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
AnnZ [28]
3 years ago
13

Three consecutive integers exist where the smallest is fifteen less than twice the larger. Find the integers

Mathematics
1 answer:
fenix001 [56]3 years ago
5 0
Consecutive integers are integers that appear one after the other. so let's call them x, x+1, and x+2.

the smallest (which is x) is 15 less than twice the larger. "the larger" is a bit unclear, but i'm assuming it is referring to the x+1 integer, because it doesn't say the "largest". so x = 2(x+1) - 15. let's try to solve for x.

x = 2(x+1) - 15
x = 2x + 2 - 15
x = 2x - 13
subtract 2x from both sides.
-x = -13
x = 13
x+1 = 14
x+2 = 15

your integers are 13, 14, and 15.
You might be interested in
1. Based on the information given, can you determine that the quadrilateral must be a
zhenek [66]

<u>Solving Q1: Given BE = ED and AE = EC.</u>

Considering triangles ΔAED and ΔCEB;

1. AE = EC (given)

2. ∠AED = ∠CEB (vertical angles)

3. ED = EB (given)

ΔAED ≡ ΔCEB (Side-Angle-Side congruency of triangles)

∠DAE = ∠BCE and AD = BC (using CPCTC)

⇒ AD║BC (Converse of Alternate Interior angles theorem)


Similarly consider triangles ΔABE and ΔCDE;

1. AE = CE (given)

2. ∠BEA = ∠DEC (vertical angles)

3. BE = DE (given)

ΔABE ≡ ΔCDE (Side-Angle-Side congruency of triangles)

∠ABE = ∠CDE and AB = CD (using CPCTC)

⇒ AB║CD (Converse of Alternate Interior angles theorem)


Since we have AB║CD, AB = CD and AD║BC, AD = BC.

Therefore, quadrilateral ABCD is a parallelogram.

****************************************************************************************************

<u>Solving Q2: The parallelogram has the angle measures shown in the diagram.</u>

It is clearly visible that both the triangles are Isosceles triangles, so opposite sides in each triangle are equal.

Consider two triangles given in the problem, we have two sets of congruent angles and one included side is common in both triangles.

Using Angle-Side-Angle congruence of triangles, both the triangles would be congruent too.

Using CPCTC, we can say opposite sides of quadrilateral would be congruent.

Therefore, all sides in given quadrilateral are equal.

Hence, Given quadrilateral is a Rhombus.

7 0
3 years ago
PLEASE! 10 POINTS! For what number A does the equation 3Ax - 24 = 5x - 9 + x have no solutions for x?
Gala2k [10]

Answer:

3Ax-6x = 15

3x(A-2)=15

If A were 2, the left side of the equation would be 0 and it wouldn't equal 15 no matter what the value of x is. So A is 2

6 0
2 years ago
Evaluate log416 -2 1/2 2
krok68 [10]

16 = 4²

So, by the definition of logarithms

\log_4{16}=2

5 0
3 years ago
What are three different ways to write 5 to the 11 power
Olin [163]
(5)(5)(5)(5)(5)(5)(5)(5)(5)(5)(5)
5^11
That is two of the three but I'm not quite sure if there is a third.
3 0
3 years ago
Read 2 more answers
Khianna is trying to help her neighbor Mrs. Johnson design and estimate the cost of a new square patio to be made from 16 inch s
Gnoma [55]

Part I: Scale Drawing

<span>Decide on a scale factor to represent the distance covered by the patio. Then, use the space below to design Mrs. Johnson’s patio to be a square that is at least 8 feet on each side.</span>

 a) Scale Factor: 1 in/ 2 ft 

Use a straightedge and a ruler to draw to scale a design for Mrs. Johnson’s patio

b) see the picture attached

Mrs. Johnson’s patio to be a square that is 10 ft x 10 ft

<span><span>c) What are the dimensions of Mrs. Johnson’s patio? </span>
</span>the dimensions of Mrs. Johnson’s patio are 10 ft x 10 ft

