express the following rational algebraic expression to its simple form.show your solution​

2. 3×-12/ 5× - 20​

Answer:

Exact area = 272 - 28.125pi  square cm

Approximate area = 183.6875 square cm  (when using pi = 3.14)

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

Explanation:

The trapezium has the parallel sides of 12+13 = 25 cm and 15 cm. Those vertical sides average to (25+15)/2 = 40/2 = 20. Multiply this with the height of the trapezium to get 20*24 = 480 sq cm as the area.

You could also use this trapezium area formula

A = h*(b1+b2)/2

A = 24*(25+15)/2

A = 480

Whichever method you use, the trapezium has an area of exactly 480 square cm.

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

The paralellogram has base of 13 and height of 16, so its area is base*height = 13*16 = 208 sq cm

The semicircle has area of 0.5*pi*r^2 = 0.5*pi*7.5^2 = 28.125pi square cm. Notice that I used r = 7.5 which is half of the diameter 15 cm.

The parallelogram and semicircle areas add to 208+28.125pi

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

Subtract this from the area of the trapezium to wrap things up

480 - (208+28.125pi)

480 - 208 - 28.125pi

272 - 28.125pi

This is the exact area of the blue shaded region in terms of pi

To get the approximate area, replace pi with something like 3.14 and compute.

So 272 - 28.125pi = 272 - 28.125(3.14) =  183.6875 is the approximate area when pi = 3.14

Use more decimal digits of pi to get a more accurate value.

Answer:

A. 56 in3

Step-by-step explanation:

Formula for Volume; LWH

L * W * H = 4* 4 * 2

16 * 2 = 32(3)

(second half of the container)

LWH = 3 * 4 * 2

12 * 2 = 24(3)

32 + 24 = 56(3)

Break into two cuboids

In cuboid

Hence

#1

Volume:-

#2

Volume:-

Total:

Answer:

32 cm^3

Step-by-step explanation:

Hope it will help you

Answer:

32 cm^3

Step-by-step explanation:

V = L x W x H

V = 2 x 2 x 8

V = 4 x 8

V = 32

The answer would be 32cm^3

I hope it helps! Have a great day!

Your Murderer~

Answer:

Exact Form:

49/4

Decimal Form:

12.25

Mixed Number Form:

12 1/4

Step-by-step explanation:

Isolate the radical, then raise each side of the equation to the power of its index.

√x-2=√x-10

x-4√x+4=x-10

-4√x+4=-10

-4√x=-10-4

-4√x=-14

√x=7

-

2

x= 49

---

44

Answer:

no

Step-by-step explanation:

no

Yes

since the hypotenuese will be forty

24×24=576

32×32=1024

1024+576=1600

√40=1600 which makes YES be the correct answer

Answer:

a) 240 grams

b) 360 grams

c) 2 packs

Step-by-step explanation:

a) 1 biscuit = 4 grams of flour

60 biscuits = 240 grams of flour

Conclusion, 240 grams of flour is needed for 60 biscuits.

b) 240×3÷2 = 360 grams of butter

c) 360÷250

= 1.44

≈ 2 packs

Hope this helps =)

Answer:

107⁰

Step-by-step explanation:

The m<g =107⁰

I hope it helped you

The measure of the angle ∠PGL will be equal to 107 degrees.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

In triangles ΔPGL and ΔNHE,

PG  = NH (given)

GL = HE (given)

If the angle ∠PGL and ∠NHE become congruent, the triangle ΔPGL and ΔNHE will be congruent to each other.

∠PGL = ∠NHE

∠PGL = 107°

The measure of the angle ∠PGL will be equal to 107 degrees.

More about the triangle link is given below.

https://brainly.com/question/25813512

#SPJ2

Answer:

£177.92

Step-by-step explanation:

To increase something by 28% would be to multiply the original value by 1.28:

So to increase £139 by 28%, we do:

£139 × 1.28 = £177.92

So this is our final answer

Answer:

acute

Step-by-step explanation:

Check using the Pythagorean Theorem:

A^2 + B^2 ≟ C^2

9^2 + 115 ≟ 11^2

196 > 121,

so this triangle is acute because the sum of each leg squared is longer than the length of the hypotenuse squared.

Answer:

125

Step-by-step explanation:

Assuming the lines are parallel :

n = 180-125

= 55

x = n

x = 55

z = 180-55

= 125

Answer:graph{-19/9(x+3)^2+5 [-10, 2, -20, 10]}

Step-by-step explanation:

y

=

−

19

9

(

x

+

3

)

2

+

5

Explanation:

If an equation representing a parabola is in vertex form such as

y

=

a

(

x

−

k

)

2

+

h

then its vertex will be at

(

k

,

h

)

. Therefore the equation for a parabola with a vertex at (-3, 5), will have the general form

y

=

a

(

x

+

3

)

2

+

5

If this parabola also passes through the point

(

0

,

−

14

)

then we can determine the

a

parameter.

