Answers
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{-6}~,~\stackrel{y_1}{7})\qquad C(\stackrel{x_2}{-4}~,~\stackrel{y_2}{4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ BC=\sqrt{[-4 - (-6)]^2 + [4 - 7]^2}\implies BC=\sqrt{(-4+6)^2+(-3)^2} \\\\\\ BC=\sqrt{2^2+(-3)^2}\implies \boxed{BC=\sqrt{13}} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~~~~~~~\textit{distance between 2 points}[/tex]
[tex]F(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-4})\qquad G(\stackrel{x_2}{1}~,~\stackrel{y_2}{-2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ FG=\sqrt{[1 - (-2)]^2 + [-2 - (-4)]^2}\implies FG=\sqrt{(1+2)^2+(-2+4)^2} \\\\\\ FG=\sqrt{9+4}\implies \boxed{FG=\sqrt{13}} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ J(\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\qquad K(\stackrel{x_2}{5}~,~\stackrel{y_2}{-2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}[/tex]
[tex]JK=\sqrt{[5 - 4]^2 + [-2 - 2]^2}\implies JK=\sqrt{1^2+(-4)^2}\implies \boxed{JK=\sqrt{17}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \overline{BC}\cong \overline{FG}~\hfill[/tex]
Related Questions
A bicycle costs $240 and it loses 3/5 of its value each year.
A. Write expressions for the value of the bicycle,in dollars, after 1,2, and 3 years
B. When will the bike be worth less than $1?
Answers
Answer:
A. $96.00, $38.40, $15.36
B. after 6 years
Step-by-step explanation:
An exponential function has the general form ...
y = (initial value) × (growth factor)^t
__
A.The growth factor is 1 more than the growth rate. Here, the "growth" is actually a decay at the rate of 60% per year, so the growth rate is -0.60. The initial value is $240. The value equation can be written ...
y = 240(1 -0.60)^t
We want the value after t=1, t=2, and t=3 years.
y = $240(0.4)^1 = $96 . . . value after 1 year
y = $240(0.4)^2 = $38.40 . . . value after 2 years
y = $240(0.4)^3 = $15.36 . . . value after 3 years
__
B.We want to find t when y < 1.
240(0.4)^t < 1
0.4^t < 1/240 . . . . . . . . . . . . divide by 240
t × log(0.4) < log(1/240) . . . take logs
t > log(1/240)/log(0.4) . . . . . . . inequality reverses because log(0.4) < 0
t > 5.98
The bike will be worth less than $1 after about 6 years.
_____
Additional comment
For part A, we have shown the values after 1, 2, and 3 years. The expressions are shown on the same line preceding the value.
Find the average rate of change between n=1 and n=3
Answers
Answer:
there is not enough information to solve
Step-by-step explanation:
You need two ordered pairs to calculate the average rate of change.
Let's say the value of the function at n = 1 is a, and the value of the function at n = 3 is b, then the average rate of change from n = 1 to n = 3 is
(b - a)/(3 - 1) = (b - a)/2
Whats the mean of 72+72+72+79+82+82+88?
Answers
Answer:
78.1428571429
Step-by-step explanation:
The owner of a music store ordered new compact disks. Of the new compact disks ordered,1/4 are Jazz, 2/7 are Classical, and the rest of the compact disks are Soft Rock. What fraction of the compact disks ordered are Soft Rock?
Answers
The fraction of the compact disks ordered by the owner of the music store that are Soft Rock is 13/28.
What are fractions?A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator. The numerator is the number above while the denominator is the number below.
What fraction is Soft Rock?1 - (1/4 + 2/7)
1 -[ (7 + 8) /28]
1 - 15/28 = 13/28
1)The mass of Sarah's dog is 6 Kg more than two times the mass of her cat. The mass of her dog is 16 Kg.What is the mass of her cat?
Answers
Answer:
10 kg
Step-by-step explanation:
Let x be the mass of her cat.
1)
2x + 6 = 16
2x = 16 - 6
2x = 10
x = 10/2
x = 5
2)
2(5)
= 10
Answer:10kg
Step-by-step explanation:
Unit 10: circles homework 2: central angles & arc measures
Answers
The central angle (127 degrees) is the angle at point K
The measures of JL and JML are 127 and 233 degrees, respectively
How to determine the measures of angles JL and JML?From the complete question, we have:
JL = 127 degrees.
The sum of angles at a point is 360 degrees
So, we have:
JML + 127 = 360
Subtract 127 from both sides
JML = 233
Hence, the measures of JL and JML are 127 and 233 degrees, respectively
Read more about circles and arcs at:
https://brainly.com/question/25305793
f(x) = 4x -8;{-2, -1,0,1,2}
What is the range? Choose the correct answer below.
