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o-na [289]
3 years ago
9

Write a power represented with a positive base and a positive exponent whose value is less then the base

Mathematics
1 answer:
sasho [114]3 years ago
6 0

Answer:

The question is open ended as i suppose since there are infinitely many possibilities. one possible form of the solution can be 5^{2}

Step-by-step explanation:

The base in this case is 5 while the exponent is simply the power to which the base is raised in which case it would be 2. Both values are positive and the exponent is less than the base.

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Fabienne rolls a ball 72 inches across the floor. This is 9 times the distance that Olivier rolls his ball across the floor. Let
RoseWind [281]

Answer:

8 inches

Step-by-step explanation:

Oliver rolls his ball 1/9th of the distance Fabienne rolls his, so just divide 72 by 9 to get your answer.

8 0
2 years ago
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What is 10.9091% to 2 decimal places
Tom [10]

Answer:

10.91%

Step-by-step explanation:

Take your number: 10.9091

Now find the first 3 decimals: 10.<u>909</u>

If the last (3rd) decimal is 5 or more raise the 2nd decimal: 10.9<u>09</u> → 10.9<u>1</u>

That is 2 decimal places

(if your teacher doesn't want it rounded then just 10.90%)

4 0
2 years ago
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Tomika heard that the diagonals of a rhombus are perpendicular to each other. Help her test her conjecture. Graph quadrilateral
Stella [2.4K]

Answer:

a. The four sides of the quadrilateral ABCD are equal, therefore, ABCD is a rhombus

b. The equation of the diagonal line AC is y = 5 - x

The equation of the diagonal line BD is y = 5 - x

c. The diagonal lines AC and BD of the quadrilateral ABCD are perpendicular to each other

Step-by-step explanation:

The vertices of the given quadrilateral are;

A(1, 4), B(6, 6), C(4, 1) and D(-1, -1)

a. The length, l, of the sides of the given quadrilateral are given as follows;

l = \sqrt{\left (y_{2}-y_{1}  \right )^{2}+\left (x_{2}-x_{1}  \right )^{2}}

The length of side AB, with A = (1, 4) and B = (6, 6) gives;

l_{AB} = \sqrt{\left (6-4  \right )^{2}+\left (6-1  \right )^{2}} = \sqrt{29}

The length of side BC, with B = (6, 6) and C = (4, 1) gives;

l_{BC} = \sqrt{\left (1-6  \right )^{2}+\left (4-6  \right )^{2}} = \sqrt{29}

The length of side CD, with C = (4, 1) and D = (-1, -1) gives;

l_{CD} = \sqrt{\left (-1-1  \right )^{2}+\left (-1-4  \right )^{2}} = \sqrt{29}

The length of side DA, with D = (-1, -1) and A = (1,4)   gives;

l_{DA} = \sqrt{\left (4-(-1)  \right )^{2}+\left (1-(-1)  \right )^{2}} = \sqrt{29}

Therefore, each of the lengths of the sides of the quadrilateral ABCD are equal to √(29), and the quadrilateral ABCD is a rhombus

b. The diagonals are AC and BD

The slope, m, of AC is given by the formula for the slope of a straight line as follows;

Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}

Therefore;

Slope, \, m_{AC} =\dfrac{1-4}{4-1} = -1

The equation of the diagonal AC in point and slope form is given as follows;

y - 4 = -1×(x - 1)

y = -x + 1 + 4

The equation of the diagonal AC is y = 5 - x

Slope, \, m_{BD} =\dfrac{-1-6}{-1-6} = 1

The equation of the diagonal BD in point and slope form is given as follows;

y - 6 = 1×(x - 6)

y = x - 6 + 6 = x

The equation of the diagonal BD is y = x

c. Comparing the lines AC and BD with equations, y = 5 - x and y = x, which are straight line equations of the form y = m·x + c, where m = the slope and c = the x intercept, we have;

The slope m for the diagonal AC = -1 and the slope m for the diagonal BD = 1, therefore, the slopes are opposite signs

The point of intersection of the two diagonals is given as follows;

5 - x = x

∴ x = 5/2 = 2.5

y = x = 2.5

The lines intersect at (2.5, 2.5), given that the slopes, m₁ = -1 and m₂ = 1 of the diagonals lines satisfy the condition for perpendicular lines m₁ = -1/m₂, therefore, the diagonals are perpendicular.

5 0
3 years ago
It costs a lumberyard $2.05 per cubic foot of lumber. If they sell the lumber back to their customers for $21.98 per cubic foot
adelina 88 [10]

Answer:

The profit per year will be $23916

Step-by-step explanation:

Cost price of 1 ft³ = $2.05

Selling price of 1 ft³ = $21.98

Profit = Selling price - cost price

profit = $21.98 - $2.05

Profit = $19.93

Profit on 1 ft³ is $19.93

If they sell 100 monthly, per year (12 months), profit will be

19.93*100*12

= $23916

7 0
3 years ago
8. Which animal is closest to sea level?<br> Shark -7<br> Sea Lion -10<br> Seagull 24<br> Turtle -6
Cloud [144]
The answer is Turtle.
6 0
2 years ago
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