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aalyn [17]
2 years ago
8

I need help on these questions

Mathematics
1 answer:
laiz [17]2 years ago
7 0

I'm using examples to show

9

a) Let,

First odd number = 5

Second consecutive odd number = 7

Sum = 5 + 7 = 12. Which is divisible by 4

b) Let the numbers be same as above

(5)² + (7)²

25 + 49

74. Which is not divisible by 4

10) Maisy is wrong because 2 has no common factor except 1 and 2. And we know that 2 is an even number and it is also a prime number

11)

a) Let,

First integer = 5

Second integer = 7

Sum = 5 + 7 = 12.

Since the sum is even but the integers are odd.

b) Let,

Integer = 8

(8)² = 64. which is divisible by 4 and 8 is also divisible by 4

12)

Let,

a = -8

b = 8

a² = (-8)² = 64

b² = (8)² = 64

a² = b²

But, a ≠ b

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Find an n^th degree polynomial with real coefficients satisfying the given conditions. n = 3; -2 and 2 i are zeros; f(-1) = 15.
Ira Lisetskai [31]
So, n = 3, is a 3rd degree polynomial, roots are -2 and 2i

well 2i is a complex root, or imaginary, and complex root never come all by their lonesome, their sister is always with them, the conjugate, so if 0+2i is there, 0-2i is there too

so, the roots are -2, 2i, -2i

now... \bf \begin{cases}
x=-2\implies x+2=0\implies &(x+2)=0\\
x=2i\implies x-2i=0\implies &(x-2i)=0\\
x=-2i\implies x+2i=0\implies &(x+2i)=0
\end{cases}
\\\\\\
(x+2)\underline{(x-2i)(x+2i)}=0\\\\
-----------------------------\\\\
\textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)\\\\
-----------------------------\\\\
(x+2)[x^2-(2i)^2]=0\implies (x+2)[x^2-(2^2i^2)]=0
\\\\\\
(x+2)[x^2-(4\cdot -1)]=0\implies (x+2)(x^2+4)=0
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x^3+2x^2+4x+8=0

now, if we check f(-1), we end up with 5, not 15
hmmm

so, how to turn our 5 to 15? well, 3*5, thus

\bf 3(x^3+2x^2+4x+8)=f(x)\implies 3(5)=f(-1)\implies 15=f(-1)

usually, when we get the roots, or zeros, if any common factor that is a constant is about, they get in a division with 0 and get tossed, and aren't part of the roots, thus, we can simply add one, in this case, the common factor of 3, to make the 5 turn to 15
6 0
3 years ago
. Using the rounding off technique, find the rough estimated difference of the given decimals.
nikitadnepr [17]

Answer:

19. 188

20. 18

21. 5

21. 4

Step-by-step explanation:

634.58 would round up to 635 and 436.79 would round up to 437.

20. 37.86 would round up to 38 and 19.92 would round up to 20.

21. 14.49 would round to 14 and 8.59 would round up to 9.

22. 7.45 would round down to 7 and 2.93 would round up to 3.

3 0
2 years ago
Malaya is making a collage of her birthday party photos and she wants to add an 8 x 10 inch. photo. Since there is not enough sp
sergij07 [2.7K]

Answer:

The answer is C. 6.4 X 8 in

Step-by-step explanation:

If the scale factor from the original to the trimmed photo is 5:4

The statement above just means the scale of the old dimension is 5 while the scale of the new dimension is 4.

To get the new dimensions, multiply each of the old dimensions by 4/5

4/5 X 10 = 8

4/5 X 8 = 6.4

Therefore the new dimension is 6.4 X 8 in

3 0
3 years ago
In triangle JKL, m of angle J = 90, m of angle K = 30, and m of angle L = 60. Which of the following statements about triangle J
Jobisdone [24]

Answer:

# Answer B is true ⇒ KL = 2(JL)

# Answer C is true ⇒ JK = √3(JL)

# Answer F is true ⇒ JK = √3/2(KL)

Step-by-step explanation:

* Lets explain the ratio between the sides of the triangle

- In Δ JKL

∵ The measure of angle J is 90°

∴ KL is the hypotenuse

∵ The measure of angle K is 30°

∴ JL is the opposite side to angle 30°

∵ The measure of angle L is 60°

∴ JK is the opposite side to the angle 60°

- There is a fact in the triangle which has angles 30° , 60° , 90°

# The length of the side opposite to the angle of measure 30° is

  half the length of the hypotenuse

∵ KL is the hypotenuse

∵ JL is the opposite side to the angle of measure 30°

∴ JL = 1/2 KL  OR KL = 2 JL

# The length of the side opposite to the angle of measure 60° is

  √3 the length of the opposite side to the angle 30°

∵ JK is the opposite side to the angle of measure 60°

∵ JL is the opposite side to the angle of measure 30°

∴ JK = √3 JL

# The length of the side opposite to the angle of measure 60° is also

  half √3 the length of the hypotenuse

∵ JK is the opposite side to the angle of measure 60°

∵ KL is the hypotenuse

∴ JK = √3/2 KL

- From the relation above

# Answer B is true ⇒ KL = 2(JL)

# Answer C is true ⇒ JK = √3(JL)

# Answer F is true ⇒ JK = √3/2(KL)

6 0
3 years ago
How many 1/4 gram doses can be obtained from a 7 1/2 gram vial of medication?
vlada-n [284]

Answer:

30 gram doses

Step-by-step explanation:

First, turn the fractions into decimals.

1/4 gram to .25 gram

7 1/2 gram to 7.5 gram

Then, divide 7.5 total grams by the .25 grams for each dose.

7.5/.25 = 30

Therefore, you can obtain 30 1/4 gram doses from a 7 1/2 gram vial of medication.

6 0
3 years ago
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