Find the missing side of the triangle.

Step-by-step explanation:

The perimeter of the rectangle is

[tex]P = 2(4x + 2x) = 12x[/tex]

The perimeter of the octagon is

[tex]P = 8(1.5x) = 12x[/tex]

So for x = 1, the perimeter of the rectangle, as well as the octagon, is 12 cm. For x = 2, its 24 cm. For x = 3, it's 36 and so on. So the pattern here is with each integer increase in x, the perimeter increases by 12 cm. Also that the perimeters of both shapes are equal.

Answer:

Sin A = o/h

= 9/41

Step-by-step explanation:

since Sin is equal to opposite over hypotenuse, from the question, the opposite angle of A is 9 and hypotenuse angle of A is 41. Thus the answer for Sin A= 9/41

Answer:

[tex]6\sqrt{3}[/tex]

Step-by-step explanation:

using the sine rule,

[tex]\frac{sin 60}{x} = \frac{sin 30}{6} \\x=\frac{sin60 * 6 }{sin30} \\x=6\sqrt{3}[/tex]

It looks like we're given the Laplace transform of f(t),

[tex]F(p) = L_p\left\{f(t)\right\} = \dfrac6{p(2p^2+4p+10)} = \dfrac3{p(p^2+2p+5)}[/tex]

Start by splitting up F(p) into partial fractions:

[tex]\dfrac3{p(p^2+2p+5)} = \dfrac ap + \dfrac{bp+c}{p^2+2p+5} \\\\ 3 = a(p^2+2p+5) + (bp+c)p \\\\ 3 = (a+b)p^2 + (2a+c)p + 5a \\\\ \implies \begin{cases}a+b=0 \\ 2a+c=0 \\ 5a=3\end{cases} \implies a=\dfrac35,b=-\dfrac35, c=-\dfrac65[/tex]

[tex]F(p) = \dfrac3{5p} - \dfrac{3p+6}{5(p^2+2p+5)}[/tex]

Complete the square in the denominator,

[tex]p^2+2p+5 = p^2+2p+1+4 = (p+1)^2+4[/tex]

and rewrite the numerator in terms of p + 1,

[tex]3p+6 = 3(p+1) + 3[/tex]

Then splitting up the second term gives

[tex]F(p) = \dfrac3{5p} - \dfrac{3(p+1)}{5((p+1)^2+4)} - \dfrac3{5((p+1)^2+4)}[/tex]

Now take the inverse transform:

[tex]L^{-1}_t\left\{F(p)\right\} = \dfrac35 L^{-1}_t\left\{\dfrac1p\right\} - \dfrac35 L^{-1}_t\left\{\dfrac{p+1}{(p+1)^2+2^2}\right\} - \dfrac3{5\times2} L^{-1}_t\left\{\dfrac2{(p+1)^2+2^2}\right\} \\\\ L^{-1}_t\left\{F(p)\right\} = \dfrac35 - \dfrac35 e^{-t} L^{-1}_t\left\{\dfrac p{p^2+2^2}\right\} - \dfrac3{10} e^{-t} L^{-1}_t\left\{\dfrac2{p^2+2^2}\right\} \\\\ \implies \boxed{f(t) = \dfrac35 - \dfrac35 e^{-t} \cos(2t) - \dfrac3{10} e^{-t} \sin(2t)}[/tex]

Answer:

0.99%

Step-by-step explanation:

Answer:

C - 136

(115+157)/2

Step-by-step explanation:

Answer:

11.75

Step-by-step explanation:

The required triangle is attached below :

The triangle AFE has it's by the mid segment as BD ;as B is the mid-point of line EA ; and D is the mid-point of line FA ;

HENCE, The Length of the midsegment BD = 1/2FE

Hence, BD =. 1/2 * 23.5

BD = 23.5 / 2 = 11.75

(2/7)m - (1/7) = 3/14

2m/7 =(3/14) + (1/7)

2m/7 = (3/14) + 2(1/7)

here we are multiplying 2 with 1/7 to make the denominator same for addition.

