Answers
Answer:
1. (3,-1) and (5,4)
[tex]Distance\ = 5.39[/tex]
2. (2,3) and (4,5)
[tex]Distance\ = 2.83[/tex]
3. (-5,7) and (8,5)
[tex]Distance = 13.15[/tex]
4. (-2,4) and (3,-1)
[tex]Distance = 7.07[/tex]
Step-by-step explanation:
Given
The attached
Required
Calculate the distance between each points;
Distance between points is calculated using;
[tex]d =\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
1. (3,-1) and (5,4)
Here; [tex]x_1 = 3; x_2 = 5; y_1 = -1; y_2 = 4[/tex]
Substitute these values in the formula above
[tex]d =\sqrt{(3 - 5)^2 + (-1 - 4)^2}[/tex]
[tex]d =\sqrt{- 2^2 + (-5^2)}[/tex]
[tex]d =\sqrt{4 + 25}[/tex]
[tex]d =\sqrt{29}[/tex]
[tex]d = 5.39[/tex] (Approximated)
2. (2,3) and (4,5)
Here; [tex]x_1 = 2; x_2 = 4; y_1 = 3; y_2 = 5[/tex]
Substitute these values in the formula above
[tex]d =\sqrt{(2 - 4)^2 + (3 - 5)^2}[/tex]
[tex]d =\sqrt{- 2^2 + (-2^2)}[/tex]
[tex]d =\sqrt{4 + 4}[/tex]
[tex]d =\sqrt{8}[/tex]
[tex]d = 2.83[/tex] (Approximated)
3. (-5,7) and (8,5)
Here; [tex]x_1 = -5; x_2 = 8; y_1 = 7; y_2 = 5[/tex]
Substitute these values in the formula above
[tex]d =\sqrt{(-5 - 8)^2 + (7 - 5)^2}[/tex]
[tex]d =\sqrt{- 13^2 + 2^2}[/tex]
[tex]d =\sqrt{169 + 4}[/tex]
[tex]d =\sqrt{173}[/tex]
[tex]d = 13.15[/tex] (Approximated)
4. (-2,4) and (3,-1)
Here; [tex]x_1 = -2; x_2 = 3; y_1 = 4; y_2 = -1[/tex]
Substitute these values in the formula above
[tex]d =\sqrt{(-2 - 3)^2 + (4 - (-1))^2}[/tex]
[tex]d =\sqrt{- 5^2 + (4+1)^2}[/tex]
[tex]d =\sqrt{- 5^2 + 5^2}[/tex]
[tex]d =\sqrt{25 + 25}[/tex]
[tex]d =\sqrt{50}[/tex]
[tex]d = 7.07[/tex] (Approximated)
Related Questions
Expression Name Expression E 3.8 + 0 F 0 + 0.5 G –8 + 0 H 9 ÷ 0 The table above shows four numeric expressions. Which expression is an integer when it's evaluated? Question 2 options: A) H B) E C) F D) G
Answers
Answer:
D) G
Step-by-step explanation:
E evaluates to 3.8 +0 = 3.8 . . . not an integer
F evaluates to 0 +0.5 = 0.5 . . . not an integer
G evaluates to -8 +0 = -8 . . . an integer
H evaluates to 9/0 = undefined . . . not an integer
__
Expression G evaluates to an integer.
Which represents the inverse of the function f(x) = 4x?
h(x) = x + 4
h(x) = x -4
h(x) = 3
h(x) =
77 X
Answers
This is the same as h(x) = x/4
In decimal form, it would be h(x) = 0.25x
=============================================
Explanation:
Inverses undo the original function. The original function tells us to take any input (x) and multiply by 4 to get the output y = f(x) = 4x
To get the inverse, we reverse the operation applied here. The opposite of multiplication is division. So we'll divide by 4 instead of multiply by 4. This is why the answer is x/4 or (1/4)x
-----------
Another approach is to do the following: Replace f(x) with y. Swap x and y. Solve for y
f(x) = 4x
y = 4x
x = 4y
4y = x
y = x/4
h(x) = x/4
We end up with the same result as before.
-----------
Extra info:
For any real number x, the following two equations are true
h( f(x) ) = x
f( h(x) ) = x
In lowa, the Hoosiers basketball team won half of its first twelve games. There are a total of
24 games in the season. In order to make it to the playoffs, the Hoosiers need to win three
fourths of their remaining games. If the team is able to win exactly three fourths of their
games, how many total games will they have won at the end of their 24-game season before
the playoffs begin?
Answers
Answer:
18
Step-by-step explanation:
3/4 of 24 is 18
30. Three apples plus twice as many pears add up to one-half the number of grapes in a fruit basket. How many grapes are
in the basket?