A. {-16,- 11,-8, -3,0)
B. {-16, -12,-8, -4,0}
C. {-17, -12,- 8, -4,1}
D. {-16, -11, -9,-3,0)
Answers
Answer:
B
Step-by-step explanation:
4(-2)-8 = -16, so not C
4(-1)-8 = -12, so not A or D
4(0)-8 = -8, so not D
4(1)-8 = -4, so not A or D
4(2)-8 = 0, so not D
The population of Hampton was 7,490 people when Malik moved there. Currently it is 10% smaller. What is the current population?
people
Answers
Answer:
6741
Step-by-step explanation:
if its 10% smaller you would have to do the original precent, which is 100%, and subtract 10%, (90%) then divide 90 by 100 to get 0.9 and multiply it by the total population, in this case 7,490, and you get your answer. i hope this helps :)
If a person is behind on his debt payments and goes to a responsible credit counseling service, what help is likely to be offered?
a.They can cancel and cut up his credit cards without his permission.
b.They can force those who loaned him money to forgive his debts.
c.They can get the federal government to apply his income taxes to pay off his debts.
d.They can work with those who loaned him the money to set up a realistic payment schedule.
Answers
Answer:
d
Step-by-step explanation:
I mean the 1st and 2nd ones are unreasonable and 3 is jus unrealistic
Each tick mark shows 1 third. What's
1
3
more than 1?
2
1
2
3
1
3
0
Answers
Answer:
Step-by-step explanation:
1/3 more than 1 is 1 1/3 or 4/3.
I have five apples and ten oranges. If a fruit basket must contain at least one piece of fruit, how many kinds of fruit baskets can I make
Answers
Answer:
answer is 15
please that is what I'm thinking
2022
Question 4
20 pts
nts
Linel and line mare parallel lines that are cut by a transversal.
Let mZ1 = (x+97)° and m2 = (2x+32)". What is mZ1?
12
m
2.
55
ооо
162
65
130
Answers
Answer: B
Step-by-step explanation:
These are vertical angles, so x+97=2x+32, meaning x=65.
So, the measure of angle 1 = 65 + 97 = 162 degrees
The value of m∠1, given that m∠1 = x + 97 and m∠2 = 2x + 32 is 162° (2nd option)
How to determine the value of m∠1?First, we shall list out the given parameters from the question. This is given below:
m∠1 = (x + 97)° m∠2 = (2x + 32)°Angle 1 (m∠1 ) =?Next, we shall obtain the value of x. Details below:
m∠1 = m∠2 (vertically opposite angle)
x + 97 = 2x + 32
Solving for x, we have:
97 - 32 = 2x - x
65 = x
Thus,
x = 65
Now, we shall obtain the value of m∠1 as follow:
m∠1 = x + 97
x = 65
Therefore,
m∠1 = 65 + 97
= 162°
Thus, the value of m∠1 is 162° (2nd option)
Learn more about vertically opposite angle:
https://brainly.com/question/29747440
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ΔA'B'C' was constructed using ΔABC and line segment EH.
2 triangles are shown. Line E H is the line of reflection. Line segment B B prime has a midpoint at point D. Line segment A A prime has a midpoint at point F. Line segment C C prime has a midpoint at point G.
For to be the line of reflection between and , which statements must be true? Select three options.
BD = DB'
DF = FG
m∠EFA = 90°
The line of reflection, EH, is the perpendicular bisector of BB', AA', and CC'.
ΔABC is not congruent to ΔA'B'C'.
Answers
Answer: 1,3,4
Step-by-step explanation:
Answer: 1., 3., and 4.
Step-by-step explanation: On Edge!!
How do I solve this problem step by step?
Answers
Answer:
392.5 in²
Step-by-step explanation:
The area of a composite figure is found by decomposing it into areas that you have formulas for. This figure is easily decomposed to a trapezoid and a rectangle.
TrapezoidThe base lengths of the trapezoid are 20 in and 9 in. Its height is the difference between the height of its top base (21 in) and the height of its bottom base (16 in). That difference is 5 in.
A = 1/2(b1 +b2)h
A = 1/2(20 in + 9 in)(5 in) = 72 1/2 in²
__
RectangleThe area of a rectangle is the product of its base and height.
A = bh
A = (20 in)(16 in) = 320 in²
__
Total areaThe area of the whole figure is the sum of the areas of its parts.
area = trapezoid area + rectangle area
area = 72 1/2 in² +320 in² = 392 1/2 in²
Explain how you know whether the numbers, 4/16 and 0.25 are equivalent numbers.
Answers
Answer:
When you divide 4/16 by 4 it equals 1/4. which is known as 0.25 or 25% of a whole.
Step-by-step explanation:
What is the constant term in the expression 8xy − 9x2 y − 5x 6
Answers
Answer:
6
Step-by-step explanation:
A constant is a term without a variable.
Every other number has a variable (x,y) to it except for 6.
Feel free to save this for whenever you get stuck on things like this! I know this section is hard.
In the expression 8xy − 9x^2+ y − 5x +6 the constant term is 6 which is a fixed quantity or cannot be changed.
What is polynomial?Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.
