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2 years ago

Solve for xxx in the diagram below

Mathematics

1 answer:

IrinaVladis [17]2 years ago

4 0

Answer:

x=20°

Step-by-step explanation:

x° + 100° + 3x° = 180° => 4x°+100°=180° => 4x=180°-100°=80° => x=80° : 4 = 20° => x=20°

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{12,16,5,2} the number of subsets

-Dominant- [34]

Answer:

I believe the answer would be 16 (subsets of a finite set)

7 0

2 years ago

In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If b = 77 centimeters and c = 85

MAVERICK [17]

Answer:

The perimeter of the triangle 198 cm.

Step-by-step explanation:

Given that,

In a right angled triangle, a and b are the length of the legs and c is length of the hypotenuse.

Pythagorean Theorem:

Sum of square of the legs is equal to square of hypotenuse.

∴a²+b²=c²

a= ?, b= 77 cm and c=85 cm

a²+77²=85²

⇒a²+5929=7225

⇒a²=7225-5929

⇒a²= 1296

⇒a = 36 cm

The perimeter of the triangle = sum of all sides

=a+b+c

=(36+77+85) cm

= 198 cm

4 0

2 years ago

Let a and b be roots of x² - 4x + 2 = 0. find the value of a/b² +b/a²

erastovalidia [21]

Answer:

$\dfrac{a}{b^2}+\dfrac{b}{a^2}=10$

Step-by-step explanation:

Given equation: $x^2-4x+2=0$

The roots of the given quadratic equation are the values of x when $y=0$ .

To find the roots, use the quadratic formula:

$x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0$

Therefore:

$a=1, \quad b=-4, \quad c=2$

$\begin{aligned}\implies x & =\dfrac{-(-4) \pm \sqrt{(-4)^2-4(1)(2)}}{2(1)}\\& =\dfrac{4 \pm \sqrt{8}}{2}\\& =\dfrac{4 \pm 2\sqrt{2}}{2}\\& =2 \pm \sqrt{2}\end{aligned}$

$\textsf{Let }a=2+\sqrt{2}$

$\textsf{Let }b=2-\sqrt{2}$

Therefore:

$\begin{aligned}\implies \dfrac{a}{b^2}+\dfrac{b}{a^2} & = \dfrac{2+\sqrt{2}}{(2-\sqrt{2})^2}+\dfrac{2-\sqrt{2}}{(2+\sqrt{2})^2}\\\\& = \dfrac{2+\sqrt{2}}{6-4\sqrt{2}}+\dfrac{2-\sqrt{2}}{6+4\sqrt{2}}\\\\& = \dfrac{(2+\sqrt{2})(6+4\sqrt{2})+(2-\sqrt{2})(6-4\sqrt{2})}{(6-4\sqrt{2})(6+4\sqrt{2})}\\\\& = \dfrac{12+8\sqrt{2}+6\sqrt{2}+8+12-8\sqrt{2}-6\sqrt{2}+8}{36+24\sqrt{2}-24\sqrt{2}-32}\\\\& = \dfrac{40}{4}\\\\& = 10\end{aligned}$

6 0

1 year ago

Read 2 more answers

According to the histogram of travel times to work from the US 2000 census (Page 6 of "Journey to Work: 2000"), roughly what per

erastovalidia [21]

Histograms are used to represent data, where the length of each bar represents the frequency of the data element

The histogram is not given; So, I will give a general explanation.

Assume that the number of commuters that travel more than 45 minutes is 450, while the total number of commuters surveyed is 500.

The percentage of commuters that travel more than 45 minutes is the quotient of the commuters that travel more than 45 minutes and the total number of surveyed commuters.

So, we have:

$\%Percentage = \frac{450}{500}$

Divide 450 by 500

$\%Percentage = 0.9$

Express as percentage

$\%Percentage = 90\%$

Hence, the percentage of commuters that travel more than 45 minutes is 90%