1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kenny6666 [7]
3 years ago
13

Which points are 19 units apart? (–14, 12) and (5, 12) (–5, 19) and (–12, 19) (–20, 5) and (1, 5) (14, 12) and (5, 12)

Mathematics
2 answers:
kaheart [24]3 years ago
5 0

Answer:

Choice a is correct answer.

Step-by-step explanation:

We have given four set of points.

(a)  (-14,12) and (5,12)

(b)  (-5,19) and (-12,19)

(c)  (-20,5) and (1,5)

(d)  (14,12)  and (5,12)

We have to find the distance between each set of points.

The formula for distance is:

d = √(x₂-x₁)²+(y₂-y₁)²

The set of points which have 19 units distance is our answer.

For (a):

d =√(5-(-14)²+(12-12)²

d = √(5+14)²+(0)²

d = 19 units

for (b) :

d = √(-12-(-5))²+(19-19)²

d = √(-12+5)²+(0)²

d = √(-7)²

d = 7 units

for (c):

d = √(1-(-20)²+(5-5)²

d = √(1+20)²+(0)²

d = 21 units

for (d):

d =√(5-14)²+(12-12)²

d = √(-9)²+(0)²

d = 9 units

Hence , correct choice is (a).

blsea [12.9K]3 years ago
3 0

Answer:

P_{1}(-14, 12) , P_{2}(5,12) are 19 units apart

Step-by-step explanation:

Answer:

We are given four pair of points and we have to find which points are 19 units apart:

P_{1}(x_{1},y_{1}) , P_{2}(x_{2},y_{2})

P_{1}(-14, 12) , P_{2}(5,12)\\\\P_{1}(-5, 19) , P_{2}(-12, 19)\\\\P_{1}(-20, 5) , P_{2}(1, 5)\\\\P_{1}(14, 12) , P_{2}(5,12)

Using distance formula to find how far the points are from each other

d = \sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}

For first pair:

P_{1}(x_{1},y_{1}) , P_{2}(x_{2},y_{2}) = P_{1}(-14, 12) , P_{2}(5,12)\\\\d = \sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}\\\\d = \sqrt{(-14 - 5)^{2} + (12-12)^{2}} = 19

For second pair:

P_{1}(x_{1},y_{1}) , P_{2}(x_{2},y_{2}) = P_{1}(-5, 19) , P_{2}(-12,19)\\\\d = \sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}\\\\d = \sqrt{(-5 - 12)^{2} + (19 - 19)^{2}} = 17

For third pair:

P_{1}(x_{1},y_{1}) , P_{2}(x_{2},y_{2}) = P_{1}(-20, 15) , P_{2}(1, 5)\\\\d = \sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}\\\\d = \sqrt{(-20 - 1)^{2} + (15 - 5)^{2}} = 23.26

For 4th pair:

P_{1}(x_{1},y_{1}) , P_{2}(x_{2},y_{2}) = P_{1}(14, 12) , P_{2}(5,12)\\\\d = \sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}\\\\d = \sqrt{(14 - 5)^{2} + (12 - 12)^{2}} = 9

You might be interested in
What is the value of the digit 5 in this number?<br> 60.35<br> A.0.5<br> B.0.05<br> C.5.0<br> D.5.00
Sergeeva-Olga [200]
B because its in the hundredths place
6 0
3 years ago
Create a list of steps, in order, that will solve the following equation 1/4(x+5)^2-1=3
julia-pushkina [17]

Answer:

either x = -1, or x = - 9

Step-by-step explanation:

given   \frac{1}{4} (x+5)^{2} -1=3

add one to both sides   \frac{1}{4} (x+5)^{2} =4

im not sure which one comes first. either you multiply both the x and the 5 in the parenthesis by \frac{1}{4}. or you square x and 5

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :   1/4*(x+5)^2-(4)=0  

Step by step solution :

Step  1  :

           1 /4

Equation at the end of step  1  :