We have an expression:
[tex]\rm 8xy-9x^2+y-5x+6[/tex]
Let's denote it with f(x,y)
[tex]\rm f(x,y) =8xy-9x^2+y-5x+6[/tex]
As we know the constant term means which cannot be changed that values are fixed or fixed quantity.
From the above expression, the constant value in the expression is 6
Thus, in the expression 8xy − 9x^2+ y − 5x +6 the constant term is 6 which is a fixed quantity or cannot be changed.
Learn more about Polynomial here:
brainly.com/question/17822016
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c) d) When 3 is subtracted from the number, the remainder is 5.
Answers
Answer:
so the equation would look like this, x - 3 = 5
the number or x = 8
Step-by-step explanation:
8 - 3 = 5
Hope this helps! :)
For each set of three lengths, determine if they can be the side lengths of a triangle.
Answers
Answer:
Yes, No, Yes, NoStep-by-step explanation:
Use the triangle inequality theorem, which states that the sum of any two side lengths must be greater than the third side length.
Apply this to each combination.
Use one inequality, compare the sum of smallest two sides with the largest side.
1) 4, 9, 8
4 + 8 = 12 > 9, so Yes2) 7, 25, 7
7 + 7 = 14 < 25, so No3) 8.8, 24, 15.8
8.8 + 15.8 = 24.6 > 24, so Yes4) 5, 9, 3
3 + 5 = 8 < 9, so NoDetermine whether each relation is a function. Explain. {(2,0), (2, 2), (2, 4), (2, 6)}
Answers
This example is not a function, as the independent variable (2) appears more than once.
The rule is that the independent variable(x) cannot appear more than once as the same value and the dependant variable(y) can appear more than once as the same value.
Hope this helps!
The area of a square is 9ft find the area of a square with 4 times as large
Answers
Answer:
36ft
Step-by-step explanation:
9ft times 4ft= 36ft
help! complete the table with the missing measurements. the perimeter is 40ft is that helps
Answers
therer sorry for the cropped pic btw lol
Sylvie bakes 4 trays of muffins. Each tray contains 8 muffins. She gives away 12 muffins to friends.
Let m represent the number of muffins Sylvie has left.
Which equation could be used to find the value of m?
4+8−12=m
4 + 8 + 12 = m
4 × 8 + 12 = m
4×8−12=m
Answers
Answer:
4x8-12=m
Step-by-step explanation:
4 trays x each containing 8 muffins - 12 muffins(giving away)
What is the circumference
Answers
multiply the radius by 2 and multiply that number with pi and you get your answer of 25.1 yards
The median weekly income for someone with a high school diploma was $678.00. If they continued their education and obtained a bachelor's degree, their median weekly income increased about 67.7%. Determine the median weekly income for someone with a bachelor's degree. (2 points) $218.99 $568.51 $799.45 $1,137.01
Answers
3. Si:{3x− (a − 2)y = 13 4x+ ay = 5 Es un sistema compatible determinado,determina el valor que no puede tomar “
Answers
Answer: yes
Step-by-step explanation:
Solve.
3y − 1 − 9y = 29
(−5, 6, −6, 5)- answer options
Answers
Step-by-step explanation:
STEP
1
:
Pulling out like terms
1.1 Pull out like factors :
-6y - 30 = -6 • (y + 5)
Equation at the end of step
1
:
STEP
2
:
Equations which are never true:
2.1 Solve : -6 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
2.2 Solve : y+5 = 0
Subtract 5 from both sides of the equation :
y = -5
One solution was found :
y = -5
Answer: y=-5
Explanation:
3y-1-9y=29
3y-9y=-6y
-6y-1=29
+1 on both sides
-6y=30
÷-6
y=-5
Is -9,8 a solution to y=-9
Answers
Answer:
No, it isn't.
Step-by-step explanation:
In (-9, 8), -9 is the x coordinate. The y is 8. In order for -9 to have been a solution, the y would have had to been -9.
Here's what I mean:
(The graph I drew is in the image. I hope it makes sense! Sorry for my bad handwriting, I'm not used to writing on computers.)
I hope this helps!
-No one
What is the value of the discriminant for x2 + 5x = -7?
Answers
Answer:
x = -1
Step-by-step explanation:
2x + 5x = -7
7x = -7
x = -1
What is the maximum age of the youngest 25% of the passengers?
Answers
Using the percentile concept, it is found that the maximum age of the youngest 25% of the passengers is of 30.
What is the percentile concept?When a measure is in the xth percentile of a data-set, it is greater than x% of the measures and lesser than (100 - x)%.
Researching the problem on the internet, it is found that the distribution of the ages is described by a box and whisker plot, which states that:
The 25th percentile is of 30.The median is of 45.The 75th percentile is of 60.Hence, the maximum age of the youngest 25% of the passengers is of 30.
More can be learned about the percentile concept at https://brainly.com/question/24495213
PLEASE HURRY
Solve the inequality and express your answer in interval notation.
x2 + 8x-7<0
Answers
I’m not sure if you’re supposed to use brackets or parentheses