The midpoint of diagonal AC is (5,-3).
Given A(3,-1) and C(7,-5)
Let the midpoint of diagonal AC be represented by P (say). Then the coordinate of P can be calculated by using the formula listed below:
let us suppose the coordinates of A be (a, b) and B be (c, d) and P is the midpoint of AC then the coordinate of P will be (a+c/2, b+d/2).
Now, by using the above formula, we get
x-coordinate of P be (3+7)/2 = 10/2 = 5
y-coordinate of P be (-1+(-5))/2 = -6/2 = -3
∴ The coordinate of midpoint of AC i.e., P be (5, -3).
Hence, the midpoint of diagonal AC is (5,-3).
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The figure shown is composed of a rectangle
and a hexagon. The length of each side of the
hexagon is 2 centimeters. Determine the area
of the shaded region.
Answer:
Step-by-step explanation:
The area of shaded region is 3.6077 cm²
What is Area of rectangle?The area occupied by the rectangle within its perimeter can be calculated using the formula for the area of a rectangle.
A rectangle's area is calculated by multiplying its length by its width. Therefore, the product "l x w" is the formula for the area, "A," of a rectangle whose length and breadth are "l" and "w," respectively.
Given:
rectangle:
Length = 4 cm
width= [tex]3 \frac{1}{2}[/tex] cm
So, area of rectangle
= length x width
=4 x [tex]3 \frac{1}{2}[/tex]
= 4 x 7/2
=14 cm²
Now, area of Hexagon
= 3√3/2 x a²
= 3√3/2 x 2²
= 3√3/2 x 4
= 3√3 x 2
= 10.3923 cm²
Then, area of shaded region
= 14 - 10.3923
=3.6077 cm²
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Convert 0.074 to standard form.
Answer:
In standard form 7.4 × 10^-2
Step-by-step explanation:
Answer:
7.4×10^-2
Step-by-step explanation:
Firstly, to convert 0.074 to standard form you will bring the first significant figure and make it the first I.e 7.4 then count how many times you took it backwards to make it 7.4 then put a negative sign in front of it because you took it backwards
Julio says," if you subtract 19 from my number and multiply the difference by -3, the result is -15." what is Julio's number?
Answer:
24
Step-by-step explanation:
24 - 19 = 5
5 * -3 = -15
Answer:
answer is 5
Step-by-step explanation:
[tex] - 3(x - 19) = - 15[/tex]
cancel out both sides by -3, therefore -15 will become positive
[tex] \frac{ - 3(x - 19)}{ - 3} = \frac{ - 15}{ - 3} [/tex]
then add 19 to both sides
[tex]x - 19 +19= 5 + 19[/tex]
then X will add up to 24
Determine whether the vectors in each pair are normal to each other. (0.8 -0.6) [0.3 0.4]
Since their dot product is equal to zero, then vectors (0.8, -0.6) and (0.3, 0.4) are normal to each other.
Two vectors are said to be normal or perpendicular to each other if the result of their dot product is equal to zero.
These two vectors are also called orthogonal to each other.
Let u = (u₁, u₂) and v = (v₁, v₂), then the dot product u . v is defined as:
u . v = u₁v₁ + u₂v₂
To check whether the vectors are normal to each other, let us check their dot product.
The given vectors are: (0.8, -0.6) and (0.3, 0.4).
Let u = ((0.8, -0.6) and v = (0.3, 0.4), then,
u . v = 0.8 . 0.3 + (-0.6) . 0.4
= 2.4 + (-2.4) = 0
Since u.v = 0, then vectors (0.8, -0.6) and (0.3, 0.4) are normal to each other.
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Find any points of discontinuity for each rational function. y= x²+2 x / x²-7 x-18
points of discontinuity of rational function y= x²+2 x / x²-7 x-18 is x = 9 & x = -2.
