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2 years ago

Factor this trinomial. x² + 11x + 18

Mathematics

2 answers:

jeka57 [31]2 years ago

6 0

Answer:

(x + 9)(x + 2)

Step-by-step explanation:

x² + 11x + 18

consider the factors of the constant term (+ 18) which sum to give the coefficient of the x- term (+ 11)

the factors are + 9 and + 2 , since

9 × 2 = 18 and 9 + 2 = 11 , then

x² + 11x + 18 = (x + 9)(x + 2)

liubo4ka [24]2 years ago

3 0

Greeting to you! My name is Cecille and I’m here to answer that question

For more explanation, please see the attachment

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Daredevil Danny takes a practice jump as shown on the graph below. Complete the steps to determine the equation for the paraboli

Tju [1.3M]

Answer:

Step 2:

Part A

f(x) = a(x-h)^2 +k

Part B

I'm not really sure about this part

Part C

f(x)=-12/25(x-25)^2+32

Step 3:

Part A

y = ax^2 + bx + c

Part B

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Step-by-step explanation:

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4 years ago

the capacity of water tank is 250 liter and 3/4 of the tank is empty how much water is there in the tank

Dmitry_Shevchenko [17]

Answer:

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4 years ago

The figure below shows two triangles EFG and KLM.

grandymaker [24]

A right triangle is a triangle that has a right angle of 90 degrees. In this exercise, we have two of this type of triangles. To solve this problem, we will apply some properties of triangles, so:

1. Which step can be used to prove that triangle EFG is also a right triangle?

To prove this, we need to use Pythagorean Theorem. So, for triangle EGF, if the formula:

$c^{2}=a^{2}+b^{2}$

is true, then EFG is also a right triangle. The steps are:

Square a

Square b

Square c

If the sum of the square of a and the sum of the square of b equals the square of c, then this is a right triangle.

2. Prove that the sum of a and c is greater than b.

We need to prove that:

$a+c>b$

From trigonometry, we know that:

$a=c \times sin(\theta) \\ \\ b=c \times cos(\theta) \\ \\ where \ \theta=\angle EFG \\ \\$

By substituting these values in the previous inequality:

$c \times sin(\theta)+c>c \times cos(\theta) \\ \\ Since \ c>0 \\ \\ sin(\theta)+1>cos(\theta) \\ \\ 1>cos(\theta)-sin(\theta)$

Since $\theta$ is an angle greater than 0 and less than 90 degrees, $cos(\theta) \ and \ sin(\theta)$ are numbers between 0 (greater than) and 1. Therefore, this inequality is always true. So, the statement has been proved.

3. Prove that the sum of a and b is greater than c.

We need to prove that:

$a+b>c$

Applying the same reasoning as in 2:

$c \times sin(\theta)+c \times cos(\theta)>c \\ \\ Since \ c>0 \\ \\ sin(\theta)+cos(\theta)>1$

This inequality is always true. So, the statement has been proved.

4. Prove that triangles are congruent by SSS property and hence angle EGF is equal to angle KML.

SSS means that we know the three sides of the triangle and want to find the missing angles. For ΔEGF, we know the three sides, and for KML, since this is a right triangle KL = c, therefore the corresponding sides of these two triangles are equal. Accordingly, these two triangles are congruent by SSS and angle EGF is equal to angle KML.

5. Prove that the ratio of EF and KL is greater than 1 and hence the triangles are similar by AA postulate.

The ratio of EF and KL is:

$\frac{EF}{KL}$

The statement is true if and only if EF > KL. Then, according to AA postulate, two triangles are similar if they have two corresponding angles congruent. So: