Answer: y = -2x
M is the midpoint of PQ
=> M(0;0)
the line PQ passes through P(2;1) and Q(-2;-1)
=> (PQ): 2x - 4y = 0
have:
(d): perpendicular (PQ)
passes throgh M(0;0)
=> (d): 4x + 2y = 0 ⇔ y = -2x
Step-by-step explanation:
The equation of the perpendicular bisector of PQ is,
⇒ y = - 2x
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point P has coordinates (2, 1) and the point Q has coordinates(-2, -1).
Hence, The slope of line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (- 1 - 1) / (- 2 - 2)
m = - 2 / - 4
m = 1/2
Thus, The slope of perpendicular line is,
⇒ m = - 2
The midpoint of coordinates (2, 1) and (- 2, - 1) is,
⇒ (- 1 + 1) / 2 , (- 2 + 2) / 2
⇒ (0, 0)
Hence, The equation of line is,
⇒ y = mx + b
⇒ 0 = - 2 × 0 + b
⇒ b = 0
Hence, The equation of the perpendicular bisector of PQ is,
⇒ y = - 2x
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three students share a bag of garri in such a way that the first student took ¼ of the garri and the second ¾ of the remainder. what fraction of garri did the third student take?
Nathan is a cat enthusiast! He currently cares for 4 different cats. He adopts 2
new cats every year. Write and graph an equation to represent how many
cats he will have after x amount of years.
what’s 50/6 reduced to a mixed number????? please i need it it’s due in 10 mins
Answer:
8 1/3
Step-by-step explanation:
50/6 =25/3 = 8 1/3
Also can u pls mark me brainliest im new
In 1990 Dallas, Texas, had an estimated population of 1,006,877. By 2000 the population had increased. 18 1/20%. What was the estimated population in 2000 for Dallas, Texas? Find the answer to the nearest whole number
What is the constant rate of change shown in the graph below?
Answer:
It will go up 3 each time
Step-by-step explanation:
If u look at it and look at the dots it will show how it goes up 3 each time
Answer: 3 up
Step-by-step explanation:
A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the exterior angle.
Answer:
1
Step-by-step explanation:
Answer:
Option 4
Step-by-step explanation:
This is a question on angles and their properties
If you would like to venture further, you can check out my Instagram page (learntionary) where I post notes and mathematics tips. Thanks!
Calculate the rate of change for each table and determine if the table is proportional
9514 1404 393
Answer:
tables A, B, E are proportional relationships
Step-by-step explanation:
Finding the rate of change involves finding the ratio of the difference of adjacent y-values to the difference of adjacent x-values. For this many tables and points, I find that to be exceptionally tedious, so I let a spreadsheet do the work.
For the four points, there are three ratios. In the attachment, each ratio is between the point on the same line and the point on the next line. Two conditions are required for the table to be proportional:
the rates of change must all be the samethe rate of change must be equal to the ratio of y to xThe green color identifies tables that are proportional.
If 1 cup has a 16 tablespoons,how many tablespoons are there in 2 1/2
Answer:
40 tablespoons
Step-by-step explanation:
What is the constant proportionality, in dollars per granola bar
Answer:
4 granola bars is $9.00 12 granola bars is $27.00 24 granola bars is $54.00
Step-by-step explanation:
Which Venn diagram correctly describes the relationship between whole numbers and integers?
Answer:
Whole numbers would be a set inside the integer set, where the integer set that is not in the whole number set would be all negative integers.
Step-by-step explanation:
whole numbers are defined to be positive numbers including zero.
A Smart TV is currently priced at $1330.00. If the store manager marks it down by 5%, how much will you save on the TV?
a
$1,396.50
b
$66.50
c
$1,263.50
d
$1,325.00
HELP I DONT KNOW! I SUCK AT MATH
Answer:
C
Step-by-step explanation:
5/2=15=6=2.5
Answer:
2.5
Step-by-step explanation:
Since there is 5 cups of flour for 2 cups of vanilla, then all you need to do is divide 5 by 2.
5/2 is 2.5
Hope this helped :)
Which transformation would accomplish this?
A translation 3 units left and 2 units up
A translation 3 units right and 2 units down
A translation 2 units left and 3 units up
A translation 2 units right and 3 units down
Answer:
If it is from figure O to figure P, it is a translation 3 units right and 2 units down
If it is from figure P to figure O, it is a translation 3 units left and 2 units up
Step-by-step explanation:
What makes a point a solution to a system of equation? 55 points
Answer:
A solution to a system of equations means the point must work in both equations in the system
Answer:
The point must work in both equations in the system, therefore, when we test the point in both equations, it must be a solution for both.
Step-by-step explanation:
Marisa wants to buy a home in Atlanta with a 30-year mortgage that has an annual interest rate of 4.9%. The house she wants is $250,000 and she will make a $55,000 down payment and borrow the remainder. What is Marisa's monthly mortgage payment to the nearest dollar?