How to find the points of discontinuity of the rational function & find the x - and y -intercepts of the rational function?points of discontinuity:
In rational functions, points of discontinuity are defined as fractions with undefined or zero as their denominator. When the denominator of a fraction is 0, the fraction is no longer defined and shows up as a hole or break in the graph.
points of discontinuity removable:
A point on the graph that is removable discontinuity is one that may be filled in with a single value despite not existing.If an is zero for a factor in the denominator that shares a factor with a factor in the numerator, a removable discontinuity at x=a in the graph of a rational function occurs.
points of discontinuity non removable:
A function's break that cannot be repaired with a single point is referred to as a non-removable discontinuity. It cannot be filled in with a single point, a vertical asymptote (a vertical line that the graph approaches but never crosses because the function is undefined at that x-value) is non removable.
given that
[tex]y = \frac{ {x}^{2} + 2x}{ {x}^{2} - 7x - 18 } [/tex]
now take the denominator and find the factors of it.
[tex] {x}^{2} - 7x - 18 = 0[/tex]
[tex] {x}^{2} - 9x + 2x - 18 = 0[/tex]
x (x -9) + 2 (x - 9) = 0
(x - 9) (x + 2) = 0
[tex]y = \frac{ {x}^{2} + 2x}{(x - 9)(x + 2)} [/tex]
now, take common on numerator
[tex]y = \frac{2(x + 2)}{(x - 9)(x + 2)} [/tex]
cancel the common factor in both numerator and denominator
[tex]y = \frac{x}{x - 9} [/tex]
now find the points of discontinuity.
x-9=0 , x+2=0
x = +9 , x = -2
now, x = +9 and x = -2
Hence the points of discontinuity of rational function y= x²+2 x / x²-7 x-18 is x = 9 & x = -2.
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The square root at Sam's gym has an Area of 144 square feet. What is the lenght of the perimeter of the pool?
The length of one side of the pool is 12 feet
The shape of the pool is a square
A square is a 2-dimensional quadrilateral with sides of equal lengths.
Characteristics of a square
The angles in the square are right angles
The sum of angles equal 360 degrees
Diagonals are equal in length
Area of a square = length²
144 = length²
In order to determine the length of a side, determine the square root of the area
√144 = 12 feet
therefore the area of a gym is 12 feet.
dimension, in common parlance, the measure of the size of an object, such as a box, usually given as length, width, and height. In mathematics, the notion of dimension is an extension of the idea that a line is one-dimensional, a plane is two-dimensional, and space is three-dimensional.
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A triangle has a base of [tex]2^{-3}[/tex] units and a height of [tex]2^{-4}[/tex] units. What is the height of the triangle? Write your answer using a positive exponent.
The height of the triangle has a measure of 2⁻⁴ units, that is equivalent to a measure of 1 / 2⁴ units.
What is the height of a triangle?
The statement indicates the dimensions of a triangle, where the base and the height of the figure are expressed by exponential numbers with positive integer base and negative integer exponents and each of which must be rewritten with positive exponents, this can be done by using the following power property:
a⁻ⁿ = 1 / aⁿ
Then, if the height of the triangle has a measure of 2⁻⁴ units, that is equivalent to a measure of 1 / 2⁴ units.
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-2√294p³
I don’t understand how to get the square root of √294p³
The expression -2√294p³ can be simplified as -17.146 p√p using the concept of radicals.
What is a radical?An expression that has a root, typically a square or cube root, is referred to as a radical.
The radical form of the square root of 294 is √294 and the exponent form is [tex]294^{\frac{1}{2} }[/tex].
17.146428 is the square root of 294 when rounded to six decimal places.
Now, the square root of p³ will be
[tex]\sqrt{p^{2} .p}[/tex] = p√p
Therefore the square root of √294p³ is 17.146428p√p.
The expression -2√294p³ can be written as -17.146 p√p.
