What is the distance between A(-8, 4) and B(4, -1)?
Answers
Answer:
The distance between A(-8, 4) and B(4, -1) is 13 units.
Step-by-step explanation:
To find the distance between any two points, we can use the distance formula given by:
[tex]\displaystyle d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
We have the two points A(-8, 4) and B(4, -1). Let A(-8, 4) be (x₁, y₁) and let B(4, -1) be (x₂, y₂). Substitute:
[tex]d=\sqrt{(4-(-8))^2+(-1-4)^2}[/tex]
Evaluate:
[tex]d=\sqrt{(12)^2+(-5)^2}[/tex]
So:
[tex]d=\sqrt{144+25}=\sqrt{169}=13\text{ units}[/tex]
The distance between A(-8, 4) and B(4, -1) is 13 units.
___________________________________
Problem:What is the distance between A(-8,4) and B(4,-1)Given:[tex]\quad\quad\quad\quad\tt{A.) x\tiny{1}\small{=-8}, y\tiny{1}\small{=4}}[/tex]
[tex]\quad\quad\quad\quad\tt{B.) x\tiny{2}\small{=4}, y\tiny{2}\small{=-1}}[/tex]
Formula for distance (d):[tex]\quad\quad\quad\quad\tt{d = \sqrt{(x \tiny{2} \small{ - x \tiny{1} \small {)}^{2} + (y \tiny{2} \small{ - y \tiny{1} \small{)}^{2} } }}} [/tex]
Solution:[tex]\quad\quad\quad\quad\tt{d = \sqrt{(4 - \small{ (- 8}{))}^{2} + ( \small{- 1)}\small{ - {4)}}^{2} }}[/tex]
[tex]\quad\quad\quad\quad\tt{d = \sqrt{ ( {12)}^{2} + {( -5)}^{2} }}[/tex]
[tex]\quad\quad\quad\quad\tt{d = \sqrt{ {144} + {25}}}[/tex]
[tex]\quad\quad\quad\quad\tt{d = \sqrt{ 169}}[/tex]
[tex]\quad\quad\quad\quad\tt{d = 13}[/tex]
So the final answer is:[tex]\quad\quad\quad\quad\boxed{\boxed{\tt{\color{magenta}d = 13}}}[/tex]
___________________________________
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✍︎ C.Rose❀
Related Questions
Amber is solving the inequality X+61- 12 < 13 by graphing. Which equations should Amber graph?
O Y1 = +6 Y2 - 25
O y1= x+6y2 = 25
O Y1 = X+61.72 = 13
O Y1 = X+6.82 = 13
Answers
Therefore, Amber should graph the equation Y1 = X+61.
What is inequality?An inequality is a mathematical statement that compares two values or expressions using one of the inequality symbols: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), or ≠ (not equal to). Inequalities are used to describe a range of possible values for a variable, rather than a single value. Inequalities can be solved by performing operations on both sides of the inequality symbol, just like equations. However, there are some important differences between solving equations and solving inequalities. For example, if we multiply or divide both sides of an inequality by a negative number, we need to reverse the direction of the inequality symbol.
Here,
To graph the inequality X+61- 12 < 13, we need to rearrange it to the form Y < MX + B, where Y is on the left-hand side and X is on the right-hand side. This gives:
Y < -X + 64
Now we can graph the line Y = -X + 64 and shade the region below it, since we want Y to be less than this expression.
Out of the equations given, Y1 = X+61 is the closest to the inequality we are trying to graph. However, the coefficients of X and Y are reversed, so we need to rearrange it to the desired form:
Y - X < 61
Y < X + 61
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While watching the Kentucky Derby horse races, you decide to guess who will win 1st, 2nd, and 3rd place. There are 17 horses in the race. What is the probability you choose all three places correctly
Answers
Answer:
1/17
Step-by-step explanation:
I he had even got 1 out of the 3 places the probability would be 3/17
But as he is guessing all three places it becomes 1/17
The probability of getting the 1st,2nd, and 3rd position will be 1/17.
What is the probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Given that while watching the Kentucky Derby horse races, you decide to guess who will win 1st, 2nd, and 3rd place. There are 17 horses in the race.
The probability is calculated by the formula,
Probability = Number of favorable outcomes / Number of sample
Number of favorable outcomes = 1
Number of samples = 17
Probability = Number of favorable outcomes / Number of sample
Probability = 1/17
Therefore, the probability of getting the 1st,2nd, and 3rd position will be 1/17.
