Two of the sides of a right triangle are 8 and 6 units long. How long is the third side? Find all possible answers.

Answer:

The student make an error in step 4.

Step-by-step explanation:

Given : A student solved for the radius of a circle with a circumference of 12π.

To find : In which step did the student make an error?

Solution :

Let us write each step to find the radius of a circle from its circumference

Step 1 - Circumference of circle,

[tex]C=2\pi r[/tex]

Step 2 - Substitute the given circumference,

[tex]12\pi= 2\pi r[/tex]

Step 3 - Divide both sides by 2π,

[tex]\frac{12\pi }{2\pi }=\frac{2\pi r}{2\pi }[/tex]

Step 4 - Solve

[tex]6=\pi r[/tex] , it is incorrect as π  get cancelled

Correct step is  [tex]6=r[/tex]

The radius of the circle is 6 cm.

Step 5 - [tex]\frac{6}{\pi }=\frac{\pi r}{\pi}[/tex]

Step 6 -  [tex]\frac{6}{\pi }=r[/tex]

The student made a mistake in step 4 so step 5 and 6 is automatically invalid.

Therefore, the student make an error in step 4.

Answer:

2+2 is 4

Step-by-step explanation:

-1 is 3 quick maths

Answer:

(- 2, 5 )

Step-by-step explanation:

Under a reflection in the line y = x

a point (x, y ) → (y, x ), thus

(5, - 2 ) → (- 2, 5 )

Answer:

That would be -5, -2

Step-by-step explanation:

Answer:

504 in³

Step-by-step explanation:

this is a rectangular prism and the volume formula is v = l * h * w

so now

v = l*w*h

v= 6*8*12

v = 576 inch³

that's not the answer, that's the volume for whole thing but there is a gap and we have to subtract it from the whole volume. you can look at the option and say it's 504 inch³ from common sense. here is the work:

the gap has 2 inch length, 6 inch width and 6 in height.

v = l*h*w

v = 6 * 2 * 6

v= 72 inch

now subtract the gap volume from total volume so

576 - 72 = 504 in³

Answer:

The answer is B.

Step-by-step explanation:

B. No, because they have a different radius length.

The two spheres are not congruent because they have a different radius length.

If two shapes are similar in size and shape, they are congruent. We can also state that if two shapes are congruent, then their mirror images are identical.

Given:

Sphere 1: Diameter = 12 cm

Sphere 2: Radius = 7 cm

The radius of Sphere 1 is 6 cm and sphere 2 is 7 cm and they are not equal.

Also, Volume of Sphere 1= 4/3 πr³

                                          =904.32 cm³

and, Volume of Sphere 2 = 4/3 πr³

                                          = 1,436.02 cm³

Learn more about Congruency here:

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Answer:

Option C, x = 6

Step-by-step explanation:

Step 1:  Divide both sides by -8

[tex]-8x = -48[/tex]

[tex]-8x / -8 = -48/-8[/tex]

[tex]x=6[/tex]

Answer:  Option C, x = 6

Answer:

x = 6

Step-by-step explanation:

Let's solve your equation step-by-step.

−8x = −48

Step 1: Divide both sides by -8.

−8x /−8  =  −48 /−8

x = 6

Answer:

l = 14 ft

Step-by-step explanation:

S = 112π ft²

πrl = 112π

π*8*l = 112π

[tex]l=\frac{112*\pi}{\pi*8}\\\\l=\frac{112}{8}\\\\[/tex]

l = 14 ft

Answer:

7 units

Step-by-step explanation:

Answer:

A: s=75w

B: s= 75(16)

s=1200

Step-by-step explanation:

equation of line has form of y=kx±b, so

Answer: C

Answer:

C

Step-by-step explanation:

i'm doing a test right now on this question

Answer: C

Step-by-step explanation:

The arc length, s, equals the radius, r, times the central angle, θ, given in radians. (In shorthand, s=r⋅θ.) If r=5 cm and θ=6 radians, the arc length is 5 cm⋅6=30 cm. If r=7 cm and θ=5 radians, the arc length is 7 cm⋅5=35 cm. If r=9 cm and θ=4 radians, the arc length is 9 cm⋅4=36 cm. An angle of 180∘ is π radians, or about 3.14. If r=10 cm, the arc length is 10 cm⋅3.14=31.4 cm. Of these choices, the longest arc is 36 cm.