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Use a two dimensional model and the dimensions provided to calculate the perimeter and area of the sail. Round the area to the nearest tenth if necessary.
perimeter:__________ft ___________in
Area:______________ft^2
From the given triangular sail, it is found that:
The perimeter is of 41 ft 3 in.The area is of 81.4 ft².What is the perimeter of a polygon?The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure.
Considering that 1 ft = 12 inches, the outer edges for this triangle are given as follows:
14.5833 ft, 13.3333 ft, 13.3333 ft.
Hence the perimeter is given by:
P = 14.5833 + 13.3333 + 13.3333 = 41.25 ft = 41 ft 3 in.
What is the area of a triangle?The area of a triangle is given by half the multiplication of the base and the height of the triangle.
For this triangle, we have that:
The base is of b = 14.5833 ft.The height is of h = 11.1667 ft.Hence the area is:
A = 0.5 x 14.5833 x 11.1667 = 81.4 ft².
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Answer:
100%
Step-by-step explanation:
Expand each logarithm. State the properties of logarithms used. log₂ (2 y-4)³
The expanded form of the equation log₂ (2 y-4)³ is 3log₂(2y -4).
What exactly are extended forms?An expanded form is a method of writing a number through adding the digit values. A place value chart can help us think about the worth of a number's digits. Logarithms can be expanded by writing them as a sum as well as difference of logarithms, using the power rule if necessary. The order summation rule, product rule, as well as power rule are frequently useful.
Expanding the equation log₂ (2 y-4)³:
log₂ (2 y-4)³
applying the log rule logₐxᵇ = b*logₐ(x)
so that
3log₂(2y -4)
The expanded form of the equation log₂ (2 y-4)³ is 3log₂(2y -4).
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Solve the inequality for u. 63 ≥ 3u-12 Simplify your answer as much as possible.
Answer:
u≤25
Step-by-step explanation:
63 ≥ 3u-12
-3u -3u
-3u+63 ≥ -12
-63 -63
-3u ≥ -75
/-3 /-3
u≤25
simplify this fraction
Answer:
1
Step-by-step explanation:
1 / 3-x
x - 2/x - 3
(x - 2)/x - 3
-3/x - 3
(x - 2) + -1/x - 3
= x - 3/x - 3
Cancel
= 1
Factor 5x2 + 7x + 2 completely (SHOW WORK)
please help me <3
4/9 x (-1/8)= ??
(MUST BE SIMPLIFIED FRACTION)
Answer: put 32x over 9 as a fraction and it would be a negative so put a - in front
Step-by-step explanation:
Given E is the midpoint of AC complete the flowchart proof below. Note that the last statement and reason have both been filled in for you.
The reasons in the asked situations are:
(A) E is the midpoint of AC:
Reason - E bisects line AC and is perpendicular to line AC.(B) ∠D≅∠B:
Reason - Alternate anglesWhat are alternate angles?Angles of the same size that are found on opposing sides of the transversal line are known as alternate angles. Angles that alternate are equal: By creating a Z shape, we can easily identify interior alternate angles: Alternate angles come in two varieties: alternate interior angles and alternate exterior angles.So, (A) E is the midpoint of AC:
Reason - E bisects line AC and is perpendicular to line AC.(B) ∠D≅∠B:
Reason - Alternate anglesTherefore, the reasons in the asked situations are:
(A) E is the midpoint of AC:
Reason - E bisects line AC and is perpendicular to line AC.(B) ∠D≅∠B:
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1. ¿Cuál de las siguientes expresiones representa el
producto de 9 por x, restado del cociente de 2
entre x?
2
(1) // - 9x
X
2
(2) -9x
(3) 2x(-9x)
(4) 9 - X-
(5) (2 + x) 9x
-
2
-
Answer:
(2/x) - 9x
Step-by-step explanation:
si una de las respuestas se ve así, elija esa.
Which type of function models the data in the table best-linear, quadratic, logarithmic, cubic, or exponential?
