The side length of the chessboard is 7 inches. Find the area of the chessboard.

Answer:

x = 27

Step-by-step explanation:

I'm going to use letters to label the parts of the triangle while explaining how to solve for x:

Angle A = x (bottom left angle of the triangle)

Angle B = 4x (top angle of the triangle)

Angle C = empty angle (bottom right angle of the triangle)

Angle D = 3x + 54 (angle outside of the triangle)

A line has a angle measurement of 180 degrees.

Angle C & D make up the line, meaning Angle C + Angle D = 180 degrees.

To find Angle C, we would subtract Angle D's equation from 180 like this:

180 - (3x + 54)

Now Angle C equals 180 - (3x + 54)

Now we have all the angles inside the triangle. To find x, we are going to sum up  Angle A, B, & C and set it equal to 180.

We set the equation to 180 because a the sum of the interior angles for a triangle is 180.

The equation looks like this:

(180 - (3x + 54)) + 4x + x = 180

Now we use basic algebra to solve it:

(180 - (3x + 54)) + 4x + x = 180

(distribute the - to (3x + 54))

180 - 3x - 54 + 4x + x = 180

(add like terms on the left side of the equation)

126 + 2x = 180

(subtract 126 from both sides)

2x = 54

(divide both sides by 2)

x = 27

To prove this answer is correct, plug it back in the original equation and you'll see that it ends up equaling 180, which is the sum of interior angles for triangle.

Hope it helps (●'◡'●)

Answer:

-|x|=-3

|x|=-3

|-x|=-3

Step-by-step explanation:

Answer:

Only -lxl = -3 works

Step-by-step explanation:

The other options don't work because they all have numbers inside of the absolute value brackets.  You would always get a positive end value when the absolute value equation is applied.

The last one is the only one that works because the negative is outside of the absolute value bracket.  Therefore, if you plug in 3 for x, it will give you -3.

Answer:

c

Step-by-step explanation:

Answer:

11x + 8 = 12x - 4

x=12

∠ 4 = 180-140 = 40°

Step-by-step explanation:

Answer:

4/3 =a

Step-by-step explanation:

10 − 3(2a − 1) = 3a + 1

Distribute

10 -6a +3 = 3a+1

Combine like terms

13 -6a = 3a+1

Add 6a to each side

13-6a+6a = 3a+6a +1

13 = 9a+1

Subtract 1 from each side

13-1 = 9a+1-1

12 = 9a

Divide by 9

12/9 = 9a/9

4/3 =a

a = 4/3

10 - 3( 2a - 1 ) = 3a + 1

10 - 3 × 2a -3 × -1 = 3a + 1

10 - 6a + 3 = 3a + 1

10 + 3 - 6a = 3a + 1

13 - 6a = 3a + 1

13 - 6a - 3a = 3a - 3a + 1

13 - 9a = 1

13 - 13 - 9a = 1 - 13

- 9a = - 12

-9a / - 9 = - 12 / - 9

a = 4/3

Answer:

g-21=129

Step-by-step explanation:

Answer:

A is the correct answer.

Answer:

The vertex form of the quadratic function, f(x) = a·(x - h)² + k

Step-by-step explanation:

The general form of a quadratic function is given as follows;

f(x) = a·x² + b·x + c

The vertex form of the quadratic function is f(x) = a·(x - h)² + k

Where;

(h, k) = The coordinates of the vertex of the parabola

h = -b/2·a, k = f(h)

Answer:

3. The number of students that rode on each bus

Step-by-step explanation:

The equation they give us is:

2b + 6 = 70

The question already tells us that in this equation:

2 is the 2 buses that the school hired

6 is the 6 leftover kids who couldn't fit on the 2 buses

The question also tells us that the 2 buses only have a total of 64 seats, so 32 seats on 1 bus (64/2 = 32).

So that means b would equal the 32 seats on 1 bus, or the number of students that rode on each bus.

