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Evgen [1.6K]
2 years ago
12

If 10 less than 5 times a number is two more than 3 times the number, then the number is

Mathematics
2 answers:
Dennis_Churaev [7]2 years ago
8 0

Answer:

4

Step-by-step explanation:

10-5x=3x+2

-10          -10

-5x=3x-8

-3x  -3x

-2x=-8

/-2    /-2

x=4

marshall27 [118]2 years ago
5 0

Answer:

x=6

Step-by-step explanation:

5x-10=3x+2

5x-3x=2+10

2x=12

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A, B and C are the vertices of a triangle.
DiKsa [7]

Answer:

see below

Step-by-step explanation:

To find the coordinates of the midpoints, add the x's and divide by 2 and add the y's and divide by 2.

The coordinates of D, the midpoint of AB, (1+3)/2 will be the x-coordinate and (4+0)/2 will be the y-coordinate.

D (2,2)

You could also see this on a graph, see image.

E, the midpoint of AC has the x-coordinate (1+-3)/2, which is -1 and y-coordinate (4+-2)/2 which is 1.

E is (-1,1)

Then we are able to calculate the slope of DE and BC.

To calculate slope, subtract the y's and put that on top of a fraction and subtract x's and put that on the bottom of a fraction. If the slopes are the same the segment are parallel.

Slope of DE:

(2-1)/(2--1)

= 1/3

Slope of BC:

(0--2)/(3--3)

=2/6

=1/3

The slopes of BC and DE are equal, so the segments are parallel.

(Alternatively, you could show that Triangle ABC and Triangle ADE are similar. Then find the segments parallel because corresponding angles are congruent.)

6 0
1 year ago
Two fractions between 2 and 2 1/2
Rudik [331]
2 1/4

2 1/3

These two fractions are both less than 2 1/2 but greater than 2
7 0
3 years ago
Read 2 more answers
3.
zheka24 [161]

Answer:

20

Step-by-step explanation:

Sn = (n/2)(a1 + a1 + d(n-1)), where S = sum, a1 = first term, n = number of terms, d = common difference

 

400 = (n/2)(1 + 1 + 2(n - 1))

400 = (n/2)(2  + 2n - 2)

400 = (n/2)(2n

400 = n2

20 = n

 

Twenty numbers are in the set.

6 0
3 years ago
Read 2 more answers
PLEASE ANSWER QUICKLY
zzz [600]
School:4230ft
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5 0
3 years ago
Read 2 more answers
Find the area of the region enclosed by f(x) and the x axis for the given function over the specified u reevaluate f(x)=x^2+3x+4
lord [1]

Answer:

A = 68 unit^2

Step-by-step explanation:

Given:-

The piece-wise function f(x) is defined over an interval as follows:

                       f(x) =  { x^2+3x+4    , x < 3

                       f(x) =  { x^2+3x+4     , x≥3

                        Domain : [ -3 , 4 ]

Find:-

Find the area of the region enclosed by f(x) and the x axis

Solution:-

- The best way to tackle problems relating to piece-wise functions is to solve for each part individually and then combine the results.

- The first portion of function is valid over the interval [ -3 , 3 ]:      

                       f(x) = x^2+3x+4

- The area "A1" bounded by f(x) is given as:

                      A1 = \int\limits^a_b {f(x)} \, dx

Where,  The interval of the function { -3 , 3 ] = [ a , b ]:

                     A1 = \int\limits^a_b {x^2+3x+4} \, dx\\\\A1 = \frac{x^3}{3} + \frac{3x^2}{2} + 4x |\limits_-_3^3 \\\\A1 = \frac{3^3}{3} + \frac{3*3^2}{2} + 4*3 - \frac{-3^3}{3} - \frac{3(-3)^2}{2} - 4(-3)\\\\A1 = 9 + 13.5 +12 + 9-13.5+12\\\\A1 =42 unit^2

- Similarly for the other portion of piece-wise function covering the interval [3 , 4] :

                     f(x) = 4x+10

- The area "A2" bounded by f(x) is given as:

                      A2 = \int\limits^a_b {f(x)} \, dx

Where,  The interval of the function { 3 , 4 ] = [ a , b ]:

                     A2 = \int\limits^a_b {4x+10} \, dx\\\\A2 = 2x^2 + 10x |\limits_3^4 \\\\A2 = 2*(4)^2 + 10*4 - 2*(3)^2 - 10*3\\\\A2 = 32 + 40 - 18-30\\\\A2 =26 unit^2

- The total area "A" bounded by the piece-wise function over the entire domain [ -3 , 4 ] is given:

                     A = A1 + A2

                     A = 42 + 26

                     A = 68 unit^2

8 0
2 years ago
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