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Answer:
She used 5.775 pints of white paint to paint her bedroom walls.
Step-by-step explanation:
This question can be solved using a system of equations.
I am going to say that:
x is the amount of white paint used.
y is the amount of blue paint used.
7.7 pints of blue paint and white paint to paint her bedroom walls.
This means that
1/4 of this amount is blue paint, and the rest is white paint.
The rest is 1-(1/4) = 3/4. That is, the amount of white paint is the triple of the amount of blue paint. That is, , or
Replacing in the first equation:
She used 5.775 pints of white paint to paint her bedroom walls.
Answer:
The 3 numbers are 9, 12, and 15.
Step-by-step explanation:
I will answer in English, below the answer you can see a translation in Catalan.
This can be translated to:
The sum of the squares of three consecutive and multiple natural numbers of 3 is equal to 450. Pose a quadratic equation and calculate the three numbers.
First, a multiple of 3 can be written as:
3*n
The consecutive multiple of 3 is:
3*n + 3
The consecutive multiple of 3 is:
3*n + 3 + 3
Then the sum of their squares is:
(3*n)^2 + (3*n + 3)^2 + (3*n + 6)^2
And we know that this is equal to 450, then we need to solve the equation:
(3*n)^2 + (3*n + 3)^2 + (3*n + 6)^2 = 450
let's solve this:
9*n^2 + (9*n^2 + 2*(3*n)*3 + 9) + (9*n^2 + 2*(3*n)*6 + 36) = 450
27*n^2 + 54*n + 45 = 450
we can write this as:
27*n^2 + 54*n + 45 - 450 = 0
27*n^2 + 54*n - 405 = 0
The solutions of this equation are given by the Bhaskara's formula, and the solutions are:
we know that our numbers are naturals, then the numbers are positives, which means that we only care for the positive solution of n, which is:
n = (-54 + 216)/54 = 3
Then the 3 numbers are:
3*n = 3*3 = 9
(3*n + 3) = (3*3 + 3) = 12
(3*n + 6) = (3*3 + 6) = 15
In Catalan:
En primer lloc, es pot escriure un múltiple de 3 com:
3 * n
El múltiple consecutiu de 3 és:
3 * n + 3
El múltiple consecutiu de 3 és:
3 * n + 3 + 3
Llavors, la suma dels seus quadrats és:
(3 * n) ^ 2 + (3 * n + 3) ^ 2 + (3 * n + 6) ^ 2
I sabem que això és igual a 450, llavors hem de resoldre l’equació:
(3 * n) ^ 2 + (3 * n + 3) ^ 2 + (3 * n + 6) ^ 2 = 450
resolem això:
9 * n ^ 2 + (9 * n ^ 2 + 2 * (3 * n) * 3 + 9) + (9 * n ^ 2 + 2 * (3 * n) * 6 + 36) = 450
27 * n ^ 2 + 54 * n + 45 = 450
podem escriure això com:
27 * n ^ 2 + 54 * n + 45 - 450 = 0
27 * n ^ 2 + 54 * n - 405 = 0
Les solucions d’aquesta equació vénen donades per la fórmula de Bhaskara, i les solucions són:
sabem que els nostres nombres són naturals, aleshores els nombres són positius, cosa que significa que només ens importa la solució positiva de n, que és:
n = (-54 + 216) / 54 = 3
Llavors els 3 nombres són:
3 * n = 3 * 3 = 9
(3 * n + 3) = (3 * 3 + 3) = 12
(3 * n + 6) = (3 * 3 + 6) = 15
Answer:
The width of the art projects of area 63.6 square inches is 7.97 inches .
Step-by-step explanation:
Given as :
The area of the square art project = 63.6 square inches
Since The shape of the art project is square
So, The Area of square = A = side × side = side²
Now, let the measure of the width of art project = w inches
I.e side = w inches
or , A = side²
Or , A = w²
Or, 63.6 = w²
So, w =
I.e w = 7.97 inches
So, the width of the projects = w = 7.97 inches
Hence The width of the art projects of area 63.6 square inches is 7.97 inches . Answer