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3 years ago

Set up an equation to find the length of the diagonal of the rectangle.

Mathematics

1 answer:

nikklg [1K]3 years ago

4 0

Answer:

Set length as l

Use the Pythagorean Theorem to find the diagonal:

$5^{2} +l^{2} =(\sqrt{125})^{2}\\ 5^{2} +l^{2} =125$

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A car is traveling at a steady speed. It travels 1 3/4 miles in 2 1/3 minutes. How far will it travel in 45 minutes? In 1 hour?

mina [271]

Answer:

33.75 miles in 45 minutes,

45 miles in an hour

Step-by-step explanation:

45 minutes: 2 1/3= 7/3 ---> 7/3*3=7,

1 3/4= 7/4 ---> 7/4*3=5.25

car travels 5.25 miles for every 7 minutes,

45/7*5.25= 33.75 miles

1 hour (60 minutes):

using that the car travels 5.25 miles for every 7 minutes,

60/7*5.25= 45 miles

Hope that makes sense!

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2 years ago

If one gallon of paint covers 825 sq. ft., how much paint is needed to cover 2640 sq. ft.?

Nutka1998 [239]

Answer:

3.2 gallons

Step-by-step explanation:

2640 / 825 = 3.2

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3 years ago

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Please help! I will mark you brainliest if you get the answer correctly , look at the picture.

SVETLANKA909090 [29]

Answer:

12 weeks

Step-by-step explanation:

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3 years ago

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Determine which of the sets of vectors is linearly independent. A: The set where p1(t) = 1, p2(t) = t2, p3(t) = 3 + 3t B: The se

defon

Answer:

The set of vectors A and C are linearly independent.

Step-by-step explanation:

A set of vector is linearly independent if and only if the linear combination of these vector can only be equalised to zero only if all coefficients are zeroes. Let is evaluate each set algraically:

$p_{1}(t) = 1$ , $p_{2}(t)= t^{2}$ and $p_{3}(t) = 3 + 3\cdot t$ :

$\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0$

$\alpha_{1}\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (3 +3\cdot t) = 0$

$(\alpha_{1}+3\cdot \alpha_{3})\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot t = 0$

The following system of linear equations is obtained:

$\alpha_{1} + 3\cdot \alpha_{3} = 0$

$\alpha_{2} = 0$

$\alpha_{3} = 0$

Whose solution is $\alpha_{1} = \alpha_{2} = \alpha_{3} = 0$ , which means that the set of vectors is linearly independent.

$p_{1}(t) = t$ , $p_{2}(t) = t^{2}$ and $p_{3}(t) = 2\cdot t + 3\cdot t^{2}$

$\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0$

$\alpha_{1}\cdot t + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (2\cdot t + 3\cdot t^{2})=0$

$(\alpha_{1}+2\cdot \alpha_{3})\cdot t + (\alpha_{2}+3\cdot \alpha_{3})\cdot t^{2} = 0$

The following system of linear equations is obtained:

$\alpha_{1}+2\cdot \alpha_{3} = 0$

$\alpha_{2}+3\cdot \alpha_{3} = 0$

Since the number of variables is greater than the number of equations, let suppose that $\alpha_{3} = k$ , where $k\in\mathbb{R}$ . Then, the following relationships are consequently found: