Which of the following correctly describes the Pythagorean theorem

1.The sum of the lengths of the legs of a right triangle is equal to the length of the hypotenuse.

2.The sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.

3.The product of the lengths of the legs of a right triangle is equal to the length of the hypotenuse.


4.The product of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.

9514 1404 393

Answer:

  a) interest: $215.33

  b) proceeds: $3584.67

  c) effective rate: 9.01%

Step-by-step explanation:

a) The problem statement tells you the loan was discounted 8.5%. The amount of interest paid is ...

  I = Prt

  I = $3800·0.085·8/12 ≈ $215.33

__

b) The proceeds of the loan are ...

  $3800 -215.33 = $3584.67

__

c) The actual rate is found using the same formula as above, solving for r:

  r = I/(Pt) = $215.33/($3584.67·2/3) ≈ 0.0901 = 9.01%

Answer:

f*g(x) =  -25

Step-by-step explanation:

f*g(x) = f(x) * g(x) = x² * (3x + 14)

f*g(x) = (-5)² * (3*-5 +14) = 25 * (-1) = -25

Answer:

Y=3/7x+8 and y=-7/3x-34/3(11 1/3)

Step-by-step explanation:

for the perpendicular line, the slope is the opposite inverse (3/7) and since 3/7×-7=-3, -3+8=5, hence, y=3/7x+8.

for the parallel line the slope is the same, and since -7/3×-7=49/3,

and 49/3-15/3(5)=34/3, the equation is y=-7/3-34/3

Answer:

D

Step-by-step explanation:

volume=1/2 ×6×8×7=168 units³

Circle B has a diameter that is 1 1/2 times as long as Circle A's diameter. What is the circumference of Circle B? Solution. 4 m. If the diameter ...

Answer:

y=1/3x + 2

Step-by-step explanation:

Since slope intercept form is y=, I first added x to each side to get x on the other side. Then I divided each side by 3 to get y, and ended up with y=1/3x+2 as my answer.

(hope this helps)

Given that,

The given expression is : [tex]16x^0+2x^2{\cdot}y^{-1}[/tex]

To find,

The value of the above expression when x = 2 and y = 4

Solution,

We have,

[tex]16x^0+2x^2{\cdot}y^{-1}[/tex]

Put x = 2 and y = 4 in the above expression.

[tex]16x^0+2x^2{\cdot}y^{-1}\\\\=16\times (2)^0+2(2)^2\times (4)^{-1}\\\\=16\times 1+2(2)^2\times\dfrac{1}{4}\\\\=16+2\\\\=18[/tex]

So, the value of the above expression is 18.

Answer:

D

Step-by-step explanation:

Leave everything the same except you add -5 and 2 =-3

Answer:

Step-by-step explanation:

13) QR ≅ BP   ;  RP ≅ PA ;  PQ ≅ AB

ΔQRP ≅ΔBPA        by Side Side Side Congruent

QR ≅ BP ; ∠R ≅ ∠BPA ;  RP  ≅ PA

ΔQRP ≅ ΔBPA            by Side Angle Side congruent

15) ML ≅ WV ; MX ≅ WX ;  LX ≅ VX;

ΔMLX ≅ ΔWVX    Side side side congruent

∠L ≅ ∠V   ;  ML ≅ WV ; ∠M ≅ ∠W

ΔMLX ≅ ΔWVX    Angle side Angle congruent

Answer:

sin A = sin B = sin C

Step-by-step explanation:

The sine rule is a law which relates all the three sides of a triangle with the sine of their opposite angles in the triangle. Given a triangle with a side of a and an opposite angle of A, side b with opposite angle B and side c with opposite angle C. The sine rule is given as:

[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]

Given that all the side of the triangle have a length of 1, that is a = b = c = 1, hence the equation becomes:

[tex]\frac{sin(A)}{1}=\frac{sin(B)}{1}=\frac{sin(C)}{1}\\\\sin(A)=sin(B)=sin(C)[/tex]

Answer:

sin A = sin B = sin C

Step-by-step explanation:

edg

Answer:

36.5

Step-by-step explanation:

To find the median, list the ages in order from smallest to largest

23, 26 , 26,  35, 38 , 45, 50 ,63

Then find the middle

23, 26 , 26,  35,    38 , 45, 50 ,63

It is halfway between 35 and 38

(35+38)/2 = 36.5

The median is 36.5

Answer:

The answer is 53, C.

