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3 years ago

select all the sets that are the three side lengths of right triangles A.8,7,15 B.4, 10, √84 C. √8, 11, √129 D. √1, 2, √3

Mathematics

1 answer:

Semenov [28]3 years ago

4 0

Answer:

Step-by-step explanation:

For any set of three side length of a triangle to be a right angled triangle, the sum of the square of the two of the sides must be equal to the square of the longest side according to pythagoras theorem.

The longest side is always the hypotenuse

For option D, 2 will be the longest side. Since 2 is the hypotenuse, the sum of the square of other two values must be equivalent to the square of 2,

$= (\sqrt{1})^{2} + (\sqrt{3})^{2} \\ = 1=3\\= 4\\= 2^{2} (hypotenuse)$

This shows that √1, 2, √3 are three sides of a right triangles.

Similarly for option C, the hypotenuse is √129 being the largest.

To show the sides are that of a right triangles;

$= (\sqrt{8}) ^{2} + 11^{2} \\= 8 + 121\\= 129\\= (\sqrt{129})^{2} \\$

Since the resulting value is the square of the hyp, then √8, 11, √129 are three sides of a right triangles.

For option B; 10 is the hypotenuse being the longest sides, To show the sides are that of a right triangles;

$=4^{2}+(\sqrt{84})^{2} \\ = 16+84\\= 100\\= 10^{2}$

Since the resulting value is the square of the hyp, then 4, 10, √84 are three sides of a right triangles.

Only option A is wrong since 15² is not equal to the sum of 8² and 7².

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I know you want to answer this question.

Alik [6]

Answer:

D. x = 3

Step-by-step explanation:

$\frac{1}{2} ^{x-4}$ - 3 = $4^{x-3}$ - 2

First, convert $4^{x-3}$ to base 2:

$4^{x-3}$ = $(2^{2})^{x-3}$

$\frac{1}{2} ^{x-4}$ - 3 = $(2^{2})^{x-3}$ - 2

Next, convert $\frac{1}{2} ^{x-4}$ to base 2:

$\frac{1}{2} ^{x-4}$ = $(2^{-1})^{x-4}$

$(2^{-1})^{x-4}$ - 3 = $(2^{2})^{x-3}$ - 2

Apply exponent rule: $(a^{b})^{c}$ = $a^{bc}$ :

$(2^{-1})^{x-4}$ = $2^{-1*(x-4)}$

$2^{-1*(x-4)}$ - 3 = $(2^{2})^{x-3}$ - 2

Apply exponent rule: $(a^{b})^{c}$ = $a^{bc}$ :

$(2^{2})^{x-3}$ = $2^{2(x-3)}$

$2^{-1*(x-4)}$ - 3 = $2^{2(x-3)}$ - 2

Apply exponent rule: $a^{b+c}$ = $a^{b}$ $a^{c}$ :

$2^{-1(x-4)}$ = $2^{-1x}$ * $2^{4}$ , $2^{2(x-3)}$ = $2^{2x}$ * $2^{-6}$

$2^{-1 * x}$ * $2^{4}$ - 3 = $2^{2x}$ * $2^{-6}$ - 2

Apply exponent rule: $(a^{b})^{c}$ = $a^{bc}$ :

$2^{-1x}$ = $(2^{x})^{-1}$ , $2^{2x}$ = $(2^{x})^{2}$

$(2^{x})^{-1}$ * $2^{4}$ - 3 = $(2^{x})^{2}$ * $2^{-6}$ - 2

Rewrite the equation with $2^{x} = u$ :

$(u)^{-1}$ * $2^{4}$ - 3 = $(u)^{2}$ * $2^{-6}$ - 2

Solve $u^{-1}$ * $2^{4}$ - 3 = $u^{2}$ * $2^{-6}$ - 2:

$u^{-1}$ * $2^{4}$ - 3 = $u^{2}$ * $2^{-6}$ - 2

Refine:

$\frac{16}{u}$ - 3 = $\frac{1}{64}$ $u^{2}$ - 2

Add 3 to both sides:

$\frac{16}{u}$ - 3 + 3 = $\frac{1}{64}$ $u^{2}$ - 2 + 3

Simplify:

$\frac{16}{u}$ = $\frac{1}{64}$ $u^{2}$ + 1

Multiply by the Least Common Multiplier (64u):

$\frac{16}{u}$ * 64u = $\frac{1}{64}$ $u^{2}$ + 1 * 64u

Simplify:

$\frac{16}{u}$ * 64u = $\frac{1}{64}$ $u^{2}$ + 1 * 64u

Simplify $\frac{16}{u}$ * 64u:

1024

Simplify $\frac{1}{64}$ $u^{2}$ * 64u:

$u^{3}$

Substitute:

1024 = $u^{3}$ + 64u

Solve for u:

u = 8

Substitute back u = $2^{x}$ :

8 = $2^{x}$

Solve for x:

x = 3

4 0

3 years ago

How many pairs of parallel line does a triangle have

sammy [17]

Answer:

None.

Step-by-step explanation:

A triangle has 3 sides so any pair of parallel lines is impossible.

3 0

3 years ago

Read 2 more answers

XY and BD are parallel lines.

tia_tia [17]

Answer:

a) Angle XBC = 55° because corresponding angles are equal.

b) Angle BXC = 70°

Step-by-step explanation:

The image of the complete question is attached to this solution.

a) Angle XBC = 55° because....

Line XY and BD are parallel.

A straight line, AB, crosses the two parallel lines, thereby making angles AXY and XBC corresponding angles because they occupy the same relative position at points where the straight line, AB, intersects the two lines XY and BD.

Since the two lines, XY and BD, are parallel, the corresponding angles related to them are said to be equal.

b) Angle BXC

Since we have found and confirmed that angle XBC is truly 55°.

Triangle BXC is an isosceles triangle, with sides BX and XC equal, the base angles XBC and BCX are both equal.

Angle XBC = Angle BCX = 55° (base angles of an isosceles triangle are equal)

Then, the sum of angles in a triangle = 180°

Hence,

(Angle XBC) + (Angle BCX) + (Angle BXC) = 180° (sum of angles in a triangle)

55° + 55° + Angle BXC = 180°

Angle BXC = 180° - 110° = 70°

Hope this Helps!!!

3 0

4 years ago

the length and width of a rectangle are whole numbers of centimeters. neither is divide by 6.the area of the rectangle is 36 squ

liraira [26]

Note that

36=1·36;
36=2·18;
36=3·12;
36=4·9;
36=6·6.

If neither (length and width) is divide by 6, then cases 1, 2, 3 and 5 are extra, because

36:6=6 (is divide by 6);
18:6=3 (is divide by 6);
12:6=2 (is divide by 6);
6:6=1 (is divide by 6).

The only possible dimensions are: width - 4 cm and length - 9 cm.

Then the perimeter is

$P=4+9+4+9=26$ cm.

Answer: 26 cm.

3 0

3 years ago

A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is appro

Pavel [41]

Answer:

The answers to the questions are

(a) P = 0.0176

(b) P = 0.5

Step-by-step explanation:

The P value is the calculated probability of obtaining extreme reults which are as extreme as observed res ult when the study null hypothesis H₀ is true

The p value is given by

P ( $\overline{\rm x}$ = 185 when μ = 175)