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Nadusha1986 [10]
3 years ago
5

Look at the image shown below

Mathematics
1 answer:
muminat3 years ago
3 0

Answer:   3:2

Step-by-step explanation:

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If 12 pencils cost $4.00, how much does 20 pencils cost?
natita [175]

Answer:

$6.66

Step-by-step explanation:

20 times 4 = 80 and 80 divided by 12 is 6.66666667

4 0
3 years ago
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-20 2 -6 -18 4 -4 put them from least to greatest
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-20 -18 -6 -4 2 4 this is the answer
6 0
3 years ago
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How many sets of three consecutive integers are there in which the sum of the three integers equals their product?
skad [1K]

Answer:

3

Step-by-step explanation:

since the 3 integers are consecutive, we are dealing with x, x+1, x+2.

and their sum is the same as their product :

x + (x + 1) + (x + 2) = x(x + 1)(x + 2)

3x + 3 = x(x² + 3x + 2) = x³ + 3x² + 2x

x³ + 3x² - x - 3 = 0

this is a polynomial of third degree.

and as such it has 3 solutions.

of course, it could be that some of them are the same or are even in the realm of complex numbers (i = sqrt(-1)), but usually these 3 solutions are different real numbers.

I tried x=1 just to see, and, hey, it is a solution for this equation.

x = 1 means that the other 2 consecutive integers are 2 and 3.

and indeed, 1+2+3 = 1×2×3 = 6.

now it is easier to find the other 2 solutions, as a zero solution can be expressed as a factor of the whole expression.

for x = 1 the factor term is (x - 1), as this term is then turning 0, when x = 1.

I can divide the main expression by this factor and then analyze the quotient about the other 2 solutions.

x³ + 3x² - x - 3 : x - 1 = x² + 4x + 3

- x³ - x²

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

0 4x² - x

- 4x² - 4x

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

0 + 3x - 3

- 3x - 3

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

0 0

so, the original expression can be written as

(x² + 4x + 3)(x - 1).

now we need to find the 2 zero solutions for x²+4x+3

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 4

c = 3

so,

x = (-4 ± sqrt(4² - 4×1×3))/(2×1) =

= (-4 ± sqrt(16 - 12))/2 = (-4 ± sqrt(4))/2 =

= (-4 ± 2)/2 = -2 ± 1

x1 = -2 + 1 = -1

x2 = -2 - 1 = -3

so, we have the additional solutions :

-1 0 1

-3 -2 -1

-1 + 0 + 1 = -1×0×1 = 0

-3 + -2 + -1 = -3×-2×-1 = -6

and there we have it fully proven :

there are 3 different sets of 3 consecutive integers with the same sum as product.

4 0
2 years ago
Find the length of the line PA.
Diano4ka-milaya [45]

RO divides the rectangle into two congruent right triangles.

The area of the one triangle is equal half area of the rectangle.

Calculate the area of rectangle:

A_R=lw\\l=12,\ w=5\\\\A_R=12\cdot5=60

The area of right triangle:

A_T=\dfrac{1}{2}A_R\to A_T=\dfrac{1}{2}\cdot60=30

Use the Pythagorean theorem to calculate the length of RO:

|RO|^2=5^2+12^2\\\\|RO|^2=25+144\\\\|RO|^2=169\to|RO|=\sqrt{169}\to|RO|=13

The formula of an area of this right triangle is:

A_T=\dfrac{1}{2}|RO||PA|

Therefore we have the equation:

\dfrac{1}{2}(13)|PA|=30\qquad|\cdot2\\\\13|PA|=60\quad|:13\\\\|PA|=\dfrac{60}{13}\\\\|PA|\approx4.62

8 0
3 years ago
How are √25 and √-25 different in the terms of a solution for both? *
Tanya [424]

Answer:

For \sqrt{25} it will be plus or minus \sqrt{5}

For \sqrt{-25} it will be plus or minus \sqrt{5i}

Step-by-step explanation:

Well for \sqrt{-25} it will be 5i

Because i = -1  

6 0
3 years ago
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