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jeyben [28]
3 years ago
15

Please help!! More pages after this one

Mathematics
1 answer:
Mademuasel [1]3 years ago
3 0
1) Since x = -4 and x = -6 are zeros, then, by definition, (x + 4) and (x + 6) are factors of the polynomial. Another way in understanding this is that when x = -4, there would be no remainders.

Thus, we can simply write it as: P(x) = (x + 4)(x + 6) = x² + 10x + 24 (ie C)

2) Using the discriminant, we can find whether a quadratic has two, one, or no roots at all. Symbolised as delta (Δ), the discriminant formula goes as follows:

Δ = b² - 4ac
Thus, if we move the 3 to the other side, we get:
Δ = (-5)² - 4(3)(-10) > 0
Since Δ > 0, then there lies two solutions.

To find rationality or irrationality, we need to check whether or not the square root of the discriminant is an integer or not. If the square root of the discriminant is not an integer, we have irrational roots.

Thus, we've worked out that the discriminant is 145. But 145 is not a perfect square, so when we take the square root of it, we get irrational roots.
Hence, we have two irrational roots.

3) Since we have a fraction, we know that the denominator cannot be zero. Thus, to find places where undefined x-values occur, we need to let the denominator equal to zero:

x² - 16 = 0
x² = 16
x = 4 and -4

These are the restricted values for x, since x cannot equal to 4, or -4.
Hence, your answer is x = 4, -4

4) We can expand and move everything to the LHS.
2(x + 2)² - 32 = 0
2(x² + 4x + 4) - 32 = 0
2x² + 8x + 8 - 32 = 0
2x² + 8x - 24 = 0

We can factorise 2 outside.
2(x² + 4x - 12) = 0

x² + 4x - 12 = 0

We can factorise this further.
(x + 6)(x - 2) = 0

x = -6, 2 are our solutions.
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Work out the value of R. Give your answer in standard form to an appropriate degree of accuracy.
Mumz [18]

Answer:

R = 8,228,571.43 (Approx)

Step-by-step explanation:

Given:

R = x²/y

x = 4.8 x 10⁵

y = 2.8 x 10⁴

Find:

Value of R

Computation:

R = x²/y

R = (4.8 x 10⁵)²/ (2.8 x 10⁴)

R = 23.04 x 10¹⁰ / (2.8 x 10⁴)

R = 8.22857.. x 10⁶

R = 8,228,571.43 (Approx)

4 0
3 years ago
Marcus mixing blue paint and yellow paint the ratio of 2 to 3 to make a red paint he wants to make 45 L of repaint he began to m
marissa [1.9K]

Answer:

do you have any image of the question? If yes please pose here.

3 0
2 years ago
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On your cell phone bill, you are charged $0.25 for each text you send. What is the dependent variable?
zhannawk [14.2K]

Answer:

The amount of the bill is dependent on the number of texts sent. Let y be the bill amount and x the number of texts. Then x is independent and y is dependent. This is because x can be any non-negative number, but y depends upon it. You cannot find the bill without knowing the number of text messages, right?

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2 years ago
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How do you write 12,430,000 in expanded form
const2013 [10]

we know that

12,430,000 in expanded form is equal to

12,430,000=1*(10,000,000)+2*(1,000,000)+4*(100,000)+3*(10,000)\\\\   12,430,000=(10,000,000)+(2,000,000)+(400,000)+(30,000)

therefore

<u>the answer is</u>

(10,000,000)+(2,000,000)+(400,000)+(30,000)

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2 years ago
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Given a point A(-3,-1), it is dilated by some scale
Sidana [21]

Answer:

B' = (-3, -15)

Step-by-step explanation:

Given

A = (-3,-1)

A' = (-9,-3)

B = (-1,-5)

Required

Determine the coordinates of B'

Since A' is the image of A; we need to first calculate the scale factor using

A' = A * Scale\ factor

Make Scale Factor the subject

Scale\ Factor = \frac{A'}{A}

Substitute values for A' and A

Scale\ Factor = \frac{(-9,-3)}{(-3, -1)}

Factorize the numerator

Scale\ Factor = \frac{3 * (-3,-1)}{(-3, -1)}

Scale\ Factor = \frac{3 * 1}{1}

Scale\ Factor = 3

The coordinates of B' is then calculated as follows:

B' = B * Scale\ Factor

Substitute values for B and Scale Factor

B' = (-1,-5) * 3

B' = (-3, -15)

3 0
2 years ago
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