80 POINTS!!!
A line segment has endpoints at (4, –6) and (0, 2). What is the slope of the given line segment? What is the midpoint of the given line segment? What is the slope of the perpendicular bisector of the given line segment? What is the equation, in slope-intercept form, of the perpendicular bisector?
Answer:
1). Slope = (-2)
2). Midpoint = (2, -2)
3). Slope of the perpendicular bisector = (1/2)
4). Equation of perpendicular bisector will be x - 2y = 6
Step-by-step explanation:
A line segment has the endpoints at (4, -6) and (0, 2).
1). Then the slope of the given line segment will be = (y - y')/(x - x') = (2 + 6)/(0 - 4) = 8/(-4) = (-2)
2). Mid point of the line segment is given by [tex](\frac{x_{1}+x_{2}}{2}) , (\frac{y_{1}+y_{2}}{2})[/tex]
Therefore midpoints of the line segment will be [tex]\frac{4+0}{2},\frac{-6+2}{2}[/tex] = (2, -2)
3). Slope of the perpendicular bisector is represented by [tex]m_{1}.m_{2}=(-1)[/tex]
⇒ (-2)×m2 = (-1)
⇒ [tex]m_{2}=\frac{1}{2}[/tex]
4). Now we have to find the equation of perpendicular bisector passing through (2, -2) and slope (1/2).
Since standard equation of the line will be given as y = mx + c
[tex]y=\frac{1}{2}x+c[/tex] passes through (2, -2).
[tex](-2) = \frac{1}{2}(2) + c[/tex]
c = (-1) - 2 = -3
Finally the equation of perpendicular bisector will be
[tex]y=\frac{1}{2}x+(-3)[/tex]
⇒ 2y = x - 6
⇒ 2y - x = -6
⇒ x - 2y = 6
Answer: the answers are in the explanation, they are also in order
Step-by-step explanation:
-2
(2,-2)
1/2
y=(1/2)x - 3
Proof that x^y + y^x > 1 for all x,y > 0 ...?
Fiona has to choose a bouquet for her wedding. The probability that she uses red roses is 98%, the probability that she uses orchids is 87%, and the probability that she uses Gerber daisies is 94%. Given the probability that she has both roses and orchids is 0.87 and the probability that she has both Gerber daisies and roses is 0.97 what is the probability that her bouquet contains roses or Gerber daisies?
the answer would be b.) .84
4 x plus= equals what
convert 5/8 to percent notation
Explain the correlation between the graph of a line, direction of the line and the positive or negative slope of the line.
One's intelligence quotient, or IQ, varies directly as a person's mental age and inversely as that person's chronological age. A person with the mental age of 25 and a chronological age of 20 has an IQ of 125. What is the chronological age of a person with a mental age of 40 and an IQ of 80?
The chronological age of a person with a mental age of 40 and an IQ of 80 is calculated to be 50 years by using the direct and inverse proportionality of the IQ, Mental Age, and Chronological Age.
Explanation:The subject of your question is related to a mathematical concept known as Direct and Inverse Proportion. In this scenario, the IQ is directly proportional to the Mental Age and inversely proportional to the Chronological Age. Therefore, the formula is given as: IQ = (Mental Age / Chronological Age) * 100.
From the first example that indicates a person with the mental age of 25 and a chronological age of 20 has an IQ of 125, we can determine the proportionality constant as follows: 125 = (25 / 20 ) * 100.
Now, to find out the chronological age of a person with a mental age of 40 and an IQ of 80, we use the same proportionality and solve the equation for chronological age: 80 = (40 / Chronological Age) * 100. Solving the equation, the Chronological Age equates to 50 years.
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To find the chronological age of a person with a mental age of 40 and an IQ of 80, we can use the fact that IQ varies directly with mental age and inversely with chronological age. The specific chronological age depends on the value of the constant of variation, k.
Explanation:To find the chronological age of a person with a mental age of 40 and an IQ of 80, we can use the fact that IQ varies directly with mental age and inversely with chronological age. Let's denote the chronological age as x. We can set up the equation as follows:
IQ = (k * mental age) / chronological age
where k is the constant of variation.