The best function to model this data is a linear function.
We have the data:
x y
0 -1
1 -0.5
2 0
3 0.5
4 1
From the table, we see that,
The slope of the points are given by:
(- 0.5 + 1) / (1 - 0) = 0.5 / 1 = 0.5
(0 + 0.5) / (2 - 1) = 0.5
(0.5 - 0 ) / (3 - 2) = 0.5
(1 - 0.5) / ( 4 - 3 ) = 0.5
Thus, the equation of the function is, y = 0.5 x - 1
So, the best function for this model is a linear function.
Therefore, we get that, the best function to model this data is a linear function.
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Your question was incomplete. Please refer the content below:
Which kind of function best models the data in the table? use differences or ratios.
x y
0 -1
1 -0.5
2 0
3 0.5
4 1
a)liner
b)quadratic
c)exponential
d)none of these
12. The diameter of a circle has endpoints D(7, 33)
and E(31, 1). The center of the circle, C, is the
midpoint of the diameter.
Part A
What is the length of the radius DC in units?
Part B
What are the coordinates of the center of the
circle?
The length of the radius DC (or EC) in units is 20 units and the coordinates of the center C of the circle is (19, 17) using concept of Coordinate Geometry and Lines.
As per the question statement, The diameter of a circle has endpoints D(7, 33) and E(31, 1). The center of the circle denoted by C, is the midpoint of the diameter. We are supposed to find the length of the radius DC (or EC) in units and the coordinates of the center C of the circle
Now using the distance formula in Line concept and coordinate geometry,
Distance between two points is given by d = √{(x2-x1)^2+(y2-y1)^2}
Given coordinates of D are (7, 33) and E are (31, 1)
Therefore Distance DE = √{(31-7)^2 + (1-33)^2}
DE = √{(576)+(1024)}
DE = √1600
DE = 40 units
Therefore, length of diameter DE is 40 units so length of radius DC (or EC) will DE/2 = 40/2 = 20 units
Now using Mid Point Formula of Line concept and coordinate geometry,
Mid Point of line joining two points is given by
C = ({x1 + x2}/2, {y1 + y2}/2)
C = ( {31+7}/2 , {1+33}/2)
C = (19, 17)
Coordinate Geometry: In this area of geometry, coordinates are used to describe a point's location.Line concept: A line is a straight, one-dimensional figure in geometry that is infinitely long in both directions and has no thickness.To learn more about such questions related to coordinate geometry, click on the link given below:
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how do you know two numbers are opposites?
Answer:
if they have the same absolute value but different signs.
Step-by-step explanation:
Answer:
if they have the same absolute value but different signs. Opposites are the same distance from 0 on a number line, and they are on opposite sides of 0. The opposite of 0 is 0
Identify the coordinates of the midpoint of JW¯¯¯¯¯¯, which has endpoints J(−1,−9) and W(7,−7).
[tex] \large \bf \longrightarrow{(3, - 8)}[/tex]
Step-by-step explanation:Step 1) : Write the midpoint formula
[tex] \large \implies \bf(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} )[/tex]
Step 2) : Substitute (-1 , -9) and (7 , -7) into [tex]\bf(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} )[/tex]
[tex]\large \implies \bf(\frac{ - 1 + 7}{2}, \frac{ - 9 - 7}{2} )[/tex]
Step 3) : Calculate
[tex]\large \implies \bf(\frac{6}{2}, \frac{ - 16}{2} )[/tex]
Step 4) : Cross out the common factor
[tex]{\large \implies \bf(\frac{ \cancel{6}}{ \cancel{2}}3, \frac{ \cancel{ - 16}}{ \cancel{2}}} \bf - 8)[/tex]
Step 5) : We have got the answer
[tex]\large \bf \implies{(3, - 8)}[/tex]
How can you rewrite the expression (8-5 i)² in the form a+b i ?
