Y = 2x + 6

What is the perimeter of this rectangle?

Scorpion4ik [409]

38 cm sum of all sides is equal to the perimeter

6 0

3 years ago

Complete the square on the following quadratic x2+10x+9=0

kakasveta [241]

Given a quadratic equation $x^{2} +ax+c=0$

1. the first thing we do when we want to compete the square, is write the coefficient of x as 2 times a number.

In our case the coefficient of x is 10, so we write 10 as 2*5

2. then we write + $5^{2}$ and - $5^{2}$ to the expression:

$x^{2} +2*5*x+ 5^{2} -5^{2}+9=0$

$(x^{2} +2*5*x+ 5^{2}) -25+9=0$

$(x+5)^{2}-16=0$

Answer: $(x+5)^{2}-16=0$

8 0

3 years ago

There are 7 ushers and 11 technicians helping at the Harper Middle School fall play.

bearhunter [10]

Answer:

<h3>The ratio of technicians to all helpers is 11 : 7, or $\frac{11}{7}$ or 11 to 7.</h3>

Step-by-step explanation:

Given that there are 7 ushers and 11 technicians helping at the Harper Middle School fall play.
Let x be the number of ushers ( or helpers ).
Therefore x=7 helpers.
Let y be the number of technicians.
Therefore y=11 technicians.

<h3>To find the ratio of technicians to all helpers :</h3>

That is to find the ratio of y to x.

We can write the ratio of technicians to all ushers(helpers) as y : x

Which implies that 11 : 7, (since y=11 and x=7)

Or $\frac{11}{7}$ or 11 to 7

<h3>The ratio of technicians to all helpers is 11 : 7, or $\frac{11}{7}$ or 11 to 7</h3>

4 0

4 years ago

A particle begins at point (1, 2) and is moving along the line segment joining (1, 2) to (3, 4). Initially, what is the rate of

Bumek [7]

Answer:

Initially, that is, at (1,2), the rate of increase of the function in the direction given = 0

Hence the function is neither increasing nor decreasing initially in the given direction.

Step-by-step explanation:

f(x,y) = 2x² - y²

Rate of Change of the function = ∇f = (fₓ, fᵧ)

And we're told to find the rate of change in a particular direction = ∇f.û

We first obtain the unit vector in that direction, û

Direction = (3,4) - (1,2) = (2,2)

Uni vector = vector/magnitude

Vector = 2î + 2j

magnitude = √(2² + 2²) = √8 = 2 √2

(2î + 2j)/(2√2) = (1/√2)î + (1/√2)j = û

Unit vector in the direction = (1/√2, 1/√2)

f = 2x² - y²

At (1,2)

fₓ = ∂f/∂x = 4x = 4

fᵧ = ∂f/∂y = -2y = -4

∇f = (4,-4)

∇f.û = (4î - 4j).((1/√2)î + (1/√2)j) = (4/√2) - (4/√2) = 0

If it was positive, then the function is increasing, if it was negative, the function is decreasing. Zero means neither of them.

Hence the function is neither increasing nor decreasing initially in the given direction.

7 0

3 years ago

Solve the equation. Check your solutions when necessary.<br><br><br>2x² − 7x = 4

prisoha [69]

Answer:

x= -1/2 = -0.500

x=4

Step-by-step explanation:

2x^2-7x-4=0

2x^2-8x+1x-4=0

2x(x-4)+1(x-4)=0

(2x+1)(x-4)=0

2x+1=0...2x= -1.. x= -1/2 x-4=0 .. x=4

checking the solution

2(-1/2)^2-7(-1/2)=4..... 4=4

2(4)^2-7(4)=4....... 4=4

5 0

3 years ago