Given that the mental age is 40 and the IQ is 80, we can plug in these values into the equation:
80 = (k * 40) / x
To solve for x, we can cross-multiply and then divide both sides by 80:
80x = k * 40
x = (k * 40) / 80
Since we don't have the value of k, we can't determine the specific value of x. However, we can determine the relationship between x and the mental age:
x = 40 / k
Therefore, the chronological age of a person with a mental age of 40 and an IQ of 80 depends on the value of the constant of variation, k.
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let f=cos^2x and g=sin^2x which of the following lie in the space spanned by f and g
a)cos2x
b)3+x^2
c)1
d)sinx
e)0 ...?
If you save two pennies on January 1, four pennies on January 2, six pennies on January 3, and continue this pattern for one year (not a leap year), what will be the value of your entire savings, in dollars, at the end of that one year? Express your answer as a decimal without commas.
...?
Answer:
1335.90
Step-by-step explanation:
Convert 0.84 into a simplified fraction
Whut is 2 pus 2 i dount no
In 2010, the United States national debt was estimated to be nearly 13,000,000,000,000 dollars. Which of the following represents the national debt in scientific notation?
a. 1.3 x 10^11
b. 1.3 x 10^12
c. 1.3 x 10^13
d. 1.3 x 10^14 ...?
Answer:
option C
Step-by-step explanation:
In United States national debt in 2010 was estimated to be nearly $13,000,000,000,000.
Now we have to convert this debt in scientific notation.
In scientific notation we have to convert this number in to 10ˣ.
13000000000000 = 1.3 × 10¹³
Therefore option C is the answer.
The dimensions of a smaller rectangle are 3 ft. by 9 ft. The dimensions of a larger rectangle are 5 ft. by 11 ft. Find the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle. Options are 11:9, 3:4, 4:3, and 5:3 ...?
Answer:
Option 3rd is correct
4: 3
Step-by-step explanation:
Perimeter(P) of rectangle is given by:
[tex]P =2(l+w)[/tex]
where, l is the length and w is the width of the rectangle respectively.
Given that:
The dimensions of a smaller rectangle are 3 ft. by 9 ft.
Perimeter of smaller rectangle= 2(3+9) =2(12) = 24 ft.
It is also given that: The dimensions of a larger rectangle are 5 ft. by 11 ft.
Perimeter of Larger rectangle = 2(5+11) =2(16) = 32 ft.
We have to find the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle.
[tex]\frac{\text{Perimeter of the larger rectangle}}{\text{Perimeter of the Smaller rectangle}}[/tex]
Substitute the given values we have;'
[tex]\frac{32}{24}=\frac{4}{3}[/tex]
Therefore, the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle is, 4 : 3
When f is defined by
f(x) = sqrt(x) ,
find a so f'(a) is two times the value of f'(4).
Choose two axioms that allow 6 + (x + 5) to be written x + 11.
A) commutative - addition
B) distributive
C) associative - multiplication
D) symmetric
E) commutative - multiplication
F) associative - addition
G) identity - addition
associative means that you can move the parenthesis around the problem and still get the same answer. like (4+2)+3=4+(2+3)
first & sixth are the true
Basic number properties:
The Distributive Property: [tex]a\cdot (b+c)=a\cdot b+a\cdot c;[/tex]The Associative Property for addition: [tex]a+(b+c)=(a+b)+c;[/tex]The Associative Property for multiplication: [tex]a\cdot (b\cdot c)=(a\cdot b)\cdot c;[/tex]The Commutative Property for addition: [tex]a+b=b+a;[/tex]The Commutative Property for multiplication: [tex]a\cdot b=b\cdot a;[/tex]Identity Property : Any number add to the zero the answer is the number itself;The symmetric property states that if one number is equal to a second number, then the second number is equal to the first number.For the expression 6 + (x + 5):
use The Commutative Property for addition - 6+(x+5)=(x+5)+6;use The Associative Property for addition - (x+5)+6=x+(5+6)=x+11.solve for x enter your answer in interval notation using grouping symbols x²+2x<8
Lamar bought 20 pounds of dog food for $4.99 for his dog, Buster. The next day, the shop down the street offered 50 pounds of the same brand of dog food for $12.50. Did Lamar get a better deal? ...?
