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Tatiana [17]
3 years ago
14

The product of two consecutive positive integers is 19 more than their sum. Find the integers.

Mathematics
1 answer:
strojnjashka [21]3 years ago
6 0
The crucial part of the wording of the problem tells us that the two integers are consecutive. So, let's call the first term x. Then the other term must be x + 1 since it comes right after it and is an integer. Now we can solve:

x(x + 1) = x  + (x + 1) + 19

x^2 + x = 2x + 20

x^2 - x - 20 = 0

Now we factor:

(x - 5)(x + 4) = 0

This means x either equals 5 or x = -4 to satisfy the above equation. We know that x is positive from the question itself, so x must be 5. The number consecutively after it then must be 6.
You might be interested in
What are the factors of the expression below? -2x+5x-3
Ipatiy [6.2K]

Answer:

-2x-15

Step-by-step explanation:

4 0
3 years ago
WHOEVER ANSWERS CORRECTLY I WILL MARK BRAINLIEST!!
gizmo_the_mogwai [7]

Answer:

Area = 342cm^2, Perimeter = 22.79 cm

Step-by-step explanation:

First, divide the shape into 3:

An arc, a square, and a triangle.

Dimensions of shapes:

Arc:

Degree = 40°

Arms = 4 cm

Square:

All sides are 4 cm

Triangle:

base = 3 cm

height = 4 cm

hypotenuse = 5 cm

To get perimeter:

Arc length = \frac{40}{360} * (2*\pi * (4))   (4 is the arm length ) = 2.7925 cm

Arc arm = 4 cm

Square sides (only two are outside) = 2 * 4 = 8 cm

Triangle (only hypotenuse and base are outside) = 5 + 3 = 8 cm

So total perimeter is 2.7925 + 4 + 8 + 8 = 22.79cm

To get area:

Arc area (the pizza shape) = \frac{40}{2\pi } * \pi * (4)^{2}   (4 is the arm length) = 320 cm^{2}

Square area  = side * side = 4 * 4 = 16 cm^{2}

Triangle =  (1/2) * base* height = (1/2) * 3 * 4 = 6cm^{2}

So total area is 320 + 16 + 6 = 342cm^2

3 0
3 years ago
Read 2 more answers
Use synthetic division and remainder theorem p(x) = 3x^3 - 5x^2 - x + 2. p(-1/3)=
Alik [6]

Answer:

5/3

Step-by-step explanation:

-1/3 goes on the outside and since we have our polynomial in standard form with no in between terms missing, 3,-5,-1,2 go inside because they are the coefficients of our polynomial.

-1/3   |   3      -5          -1          2

       |

         -------------------------------------

First step bring the 3 down inside. (3+0=3)

-1/3   |   3      -5          -1          2

       |

         -------------------------------------

           3

Whatever goes below the bar, must be multiplied by outside number and put directly below next number inside.

-1/3   |   3      -5          -1          2

       |             -1

         -------------------------------------

           3

The numbers lined up vertically are added to get the numbers underneath the bar.

-1/3   |   3      -5          -1          2

       |             -1

         -------------------------------------

           3        -6

Again any number below the bar gets multiply to the number outside.

-1/3   |   3      -5          -1          2

       |             -1          2

         -------------------------------------

           3        -6

Again the numbers lined up vertically above the bar get added to get the number that goes underneath the bar there.

-1/3   |   3      -5          -1          2

       |             -1          2

         -------------------------------------

           3        -6          1

Multiply to outside number 1(-1/3)=-1/3.

This goes under the 2 inside.

-1/3   |   3      -5          -1          2

       |             -1          2          -1/3

         -------------------------------------

           3        -6          1

The last number we are fixing to be put is the remainder of (3x^3-5x^2-x+2)/(x+1/3) or you could say it is the value of p(-1/3) since:

P(x)/(x-c)=Q(x)+R/(x-c)

Multiply both sides by (x-c):

P(x)=Q(x)(x-c)+R

If you evaluate P at x=c, we get R:

P(c)=Q(c)(c-c)+R

P(c)=Q(c)*0+R

P(c)=R.

Let's finish:

-1/3   |   3      -5          -1          2

       |             -1          2          -1/3

         -------------------------------------

           3        -6          1         5/3

This means p(-1/3)=5/3.

We could have also got this by directly plugging in (-1/3) for x into 3x^3-5x^2-x+2.

7 0
3 years ago
Can u help fast please
kotegsom [21]
Color 4 boxes because 4/1 times 1/3 equals 4/3 witch is 4 boxes
5 0
3 years ago
Read 2 more answers
John is buying a cake for his sister's birthday. He wants to get the most cake he can. One cake (A) is 9.5 inches wide, 13 inche
mart [117]
I think the answer is B i'm not sure though
5 0
3 years ago
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