(A) 8
(B) 18
c.28
d.38
Answers
Answer:
3 + 6 = 1/2(#grapes)
3 + 6 = 9
9 = 1/2(#grapes)
2(9) = 1(#grapes)
18 = # of grapes
Step-by-step explanation:
I need the answer ASAP
Answers
Answer:
5
Step-by-step explanation:
When squaring the number 5 (i.e [tex]5^2[/tex] ) the answer is 25. [tex]5^{2}[/tex] is the same thing as 5 times 5. Basically with the square root, you are going backwards, so you are therefore finding the base of it all.
We have a square that has area of 25 square units. The question is: what is the side length? That would be 5 since 5*5 = 25. You would use guess and check if you weren't familiar with square roots. A better option is to use the square root function on the calculator.
Note: the square root undoes the squaring operation
The displacement vector r=2i-j+3k is aligned to the same direction as the force (F) whose magnitude is F =20N Determine the comple description of the force F
Answers
Answer:
Step-by-step explanation:
Displacement vector R = 2i + j + 3k
Unit vector along displacement vector
= R / I R I
= ( 2i + j + 3k ) / √ ( 2² + 1² + 3² )
= ( 2i + j + 3k ) / √ 14
Now force F acts in the direction of this unit vector . It is magnitude of 20 N
So this vector can be represented by the following expression
F = 20 [ ( 2i + j + 3k ) / √ 14 ]
[tex]F= \frac{20}{\sqrt{14} } \times ( 2i+j+3k)[/tex]
is this right?? please help!
Answers
Answer:
6 < x < 8
Step-by-step explanation:
The compound inequality in this instance represent the "and" condition, not the "or" condition.* We might solve it like this.
-47 > 1 -8x > -63 . . . . given
Multiply by -1:
47 < -1 +8x < 63
Add 1:
48 < 8x < 64
Divide by 8:
6 < x < 8
______
* You can tell this is the case by looking at the ends of the given statement:
-47 > -63 . . . . a true statement, so the solution set will be an intersection, not a union.
PRE algebra !!! PLEASE HELP! Ruth plays on the school basketball team. The table shows the team's results and Ruth's results for each game. What is the experimental probability that Ruth will score 9 or more points in the next game? Express your answer as a fraction in simplest form. 1/7 7/6 6/7 7/1
Answers
Answer:
6/7
Step-by-step explanation:
Ruth has played 7 games. She has scored 9 or more points in 6 of them. That means she has a 6/7 probability of doing so again.
Answer:
6/7
Step-by-step explanation:
solve for y: y÷1 7/9 = 3/4
Answers
Answer:
y = 4/3
Step-by-step explanation:
The required value of fraction y is 4/3.
Given that,
[tex]\frac{y}{1\frac{7}{9} } = 3/4[/tex]
Fraction y is to be determined by simplification.
The process in mathematics to operate and interpret the function to make function simple or more understandable is called simplifying and the process is called simplification.
What is the fraction?Fraction is defined as the number of compositions that constitute the Whole. Fraction is represented as x = a / b where the upper value is termed as the numerator and the lower value is the denominator.
⇒Simplification
[tex]\frac{y}{1\frac{7}{9} } = 3/4[/tex] ( 1 + 7 / 9 = 16 / 9)
[tex]\frac{y}{\frac{16}{9} } = 3/4[/tex] (Transposition of 16/9 from the denominator to the right)
y = 3 / 4 * 16 / 9
y = 4 / 3
Thus, the required value of fraction y is 4/3.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ2
? Question
Using the scenario and your equation from part A, find the number of shots each player attempted,
Type the correct answer in each box. Use numerals instead of words,
Jared attempted
shots,
Zach attempted
shots,
Answers
Answer:
Jared attempted 60 shots.
Zach attempted 70 shots.
Step-by-step explanation:
Please help..........
Answers
See the attached picture:
Write them in a standard form.
Answers
The equation turns into:
400+70+6+0.6+0.03+0.07
which equals:
476.637
The second equation becomes 4+ 68/1000, which becomes 4.068.
Hope this helps!
What is (7 / 14) * (b - 6) when b is 7?
Answers
Answer:
1/2
Step-by-step explanation:
Well if b is 7 we plug it into the following equation,
(7 / 14) * (b - 6)
So if b is 7, we do 7-6 which is 1.
Then 7 / 14 which is 1/2.
So 1/2 * 1 is 1/2.
Answer:
1/2 or 0.5 (same thing)
Step-by-step explanation:
If you simplify 7/14, you get 1/2, or 0.5.
