Find the length of x
. Assume the triangles are similar.

9514 1404 393

Answer:

  c = 14

  no extraneous solutions

Step-by-step explanation:

You can subtract the right-side expression, combine fractions, and set the numerator to zero.

  [tex]\dfrac{c-4}{c-2}-\left(\dfrac{c-2}{c+2}-\dfrac{1}{2-c}\right)=0\\\\\dfrac{c-4}{c-2}-\dfrac{1}{c-2}-\dfrac{c-2}{c+2}=0\\\\\dfrac{(c-5)(c+2)-(c-2)^2}{(c-2)(c+2)}=0\\\\\dfrac{(c^2-3c-10)-(c^2-4c +4)}{(c-2)(c+2)}=0\\\\\dfrac{c-14}{(c-2)(c+2)}=0\\\\\boxed{c=14}[/tex]

__

Check

  (14 -4)/(14 -2) = (14 -2)/(14 +2) -1/(2 -14) . . . . substitute for c

  10/12 = 12/16 -1/-12

  5/6 = 3/4 +1/12 . . . . true

There is one solution (c=14) and it is a solution to the original equation. There are no extraneous solutions.

Let numerator be x

ATQ

[tex]\\ \sf\longmapsto x+x+2=12[/tex]

[tex]\\ \sf\longmapsto 2x+2=12[/tex]

[tex]\\ \sf\longmapsto 2x=12-2[/tex]

[tex]\\ \sf\longmapsto 2x=10[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{10}{2}[/tex]

[tex]\\ \sf\longmapsto x=5[/tex]

Now the fraction is

[tex]\\ \sf\longmapsto \dfrac{x}{x+2}[/tex]

[tex]\\ \sf\longmapsto \dfrac{5}{5+2}[/tex]

[tex]\\ \sf\longmapsto \dfrac{5}{7}[/tex]

-- Their sum is 12.

-- If they were equal, each would be 6.

-- To make them differ by 2 without changing their sum, move 1 from the numerator (make it 5), to the denominator (make it 7).

Answer:

[tex]\huge\boxed{width=12cm}[/tex]

Step-by-step explanation:

[tex]l-length\\w-width\\P-perimeter[/tex]

The formula of perimeter of the rectangle:

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

Substitute:

[tex]l=6w\\\\P=168cm[/tex]

[tex]168=2(6w+w)\\168=2(7w)\\168=14w\qquad|\text{divide both sides by 14}\\\\\dfrac{168}{14}=\dfrac{14w}{14}\\\\12=w\Rightarrow w=12(cm)[/tex]

Answer:

Width of rectangle = 12 cm

Step-by-step explanation:

Let us assume that,

→ Length = 6x

→ Width = x

→ Perimeter = 168 cm

Perimeter of rectangle,

→ P = 2(L + W)

Forming the equation,

→ 168 = 2(6x + x)

Now the value of x will be,

→ 168 = 2(6x + x)

→ 2 × 7x = 168

→ 14x = 168

→ x = 168/14

→ [ x = 12 ]

Then the length and width is,

→ Length = 6x = 6(12) = 72 cm

→ Width = x = 12 cm

Hence, required width is 12 cm.

Answer:

SOH-CAH-TOA

[tex]\sin \left(x\right)=\frac{6}{\sqrt{49+36}}[/tex] = 40.60°

SOH = SIN = OPP/HYP

SIN(Θ) = 6/[tex]\sqrt{49+36 }[/tex]

Step-by-step explanation:

Answer:

x = 3

y = 2

Step-by-step explanation:

3x - y = 7   ------------(i)

2x - 2y = 2 ---------(ii)

Multiply equation (i) by (-2)

(i)*(-2)          - 6x + 2y = -14

(ii)                 2x  - 2y =2     {Add both equation. now y will be eliminated}

                    -4x         = -12          {Divide both sides by -4}

                             x = -12/-4

x = 3

Plug in x = 3 in equation (i)

2*3 - 2y = 2

6 - 2y = 2    

Subtract 6 from both sides

 -2y = 2 - 6

  -2y = -4

Divide both sides by 2

      y = -4/-2

y = 2

Answer:

x = 3, y = 2

Step-by-step explanation:

Given the 2 equations

3x - y = 7 → (1)

