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3 years ago

How would the expression x^2-9 be written using difference of swuares

Mathematics

2 answers:

Alex73 [517]3 years ago

8 0

Answer:

(x-3)(x+3)

Step-by-step explanation:

Here we have to represent our algebraic expression as difference of square.

In order to do so we have use the formula given under.

$(x^2-a^2)=(x-a)(x+a)$

Hence first we have to guess the square root of the 9 , which is 3 and represent our numeric term in our expression as square of it.

Hence

$(x^2-9)\\= (x^2-3^2)$

Now we apply the formula

$(x^2-3^2)=(x-3)(x+3)$

Hence the above expression is our answer.

Ludmilka [50]3 years ago

4 0

x squared and -9 are both square numbers.

the square root of x^2 is x

the square root of -9 is 3. so you just need to write (x+3)(x-3)

you can check by expanding the brackets and the middle x terms should cancel out

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Determine if the given side lengths could be used to form a unique triangle, many different triangles, or no triangles. explain

ehidna [41]

Given sides of length 300 mm or 190 mm, you can form 4 different triangles:

equilateral with sides 190 mm
equilateral with sides 300 mm
isosceles with two sides 190 mm and one side 300 mm
isosceles with two sides 300 mm and one side 190 mm

The triangle inequality requires the sum of the lengths of any two sides be not less than the length of the third side. Since 2×190 > 300, you can mix and match these side lengths any way you want. With three sides and 2 choices for each, there are only a limited number of possibilities.

In the above, we have not listed ones that are simply rotations or reflections of a congruent triangle. (A 190-190-300 triangle looks the same as a 190-300-190 triangle, for example.)

6 0

3 years ago

To gain a pass a student needs to achieve a mean of at least 60% in eight tests. In the first seven

Tanzania [10]

Step-by-step explanation:

the mean value is the sum of all data points divided by the number of data points.

first we have 7 tests and their mean value :

(t1 + t2 + t3 + t4 + t5 + t6 + t7) / 7 = 54

that means

(t1 + t2 + t3 + t4 + t5 + t6 + t7) = 54 × 7 = 378

in order for the mean value to be at least 60% after 8 tests, we need to add a t8, so that

(t1 + t2 + t3 + t4 + t5 + t6 + t7 + t8) = 60 × 8 = 480

because only then we have

(t1 + t2 + t3 + t4 + t5 + t6 + t7 + t8) / 8 = 60

and the student passes.

so,

(t1 + t2 + t3 + t4 + t5 + t6 + t7) + t8 = 480

378 + t8 = 480

t8 = 480 - 378 = 102%

the student would have to achieve 102% on the 8th test.

which would be normally impossible, but maybe the tests involve some bonus points.

6 0

2 years ago

The statue of Liberty stands on a 150 ft. pedestal. From a point 250 ft. from the base of the

bekas [8.4K]

Answer:

148ft

Step-by-step explanation:

To solve this question, you'll have to imagine the statue makes a right angle triangle with the base since it has an angle of elevation from the base to the top of the torch.

Assuming the height from the pedestal to the top of the torch is y

The height of the statue is x

But we know the height of the pedestal = 150ft

The distance from the observer to the base of the pedestal = 250ft

And the angle of elevation = 50°

See attached document for better illustration.

Tanθ = opposite / adjacent

θ = 50°

Adjacent = 250

Opposite = y

Tan50 = t / 250

y = 50 × tan50

y = 50 × 1.1917

y = 297.925ft

The height of the statue from the base of the pedestal to the top of the torch is 297.925ft

The height of the statue = x

x = (height of the statue + height of the pedestal) - height of the pedestal

x = y - 150

x = 297.925 - 150

x = 147.925ft

Approximately 148ft

The height of the statue is 148ft

4 0

3 years ago

An airplane on a transatlantic flight took 4 hours 20 minutes to get from New York to its destination, a distance of 3,000 miles

ankoles [38]

738.

3200/4.33= 739.01

The closest to that is 738

4 0

3 years ago

9. PLEASE HELP ME

gizmo_the_mogwai [7]

Answer:

C. (3, 3)

Step-by-step explanation:

8 0

3 years ago