Answer:

3) 3(5/12) = 5/4 hour = 1 1/4 hours

Answer: The answer is x=9

(PLEASE VOTE ME BRAINLIEST. I NEED TO LEVEL UP LOL)

Answer: -x^2+3x+7

Step-by-step explanation:

this is the explanation

Step-by-step explanation:

5x=75

22+5x=97

11y-5=106

7y+13=83

to conclude it all adds up to 360

360=83+106+97+75

Answer:

5.7

Step-by-step explanation:

pythagorean theorem

A^2 + B^2 = C^2

sub in

A^2 + 7^2 = 9^2

simplify

A^2 + 49 = 81

solve

A^2 = 32

solve further

A = [tex]\sqrt{32[/tex]

use calculator and get:

5.65685

round and get:

5.7

Answer:

TS = 11.

Step-by-step explanation:

Consider triangles UTO and UCS.

m < C = m < UTO (Given)

< U is common to both triangles.

Therefore triangles UTO and OCS are similar.

So  corresponding sides are in the same ratio and:

5 / (TS + 4) = 4/ (7+5)

5 * (7 + 5) = 4(TS + 4)

TS + 4 =   5*12 / 4

TS + 4 = 15

TS = 11.

Your answer here is

C. nx 0.14

Answer:

Common ratio = -8

Step-by-step explanation:

The common ratio of the geometric sequence will be - 8.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The geometric sequence is,

⇒ 3/8, -3, 24, - 192,

Now,

Since, The geometric sequence is,

⇒ 3/8, -3, 24, - 192,

Hence, The common ratio = Second term ÷ First term

                                         = - 3 ÷ 3/8

                                         = - 3 × 8/3

                                         = - 8

Thus, The value of common ratio = - 8

Learn more about the divide visit:

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Answer:

d = 2 km

Step-by-step explanation:

The diameter is twice the radius

d= 2r

We know the radius is 1 km

d = 2* 1 km

d = 2 km

Answer:

The diameter is 2 km.

Step-by-step explanation:

Diameter = radius * 2.

Answer:

14

Step-by-step explanation:

the distance between -6 and 8

6 + 8

= 14

Thus, the distance between -6 and 8 is 14

Based on the calculations, the measure of arc LP is equal to 17°.

In Mathematics and Geometry, a perpendicular bisector is a segment, or ray that bisects a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.

Based on the definition of a perpendicular bisector, we can logically deduce that the two larger arcs have the same measure;

mLM = mNP

8x - 56 = 5x + 22

8x - 5x = 22 + 56

3x = 78

x = 78/3

x = 26°

Since the sum of all the four (4) arcs form a full circle, we would set up an equation and equate it to 360 degrees;

mLM + mNP + mMN + mLP = 360°

8x - 56 + 5x + 22 + 39 + mLP = 360°

8(26) - 56 + 5(26) + 22 + 39 + mLP = 360°

152 + 152 + 39 + mLP = 360

mLP = 360 - 343

mLP = 17°

Missing information:

The question is incomplete and the missing figure is shown in the attached picture.

Answer:

-80

Step-by-step explanation:

We have: -6 = [tex]\frac{x}{8}[/tex] + 4. In order to solve for x, we need to isolate it; in order to isolate x, we have to "undo" order of operations.

The regular order of operations is PEMDAS: parentheses, exponents, multiplication, division, addition, subtraction.

Here, since we're solving for x, we need to go backwards. So, first, subtract 4 from both sides:

-6 - 4 = [tex]\frac{x}{8}[/tex] + 4 - 4  ⇒  -10 = [tex]\frac{x}{8}[/tex]

Then, multiply by 8 on both sides:

-10 * 8 = [tex]\frac{x}{8}[/tex] * 8  ⇒  x = -80

Thus, x = -80.

Hope this helps!

Answer:

x = -80

Step-by-step explanation:

Alright let's get started!

Rewrite the equation as ,

x/8 + 4 = -6

Move all terms not containing x to the right side of the equation.

(Subtract 4 from both sides of the equation.)

x/8 = -10

Multiply both sides of the equation by 8 to get rid of the denominator,

8 * x/8 = -10 * 8

8 cancels out on the left side,

x = -80

Answer:

23 degrees

Step-by-step explanation:

We see that arc LM is 67 degrees. By definition, that means that the central angle <LPM also equals 67 degrees.

