Answer: HIJK is a parallelogram because the midpoint of both diagonals is (1,0) , which means the diagonals bisect each other.
Step-by-step explanation:
Given: The coordinates of parallelogram H I J K as
H is at (- 2, 2), point I is at (4, 3), point J is at (4, - 2), and point K is at (- 2, - 3).
Diagonals : HJ and IK [join opposite vertices]
Mid point of HJ = [tex](\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]
[tex]=(\dfrac{-2+4}{2},\dfrac{2+(-2)}{2})=(1,0)[/tex]
i.e. Mid point of HJ = (1,0)
Mid point of IK = [tex](\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]
[tex]=(\dfrac{4+(-2)}{2},\dfrac{3+(-3)}{2})=(1,0)[/tex]
i.e. Mid point of IK = (1,0) =Mid point of HJ
When mid points of both diagonals are equal then that means the diagonals bisect each other.
Thus, HIJK is a parallelogram because the midpoint of both diagonals is (1,0) , which means the diagonals bisect each other.
Answer:
(1,0)
Step-by-step explanation:
plz answer this asap
Answer:
50%
Step-by-step explanation:
A daycare facility is enclosing a rectangular area along the side of their building for the children to play outdoors. They need to maximize the area using 180ft of fencing on three sides of the yard. The quadratic equation A=−2x2+180x gives the area, A, of the yard for the length, x, of the building that will border the yard. Find the length of the building that should border the yard to maximize the area, and then find the maximum area.
Answer:
a) length x = 45ftb) maximum area = 4050 ft²Step-by-step explanation:
Given the quadratic equation A=−2x2+180x that gives the area A of the yard for the length x, to maximize the area of the yard then dA/dx must be equal to zero i.e dA/dx = 0
If A=−2x²+180x
dA/dx = -4x + 180 = 0
-4x + 180 = 0
Add 4x to both sides
-4x + 180 + 4x = 0 + 4x
180 = 4x
x = 180/4
x = 45
Hence the length of the building that should border the yard to maximize the area is 45 ft
To find the maximum area, we will substitute x = 45 into the modelled equation of the area i.e A=−2x²+180x
A = -2(45)²+180(45)
A = -2(2025)+8100
A = -4050 + 8100
A = 4050 ft²
Hence the maximum area of the yard is equal to 4050 ft²
In a group of 25 people, only three languages are spoken – English, Spanish and German. If there is at least one person who speaks all the three languages, how many people can interact with each other in English and German? 4 people speak two languages but do not speak Spanish One fifth of the group speaks more than one language.
Answer:
x + a=5
Step-by-step explanation:
Let
number of people who speak only English = E
the number of people who speak only German = G
the number of people who speak only Spanish = S
the number of people who speak only English & German but not Spanish = x
the number of people who speak only English & Spanish but not German = y
the number of people who speak only German & Spanish but not English = z;
the number of people who speak only German & Spanish & English = a
Find the the value of (x + a).
Statement 1: 4 people speak two languages but do not speak Spanish.
x = 4.
x+a
Value for a is unknown.
(x + a). Insufficient.
Statement 3: One-fifth of the group speaks more than one language.
x + y + z + a
= 25/5
= 5
value of (x + a) unknown
Insufficient.
Putting (1) and (2) together
x + y + z + a = 5
x = 4 and a=1,
we have only one possible solution from
x + y + z + a = 5
x + a
= 4 + 1
= 5.
Sufficient.
20 POINTS AND BRAINLIEST!! Which of the following statements can be supported by the evidence shown in the graph?
A. The line best fit shows a positive correlation between month number and minutes
B. The line of best fits shows a negative correlation between the number of months and the number of minutes
C. The line of best fits shows no correlation between the month number and the number of minutes
Answer:
B. The line of best fits shows a negative correlation between the number of months and the number of minutes
Step-by-step explanation:
In a scatter plot, when the data points are clustered along the line of best fit, it shows a trend, and it implies there's a correlation between the x-variable and the y-varisble.
Also, when the line of best fit slopes upward, from your left to your far right, it shows a positive correlation between the variables on the x-axis and y-axis.
On the other hand, if the line of best fit slopes downwards, from your left down to your right, this shows a negative correlation.
Thus, considering the line of best fit in the question, the line of best fit shows a negative correlation between the number of months and the number of minutes. The line of best fit slopes downwards, from your left to your right.
This shows that, as month number increases, number of minutes decreases.
Help please!!!! Thank you
Answer:
E) 15pi/2
Step-by-step explanation:
The total circle area is pi*r^2. r = 6. so the total area is 6^2pi, or 36pi.
However, we are dealing with 75/360 of a circle, or 5/24 of a circle. 5/24 * 36pi = 15pi/2.