2m/7 = (3/14) +(2/14)

2m/7 = (3 + 2)/14

2m/7 = 5/14

2m = (5 *7)/14

2m = 35/14

2m = 5/2

m = 5/4

m = 1.25

So the value of "m" is 1.25

[tex]\\ \large\sf\longmapsto -\dfrac{4x^3}{3y^2}[/tex]

[tex]\\ \large\sf\longmapsto -\dfrac{4(3)^3}{3(4)^2}[/tex]

[tex]\\ \large\sf\longmapsto -\dfrac{4(27)}{3(16)}[/tex]

[tex]\\ \large\sf\longmapsto -\dfrac{108}{48}[/tex]

[tex]\\ \large\sf\longmapsto -\dfrac{9}{4}[/tex]

Answer:

(-2, 2)

Step-by-step explanation:

If you have a point (x, y) and you do a dilation by a scale factor K centered at the origin, the new point will just be (k*x, k*y)

So, if the original point is (-8, 8)

And we do a dilation by a scale factor k = 1/4

Then the image of the point will be:

(-8*(1/4), 8*(1/4))

(-8/4, 8/4)

(-2, 2)

9514 1404 393

Answer:

  c)  x^2 - 9x - 22 = 0

Step-by-step explanation:

Consider the generic case ...

  (x -a)(x -b) = 0 . . . . . . . has solutions x=a, x=b

Multiplying this out gives ...

  x^2 -ax -bx +ab = 0

  x^2 -(a+b)x +ab = 0

This tells you ...

The sum of roots is 11 +(-2) = 9, and the opposite of that is -9. You are looking for an equation with the term -9x. (Choice C matches)

The product of roots is (11)(-2) = -22. You are looking for an equation with a constant of -22. (Choice C matches that, too.)

The equation is ...

  x^2 -9x -22 = 0

Answer:

3.3km

Step-by-step explanation:

200m on first day

Increase 200 by 100 = 300 (200+100)

From 2nd day to 11th day

300×11

3300m

If 1000m = 1km

3300m =?

3300/1000

3.3km

I hope it helps

Answer:

2.5/ft per sec

Step-by-step explanation:

its vertica.

The height of the ladder is decreasing at a rate of 24 ft/sec.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

Let's denote the distance between the base of the ladder and the wall by x.

The length of the ladder = L.

Now,

L = 10 ft

dx/dt = 4 ft/sec

x = 6 ft.

The rate of change of the height of the ladder with respect to time.

Using the Pythagorean theorem, we have:

L² = x² + y²

Differentiating both sides with respect to time t, we get:

2L (dL/dt) = 2x(dx/dt) + 2y(dy/dt)

Substituting L = 10 ft, x = 6 ft, and dx/dt = 4 ft/sec.

20(dL/dt) = 12(4) + 2y(dy/dt)

Simplifying and solving for dy/dt.

dy/dt = (20/2y)(dL/dt) - 24

Now,

The height of the ladder.

Using the Pythagorean theorem again, we have:

y² = L² - x²

   = 100 - 36

   = 64

y = 8

Now,

Substituting y = 8 ft, dL/dt = 0

(since the length of the ladder is constant), and dx/dt = 4 ft/sec.

dy/dt

= (20/2(8))(0) - 24

= -24 ft/sec

Therefore,

The height of the ladder is decreasing at a rate of 24 ft/sec.

Learn more about the Pythagorean theorem here:

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Answer:

5

Step-by-step explanation:

2x-7=3x-12

2x-3x=-12+7

-x=-5

x=5

[tex] \sqrt{2x - 7} - \sqrt{3x - 12 } = 0 \\ \sqrt{10 - 7} - \sqrt{15 - 12} = 0 \\ \sqrt{3} - \sqrt{3} = 0[/tex]

Answer: See below

Step-by-step explanation:

Answer:

Answer below

Step-by-step explanation:

Answer:

∡A =41°

~~~~~~~~~~~~

BC=21

~~~~~~~~~~~~~~

sin(24)/AC=sin(41)/21

AC=13

~~~~~~~~~~~~~~

sin(115)/AB=sin(41)/21

AB=29

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sales revenue x (100%+sales tax rate) = total sales including tax

sales revenue x 1.085 (100% + 8.5%) = 78120

sales revenue = 78120/1.085

sales revenue = 72000

total sales including tax - sales revenue = sales tax

78120 = 72000 = 6120

Journal entry:

cash.      78120

  Sales revenue.     72000

  Sales tax payable.  6120

Answer:

Step-by-step explanation:

2|x-1|+5 < 13

2|x-1| < 8

|x-1| < 4

-4 < x-1 < 4

-3 < x < 5

Answer:

D

Step-by-step explanation:

f(x)=-x(x-4)

f(x)=-x²+4x

-x²+4x=0

x(-x+4)=0

x=0, x=4

(2)

4x²-x-3=0

(4x²+3x)-(4x-3)=0

x(4x+3)-1(4x+3)=0

x=1, x=-3/4

Answer:

[tex]\boxed {\boxed {\sf 120 \ units^2}}[/tex]

Step-by-step explanation:

We are asked to find the area of a triangle. The formula for calculating this is:

[tex]a= \frac{1}{2} bh[/tex]

This is a right triangle, so the base and height are the legs of the triangle. The 2 smallest sides are the legs because the longest side is the hypotenuse. Since the side lengths are 10, 26, and 24, the base and height must be 10 units and 24 units.

Substitute these values into the formula.

[tex]a= \frac{ 1}{2} ( 10 \ units)(24 \ units)[/tex]

Multiply the numbers in parentheses.

[tex]a= \frac{1}{2}(240 \ units^2)[/tex]

Multiply by 1/2 or divide by 2.

[tex]a= 120 \ units^2[/tex]

The area of the triangle is 120 units squared.

Answer:

√245

Step-by-step explanation:

altitude on hypotenuse theorem:

m^2=7*35

m^2=245

m=√245

Answer:

D. There is no x value as there is no solution to this system

Step-by-step explanation:

2x − 3y = 3                                  5x − 4y = 4

5x - 4y = 4               -4y = -5x + 4                         y = 5/4x - 1

2x - 3(5/4x - 1) = 3

2x - 15/4x + 3 = 3

-7/4x = 0

x = 0

Answer:

Sinx = 21/40

x = inverse of sin (21/40)

x= 31.6682

hope u got it

Answer:

31.6 degrees

Step-by-step explanation:

sin-¹(p/h) = 31.6

Answer:

=32÷40%

=32÷0.4

=80

the owner have total 80 stores

Step-by-step explanation:

th

Answer:

80.

Step-by-step explanation:

40 % = 32 stores, so:

10% = 32/4 = 8 stores, and

100% = 8*10 = 80 stores.

Triangle DEF is scalene

Must click thanks and mark brainliest

The triangle DEF will be a scalene triangle as all the sides of the triangle are unequal.

A scalene triangle is a type of triangle which have all the sides to be unequal and similarly, all the angles will also be unequal to each other.

Given that:-

it is given that all the sides of the triangle are x, x+3, and x−1 we can clearly see that for any value of x all the three sides will have different values. we can conclude from this that the triangle DEF is a scalene triangle.

Therefore triangle DEF will be a scalene triangle as all the sides of the triangle are unequal.

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Answer:

0

Step-by-step explanation:

0co

Answer:

five kids .each 6 sweaters and 9 trousers

Step-by-step explanation:

9514 1404 393

Answer:

  a) CP = SP/1.1

  b) CP = $59.50

  c) GST = $5.95

Step-by-step explanation:

a) Divide by the coefficient of CP.

  SP = 1.1×CP

  CP = SP/1.1

__

b) Use the formula with the given value.

  CP = $65.45/1.1 = $59.50

__

c) You can do this two ways: subtract CP from SP, or multiply CP by 0.1.

  GST = SP -CP = $65.45 -59.50 = $5.95

  GST = CP×0.10 = $59.50 × 0.10 = $5.95