Expand and simplify 2 (x+7)+3(x+1)
A school soccer team has just purchased new uniforms. The team now has 2 different colors of shorts (white and red) and 3 different colors of shirts (white, red, and gold).
How many different uniform combinations are there? ...?
Austin takes 1 minute and 45 seconds to run three-quarters of a circular track. His rate of motion is π/ radians per second.
how many times does 28 go into 126
What value(s) of x make the equation x2 - 18x + 81 = 0 true?
Answer:
9
Step-by-step explanation:
What fraction of an hour is 46 minutes??
Write a function rule for the area A of a triangle whose base, b, is 2 cm less than seven times the height, h. What is the area of the triangle when the height hits 16 cm.
A. 4h^2-5h;944cm^2
B. 4h-5/2; 29.5***********
C. 4h^3-5h/2; 427
D. 4h-5; 59cm
I think it is B
if the tank is half full, approximately how many miles has troy driven since last filling up his tank
BTW troy truck has a 30 gallon gas tank and gets an average of 21 miles per gallon
ASAP plz I really need help
Answer:
Toy truck will drive 315 miles since last the tank was filled.
Step-by-step explanation:
BTW troy truck has tank of capacity = 30 gallons
Since the toy truck is half filled so gas in the tank = [tex]\frac{30}{2}[/tex]
= 15 gallons of gas
Average of the toy truck is given as = 21 miles per gallon
That means in 1 gallon truck travels = 21 miles
Therefore in 15 gallons of gas truck will travel = 21 × 15
= 315 miles
Toy truck will drive 315 miles since last the tank was filled.
How many solutions does this linear system have?
y = x+ 2
6x – 4y = –10
one solution: (–0.6, –1.6)
one solution: (–0.6, 1.6)
no solution
infinite number of solutions
The solution of a linear system of an equations is (-1, 1).
The given linear system of equations are y = x+ 2 and 6x – 4y = –10.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The system of linear equations can be solved as follows
x-y=-2 --------(1)
6x – 4y = –10 --------(2)
Multiply equation (1) by 4
That is, 4x - 4y= -8 --------(3)
Subtract equation (3) from the equation (2)
So, 6x-4y-(4x-4y)=-10-(-8)
2x=-2
⇒ x=-1
Put x=-1 in x-y=-2
Now, y=1
So, solution is (-1, 1)
Therefore, the solution of a linear system of an equations is (-1, 1).
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A basketball court is in the shape of a rectangle. It has a length of (x − 7) meters and a width of (x + 3) meters. The expression below represents the area of the court in square meters.
(x − 7)(x + 3)
Which of the following simplified expressions represents the area of the basketball court in square meters?
− 6x + 3
x2 − 21
x2 − 4x − 21
x2 − 7x + 3 ...?
The expression x²- 4x - 21 represents the area of the basketball court in square meters.
What is Area ?The area can be defined as the space occupied by a flat shape or the surface of an object.
The area of a figure is the number of unit squares that cover the surface of a closed figure.
It is given that the area of a rectangle is (x − 7)(x + 3)
when It has a length of (x − 7) meters and a width of (x + 3) meters.
The simplified expression of the area is equal to
(x-7)(x-3)
This can also be written as
x *(x+3) - 7*(x+3)
x²+3x-7x-21
x²- 4x - 21
Therefore x²- 4x - 21 represents the area of the basketball court in square meters .
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betty has a cow.the cow produces 5 liters of milk in a day. if the cows diet is improved the cow will produce 200% more milk.how much milk would the cow make in a day.
What is the prime factorization of 19??
The prime factorization of 19 is 19, as it is a prime number and can only be divided by 1 and itself.
To determine the prime factorization of a number, we identify all the prime numbers that multiply together to give the original number. In the case of 19, we need to check if it can be divided by any primes (like 2, 3, 5, 7, 11, 13, 17).
After testing, we find that 19 is only divisible by 1 and itself, making it a prime number. Therefore, the prime factorization of 19 is simply 19.
In triangle abc, sin a = 2425. which other expression has a value of 2425?