Use the distance formula to find the distance between each pair of points round to the nearest 10th if necessary
Answers
Given:
The pairs of points are:
a. A(-6,-4), B(-3,-1)
b. C(3.5,1), D(-4,2.5)
c. X(5,-5), Y(-5,5)
To find:
The distance between the pair of points by using the distance formula.
Solution:
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
a.
Using the distance formula, the distance between the points A(-6,-4) and B(-3,-1) is:
[tex]AB=\sqrt{(-3-(-6))^2+((-1-(-4))^2}[/tex]
[tex]AB=\sqrt{(3)^2+(3)^2}[/tex]
[tex]AB=\sqrt{2(3)^2}[/tex]
[tex]AB=3\sqrt{2}[/tex]
[tex]AB\approx 4.2[/tex]
Therefore, the distance between the points A(-6,-4) and B(-3,-1) is about 4.2 units.
b.
Using the distance formula, the distance between the points C(3.5,1) and D(-4,2.5) is:
[tex]CD=\sqrt{(-4-3.5)^2+(2.5-1)^2}[/tex]
[tex]CD=\sqrt{(-7.5)^2+(1.5)^2}[/tex]
[tex]CD=\sqrt{56.25+2.25 }[/tex]
[tex]CD=\sqrt{58.5 }[/tex]
[tex]CD\approx 7.6[/tex]
Therefore, the distance between the points C(3.5,1) and D(-4,2.5) is about 7.6 units.
c.
Using the distance formula, the distance between the points X(5,-5) and Y(-5,5) is:
[tex]XY=\sqrt{(-5-5)^2+(5-(-5))^2}[/tex]
[tex]XY=\sqrt{(-10)^2+(10)^2}[/tex]
[tex]XY=\sqrt{100+100}[/tex]
[tex]XY=\sqrt{200}[/tex]
[tex]XY\approx 14.1[/tex]
Therefore, the distance between the points X(5,-5) and Y(-5,5) is about 14.1 units.
Related Questions
If there was only one government class, and Wes and Maureen were in that class of 38 students, what would be the probability that both Wes and Maureen would be selected as the two students to go to Washington? Is this still an example of independent events
Answers
The probability of an event is 1/19. Therefore, the given situation is not an independent event.
Given that, Wes and Maureen were in the government class of 38 students.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Total number of outcomes =38
Number of favourable outcomes = 2
So, probability =2/38
= 1/19
Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event.
The probability of an event is 1/19. Therefore, the given situation is not an independent event.
To learn more about the probability visit:
https://brainly.com/question/11234923.
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Write a number y divided by 6 as an expression.
Answers
Answer:
y ÷ 6.
Step-by-step explanation:
An expression is a combination of a number(s) and a variable.
Here, we simply need to write the expression from the word problem in mathematical form.
"Number" is unknown.
Variables are used to represent an unknown value.
(The variable in this expression is y).
The word problem says a number y divided by 6.
This simply means: y ÷ 6.
What is the center and radius of the circle?
(x-1)^2 + y^2= 36
Answers
Answer:
Center = ( 1, 0)
Radius = 6 units
Step-by-step explanation:
[tex] {(x - 1)}^{2} + {y}^{2} = 36 \\ \\ {(x - 1)}^{2} + {(y - 0)}^{2} = {6}^{2} \\ \\ equating \: it \: with \\ \\ {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} \\ \\ h = 1 \\ k = 0 \\ r = 6 \\ \\ Center = (h, \: k) = (1, \: 0) \\ Radius \: = 6 \: units[/tex]
An experiment compares the height of two plants over time. A plant was 2cm tall at the beginning of the experiment and grew 0.5 centimeters each day. The functions f(t)=0.5+2 represents the height of the plant in centimeters after t days . Which plant for f, or g was growing faster ?
Answers
Answer:
Plant F;
Plant G;
Plant G
Step-by-step explanation:
Given that:
Plant F :
f(t)=0.5x+2
From the growth graph given for the second plant ; plant G
Point 1 (0, 5) ; point 2(16, 9)
Slope = Rise / Run = (9 - 5) / (16 - 0) = 4 / 16 = 0.25
Intercept = 5 ( point where fitted line crosses the y-axis)
Linear slope intercept relation : y = mx + c
m = slope ; c = intercept
g(x) = 0.25x + 5
The slope value of plant F = 0.5
Slope value of plant G = 0.25
F > G
Hence, F is growing at a faster rate
The starting height is given by the intercept value of the two equations ;
Plant F, intercept = 2
Plant G, intercept = 5
G > F
Hence, G was taller, to begin with
Height after 8 days :
x = 8
f(8)=0.5(8)+2
f(8) = 4 +2 = 6
g(8) = 0.25(8) + 5
g(8) = 2 + 5 = 7
Hence, G was taller after 8 days
Determine the length of the hypotenuse. Round your answer to the nearest tenth, if necessary.
