What property is x+(3x+20)=180

Mathematics

1 answer:

Aleksandr [31]3 years ago

6 0

The answer is the distributive property

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A square has a side of 6.25 feet. What is the area in square feet? Round to the correct significant digits.

denis23 [38]

Area of a square = side^2
area = 6.25^2 = 39.0625 square feet

= 39.06 (rounded)

4 0

2 years ago

The answer choices are 11 1 2.48 6

Fudgin [204]

Answer:

The ball reached its maximum height of ( $11\ yards$ ) in ( $1\ second$ ).

Step-by-step explanation:

This question is essentially asking one to find the vertex of the parabola formed by the given equation. One could plot the equation, but it would be far more efficient to complete the square. Completing the square of an equation is a process by which a person converts the equation of a parabola from standard form to vertex form.

The first step in completing the square is to group the quadratic and linear term:

$h(t)=-5t^2 + 10t + 6\\\\h(t) = (-5t^2 + 10t) + 6$

Now factor out the coefficient of the quadratic term:

$h(t)=-5(t^2 -2t) + 6$

After doing so, add a constant such that the terms inside the parenthesis form a perfect square, don't forget to balance the equation by adding the inverse of the added constant term:

$h(t) = -5(t^2 -2t) + 6\\\\h(t) = -5(t^2 -2t + 1 -1 ) + 6$

Now take the balancing term out of the parenthesis:

$\\\\h(t)=-5(t^2 -2t + 1) + 6 + ((-1)(-5))$

Simplify:

$h(t) = -5(t^2 -2t + 1) + 6 + 5\\\\h(t) = -5(t-1)^2 + 11$

The x-coordinate of the vertex of the parabola is equal to the additive inverse of the numerical part of the quadratic term. The y-coordinate of the vertex is the constant term outside of the parenthesis. Thus, the vertex of the parabola is:

$(1, 11)$

8 0

2 years ago

Taylor surveys students in one grade level who own at least one pet. She finds that 50% of the students surveyed own 2 pets, 3 s

Llana [10]

First, we need to work out the total number of students who were being surveyed.

We know that half of the students has two pets. The rest of the students make up the other half. So, we have 3 students + 2 students + 8 students = 13 students that make half of the sample population

That means total number of students being surveyed is 13+13=26 students

Then we work out the probability
P(One pet) = 8/26 = 4/13
P(Two pets) = 1/2
P(Three pets) = 3/26
P( Four pets) = 2/26 = 1/13

The probability distribution is shown in the table below. Let $x$ be the number of pets and $P(X=x)$ is the probability of owning the number of pets