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
Snowcat [4.5K]
3 years ago
15

The sum of three numbers is 26. Twice the first minus the second is the third less 2. The third is the second minus 3 times the

first.
Mathematics
1 answer:
Agata [3.3K]3 years ago
6 0

Let a, b, c represent the three numbers. The problem statement gives rise to three equations:

  • a +b +c = 26
  • 2a -b = c -2
  • -3a +b = c

Adding the first two equations gives

... (a +b +c) +(2a -b) = (26) +(c -2)

... 3a +c = 24 +c . . . . . simplify

... 3a = 24 . . . . . . . . . . subtract c

... a = 8 . . . . . . . . . . . . divide by 3

Adding the second and third equations gives ...

... (2a -b) +(-3a +b) = (c -2) +(c)

... -a = 2c -2 . . . . simplify

... -6 = 2c . . . . . . add 2, substitute for a

... -3 = c . . . . . . . . divide by 2

Using the third equation we can find b.

... -3·8 +b = -3 . . . . substitute for a and c

... b = 21 . . . . . . . . .add 24

The numbers are 8, 21, -3.

_____

The method above is sort of "ad hoc", taking advantage of the numbers in this particular set of equations. You can use more formal methods of Gaussian elimination or Cramer's Rule to solve these by just following a procedure. Or, your graphing calculator can do it for you.

You might be interested in
A solid oblique pyramid has a regular hexagon base with an area of 54_/3 cm^2 and an edge length of 6cm. Angle BAC measures 60 d
Lady_Fox [76]

Answer: The answer is (C) 324 cubic cm.


Step-by-step explanation: As given in the question, given a solid oblique pyramid with a regular hexagonal base and area 54√3 cm². Also, the edge length of the base is 6cm and ∠BAC = 60°.

We are to find the volume of the pyramid.

The formula for finding the volume of a pyramid is given by

V=\dfrac{1}{3}b\times h,

where, 'b' is the base area and 'h' is the perpendicular height of the pyramid.

Here, b = 54√3 cm², h = ?

Now, from the right-angled triangle ABC, we have

\dfrac{\textup{BC}}{\textup{AC}}=\tan 60^\circ\\\\\Rightarrow \dfrac{h}{6}=\sqrt 3\\\\\Rightarrow h=6\sqrt 3.

Therefore, the volume of the pyramid is

V=\dfrac{1}{3}b\times h=\dfrac{1}{3}\times 54\sqrt 3\times 6\sqrt 3=324.

Thus, the required volume is V=324~\textup{cm}^3. This makes (C) as the correct option.



5 0
4 years ago
Kelly goes to the store and buys 9 boxes of cookies. The cost of each box is represented with the letter c. Which expression cou
MatroZZZ [7]

Answer:

9c because you don't know how much money Kelly actually spent so instead of doing 9 x the price of each box, you replace it with c, so it's 9c

Step-by-step explanation:

6 0
3 years ago
What is the quotient of 8/9 and 1 1/3
Art [367]
Hello,

To divide by a fraction, multiply by its reciprocal.

Solution:

8/0 x 3/11 

The greatest common factor is 3; cancel 3 out.

The problem will simplify to 8/33.



Faith xoxo
5 0
3 years ago
Write an equation of the circle with center , −45 and radius 6 .
IceJOKER [234]
The general equation for a circle, x^2+y^2=1, falls out of the Pythagorean Theorem, which states that the square of the hypotenuse of a right triangle is always equal to the sum of the squares of its legs (you might have seen this fact written like a^2+b^2=c^2, where <em>a </em>and <em>b</em> are the legs of a right triangle and <em>c </em>is its hypotenuse. When we fix <em /><em>c</em> in place and let <em>a </em>and <em>b </em>vary (in a sense, at least; their values are still dependent on <em>c</em>), the shape swept out by all of those possible triangles is a circle - a shape defined by having all of its points equidistant from some center.

How do we modify this equation to shift the circle and change its radius, then? Well, if we want to change the radius, we simply have to change the hypotenuse of the triangle that's sweeping out the circle in the first place. The default for a circle is 1, but we're looking for a radius of 6, so our equation, in line with Pythagorus's, would look like x^2+y^2=6^2, or x^{2} +y^2=36.

Shifting the center of the circle is a bit of a longer story, but - at first counterintuitively - you can move a circle's center to the point (a,b) by altering the x and y portions of the equation to read:

(x-a)^2+(y-b)^2
7 0
3 years ago
42 is 53.6% of what number? Round to the nearest tenth if necessary
Orlov [11]
The answer is 78.4. Hope this helps!
5 0
4 years ago
Read 2 more answers
Other questions:
  • glenn races his motorcycle 30 times last season. he finished first 12 times, second 5 times and crashed in 9 races. what percent
    8·1 answer
  • Jaleesa bought two
    12·1 answer
  • The ratio of boys to girls in a class is 4 : 5
    5·2 answers
  • In a large on-the-job training program, half of the participants are female and half are male. In a random sample of six partici
    13·1 answer
  • Which graphs are functional?
    12·1 answer
  • HELP URGENT PLZ PLZ PLZ
    12·1 answer
  • What was a effect on the war of 1812 <br>PLEASE HURRY AND HELP ME ​
    13·1 answer
  • Please answer these questions in the image ( click image to see fully )
    15·1 answer
  • Help guys show your solution and answer the question​
    15·1 answer
  • EASY POINTS PLEASE HELP ASAP
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!