distance between 1,3 and -3, -1

Answers

Answer 1

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 1 &,& 3~) % (c,d) &&(~ -3 &,& -1~) \end{array}~~~ % distance value d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(-3-1)^2+(-1-3)^2}\implies d=\sqrt{(-4)^2+(-4)^2} \\\\\\ d=\sqrt{32}\implies d=\sqrt{16\cdot 2}\implies d=\sqrt{4^2\cdot 2}\implies d=4\sqrt{2}[/tex]

Related Questions

what is the change of entropy for a heat engine using 500.0j at 20.0c

Answers

1.71 J/K
hope it helps :D!!

The formula to find change in entropy is given by :

[tex] Change in entropy = \frac{Q}{T} [/tex]

where Q is change in heat and T is temperature.

We are given Q = 500 joule and T = 20 degree C

Plugging these values in the formula,

[tex] Change in entropy = \frac{500}{20} [/tex]

We get change in entropy = 25 J/Celsius.

Amir's checking account charges a $9.75 monthly service fee and a $0.12 per-check fee. If Amir writes 15 checks per month, should he switch to a checking account that charges an $11.50 monthly service fee and no per-check fee

Answers

[tex]0.12(15) = 1.80 [/tex]
[tex]1.80 + 9.75 = 11.55[/tex]
Yes Amir should switch because it's a nickel less

Simplify (3x − 5) − (5x + 1).

−2x + 6

−2x − 6

2x − 6

2x + 6
can you please work this out for me?
thank you verymuch.

Answers

we have been asked to simplify

[tex] (3x-5)-(5x + 1) [/tex]

To Simplify this, we will first open the parenthesis, as below

[tex] (3x-5)-(5x + 1)=3x-5-5x-1\\
\\
\text{take the like terms together and simplify we get}\\
\\
(3x-5)-(5x + 1)=3x-5x-5-1\\
\\
(3x-5)-(5x + 1)=-2x-6\\
\\

[/tex]

Hence the simplified expression is -2x-6

Answer:

-2x-6

Step-by-step explanation:

Is the system of equations is consistent, consistent and coincident, or inconsistent?

y=−3x+12y=−6x+2

Select the correct answer from the drop-down menu.

Answers

The slope of (y=-3x+12) is -3 while the slope of (y=-6x+2) is -6. Therefore, it's Inconsistent.
Coincident is one line on the graph
Consistent is two parallel lines

Answer:

The given system of equations is inconsistent.

Step-by-step explanation:

We have been given a system of equations and we are asked to find whether our given system of equation is consistent, consistent and coincident, or inconsistent.

[tex]y=-3x+12...(1)[/tex]

[tex]y=-6x+2...(2)[/tex]

Since we know that a system of equations is inconsistent if it has no solution. Parallel lines are inconsistent because they do not intersect.

Consistent system of equations can have one or infinitely many solution. As if two lines are same then they will have infinitely many solution. If lines intersect at only one point, then they will have only one solution.

Now let us check slope of given lines.

Upon dividing equation (2) by 2 we will get,

[tex]y=-3x+1...(2)[/tex]

We can see that both lines have slope of negative 3. Since y-intercept of both equations are different, so they will not intersect at any point.

Since our given equations represent parallel lines, therefore, our given system of equations is inconsistent.

Solve for x in the equation x2+20x+100=36

Answers

The answer is:
[tex] x = - 64 \div 22 = -2.909091[/tex]
But if x2 was supposed to be x^2 then the answer is:
[tex]x = - 4.-16[/tex]

Answer:

x = -4 and x = -16.

Step-by-step explanation:

We have the equation,

[tex]x^{2}+20x+100=36[/tex]

i.e. [tex]x^{2}+20x+64=0[/tex]

As the solution of a quadratic equation [tex]ax^{2}+bx+c=0[/tex] is given by [tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex].

On comparing, a = 1, b = 20, c = 64.

