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2 years ago

one side of a right angled triangle is 10cm the other two are both of length x calculate x to 2 decimal place

Mathematics

1 answer:

shepuryov [24]2 years ago

8 0

Answer: $x = 7.07$

Step-by-step explanation:

Using Pythagoras theorem , since it is a right angled triangle ,

side 1 = 10cm

side 2 = x cm

side 3 = x cm

Pythagoras theorem states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides. That is

$10^{2}=x^{2} +x^{2}$

100 = $2x^{2}$

divide through by 2 , we have

50 = $x^{2}$

find the square root of both sides

$x = \sqrt{50}$

$x = 7.07$

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Which sequence could be partially defined by the recursive formula f (n + 1) = f(n) + 2.5 for n ≥ 1?

horrorfan [7]

Option C: –10, –7.5, –5, –2.5, … is the sequence that could be partially defined by the recursive formula $f(n+1)=f(n)+2.5$

Explanation:

The given recursive formula is $f(n+1)=f(n)+2.5$ for $n\geq 1$ and $f(1)=-10$

We need to determine the sequence.

The sequence can be determined by substituting n = 1, 2, 3, 4,....

2nd term of the sequence:

Substituting n = 1 in the formula $f(n+1)=f(n)+2.5$ , we get,

$f(1+1)=f(1)+2.5$

Simplifying, we have,

$f(2)=-10+2.5=-7.5$

Thus, the 2nd term of the sequence is -7.5

3rd term of the sequence:

Substituting n = 2 in the formula $f(n+1)=f(n)+2.5$ , we get,

$f(2+1)=f(2)+2.5$

Simplifying, we have,

$f(3)=-7.5+2.5=-5$

Thus, the 3rd term of the sequence is -5

4th term of the sequence:

Substituting n = 3 in the formula $f(n+1)=f(n)+2.5$ , we get,

$f(3+1)=f(3)+2.5$

Simplifying, we have,

$f(4)=-5+2.5=-2.5$

Thus, the 4th term of the sequence is -2.5

Therefore, the sequence is –10, –7.5, –5, –2.5, …

Hence, Option C is the correct answer.

3 0

1 year ago

Figure ABCD is transformed to obtain figure A'B'C'D': A coordinate grid is shown from negative 6 to 6 on both axes at increments

nika2105 [10]

Given:

Vertices of ABCD are A(-4,4), (-2,2), C(-2,-1) and D(-4,1).

Vertices of A'B'C'D' are A'(3,-4), B'(5,-2), C'(5,1) and D'(3,-1).

To find:

The sequence of transformations that changes figure ABCD to figure A'B'C'D'.

Solution:

Part A:

The figure ABCD reflected across the x-axis, then

$(x,y)\to (x,-y)$

Using this rule, we get

$A(-4,4)\to A_1(-4,-4)$

Similarly, the other points are $B_1(-2,-2),C_1(-2,1),D_1(-4,-1)$ .

Then figure translated 7 units right to get A'B'C'D'.

$(x,y)\to (x+7,y)$

$A_1(-4,-4)\to A'(-4+7,-4)=A'(3,-4)$

Similarly, the other points are $B'(5,-2), C'(5,1),D'(3,-1)$ .

Therefore, the figure ABCD reflected across the x-axis and then translated 7 units right to get A'B'C'D'.

Part B:

Reflection and translation are rigid transformation, it means shape and size of figures remains same after reflection and translation.

Therefore, the two figures congruent.

8 0

2 years ago

A composite figure is comprised of a square, trapezoid, and a rectangle. The square has side lengths of 10 centimeters. The trap

Evgesh-ka [11]

The area of the composite figure is 264 square centimeters, if a composite figure comprised of a square, trapezoid and a rectangle.

Step-by-step explanation:

The given is,

Dimensions of square has length of 10 cm

Trapezoid has base lengths of 8 cm and 14 cm

The length of the trapezoid is 4 cm

Rectangle has side length of 20 cm and 6 cm

Step:1

Area of composite figure = Area of square + Area of Trapezoid

+ Area of rectangle.......................(1)

Step:2

Formula for area of square,

$A_{square} = a^{2}$

where, a - side of length = 10 cm

$=10^{2}$

$=100$

Area of square, $A_{square}$ = 100 Square centimeter

Step:3

Formula for area of Trapezoid,

$A_{Trapezoid}$ = $\frac{a+b}{2} h$ .......................................(2)

Where, a - 8 cm

b - 14 cm

h - 4 cm

From equation (2)

= $\frac{8+14}{2} 4$

= $(11)(4)$

= 44

Area of Trapezoid, $A_{Trapezoid}$ = 44 square centimeters

Step:4

Formula for area of rectangle,

$A_{Rectangle} =lb$ ......................................(3)

Where, l = 20 cm

b = 6 cm

Equation (3) becomes,

$= (20)(6)$

= 120

Area of rectangle, $A_{Rectangle}$ = 120 square centimeters

Step:5

From Equation (1),

$A_{Composite}$ = 100 + 44 + 120

= 264 square centimeters

Result:

The area of the composite figure is 264 square centimeters, if a composite figure comprised of a square, trapezoid and a rectangle.

4 0

2 years ago

Read 2 more answers

A researcher carefully calculates the correlation coefficient and gets a value of r=1.23. What does this value mean?

Vaselesa [24]

Answer: An error was made! All correlation coefficients: -1 ≤ r ≤ 1.

4 0

1 year ago

The formula P = 0.68x2 - 0.048x + 1 models the approximate population P, in thousands, for a species of fish in a local pond, x

marshall27 [118]

Answer:

The answer to your question is 2184

Step-by-step explanation:

Data

Equation P(x) = 0.68x² - 0.048x + 1

x = years

population = 33984

Process

1.- Substitute the population in the equation

33984 = 0.84x² - 0.048x + 1

2.- Equal to zero

0.84x² - 0.048x + 1 - 33984 = 0

3.- Simplify

0.84x² - 0.048x - 33983 = 0

4.- Solve for x

$x = \frac{0.048 +- \sqrt{(0.048^{2}) - (4)(0.84)(-33982)}}{2(0.84)}$

$x = \frac{0.048 +- \sqrt{337.9}}{1.68}$

x1 = 201.2

x2 = -201.2

Only x1 is correct because time can not be negative

5.- Calculate the year

Year = 1997 + 201

Year = 2184

8 0

1 year ago