2x - 2y = 2 → (2)

Multiplying (1) by - 2 and adding to (2) will eliminate the y- term

- 6x + 2y = - 14 → (3)

Add (2) and (3) term by term to eliminate y

- 4x + 0 = - 12

- 4x = - 12 ( divide both sides by - 4 )

x = 3

Substitute x = 3 into either of the 2 equations and solve for y

Substituting into (1)

3(3) - y = 7

9 - y = 7 ( subtract 9 from both sides )

- y = - 2 ( multiply both sides by - 1 )

y = 2

solution is (3, 2 )

Answer:

-0.6

Step-by-step explanation:

Answer:

⅗ as a decimal is -0.6

Answer:

gradient = slope = 1

Y =1X +1  is the equation

Step-by-step explanation:

x1 y1  x2 y2

4 5  1 2

(Y2-Y1) (2)-(5)=   -3  ΔY -3

(X2-X1) (1)-(4)=    -3  ΔX -3

slope= 1          

B= 1          

Y =1X +1    

Answer:

1/8

Step-by-step explanation:

Let "A" = the next call of a customer's complaint

Let "B" = the next call completed under 5 minutes

P(A) = 1/4

P(B) = 1/2

So ----> P(AB) = P(A) times P(B) P(AB)

                       = 1/4 times 1/2 = 1/8

Answer:

1. Given

2. Def of Vertical Angles

3. Alternate Interior Angles

4. Def of Vertical angles

5. Opposite exterior angles

Step-by-step explanation:

Answer:

765(7-()83)₹8_!_?84?8₹92092)8₹+!_()

Answer:

[tex]2 \div \frac{8}{9} = 2 \times \frac{9}{8} = \frac{9}{4} = 2.25[/tex]

I hope I helped you^_^

Answer:

Step-by-step explanation:

Use KCF method for fraction division.

K- Keep the first fraction.

Change the division to multiplication.

Flip the second fraction

2 ÷ 8/9 = [tex]2 * \dfrac{9}{8}[/tex]

             [tex]= 1*\dfrac{9}{4}=\dfrac{9}{4}\\\\= 2\dfrac{1}{4}[/tex]

Answer: -1

Step-by-step explanation:

12x^2-7x-12 = (4x+3)(3x-4)

4x+3=0. X = -3/4

3x-4=0. X = 4/3

(-3/4) (4/3) = -1

Answer:

all except the first

Step-by-step explanation:

do u really want an explanation

Answer:

y = a^x is an exponential function with an x intercept.

Step-by-step explanation:

y = a^x is the standard form of an exponential function.

Answer:

X1=6

X2=7

y1= -1

y2= 3

now,

slope = y2-y1/x2-x1

= 3+1/7-6

=4/1

=1

hence slope= 1

Answer: C

Step-by-step explanation:

Answer:

An angle bisector

Step-by-step explanation:

An angle bisecter

Answer:

[tex] = \frac{2}{4} \div \frac{1}{4} [/tex]

find reciprocal of ¼:

[tex] = \frac{2}{4} \times \frac{4}{1} \\ \\ = \frac{2}{1} \\ \\ = 2[/tex]

Answer:

2

Step-by-step explanation:

the first step is to change the sign from a division sign to a multiplication sign and when you change the sign you also have to swap one side by placing the numerator down and the denominator up

2/4÷1/4

2/4×4/1

8/4

2

I hope this helps

Step-by-step explanation:

5.

[tex](5 + 4 \sqrt{7} ){x}^{2} + (4 - 2 \sqrt{7} ) x- 1 = 0[/tex]

Simplify both radicals.

[tex](5 + \sqrt{112) {x}^{2} } + (4 - \sqrt{28} )x - 1 = 0[/tex]

Apply Quadratic Formula

First. find the discramnint.

[tex](4 - \sqrt{28} ) {}^{2} - 4(5 + \sqrt{112} )( - 1) = 64[/tex]

Now find the divisor 2a.

[tex]2(5 + \sqrt{112} ) = 10 + 8 \sqrt{7} [/tex]

Then,take the square root of the discrimant.

[tex] \sqrt{64} = 8[/tex]

Finally, add -b.