So, the solution is,

[tex]x=\frac{-20\pm \sqrt{(20)^{2}-4\times 1\times 64}}{2a\times 1}[/tex].

i.e. [tex]x=\frac{-20\pm \sqrt{400-256}}{2}[/tex].

i.e. [tex]x=\frac{-20\pm \sqrt{144}}{2}[/tex].

i.e. [tex]x=\frac{-20\pm 12}{2}[/tex].

i.e. [tex]x=\frac{-20+12}{2}[/tex] and [tex]x=\frac{-20-12}{2}[/tex].

i.e. [tex]x=\frac{-8}{2}[/tex] and [tex]x=\frac{-32}{2}[/tex].

i.e. x = -4 and x = -16

Thus, the solution of the given equation is x = -4 and x = -16.

The area of a playground is 204 yards squared the width of a playground at 5 yards longer than its length whats the length and the width of the playground

Answers

w= width= L+5
L= length
Area= 204

Area= LW
204 square yards= LW
substitute w=L+5 for w
204= (L)(L+5)
204= L^2 + 5L
subtract 204 from both sides
0= L^2 + 5L - 204
factor
0= (L+17)(L-12)

0= L+17
-17= L

0= L-12
12 yards= L

WIDTH
Since the area cannot be a negative number, we'll use L=12 to find the width.

w=L+5
w=12+5
w=17 yards

CHECK:
204=(12)(17)
204=204

ANSWER: The length is 12 yards and the width is 17 yards.

Hope this helps! :)

Please help out with this question! Thanks :)

Answers

On the horizontal line P=6, it looks like the values W=10, 11, 12 may be in the doubly-shaded region. We know that each of those will give a purchase of at least 16 fruits, but we don't know if the budget constraint is met with 12 watermelons. You'd have to check prices to make sure.

If 11 is among the choices, that is the answer I'd choose.

What is 59.69 in expanded form

Answers

Expanded Notation Form:
50 +9 + 0.6+ 0.09
Expanded Factors Form:
5 × 10 +9 × 1 +6 × 0.1+9 × 0.01
Expanded Exponential Form:
5 × 101+9 × 100+6 × 10-1+9 × 10-2
Word Form:

fifty-nine and sixty-nine hundredths

PLEASE HELP I NEED THE ANSWER TO THIS ASAP. YOU JUST NEED TO MATCH EACH THING ON THE LEFT TO ITS CORRECT ANSWER ON THE RIGHT.
Match the following items.

Complete the proof for Theorem 3-13. (if you dont know what this theorem is i added a picture that explains it so you can help)

Answers

The only thing is with this one... I don't have an image showing where angles 1 2 3 4 are.

But I'll give it a try:

1) l // m ___ Given

2) <1 = <3 ___ if parallel lines, then corresponding angles (<s) are equal

3) <2 = <3 ___ Vertical <s are equal

4) <1 = <2 ___ Substitution

The complete proof of the theorem in chronological order is;

GivenIf lines are ∥, corresponding angles are equal.Vertical angles are equalSubstitution

How to complete a proof?

The proof that when a transversal cut two parallel lines, alternate angles are equal.

Statement: l ∥ m

Reason: Given

Statement: m ∠ 1 = m ∠ 3

Reason: If lines are ∥, corresponding angles are equal.

Statement: m ∠ 2 = m ∠ 3

Reason: Vertical angles are equal

Statement: m ∠ 1 = m ∠ 2

Reason: Substitution

Therefore, alternate exterior angles are equal when a transversal cut two parallel lines,

Answers

The number that goes into 15 and 25 is 5. So after you factor this it would be 5(3a+5b).

Final answer:

The factored form of the expression 15a + 25b with respect to the Greatest Common Factor (GCF) is 5 (3a + 5b). The GCF of 15 and 25 is 5.

Explanation:

To factor the Greatest Common Factor (GCF) from 15a + 25b, we first have to identify the GCF. The GCF of 15 and 25 is 5. Hence, we divide each term in the expression by this GCF.

We get: 5 (3a + 5b). So, the expression 15a + 25b factored by the GCF is 5 (3a + 5b).

