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Alekssandra [29.7K]
3 years ago
8

Expand and simplify 4(2x-1)+3(2+5)

Mathematics
1 answer:
zavuch27 [327]3 years ago
8 0

Answer:

8x + 17

Step-by-step explanation:

4(2x- 1) + 3(2 + 5)

=4*2x - 4*1 + 3*7

=8x - 4 +21

=8x + 17

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Step-by-step explanation:

any expression divided by one stays the same; simplify the expression using the symmetry of trigonometric functions.

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1) Find the slope and the y-byintercept of the line that passes through the points (1,5) and (3,9)
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Answer: slope= 2, y-intercept= 3

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3 years ago
0.0007716049 as a fraction
elena55 [62]

To write 0.0007716049 as a fraction you have to write 0.0007716049 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.

0.0007716049 = 0.0007716049/1 = 0.007716049/10 = 0.07716049/100 = 0.7716049/1000 = 7.716049/10000 = 77.16049/100000 = 771.6049/1000000 = 7716.049/10000000 = 77160.49/100000000 = 771604.9/1000000000 = 7716049/10000000000

so your answer is: 7716049/10000000000

7 0
3 years ago
Kaliska is jumping rope. The vertical height of the center of her rope off the ground R(t) (in cm) as a function of time t (in s
xz_007 [3.2K]

Answer:

R (t) = 60 - 60 cos (6t)

Step-by-step explanation:

Given that:

R(t) = acos (bt) + d

at t= 0

R(0) = 0

0 = acos (0) + d

a + d = 0 ----- (1)

After \dfrac{\pi}{12} seconds it reaches a height of 60 cm from the ground.

i.e

R ( \dfrac{\pi}{12}) = 60

60 = acos (\dfrac{b \pi}{12}) +d --- (2)

Recall from the question that:

At t = 0, R(0) = 0 which is the minimum

as such it is only  when a is  negative can acos (bt ) + d can get to minimum at t= 0

Similarly; 60 × 2 = maximum

R'(t) = -ab sin (bt) =0

bt = k π

here;

k  is the integer

making t the subject of the formula, we have:

t = \dfrac{k \pi}{b}

replacing the derived equation of k into R(t) = acos (bt) + d

R (\dfrac{k \pi}{b}) = d+a cos (k \pi) = \left \{ {{a+d  \ for \ k \ odd} \atop {-a+d \ for k \ even}} \right.

Since we known a < 0 (negative)

then d-a will be maximum

d-a = 60  × 2

d-a = 120 ----- (3)

Relating to equation (1) and (3)

a = -60 and d = 60

∴ R(t) = 60 - 60 cos (bt)

Similarly;

For R ( \dfrac{\pi}{12})

R ( \dfrac{\pi}{12}) = 60 -60 \ cos (\dfrac{\pi b}{12}) =60

where ;

cos (\dfrac{\pi b}{12}) =0

Then b = 6

∴

R (t) = 60 - 60 cos (6t)

7 0
3 years ago
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