Use the distance formula to find the length of the line with endpoints at (1,3) and (3,1)?
√8
8
√32
32
Answers
[tex] \sqrt{(3-1)^{2} +(1-3)^{2} } [/tex]
(1,3) is x₁ and (3,1) is x₂
Begin to simplify within the parenthesis:
[tex] \sqrt{2^{2}+(-2)^{2} } [/tex]
Square the two numbers:
[tex] \sqrt{4 + 4} [/tex]
Add the two to get:
[tex] \sqrt{8} [/tex]
Since 8 is not a square number, this is as far as we can simplify this. Hope this helps!
Related Questions
How would the domain and range of the function y= 1/4x-6 be determined
Answers
Answer: Create a table or a graph of the function. The domain represents all input values and the range represents all output values. The domain and range contain all real numbers
The president of the math club is conducting a survey to see where the twelfth-grade class wants to go on their field trip. Instead of asking the whole class, she surveys only the twelfth-grade members of the math club. She records their choices and plans to present the results to the school principal. What type of sampling did she use?
Answers
The answer is convenience sampling.
Step-by-step explanation:
As per the given scenario, the president of the math club is conducting a survey to see where the twelfth-grade class wants to go on their field trip and she surveys only the twelfth-grade members of the math club.
This is convenience sampling as here the samples are the closest people available. Convenience sampling is a method where the samples are taken who are close to hand.
Here also the math club president is asking the math club students only. This is why it is convenience sampling.
Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two sides of this triangle?
5 cm and 8 cm
6 cm and 7 cm
7 cm and 2 cm
8 cm and 8 cm
Answers
8 cm and 8 cm
_____
Sometimes, the triangle inequality is expressed as
a + b ≥ c
For that version, all except the 3rd choice would be viable.
Answer:
D
Step-by-step explanation:
help me please show ur work
Answers
So according to the equation x.3/4x = 432
x^2. 3/4 =432
x^2 =432 times 4/3
x^2 =1728/3 =576
x= 24
The length is 24 ft
what is the discount on shirts if shirts cost $24 and there is a discount 25%
Answers
Step-by-step explanation:
25% × $24 = $6
Subtract the discount from the original
24 - 6 = $18.00
You buy a house for $130,000. It appreciate 1.6% per year. identify the initial amount, growth rate and growth factor for the situation above. Then great an equation that will model it.
Answers
Find the volume of the tetrahedron having the given vertices. (3, −1, 1), (5, −2, 4), (1, 1, 1), (0, 0, 1)
Answers
A(3,-1,1), B(5,-2,4), C(1,1,1), D(0,0,1)
The simplest method is to use vectors.
Here, we calculate the volume of a parallelepiped defined by vectors AB, AC, AD. The volume of a tetrahedron is one-sixth of the volume of the parallelepiped, V, given by AB.(ACxAD).
Here are the steps:
1. Choose a vertex, say A. Calculate vectors AB, AC and AD
AB=(5-2,4)-(3,-1,1) = <2, -1, 3>
AC=(1,1,1)-(3,-1,1) = <-2, 2, 0>
AD=(0,0,1)-(3,-1,1) = <-3, 1, 0>
2. Calculate vector cross product ACxAD = <-2,2,0>x<-3,1,0>
i j k
-2 -2 0
-3, 1, 0
=<0-0, 0-0, -2-(-6)>
= <0, 0, 4>
3. Calculate volume of parallelepiped, equal to the dot product AB.(ACxAD), ignore sign, which is arbitrary.
V = |<2, -1, 3>.<0,0,4>| = |12| = 12
4. Calculate volume of tetrahedron, which is one-sixth of volume of parallelepiped
V(tetrahedron) = V/6= 12/6 = 2
Lars deposited $50 into a savings account. According to the rule of 72, what interest rate will cause his money to double in approximately 29 years?
Answers
Suppose the account used was using compound interest. Thus to determine his future value we shall use the formula:
FV=P(1+r)^n
where:
FV is future value
p=principle
r=rate
n=periods
from the information given
FV=$100
p=$50
n=29 years
we are required to find r
thus
100=50(1+r)^29
100/50=(1+r)^29
2=(1+r)^29
2^(1/29)=1+r
1.02419=1+r
hence:
r=0.02419~2.419%
Answer:
Step-by-step explanation:
The answer is 2.5%
Use the inverse of the function y = x2 − 18x to find the unknown values. y=+/= square root of bx+c+d
Answers
We look for the inverse of the function.
