Answer:
Yes, we can take either points as x and y because addition is commutative
Step-by-step explanation:
First of all, the midpoint formula is given as;
(x, y) = [((x₁ + x₂)/2), ((y₁ + y₂)/2)]
For example, if we assume that we have two endpoints having coordinates as (2, 5) and (4, 7)
Now, let (2, 5) represent the first coordinate and (4, 7) represent the second coordinate.
Thus, Coordinates of midpoint = [((2 + 4)/2), ((5 + 7)/2)]
This gives;
(x, y) = (3, 6)
Now,if we change the order of the coordinates by making (4, 7) to be the first coordinate and (2, 5) to be the second coordinate. Thus;
Coordinates of midpoint = [((4 + 2)/2), ((7 + 5)/2)] = (3, 6)
We can see that the coordinates of the midpoint remains the same even after interchanging the coordinates as first and second.
This is because we are adding two numbers and addition is commutative (in commutative properties, changing the order of the operands will not change the result). Thus, it doesn't matter in which order we have the endpoints.
Janelle is in charge of bringing in dry erase markers for everyone in her math group to use to work on a project. She brings 3 markers for each person in her group and 5 extra markers for everyone to share. If Janelle brings in 23 markers in all, which equation represents the information?
Let x represent the number of students in Janelle’s group.
3x = 23 + 5
3x = 23
3x – 5 = 23
3x + 5 = 23
Answer:
3x+5=23
Step-by-step explanation:
Answer:
D. 3x+5=23
Step-by-step explanation:
Round 4.028 to the nearest tenth.
Answer:
4.0
Step-by-step explanation:
Look at the decimal place next to the tenths place. It has a 2 in its place. The rule for rounding is that any number 4 or lower is rounded down. Any number 5 or above is rounded up. The number is 2, which is below 4, so we round down. The tenths place would stay the same because it can't get any smaller. Therefore, 4.028 is rounded down to 4.0
To multiply a sum by a number, multiply each term inside the parentheses by the number outside the parentheses.
a Simplify
b Integer
c Distributive Property
d Numerical expression
Answer:
Numerical expression
The two triangles are similar. What is the value of x?
Answer:
x=5
Step-by-step explanation:
We can write ratios to help us solve
4x 12 +3
---------- = ------------
3x+1 12
Using cross products
4x*12 = (3x+1) * (15)
48x = 45x +15
Subtract 45x from each side
3x =15
Divide by 3
3x/3 =15/3
x=5
A number is chosen at random from the set {1,2,3,4,5,6,7,8,9,10} find the probability that it is a perfect square
Step-by-step explanation:
Perfect squares = 1, 4,9
Probability = 3/ 10
i have 18ones,15hundreds,15tens,and 8 thousands
9668
Explanation:
18 ones, 18x1=18
15 hundreds, 15x100 =1500
15 tens, 15x10=150
8 thousands,8x1000=8000
8x1000=800018+1500+150+8000=9668
Hope this answer correct :)
Let f(x) = 5x + 12. Find f−1(x)
Answer:
(x-12)/5
Step-by-step explanation:
Answer:
f⁻¹(x) = (x - 12)/5
Step-by-step explanation:
To find the inverse of f(x), you have to switch the places of the x and y. You then have to rearrange the equation so that it is equal to y.
f(x) = 5x + 12
x = 5y + 12
x - 12 = (5y + 12) - 12
x - 12 = 5y
(x - 12)/5 = 5y/5
(x - 12)/5 = y
f⁻¹(x) = (x - 12)/5
How does mass affect friction?
Plz help
An object of large mass is pulled down into the surface with a greater force than an object of low mass and as a consequence , there is greater friction between the surface of heavy objects than between the surface and the light object
draw a circle whose radius is 3 and centered at (1,2)
First graph the center at (1,2). Then use your given radius to graph four points around the center. One vertical point above and one below the center, and one horizontal point to the right and one to the left of the center. Those points should be:
• (1,5)
• (1,-1)
• (-2,2)
• (4,2)
Then, to the best of your ability, draw a circle connecting those points.
I hope this makes sense. Please let me know if you have any further questions!
