Can someone please finish this puzzle, just need one more! Just need number 14

Harry solves the equation 1/3t = 15. He says the solution is 30. Is his answer correct? Fill in the blanks to explain how Harry

aksik [14]

Harry can first substitute 30 for t

He can then multiply $\frac{1}{3}$ by 30 to get a product of 10

Since, 10 is not equal to 15, Harry's solution is not correct.

Solution:

Given that,

Harry solves the equation:

$\frac{1}{3}t = 15$

He says the solution is 30

We have to check if his answer is correct or not

Fill in the blanks to explain how Harry can check whether his solution is correct

Harry can first substitute 30 for t

$\frac{1}{3} \times 30 = 15$

He can then multiply $\frac{1}{3}$ by 30 to get a product of 10

$10\neq 15$

Since, 10 is not equal to 15, Harry's solution is not correct

Correct solution:

$\frac{1}{3}t = 15\\\\t = 15 \times 3\\\\t = 45$

Thus correct solution is 45

5 0

3 years ago

Help, Help, Please

Lesechka [4]

Answer:

θ = $\frac{\pi }{3}$ (60° )

Step-by-step explanation:

Using the identity

sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x

Given

cos²θ - sin²θ = 2 - 5cosθ

cos²θ - (1 - cos²θ) = 2 - 5cosθ

cos²θ - 1 + cos²θ = 2 - 5cosθ

2cos²θ - 1 = 2 - 5cosθ ( subtract 2 - 5cosθ from both sides )

2cos²θ + 5cosθ - 3 = 0 ← in standard form

(cosθ + 3)(2cosθ - 1) = 0 ← in factored form

Equate each factor to zero and solve for θ

cosθ + 3 = 0

cosθ = - 3 ← not possible as - 1 ≤ cosθ ≤ 1

2cosθ - 1 = 0

cosθ = $\frac{1}{2}$ , so

θ = $cos^{-1}$ ( $\frac{1}{2}$ ) = $\frac{\pi }{3}$ ( or 60° )

8 0

3 years ago

Read 2 more answers

3/10 as an equivalent fraction with a denominator of 100

viktelen [127]

30/100.

To get to this, you need to change the denominator to 100. 10 x 10 = 100 so whatever you do to the denominator, you do to the numerator. 3 x 10 = 30 so your answer would be 30/100.

8 0

3 years ago

in a right triangle, if angle O is equal to 39 and the side adjacent to is equal to 12.0 centimeters, what is the approximate le

lesya [120]

Approximated: $9.7$ cm
Exact: $12tan(39)$ or $\frac{12}{tan51}$

Explanation:
It's always best for these types of questions to visualise it. A right triangle has base angle of 90°. Mark in what you know, and leave out the rest. Notice how the question doesn't ask for a hypotenuse. This means that you might be using the tangent function as the tangent function also doesn't require a hypotenuse.

So now, you have a side of 12cm, with the corresponding 39° angle marked.
To find the missing length, you can use the tangent function to approximate the length:

$tan39 = \frac{x}{12}$ (opposite/adjacent)

Now, isolate the variable, x:
$x = 12tan39$ (exact form)
$x = 9.7$ cm (approximated to 1 decimal place)

8 0

3 years ago

Read 2 more answers

Simplify 9 to the 2nd over 9 to the 7th. (4 points)

Blizzard [7]

1 over 9 to the 5th. The math is attached below

4 0

3 years ago