Find the distance between the points (-2, 4) and (4, -6).
2√2
2√(10)
2√(34)
Answers
Answer: The correct option is (C) 2√34.
Step-by-step explanation: We are given to find the distance between the points (-2, 4) and (4, -6).
We have the distance formula as follows :
DISTANCE FORMULA :
The distance between the points (a, b) and (c, d) is given as
[tex]D=\sqrt{(c-a)^2+(d-b)^2}.[/tex]
Therefore, the distance between the points (-2, 4) and (4, -6) is given by
[tex]D\\\\=\sqrt{(4-(-2))^2+(-6-4)^2}\\\\=\sqrt{6^2+10^2}\\\\=\sqrt{36+100}\\\\=\sqrt{136}\\\\=\sqrt{4\times34}\\\\=2\sqrt{34}.[/tex]
Thus, the required distance between the given points is 2√34 units.
Option (C) is CORRECT.
Related Questions
Anna has 5 muffins but 8 friends coming over. How much will each friend get
Answers
A couch and coffee table cost a total of $1017. The cost of the couch is two times the cost of the coffee table. Find the cost of each item.
cost of couch:
cost of coffee:
Answers
Answer:
Using the concept of linear equations, we made two equations. Solving those two equations, we find that the cost of couch is $678 and that of coffee is $339.
Step-by-step explanation:
Concept: Let the cost of couch be $x and that of coffee be $y. The total cost is $1017, so,
x + y = 1017
Also, the cost of couch is two times that of coffee. So,
x = 2y
Substitute the value of x in first equation
2y + y = 1017
3y = 1017
y = 339
And, x + y = 1017
x + 339 = 1017
x = 678
Using the two equations, we find that y = $339 and x = $678.
So, the cost of couch is $678 and that of coffee is $339.
For more explanation, refer the following link:
https://brainly.com/question/22052132
#SPJ10
I NEED HELP SOOOO MUCH IM SOOO LOST I WILL GIVE A BRAINLIEST TO THE PERSON WHO INCLUDES ALL WORK, CORRECT ANSWER,AND EVERYTHING MAKES SENSE.
(Variables on both sides of an equation)
Solve: 5(a-1)-15=3(a+2)+4
Answers
Open all parenthesis and distribute
5a - 5 - 15 = 3a + 6 + 4
Simplify
5a - 20 = 3a + 10
Add both sides by 20 and subtract both sides by 3a
2a = 30
a = 15
Putting those back into our equation, we have:
[tex]5a-5-15=3a+6+4[/tex]
Next, we combine all of the constants on either side:
[tex]5a-20=3a+10[/tex]
Finally, we want to get the variable a by itself on one side of the equation, so we perform the following steps to isolate it:
[tex]5a=3a+30[/tex] (Add 20 to both sides)
[tex]2a=30[/tex] (Subtract 3a from both sides)
[tex]a=30/2=15[/tex] (Divide both sides by 2 to isolate a)
So, we obtain our answer of [tex]a=15[/tex].
Choose all of the following relationships that represent functions. please help!!
Answers
You CANNOT have one x-value with multiple different y values in the same function. You can however have different x values with the same y value.
Also for reference: independent means x value and dependent means y- value.
The first answer is not a function because as you can see there is one x-value with multiple y values.
second answer IS a function because as I said before you can have different x values with the same y value
third answer is a function again because you can have different x values with same y value
number four isn't a function bc again the -2 x value has 2 different y Values.
The answers are B and C
C;
For a car rental, the rental agency charges $21.00$21.00 per day, plus $0.23$0.23 for each additional mile above 125125. find a function for the cost of a rental where x is the number of miles driven.
Answers
You plan to take $450 u.s. on a trip to south africa. how many rands is this if one u.s. dollar equals 3.70 rands?
Answers
$450 is the same as 450 * $1, so multiply both sides of the conversion equation above by 450.