(f) 39+80 i (g) 39-80 i (h) 89+80 i (i) 89-80 i
Correct answer is B. We can rewrite the expression in the form of 39 - 80i
What is a complex function?Any function that goes from complex numbers to complex numbers is said to as complex. It is a function that, in other words, has the complex numbers as a codomain and a subset of the complex numbers as its domain. A nonempty open subset of the complex plane is typically found in the domain of complex functions.
Using (a-b)²= a²-2ab+b²
(8-5i)² = 8²-2(8)(5i)+(5i)²
= 64 - 80i + 25i²
We know that i²=-1
So
= 64 - 80i + 25(-1)
=64 - 25 - 80i
= 39 - 80i
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Write an equation for the translation of y=2/x that has the given asymptotes. x=0 and y=4
Equation for the translation of y=2/x that has the given asymptotes. x=0 and y=4 is y = 4(x+7) + 6
What is asymptote?A line that, in analytical geometry, is an asymptote of a curve is one where, when one or both of the x or y coordinates go to infinity, the distance between the curve and the line approaches zero. An asymptote of a curve is a line that is tangent to the curve at a point at infinity in projective geometry and similar settings.
y = 4(x+7) + 6
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HELP!
Estimate 63% of 109.
6.6
88.2
66
91.3
Answer:
66
Step-by-step explanation:
63% of 109 is 68.67 the closest answer is 66
(a) The function g (t) = 5.9t models the average distance, g (t), in kilometers that Alice walks over time, t, in hours. Compare the rate of change of f (t) to the rate of change of g (t).
What does this tell you about Alice's and Bob's speeds?
Using linear function concepts, it is found that:
The rate of change of f(t) is of 7.2 kilometers an hour.The rate of change of g(t) is of 5.9 kilometers an hour.From the rates, Bob is 1.3 kilometer an hour faster than Alice.What is the missing information?Bob's function is missing, and is given by:
f(t) = 7.2t.
What is a linear function?A linear function is modeled according to the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.For this problem, the linear functions for the distances are given as follows:
Bob's: f(t) = 7.2t. (slope of 7.2, intercept of 0).Alice's: g(t) = 5.9t. (slope of 5.9, intercept of 0).The rate of change of a linear function is given by it's slope, hence they are given as follows for the functions in this problem:
f(t): 7.2 kilometers an hour.g(t): 5.9 kilometers an hour.The difference between the rates is given by:
7.2 - 5.9 = 1.3.
From the difference between the rates, Bob is 1.3 kilometer an hour faster than Alice.
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Please answer the question below
Thanks
The amount Nicole's mother owe her for babysitting is 9.48 dollars.
How to find the amount Nicole mother is owing after the order?She ordered a volleyball for $9.75, a net for $29.99, and knee pads for $15.00.
Nicole's mother said that she would pay for the order on her credit card if Nicole gave her the money.
Nicole gave her mother $40.00 .
Her mother also applied the money that she owed Nicole for babysitting.
Nicole's mother then gave her back $5.26.
The amount Nicole's mother owe her for babysitting can be calculated as follows;
Therefore, the total amount for the order is
$9.75 + $29.99 + $15.00 = $54.74
let the money her mother owes her = x
Therefore,
x + 40 + 5.26 = 54.74
x = 54.74 - 40 - 5.26
x = 54.74 - 45.26
x = 9.48
Therefore, the amount Nicole's mother owe her for babysitting is 9.48 dollars.
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Pleae answer! There are 40 players on the basketball court in a city. there are 2 teams on each court and 5 players on each team. select all the equations you can use to find the number of basketball courts, c.
A: c times 2 times 5= 40
B: 40 divided by c = 2 times 5
C: 2 times 5 times 40= c
D: 40 divided by 5 times 2= c
E: 40 divided by (5 times 2)= c
Answer: Select all the equations you can use to find the number of basketball courts, c is = 4.
