The earth is 146 000 000 kilometres from the sun, what is the number in standard form?

PLEASE HELP A store has sales of $500 in their first month. If sales increase at a rate of $10 each month, they can be modeled b

Lesechka [4]

Answer: 131,400$

Step-by-step explanation:

The sale for first month is $500.

The sale increases by $10 each month, as modelled by the equation:

a_k=500+(k-1)10

where, k = 1 (first month)

k = 2 (second month)

.... and so on.

we have to calculate the sale for the first 10 years, that means for 10*12 = 120 months (1 year = 12 months)

Total sales = ∑ a_k

∑ a_k = ∑ (500+(k-1)10)

= 500k + ∑ (10k - 10)

= 500k + 10∑k - 10k

= 490k + 10∑k

= 490k + 10 {k*(k+1)/2}

= 490k + 5{k*(k+1)}

= 490k + 5k^2 + 5k

= 5k^2 + 495k

∴∑ a_k = 5k^2 + 495k

For calculating the total sales of 10 years, we will put the value of k = 120 (120th month after the first month)

= 5*(120*120) + 495*120

= 72,000 + 59, 400

= 131,400$

6 0

4 years ago

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ABCD is a quadrilateral with A(8,21),B(10,27),C(26,26) and D(18,2). Determine whether ABCD is a trapizoid

Svetradugi [14.3K]

<h2>Answer:</h2>

ABCD is a trapezoid

<h2>Step-by-step explanation:</h2>

<em>Given points of the quadrilateral:</em>

A(8,21),B(10,27),C(26,26) and D(18,2)

To show whether ABCD is a trapezoid, we find a pair of parallel sides in ABCD. If two of its sides are parallel to each other then ABCD is a trapezoid.

<em>Step 1:</em> With the given points, sketch a graph. The diagram is attached to this response.

<em>Step 2:</em> As shown in the diagram, the two sides that are likely to be parallel are AB and CD

If these two sides have same gradient/slope, then the quadrilateral is a trapezoid.

Now calculate the slopes of those sides using the slope formula;

m = $\frac{y_2 - y_1}{x_2 - x_1}$

<em>Calculate the slope of AB </em>(where x₁ = 8, y₁ = 21, x₂ = 10, y₂ = 27)

m(AB) = $\frac{27-21}{10-8}$

m(AB) = $\frac{6}{2}$

m(AB) = 3

<em>Calculate the slope of CD </em>(where x₁ = 26, y₁ = 26, x₂ = 18, y₂ = 2)

m(CD) = $\frac{2-26}{18-26}$

m(CD) = $\frac{-24}{-8}$

m(CD) = 3

Since the two slopes - m(AB) and m(CD) slopes are equal to 3, the quadrilateral ABCD is a trapezoid.

5 0

3 years ago

a baseball diamond is a square with sides of 90 feet. What is the shortest distance, to the nearest tenth of a foot, between fir

nika2105 [10]

<span>127.3 feet This problem requires the use of pythagoras theorem. Ignore the face that it's a baseball diamond. All you're concerned with is that you have a square that's 90 feet per side and you want to know what the length of the diagonal. So you have a right triangle with 2 sides of 90 feet each and you want to know the length of the hypotenuse. The formula is C^2 = A^2 + B^2 Both A and B are 90, so plugging them into the formula gives C^2 = 90^2 + 90^2 = 8100 + 8100 = 16200 So C^2 = 16200 Take the square root of both sides C = 127.2792 Round to the nearest tenth, giving C = 127.3</span>

7 0

3 years ago

Answer fast!!!!!!!!!!!

solmaris [256]

B.) is the answer........
.because the object is in axonometry, and the front view will be a square

4 0

4 years ago

Find the sum: 58.823 + 0.001

yarga [219]

The answer is A. just go by your placements

4 0

3 years ago

Read 2 more answers