The triangle with the given vertices (-1, -1), (2, 3), and (-4, 3) is not an equilateral triangle.
What is an equilateral triangle?An equilateral triangle can be defined as a special type of triangle that has equal side lengths and all of its three (3) interior angles are equal.
In order to determine whether the triangle with the given vertices is an equilateral triangle, we would apply the distance formula to calculate the length of each side of this triangle as follows:
Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
For the vertices (-1, -1) and (2, 3), we have;
A = √[(2 - (-1))² + (3 - (-1))²]
A = √[(2 + 1)² + (3 + 1)²]
A = √[3² + 4²]
A = √[9 + 16]
A = √25
A = 5 units.
For the vertices (2, 3) and (-4, 3), we have;
B = √[(-4 - 2)² + (3 - 3)²]
B = √[-6² + 0²]
B = √[36 + 0]
B = √36
B = 6 units.
For the vertices (-1, -1) and (-4, 3), we have;
C = √[(-4 - (-1))² + (3 - (-1))²]
C = √[(-4 + 1)² + (3 + 1)²]
C = √[-3² + 4²]
C = √[9 + 16]
C = √25
C = 5 units.
Therefore, the triangle with the given vertices is not an equilateral triangle because C = A ≠ B.
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Complete Question:
An equilateral triangle has sides of equal length. Determine whether the triangle with vertices (-1, -1), (2, 3), (-4, 3) is equilateral.
an isosceles trapezoid has legs of length 30 cm each, two diagonals of length 40 cm each and the longer base is 50 cm. what is the trapezoid’s area?
768 cm'^2 is the trapezoid’s area.
What is isosceles trapezoid?
Isosceles trapezoids have equal length non-parallel sides, hence the name "isosceles" which means "equal legs". The "legs" are another name for these equal sides.
Let 50 cm = the bottom base
We can find the area of one of the triangles that comprise the area of the trapezoid.....its sides are 30, 40 and 50 cm
Let s be the semi-perimeter of one of the triangle = [ 50 + 40 + 30 ] / 2 = 60 cm
And the area of of this triangle = sqrt [ s ( s - a) (s - b) ( s -c) ] where a,b, c are the sides
So...we have sqrt [ 60 ( 60 - 30) (60 - 40) (60 - 50) ] = sqrt [ 60 * 30 * 20 * 10 ] =
sqrt [ 1800 * 200] = sqrt [ 3600 * 100] = 60 * 10 = 600 cm ^2
Now the base of this triangle = 50 and the height can be found as
follows :
Area = (1/2) 50 * height
600 = 25 * height
height = 24 cm and this is the height of the trapezoid
Now....the top base can be found as 50 - 2 sqrt [ 30^2 - 24^2 ] = 14 cm
So....the area of the trapezoid = (1/2) height ( sum of the bases) = (1/2) (24) ( 50 + 14) = 12 ( 64) = 768 cm'^2
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A quantity increases from 225 to 250. what is the percentage increase? round your answer to the nearest tenth of a percent.
The percentage increase for given quantity is 11.1%
In this question,
A quantity increases from 225 to 250.
So, the absolute change in the quantity would be,
|225 - 250| = 25
The relative increase of the quantity would be,
R = [tex]\frac{|225 - 250|}{225}[/tex]
R = 25 / 225
R = 0.111
We know that, the percentage increase of the quantity is the relative increase multiplied by 100.
So, the percentage increase of given quantity would be,
P = 0.111 × 100
P = 11.1%
Therefore, the percentage increase for given quantity is 11.1%
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How would you write the name of a segment differently than the name of a line? What
symbols would you use?
The way to write the name of a segment differently than the name of a line is that a line is written with the use of two arrowheads on the ends. While a line segment is just written down by an overbar with endpoints.
What is the line segment about?A line is known to be a kind of a one-dimensional figure that moves from infinitely in 2 directions.
A line segment is seen as a part of a line that is known to be made up of definite attributes where it has two endpoints as well as a fixed length.
Therefore, The way to write the name of a segment differently than the name of a line is that a line is written with the use of two arrowheads on the ends. While a line segment is just written down by an overbar with endpoints.
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Find the dimensions of a rectangle if the perimeter is 318 inches and the
length is half the width plus nine inches.