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In the diagram of circle O shown to the right, PA and PB are tangent to circle O at points A and B, respectively. If mACB 266, then mAPB
Answers
Answer: 86 degrees
Step-by-step explanation:
Which statement is true about the function shown in the graph?
Answers
Answer:
A
Step-by-step explanation:
The function that is shown in the graph is strictly decreasing
What is a function?"A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function."
The given function has a value of (- 5) at a certain point.
After that the function is decreased to a value of (- 10).
Therefore, we can conclude that the function is strictly decreasing.
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out of 80,000 seats in a cricket stadium 12% seats were there occupied by vips and 39040 seats by general public what percentage of the stadium remained un occupied?
Answers
Answer:
% of unoccupied seats = 63.2 %
Step-by-step explanation:
Total seats = 80, 000
VIP seats = 12 % of 80, 000
[tex]= \frac{12}{100} \times 80000\\\\= 9600[/tex]
General Seats = 39040
Remaining seats = 80000 - 9600 - 39040 = 50, 560
Percentage of un-occupied seats,
[tex]= \frac{50560}{80000} \times 100 = 63.2 \%[/tex]
Answer:
THE NUMBER OF SEATS OCCUPIED BY VIPS=80000×12/100
=9600
occupied seats=9600+39040
=48640
number of unoccupied seats=80000-48640
=31360
percentage of unoccupied seats=31360/80000×100%
=39.2%
In Oregon, the mean annual rainfall in Rockaway Beach is 118.88 inches and the mean annual rainfall in Falls City is 122.28 inches. Which conclusion can you make using this information?
Answers
Answer:
Step-by-step explanation:
Based on this information, you could conclude that the annual rainfall in Falls City is generally more than that of the annual rainfall in Rockaway Beach. This is based on the information provided since the numbers given are the mean annual rainfall. Meaning that this is the average amount of rain that falls in any given year in that specific location. Since the amount provided for Falls City is a larger number then it means it gets more rainfall than Rockaway Beach on average and would therefore be the safest conclusion that can be made.
Answer:
I hope this helps
Step-by-step explanation:
Write image as a complex number. Question 6 options: A) 3 + i B) 3 – i C) –3 + i D) –3 – i
Answers
Answer:
that's right B) 3 - √3i
Step-by-step explanation:
(12 - √-48) / 4 =
12/4 - √-48 /4
= 3 - √(-48/16)
= 3 - √-3
= 3 - √ 3i
[tex]\\ \rm\Rrightarrow \dfrac{12-\sqrt{-48}}{4}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{12}{4}-\dfrac{\sqrt{48}i}{4}[/tex]
[tex]\\ \rm\Rrightarrow 3-4\sqrt{3}i/4[/tex]
[tex]\\ \rm\Rrightarrow 3-\sqrt{3}i[/tex]
PLEASE HELP!!!
WILL MARK BRAINLIEST!!!
If A=28, then the measure of arc BA is_____
Answers
Answer:
124
Step-by-step explanation:
Have a nice day :)
Arc AC is 180º, arc BC is 56º:
[tex]180+56 +\arc{BA} = 360\implies BA = 124[/tex]
Plz help solve this thanks
Answers
Answer:
y= -3/2
Step-by-step explanation:
........................
write a quadratic function f whose zeros are 2 and -6
Answers
Answer:
hope this will help u
Step-by-step explanation:
⇒ Given zeros are α=2 and β=−6.
⇒ Sum of zeros =α+β=2+(−6)=−4
⇒ Product of zeros =α×β=2×(−6)=−12
⇒ Quadratic polynomial =x
2
−(α+β)x+(α×β)
⇒ Quadratic polynomial =x
2
−(−4)x+(−12)
∴ Quadratic polynomial =x
2
+4x−12
The quadratic function having 2 and -6 as zeros is f(x) = x² + 4x - 12.
What is the quadratic function with roots 2 and -6?Given the parameters:
Zeros of the function: 2 and -6.
To find the quadratic function f(x) with zeros at 2 and -6, first set up the equation:
x = 2 and x = -6
These are the real solutions to the quadratic equation:
This means that; ( x - 2 ) and ( x + 6 ) are the factors of the quadratic equation:
Hence:
( x - 2 )( x + 6 ) = 0
Expand using distributive property:
x( x + 6 ) - 2(x + 6 ) = 0
x² + 6x - 2x - 12 = 0
Collect and add like terms:
x² + 4x - 12 = 0
Therefore, the function will be:
f(x) = x² + 4x - 12.
