2 + dx^2 + dy^2 + dz^2,
where c is the speed of light, dt represents the temporal component, and dx, dy, dz represent the spatial components.
To determine the locus of points equidistant from the origin, we need to find the set of points where the spacetime interval from the origin is constant. Setting ds^2 equal to a constant value, say k^2, we have:
-c^2*dt^2 + dx^2 + dy^2 + dz^2 = k^2.
If we focus on a spacetime plane where dy = dz = 0, the equation simplifies to:
-c^2*dt^2 + dx^2 = k^2.
This equation represents a hyperbola in the spacetime plane. It differs from a circle in Euclidean space due to the presence of the negative sign in front of the temporal component, which introduces a difference in the geometry.
Therefore, the locus of points equidistant from the origin in a spacetime plane is a hyperbola.
(Note: The explanation provided assumes a flat spacetime geometry described by the Minkowski metric. In the case of a curved spacetime, such as that described by general relativity, the shape of the locus of equidistant points would be more complex and depend on the specific curvature of spacetime.)
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A drawer contains 6 white socks and 10 black socks. If 2 socks are chosen at random, what is the probability that they will have the same color
Answers
50% is the probability that they will have the same color.
What is probability?
Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.Classical: (equally probable outcomes) Let S=sample space (set of all possible distinct outcomes). Relative Frequency Definition. Subjective Probability.there are 16 socks in the drawer
probability of 2 white socks or 2 black socks
6/16 *5/15 + 10/16*9/15 no replacement on socks
30/240 + 90/240
120/240
1/2 = 50%
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Evaluate the following expression when m=16 and g = 4
g (9 – m) + 5
show ur work
Answers
4(9-16)+5
=4(-7)+5
=-28+5
=-23
Answer:
-23
Step-by-step explanation:
given: g(9-m)+5
substitute the values you have been given
4(9-16)+5
4(-7)+5
-28+5
=-23
Fill in the blank: 2(12x - 9) = 24x__
Answers
Answer:
- 18
Step-by-step explanation:
2*12x - 2*9
= 24x -18
Hope this helps you !
Have a nice day
Bye :-)
Answer:
24x-18-0
24x-18+18=0+18
24x=18
24/24 18/24
3/4
60% of the books on a bookshelf are english books. If there are 35 english books on the bookshelf, find the number of the books in the book shelf
Answers
Answer: 58 books
Step-by-step explanation:
There are 35 English books on the shelf and this constitutes 60% of the total number of books on the shelf.
Denoting the total number as x, the total number is:
35 = 60% * x
x = 35 / 60%
= 58 books