Answers
Answer:
12.7
Step-by-step explanation:
[tex]9^{2}+9^{2}= 162\\\\\sqrt{162}= 12.7[/tex]
Solutions 5x + 10 = 5x
Answers
Answer:
I think there is no solution to the equation. (I'm not sure what your asking)
Step-by-step explanation
The equation should equal 0, so you subtract 5x from both sides. Once you do that, it cancels out the 5x and leaves 10=0 which is a false statement.
my question is the picture
Answers
Answer:
20 students
Step-by-step explanation:
You first have to add the number of students all up and you get 200.Then you do cross multiplication.
40/200 x s/100=
40x100= 4000=
200xs= 200s=
200s/200=
4000/200=
20=
x+y=-9. I need help asap! Thank you!
Answers
Answer: -5 and -4
Step-by-step explanation:
Answer:
-6, -3
-9, 0
20, -29
-5,-4
etc.
Step-by-step explanation:
There are many. Did they give you any other info???
A movie theater charges $10 for adults and $6 for seniors. On a particular day when 357 people paid in admission, the total receives were $2414
How many who paid were adults?
How many who paid were seniors?
Answers
Answer:
Step-by-step explanation:
Determine the types of tickets involved.
There are student tickets and adult tickets.
Create a table to organize the information.
Type
Number
Value ($)
Total Value ($)
Student
6
Adult
9
1
,
506
Step 2. Identify what you are looking for.
We are looking for the number of student and adult tickets.
Step 3. Name. Represent the number of each type of ticket using variables.
We know the number of adult tickets sold was
5
less than three times the number of student tickets sold.
Let
s
be the number of student tickets.
Then
3
s
−
5
is the number of adult tickets.
Multiply the number times the value to get the total value of each type of ticket.
Type
Number
Value ($)
Total Value ($)
Student
s
6
6
s
Adult
3
s
−
5
9
9
(
3
s
−
5
)
1
,
506
Step 4. Translate: Write the equation by adding the total values of each type of ticket.
6
s
+
9
(
3
s
−
5
)
=
1506
Step 5. Solve the equation.
6
s
+
27
s
−
45
=
1506
33
s
−
45
=
1506
33
s
=
1551
s
=
47
students
Substitute to find the number of adults.
3
s
−
5
=
number of adults
3
(
47
)
−
5
=
136
adults
Step 6. Check. There were
47
student tickets at
$6
each and
136
adult tickets at
$9
each. Is the total value
$1506
?
We find the total value of each type of ticket by multiplying the number of tickets times its value; we then add to get the total value of all the tickets sold.
47
⋅
6
=
282
136
⋅
9
=
1224
_____
1506
✓
Step 7. Answer the question. They sold
47
student tickets and
136
adult tickets.
y=6x+4
y=-3-5
how would you find the x and y values?
Answers
Step-by-step explanation:
Substitution
substitute -3-5 into y
it becomes -3-5=6x+4
solve the equation to find the answer for X
then substitute the value of X you found again into the equation to find Y
i need help can someone help me
Answers
the mode is $6.00
thats the number there is the most of
620 000 divided by 10 to the 3rd power plz help
Answers
Answer: 620
Step-by-step explanation: 620,000 / 10^3 = 620
Answer:
620
Step-by-step explanation:
10^3 = 10x10x10 =1000
620,000/1,000=620
A and B are both positive integers. which expression is equivalent to -A- (-B) ?
answer choices:
B-A
-A - B
A - B
A + B
Answers
how many ounces are equal to 1 1/2 pounds
Answers
A store pays $147 for a skateboard. If the store marks it up 75%, then marks it down 22%. What is the new cost
Answers
Answer:
$200.65
Step-by-step explanation:
If they bought it for 147 then marked it up 75% you would do
$147+75% = 257.25
THEN they mark down
257.25 - 22% = $200.255 which would be
$200.25 orrr $200.26
Marcus ate one-half of a pizza with a radius
of 7 inches. If the pizza has 8 calories per square
inch, how many calories did he eat?
Answers
Answer:
175.929
Step-by-step explanation:
7pi = area of half of pizza
21.99x8 = calories in half of pizza
1 Kembangkan setiap yang berikut.
(a) 3x(2 - xy)
(b) (4p + 9(-2)
Answers
Answer:
6x*2-3x*2y
4p-18
Step-by-step explanation:
Find the radius of a circle with an area of 1017.36 in?, Use 3.14 for pi
Answers
area of a circle = πr², where r = the radius of the circle
We can rearrange the formula to solve for r:
[tex]r=\sqrt{\frac{\mathrm{area}}{\pi}}.[/tex]
Given an area of 1017.36 in² and using 3.14 for our value for π, the radius of our circle would be:
[tex]r=\sqrt{\frac{\mathrm{area}}{\pi}} = \sqrt{\frac{\textrm{1017.36 }\mathrm{in^2}}{3.14}} \\ r = 18 \text{ } \mathrm{in^2}.[/tex]
The area of a rectangle is 8w + 18 square feet. The length of the rectangle is 2 feet. Use factoring to write an expression
to represent the width of the rectangle.