What is the coefficient of the variable in the expression 2 - 5x – 4 + 8?
a
-5
b
-4
с
2
d
8
Answer:
-5
Step-by-step explanation:
The coefficient is the number attached to the variable.
There is a point $A$ with positive coordinates such that the sum of the coordinates of $A$ is $14$. If the $x$-coordinate of $A$ is $a$, then point $P$ is at $(3a, a^2+13a-11)$. If the slope of a line passing through $A$ and $P$ is $7$, find $a$.
Answer:
5
Step-by-step explanation:
Given:
A = (a, 14-a)
P = (3a, a^2 +13a -11)
the slope of AP is 7
a > 0
Find:
a
Solution:
The slope of AP is ...
m = (Py -Ay)/(Px -Ax)
7 = (a^2 +13a -11 -(14 -a))/(3a -a)
14a = a^2 +14a -25
25 = a^2
a = √25 = 5 . . . . . the positive solution
The value of 'a' is 5.
_____
Check
The point A is (a, 14-a) = (5, 9).
The point P is (3a, a^2 +13a -11) = (15, 79)
The slope of AP is (79 -9)/(15 -5) = 70/10 = 7.
BRAINLIEST!!! Plz help ASAP
M(5, 7) is the midpoint of side RS.The coordinates of S are (6, 9). What are the coordinates of R?Please answer with full explanation and no non sense answers will reports. Will give brainiest to those who answered correctly with full explanation. Thank you.
Answer: R = (4, 5)
Step-by-step explanation: Midpoint is simply the center of a line. So, the equation for it is ((x1+x2)/2, (y1+y2)/2). Hence for this,
x coordinate- (6+x)/2=5
x=4
y coordinates- (9+y)/2=7
y=5
And therefore R is (4, 5)
how many are 6 raised to 3 ???
Answer:
216
Step-by-step explanation:
When you say "6 raised to 3", it means you multiply 6, 3 times. Meaning:
6✖️6✖️6=216
Hope this helped!
Have a nice day:)
Right or wrong ????
Octagon ABCDEFGH and its dilation, octagon A'B'C'D'E'F'G'H', are shown on the coordinate plane below:
G
H
5
G
Н"
F
2
A
חד
A
2
7
B
B
-7-6-5-4-2-2=1
E
-2
E
D.
-5
D
C
С
If the center of dilation is at the origin, by what scale factor was octagon ABCDEFGH dilated? (4 points)
Answer:
c 1/2
Step-by-step explanation:
You are incorrect.
We are going from ABCDEFGH to A'B'C'D'E'F'G'H'. We are going from the large octagon to the small octagon. The scale factor of a dilation is the number you multiply the original lengths to get the lengths of the dilation.
[tex]scale~factor = \dfrac{length~of~dimension~in~dilated~image}{length~of~corresponding~dimension~in~original~figure}[/tex]
Look at point (6, 0) which becomes (3, 0) in the dilation.
The distance from the origin to (6, 0) is 6 units.
The distance from the origin to (3, 0) is 3 units.
scale factor = dilated/original = 3/6 = 1/2
The scale factor of the dilation is 1/2.
Also look at segment AB whose length is 4. The length of segment A'B' is 2.
scale factor = dilated/original = 2/4 = 1/2
Answer: 1/2
If PR = 4X - 2 AND RS = 3X - 5 which expression represents PS?
Answer:
7x - 7
Step-by-step explanation:
If PR, RS, and PS are line segments then the equation below will work.
PR + RS = PS
(4x-2) + (3x-5) = 7x - 7
(−2a+5−b)⋅(−5) <- does this equal to 10a−25+5b?
Answer:
Yes!
Step-by-step explanation:
I need help pls and I will give a 5 star rating and a big thank you comrades.
Answer:
Option (C) : y = 6 / 11
Step-by-step explanation:
To find Horizontal Asymptote of the function, you need to see degree of of numerator and denominator.
Since, the degrees of the numerator and denominator are the same,
Horizontal Asymptote = leading coefficient of the numerator divided byleading coefficient of the denominator
Therefore,
Horizontal Asymptote = 6 / 11
The amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of minutes and a standard deviation of minutes. Find the probability that a randomly selected athlete uses a stairclimber for (a) less than minutes, (b) between and minutes, and (c) more than minutes. (a) The probability that a randomly selected athlete uses a stairclimber for less than minutes is nothing. (Round to four decimal places as needed.) (b) The probability that a randomly selected athlete uses a stairclimber between and minutes is nothing. (Round to four decimal places as needed.) (c) The probability that a randomly selected athlete uses a stairclimber for more than minutes is nothing.