−

14

=

a

(

0

+

3

)

2

+

5

9

a

=

−

19

a

=

−

19

9

So our equation in vertex form is

y

=

−

19

9

(

x

+

3

)

2

+

5

graph{-19/9(x+3)^2+5 [-10, 2, -20, 10]}

Answer: The unit rate is 1/3

Step-by-step explanation:

The slope of the line, which also represents the unit rate, is 1/3.

The function h(t)=6+3ln(t+1) is a logarithmic function

The height of the tree will exceed 18 feet after 53.6 years

The function is given as:

h(t)=6+3ln(t+1)

When the height is 18 feet, we have:

6+3ln(t+1) = 18

Subtract 6 from both sides

3ln(t+1) = 12

Divide both sides by 3

ln(t+1) = 4

Take the exponent of both sides

t + 1 = e^4

Evaluate the exponent

t + 1 = 54.6

Subtract 1 from both sides

t = 53.6

This means that the height of the tree will exceed 18 feet after 53.6 years

Read more about logarithmic functions at:

https://brainly.com/question/25953978

Answer:

D

Step-by-step explanation:

[tex]\frac{x+2}{3}[/tex] = [tex]\frac{2x-4}{2}[/tex] ( cross- multiply )

3(2x - 4) = 2(x + 2) ← distribute parenthesis on both sides

6x - 12 = 2x + 4 ( subtract 2x from both sides )

4x - 12 = 4 ( add 12 to both sides )

4x = 16 ( divide both sides by 4 )

x = 4

[tex] \longrightarrow \frac{x + 2}{3} = \frac{2x - 4}{2} [/tex]

In this question we have to find the value of x .

[tex]\longrightarrow \frac{x + 2}{3} = \frac{2x - 4}{2} [/tex]

So , by cross multiplying :

[tex] \longrightarrow \: 2(x + 2) = 3(2x - 4)[/tex]

Now , calculation left hand side as well as right hand side :

[tex]\longrightarrow \: 2x + 4 = 6x - 12[/tex]

Now , transposing 6x to left hand side and 4 to right hand side :

[tex]\longrightarrow \: 2x - 6x = - 12 - 4[/tex]

Now , solving left hand side and right hand side :

[tex]\longrightarrow \: - 4x = - 16[/tex]

As negative sign is present on both the side , so it will cancel out :

[tex]\longrightarrow \: \cancel - 4x = \cancel- 16[/tex]

Now we have :

[tex]\longrightarrow \: 4x = 16[/tex]

Now we are transposing 4 to right side and it will change into division from multiplication :

[tex]\longrightarrow \: x = \cancel \frac{16}{4} [/tex]

So we get :

[tex]\longrightarrow \: \green{ \boxed{ \bold x = 4}}[/tex]

We are verifying our answer by putting value of x in given question :

[tex]\longrightarrow \frac{4 + 2}{3} = \frac{2(4) - 4}{2} \: [/tex]

Solving ,

[tex]\longrightarrow \: \frac{6}{3} = \frac{8 - 4}{2} [/tex]

Now subtracting 8 and 4 :

[tex]\longrightarrow \: \frac{6}{3} = \frac{4}{2} [/tex]

Now , dividing 6 by 3 and 4 by 2 :

[tex]\longrightarrow \cancel{\frac{6}{3} } = \cancel{\frac{4}{2} }[/tex]

We get :

[tex]\longrightarrow \: \bold{2 = 2}[/tex]

That means ,

[tex]\longrightarrow L.H.S = R.H.S[/tex]

Answer:

x = 5, x = 7

Step-by-step explanation:

to find the zeros let f(x) = 0 , that is

x² - 12x + 35 = 0 ( subtract 35 from both sides )

x² - 12x = - 35

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 6)x + 36 = - 35 + 36

(x - 6)² = 1 ( take the square root of both sides )

x - 6 = ± [tex]\sqrt{1}[/tex] = ± 1 ( add 6 to both sides )

x = 6 ± 1

then

x = 6 - 1 = 5

x = 6 + 1 = 7

A dodecagon is a twelve-sided polygon that's equally spaced around a circle and with all sides, the same length.