Hope it helps (●'◡'●)

Answer:

Independent variable: Number of laptops

Dependent variable: Grades

Step-by-step explanation:

According to the Question,

Answer:

Step-by-step explanation:

I'll answer the question, but before I do, let me crab about the reliance on a diagram. You should never have to answer a question where you make assumptions about the diagram. It should state the the longest leg in one triangle = 2x - 4, and the hypotenuse in the larger triangle is 42, while in the smaller one it is x + 8\

Added to which you have to state that there is a ratio between the large triangle and the small one.

24/(2x - 4) = (x + 8)/42             Cross Multiply

24*42 = (x + 8)*(2x - 4)             Remove the brackets. Combine the left

1008 = 2x^2 - 4x + 16x - 32     Combine the right   and switch

2x^2 + 12x - 32 = 1008             Subtract 1008

2x^2 + 12x - 1040 = 0                Divide by 2

x^2 + 6x - 520  = 0

(x + 26)(x - 20) = 0

x = - 26 which has no meaning

x = 20 which is the answer.

2x - 4 = 2*20 - 4 = 36

x + 8 = 28

I'm not sure what you want -- the side lengths or just x.

Step-by-step explanation:

the ratio

24:2x-4=x+8:42

24/2x-4=x+8/42

24×42=(x+8)(2x-4)

1008=2x(x+8)-4(x+8)

1008=2x²+16x-4x-32

1008=2x²+12x-32

1008+32=2x²+12x

1040=2x²+12x

0=2x²+12x-1040

OR

24/2x-4=x+8/42

LCM=42(2x-4)

42(2x-4)×24/2x-4=42(2x-4)×x+8/42

42×24=(2x-4)(x+8)

1008=2x(x+8)-4(x+8)

1008=2x²+16x-4x-32

1008=2x²+12x-32

1008+32=2x²+12x

1040=2x²+12x

0=2x²+12x-1040

Answer:

C

Step-by-step explanation:

I took the quiz and it was C! Hope this helps :)

Answer:

(a) T = 16√x

Step-by-step explanation:

T is directly proportional to √x, so we can say,

T=k√x (where k is a constant)

now, according to the question,

400=k×√625

400=k×25

k=16

so, putting the value of k in the equation, T=16√x

Answered by GAUTHMATH

Step-by-step explanation:

Given that ,

Mathematically we can write it as ,

[tex]\implies T \propto \sqrt{x}[/tex]

Let k be the constant , therefore ,

[tex]\implies T = kx [/tex]

Now when T = 400 and x = 625 , lets find the value of k , as ,

[tex]\implies 400 = k\times 625 \\\\\implies k =\dfrac{400}{625}\\\\\implies k= 0.64 [/tex]

Therefore the required formula will be ,

[tex]\implies \underline{\underline{ T = 0.64x}} [/tex]

Answer:

14 m/s²

Step-by-step explanation:

From the question

a ∝ F/m.............. Equation 1

Where a = aceleration, m = mass, F = force

make F the subject of the equation

F = ma............ equation 2

Given: m = 7 kg, a = 4 m/s²

Therefore,

F = 7(4)

F = 28 N

For another object whose mass is 2 kg,

Make a the subject of equation 2

a = F/m

a = 28/2

a = 14 m/s²

Step-by-step explanation:

1+2+3+4+5=14 divided by 5=2.8 so, A.would be your answer.

Answer: B. Square

Step-by-step explanation:

The answer is B.), because if you have two pairs of parallel sides that means it looks like a square 1. || 2. _

                                                            _

- Chilio

Answer:

Step-by-step explanation:

The diagonals of a rhombus are perpendicular

Answer: Choice B) The diagonals of a rhombus are perpendicular

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

Explanation:

Let's go through the answer choices to see which are true statements, and which are false.

Answer:

<BCO​ = <BAO​ = 20degrees

Step-by-step explanation:

If <ABC measures 100 and is inscribed in a circle O. find <BAO and <BCO​

To get <BAO and <BCO​, we need to get <AOC first.