Learn more about Factoring here:

https://brainly.com/question/33624529

#SPJ11

Easy Geometry! Easy Geometry! Easy Geometry!

Answers

Answers:

b. Linear Pair
c. Definition of supplementary
d. Substitution; Combine like terms
e. Division Property of Equality
f. Definition of Right Angle
g. Definition of Perpendicular
=========================================

Further Explanations:

b. A linear pair is simply a result of cutting a straight angle into two pieces. They are adjacent and supplementary (add to 180 degrees)

c. If two angles are supplementary then they add to 180. This is simply a definition to memorize.

d. The "m < 2" is replaced with "m < 1" through the substitution property. This is possible because of statement (a) on the first line of the proof. The teacher has also combined like terms. Technically this step would require its own line.

e. Think of this as 2x = 180 solving to x = 90. The step done here is dividing both sides by 2, which uses the division property of equality. Alternatively you can use the multiplication property of equality to multiply both sides by 1/2 = 0.5

f. If an angle is 90 degrees, then by definition it is considered a right angle. This is another thing you memorize.

g. Also to be memorized is the fact that if two segments form a right angle, then they are considered perpendicular segments. The upside down T symbol means "perpendicular to"

Answer:

b) Linear Pair

c) Definition of supplementary

d) Substitution; Combine like terms

e) Division Property of Equality

f) Definition of Right Angle

g) Definition of Perpendicular

which figures can be precisely defined by using only undefined terms? check all that apply
1) angle
2) arc
3) circle
4) line segment
5) parallel lines

Answers

i think it is answer choices 1, 3, 4, and 5

The rectangle is the image after a dilation with the center of dilation at the origin of rectangle ABCD. The pre-image of A' point A, has coordinates of (–4, 3.2). What is the scale factor of the dilation and what are the coordinates of point C?

Answers

Answer:

The scale factor is 2.5 and the coordinates of point C are (–2.4, –0.8).

Step-by-step explanation:

which statement about sqrt x-5 minus sqrt x=5 true?

-3 is a true solution

-3 is a extraneous solution

9 is a true solution

9 is a extraneous solution

Answers

Answer:

9 is an extraneous solution.

Step-by-step explanation:

Extraneous solution is a solution that when plugged into the equation do not hold true.

Here we are given an algebraic equation in terms of single variable x as:

[tex]\sqrt{x-5}-\sqrt{x}=5-----(1)[/tex]

Now, we will solve this equation to obtain the solution as:

on squaring both side of the equation we obtain:

[tex](\sqrt{x-5}-\sqrt{x})^2=5^2[/tex]

[tex]x-5+x-2\sqrt{x-5}\sqrt{x}=25\\\\2x-5-2\sqrt{x-5}\sqrt{x}=25\\\\2x-30=2\sqrt{x-5}\sqrt{x}\\\\on\ dividing\ both\ side\ by\ 2\ we\ obtain:\\\\x-15=\sqrt{x-5}\sqrt{x}[/tex]

Again on squaring both side of the equation we obtain:

[tex]x^2+225-30x=(x-5)x\\\\\x^2+225-30x=x^2-5x\\\\225=-5x+30x\\\\225=25x\\\\x=9[/tex]

Now when we plug x=9 back to the original equation i.e. equation (1) we get:

[tex]\sqrt{9-5}-\sqrt{9}=5\\\\\sqrt{4}-\sqrt{9}=5\\\\2-3=5\\\\-1=5[/tex]

Hence, the equation does not hold true.

Hence, 9 is a extraneous solution

A 4040 inch wire is to be cut. one piece is to be bent into the shape of a square, whereas the other piece is to be bent into the shape of a rectangle whose length is twice the width. find the width of the rectangle that will minimize the total area. what is the width of the rectangle that will minimize the total area?