Step-by-step explanation:

10 * 5 + 3

50 + 3

53

Step-by-step explanation:

❀ [tex] \underline{ \underline{ \text{Given}}} : [/tex]

❀ [tex] \underline{ \underline{ \text{To \: find}}} : [/tex]

❀ [tex] \underline{ \underline{ \text{Solution}}} : [/tex]

~Plug the value of y at first :

➾ [tex] \sf{ {-4}^{2} + 5 \times (-4 )+ 1}[/tex]

~ Evaluate the power : 4²

➾ [tex] \sf{16 + 5 \times (-4 )+ 1}[/tex]

Follow the BODMAS { Bracket , Of , Division , Multiplication , Addition and Subtraction } rule :

~Multiply -5 and 4

➾ [tex] \sf{16 + (-20)+ 1}[/tex]

~ Multiply the signs : ( + ) and ( - ) :

➾ [tex] \sf{16 - 20 + 1}[/tex]

~Add the numbers : 16 and 1

➾ [tex] \sf{17-20}[/tex]

~ Subtract 20 from 17

➾ [tex] \sf{-3}[/tex]

[tex] \pink{ \boxed{ \boxed{ \tt{⟿ \: Our \: final \: answer : -3}}}}[/tex]

Hope I helped ! ♡

Have a wonderful day / night ツ

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Answer:

y= m(x-x1) +y1

Step-by-step explanation:

that is point slope form

Answer:

answer 4 is correct

y-y1=m(x-x1)

putting value of m that is slope formula .

Answer:

B

Step-by-step explanation:

Answer: 1.3

Step-by-step explanation:

If u subtract 6-4.7 u will get 1.3 and you can also do it for all and u will still get the same answer

==============================================

Explanation:

The phrasing "translated along <4,6>" is another way of saying "shift 4 to the right, shift 6 up"

In general, "translated along <m,n>" is the same as writing [tex](x,y) \to (x+m, y+n)[/tex]. If m is positive, then we shift m units to the right. If m is negative, then we shift to the left. The same story happens with the n, but we focus on the y coordinate.

-------------

With all that in mind, starting at F(-5,-9) and translating along <4,6> has us arrive at (-1, -3). Add 4 to the x coordinate and add 6 to the y coordinate.

We can say

[tex](x,y) \to (x+4,y+6)\\\\(-5,-9) \to (-5+4,-9+6)\\\\(-5,-9) \to (-1,-3)\\\\[/tex]

Showing that (-5,-9) moves to (-1,-3)

This is after the first translation, but there's a second translation.

We'll apply the same idea, but different numbers this time

[tex](x,y) \to (x+3,y+5)\\\\(-1,-3) \to (-1+3,-3+5)\\\\(-1,-3) \to (2,2)\\\\[/tex]

So (-1,-3) moves to (2,2)

Overall we have

Therefore, the original point ends up at (2,2) which is the final answer

--------------

Extra info:

A nice shortcut is that the vectors <4,6> and <3,5> can be added to get <4+3,6+5> = <7,11>. So overall, we're shifting 7 units to the right and 11 units up when we combine the two translation vectors.

Answer:

x²+6x +8 ≥ 195

Step-by-step explanation:

The age of C is represented by  c=  x .

Building B was built two years before building C.

Age of Building B   b = x+ 2

Building D was built two years before building B

Age of Building d= x+4

The product of the building B’s age and building D’s age is at least 195.

b*d ≥ 195

≥ means product is greater than or equal to 195 at least 195

Putting the values of b and d

(x+ 2) (x+4) ≥ 195

It can be further solved

x²+6x +8 ≥ 195

Answer:

x^2+6x+8>195

Step-by-step explanation:

Answer:

11/5-1/2     =    22/10-5/10= 17/10   =   1  7/10

Step-by-step explanation:

The answer is 1  7/10

Answer:

17/10 or in mixed numbers 1 and 7/10

Step-by-step explanation:

So first they both have to share a common denominator which will be 10 so for 11/5 you multiply 2 to the denominator. Whatever you do to the bottom you do to the top so 2 times 11 is 22. For 1/2 you multiply the bottom by 5, whatever you do to the bottom you do to the top so 5 times 1 is 5, everything converted should be 22/10-5/10 and that equals 17/10

Answer:

The answer would be Scale factor of 3

Answer:

Step-by-step explanation:

volume=1/3 πr²h

=1/3×π×3²×4

=12π ft³

≈37.70 ft³

Here we have to calculate the volume of the cone which is provided in the figure.

As we know that volume of cone is calculated by the formula :

Here,

We have :

Putting the values in the formula :

[tex]\longrightarrow \: \sf{V \: = \: \dfrac{1}{3} \: \pi \:r {}^{2}h } \\ \\ \longrightarrow \: \sf{V \: = \: \dfrac{1}{3} \: \times \dfrac{22}{7} \:(3) {}^{2}(4) } \\ \\ \longrightarrow \: \sf{V \: = \: \dfrac{1}{3} \: \times \dfrac{22}{7} \:(3 \times 3)(4) } \\ \\ \longrightarrow \: \sf{V \: = \: \dfrac{1}{3} \: \times \dfrac{22}{7} \:(9)(4) } \\ \\ \longrightarrow \: \sf{V \: = \: \dfrac{1}{3} \: \times \dfrac{22}{7} \: \times 9(4) } \\ \\ \longrightarrow \: \sf{V \: = \: \dfrac{1}{3} \: \times \dfrac{22}{7} \: \times 9 \times 4 } \\ \\ \longrightarrow \: \sf{V \: = \: \dfrac{1}{ \cancel3} \: \times \dfrac{22}{7} \: \times \cancel9 \times 4 } \\ \\ \longrightarrow \: \sf{V \: = \: \dfrac{1}{1} \: \times \dfrac{22}{7} \: \times 3 \times 4 } \\ \\ \longrightarrow \: \sf{V \: = \: \dfrac{22}{7} \: \times 3 \times 4 } \\ \\ \longrightarrow \: \sf{V \: = \: \dfrac{22 \times 3 \times 4}{7} } \\ \\ \longrightarrow \: \sf{V \: = \: \dfrac{66 \times 4}{7} } \\ \\ \longrightarrow \: \sf{V \: = \: \dfrac{264}{7} } \\ \\ \longrightarrow \: \sf{V \: = \: \cancel\dfrac{264}{7} } \\ \\ \longrightarrow \: \underline{\underline{\red{\bf{V \: = \: 37.7 }}}}[/tex]