To do this, let's determine the value of x:
y = x2 - 18x
y = (x + (-18/2)) ^ 2 - ((-18) ^ 2/4) + 0
y = (x - 9) ^ 2 - 81
y + 81 = (x - 9) ^ 2
+/- root (y + 81) = (x - 9)
+/- root (y + 81) + 9 = x
We return the change:
f (x) ^ - 1 = +/- root (x + 81) + 9
Therefore, the values sought are:
b = 1
c = 81
d = 9
Answer:
f (x) ^ - 1 = +/- root (x + 81) + 9
b = 1
c = 81
d = 9
The inverse of a function is its opposite
The values of the unknown are: b = 1, c = 81 and d = 9
The function is given as:
[tex]y = x^2 - 18x[/tex]
Rewrite the equation in vertex form as:
[tex]y = (x - 9)^2 - 81[/tex]
Swap the positions of x and y
[tex]x = (y - 9)^2 - 81[/tex]
Add 81 to both sides
[tex](y - 9)^2 = x + 81[/tex]
take the square roots of both sides
[tex]y - 9 = \pm\sqrt{x + 81}[/tex]
Add 9 to both sides
[tex]y = \pm\sqrt{x + 81} + 9[/tex]
By comparison, the values of the unknown are:
b = 1, c = 81 and d = 9
Read more about inverse functions at:
https://brainly.com/question/14391067
Ben has b dollars. Cam has 7 fewer dollars than Ben. How many dollars does Cam have? Write your answer as an expression.
Answers
B is the number of dollars Ben has and Cam has 7 less so you just subtract 7 from b
Answer:
Cam has [tex]b-7[/tex] dollars.
Step-by-step explanation:
Here b represents the number of dollars Ben has,
Given,
Cam has 7 fewer dollars than Ben,
So, the number of dollars cam has = The number of Ben's dollar - 7
[tex]=b-7[/tex]
Hence, the expression that represents cam's dollar is,
[tex]' b-7 '[/tex]
If s = 1 over 2 unit and A = 12s2, what is the value of A, in square units? ____ square unit(s). (Input whole number only.)
Answers
3 square unit(s)
Explanation
The question is testing the concept of substitution.
A=12s^2
If s=1/2 , what is the value of A?
Substituting s with 1/2 we get;
A=12(1/2)^2
=12×1/4
=3
The answer is 3 unit squared. The is not fraction in the answer.
the answer is three square units
A probability experiment consists of rolling a a 6 6-sided die. find the probability of the event below. rolling a number with exactly 2 not necessarily unique prime factors number with exactly 2 not necessarily unique prime factors
Answers
The probability of rolling a number with exactly two prime factors on a six-sided die is 1/3, as there are two outcomes (4 and 6) with exactly two prime factors and six possible outcomes in total.
The student is asking about the probability of an event in a probability experiment involving rolling a single six-sided die. The specific event of interest is rolling a number with exactly two, not necessarily unique, prime factors. On a standard six-sided die, the faces are labeled with the numbers 1 through 6. When considering the numbers on a die with two prime factors, we must first identify which of these numbers have exactly two prime factors. The numbers are:
4 has two prime factors: 2 and 2 (2 squared).6 has two prime factors: 2 and 3.The other numbers (1, 2, 3, and 5) have fewer than two prime factors. Since 4 and 6 are the only outcomes with exactly two prime factors, we have two favorable outcomes out of six possible outcomes on a six-sided die.
Thus, the probability of rolling a number with exactly two prime factors is:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 2 / 6 = 1 / 3
Therefore, the probability of the event is 1/3, or approximately 0.3333 (repeating).
HELP ME ASAP! (graphing problem)
Answers
way 1: using the picture, if x=-3 then y=-6.
way 2: the equation of this line is y=x-3; it means that y(-3)=-6.
If the graph of the function h defined by h(x)=-3x^2+3 is translated vertically upward by 3 units , it becomes the graph of a function g. Find the expression for g(x)
Answers
g(x) = (-3x² +3) +3
g(x) = -3x² +6 . . . . . . . . . the desired expression for g(x)
how do you solve 7 over 20=?
Answers
Earth's diameter at the equator is 7,926 miles. Find the distance around Earth at it's equator to the nearest tenth.
Answers
Are there any points on the hyperboloid x^2 - y^2 - z^2 =1 where the tangent plane is parallel to the plane z = x + y ?
Answers
Simplify the sum 4/m+9+5/m^2-81
A. 9/(m-9)(m+9)
B. 4m+41/(m-9)(m+9)
C.9/m2+m-72
D.4m-31/(m-9)(m+9)
Answers
4/ ( m+9) +5 / ( m-9)(m+9)=
4(m-9)/(m+9)(m-9)+ 5 / (m+9)(m-9)=
(4m-36+5)/(m+9)(m-9)=
4m-31/ (m+9)(m-9)
the answer is D
D
Explanation:
1- The given expression is:
[tex] \frac{4}{m+9} [/tex] + [tex] \frac{5}{m^2 - 81} [/tex]
2- Factorize the denominator of the second term:
[tex] \frac{4}{m+9} [/tex] + [tex] \frac{5}{(m+9)(m-9)} [/tex]
3- Get the common denominator for both terms. In this case, the common denominator would be (m+9)(m-9):
[tex] \frac{4(m-9)}{(m-9)(m+9)} [/tex] + [tex] \frac{5}{(m-9)(m+9)} [/tex]
This will give:
[tex] \frac{4m-36}{(m+9)(m-9)} [/tex] + [tex] \frac{5}{(m-9)(m+9)} [/tex]
4- Add the numerators normally since the two terms have common denominator:
[tex] \frac{4m-36+5}{(m-9)(m+9)} [/tex] = [tex] \frac{4m-31}{(m-9)(m+9)} [/tex]
Comparing the calculated result with the given options, we will find that the correct option is the last one
Hope this helps :)
inverse of f(x)=5x+4
Answers
Switch x and y
Solve for y
A video game club has 42 members. The number of high school members is six less than twice the number of middle school members. Which expression represents the number of high school members in the club?