Answers

Let the square have sides s and the rectangle have sides r and 2r.
perimeters: 40 = 4s + 2(r + 2r) = 4s + 6r → s = (1/4)(40 - 6r) = 10 - 1.5r areas: A = s² + 2r² = (10 - 1.5r)² + 2r² = 100 - 30r + 4.25r²
Then dA/dr = 0 = 9.5r - 30 r = 30/9.5 = 3.16 in ← width of rectangle (length is twice the width) d²A/dr² = 9.5 > 0, so it is a minimum.

helppppppppppppppppppppppppppppp

Answers

For this case, you must rewrite the expression correctly.
We have then:
2 (16x ^ 3y) ^ (1/3) + 4 (54x ^ 6y ^ 5) ^ (1/3)
We then have to use properties of exponents:
4 ((2 ^ (1/3) xy ^ (1/3)) + 12 ((2 ^ (1/3)) x ^ 2y ^ (5/3))
4 ((2 ^ (1/3) xy ^ (1/3)) + 12 ((2 ^ (1/3)) x ^ 2 * y * y ^ (2/3))
We rewrite:
4x ((2y) ^ (1/3)) + 12 * x ^ 2 * y ((2y ^ 2) ^ (1/3))
Answer:
4x ((2y) ^ (1/3)) + 12 * x ^ 2 * y ((2y ^ 2) ^ (1/3))
option 1

Find the midpoint of the line segment whose endpoints are (7,5) and (7,11)

Answers

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points }\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 7 &,& 5~) % (c,d) &&(~ 7 &,& 11~) \end{array}\qquad % coordinates of midpoint \left(\cfrac{ x_2 + x_1}{2}\quad ,\quad \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{7+7}{2}~~,~~\cfrac{11+5}{2} \right)\implies \left( \cfrac{14}{2}~~,~~\cfrac{16}{2} \right)\implies (7~,~8)[/tex]

The circumference (C) of a swimming pool is 47 feet. Which formula can you use to find the radius (r) if you know that C = 2πr ?

Answers

1. divide each side by 2π
2. you get r = c/2π

Answer:

r=C/2*pie

Step-by-step explanation:

I got it correct on TTM

Organize the following expressions from greatest to least by number of terms: x + 2xyz 9x2yz 18x2 + 5ab − 6y 4x3 + 3x2 − x − 4

Answers

i believe the answer would be 2xyz9x2yz18x2 - 6y4x3 + 5ab - 4. the x canceled itself out.

Answer:

The answer is the option C

IV, III,I,II

Step-by-step explanation:

Your team gets an ice sculpture in the shape of a basketball. It has a radius of 12 inches. What is the volume of the ice? Use 3.14 for pi. Round your answer to the nearest hundredth.

Answers

The answer is 7234.56 inches cubed. The equation to find the volume of a sphere is 4/3*pi*r^3.

The equation would be 4/3 * 3.14 * 12^3.

4/3 * 3.14 * 1728

4/3 * 5425.92

7234.56

Is it possible to toss a coin 20 times and have it land heads-up 20 times? Is this likely to happen? explain.

Answers

No, because the coin has 2 sides so it mostly likely wont let on heads them 20 times. Hope i helped u :)

Yes, it is possible, but very unlikely. There is two sides to a dice, so the probability of heads is 1/2 each time. (1/2)^20 would make the probability very low. So: Yes it is possible but no is is not likely.

Raul used the steps shown below to solve the equation. In which step did Raul make a mistake?
5x-3(2x+7)=2x+9
Step 1: 5x-6x-21=2x+9
Step 2: -11x-21=2x+9
Step 3: -12x=30
Step 4: x=-30/12

A. Step 1
B. Step 2
C. Step 3
D. Step 4

Answers

I believe a mistake was made on step 2.