From the figure, it can be seen that triangle ABC is an isosceles trinagle. Hence;

<BAC + <BCA + 100 = 180

Since <BAC = <BCA

<BAC + <BAC = 180 - 100

2<BAC = 80

<BAC = 80/2

<BAC = 40

Also;

<BAO = <BCO​ and <BAO = <BAC/2

<BAO = 40/2 = <BCO​

Hence <BCO​ = <BAO​ = 20degrees

Answer:

cuadradas 777,2 unidades

Step-by-step explanation:

Answer:

67.7

Step-by-step explanation:

i just took the quiz

ok so we see that TR is 17 units, so RV is the same amount

3x+2 so 3x=15 so divide both sides by 3 we get x=5

now we know x=5 4x+1=21 and 9x-4=41

*drops microphone*

Answer:

TR = 12

=> 3x + 2 =17

=> x = 5

We have QT = QV (because QTV is an isosceles triangle)

=> QT = 4x+1=4x5+1=21 units

We have TS = SV (because TSV is an isosceles triangle)

=>SV = 9x-4= 9x5-4=41 units

Answer:

[tex]n=\frac{S}{180}+2[/tex]

Step-by-step explanation:

Hi there!

[tex]S=(n-2)180[/tex]

We can isolate n by performing inverse operations on both sides to cancel out values.

First, divide both sides by 180 to isolate n-2:

[tex]\frac{S}{180}=n-2[/tex]

Now, add 2 to both sides to isolate n:

[tex]\frac{S}{180}+2=n\\n=\frac{S}{180}+2[/tex]

I hope this helps!

Answer:

y=0

Step-by-step explanation:

9514 1404 393

Answer:

  y = 0

Step-by-step explanation:

Factor out 3^y:

  3^(2y-1) +2(3^(y-1)) = 1 . . . . . . given

  (3^y)^2(3^-1) +2(3^y)(3^-1) = 1 . . . . factor out 3^y

  (3^y)^2 +2(3^y) -3 = 0 . . . . . . . . . . subtract 1, multiply by 3

Let x = 3^y. Substituting, we have ...

  x^2 +2x -3 = 0

  (x -1)(x +3) = 0

  x = 1  or  x = -3 . . . . . values of x that satisfy this equation

Then the corresponding values of y are ...

  x = 3^y . . . . . . . . . . . . relation of x and y

  log(x) = y·log(3) . . . . . take logs to solve for y

  y = log(x)/log(3) . . . . . divide by the coefficient of y

For x = 1, this is y = log(1)/log(3) = 0

For x = -3, this is y = log(-3)/log(3) . . . . no real solutions

The only real solution is y = 0.

_____

The attachment shows the solution of f(x) = 0, where ...

  [tex]f(x)=3^{2x-1}+2\times3^{x-1}-1[/tex]

That solution is x=0. This means the (real) solution to the given equation is y=0.

Answer:

8(X^2+1)

Step-by-step explanation:

(X²+3)²-(X²-1)

(X²+3)(X²+3)-(X²-1)(X²-1)

X⁴+3X²+3X²+9-(X⁴-X²-X²+1)

X⁴+6X²+9-(X⁴-2X²+1)

X⁴+6X²+9-X⁴+2X²-1

8X²+8

Answer:

x = 48.125

Step-by-step explanation:

Explanation in progress! (●'◡'●)

Answer:

48.25

Step-by-step explanation:

first wirte the same qa and write long qa and write the ans in procesa

Answer:

let the number be a

product of a number and six = 6 times a=6a

three less than the product of a number= 6a-3

then the full equation will be 6a-3=27

Answer:

3rd choice

Step-by-step explanation:

You can find the attached files

Answer:

B

Step-by-step explanation:

We know that

cos A = adjacent / hypotenuse

sin A = opposite / hypotenuse

Therefore, sin A / cos A =

(opposite / hypotenuse)  / (adjacent / hypotenuse)

= (opposite/hypotenuse) * (hypotenuse / adjacent)

= opposite / adjacent

= tan A

Therefore, tan A = sin A / cos A = y/x

Answer: 3

Step-by-step explanation:

Let the number be x.

4*(x squared) = 12x

Divide both sides by 4,

X squared = 3x,

divide both sides by x,

X=3