Answers
Answer:
area(rectangle) = Length * width
8w + 18 = 2 * w
8w + 18 = 2w
Jim wants to buy a new tablet for his homework. His budget is $350. If the tablet costs $330 plus 4.5% sales tax, can he buy it for $350 or less?
Answers
Answer:
Yes, he can buy it for $350 or less
Step-by-step explanation:
330.00 x 4.5%
330.00 x 0.045 = 14.85
330.00 + 14.85 = 344.85
or
330.00 x 1.045 = 344.85
Vincent has a box of popsicles. There are 12 cherry, grape 10 orange, and 6 blue raspberry If he reaches in the box and pulls one out at random, what the probability it will be blue raspberry?
Answers
Answer:
6:28 or 3:14
Step-by-step explanation:
if you add all the flavor amounts up, which is 12 + 10 + 6, you get 28. 6 of those 28 popsicles are blue raspberry, so the ratio is 6:28. if it needs to be simplified, its 3:14 because 6/2 is 3 and 28/2 is 14
Answer:
6:28 if you add all Popsicles it gives you 28,so the probability that he will pick raspberry are 6 ,so if you simplyfy further its 3:14
The school buses at a middle school each hold 38 students. The school has, b, buses.
Write an equation that shows the total number of students, s, that can be carried by all of its buses.
Answers
Answer:
38b = s
Step-by-step explanation:
38 students multiplied by the number of buses = the total number of students that can be carried by bus.
Please lmk if you have questions
Use the annual compound interest formula to find the amount in the savings account at the end of the time period and then find the total interest earned.
$8,000 at 5% for 3 years.
It is one of these answers if it helps...
$12,700 in account $4,700 interest
$10,520 in account $2,520 interest
$8,315 in account $315 interest
$9,216 in account $1,261 interest
Answers
Answer:
$9,216 in account $1,261 interest.
Step-by-step explanation:
The compound interest is given by:
[tex]a = p(1 + \frac{r}{n})^{nt} [/tex]
P = Principal
r = rate
n = Number of times interest is compounded per unit t
t = time
so:
[tex]a = 8000(1 + \frac{0.05}{1} ) ^{1 .3} \\ a = 9261[/tex]
therefore, the answer is:
$9,216 in account $1,261 interest
Evaluate the expression for v = 8
Answers
V = 8, because it can’t be simplified any further.
Triangle abc and xyz are congruent ,/_A is one half the size of /_B,/_y is 90° ./_c and /_z each have a measure of 45°.What is the measure of /_ a?
Answers
Answer:
∠a = 45°
Step-by-step explanation:
We are told that △abc and △xyz are congruent.
Thus;
∠a = ∠x
∠b = ∠y
∠c = ∠z
We are given;
∠y = 90°
Thus, ∠b = 90°
Now,we are told that ∠a is one half the size of ∠b.
Thus; ∠a = ½ × ∠b
∠a = ½ × 90
∠a = 45°
Andrew has a monthly cell phone bill. He pays a
monthly fee and a cost per minute. The graph to the
right shows his
cost per month depending on the
minutes used. What is the monthly fee for Andrew's
phone bill?
A. $49
B. $120
C. $60
D. $72
Answers
Answer:
C, $60
Step-by-step explanation:
It is where the graph starts even with 0 minutes.
Topografía. La superficie de una montaña se modela mediante la ecuación ℎ(, ) = 5000 − 0.001 2 − 0.004 2 . Un montañista se encuentra en el punto (500, 300, 4390). ¿En qué dirección debe moverse para ascender con la mayor rapidez?
Answers
Respuesta:
(-1, - 2,4)
Explicación paso a paso:
Dada la función:
ℎ (x, y) = 5000 - 0,001x2 - 0,004y2
Tomando la derivada parcial con respecto a ambas direcciones (xey) se obtiene la dirección del vector de gradiente, donde es posible el movimiento más rápido
H '(x, y) = (dh / dx, dh / dy)
dh / dx = 2 (-0.001x) = - 0.002x
dh / dy = 2 (-0.004y) = - 0.008y
H '(500, 300) = (- 0,002 (500); - 0,008 (300))
H '(500, 300) = (- 1; - 2,4)
Por lo tanto, el montañista ascenderá con la mayor velocidad en el punto (-1, - 2.4)
If the square root of the length of the hypotenuse of a right triangle is 2 units, what is the sum of the squares of the length of the two other sides?
Whoever answers first will get all my 38 points!!
Answers
sqrt (hyp) = 2
hyp = 4
hyp^2 = 16 then from above a^2 + b^2 = 16
Rebecca wants to prove that if the diagonals in parallelogram are perpendicular, then it is a rhombus. Select the appropriate rephrased statement for Rebecca's proof
Answers
Answer:
The answer is C
Step-by-step explanation:
Khan Academy
Answer:
C
Step-by-step explanation:
Pleas help! this is very hard!
Answers
Answer:
190
72
36
Step-by-step explanation:
Answer:
190
72
36
hope that helps