5x-3(2x+7)=2x+9

This is the equation and Raul had to solve it for x

So he started with simplifying the parenthesis first

To simplify the parenthesis -3 gets multiplied with 2x and 7 , to get rid of parenthesis

So it came out to be

5x-3(2x+7)=2x+9

STEP-1

5x-6x -21 = 2x+9 , So the STEP-1 is correct,

After this in Step -2 , he has combined the like terms on left side, the like terms are 5x and -6x , 5x-6x should combine to -x , because 5-6 = -1

STEP-2

-x -21 = 2x+9 , So STEP -2 is INCORRECT

So he made a mistake in STEP-2

After that subtract 2x from both sides

-3x -21 = 9

add 21 to both sides

-3x = 30

divide both sides by -3

x=-10

Hence Option B is correct , he made a mistake in STEP -2

How many times would a coin have to show heads in 50 tosses to have an experimental probability of 20% more than the theoretical probability of getting heads? 10 25 35 45

Answers

35. The theoretical probability of getting head is 50% for a fair coin. Since the experimental(the actual) probability is 20% more, the experimental probability is 50+20=70%. 70% percent of the coin tosses are heads. 50*70%=35.

Hellllllllłllllllllllllllllllllllllllllllllllpp

Answers

150ft. Hope u get it right

129 ft is the correct answer

The hypotenuse of a right triangle is 50 and the short leg is 30, find the projection of the leg onto the hypotenuse

Answers

Consider the attached figure. All the triangles shown are similar, so

CB/CA = CD/CB
30/50 = projection/30
projection = 30^2/50
projection = 18

HELP PLEASE HELP HELP

Answers

[tex]( \sqrt{x} )^5=(x^{ \frac{1}{2} })^5=x^{ \frac{1}{2}*5 }=x ^{\frac{5}{2} }[/tex]

The answer is D

Parts of Complex Numbers
z=4.1i+85
Re(z)=_____
Im(z)=_____

Answers

Variable z = a+bi is normally used to represent a complex number.
where a is the real number of z (Re z) while b is the imaginary part of z (im z)
Therefore in this case; z=4.1 i +85, therefore
Re(z) =85
Im(z) = 4.1

The equation y=4.75x+20 gives the cost y of towing a car if the car is towed x miles.
According to to the model, what is the best estimate of the cost for towing a car 22 miles.

A. $24.75
B $46.25
C $104.50
D $124.50

Answers

The answer to the question is D

Answer: $124.50

Step-by-step explanation:

We are given that the equation y=4.75x+20 gives the cost y of towing a car if the car is towed x miles.

To find the best estimate of the cost for towing a car 22 miles., we substitute x= 22 in the above equation, we get

Cost of towing a car 22 miles=[tex]y=4.75(22)+20=[/tex]

[tex]\rightarrow\ y=104.50+20=124.50[/tex]

Therefore, the best estimate of the cost for towing a car 22 miles = $124.50

With $3500 each, Martin and Edward opened separate accounts. Each account offered 4.5% interest over 10 years. At the end of 10 years, Edward earned more than Martin. Why? A. Edward invested for a different amount of time than Martin. B. Edward had a different interest rate than Martin. C. Edward earned compound interest, and Martin earned simple interest. D. Edward e

Soomeone helpppp meeee

Answers

Given that Edward and Martin invested the same amount of $3500, with interest rate of 4.5% and time period of 10 years: The difference in the amount of money will be brought about by different schemes in which they both invested the money.
The interest earned from above cash under simple interest will be:
S.I=(PRT)/100
S.I=3500*4.5/100*10=$1575
the total amount after 10 years will therefore be:
1575+3500
=$5075

The same amount if it was compounded annually, the amount after 10 years will be:
FV=P(1+r/100)^n
FV=3500(1+3.5/100)^10
FV=4,937.10
we therefore conclude that the answer is:
Edward must have earned simple interest while Martin earned compound interest.

Triangle FGH is similar to JKM.

If f = 14.4 cm, g = 16.56 cm, h = 25.92 cm, and k = 9.2 cm, what is the measure of m?
A. 5.104 cm
B. 14.4 cm
C. 10.58 cm
D. 8 cm

Answers

k is similar to g
so we can find the scale that FHG was dilated by.
[tex]16.56 \div 9.2 = 1.8[/tex]
so the sides of the triangle KMJ were multiplied by 1.8.
to find m :
[tex]25.92 \div 1.8 = 14.4[/tex]
m=14.4
hope this helps

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