Answer:
Step-by-step explanation:
Let S be the sample space, n(S) = 60
a) Let A be the event that the selected athlete uses
s less than a minute, n(A) = 59
The probability that a randomly selected athlete uses less a minute, P(A) = n(A)/n(S) = 59/60 = 0.9833
b) 1 - 0.9833 = 0.0167
c) 1 - 1 = 0
In which direction must the graph of Ax) = x be shifted to produce the graph of g(x) = f(x) - 4?
ОА. up
OB. down
O c. left and down
OD. right and up
Answer: B. down
Step-by-step explanation:
Translation rules:
For a function h(x):
h(x+c) is a left-shift by c units.h(x-c) is a right-shift by c units.h(x)+c is a up-shift by c units.h(x)-c is a down-shift by c units.Here, the graph of f(x) becomes the graph of g(x) =f(x)-4 which is similar to "h(x)-c".
That means , f(x) is shifted 4 units down to become g(x).
So, correct option : B. down
Consider a triangle ABC like the one below. Suppose that a =53, b=18, and A=130º. (The figure is not drawn to scale.) Solve the triangle.
Carry your intermediate computations to at least four decimal places, and round
your answers to the nearest tenth.
If no such triangle exists, enter "No solution." If there is more than one solution, use the button labeled "or".
Answer:
B = 15.1°, C = 34.9°, c = 39.6
Step-by-step explanation:
law of sines
53/sin 130 = 18/sin B
sin B = .26; B = 15.1°
C = 180 - 15.1 - 130 = 34.9°
c/sin 34.9 = 53/sin 130
c = 39.6
A circle is circumscribed around a square and another circle is inscribed in the square. If the area of the square is 9 in2, what is the ratio of the circumference of the circumscribed circle to the one of the inscribed?
Answer:
√2:1
Step-by-step explanation:
First we need to know that the length of the side of the square is equal to the diameter of the inscribed circle i.e
L = di
Given the area of the square to be 9in², we can get the length of the square.
Area of a square = L²
L is the length of the square.
9 = L²
L = √9
L = 3in
Hence the length of one side of the square is 3in
This means that the diameter of the inscribed circle di is also 3in.
Circumference of a circle = π×diameter of the circle(di)
Circumference of inscribed circle = π×3
= 3π in
For the circumscribed circumscribed circle, diameter of the outer circle will be equivalent to the diagonal of the square.
To get the diagonal d0, we will apply the Pythagoras theorem.
d0² = L²+L²
d0² = 3²+3²
d0² = 9+9
d0² = 18
d0 = √18
d0 = √9×√2
d0 = 3√2 in
Hence the diameter of the circumscribed circle (d0) is 3√2 in
Circumference of the circumscribed circle = πd0
= π(3√2)
= 3√2 π in
Hence, ratio of the circumference of the circumscribed circle to the one of the inscribed will be 3√2 π/3π = √2:1
Which statement is false? Question 4 options: All whole numbers are integers. All natural numbers are whole numbers. All real numbers are irrational numbers. All whole numbers are real numbers.
Answer:
C
Step-by-step explanation:
Not all real numbers are irrational.
How many solutions does the system have?
Answer:
B. no solutionsStep-by-step explanation:
Left sides of both equations are the same sum (8x+2y), so the right sides also has to be the same. They are not so there is no solutions.
{If they are the same then system has infinitely many solutions.}
Let P (2,-3), Q (-2, 1) be the vertices of the triangle PQR. If the centroid of ΔPQR lies on the line 2x +3y = 1, then the locus of R is a. 2x + 3y = 9 b. 2x - 3y = 9 c. 3x + 2y = 5 d. 3x - 2y = 5
Answer:
Correct answer is a. 2x + 3 y = 9.
Step-by-step explanation:
Let the coordinates of centroid be (h,k)
{h/3 , (-2+k)/3}
h = (2 – 2 + a)/3 = a/3 ---eqn 1
k= ( - 3+ 1 + b )/3 = (-2 + b)/3 -----eqn 2
Where (x,y) are any point on the line 2x+3y=1
3h = a and 3k + 2 = b
From 2x +3y = 1,
Then, 2h +3k = 1, 3k = 1 - 2h -----eqn 3
b = 1 - 2h + 2 = 3 - 2h
also b = 3 - 2a/3
b = (9 -2a)/3
3b = 9 - 2a
3b + 2a = 9
Now (x,y) satisfy the point on the line 2x+3y=9
So the locus is 2x + 3 y = 9.
i back at you with another question..!
Answer:
Identity Property of Multiplication
Step-by-step explanation:
The Identity Property of Multiplication states that any number multiplied by 1 will equal the same number.
Since we have one item that costs $14.50, we know that the total cost will be $14.50 since we are multiplying $14.50 by 1.
Hope this helped!
Answer:
Identity property of multiplication.
Step-by-step explanation:
When we multiply any number by 1, we will get the same number.