450 * $1 = 450 * 3.70 rand
$450 = 1665 rand
Rita earns $17.00 per hour. If she gets a 6% raise, what will be her new hourly wage?
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multiply 17 by 6%
17 * 0.06 = 1.02 increase
17 +1.02 = 18.02 new hourly wage
6 shirts 4 different pairs of pants, how many different combinations could she wear?
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the pants can be called 1, 2, 3, 4.
if you combine these together you get
A1, A2, A3, A4, B1, B2, B3, B4, C1, C2, C3, C4, D1, D2, D3, D4, E1, E2, E3, E4, F1, F2, F3, F4 OR 24
You get 24 outfits.
Which linear function represents the line given by the point-slope equation y + 1 = –3(x – 5)?
Answers
Answer:
[tex]y=-3x+14[/tex], slope intercept form
[tex]3x+y =14[/tex], standard form
Step-by-step explanation:
[tex]y + 1 = -3(x - 5)[/tex]
We need to write the given equation in slope intercept form or standard form
slope intercept form is [tex]y=mx+b[/tex]
To get slope intercept form , we need to get y alone
[tex]y + 1 = -3(x - 5)[/tex] ( multiply -3 inside the parenthesis )
[tex]y+1=-3x+15[/tex] , subtract 1 on both sides
[tex]y=-3x+14[/tex]
Standard form is [tex]Ax + By = C[/tex]
To get standard form we keep x term and y term on the left hand side
[tex]y=-3x+14[/tex]
Add 3x on both sides
[tex]3x+y =14[/tex]
In a study, the sample is chosen by writing everyones name on a playing card, shuffling the deck, then choosing the top 20 cards what is the sampling method
Answers
Simple random sampling is much better than others because it saves time and it is the most reliable method of obtaining information where every single member of the population is chosen randomly. or by chance. Each has an equal chance to be selected.
SamplingIt is a process applied in statistical analysis in which a predetermined number of observations is taken from a large population.
Given
The sample is chosen by writing everyone's name on a playing card, shuffling the deck, then choosing the top 20 cards.
To find
The sampling method for this condition.
How to choose the sampling method?So, simple random sampling is much better than others because it saves time and it is the most reliable method of obtaining information where every single member of the population is chosen randomly. or by chance. Each has an equal chance to be selected.
More about the sampling link is given below.
https://brainly.com/question/350477
y=x^2+8x+6 16x-2y=-44
Answers
Use k as the constant of proportionality to write the equation expressing the relationship: y varies inversely as x.
If y = 25 and k = 50, what is x?
1/2
2
1,250
Answers
k = xy
Now insert the number we know into the equation. We know y = 25 and k = 50
k = xy
50 = x25
50 = 25x
50 / 25 = 25x/ 25
2 = x
x = 2 <-----answer
Answer: 2
Step-by-step explanation: i got it right :)
Help?
Simplify. 9√56x^7y^12 Assume x and y are nonnegative.
Answers
Applying the product property of square roots to the expression 9 * √(56) * √(x^7) * √(y^12), we simplify to 18y^6 * √(14x) * |x^3|.
Apply the product property of square roots:
9 * √(56) * √(x^7) * √(y^12)
Evaluate the square root:
9 * 2 * √(2 * 7) * √(x^7) * √(y^12)
Multiply the numbers:
9 * 2 * √(14) * √(x^7) * √(y^12)
Simplify the square root of an exponential expression:
9 * 2 * √(14) * |x^3| * √(x) * √(y^12)
Simplify the square root of an exponential expression:
9 * 2 * √(14) * √(x) * |x^3| * y^6
Apply the product property of square roots to the product of square roots is equal to the square root of the product:
9 * 2 * y^6 * |x^3| * √(14x)
Multiply the numbers:
18 * y^6 * √(14x) * |x^3|
Describe the transformation.