  1                  

 (— • (x + 5)2) -  4  = 0  

  4                  

Step  2  :

Equation at the end of step  2  :

 (x + 5)2    

 ———————— -  4  = 0  

    4        

Step  3  :

Rewriting the whole as an Equivalent Fraction :

3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  4  as the denominator :

        4         4 • 4

   4 =  —  =  ———

        1            4  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(x+5)2 - (4 • 4)     x2 + 10x + 9

———————     ———————  =  ——

       4                        4      

Trying to factor by splitting the middle term

3.3     Factoring  x2 + 10x + 9  

The first term is,  x2  its coefficient is  1 .

The middle term is,  +10x  its coefficient is  10 .

The last term, "the constant", is  +9  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 9 = 9  

Step-2 : Find two factors of  9  whose sum equals the coefficient of the middle term, which is   10 .

     -9    +    -1    =    -10  

     -3    +    -3    =    -6  

     -1    +    -9    =    -10  

     1    +    9    =    10    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  1  and  9  

                    x2 + 1x + 9x + 9

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x+1)

             Add up the last 2 terms, pulling out common factors :

                   9 • (x+1)

Step-5 : Add up the four terms of step 4 :

                   (x+9)  •  (x+1)

            Which is the desired factorization

Equation at the end of step  3  :

 (x + 9) • (x + 1)

 —————————————————  = 0  

         4        

Step  4  :

When a fraction equals zero :

4.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 (x+9)•(x+1)

 ——————————— • 4 = 0 • 4

      4      

Now, on the left hand side, the  4  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  (x+9)  •  (x+1)  = 0

Theory - Roots of a product :

4.2    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

4.3      Solve  :    x+9 = 0  

Subtract  9  from both sides of the equation :  

                     x = -9

Solving a Single Variable Equation :

4.4      Solve  :    x+1 = 0  

Subtract  1  from both sides of the equation :  

                     x = -1

Supplement : Solving Quadratic Equation Directly

Solving    x2+10x+9  = 0   directly  

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

6 0
3 years ago
Talya so go to swim 30 miles over the summer she plans to swim 3/ 4 miles per detail she reaches her goal how many days will it
natka813 [3]

The answer would be 40 days

We achieve this answer by dividing the distance of the trip, 30 miles, by the distance traveled per day, 3/4 miles.

6 0
3 years ago
QUESTION 3<br>3.1 Round the following number up to the nearest whole number<br>R13492.39​
ivolga24 [154]

Answer:

the answer is R13492

Step-by-step explanation:

hope it helps

3 0
2 years ago
Prove that the diagonals of a parallelogram bisect each other.<br> The midpoint of AC is
iren2701 [21]

Answer:

Theorem: The diagonals of a parallelogram bisect each other. Proof: Given ABCD, let the diagonals AC and BD intersect at E, we must prove that AE ∼ = CE and BE ∼ = DE. The converse is also true: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • Can some pls help me with these two questions plss
    8·1 answer
  • Angle EFG and gfh are a linear pair the measure of EFG equals 4n + 25 and the measure of gfh equals 3n + 15 what are the measure
    11·1 answer
  • Complete the equation of this circle:
    15·2 answers
  • An inchworm (exactly one inch long, of course) is crawling up a yardstick (guess how long that is?). After the rst day, the inch
    7·1 answer
  • I need help with numbers 32 , 34 , 36 , WILL MARK BRILLIANT!!
    11·2 answers
  • What is the value of x?<br> a. x = 18<br> b. x = 48<br> c. x = 82 <br> d. x = 98
    11·1 answer
  • When graphing do you use an open or closed circle for &gt;
    9·1 answer
  • What is the result of converting 60 ounces to punds remember there are 16 ounces in a pound pleasdnsjjsjs
    9·1 answer
  • 50 pts if you answer plz plz
    5·1 answer
  • The circumference of a circle is 11 inches. What is the area, in square inches, of the circle? Express your answer in terms of p
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!