The equation of the circle that has a center at (1, 2) and a radius of 3 units will be (x - 1)² + (y - 2)² = 9. The circle is drawn below.
What is the equation of a circle?Let r be the radius of the circle and the location of the center of the circle be (h, k).
Then the equation of the circle is given as,
(x - h)² + (y - k)² = r²
The center of the circle is (1, 2) and the radius of the circle is 3 units. Then the equation of the circle is given as,
(x - 1)² + (y - 2)² = 3²
(x - 1)² + (y - 2)² = 9
The equation of the circle that has a center at (1, 2) and a radius of 3 units will be (x - 1)² + (y - 2)² = 9. The circle is drawn below.
More about the equation of the circle link is given below.
https://brainly.com/question/10618691
#SPJ2
What concepts do you think belong in this branch of mathematics?
3. Use completing square method to evaluate 6x2 + 11x +3 = 0
Answer:
-b+or-
[tex] - b - + \sqrt{a {}^{2} - 4ac } \div 2a[/tex]
Nearly x=-1.416
Or x=-0.416
Answer:
x=-1/3 or x = -3/2
Step-by-step explanation:
6x²+11x+3=0
divide through by 6
x² +11x/6 + 3/6 =0
collect like terms that is those with x should be left on one side nd the one without x should be on the other side
x² +11x/6 = -1/2
add the square of the half of the co efficient of B i.e 11x/6 to both sides
(x+11/12)² = 121/144 -1/2
(x+11/12)² = 121-72/144
square root of both sides
x+11/12 =+or - √49/144
x= -11/12 ± 7/12
x= -1/3 or x= -3/2
One pound of grapes cost a 1.55.Which equation correctly shows a pair of equivalent ratios that can be used to find the cost of 3.5 pounds of grapes
Answer:
x times 1.55
Step-by-step explanation:
3.5 times 1.55 = 5.325
Answer:
5.325
Step-by-step explanation:
Find the area of a parallelogram with a base of 7 metres and a height of 8 metres. Show full working out
Answer:
[tex]56m^2[/tex]
Step-by-step explanation:
Step 1: Area of Parallelogram Formula
A=bxh
Step 2: Plug in the information and solve
A=7mx8m
A=[tex]56m^2[/tex]
Therefore the area of the parallelogram is [tex]56m^2[/tex]
Answer:
56 Meters Squared
Step-by-step explanation:
Area of a Parallelogram is: [tex]A=b*h[/tex]
We are given the base of 7 meters and the height of 8 meters.
[tex]A=7*8\\\\A=\boxed{56}[/tex]
The area of the parallelogram is 56 square meters.
What is the perimeter of the given figure? A.19 pie symbol inches B. 24+ 5 pie symbol inches C.29 pie symbol inches D.14 + 5 pie Symbol inches
Answer:
Perimeter of the shape = (14+5π )inchesStep-by-step explanation:
The shape is made up of a semicircle and a right angled triangle.
Perimeter of the shape = perimeter of a semicircle + perimeter of the right angle triangle.
Since perimeter of a circle = 2πr
Perimeter of a semicircle = 2πr/2 = πr wherr r is the radius
r = 10in/2 = 5in
Perimeter of the semicircle = 5π in
Perimeter of a triangle = s1+s2+s3 where s1, s2 and s3 are the sides of the triangle.
We only have 2 sdies of the triangle, hence we need to get the third side using pythagoras theorem.
let s1 = 10in, s2 = 6in
10² = 6²+s3²
s3 = √10²-6²
s3 = √100-36
s3 = √64
s3 = 8in
Perimeter of the triangle = 10in+6in+8in = 24in
Perimeter of the shape = (24in + 5π in) - 10in (10 in was subtracted since it is common to both shapes)
Perimeter of the shape = (14+5π )inches
sanji has a room with a perimeter of 42.5 feet if she wants to hand a curtain along one full side of the room how long dose the curtain need to be
Answer:
The length of the curtain is 10.625 feet
Step-by-step explanation:
The length of the curtain to cover one side of the room depends on the shape of the room
Given a room shape of a square, we have;
Perimeter = 4 × Side length of the room
Length of the curtain = Side length of the room
Therefore;
Perimeter = 4 × Length of the curtain
42.5 feet = 4 × Length of the curtain
Length of the curtain = (42.5 feet)/4 = 10.625 feet
The length of the curtain = 10.625 feet.
