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Elina [12.6K]
3 years ago
7

2. Geoff planted dahlias in his garden. Dahlias have bulbs that divide and reproduce underground. In the first year, Geoff’s gar

den produced 6 bulbs. In the second year, it produced 12 bulbs, and in the third year, it produced 24 bulbs. If this pattern continues, how many bulbs should Geoff expect in the eighth year? (1 point)
48 bulbs
384 bulbs
768 bulbs
1,536 bulbs

3. What are the first four terms of the sequence represented by the expression n(n – 1) – 5? (1 point)
–7, –5, –3, 1
–5, –10, –15, –20
0, 2, 6, 12
–5, –3, 1, 7

6. Given the function rule f(x) = x² – 5x + 1, what is the output of f(–3)? (1 point)
7
–5
25
5

7. Suppose you earn $10 each hour you babysit. Which function describes the relationship between your total earnings E and the number of hours you babysit, h? (1 point)
E(h) = 10h
E(h) = h + 10
E(h) = h – 10
h = 10E

Melanie charges $4.50 per hour when she washes cars, plus $5.00 for supplies. Which function rule represents the amount y Melanie charges to wash cars for x hours? (1 point)
y = 0.50x
y = 4.50x + 5.00
y = 5.00x + 4.50
y = 9.50x

14. The sale price of apples at a local grocery store is $1.35 for the first pound and $1.10 for each additional pound. Which function rule shows how the cost of apples, y, depends on the number of pounds, x? (1 point)
y = 1.10(x – 1) + 1.35
y = 1.10x + 1.35
y = 1.35x + 1.10
y = (1.10 + 1.35)x
PLEASE HELP
Mathematics
1 answer:
lys-0071 [83]3 years ago
5 0

2. In the first year, Geoff’s garden produced 6 bulbs. In the second year, it produced 12=6·2 bulbs, and in the third year, it produced 24=12·2 bulbs. If this pattern continues, then he can expect 24·2=48 bulbs in the fourth year, 48·2=96 bulbs in the fifth year, 96·2=192 bulbs in the 6th year, 192·2=384 bulbs in the 7th year and 384·2=768 bulbs in the 8th year.

Answer 2: correct choice is C.

3. Given n(n – 1) – 5 you can find:

  • for n=1, 1·(1-1)-5=-5;
  • for n=2, 2·(2-1)-5=-3;
  • for n=3, 3·(3-1)-5=1;
  • for n=4, 4·(4-1)-5=7.

Answer 3: correct choice is D.

6. Given the function rule f(x) = x² – 5x + 1,

f(-3)=(-3)²-5·(-3)+1=9+15+1=25.

Answer 6: correct choice is C.

7. Suppose you earn $10 each hour you babysit and your total earnings E depending on the number of hours h you babysit is

E(h)=10·h.

Answer 7: correct choice is A.

8. If Melanie charges $4.50 per hour, then she she charges $4.50·x for x hours. Plus $5.00 for supplies, then the function rule is

y=4.50x+5.00.

Answer 8: correct choice is B.

14. The sale price of apples at a local grocery store is $1.35 for the first pound and $1.10 for each additional pound. If x is the number of sold pounds then 1 was sold for $1.35 and rest x-1 were sold for $1.10. This means that

y=1.10(x-1)+1.35

Answer 14: correct choice is A.


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3 years ago
Given that sec (x) = 2 and cosec (x) is negative,
weeeeeb [17]

Answer:

i) sin(2x) = -\frac{\sqrt{3}}{2}

ii) cot(x+360) = -\frac{\sqrt{3}}{3}

iii) sin(x-180) = \frac{\sqrt{3}}{2}

Step-by-step explanation:

sec(x) = 2

Since cos(x) is reciprocal of sec(x), this means:

cos(x) = \frac{1}{2}

cosec(x) is negative , this means sin(x) is also negative. The only quadrant where cos(x), sec(x) are positive and sin(x), cosec(x) are negative is the 4th quadrant. Hence the terminal arm of the angle x is in 4th quadrant.

Part i)

sin(2x) can be simplified as:

sin(2x) = 2 sin(x) cos(x)

First we need to find the value of sin(x). According to Pythagorean identity:

sin^{2}(x)=1-cos^{2}(x)\\\\ sin(x)=\pm \sqrt{1-cos^{2}(x)}

Since, angle is in 4th quadrant, sin(x) will be negative. So considering the negative value of sin(x) and substituting the value of cos(x), we get:

sin(x)=- \sqrt{1-cos^{2}(x)}\\\\ sin(x)=-\sqrt{1-(\frac{1}{2})^{2}}\\\\ sin(x)=-\frac{\sqrt{3}}{2}

So,

sin(2x)=2 \times -\frac{\sqrt{3} }{2} \times \frac{1}{2}\\\\ sin(2x)=-\frac{\sqrt{3}}{2}

Part ii)

We have to find cot(x + 360)

An addition of 360 degrees to the angle brings it back to the same terminal point. So the trigonometric ratios of the original angle and new angle after adding 360 or any multiple of 360 stay the same. i.e.

cot(x + 360) = cot(x)

cot(x) = \frac{cos(x)}{sin(x)}\\

Using the values, we get:

cot(x)=\frac{\frac{1}{2}}{-\frac{\sqrt{3}}{2} }\\\\ cot(x)=-\frac{\sqrt{3}}{3}

Part iii)

We need to find the value of sin(x - 180)

sin(x - 180) = - sin(x)

Addition or subtraction of 180 degrees changes the angle by 2 quadrants. The sign of sin(x) becomes opposite if the angle jumps by 2 quadrants. For example, sin(x) is positive in 1st quadrant and negative in 3rd quadrant.

So,

sin(x - 180) = -(-\frac{\sqrt{3}}{2}) = \frac{\sqrt{3}}{2}

6 0
3 years ago
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