We also see that arc LMO is just a semicircle, which means that it is 180 degrees, by definition (because a whole circle is 360 degrees and a semicircle is just half a circle). In addition, angle MPN has that little square in its angle, which means that it is 90 degrees. By definition, its arc MN is also equal to 90 degrees. Then:

Arc LMO = arc LM + arc MN + arc ON

180 = 67 + 90 + arc ON

Solving, we get that arc ON = 180 - 67 - 90 = 23 degrees. By definition, that means the corresponding central angle <NPO is also equal to 23 degrees.

Notice that angles NPO and KPL are vertical angles, which means that by definition, they are equal in degree measure. So, since <NPO = 23, then <KPL = 23. Arc KL is the corresponding arc of <KPL, so by definition, arc KL is also 23 degrees.

Thus, the answer is 23 degrees.

Hope this helps!

Answer:

23°

Step-by-step explanation:

Angle KL = Angle MK - Angle ML

= 90 - 67

= 23

Answer:

Positive Slope-A positive slope means that two variables are positively related—that is, when x increases, so does y, and when x decreases, y decreases also. Graphically, a positive slope means that as a line on the line graph moves from left to right, the line rises. Another words, the line goes up.

Negative Slope-A line with a negative slope is a line that is trending downward from left to right. In other words, the line's rise to run ratio is a negative value. Or the line goes down

Undefined Slope- An undefined slope is the slope of a vertical line! The x-coordinate never changes no matter what the y-coordinate is.

Zero Slope-A zero slope is just the slope of a horizontal line. The y-coordinate never changes no matter what the x-coordinate is.

Step-by-step explanation:

Hope this helped

Answer:

I'd say 16 meters since that's the height when they started on the roof. I don't know where you got 25. That's the highest the balloon went.

Answer:

5 =  (x - 2)^2

Step-by-step explanation:

sqrt(5) = x - 2

Square each side

(sqrt(5))^2 = (x - 2)^2

5 =  (x - 2)^2

Okay this is easier than you think!

if (x - 2) equals [tex]\sqrt{5}[/tex]

then that means  [tex](x-2)^{2}[/tex] = [tex]\sqrt{5} ^ {2}[/tex]

Anything under a square root when sqared, is itself

[tex]\sqrt{5} ^{2} = 5[/tex]

so the value of [tex](x-2)^{2}[/tex] = 5

I hope I helped! Comment if you have questions or vote this answer as the brainliest ! :)

Given:

The length of a basketball court is twice its  width.

The perimeter of the perimeter is 150 feet.

To find the length and width of the basketball court.

Formula

The perimeter of the rectangle is

[tex]P = 2(l+b)[/tex]

where, l be the length of the rectangle and

b be the width of the rectangle.

Now,

As per the problem,

Let, the width be [tex]x[/tex], so the length be [tex]2x[/tex]

So,

The perimeter is = [tex]2(x+2x) = 6x[/tex]

According to the problem,

[tex]6x = 150\\or, x = \frac{150}{6}[/tex]

[tex]or, x = 25[/tex]

Therefore,

the width of the court is 25 ft and length = 2×25 = 50 ft

Hence,

The length and width of the basketball court is 50 ft and 25 ft respectively.

Final answer:

The width of the basketball court is 25 feet and the length is 50 feet.

Explanation:

Let's assume the width of the basketball court is 'x' feet. Since the length is twice the width, we can say the length is '2x' feet.

The perimeter of a rectangle is calculated by adding all of its sides. So, in this case, we have 2 lengths and 2 widths.

Perimeter = 2(length) + 2(width)

Given that the perimeter is 150 feet, we can write the equation: 150 = 2(2x) + 2(x)

Simplifying the equation, we get: 150 = 6x

Dividing both sides by 6, we find: x = 25

Therefore, the width of the basketball court is 25 feet and the length is 2x, which is 2 * 25 = 50 feet.

Since you know the value of x, you can substitute/plug it into the equation to find the value of y:

y = 2x + 5      Plug in 1 into "x" since x = 1

y = 2(1) + 5

y = 7

When x = 1, y = 7 -->  (x, y) = (1, 7)       Your answer is #4