[tex] - (4 + 2 \sqrt{7} )[/tex]

So our possible root is

[tex] - (4 + 2 \sqrt{7} ) + \frac{8}{10 + 8 \sqrt{7} } [/tex]

Which simplified gives us

[tex] \frac{ 4 + 2 \sqrt{7} }{10 + 8 \sqrt{7} } [/tex]

Rationalize the denominator.

[tex] \frac{4 + 2 \sqrt{7} }{10 + 8 \sqrt{7} } \times \frac{10 - 8 \sqrt{7} }{10 - 8 \sqrt{7} } = \frac{ - 72 - 12 \sqrt{7} }{ - 348} [/tex]

Which simplified gives us

[tex] \frac{6 + \sqrt{7} }{29} [/tex].

6. The answer is 2.

9514 1404 393

Answer:

  5. x = (6 +√7)/29; a=6, b=1, c=29

  6. x = 2

Step-by-step explanation:

The quadratic formula can be used, where a=(5+4√7), b=(4-2√7), c=-1.

  [tex]x=\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{-(4-2\sqrt{7})+\sqrt{(4-2\sqrt{7})^2-4(5+4\sqrt{7}})(-1)}{2(5+4\sqrt{7})}\\\\=\dfrac{-4+2\sqrt{7}+\sqrt{16-16\sqrt{7}+28+20+16\sqrt{7}}}{10+8\sqrt{7}}=\dfrac{4+2\sqrt{7}}{2(5+4\sqrt{7})}\\\\=\dfrac{(2+\sqrt{7})(5-4\sqrt{7})}{(5+4\sqrt{7})(5-4\sqrt{7})}=\dfrac{10-3\sqrt{7}-28}{25-112}=\boxed{\dfrac{6+\sqrt{7}}{29}}[/tex]

__

Use the substitution z=3^x to put the equation in the form ...

  z² -3z -54 = 0

  (z -9)(z +6) = 0 . . . . . factor

  z = 9 or -6 . . . . . . . . value of z that make the factors zero

Only the positive solution is useful, since 3^x cannot be negative.

  z = 9 = 3^2 = 3^x . . . . use the value of z to find x

  x = 2

Answer:

a/b

Step-by-step explanation:

Tan = Opposite/Adjacent

Therefore, Tan M = a/b.

Answer:

x = 1

y=1.5

Step-by-step explanation:

3*1+2*1.5=6

The values of x and y in equation 6=3x+2y is for x is 1 and for y is 1.5.

We have given that,

x and y are integers and 0 < x < y.

6 = /3x+2y.

x=1 then

A statement of an order relationship greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions.

6=3+2y

6-3=2y

3/2=y

y=1.5

3*1+2*1.5=6

Therefore we get the values of x and y is for x is 1 and for y is 1.5.

To learn more about the values visit:

https://brainly.com/question/25770607

#SPJ2

Answer:

Step-by-step explanation:

Let's write that out completely:

[tex]ln_e(x)=7[/tex] The rule for going from log to exponential is what I call the "circular rule" in my classes and the kids never forget it. Take the base of the log, raise it to the power of the number on the other side of the equals sign, and then circle back to set it equal to the argument.

e is the base. Raise e to the 7th and circle back to set the whole thing equal to x (x is called the argument):

[tex]e^7=x[/tex] choice C.

Answer:

AED 972

Step-by-step explanation:

Area of the wall = 9² = 81 m²

each m² costs AED 12

so 81 m² will cost 12×81 = AED 972

Answer:

5.1

Step-by-step explanation:

ik i am in the future

Answer:

b is the correct answer

Step-by-step explanation:

Answer:

No mode

Step-by-step explanation:

There are no any numbers which are repeated. So there is no mode.

Answer:

The answer is C.no mode because the mode of a data set is the number that occurs most frequently in the set. To easily find the mode, but the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode!

Answer:

4

Step-by-step explanation:

64^1/3

cube root of 64 is

4

Answer:

C

Step-by-step explanation:

Using the rule of exponents

[tex]a^{\frac{1}{3} }[/tex] ⇔ [tex]\sqrt[3]{a}[/tex] , then

[tex]64^{\frac{1}{3} }[/tex] = [tex]\sqrt[3]{64}[/tex] = 4 → C