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3 years ago

Find the values of a and b such that x^2-4x+9=(x+a)^2+b

Mathematics

1 answer:

m_a_m_a [10]3 years ago

6 0

Answer:

a = -2

b = 5

Step-by-step explanation:

We can identify the right side of the equation as completing the square. So, we simply complete the square for x² - 4x + 9 to find our answer,

Step 1: Isolate xs

x² - 4x = -9

Step 2: Complete the square

x² - 4x + 4 = -9 + 4

(x - 2)² = -5

Step 3: Move -5 over

(x - 2)² + 5

And we have our answer!

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10 raised to negative 3 in standard notation

larisa86 [58]

Standard notation simply means the normal way or writing numbers.
10^-3= 1/10^3
1/10^3=1/1000
1/1000=0.001
Final answer: 0.001

4 0

3 years ago

From a radar station, the angle of elevation of an approaching airplane is 32.5 degree. The horizontal distance between the plan

denis23 [38]

Answer: 42.21 km

Step-by-step explanation:

We can solve this using trigonometry, since we have the following data:

$\theta=32.5\°$ is the the angle of elevation

$d=35.6 km$ is the horizontal distance between the plane and the radar station

$x$ is the hypotenuse of the right triangle formed between the radar station and the airplane

Now, the trigonometric function that will be used is <u>cosine</u>:

$cos\theta=\frac{d}{x}$ because $d$ is the adjacent side of the right triangle

$cos(32.5\°)=\frac{35.6 km}{x}$

Finding $x$ :

$x=\frac{35.6 km}{cos(32.5\°)}$

$x=42.21 km$

4 0

3 years ago

The lengths, in centimeters, of nine earthworms are shown below. 3, 4, 5, 5, 6, 7, 8, 9, 10 What is the median of the data?

mel-nik [20]

The median of the problem is 6 because it is in the middle of the number set of the earthworm sizes.

6 0

3 years ago

Graph the image of this triangle after a dilation with a scale factor of 2 centered at the origin. Use the polygon tool to graph

Olenka [21]

The triangle is illustrated below.

<h3>How to explain the triangle?</h3>

The first thing you should find are the new vertices:

(x, y) ---> (2x, 2y) ---> (x', y')

(0, 0) ---> (2 (0), 2 (0)) ---> (0, 0)

(-4, 4) ---> (2 (-4), 2 (4)) ---> (-8, 8)

(-4, -2) ---> (2 (-4), 2 (-2)) ---> (-8, -4)

Then, you must join the ordered pairs and graph the new triangle.

See the attached graph.

Learn more about triangles on:

brainly.com/question/1058720

#SPJ1

5 0

2 years ago

Can You Solve This?<br> 6 = 2(1+2) =

nata0808 [166]

Answer: 6 = 2(1+2), this is true.

Step-by-step explanation:

To solve this, 6 = 2(1 +2) =

This question is to proove that 2(1 +2) = 6

First we open the bracket:

(2 × 1) + (2 × 2)

Multiply 2 by 1 = 2

Multiply 2 by 2 = 4

2 + 4 = 6

I hope this helps.

8 0

3 years ago

Read 2 more answers