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erma4kov [3.2K]
2 years ago
11

Lorna created a sculpture in the shape of a right rectangular prism. The volume of the sculpture is 2014 cubic meters, the lengt

h is 6 meters, and the width is 412 meters.
What is the height of Lorna's sculpture?

Enter your answer as a fraction in simplest form in the box.
Mathematics
1 answer:
Allushta [10]2 years ago
6 0

Answer:

\frac{1007}{1236}

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Write an equation of the line that passes through each points (5,6) (3.4)
ioda

Answer:

y = x + 1.

Step-by-step explanation:

Start by finding the slope of this line.

If a slanting line goes through (x_{0},\, y_{0}) and (x_{1},\, y_{1}), where x_{0} \ne x_{1}, the slope of this line would be:

\begin{aligned}m &= \frac{y_{1} - y_{0}}{x_{1} - x_{0}}\end{aligned}.

The line in this question goes through (5,\, 6) and (3,\, 4). Hence, the slope of this line would be:

\begin{aligned}m &= \frac{y_{1} - y_{0}}{x_{1} - x_{0}} \\ &= \frac{6 - 4}{5 - 3} \\ &= 1\end{aligned}.

If a slanting line with a slope of m and goes through the point (x_{0},\, y_{0}), the equation of this line in the point-slope form would be:

y - y_{0} = m,\, (x - x_{0}).

For the line in this question, the slope is m = 1. Take (5,\, 6) as the chosen point on this line. The point-slope form equation of this line would be:

y - 6 = (x - 5).

Rewrite to obtain the equation of this line in the slope-intercept form:

y = x + 1.

7 0
2 years ago
1a. If
mestny [16]
Idk what the dollar signs or what the letters represent, would help but doesnt make sense
4 0
3 years ago
Read 2 more answers
A waitress sold 11 ribeye steak dinners and 12 grilled salmon​ dinners, totaling ​$560.63 on a particular day. Another day she s
Eduardwww [97]

The cost of each ribeye steak dinner is $ 29 and cost of each grilled salmon dinner is $ 20

<em><u>Solution:</u></em>

Let "a" be the cost of each ribeye steak dinners

Let "b" be the cost of each grilled salmon dinners

<em><u>A waitress sold 11 ribeye steak dinners and 12 grilled salmon​ dinners, totaling ​$560.63 on a particular day</u></em>

Thus we frame a equation as:

11 x cost of each ribeye steak dinners + 12 x cost of each grilled salmon dinners = 560.63

11 \times a + 12 \times b = 560.63

11a + 12b = 560.63 -------- eqn 1

<em><u>Another day she sold 16 ribeye steak dinners and 6 grilled salmon​ dinners, totaling ​$584.46</u></em>

Thus we frame a equation as:

16 x cost of each ribeye steak dinners + 6 x cost of each grilled salmon dinners = 584.46

16 \times a + 6 \times b = 584.46

16a + 6b = 584.46 ------------ eqn 2

<em><u>Let us solve eqn 1 and eqn 2</u></em>

<em><u>Multiply eqn 2 by 2</u></em>

32a + 12b = 1168.92 ------- eqn 3

<em><u>Subtract eqn 1 from eqn 3</u></em>

32a + 12b = 1168.92

11a + 12b = 560.63

( - ) ----------------

21a = 1168.92 - 560.63

21a = 608.29

Divide both sides by 21

a = 28.96 \approx 29

<em><u>Substitute a = 29 in eqn 1</u></em>

11(29) + 12b = 560.63

319 + 12b = 560.63

12b = 560.63 - 319

12b = 214.63

Divide both sides by 12

b = 20.13 \approx 20

Thus cost of each ribeye steak dinner is $ 29 and cost of each grilled salmon dinner is $ 20

5 0
3 years ago
Find two numbers whose difference is 102 and whose product is a minimum. Step 1 If two numbers have a difference of 102, and one
NISA [10]

Answer:

The two numbers would be -51 and 51

Step-by-step explanation:

To find these, first set the equation for the first number as x. You can then set the second number as x + 102. Now, find their product.

x(x + 102) = x^2 + 102x

Now, to find the minimum, find the value of x in the vertex of this equation.

-b/2a = -102/2(1) = -102/2 = -51

So we know -51 is the first number. Now we find the second using the prewritten equation.

x + 102 = -51 + 102 = 51

4 0
3 years ago
What is the surface area of a square pyramid with a height of 12 mm and a base that measures 8 mm on each side?
Nostrana [21]

Answer:

266.39mm²

Step-by-step explanation:

The formula for surface area of a square based pyramid =

S.A = a² + 2a √a²/4 + h²

Where

a = base length = 8mm

s = Height of the pyramid = 12mm

Hence,

S.A = 8² + 2 × 8 × √8²/4 + 12²

S.A = 64 + 16 ×√64/4 + 144

S.A = 80 × √16 + 144

S.A = 80 × √160

S.A = 266.39 mm²

Therefore, the surface area of a square pyramid is 266.39 mm²

8 0
2 years ago
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