5 *1 = 5
-8 * 1 = -8
Does anyone know this?
Answer:
f(-4) = 92
Step-by-step explanation:
f(x) = 3x^2 - 10x + 4
f(-4) = 3(-4)^2 - 10(-4) + 4
= 3(16) + 40 + 4
= 48 + 40 + 4
= 92
Directions: Simplify each expression by combining like
Terms (pls help if u can )
Answer:
1. -y
3. 9a-7
5. 14x-2
7. 7d-6
Step-by-step explanation:
1. 8y-9y=-y
3. 8a-6+a-1
=(8a+a)-(6+1)
=9a-7
5. -x-2+15x
=(-x+15x)-2
=14x-2
7. 8d-4-d-2
=(8d-d)-(4+2)
=7d-6
Answer:
1. -x
3. 9a-7
5. 14x-2
7. 7d-6
Step-by-step explanation:
To do the first one you would just subtract 8 by 9 which is -1 so you would get -x as 1.
To do the third one would would just move the numbers around so you get 8a+a-6-1 and when you simplify you get 9a-7.
To do the fifth one you just have to move the numbers so you get -x+15x-2 and when you simplify you get 14x-2
To do the seventh one you just have to move the numbers so you get 8d-d-4-2 and when you simplify you get 7d-6.
Please answer answer question
Answer:
c=13.42
Step-by-step explanation:
[tex]A^2+B^2=C^2\\6^2+14^2=C^2\\C^2=144+36\\C^2=180\\\sqrt{c^2}=\sqrt{180} \\c=13.42[/tex]
Work out the value of angle x
======================================================
Explanation:
The given exterior angle 97 is adjacent to the interior angle 180-97 = 83. This is the base angle of the isosceles triangle. The other base angle is directly above it. The base angles are always opposite the congruent sides.
The missing interior angle (adjacent to the blue angle x) is unknown, so we'll call it angle y. This angle adds to the other two base angles (83 each) to get a sum of 180. Adding any three interior angles of a triangle always gets you 180
y+83+83 = 180
y+166 = 180
y = 180-166
y = 14
Angle x and y are supplementary. They form a 180 degree angle
x+y = 180
x = 180-y
x = 180-14
x = 166
As you can see, the base angles combine to form the exterior angle we're after. This is because of the remote interior angle theorem.
Simplify the following expression.
Answer:
3x+11y-3
Step-by-step explanation:
Hey! So here is what you do to solve the problem-
Combine like terms:
(x) 5x-2x=3x
(y) 3y+8y=11y
(#) 7-10 =-3
So....
3x+11y-3 is your answer!
Hope this helps!:)
Please give me the correct answer
Answer:
Area= 452.23 ft²
Step-by-step explanation:
Angle at U = 180-48-20
Angle at U = 112°
UT/sin 112=46/sin 48
UT= 0.9272*46/0.7431
UT=57.4 ft
UV= sin 20*46/sin48
UV= 0.3420*46/0.7431
UV= 21.2 ft
S=( 21.2+57.4+46)/2
S=124.6/2
S= 62.3
Area= √((62.3)(62.3-21.2)(62.3-57.4)(62.3-46))
Area= √((62.3)(41.1)(4.9)(16.3))
Area= √204509.5311
Area= 452.23 ft²
The product of 2 rational numbers is -16/9 . If one of the numbers is -4/3 find the other plz fast
Answer:
4/3
Step-by-step explanation:
let the other number be x.
-4/3 x=-16/9
x=-16/9×-3/4=4/3
What is the image of (-1,-4) after a reflection over the line y=-x
Answer:
[tex]\huge\boxed{(4,1)}[/tex]
Step-by-step explanation:
The point is (-1,-4)
It is reflected over y = - x, So, the coordinate will be like: ( -y , -x )
So, when it is reflected over y = -x , it becomes (4,1)
When a point is reflected, it must be reflected over a line.
The image of (-1,-4) after a reflection over the line y=-x is (4,1).
The point is given as:
[tex]\mathbf{(x,y) = (-1,-4)}[/tex]
The rule of reflection over line y = -x is:
[tex]\mathbf{(x,y) \to (-y,-x)}[/tex]
So, we have:
[tex]\mathbf{(x,y) \to (-(-4),-(-1))}[/tex]
[tex]\mathbf{(x,y) \to (4,1)}[/tex]
Hence, the image of (-1,-4) is (4,1).
Read more about reflections at:
https://brainly.com/question/938117
Caculate the value of x on the figure below
Answer:
x = 58
Step-by-step explanation:
The angle at the centre is twice the angle at the circumference subtended by the same arc, thus
x + 62 = 2(x + 2)
x + 62 = 2x + 4 ( subtract x from both sides )
62 = x + 4 ( subtract 4 from both sides )
58 = x