Given :
Marisa wants to buy a home in Atlanta with a 30-year mortgage that has an annual interest rate of 4.9%.
The house she wants is $250,000 and she will make a $55,000 down payment and borrow the remainder.
To Find :
What is Marisa's monthly mortgage payment to the nearest dollar.
Solution :
Money remains, m = $( 250000 - 55000 ) = $195000 .
Total price after interest, T = m( 1 + rt )
T = 195000×( 1 + 0.049×1)
T = $204555
Monthly payment,
[tex]M = \dfrac{m}{12}\\\\M = \dfrac{204555}{12}\\\\M =\$ 17046.25[/tex]
Therefore, monthly payment is $17046.25 .
Hence, this is the required solution.
If you can run 3 miles in 20 minutes, how far can you run in one hour?
Answer:
I think it would be 9 miles.
Which relation is a function? Select all that apply
{(5,1), (4,1), (3, 1), (2,1)}
{(5,3). (4,1), (3, 2), (2,0)}
{(5,2), (2,5), (5. 3), (3,5)}
{(5,5). (4,4), (3, 3), (2,2}
{(5,1), (5,2), (5, 3), (5.4)}
Answer:
These are the correct answers:
PLEASE HELP!!!!!!!!!
Answer:
The scale factor is 1/2 or .5
Step-by-step explanation:
Triangle XYZ scales down by 1/2 to form the new XYZ triangle
For example: on the left side, X is (6,4) and on the right side, X is (3,2)... it's cut in half meaning the scale factor is 1/2 or .5
Hopefully this isn't confusing and it helps... :)
Which statement is true concerning the vertex and the axis of symmetry of g(x)=5x2−10x? The function written in vertex form is g(x)=5(x−1)2−5. The vertex is at (1, –5) and the axis of symmetry is x=1. The vertex is at (1, –5) and the axis of symmetry is y = 1. The vertex is at (0, 0) and the axis of symmetry is x = 1. The vertex is at (0, 0) and the axis of symmetry is y = 1.
Answer:
A
Step-by-step explanation:
The true statement is, the vertex is (1, -5) and the axis of symmetry is x = 1.
What are Quadratic Functions?Quadratic functions are polynomial functions consisting of variables and exponents and the degree of the variable is 2.
The general form of a quadratic function is f(x) = ax² + b x + c.
Given is a quadratic function,
g(x) = 5x² - 10x
The function written in vertex form is,
g(x) = 5(x - 1)² - 5
Vertex form of a quadratic equation is,
y = a(x - h)² + k, where (h, k) is the vertex.
Here vertex = (h, k) = (1, -5)
Axis of symmetry = -b/2a = -(-10)/10 = 1
Axis of symmetry is, x = 1
Hence the correct option is A.
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Factor each polynomial
4z^2+4z-15
Answer:
(2z + 5)(2z - 3)
Step-by-step explanation:
4z² + 4z - 15
4z² + 10z - 6z - 15
2z (2z + 5) - 3 (2z + 5)
(2z + 5)(2z - 3)
Answer:
(2z+5) (2z-3)
Step-by-step explanation:
First, multiply the first coefficient by the third.
4*-15=-60
Then find factors of -60 that add up to the middle term.
The factors are: -6 and 10-------> -6*10=-60 and -6+10=4 so -6 and 10 are the correct factors.
Break up the middle term with the factors that you got above. The new equation will be: 4[tex]z^{2}[/tex]-6z+10z-15
Factor by grouping.
First, break the equation into two
(4[tex]z^{2}[/tex]-6z) (10z-15)
Then, factor out the greatest number you can
2z(2z-3) 5(2z-3)
You are then left with a common binomial of 2z-3. COmbine the common binomial into 1 and combine the 2 numbers you factored out in the step above (2z and 5) The final equation will be this:
(2z+5) (2z-3)
can someone help me with math its homework that I don't get
Answer:
60
Step-by-step explanation:
look at the photo lol, tried to draw it out
What is the Slope of the Function? f (x) = 5(x - 3)2 + 6 Your answer
Answer:
m=10
Step-by-step explanation:
using y=mx+b
i need help for this problem. thanks!
Answers:
x = 12
angle A = 30 degrees
===========================================================
Explanation:
Check out the attached image below.
Note the pair of (8x+4) angles which are congruent vertical angles.
Also, notice that 50+130 = 180 since those adjacent angles are supplementary. In other words, they form a straight line.
Now that we know the expressions for each interior angle, we add them up and set the sum equal to 180. Recall that for any triangle, the interior angles always add to 180.
