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4 years ago

Which of the following graphs is described by the function given below? y = 2x^2 + 8x +3

Mathematics

2 answers:

Masja [62]4 years ago

8 0

Answer:

Step-by-step explanation:

y = 2x² + 8x + 3

Complete the square:

y = 2(x² + 4x) + 3

y = 2(x² + 4x + 4) + 3 - 2(4)

y = 2(x + 2)² - 5

So the vertex is at (-2, -5). The graph must be Graph A.

Alekssandra [29.7K]4 years ago

3 0

Answer:

The answer is Graph (A.)

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Vector question. Let v=<-2,1> u=<3,-5> , find:

lyudmila [28]

Answer:

1. ) $\vec {v}.\vec{u}= -11$

2.) The angle between v and u is 147.52°.

Step-by-step explanation:

Given:

$\vec {v}= ( -2 , 1 )\\\vec {u}= ( 3 , -5 )$

To Find:

1. $\vec {v}.\vec{u}= ?$

2. $\theta = ?$

Solution:

$\vec {v}.\vec{u}$ is scalar product given as,

$\vec {v}.\vec{u}=|\vec {v}||\vec {u}|\cos \theta$

$|\vec {v}|=|(-2, 1)|=\sqrt{(-2)^{2} +1^{2}}=\sqrt{5}\\|\vec {u}|=|(3, 5)|=\sqrt{(3)^{2} +(-5)^{2}}=\sqrt{34}$

$\vec {v}.\vec{u}=(-2i +j).(3i-5j)\\$

Here only i.i = j.j =1 and i.j = j.i = 0

∴ $\vec {v}.\vec{u}=(-2\times 3 +1\times -5)\\\vec {v}.\vec{u}=-6-5=-11 \\$

Now, Substituting the above values we get

$-11=\sqrt{5}\times \sqrt{34}\cos \theta\\ \cos \theta=\frac{-11}{\sqrt{170}} \\ \cos \theta =-0.84366\\\therefore \theta =cos^{-1}(-0.84366)\\\therefore \theta =147.52\°$

As it is negative mean $\theta$ is in Second Quadrant Because Cosine is negative in Second Quadrant.

1. ) $\vec {v}.\vec{u}= -11$

2.) The angle between v and u is 147.52°.

5 0

3 years ago

Solve for x.<br> 3:12 = x:16<br> 64<br> 4<br> 2 1/4

Savatey [412]

Hi!

i think We can set up a proportion to solve this

\frac{3}{12} \frac{x}{16}

Cross multiply

3 x 16 = 48

48/12 = 4

The answer is 4

Hope this helps! :)

7 0

3 years ago

What is an equation in point-slope form of the line shown below? (-2,1) (4,4)

Natali [406]

Answer:

y = 1/2x +2

Step-by-step explanation:

y-y1= m (x-x1)

first find slope

m= 4-1 / 4 - (-2)

m= 3 / 4+2

m= 3/ 6

m = 1/2

you can pick any of the two points to solve for point slope form

y-4 = 1/2 (x-4)

y-4= 1/2x -2

add 4 on both sides

y = 1/2x +2

y-1= 1/2 (x- (-2))

y-1= 1/2 (x+2)

y-1= 1/2x +1

add 1 on both sides

y= 1/2x +2

you should get the same answer with any of the two points you chose

you might want to use a calculator to solve this

if you want to use both points to make sure the answer is correct, you can

if you don't get the same answer with both points then u did something wrong during the equation.

4 0

3 years ago

What are some examples of Adjacent Congruent Angles.

Anastasy [175]

Answer:

base angles of an isosceles triangle
angles at successive corners of any regular polygon
angles either side of an angle bisector
angles made by a perpendicular to a line (excluding vertical angles)

Step-by-step explanation:

When it comes to angles, the term "adjacent" means different things in different contexts. Any pair of angles in a triangle are considered to be adjacent. The base angles of an isosceles triangle are adjacent congruent angles.

Angles at successive corners of any regular polygon are congruent adjacent angles.

Angle that have a common vertex and a common side are also called adjacent angles. Angles on either side of an angle bisector are adjacent congruent angles. Likewise any non-vertical pair of angles where lines cross at right angles are adjacent congruent angles.

3 0

3 years ago

Ana can swim at a rate of

NeTakaya

It’s 60 miles an hour rate

5 0

3 years ago