The quadratic function is f(x) = x² + 4x - 12.
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The linear function g is defined by g(x) = 4x.
a. Determine g(3).
b. Determine g(2).
c. Determine g(3) - g(2)
Answers
Answer:
the answer is D.
Step-by-step explanation:
well, the y-intercept for f(x) is at
as you can see from the slope-intercept form is at 4, and it has an slope of 2/3.
for g(x), well an y-intercept is when x = 0, what is it from that table? well, is at 0,3, so when x = 0, y = 3, so no dice on that one.
c)
whenever an x-intercept occurs, y = 0, for f(x) that's at
what about the x-intercept for g(x)? well, let's check, when is y = 0? aha! at -9, 0, so when y = 0, x = -9, so no dice on that one either.
d)
well, what is the slope of g(x) anyway? well, let's pick two points off the table to get it hmmm the first two let's use,
and from a), using the slope-intercept form, we know f(x) has a slope of 2/3.
well, 2/3 is larger than 1/3, so no dice.
b)
well, you already know.
Item 23
What kind of angle is angle BCA ?
acute
obtuse
right
Answers
Answer:
BCA is obtuse
Step-by-step explanation:
BCA = 98 degrees
greater than 0 to less than 90 is acute angles
90 - right angle
greater than 90 to less than 180 is obtuse
98 is obtuse
What is the distance between (-5, -6) and (-3, -8)?
Answers
A file that is 226 megabytes is being downloaded if the download is 12.&% complete, how many megabytes have been downloaded? Round your answer to the nearest tenth
Answers
Answer:
28.7
Step-by-step explanation:
12.7% = 0.127
226 * 0.127 = 28.702
Rounded
28.7
Helpppppppppppppppp please y’all
Answers
[tex]\sf{3. \ \ Given : \dfrac{2}{3} - \dfrac{5}{4} + \dfrac{7}{2}}[/tex]
Let us solve the first two fractions : The LCM of 3 and 4 is 12
[tex]\sf{\implies \dfrac{4(2) - 5(3)}{12} + \dfrac{7}{2}}[/tex]
[tex]\sf{\implies \dfrac{8 - 15}{12} + \dfrac{7}{2}}[/tex]
[tex]\sf{\implies \dfrac{-7}{12} + \dfrac{7}{2}}[/tex]
LCM of 2 and 12 is 12
[tex]\sf{\implies \dfrac{-7 + 7(6) }{12}}[/tex]
[tex]\sf{\implies \dfrac{-7 + 42}{12}}[/tex]
[tex]\sf{\implies \dfrac{35}{12}}[/tex]
[tex]\sf{\implies 2 +\dfrac{11}{12}}[/tex]
[tex]\sf{\implies 2 \dfrac{11}{12}}[/tex]
---------------------------------------------------------------------------------------
[tex]\sf{4. \ \ Given : \dfrac{(2 - 7)^2 + 5}{3}}[/tex]
[tex]\sf{\implies \dfrac{(-5)^2 + 5}{3}}[/tex]
[tex]\sf{\implies \dfrac{25 + 5}{3}}[/tex]
[tex]\sf{\implies \dfrac{30}{3}}[/tex]
[tex]\sf{\implies 10}[/tex]
Answer:
2/3-5/4+7/2
Step-by-step explanation:
collect like terms. that is the positive and negative terms2/3+7/2-5/4lcm of 3 and 2 is 6 hence 2/3+7/2= 25/625/6-5/4....lcm of 6 and 4 is 12 hence 25/6-5/4=35/12 the answer in its mixed fraction is 2 and 11/12Answer to the question
Answers
Answer:
7
Step-by-step explanation:
Step-by-step explanation:
AB//CD (Opposite sides of parallelogram are parallel)
Angle A + Angle B = 180 (Sum of interior angles=180)
179 + 3x - 20 = 180
3x - 20 = 180 - 179
3x - 20 = 1
3x = 1 + 20
3x = 21
x = 21/3
x = 7
Patterson Planning Corp.,
You have been hired by Patterson Planning Corp., an events planning company that recently had a fire in which some of the accounting records were damaged.