<span><span>d) Calculate the area of Mrs. Johnson’s patio.  Show all work.  
</span> </span>
area of the square=b²
where b is the length side of the square
b=10 ft
so
Area=10²-----> area =100 ft²

<span><span>e) How many pavers will be needed?  Show all work. </span>
</span>
we know that
1 paver is 16 in x 16 in dimensions
convert to ft
1 ft----------->12 in
x ft-----------> 16 in
x=16/12-----> x=4/3 ft
so
1 paver is (4/3) ft x (4/3) ft dimensions

area of one paver=(4/3)²----> 16/9 ft²

if one paver has an area of----------------> 16/9 ft²
x pavers----------------------->  100 ft²
x=100/(16/9)------> x=100*9/16-----> x=56.25 pavers

if one box --------------> 12 pavers
x box---------> 56.25 pavers
x=56.25/12-----> x=4.68 box-------> x=5 boxes
5 boxes of pavers will be needed 

<span><span>f) What will it cost to build the patio?  Show all work. 
 </span> </span>
the cost of one box is--------> $99.99
5 boxes-----------> x
x=5*$99.99------>x=$499.95

the cost to build the patio is $499.95

Part II: Bigger Design

<span>There is a saying that bigger is better, so why not double the dimensions of Mrs. Johnson’s patio to make the side measurement twice as big? Mrs. Johnson and I think that it would better meet her needs.  After seeing the original estimation, she thinks that she could afford to double the size. I explained that making the patio twice as big would mean twice the cost. Mrs. Johnson says, “Let’s do it!”</span>

 

<span>a) What would be the new dimensions of Mrs. Johnson’s patio?
</span>the new  dimensions of Mrs. Johnson’s patio are 20 ft x 20 ft

<span>b) Calculate the new area of Mrs. Johnson’s patio.  Show all work.
</span>area of the square=b²
where b is the length side of the square
b=20 ft
so 
Area=20²-----> area =400 ft²<span>  
</span>
<span><span>c) How many pavers will be needed for the new design?  Show all work.
</span> </span>
1 paver is (4/3) ft x (4/3) ft dimensions

area of one paver=(4/3)²----> 16/9 ft²

if one paver has an area of----------------> 16/9 ft²
x pavers----------------------->  400 ft²
x=400/(16/9)------> x=400*9/16-----> x=225 pavers

if one box --------------> 12 pavers
x box---------> 225 pavers
x=225/12-----> x=18.75 box-------> x=19 boxes
19 boxes of pavers will be needed 

<span>d) What will it cost to build the bigger patio?  Show all work. 
</span>the cost of one box is--------> $99.99
19 boxes-----------> x
x=19*$99.99------>x=$1899.81
the cost to build the bigger patio is $1899.81

<span><span>e) Is Khianna right?  Will doubling the size of the patio, double the cost?</span>
</span>
<span>Khianna is wrong to double the dimensions the cost quadruples</span>

5 0
3 years ago
Other questions:
  • What is the distance between the two endpoints in the graph below? if necessary,round your answer to two decimal places
    7·2 answers
  • A radio station plays 24 minutes of music out of every 30 minutes. Write two ratios that are equivalent to the ratio 24/30
    12·1 answer
  • 2, 3, 5, 9, 17...
    6·2 answers
  • What belongs in the box marked with the question mark in the proof?
    6·1 answer
  • ASAP!!!
    14·1 answer
  • A gardener has 27 pansies and 36 daises. He plants and an equal number of each type of flower in each row. What is the greatest
    15·1 answer
  • Prove using the notion of without loss of generality that 5x 5y is an odd integer when x and y are integers of opposite parity.
    11·1 answer
  • What is the remainder when 73,847 is divided by 43? Enter your answer as a whole number in the box
    6·1 answer
  • HELP FAST!!! <br> Solve using substitution.<br> y = 8<br> 5x – 3y = -9
    11·1 answer
  • Exterior angle theorem <br> what is the value of u? I’m willing to give brainlist!!
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!