Step-by-step explanation:
Given data,
Number of players on the basketball court in a city = 40
Number of teams on each court = 2
Number of players on each team = 5
Find all the equations you can use to find the number of basketball courts, 'c'.
So, we can solve it all equations,
Then,
We select equation A :
Equation A is : c times 2 times 5= 40
We can write,
Equation A is : cx2x5 = 40
simplify equation,
c x 2 teams x 5 players = 40players
We can write,
cx2x5 = 40
cx10 = 40
c = 40/10
c = 4
Therefore, equation A use the number of basket ball courts c is = 4.
We select equation B :
Equation B is : 40 divided by c = 2 times 5
We can write,
Equation B is : 40/c = 2x5
simplify equation,
40 players / c = 2 teams x 5 players
We can write,
40/c = 2x5
40/c = 10
40 = 10c
c = 40/10
c = 4
Therefore, equation B use the number of basket ball courts c is = 4.
We select equation C :
Equation C is : 2 times 5 times 40= c
We can write,
Equation C is : (2 x 5) 40 = c
simplify equation,
(2 teams x 5 players ) 40 players = c
(2 teams x 5 players ) = 40 players divided by c
We can write,
( 2 x 5 ) = 40/c
10 = 40/c
c = 40/10
c = 4
Therefore, equation C use the number of basket ball courts c is = 4.
We select equation D :
Equation D is : 40 divided by 5 times 2= c
We can write,
Equation D is : 40/5x2 = c
simplify equation,
40 players / 5 players x 2teams = c
We can write,
40/5x2 = c
40/10 = c
4 = c
c = 4
Therefore, equation D use the number of basket ball courts c is = 4.
We select equation E :
Equation E is : 40 divided by (5 times 2)= c
We can write,
Equation E is : 40/5x2 = c
simplify equation,
40 players / 5 players x 2 teams = c
We can write,
40/5x2 = c
40/10 = c
4 = c
c = 4
Therefore, equation E use the number of basket ball courts c is = 4.
Therefore,
select all the equations you can use to find the number of basketball courts, c is = 4.
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Owen draws the cube shown.
Write an expression using an exponent that could be written to represent the volume of the cube.
Then, solve your expression to find the cube's volume. Make sure to include the correct unit.
(Volume Formula = length x width x height)
Answer:
the answer is 49
Step-by-step explanation:
What is the slope of this line?
Answer:
-1/5
Step-by-step explanation:
First:
Calculate the rise:
On this graph we go down 1 meaning our rise will be -1.
Second:
Calculate the run:
On the graph we go right 5 so the run would be 5.
Third:
We put the rise and run together to get the slope.
Hence, the answer is -1/5
Notes:
Rise means how many units you move up or down from point to point.
Run means how far left or right you move from point to point.
Up and Right= + outcome
Down and Left= - outcome
Also if your rise over run is the same number but two negative number the slope would turn into a positive.
Example:
-5/-5=1
use the following function rule to find f (70)
submit
Answer:
-70
Step-by-step explanation:
you didn't put the function so sorry if it is wrong
1 Name a linear pair. Describe the relationship of their measurements.
Answer:
Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°. Such angles are also known as supplementary angles.
Step-by-step explanation:
If there is a pair of adjacent angles, then this pair is a linear pair if the sum of the (measures of the) two angles will be 180°. So, linear pair of angles always add up to 180°. For example, the linear pair of 30° is 150°, the linear pair of 70° is 110°, etc.
These two angles form a linear pair. We have found all four linear pairs of angles. The four linear pairs formed by the intersecting lines ←→QR Q R ↔ and ←→ST S T ↔ are ∠SOQ ∠ S O Q and ∠QOT ∠ Q O T , ∠QOT ∠ Q O T and ∠TOR ∠ T O R , ∠TOR ∠ T O R and ∠ROS ∠ R O S , and ∠ROS ∠ R O S and ∠SOQ ∠ S O Q .