Plug in 7 for b. 7-6 is 1, so 1/2 * 1 is 1/2.
alice drank 18 ounces of gatorade after her gymnastic meet. there were 14 ounces left.How many ounces of gatorade was origanally in the container.
Answers
Answer:
32 ounces
Step-by-step explanation:
18+14=32
32 is the total
Answer:
32 ounces
Step-by-step explanation:
She already drank 18 ounces and 14 ounces was left which means that If she didn't drink anything it would have been 32 ounces as 18 + 14 = 32
Hope this helps and pls mark as brainliest : )
4) Kevin and his team do not know what direction Mike went when he left the trail. This means that they will have
to search a circular area based on how fast Mike walks. He has been missing for 12 hours and his estimated
speed is 4 km per hour. Determine the surface area of the circle to be searched.
Answers
Answer:
Step-by-step explanation:
Distance traveled by Mike in 12 hours = 4 * 12 = 48 km
This will become the radius of the circle
r = 48 km
Area of the circle to be searched = πr²
= 3.14 * 48 * 48
= 7234.56 square km
order the following values from least to greatest: 22.4, -28, 27, -17
Answers
Answer:
asDawas
Step-by-step explanation:
sadasda
Answer: -28, -17, 22.4, 27
hope this helps
Suppose that a population begins at a size of 100 and grows continuously at a rate of 200% per year. Give the formula for calculating the size of that population after t years. Question 3 options: A) A = 100 + 2et B) A = 100e2t C) A = 100 + te2 D) A = 100 + e2t
Answers
The formula for calculating the size of the population after t years using continuous growth is [tex]A = 100e^{2t}[/tex], making option B the right choice.
Continuous growth in the initial amount P, after time period t, and at the rate of r per time period gives the final amount as: [tex]A = Pe^{rt}[/tex]
In the question, we are asked to suppose that a population begins at a size of 100, and grows continuously at a rate of 200% per year, and are asked for the formula for calculating the size of that population after t years.
The given case can be shown as a continuous growth, with:
Initial population, P = 100,
Rate of growth, r = 200% = 2, and,
The time period, t years.
Thus, the formula for calculating the size of that population after t years can be shown using the formula: [tex]A = Pe^{rt}[/tex], as:
[tex]A = 100e^{2t}[/tex].
Hence, the formula for calculating the size of the population after t years using continuous growth is [tex]A = 100e^{2t}[/tex], making option B the right choice.
Learn more about continuous growth at
https://brainly.com/question/20115298
#SPJ1
what is the line of symmetry for the parabola whose equation is y=-x^2-x+2
Answers
Answer:
[tex]\huge \boxed{\sf \ \ x=-\dfrac{1}{2} \ \ }[/tex]
Step-by-step explanation:
Hello,
We need to express this parabola using this kind of expression
[tex]y=a(x-b)^2+c[/tex]
and then, the line of symmetry will be the line x = b
Let's do it !
[tex]\text{*** Complete the square ***} \\ \\ x^2+x=x+2\cdot \dfrac{1}{2}\cdot x=(x+\dfrac{1}{2})^2-\dfrac{1^2}{2^2}=(x+\dfrac{1}{2})^2-\dfrac{1^2}{4} \\ \\ \text{*** Apply it to our parabola } \\ \\y=-x^2-x+2=-(x^2+x)+2=-[(x+\dfrac{1}{2})^2-\dfrac{1}{4}]+2 = -(x+\dfrac{1}{2})^2+\dfrac{1+2*4}{4}= -(x+\dfrac{1}{2})^2+\dfrac{9}{4} \\ \\ \text{*** It comes ***} \\ \\ \Large \boxed{\sf \ \ y=-(x+\dfrac{1}{2})^2+\dfrac{9}{4} \ \ }[/tex]
So the line of symmetry is
[tex]\huge \boxed{\sf \ \ x=-\dfrac{1}{2} \ \ }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Which of the following equations is of a parabola with a vertex at (0, 6)?
O y= (x - 6)2
O y= (x + 6)2
O y=x2-6
Oy= x2 + 6
Answers
Answer:
y= x^2 + 6
Step-by-step explanation:
y= x2 + 6 (which should be written as y= x^2 + 6) has the form y - k = a(x - h)^2. For y= x^2 + 6, h = 0 and k = 6. Thus the vertex is (0, 6)
To the nearest degree, find the measure of
Answers
Answer:
the hypotenuse(b) is 50 if that helps
Step-by-step explanation:
a=40 & c=30 if you square these two numbers, add them and find the square root you get the hypotenuse(a^2+b^2=the square root of c^2)
please help! sketch :y = 3x − 2 on a graph
Answers
Answer:
The graph of the equation y=3x-2 is shown in the picture below!!