The dimensions of the rectangle are 59 by 50 inches
How to fnd the dimensions of a rectangle?The given parameters are
Length (l) = 1/2 width (w) + 9
Perimeter (P) = 318
Perimeter is calculated as
P = 2 (l + w)
Substitute l = 1/2w + 9 in P = 2(l + w)
So, we have
2 * (1/2w + w + 9) = 318
Evaluate the like terms
2 * (1.5w + 9) = 318
Divide by 2
1.5w + 9 = 159
So, we have
1.5w = 150
Divide by 15
w = 100
Substitute w = 100 in l = 1/2w + 9
l = 1/2 * 100 + 9
Evaluate
l = 59
Hence. the dimensions of the rectangle are 59 by 50 inches
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The average of a list of 4 numbers is 88.0. A new list of 4 numbers has the same first three numbers as the original list, but the fourth number in the original list is 82, and the fourth number in the new list is 96. What is the average of this new list of numbers?
A. 90
B. 91.5
C. 92
D. 92.5
E. 93.5
Answer:
C. 92
Step-by-step explanation:
88 + 96 = 184
184/2 = 92
Hope this helps :)
What is the formula for the sum of two whole numbers is 72. The difference is 48 what are the two numbers
Answer:
It works in both equations, so the two numbers are 60 and 12.
Step-by-step explanation:
Options are
A. (2, 2)
B. (8, 2)
C. (3, 11)
D. (5, 1)
Answer: The answer is C(3,11)
Step-by-step explanation:
If you replace x with 3 that will be 3 to the third power 3 x 3 is 9 so 9 plus 2 is 11 you can use 11 in y, therefor your answer is C.(3,11)
please I want a beautiful and nice sentences in12 words:bedrock,robust,isolation,eliminate,ritual, endure, diagnose, outlive, relieve,ailment, relentless and mortality.and thanks
Answer:
Step-by-step explanation:
x^2+3 divided by x-2
Answer:
x2 + 3x − 2
Explination: trust pls
Need help right now again
Answer:
I gotchu! The answer is 80.
Step-by-step explanation:
To find the mean, you need to add up all the scores and divide it by how many scores there are. In this case, there are 5 scores, so we can first add them all up.
70+75+80+85+90=400
Now, since there are 5 scores, you need to divide 400 by 5.
400/5=80
The mean would be 80.
Hope that helped!
Have a great day!
:D
Eva left her house at time zero and drove to the store, which is 3 blocks away, at a
speed of 1 block per minute. Then she stopped and went into the store for 3 minutes.
From there, she drove in the same direction at a speed of 1 block every 2 minutes
until she got to the bank, which is 3 blocks away from the store. She stopped at the
bank for 6 minutes. Then she drove home at a speed of 1 block every minute. Make a
graph of showing the number of blocks away from home that Eva is a minutes after
she leaves her house, until she gets back home.
The function f(x), representing the number of blocks Eva is away from her house after x minutes is
[tex]f(x) = \begin{cases} & 0\text{ if } x= 0\\ & x\text{ if } 0 < x\leq 3 \\ & 3\text{ if } 3 < x\leq 6\\ & x/2\text{ if } 6 < x\leq 12\\ & 6\text{ if } 12 < x\leq 18\\ & 24-x\text{ if } 18 < x\leq 24 \\ & 0\text{ if } x > 24 \end{cases}[/tex]
The graph for the same is attached.
In the question, we are asked to form a graph showing the number of blocks, that Eva is away from her home at x minutes, after she leaves her home.
To form the graph, we first try to make a function for x minutes, f(x), showing the number of blocks Eva is away from her home after x minutes.
Since x represents time, it cannot be negative.
At x = 0, f(x) = 0, as she is at her home at 0 minutes.
Then, Eva visits the store, 3 blocks away from her home at a speed of 1 block per minute.
Thus, she moves 1 block every minute up to 3 minutes.
Thus, we get f(x) = x, 0 < x ≤ 3.
After this, she spends 3 minutes at the store, giving f(x) = 3, 3 < x ≤ 6.
Then she moves towards the bank, in the same direction, 3 blocks away at the speed of 1 block every 2 minutes.
Thus, in every minute, she travels 1/2 block.
Thus, the function can be designed as follows:
f(x) = 3 + (1/2)(x - 6), 6 < x ≤ 12,
or, f(x) = x/2, 6 < x ≤ 12.
Now, we are given that she stops at the bank for 6 minutes.
Thus, we get, f(x) = 6, 12 < x ≤ 18.