Answer:

86.6

Step-by-step explanation:

Answer:

First, we know that the function IxI works as follows:

IxI = x   if x ≥ 0

IxI = -x  if x < 0

So IxI is always positive.

then:

a) f(x) = Ix - 2I

this is:

f(x) = (x - 2)           if   (x - 2) ≥ 0

       -(x - 2)          if    (x - 2) < 0

Then the graph of this function will be two lines (where the separation of the lines depends on the vale of x)

For the case of b we have

g(x) = -IxI + 1

then we have:

g(x) = -x + 1          if   x ≥ 0

g(x) = -(-x) + 1       if   x < 0

To graph the functions, you need to graph these lines for the given values of x. You also can see the graphs below. Where the red graph is the one for the point 4a, and the blue graph is the one for point 4b.

Now, let's find the domain and range:

4a) f(x) = Ix  - 2I

The domain is the set of the possible values of x that we can input in that function. For this case, we do not have any value of x that generates a problem (like a zero in a denominator, for example) then the domain is the set of all real numbers:  x ∈ R

The range is the set of the possible values of y.

f(x) = Ix - 2I is always equal or greater than zero (as you can also see in the graph) then the range will be:

R: y ∈ R, such that y ≥ 0.

4b) g(x) = -IxI + 1

Similar as the prior case, here the domain is the set of all real numbers:

D: x ∈ R

For the range, now we have:

y = -IxI + 1

if IxI is always equal or larger than zero, then -IxI is always equal or smaller than zero. If we add a + 1 to that, then the function will be always equal or smaller than 1.

Then the range is:

R: y ∈ R, such that y ≤ 1

Answer:

[tex]\huge\boxed{\sf x = 2 , y = -2}[/tex]

Step-by-step explanation:

The common point where the lines of the two equations meet is exactly the solution of the system of equations.

So,

The common point is (x,y) = (2,-2)

This means that x = 2 and y = -2.

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

n = -4, -1/3.

Step-by-step explanation:

3n^2 + 13n+4= 0

3n^2 + 12n + n + 4 = 0

3n(n + 4) + 1(n + 4) = 0

(3n + 1)(n + 4) = 0

n = -4, -1/3.

Answer:

Int 2520, Ext 360

Int 3960, Ext 360

Int 5040, Ext 360

Int 2160, Ext 360

Int 3600, Ext 360

Int 6840, Ext 360

Step-by-step explanation:

Interior angles of a polygon = (sides - 2) × 180

Exterior angles are always 360

Please Mark as Brainliest if you found it helpful!

The measures of an exterior angle are 2520°, and an interior angle is 360° in the given regular polygon with 16 sides.

An interior angle is defined as an angle produced on the inside of a polygon by extending the sides of the polygon.

Interior angles of a polygon = (sides - 2) × 180°

To determine the measures of an exterior angle and an interior angle given a regular polygon with 16 sides.

Interior angles of a polygon = (sides - 2) × 180°

In this case, the number of sides is 16

Interior angles of a polygon = (16 - 2) × 180

Interior angles of a polygon = (14) × 180

Interior angles of a polygon = 2520

And, Exterior angles are always 360° in the regular polygon.

Similarly, the other regular polygons :

A regular polygon with 24 sides: Int 3960, Ext 360

A regular polygon with 30 sides: Int 5040, Ext 360

A regular polygon with 14 sides: Int 2160, Ext 360

A regular polygon with 22 sides: Int 3600, Ext 360

A regular polygon with 40 sides: Int 6840, Ext 360

Learn more about the exterior angles here :

https://brainly.com/question/28835566

#SPJ2

Answer:

The picture is to blurry to read

Step-by-step explanation:

Answer:

This question is asking us to solve both of these equations, so let's do exactly that!

First equation:

[tex]n(n+1)+2n+2\\n^2+1n+2n+2\\n^2+3n+2[/tex]

Second Equation:

[tex](n+1)(n+2)\\n^2+2n+1n+2\\n^2+3n+2[/tex]

Both of the equations result with the same answer, therefore n(n+1)+2n+2 is equivalent to (n+1)(n+2).

Hope that helped! :)