Step-by-step explanation:
I hope this helps, if it does please mark brainliest!! Thank you!! Have a great day!
30 points high school geometry question.
Answers
Answer:
2.7
Step-by-step explanation:
2.5/5.8 = BD/6.2
BD = 2.7
Answer: 2.7
Step-by-step explanation: 2.5/5.8 = BD/6.2
BD = 2.7
......................................
Answers
Answer:
Towards the left
Step-by-step explanation:
Sphere A has a radius of 24 centimeters, and sphere B has a diameter of 42 centimeters. The radius of sphere A is
multiplied by what factor to produce the radius of sphere B?
c
+ N100 N
AN
Mark this and return
Save and Exit
Answers
Answer:
multiply by a factor of 7/8
Step-by-step explanation:
sphere A radius is 24 and Sphere B radius is 21
24x=21
x = 7/8
Answer:
multiply by a factor of 7/8
Which points are solutions to the system of inequalities shown below? Check all that apply!
Answers
Answer:
y>x+4 (A,B)
y≤3x (B,C,D,E,F)
x≥7(A,B,D)
i realllyyyyyyyy HOPE THIS HELPS YOUUU!!!
so A =3x2+4x+1,B=5x2−3x+8,C=4x2−7x−3, find the value of B + C –A.
Answers
Answer:
6x² - 14x - 4Step-by-step explanation:
A =3x² + 4x + 1
B = 5x² - 3x + 8
C = 4x² - 7x - 3
B + C –A is
5x² - 3x + 8 + 4x² - 7x - 3 - ( 3x² + 4x + 1)
Expand and simplify
We have
5x² - 3x + 8 + 4x² - 7x - 3 - 3x² - 4x -1
Group like terms
5x² + 4x² - 3x² - 3x - 7x - 4x + 8 - 3 - 1
We have the final answer as
6x² - 14x - 4Hope this helps you
Identify the sequence as arithmetic or geometric. 14, 11, 8, 5,
Answers
Answer:
sequence is arithmetic
Step-by-step explanation:
A geometric sequence has a common ratio r between consecutive terms.
An arithmetic sequence has a common difference d between consecutive terms, thus
11 ÷ 14 ≠ 8 ÷ 11 ≠ 5 ≠ 8 ← not geometric
11 - 14 = - 3
8 - 11 = - 3
5 - 8 = - 3
There is a common difference d between consecutive terms
Thus sequence is arithmetic.
Answer:
Step-by-step explanation:
This is an arithmetic sequence.
First term = a = 14
Second term = 11
Common difference = second term - first term
= 11 - 14
= - 4
Each term is got by adding (-4) to the previous term
Third term = 11 + (-4) = 11 -4 = 8
what is the nth term of this sequence 7, 9, 11, 13
Answers
Answer:
The nth term of the sequence is
5 + 2nStep-by-step explanation:
The sequence above is an arithmetic sequence
For an nth term in an arithmetic sequence
A(n) = a + ( n - 1)d
where a is the first term
n is the number of terms
d is the common difference
From the question
a = 7
d = 9 - 7 = 2 or 11 - 9 = 2
So the nth term for the sequence is
A(n) = 7 + ( n - 1)2
= 7 + 2n - 2
A(n) = 5 + 2nHope this helps you
What is the slope of the line that passes through the points (–20, 18) and (30, 14)?
Answers
Explanation:
Use the slope formula. We subtract the y values together, and do the same for the x values as well. Subtract in the same order each time. Then you divide the two results. Reduce the fraction if possible.
m = (y2 - y1)/(x2 - x1)
m = (14 - 18)/(30 - (-20))
m = (14 - 18)/(30 + 20)
m = -4/50
m = -2/25
Answer:
[tex]-\frac{2}{25}[/tex]
Step-by-step explanation:
Slope is rise over run.
[tex]m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}[/tex]
We are given the points (–20, 18) and (30, 14).
[tex]m=\frac{14-18}{30+20}=\frac{-4}{50}=-\frac{4}{50}=-\frac{4/2}{5/2}=\boxed{-\frac{2}{25}}[/tex]
The slope is -2/25.
Brainilest Appreciated.
Find the variation constant and an equation of variation where y varies directly as x and y=16 when x=2
Answers
Answer:
variation constant = k = 8
equation of variation : y = 8x
Step-by-step explanation:
Any relationship of variation can be written as y = kx
where k is the variation constant.
_______________________________________
Let the equationof relation between y and x be y =kx here as well
given
y = 16 when x = 2
substituting this value in the equation y = kx
16 = k*2
=> k = 16/2 = 8
Thus,
variation constant = k = 8
equation of variation : y = 8x