Answer:

No

Step-by-step explanation:

x + 1 is not a factor of the polynomial because the remainder is 2 and not 0

Answer:

Option A

Step-by-step explanation:

To simplify this fraction:

We subtract the powers:

[tex]\frac{6^{3} }{6^{6} } = 6^{3-6}[/tex]

[tex]6^{-3}[/tex] = [tex]\frac{1}{6^{3} }[/tex] = 1/216

These answers I wrote in the last line are options B,C and D.

Therefore Option A is not equivalent.

Given,

[tex] \: [/tex]

To Find,

[tex] \: [/tex]

Solution :

First of all, we'll find the circumference of the circle :

[tex]\\{ \longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{ \: \: Circumference_{(circle)} = 2 \pi r}}}}}} \: \: \bigstar \\ \\[/tex]

Now, we'll substitute the required values in the formula :

[tex]\\ { \longrightarrow \qquad{ \sf{ \: \: Circumference_{(circle)} = 2 \times 3.14 \times 3.5}}} \: \: \\ \\[/tex]

[tex] { \longrightarrow \qquad{ \sf{ \: \: Circumference_{(circle)} = 3.14 \times 7}}} \: \: \\ \\[/tex]

[tex] { \longrightarrow \qquad{ \sf{ \pmb{ \: Circumference_{(circle)} = 21.98}}}} \: \: \\ \\[/tex]

Therefore,

[tex] \: [/tex]

Now, we'll find the area of the circle :

[tex]\\{ \longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{ \: \: Area_{(circle)} = \pi r^2}}}}}} \: \: \bigstar \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ {{ { \sf{ \: \: Area_{(circle)} = 3.14 \times { \times (3.5)}^{2} }}}}}} \: \: \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ {{ { \sf{ \: \: Area_{(circle)} = 3.14 \times { \times 3.5 \times 3.5 }}}}}}} \: \: \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ {{ { \sf{ \: \: Area_{(circle)} = 3.14 \times 12 .25 }}}}}} \: \: \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ {{\pmb { \sf{ \: \: Area_{(circle)} = 38.465 }}}}}} \: \: \\ \\[/tex]

Therefore,

Answer:

6.9

Step-by-step explanation:

I took the USATP hope it helps

Answer:

C. 12 feet

Step-by-step explanation:

If a rectangle measures 1 foot by 5 feet, that means that one side is 1 foot and one side is 5 feet. Since a rectangle has two sets of parallel sides, the other sides of the rectangle will also measure 1 foot by 5 feet.

Adding all of the side lengths will give us the perimeter.

1 + 5 + 1 + 5 = 12

hope this helps :)

[tex]\textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\\ [1-sin^2(x)]csc(x)~~ = ~~cos(x)cot(x) \\\\[-0.35em] ~\dotfill\\\\\ [1-sin^2(x)]csc(x)\implies cos^2(x)csc(x)\implies cos^2(x)\cdot \cfrac{1}{sin(x)} \\\\\\ cos(x)\cdot \cfrac{cos(x)}{sin(x)}\implies cos(x)cot(x)[/tex]

The hypotenuse is the longer of the 3 sides:

answer: b.26

Answer:

[tex]\huge\boxed{\bf\: b. \: 26 \rightarrow hypotenuse }[/tex]

Step-by-step explanation:

Consider a right angled triangle with sides as 10, 26 & 24 units.

Here, we need to find the hypotenuse of the triangle.

The hyptenuse is the side which is opposite to the right angle (90°) & is also the longest side of the triangle.

Then, among the given values, we can clearly say that 26 > 10, 24.

Therefore, [tex]\boxed{\bf\: 26 \: units }[/tex] is the hypotenuse  of the triangle with side lengths as 10, 26, 24 units.

[tex]\rule{150pt}{2pt}[/tex]

Answer:

They are similar because triangle AMY has sides double the size of CED. If you divide AMY's triangle sides by 2, you will have a triangle that is the exact size of CED. :)

Have an amazing day!!

Please rate and mark brainliest!!!

Answer:

The triangles are similar

Step-by-step explanation:

To tell whether the triangles are similar or not we can compare their side lengths

if the triangle are similar then their side lengths' will be proportional:

MY/CD = AY/ED

10/5 = 8/4 cross multiply expressions

40 = 40 as we can see from this result, the side lengths are proportional so we can say these triangles are similar

Answer:

c. 11

Step-by-step explanation:

Bottom row: 6 cubes

middle row: 4 cubes

top row: 1 cube

11 cubes total.

subtraction/algebraic subtraction

What you have looks right, the reason for step 7 should just be algebraic subtraction since there is a DG on both sides that can be simplified out of the equation

I’m not sure what exact answer your question will allow, but it’ll be something along the lines of subtraction