In reviewing the fixed asset records, you find three depreciation schedules that are not labeled. They are listed in the following table. One of the assets has a depreciation rate of $4.30 per hour.
Answers
Answer:
Total depreciation now will be $51500 and the depreciation for you will be $5575
Step-by-step explanation:
Your welcome! :)
The pentagon shown could be reflected over which line to be carried onto itself?
Answers
Answer:
on the x axis because it is reflected there
how to find coefficient of x²in 2+x²+c
Answers
Answer:
1 is cofficient of X ²
I hope it's helpful for u ...Type the correct answer in each box.
Find the solution for this system of equations.
2x + 4y = 8
x = 3y − 6
Answers
AnswerY=2
Answer:
X=0
Y=2
Step-by-step explanation:
Just finished and i got it right
find the product. write your answer in exponential form 9²•9-⁶
Answers
Answer:
9^8
Step-by-step explanation:
9²•9⁶ = 9^(2+6) = 9^8
Answer:
IF the 6 is negative : [tex]9^{2}[/tex] · [tex]9^{-6}[/tex] then the answer is 1/[tex]9^{4}[/tex]
If the 6 is positive then the answer is [tex]9^{8}[/tex]
Step-by-step explanation:
Exponents are add when their bases are similar.
How to solve and what is the answer for this question
Answers
Answer:
O DC = 65 and DE = 33.5
Step-by-step explanation:
DC is already given by AB
so DC is 65
DE would be BD split
DE is 33.5
Answer: O DC = 65 and DE = 33.5
Which shows a graph of a linear equation in standard form Ax + By = C, where A = 0, B is positive, and C is negative? A coordinate plane with a vertical line passing through (1, negative 4), (1, 0) and (1, 4). A coordinate plane with a vertical line passing through (negative 2, negative 4), (negative 2, 0) and (negative 2, 4). A coordinate plane with a horizontal line passing through (negative 4, 4), (0, 4) and (negative 4, 4). A coordinate plane with a horizontal line passing through (negative 4, negative 3), (0, negative 3) and (4, negative 3).
Answers
Answer:
A coordinate plane with a horizontal line passing through (negative 4, negative 3), (0, negative 3) and (4, negative 3).
Step-by-step explanation:
Ax + By = C, where A = 0, B is positive, and C is negative
By= C or y= C/B which is negative
Since A is zero and C is negative, the line is parallel to x- axis and has negative value for y, so it is a horizontal line below zero
---------------
A coordinate plane with a vertical line passing through (1, negative 4), (1, 0) and (1, 4).
no, the line is horizontal
A coordinate plane with a vertical line passing through (negative 2, negative 4), (negative 2, 0) and (negative 2, 4).
no, the line is horizontal
A coordinate plane with a horizontal line passing through (negative 4, 4), (0, 4) and (negative 4, 4).
no, the y-values should be negative
A coordinate plane with a horizontal line passing through (negative 4, negative 3), (0, negative 3) and (4, negative 3).
yes, this is horizontal line below zero
Answer:
D
Step-by-step explanation:
Joelle would like to tip her hairdresser 20%. If her haircut costs $38.00, which expression should she use to find the tip amount?
Answers
20%=1/5 so the tip amount is 1/5*($38.00)=$7.60
6. Which of the following is equivalent to the expression shown?
(x - 5)(x + 5)
(A) x2 – 10x - 25
(C) x2 – 25
x2 - 10x + 25
(D) x2 + 25
(x–52) (x+5)
x²-524
X2-10
I’m stuck on this help anyone ? :(
Answers
Answer:
its x^2 -25
Step-by-step explanation:
simply we know,
a^2-b^2=(a-b)(a+b)
brainlest! to first one pls help mehh
Answers
Answer:
A
Step-by-step explanation:
Answer:
option a and b
Step-by-step explanation:
peanuts=1/4 cup ratio=1:4
raisins=1/2 cup ratio=1:2
chocolate chips=3/4 cup ration=3:4
granola =1 cup ration=1:1
a. ratio of cop of rasins to cup of peanuts=2:1 or 2/1
1/2 = 1/4=2/1
do cross multiplication
4*1=2*1=2/1
4/2=2/
2/1=2/1
2:1=2:1 this is satisfied
b.ratio of cup of granola to cup of peanuts=1:4 or 1/4
1/1=1/4
do crss multiplication
1*1/4*1=1/4
1/4=1/4
1:4=1:4 this is satisfied as both are equal
c.the ratio of cup of chocolate chips to cup of raisins=3:1 or 3/1
3/4=1/2
do cross multiplication
3*2=4*1=3/1
6/4=3/1
6:4=3:1 this is not satisfied as they are different.