Answers
x= # middle school members
2x-6= # high school members
Two times the number of middle school students is 2 times x. 6 less means to subtract 6 from 2x.
ANSWER: 2x-6 is an expression representing the number of high school members.
Hope this helps! :)
Answer:
2x-6
Step-by-step explanation:
Combine like terms to simplify the expression below 5y-8x-y+12x
Answers
Hope this helps!
These are the first sentences in the short story, “The Gift of the Magi,” by O. Henry: one dollar and eighty-seven cents. That was all. And sixty cents of it was in pennies.” A. Simplify the equation that represents the value of the coins. Make it an equation that expresses the value of quarters, dimes, and nickels. B. Is it possible to have exactly 60 pennies in $1.87? Explain.
Answers
Answer:
From the given problem statement of the this question,the amount of the gift is 1 dollar and sixty cents
x=60*B
Yes is it possible to have 60 pennies in $1.87
What would happen to a monthly payment if the interest rate increased
Answers
If the interest rate increases it is expected the monthly payment also increases.
What is the interest rate?This is usually a low percentage of money paid to the bank or a similar institution for borrowing money. The interest rate is established when the loan is approved and it is proportional to the amount of money that needs to be paid.
What would happen if the interest rate increased?As both the payment and the interest rate are directly related if the interest rate increases, the amount of money to be paid would also increase.
Learn more about interest rate in https://brainly.com/question/13324776
#SPJ1
How many inches are in 12 feet?
Answers
Remember, there are 12 inches in 1 foot so multiply 12 by 12 . . .
12 x 12 = 144 <-------
The answer to your question is 144 inches.
There are 144 inches in 12 feet.
Hope this helps you.
Have a great day!
Answer:
There are 144 inches in 12 feet.
Can anyone help me with this?
Answers
.. x = (1/2)√(24² -19.2²)
.. x = 7.2
The 2nd selection is the correct one.
Please help!! Dexter made a frequency distribution, setting up groups for the data shown.
His first group was for 20-24. What was the frequency of his forth group?
42 33 28 27 51 29 31 42 38 49 35 30 22 27 26 41 47 33
Answers
The frequency of Dexter's fourth group (35-39) in his frequency distribution is 2. This was determined by counting the numbers within the 35-39 range from the provided data set.
Calculating the Frequency of the Fourth Group:
To calculate the frequency of the fourth group in Dexter's frequency distribution, let's first establish the groups.
First Group: 20-24Second Group: 25-29Third Group: 30-34Fourth Group: 35-39Next, we'll count how many data points fall within each range:
3538Thus, there are 2 data points in the fourth group (35-39).
Find all the points where the tangent plane to this ellipsoid is parallel to the plane y-8x-4z = 0
Answers
Clayton wants to make a cylindrical case that will fit a bass drum with a height of 14 inches and a diameter of 24 inches. With is the surface area of the case? Use 3.14 \pi[tex] \pi [/tex]
Answers
A=2πr²+2πrh
"A" is the surface area of the cylinder.
"r" is the radius.
"h" is the height of the cylinder (h=14 inches).
2. You need to calculate the radius. So, you have:
r=Diameter/2
r=24 inches/2
r=12 inches.
3. You already have the height and the radius, so you can substitute these values into the formula (A=2πr²+2πrh) for calculate the surface area of the case:
A=2πr²+2πrh
A=2(3.14)(12 inches)²+2(3.14)(12 inches)(14 inches)
A=904.32 inches²+1055.04 inches²
A=1959.36 inches²
Sean tried to drink a slushy as fast as he could. He drank the slushy at a constant rate. There were originally 275 milliliters of slushy in the cup. After 13 seconds, 210 milliliters remained. How long did it take Sean to drink all the slushy?
Answers
Answer: It took Sean 55 seconds to drink all the slushy
Solution:
Original Volume: Vo=275 milliliters
After t1=13 seconds, 210 milliliters remained: V1=210 milliliters
He drank the slushy at a constant rate: r
Sean drank V=Vo-V1=275 milliliters-210 milliliters→V=65 milliliters
r=V/t1
r=65 milliliters / 13 seconds
r=5 milliliters/second
Sean will drink the remained volumen in a time t2:
t2=V1/r
t2=210 milliliters / (5 milliliters/second)
t2=42 seconds
Total time to drink: t
t=t1+t2
t=13 seconds + 42 seconds
t=55 seconds
Answer:
Sean drank at a rate of 5 milliliters per second.
It took Sean 55 seconds to drink all the slushy.
Step-by-step explanation:
Hope it helps in the picture below.
Write the fraction as money amount 65/100