Now, she drove back home, at the speed of one block every minute.
Thus, we get f(x) = 6 - (x - 18), 18 < x ≤ 24,
or, f(x) = 24 - x, 18 < x ≤ 24.
At the 24th minute, Eva reaches her house back, giving f(x) = 0, x > 24.
Thus, the complete function can be shown as:
[tex]f(x) = \begin{cases} & 0\text{ if } x= 0\\ & x\text{ if } 0 < x\leq 3 \\ & 3\text{ if } 3 < x\leq 6\\ & x/2\text{ if } 6 < x\leq 12\\ & 6\text{ if } 12 < x\leq 18\\ & 24-x\text{ if } 18 < x\leq 24 \\ & 0\text{ if } x > 24 \end{cases}[/tex]
The graph for this function is attached.
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Show your work given the rule of (x,y)—->(x-7.5,y+6.8)
Original coordinate (5,3)
The translation of the point, (5, 3) according to the rule, (x, y) → (x - 7.5, y + 6.8), gives the point, (-2.5, 9.8)
What is a translation transformation?A translation transformation is one in which the image of a pre–image is located at a position according to a rule. such that the difference between the image and the pre-image is a change in location.
Given parameters;
The coordinates of the given point = (5, 3)
The rule for the given transformation = (x, y) → (x - 7.5, y + 6.8)
The original coordinates of the point = (5, 3)
The coordinates of the image following the transformation is therefore;
[tex](5, 3) \: \underrightarrow{ T } \: (5 - 7.5,\: 3 + 6.8) [/tex]
Where;
[tex]T = T_{ (- 7.5,\: 6.8)}[/tex]
(5 - 7.5, 3 + 6.8) = (-2.5, 9.8)
Which gives;
[tex](5, 3) \: \underrightarrow{ T_{( - 7.5,\: 6.8)} } \: ( - 2.5,\: 9.8) [/tex]
The transformation of the point (5, 3) according to the rule (x, y) → (x - 7.5, y + 6.8), gives (-2.5, 9.8)
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The mass of a textbook is approximately 0.00165 metric ton. How is this number written in scientific notation?
Answer: 1.65 × 10⁻³
Step-by-step explanation: hope this helps!!!
A shop in the mall is 5 meters by 15 meters. How much would it cost to recarpet the shop with carpet that costs $5.00 per square meter?
Work Shown:
The floor area is length*width = 5*15 = 75 square meters
1 square meter = 5 dollars
75*(1 square meter) = 75*(5 dollars)
75 square meters = 375 dollars
Use the following diagram to answer Parts A and B. A(-6,5) B (-6,1) (-2,1 (2.1) (6.1) (6,5) A' Part A: Identify the transformation that took triangle ABC to triangle A'B'C'. Part B: If the same transformation was applied to point J(5, -4), what are the coordinates for J'? Edit View Insert Format Tools Table 12pt Paragraph I BIU 2T²00
Using translation concepts, it is found that:
A. The triangle was reflected over the y-axis.
B. The coordinates for J' are (-5,-4).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For item a, we have that the rule applied at each vertex is given by:
(x,y) -> (-x,y).
This rule means that the triangle was reflected over the y-axis.
In item b, supposing point J(5,-4), the image is given by:
(5,-4) -> (-5,-4).
The coordinates for J' are (-5,-4).
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Need the answer as soon as possible.
A bank loaned out $8200, part of it at a rate of 7.9% per year and the rest of it at a rate of 7.4% per year. The total amount of interest owed to the bank at the end of one year was $614.67.
Find the amount of money that the bank loaned out at 7.9%.
The amount that the bank loaned out at 7.9% is $1,574.00
How do represent the amounts lent at different rates?
On the assumption that x amount was loaned at 7.9% and that the remaining amount, (8,200-x) was loan out at 7.4%, we can determine the interest charged on each loan as the loan multiplied by the interest rate
interest on 7.9% loan=7.9%*x=0.079x
interest on 7.4% loan=7.4%*(8200-x)
interest on 7.4% loan=606.80-0.074x
total interest=0.079x+606.80-0.074x
total interest=0.005x+606.80
total interest on loans=614.67
614.67=0.005x+606.80
614.67-606.80=0.005x
7.87=0.005x
x=7.87/0.005
x=amount loaned at 7.9%=$1,574.00
y=$8200-$1574
y=$6,626.00
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Help with 4 I don’t get it
you need to draw the exact graph of f(x), but moved 3 units to the right and 5 units up.