d.the ratio of cup of raisins to cup of granola=1:3 or 1/3
1/2=1/1
do cross multiplication
1*1=2*1=1/3
1/2=1/3
1:2=1:3 this is not satisfied as they are different.
e. the ratio of cup of granola to cup of chocolate chips =4:3 or 4/3
1/1=3/4
do cross multiplication
3*1=4*1=4/3
3/4=4/3
3:4=4:3 this is not satisfied as they are not equal
therefore ur answer is option a and b.
Select all the pairs of expressions that are equivalent.
•14d + 21 and 7(2d + 3)
•9(5r - 2) and 14r - 7
•8(69 - 9) and 489 - 72
•16 + 4w and 2(2w + 8)
•32t + 16 and 16(2 – t)
Answers
Answer:
14d + 21 = 7(2d + 3)
16 + 4w = 2(2w + 8)
Step-by-step explanation:
14d + 21
7(2d + 3)
14d + 21
14d + 21 = 7(2d + 3)
9(5r - 2)
45r - 18
14r - 7
9(5r - 2) ≠ 14r - 7
8(69 - 9)
552 - 72
489 - 72
8(69 - 9) ≠ 489 - 72
16 + 4w
2(2w + 8)
4w + 16
16 + 4w = 2(2w + 8)
32t + 16
16(2 - t)
32 - 16t
32t + 16 ≠ 16(2 - t)
The pairs of expressions that are equivalent are 14d + 21 and 7(2d + 3) and 16 + 4w and 2(2w + 8)
How to determine the equivalent expressions?To do this, we test each pair of expression.
This is done as follows
14d + 21 = 7(2d + 3)
Expand
14d + 21 = 14d + 21 --- this is true
9(5r - 2) = 14r - 7
Expand
45r - 18 = 14r - 7 --- this is false
8(69 - 9) = 489 - 72
Expand
552 - 72 = 489 - 72 --- this is false
16 + 4w = 2(2w + 8)
Expand
16 + 4w = 4w + 16 ---- this is true
32t + 16 = 16(2 – t)
Expand
32t + 16 = 32 - 16t --- this is false
Hence, the pairs of expressions that are equivalent are 14d + 21 and 7(2d + 3) and 16 + 4w and 2(2w + 8)
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Solve the system of equations.
y=8x-6
y=5x+9
Answers
Answer:
x= 5 , y = 34
Step-by-step explanation:
8x-6=5x+9
3x-6=9
3x=15
x=5
-
8(x5) - 6 =
34
25(x5) +9 =
34
Answer:
x = 5 and y = 34
Step-by-step explanation:
I used substitution method and did this ;
8x - 6 = 5x + 9 .....put like terms together
8x - 5x = 9 + 6
3x = 15
x = 5
y = 8 (5) - 6
y = 40 - 6
y = 34
Multiply x^2+2x+3 times 4x^2-2x+1
Answers
Answer:
4x^4 + 6x^3 + 9x^2 − 4x + 3
Step-by-step explanation:
Simplify the expression. 4x^4 + 6x^3 + 9x^2 − 4x + 3
Step-by-step explanation:
Answer:
answer for this solution is 4x^4+6x^3+9x^2-4x+3
Please help with this!! Urgent
Answers
9514 1404 393
Answer:
see attached
Step-by-step explanation:
When p and q are roots, (x -p) and (x -q) are factors. The quadratic equation is then ...
0 = (x -p)(x -q) = x^2 -(p+q)x +pq
That is, the constant term is the product of the roots and the linear term coefficient is the opposite of the sum of the roots.
Using the given sum and product, the equation can be written ...
0 = x^2 -(-5/4)x +3/4
Multiplying by -8 gives ...
0 = -8x^2 -10x -6 . . . . . matches lower right choice
_____
Check
The product of roots is positive, so both roots have the same sign. The sum of roots is negative, so both roots are negative. That means there are no positive real roots to the equation. Descartes' Rule of Signs tells you this means the sequence of coefficients has no sign changes. Only the choice shown below has no sign changes. All of the others have at least 1 sign change.
