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3 years ago

Write the sentence as a conditional statement. All acute angles have measures less than 90°.

Mathematics

2 answers:

Fiesta28 [93]3 years ago

8 0

Given statement is "All acute angles have measures less than 90°."

Now we have to rewrite that sentence as a conditional statement.

Given statement is mixture of two simple statements "All acute angles" and "measures less than 90°".

So let

P = Angle is acute.

Q = Angle measures less than 90°.

conditional statement using p and q is given by " If P then Q"

so the final answer in conditional format "If P then Q" can be written as:

"If an angle is acute then that angle measures less than 90°.

Andrews [41]3 years ago

8 0

Answer:

To write a conditional statement for the following:

"All acute angles have measures less than 90°.

Conditional Statement is a statement that can be written in the form:

"If p, then q".

Hypothesis in the conditional statement is "If"

Conclusion in the conditional statement is "then"

Therefore, conditional statement for the given statement:

If an angle is acute, then it has measures less than 90°.

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Don't forget S is measured in thousands of units so you are solving for :

100 < 74.5 + 43.75Sin(πt/6)
25.5 < 43.75Sin(πt/6)
Sin(πt/6) >25.5/43.75 = 0.582857
ASrcSin(πt/6) > 0.62224 radians
πt/6 > 0.62224
t > 6 x 0.62224/π = 1.1884 (4dp)

This initial value occurs when the sine value is increasing and it will reach its maximum value of 1 when Sin(πt/6) = Sinπ/2, that is when t = 3.
Consequently, monthly sales exceed 100,000 during the period between t = 1.1884 and 4.8116
[3 - 1.1884 = 1.8116 so the other extreme occurs at 3 + 1.8116]

Note : on the basis of these calculations, January is 0 ≤ t < 1 : February is 1 ≤ t < 2 :....May is 4 ≤ t < 5
So the period when sales exceed 100,000 occurs between Feb 6 and May 25 and annually thereafter.

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Al factorizar el trinomio cuadrado perfecto, obtenemos el siguiente resultado: (que no se como resolver) xd algun pro que sepa r

PolarNik [594]

Answer:

$\displaystyle \frac{100}{81}m^8p^{12}q^{16}z^2-\frac{20}{63}m^5p^7q^8z^5+ \frac{1}{49}m^2p^2z^8=\left(\frac{10}{9}m^4p^{6}q^{8}z-\frac{1}{7}mpz^4\right)^2$

Step-by-step explanation:

Trinomio Cuadrado Perfecto

El producto notable llamado cuadrado de un binomio se expresa como:

$(a-b)^2=a^2-2ab+b^2$

Si se tiene un trinomio, es posible convertirlo en un cuadrado perfecto si cumple con las condiciones impuestas en la fórmula:

* El primer término es un cuadrado perfecto

* El último término es un cuadrado perfecto

* El segundo término es el doble del proudcto de los dos términos del binomio.

Tenemos la expresión:

$\displaystyle \frac{100}{81}m^8p^{12}q^{16}z^2-\frac{20}{63}m^5p^7q^8z^5+ \frac{1}{49}m^2p^2z^8$

Calculamos el valor de a como la raiz cuadrada del primer término del trinomio:

$\displaystyle a=\sqrt{\frac{100}{81}m^8p^{12}q^{16}z^2}$

$\displaystyle a=\frac{10}{9}m^4p^{6}q^{8}z$

Calculamos el valor de a como la raiz cuadrada del primer término del trinomio:

$\displaystyle b=\sqrt{\frac{1}{49}m^2p^2z^8$

$\displaystyle b=\frac{1}{7}mpz^4$

Nos cercioramos de que el término central es 2ab:

$\displaystyle 2ab=2\frac{10}{9}m^4p^{6}q^{8}z\frac{1}{7}mpz^4$

Operando:

$\displaystyle 2ab=\frac{20}{63}m^5p^7q^8z^5$

Una vez verificado, ahora podemos decir que:

$\displaystyle \frac{100}{81}m^8p^{12}q^{16}z^2-\frac{20}{63}m^5p^7q^8z^5+ \frac{1}{49}m^2p^2z^8=\left(\frac{10}{9}m^4p^{6}q^{8}z-\frac{1}{7}mpz^4\right)^2$

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