How to graph the given function?First, we know the graph of f(x), and now we want to find the graph of the function:
f(x - 3) + 5.
Remember that a horizontal translation of N units is written as:
f(x + N)
If N > 0, the translation is to the left.if N < 0, the translation is to the right.Remember that a vertical translation of N units is written as:
f(x + N)
If N > 0, the translation is upif N < 0, the translation is downwards.Then the function:
f(x - 3) + 5
Is a translation of 3 units to the right and 5 units upwards.
This means that you need to draw the exact graph of f(x), but moved 3 units to the right and 5 units up.
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What is 6•w•w•z•z in exponent
6w^2z^2
I hope this helps!
Simplify
45 - (31 - 9)
Answer:
23
Step-by-step explanation:
you always do whatever is in the brackets first,
31 - 9 = 22
then the equation would be,
45 - 22
so the answer is 23
hope this helped xx
Simplify 1 3/4 and 2 1/2
Answer: 1 3/4=7/4
2 1/2=5/2
Step-by-step explanation:
1 3/4=
1 + 3/4=
4/4 + 3/4=
(4+3)/4=7/4
2 1/2=
2+1/2=
4/2+1/2=5/2
I need help with this :)
Answer:
-2 1/4Correct placement.Absolute values:
Absolute values are specific values in math interpreted by vertical bars and a plus/minus symbol to represent addition, subtraction, or if they are negative / positive. Mostly, if the absolute value is positive, you can write the vertical bars to represent its absolute value. No need for a plus symbol. However, negative numbers are often different.
Exempli gratia(e.g): |2|, |-2|, |+2|
Please I need help ASAP what’s the distance between the 2 points
Answer:
7 grids
Step-by-step explanation:
-start at one of your points
-count up or down the y-axis to the other point.
-count along the x-axis to your other point.
-add the 2 lengths.
two and half of a number added to three quarters of the same number gives you 13.find the number.
Answer:
52/21
Step-by-step explanation:
Translate the word equation into an algebraic equation as follows:
Let the number be X
two-and-a-half of a number --> (2 1/2) X
2 1/2 = (2 x 2 + 1) = 5/2
So two-and-a-half of a number --> (9/2)X = 9X/2
three-quarters of the same number --> (3/4)X --> 3X/4
two and half of a number added to three quarters of the same number becomes 9X/2 + 3X/4
gives you 13 --> = 13
So we get the equation:
9X/2 + 3X/4 = 13
Multiply both sides by 4 to get rid of the denominators
4.(9X/2) + 4(3X/4) = 4 x 13 = 52
36X/2 + 12X/4 = 52
==> 18X + 3X = 52
==> 21X = 52
==> X = 52/21
PLEASE HELP ASAP!! will mark brainlest
Answer: read first :)
Step-by-step explanation:
the first equation, x= -4 + 3y/5
y= 20/3 + 5x/3
the second equation, x= 4 - 2y/3
y= 6 - 3x/2
cocoa drank 1/3 milk on monday. on tuseday she drank 1/4 gallon of milk. how much milk did she drank inb all
please help me !! :)
i absolutely suck at this & have yo submit this assignment in 10 minutes
Answer: a=123
b=230
Step-by-step explanation:
In Exercises 11 and 12, write a rule for the translation of LMN to L'M'N'
The rule for the translation from LMN to L'M'N' is:
(x,y) -> (x + 3, y + 1).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For this problem, we have that each vertex of LMN was:
Shifted 3 units right, hence x -> x + 3.Shifted 1 unit up, hence y -> y + 1.Thus the rule for the translation from LMN to L'M'N' is:
(x,y) -> (x + 3, y + 1).
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what is 9 4/9 dividedby 5/9
Answer:
17
Step-by-step explanation:
Answer:
17
Step-by-step explanation:
Can you give me brainliest?
last year, nine hundred forty-nine thousand people visited the museum. what is the number written in standard form?
The number of written in standard form is 9.45 × 10⁵
Writing in Standard formFrom the question, we are to write the given number in standard form
The given number is
Nine hundred forty-nine thousand
That is,
945000
To write a number in standard form, we will write the number as a decimal number between 1.0 and 10.0, multiplied by a power of 10.
The number, 945000, written in standard form is
9.45 × 10⁵
Hence, the number of written in standard form is 9.45 × 10⁵
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