Which numbers are rational.
3
1.8989
را با
0.5
2.0
Answer:
All of those numbers are rational
You received $112 in all selling paintings. You sold one painting for $27
and the rest for $17 each. Solve the equation below to find x, the number
of $17 paintings you sold.
17x + 27 = 112
Answer:
5
Step-by-step explanation:
17x = 85
17x/17 = 85/17
x = 5
What is the midpoint of AB
Answer:
A= (-5, -4)
B = (-3, 3)
x1 = -5 , x2 = -3
y1 = -4 , y2 = 3
[tex]midpoint = ( \frac{x1 + x2}{2} \: \: \frac{y1 + y2}{2} )[/tex]
[tex] = (\frac{ - 5 - 3}{2} \: \: \frac{ - 4 + 3}{2} )[/tex]
= (-4, -0.5)
number added to the difference between triple the number and thirteen Translate into a variable expression. (Use x for your variable. Do not simplify.)
Answer:
[tex]4x - 13[/tex]
Step-by-step explanation:
Given
Represent the number with x
Required
Translate the statements to expression
First, we need to get triple of x:
[tex]Triple\ of\ x= 3 * x[/tex]
[tex]Triple\ of\ x= 3 x[/tex]
Next is to get the difference between 3x and 13
This is represented as [tex]3x - 13[/tex]
Lastly, Add x to the above:
[tex]x + 3x - 13[/tex]
[tex]4x - 13[/tex]
Hence, the variable expression is 4x - 13
Consider triangle GHJ. Triangle G H J is shown. Angle G H J is a right angle. The length of the hypotenuse is 10 and the length of another side is 5. What is the length of line segment HJ?
Answer:
[tex]\bold{\sqrt{75}}[/tex]
Step-by-step explanation:
Given
A [tex]\triangle GHJ[/tex] in which
[tex]\angle GHJ = 90^\circ[/tex]
Hypotenuse = 10
Length of another side = 5
To find:
HJ = ?
Solution:
Kindly refer to the image attached in the answer area.
We know that there are only 3 sides in a triangle.
We are given hypotenuse is 10.
i.e. GJ = 10
To find HJ, Base = ?
So, we are given the side length of GH, perpendicular i.e. 5.
Kindly refer to attached image for further details.
Let us use Pythagorean theorem here.
According to Pythagorean theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow GJ^{2} = GH^{2} + HJ^{2}\\\Rightarrow 10^2=5^2+HJ^2\\\Rightarrow HJ = \sqrt{100-25}\\\Rightarrow \bold{HJ = \sqrt{75}}[/tex]
Answer:
hJ = B 5 route 3
Step-by-step explanation:
got it right on edg 2020-2021
Tell whether the statement true or false. If it is false, give a counter example.
Can anyone help me with these? Thank you so much if you can!
Answer:
25) true
for example if x is -3 then x^2 will be +9
26) false
for example -3×-3×3 can give you positive answer 27
27) true
because any number when multiplied with 0 will only give you 0 answer
Step-by-step explanation:
Given f(x) = x2 − 4x + 5, find each value. a. f(2) b. f(−6)
Answer:
This problem requires you to plug in the values to get an answer.
f(2)=1
f(-6)= 65
Step-by-step explanation:
You need to plug in each value in the equation.
[tex]f(2) = 2^{2} - 4(2) + 5[/tex]
[tex]f(2) = 4 - 8 + 5[/tex]
[tex]f(2) = - 4 + 5[/tex]
[tex]f(2) = 1[/tex]
For f(-6):
[tex]f( - 6) = ( - 6)^{2} - 4( - 6) + 5[/tex]
[tex]f( - 6) = 36 + 24 + 5[/tex]
[tex]f( - 6) = 65[/tex]
What’s the absolute value for this ?
