Name the marked angle in 2 different ways.

△ABC is a right triangle with right angle C. Side AC is 6 units longer than side BC . If the hypotenuse has length 52–√ units,

Evgesh-ka [11]

Answer:

AC = 7.12 units

Step-by-step explanation:

A right triangle has two legs and a hypotenuse. The hypotenuse is opposite the right angle. As Angle C is the right angle, then the triangle can be constructed as shown in the picture attached. The sides of the triangle have a relationship known as the Pythagorean Theorem a² + b² = c². In the theorem, the legs of the triangle are a and b while the hypotenuse is c. Substitute a = x, b = x+6, and c = √52. Simplify and solve.

a² + b² = c²

x² + (x+6)² = √52²

x² + x² + 12x + 36 = 52

2x² + 12x - 16 = 0

You can use the quadratic formula to solve by substituting a = 2, b = 12, and c = -16.

The quadratic formula is $x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}$ .

Substitute and you'll have:

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a} =\frac{-12+/-\sqrt{12^2-4(2)(-16)} }{2(2)}=\frac{-12+/-\sqrt{144+128} }{4)}$

$\frac{-12+/-\sqrt{272} }{4}=\frac{-12+/-16.5 }{4} = 1.12, 7.13$

Only 1.12 is a solution since 7.13 will not satisfy the Pythagorean theorem

Side AC is 6 units longer than side BC. This means x = BC and AC = x + 6.

AC = 1.12 + 6 = 7.12

6 0

3 years ago

Find the area of the figure.( sides meet at right angles.)

TiliK225 [7]

The answer should be 41 in^2

6 0

3 years ago

Y=4.76x what is the constant of proportionality

zalisa [80]

Answer:

4.76

Step-by-step explanation:

constant of proportionality=slope

slope=m

y=mx+b

m=4.76

4 0

3 years ago

Given the inequality -8 < 2, explain what happens when you multiply or divide both sides by 2 and what happens when you multi

Gnoma [55]

Answer:

The inequality sign remains same while multiply or divide both sides by positive numbers.

The inequality sign changes while multiply or divide both sides by negative numbers.

Step-by-step explanation:

The given inequality is - 8 < 2.

Now, if we multiply 2 in both sides then - 16 < 4

Again, if we divide by 2 into both sides then - 4 < 1

Therefore, the inequality sign remains the same while multiply or divide both sides by positive numbers.

Now, if we multiply -2 in both sides then 16 > -4

And, if we divide -2 into both sides then 4 > -1

Therefore, the inequality sign changes while multiply or divide both sides by negative numbers. (Answer)

3 0

3 years ago

Read 2 more answers

765ab4 is divisible by 36. Compute all ordered pairs (a, b) for which this is possible

tia_tia [17]

Answer:

All the ordered pairs (a,b) are

(0,5), (2,3), (4,1), (6,8), and (8,6).

Step-by-step explanation:

765ab4 to be divisible by 36, it must be divisible by both 9 and 4.

For any number to be divisible by 4, the last two digits of the number must be divisible by 4.

Here, the last two digits are b4, so as the number b4 is divisible by 4, b can be 0,2,4,6, and 8.

For any number to be divisible by 9, the sum of all the digit of the number must be divisible by 9.

Here, the sum of all the digits, S= 7+6+5+a+b+4=22+a+b.

Now, we have b={0,2,4,6, 8}

For b=0,

S=22+a+0=22+a which is a multiple of 9.