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Anna [14]
2 years ago
14

A) Show that 4x² -6x+9 is positive for all values real numbers x.

Mathematics
1 answer:
wolverine [178]2 years ago
7 0

Answer:

(4x² -6x+1.5²) +9-1.5²= (2x-1.5)²+9-2.25= (2x-1.5)²+6.75

(2x-1.5)² is greater or equal to 0 , 6.75>0 so expression is positive for all real numbers x

Step-by-step explanation:

a) Use the formula a²-2ab+b²= (a-b)² (You need to make squared expression because it is always positive)

Consider 4x² as a² and -6x=-2ab

4x²=a² a=2x  ab=3x 2x*b=3x

b=1.5

Express 4x² -6x+9= (4x² -6x+1.5²) +9-1.5²= (2x-1.5)²+9-2.25= (2x-1.5)²+6.75

(2x-1.5)² is greater or equal to 0 , 6.75>0 so expression is positive for all real numbers x

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3. If triangle ABC has the following measurements, find the measure of angle A.
klio [65]

9514 1404 393

Answer:

  (a)  42.3°

Step-by-step explanation:

Side 'a' is the shortest of three unequal sides, so angle A will be the smallest angle in the triangle. Its measure can be found from the Law of Cosines.

  a² = b² +c² -2bc·cos(A)

  cos(A) = (b² +c² -a²)/(2bc) = (21² +25² -17²)/(2·21·25) = 777/1050

  A = arccos(777/1050) ≈ 42.3°

The measure of angle A is about 42.3°.

_____

<u><em>Additional comment</em></u>

The smallest angle in a triangle can never be greater than 60°. This lets you eliminate choices that exceed that value.

5 0
2 years ago
Alice needs 3/7 kilograms of flour for making a cake. How many of flour does she needs for making 42 cakes?
Oduvanchick [21]
Hey there!

3/7 is needed for 1 cake

If she needs to make 42 cakes, then multiply the amount for 1 by 42

42 × 3/7 = 126/7 = 18

She needs 18 kilograms of flour to make 42 cakes

Hope this helps :)
3 0
3 years ago
(3x + 1) &gt; -7+ 3x<br> Plz help me
Luda [366]

Answer:

0, -1

Step-by-step explanation:

This question was answered in another place since you asked it twice. Please refer to the other place that you asked the same question.

5 0
2 years ago
Please help and thank you
tatiyna

Answer:

b_{1}=\frac{2A}{h}-b_{2}

Step-by-step explanation:

Given: A=\frac{1}{2}(b_{1} +b_{2})h

We need to completely isolate b_{1} to solve.

A=\frac{1}{2}(b_{1} +b_{2})h

A=(\frac{1}{2}b_{1} +\frac{1}{2} b_{2})h

A=\frac{1}{2}b_{1} h+\frac{1}{2}b_{2}h

-\frac{1}{2}b_{1}h+A=\frac{1}{2}b_{2}h

-\frac{1}{2}b_{1}h=-A+\frac{1}{2}b_{2}h

-\frac{1}{2}b_{1}=\frac{-A}{h}+\frac{1}{2}b_{2}

Finally, multiply both sides by -2 to completely isolate b_{1}.

b_{1}=\frac{2A}{h}-b_{2}

5 0
3 years ago
Read 2 more answers
The equation T^2=A^3 shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A
Sergio039 [100]
The answer for your question is going to be. 2^((3)/(2)) I know this cause I just took a quiz with this question on it
8 0
3 years ago
Read 2 more answers
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