Answer:
The absolute value for x = 1/6
Step-by-step explanation:
Leave |x + 3| alone
2/3|x + 3| = 11/6 + 1/2 ➡ 2/3|x + 3| = 14/6
|x + 3| = 14/6 ÷ 2/3 ➡ |x + 3| = 7/2 now we write two equations
x + 3 = 7/2 or x + 3 = -7/2 first we subtract 3 from all
x = 1/6 or x = -13/6 since we are asked to find the absolute value, the answer would be 1/6
Please solve, 1-2x= -1+8+8x-8x
Answer: [tex]x=-3[/tex]
Simplify both sides of the equation
[tex]1+-2x=-1+8+8x+-8x[/tex]
[tex]-2x+1=(8x+-8x)+(-1+8)[/tex] (Combine Like Terms)
[tex]-2x+1=7[/tex]
Subtract 1 from both sides
[tex]-2x+1-1=7-1\\-2x=6[/tex]
Divide both sides by -2
[tex]-2x/-2=6/-2\\x=-3[/tex]
Answer:
[tex]\Huge \boxed{x=-3}[/tex]
Step-by-step explanation:
[tex]1-2x= -1+8+8x-8x[/tex]
Combining like terms.
[tex]1-2x= 7[/tex]
Subtracting 1 from both sides.
[tex]-2x= 7-1[/tex]
[tex]-2x=6[/tex]
Dividing both sides by -2.
[tex]x=-3[/tex]
Does anyone know this?
Answer:
-6
Step-by-step explanation:
Hello!
Since we are finding f(-1) we put -1 in for x
2(-1)^2 + 8(-1)
Follow PEMDAS
2 * 1 + 8(-1)
2 * 1 + -8
2 + -8 = -6
The answer is -6
Hope this helps!
What is the opposite of 100
Answer:
-100
Step-by-step explanation:
The opposite of any positive number is the same number but negative.
Factor the trinomial below.
x2 + 14x + 48
O A. (x+6)(x+8)
B. (x+4)(x+12)
O C. (x-6)(x-8)
O D. (x-4)(x - 12)
Answer:
( x+6)(x+8)
Step-by-step explanation:
x^2 + 14x + 48
What 2 numbers multiply to 48 and add to 14
6*8 = 48
6+8 = 14
( x+6)(x+8)
x² + 14x + 48 [ Given ]
By split middle term ,we get:
=> x² + 8x + 6x + 48
=> x ( x + 8 ) + 6 ( x + 8 )
=> ( x + 6 ) ( x + 8 )
Does the function model exponential growth or decay f(x)=3*(7/4)^x
Answer:
Exponential functions are patterns that get continuously multiplied by some number. It's exponential growth when the base of our exponential is bigger than 1, which means those numbers get bigger. It's exponential decay when the base of our exponential is in between 1 and 0 and those numbers get smaller.
Answer:
It models exponential growth.
Step-by-step explanation:
7/4 > 1, so f(x) grows at an exponential rate as x increases.
A graph of f(x) is attached below, showing the exponential growth.
The level of a pond receded at the rate of 4 centimeters per day. Find the change in the water level of the pond after 7 days.
Answer:
28 centimeters
Step-by-step explanation:
The level of the pond is dropping each day by 4 cm. 7 days passed, and each day it was dropping at a constant rate. In order tto find how many centimeters the level of the pond dropped in 7 days, you have to multiply the days passed by the amount dropped each day.
So, 7 days times 4 cm. a day= 28 centimeters dropped.
Write an equation of the line below.
Answer: y = -2/5x -4
Step-by-step explanation:
First we can notice that the line is not going through the origin but is is going through the y-intercept which is -4.In this case the the equation of the line has be in slope intercept form as if y=mx +b where only m and b is indicated and m is the slope and b is the y intercept. So since we already know the y intercept is -4 we need to find the slope using the points on the line.
The points (0,-4) and ( -5,-2) lies on the line and we could use them to find the slope. To find the slope,we need to find the change in the y coordinates and divide it by the change in the x coordinates.
-4 -(-2) = -2
0 - (-5) = 5
slope: -2/5
So since the slope is -2/5 and the y intercept is -4 then we will have the equation,
y= -2/5x - 4