Let's solve for x
(3x-6) + (8x+4) + (50) = 180
11x + 48 = 180 .... combine like terms
11x = 180-48 ..... subtract 48 from both sides
11x = 132
x = 132/11 ..... divide both sides by 11
x = 12
Use this to find the value of angle A
A = 3x-6
A = 3*12-6
A = 36 - 6
A = 30
For the sake of completeness, let's find 8x+4 as well. This part is optional
8x+4 = 8*12+4 = 96+4 = 100
The three interior angles of the triangle are: 30, 100, 50
Note how 30+100+50 = 180 to help confirm the answer.
Which value for k makes the equation 42 ÷ k = 14 true
Answer:
k=3
Step-by-step explanation:
Standing on the edge of a cliff, Fernando throws a rock upward from a height 512 feet above the water at a speed of 64 feet per second. How long will it take for the rock to land in the water?
Answer: 7.6875 seconds.
Step-by-step explanation:
Let's writhe the motion equations for the rock.
The only force acting on the rock will be the gravitational force, then the acceleration of the rock will be the gravitational acceleration g ≈ 32 ft/s^2
A(t) = -32ft/s^2
Where we have a negative sign because this acceleration pulls the rock downwards.
For the velocity, we must integrate over time, and the constant of integration will be equal to the initial velocity of the rock = 64 ft/s, then the velocity equation is:
V(t) = (-32ft/s^2)*t + 64m/s
For the position, we integrate again over time, and this time the constant of integration will be the initial position, 512ft (Then the water level is at 0 ft)
P(t) = (1/2)*(-32ft/s^2)*t^2 + 64m/s*t + 512 ft
Now we want to find the value of t, the time, such that the rock hits the water.
The rock will land in the water when P(t) = 0ft, becuse we defined the zero in the position as the water.
Then we must solve:
P(t) = 0ft = (1/2)*(-32ft/s^2)*t^2 + 64m/s*t + 512 ft
for t, let's solve this:
0ft = (-16ft/s^2)*t^2 + 64m/s*t + 512 ft
This is a quadratic equation. the two solutions can be found by using the Bhaskara equation, then the solutions will be:
[tex]t = \frac{ -64ft/s +- \sqrt{(64ft/s)^2 - 4*(-16ft/s^2)*512ft} }{2*(-16ft/s^2)} = \frac{-64ft/s +- 192ft/s}{-32ft/s}[/tex]
Then the two solutions are:
t = (-64ft/s + 192ft/s)/(-32ft/s^2) = -4s (This time is negative, which is no really defined for this problem, so we can discard this solution)
The other solution is:
t = (-64ft/s - 192ft/s)/(-32ft/s^2) = 7.6875 s
This solution makes sense with the problem, then the answer is 7.6875 seconds.
HELP ASAP I NEED HELP AND I'M DESPERATE.
Answer:
Blank 1. -2x+4
Blank 2. x+2
Step-by-step explanation:
12-(4y+8)=0.5(8y-16)
Step-by-step explanation:
hope this will help u............
The value of y for the given expression 12-(4y+8)=0.5(8y-16) is 3/2.
What is an expression?An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation.
As per the given expression,
12-(4y+8)=0.5(8y-16)
12 - 4y - 8 = 4y - 8
4y + 4y - 8 = 12 - 8
8y = 12
y = 12/8 = 3/2
Hence "The value of y for the given expression 12-(4y+8)=0.5(8y-16) is 3/2".
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How are integers and rational
numbers different?
Answer:
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Step-by-step explanation: its not a number ☺️
Answer:
Every integer is a rational number, since each integer n can be written in the form n/1. For example 5 = 5/1 and thus 5 is a rational number. However, numbers like 1/2, 45454737/2424242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers.
Step-by-step explanation:
The terms even and odd only apply to integers; 2.5 is neither even nor odd. Zero, on the other hand, is even since it is 2 times some integer: it's 2 times 0. To check whether a number is odd, see whether it's one more than some even number: 7 is odd since it's one more than 6, which is even.
Another way to say this is that zero is even since it can be written in the form 2*n, where n is an integer. Odd numbers can be written in the form 2*n + 1. Again, this lets us talk about whether negative numbers are even and odd: -9 is odd since it's one more than -10, which is even.
the scale on a map is 1:10 000
a) two towns are 17km apart
how far apart would the be on the map?
give your answers in centimeters.
b) the viewpoint and the pier are 7.1cm apart on the map.
how far apart would they be in real life?
give your answers in kilometers.
I GIVE BRAINIEST “What is the solution of a system of equations if the sum of the
equations is 0 = 2?”
Answer:
At the bottom!!
Step-by-step explanation:
y=2
2=0+x
x=2
Solution of a system of equations:A system of linear equations contains two or more equations e.g. y=0.5x+2 and y=x-2. The solution of such a system is the ordered pair that is a solution to both equations. ... The solution to the system will be in the point where the two lines intersect.
Hope this helps!!