A) translation 6 units down
B) translation 2 units down
C) reflection across the x-axis
D) reflection across the y-axis
Answers
Answer: C is the answer
Step-by-step explanation:
Use laws of sine to answer
Answers
[tex] \frac{18}{ \sin(32) } = \frac{bc}{ \sin(118) } [/tex]
so:
[tex]bc = \frac{18 \times \sin(118) }{ \sin(32) } \\ bc = 29.991... \\ bc = 30.0 \: (to \: 3 \: sig.figs)[/tex]
Describe how to graph the solution of y ≤ −x² + 2x.
Answers
with the vertex at (1, 1),factor the quadratic as y < (less than or equal to) –1(x)(x – 2),find the roots of the parabola to be 0 and 2,graph the parabola with a solid boundary line,test a point that is not on the boundary,and shade inside the parabola.
14 minus the product of three and the number has 26
Answers
14 - 3 (x) = 26
Subtract 14 from both sides
-3x = 12
Divide both sides by -3
X= -4
Some of the cds produced by a manufacturer are defective. from the production line, 5 cds are selected and inspected. how many sample points exist in this experiment?
Answers
Final answer:
There are 32 sample points in this experiment.
Explanation:
In this experiment, the manufacturer selects 5 CDs from the production line to inspect. To determine the number of sample points in this experiment, we need to consider the possible outcomes for each CD. For each CD, it can either be defective or non-defective, meaning there are 2 possible outcomes. Since there are 5 CDs being inspected, we multiply the number of outcomes for each CD by itself 5 times to find the total number of sample points. Therefore, there are 32 sample points in this experiment.
Therefore, the total number of sample points in this experiment is 32, calculated by multiplying the number of outcomes for each CD (2) by itself 5 times . This accounts for all possible combinations of defective and non-defective CDs in the sample of 5.
the quotient of two numbers subtracted from 20
Answers
A number cube is rolled 25 times. A number less than four comes up 20 times. What is the experimental probability that a number less than four is rolled?
Answers
a number less than four came up 20 out of 25 rolls
so the probability was 20/25 which reduces to 4/5
A clydesdale drinks about 120 gallons of water every 4 days.At this rate,about how many gallons of water does a clydesdale drink in 28 days
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State the vertex as an ordered pair.
y = -|3x +5|+7
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well, we can check by simply setting it to 0 and solving for x.
[tex]\bf 3x+5=0\implies 3x=-5\implies \boxed{x=-\cfrac{5}{3}}\\\\ -------------------------------\\\\ \textit{therefore, the vertex of }y = -|3x+5|\boxed{+7}\textit{ is at }\left(-\frac{5}{3}~,~7 \right)[/tex]
notice, all you do is, get the x-value that makes the expression to 0, and then append the constant outside it as the y-value, and that's the vertex.
Please help me with this
Answers
for an isosceles right triangle the legs would be 2 times the square root of the hypotenuse
so for this:
the legs would be 2sqrt(10)
The areas of: FGHM is 12, MHIJ is 36, EFNL is 24, LNJK is 48. EGIK is a rectangle cut into the rectangles with given areas. What is the area of the shaded quadrilateral EMIN?
Answers
Overall area of quadrilateral EGIK is 12+36+24+48 = 120. I'll call the length of EK to be w, and EG to be h, representing width and height.
The line FJ splits EGIK into EFJK and FGIJ which have areas of 72 and 48 respectively. Since EFJK and FGIJ have the width, their heights have to be in the ratio of 72/48 = 3/2. So GF = 2h/5 and EF = 3h/5
Now FGHM and MHIJ share the same height, so their widths have to be in the ratio 12/36 = 1/3, so GH = w/4 and HI = 3w/4
And EFNL and EMIN also share the same height, so their widths have to be in the ratio 24/48 = 1/2, so EL = w/3 and LK = 2w/3.
