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g100num [7]
3 years ago
5

What is the length of the diagonal of the rectangle? Round to two decimal places

Mathematics
1 answer:
yan [13]3 years ago
3 0

Answer:

Option C

Step-by-step explanation:

By the property of a rectangle,

"All interior angles of a rectangle measure 90°"

Therefore, m∠ABC = 90°

By applying cosine rule in the right triangle ABC,

cos(∠CAB) = \frac{\text{Adjacent side}}{\text{Hypotenuse}}

cos(25°) = \frac{AB}{AC}

AC = \frac{AB}{\text{cos}(25)}

AC = \frac{18}{\text{cos}(25)}

AC = 19.86

Therefore, Option C will be the answer.

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yanalaym [24]

Answer: 135.42

Step-by-step explanation:

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3 years ago
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(I REALLY NEED HELP, I'M STUCK, PLEASE EXPLAIN YOUR ANSWER!!!)
Papessa [141]
A) x ≈ 9.3 or x≈ -6.3
B) x ≈ 3.2 or x ≈ -4.7
C) x ≈ 6.4 or x ≈ -9.4

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2 years ago
Five times the sum of a number and 27 is greater than or equal to six times the sum of that
AleksAgata [21]

The complete version of question:

<em>Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26. What is the solution of this problem.</em>

Answer:

5\left(x+27\right)\ge \:6\left(x+26\right)\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-21\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-21]\end{bmatrix}

Step-by-step explanation:

As the description of the statement is:

'<em>Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26'.</em>

<em />

As

  • <em>Five times the sum of a number and 27  </em>is written as: 5(x + 27)
  • <em>greater than or equal </em>is written as:  \geq
  • <em>six times the sum of that number and 26'  </em>is written as: 6(x + 26)

so lets combine the whole statement:

<em />5\left(x\:+\:27\right)\ge \:6\left(x\:+\:26\right)<em />

solving

<em />5\left(x\:+\:27\right)\ge \:6\left(x\:+\:26\right)<em />

<em />5x+135\ge \:6x+156<em />

<em />5x+135-135\ge \:6x+156-135<em />

<em />5x\ge \:6x+21<em />

<em />5x-6x\ge \:6x+21-6x<em />

<em />-x\ge \:21<em />

<em />\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}<em />

<em />\left(-x\right)\left(-1\right)\le \:21\left(-1\right)<em />

<em />x\le \:-21<em />

Therefore,

5\left(x+27\right)\ge \:6\left(x+26\right)\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-21\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-21]\end{bmatrix}

6 0
3 years ago
A square fits exactly inside a circle with all of its vertices being on the circumference of the circle.
anygoal [31]

The side of the square is 5.9 cm

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

Area of the circle = 56 square cm

Side of the square= x

Area = π(r x r)

56 = π (r x r)

√17.83 = r

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Diameter = 8.44cm

The diameter is equal to the diagonal of the square.

8.44 = x√2

x = 8.44/√2

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The side of the square is 5.9 cm

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Farmer had 612 tomatoes, he put them in baskets of 100..how many baskets did he fill completely?
julsineya [31]
612/100 = 6 with 12 remaining so he filled 6 baskets completely and he is left with 12 tomatoes.
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