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2 years ago

Question 2c: Which dog sitting service is better if you need 5 hours of service? Explain your answer PLEASE!

Mathematics

1 answer:

Juliette [100K]2 years ago

8 0

Jacobs dog: $5 x 5 hours plus $ 12 service is $37
Jacks dog : $3 x 5 hours plus $18 service is $ 33
So it’s cheaper to go with jacks dog service

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What is the solution of 15=-4+z/3

lana [24]

15=-4+z/3

+4 +15 = +4 -4 +z/3
cancels the 4 on the right side

19 = z/3

3 x 19 = z/3 x 3
cancels 3 on the right side

I think the answer is z = 57

4 0

2 years ago

Read 2 more answers

Sam Houston's Arms

OLga [1]

Answer:

The length of the statue's arm is<u> 26.22 ft.</u>

Step-by-step explanation:

Let the length of the statue's arm be 'x'.

Given:

Height of statue is, $H=67\ ft$

Height of male is, $h=5\ ft\ 9\ in=5\ ft+\frac{9}{12}\ ft=5+0.75=5.75\ ft$

Length of the male's arm is, $l=27\ in=\frac{27}{12}=2.25\ ft$

Now, as the size of Sam Houston's statue is proportional to that of an adult male, therefore, their heights and arm lengths will also be in proportion. So,

$\frac{H}{h}=\frac{x}{l}\\x=\frac{H}{h}\times l$

Now, plug in the given values and solve for 'x'.

$x=\frac{67}{5.75}\times 2.25\\x=26.22\ ft$

Therefore, the length of the statue's arm is 26.22 ft

7 0

2 years ago

What is the shorter length 60in or 8 feet

Kryger [21]

1 foot = 12 inches

12 * 5 = 60 and 8 * 12 = 96

Therefore, 60 inches is a shorter length than 8 feet.

4 0

3 years ago

Read 2 more answers

Please someone help me to prove this.

morpeh [17]

Answer: see proof below

<u>Step-by-step explanation:</u>

Use the Double Angle Identity: sin 2Ф = 2sinФ · cosФ

Use the Sum/Difference Identities:

sin(α + β) = sinα · cosβ + cosα · sinβ

cos(α - β) = cosα · cosβ + sinα · sinβ

Use the Unit circle to evaluate: sin45 = cos45 = √2/2

Use the Double Angle Identities: sin2Ф = 2sinФ · cosФ

Use the Pythagorean Identity: cos²Ф + sin²Ф = 1

<u />

<u>Proof LHS → RHS</u>

LHS: 2sin(45 + 2A) · cos(45 - 2A)

Sum/Difference: 2 (sin45·cos2A + cos45·sin2A) (cos45·cos2A + sin45·sin2A)

Unit Circle: 2[(√2/2)cos2A + (√2/2)sin2A][(√2/2)cos2A +(√2/2)·sin2A)]

Expand: 2[(1/2)cos²2A + cos2A·sin2A + (1/2)sin²2A]

Distribute: cos²2A + 2cos2A·sin2A + sin²2A

Pythagorean Identity: 1 + 2cos2A·sin2A

Double Angle: 1 + sin4A

LHS = RHS: 1 + sin4A = 1 + sin4A $\checkmark$

6 0

2 years ago

Please help me in this questions....

Ivahew [28]

Part (i)

I'm going to use the notation T(n) instead of $T_n$

To find the first term, we plug in n = 1

T(n) = 2 - 3n

T(1) = 2 - 3(1)

T(1) = -1

The first term is -1

Repeat for n = 2 to find the second term

T(n) = 2 - 3n

T(2) = 2 - 3(2)

T(2) = -4

The second term is -4

<h3>Answers: -1, -4</h3>

==============================================

Part (ii)

Plug in T(n) = -61 and solve for n

T(n) = 2 - 3n

-61 = 2 - 3n

-61-2 = -3n

-63 = -3n

-3n = -63

n = -63/(-3)

n = 21

Note that plugging in n = 21 leads to T(21) = -61, similar to how we computed the items back in part (i).

<h3>Answer: 21st term</h3>

===============================================

Part (iii)

We're given that T(n) = 2 - 3n

Let's compute T(2n). We do so by replacing every copy of n with 2n like so

T(n) = 2 - 3n

T(2n) = 2 - 3(2n)

T(2n) = 2 - 6n

Now subtract T(2n) from T(n)

T(n) - T(2n) = (2-3n) - (2-6n)

T(n) - T(2n) = 2-3n - 2+6n

T(n) - T(2n) = 3n

Then set this equal to 24 and solve for n

T(n) - T(2n) = 24

3n = 24

n = 24/3

n = 8

This means 2n = 2*8 = 16. So subtracting T(8) - T(16) will get us 24.

<h3>Answer: 8</h3>

4 0

3 years ago