So the length of MN will be FN - FM. And FN is the same as EL which is w/3, and FM is the same as GH which is w/4. So
w/3 - w/4 = 4w/12 - 3w/12 = w/12
If you look at quadrilateral EMIN, you'll see that it's area is the sum of triangles MNI and MNE. And the area of a triangle is 1/2 bh. And conveniently, we have MN as the base with a length of w/12 for both triangles.
area MNI = 1/2 MN * GF = 1/2 * w/12 * 2h/5 = 2hw/120
area MNE = 1/2 MN * EF = 1/2 * w/12 * 3h/5 = 3hw/120
And their sums are 2hw/120 + 3hw/120 = 5hw/120.
And hw is the total area of EGIK which is 120. So we get:
5 * 120/120 = 5 * 1 = 5
So the area of quadrilateral EMIN is 5.
Liz wants to buy a shirt for $25. How much will Liz's shirt cost in Springfield(4.1%) Round up to the nearest cent? Show your work
Answers
4.1/100 = 0.041 %
Next multiply the cost of the shirt before tax by the tax in decimal form:
25 * 0.041 = 1.025
After that you will add the tax cost and the shirt cost:
25 + 1.025 = 26.025
Finally round to the nearest cent:
26.03
Hope this helps and let me know if you have more questions!
the slope of the line below is 2/5 and the y-intercept is (0,4) what is the slope intercept equation of the line?
Answers
Hope this helps!
b) Imagine that you earned $8,425 in one year. If the government enforces a 15% income tax, how much money would you owe in taxes at the end of the year? Show your work.
Answers
Take 8425 multiply it by 0.15 to get your answer
Answer:
The tax would be $ 1,263.75
Step-by-step explanation:
Given,
Total earning in one year = $ 8,425,
Income tax percentage per year on earning = 15%
Hence, the amount of tax at the end of one year
= 15% of the total earnings
= 15% of 8425
[tex]=\frac{15\times 8425}{100}[/tex]
[tex]=\frac{126375}{100}[/tex]
= $ 1,263.75
Help me solve this plzz!!Simplify:
Answers
You can use the rule:
[tex](a^b)^c=a^{b*c} [/tex]
So, let's do it:
[tex](27x^6)^ \frac{1}{3} = 27 x^{6* \frac{1}{3} } [/tex]
Simplify:
[tex](27x)^2[/tex]
And there you have it. If you need it one step further, then square 27, but take the parenthesis out.
If you need further help, feel free to ask for it.
Yori has 14.25 cups of cupcake batter if each cupcake used 0.75 cup of batter how many cups cakes can yori make?
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0.75=1 cupcake
14.25=Y cupcakes
I represented the unknown with Y.
Next, cross and multiply. 14.25 will multiply 1 to give 14.25 and 0.75 will multiply Y to give 0.75Y. That will be;
0.75Y=14.25
Divide both sides by 0.75
Y=14.25/0.75
Y=19
She can make 19 cupcakes. Hope that helped. Have a nice day
The perimeter of a triangle is 29 feet where one side of the triangle is twice the length of the shortest side. the largest side is 13 feet more than the shortest side. how long is the shortest side
Answers
3x + x + 13 = 29
4x = 29 - 13
4x = 16
x = 16/4
x = 4
The length of the shortest side is 4 ft
Answer:
The shortest side is 4 feet.
Step-by-step explanation:
The perimeter is the border of a geometric figure and corresponds to the sum of the length of all its sides.
So the perimeter in the case of a triangle is the sum of its three sides:
L₁ + L₂ + L₃ =Perimeter
In this case, the perimeter is known and it is necessary to calculate the value of the shortest side. In that case it will be called L₁. So, you know:
L₁= shortest sideL₂=twice the length of the shortest side → L₂=2*L₁L₃=largest side (13 feet more than the shortest side) → L₃=L₁ + 13Perimeter= 29 feetReplacing:
L₁ + 2*L₁ + L₁ + 13= 29
Solving:
(1+2+1)*L₁ + 13= 29
4*L₁ + 13=29
4*L₁ = 29-13
4*L₁ =16
L₁= 16÷4
L₁=4
The shortest side is 4 feet.