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Solnce55 [7]
2 years ago
12

Given that2025=

title=" {3}^{k \times } {5}^{t} " alt=" {3}^{k \times } {5}^{t} " align="absmiddle" class="latex-formula">
state the values of k and t​
Mathematics
1 answer:
damaskus [11]2 years ago
8 0

Answer:

k = 4, t = 2

Step-by-step explanation:

Express 2025 as a product of its prime factors

2025 = 3^{4} × 5², that is

3^{4} × 5² = 3^{k} × 5^{t}

Comparing exponents of same bases on both sides, gives

k = 4 and t = 2

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Find the area of the trapezoid. points are (-5,-3)(4,-3)(6,-7)(-7,-7)​
Olegator [25]

Answer:

44 square units

Step-by-step explanation:

The area of a trapezoid with bases b₁ and b₂ and height h is given by the formula

A=\left(\dfrac{b_1+b_2}{2}\right)h

If you're wondering how we get this formula, check the attached illustration (remember the area of a parallelogram is its base multiplied by its height)! Moving on to our trapezoid, the pairs of points (-5,-3)(4,-3) and (6,-7)(-7,-7) form two horizontal segments, which form b₁ and b₂, and our height is the distance between the y-coordinates -3 and -7, which is 4. We can find b₁ and b₂ by finding the distance between the x coordinates in their pairs of points:

b_1=|-5-4|=|-9|=9\\b_2=|6-(-7)|=|6+7|=13

Putting it altogether:

A=\left(\dfrac{9+13}{2}\right)(4)=\left(\dfrac{22}{2}\right)(4)=(11)(4)=44

So the area of our trapezoid is 44.

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3 years ago
Sam made $80,000 as a financial analyst her first year out of college. She calculated her above-the-line deductions to be $5,500
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Answer:

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Write the first five terms of each sequence described and identify the sequence as
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Step-by-step explanation:

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A box is to be constructed with a rectangular base and a height of 5 cm. If the rectangular base must have a perimeter of 28 cm,
Svetradugi [14.3K]

Answer:

The quadratic equation that best models the volume of the box (in terms of W) is:

70W-5W^2

Step-by-step explanation:

The perimeter of the rectangular base = 28cm

Perimeter of a rectangle = 2(L+W)

2(L+W)=28

L+W=14

L=14-W

Volume of the Box= LWH

Since L=14-W and Height Of the Box= 5cm

Volume of the Box= (14-W)W X 5

=5(14W-W^2)\\                             =70W-5W^2

6 0
3 years ago
Read 2 more answers
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