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3 years ago

Simplify. 57r−27r this problem

Mathematics

2 answers:

Rashid [163]3 years ago

7 0

Answer:

$\boxed{=30r}$

$\boxed{r=30}$

Step-by-step explanation:

Distributive property: ⇒ $a(b+c)=a(b)+a(c)$

First you had to add 57 from both sides of an equation form.

$57r+57-27+57$

$57+-27=30$

Hope this helps!

And thank you for posting your question at here on brainly, and have a great day.

-Charlie

Leno4ka [110]3 years ago

5 0

The answer should be 30r

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Please help me <br> 30 points <br> Show you work

GenaCL600 [577]

Answer:

(a) A translation is a rigid transformation. How does this statement support line s being parallel to line r?

Because ALL of the points of line r move the same distance in the same direction, then the inclination of the line s doesn't change with respect line r.

(b) Write and expression for the slope of line r:

(k-n)/(j-m)

(d) Line q is a vertical is a vertical translation of line s 3 units down. P'' is the image of P'. What are the coordinates of P''?

The coordinates of P'' are:

P''=(m,n+ϴ-3)

Step-by-step explanation:

(a) A translation is a rigid transformation. How does this statement support line s being parallel to line r?

Because ALL of the points of line r move the same distance in the same direction, then the inclination of the line s doesn't change with respect line r.

(b) Write and expression for the slope of line r.

Line r goes through the points:

P=(m,n)=(xp,yp)→xp=m, yp=n

Q=(j,k)=(xq,yq)→xq=j, yq=k

Slope of line r is:

mr=(yq-yp)/(xq-xp)

Replacing the coordinates, the expression for the slope of line r is:

mr=(k-n)/(j-m)

Line s goes through the points:

P'=(m,n+ϴ)=(xp',yp')→xp'=m, yp'=n+ϴ

Q'=(j,k+ϴ)=(xq',yq')→xq'=j, yq'=k+ϴ

Slope of line s is:

ms=(yq'-yp')/(xq'-xp')

Replacing the coordinates, the expression for the slope of line s is:

ms=[(k+ϴ)-(n+ϴ)]/(j-m)

Eliminating the parentheses in the numerator:

ms=[k+ϴ-n-ϴ]/(j-m)

Simplifyng:

ms=(k-n)/(j-m)

(d) Line q is a vertical is a vertical translation of line s 3 units down. P'' is the image of P'. What are the coordinates of P''?

3 units down, then change only the ordinate y:

P''=(xp',yp'-3)

Replacing xp' and yp':

P''=(m,n+ϴ-3)

7 0

3 years ago

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A piece of cardboard is 13 inches by 26 inches. A square is to be cut from each corner and the sides folded up to make an open-t

Vanyuwa [196]

Answer:

Hence the maximum possible volume will be the 778.53 c.c

Step-by-step explanation:

Given:

A rectangle with 13 x 26 dimensions

And corners are cut to form side squares.

To Find:

Maximum possible volume for box

Solution :

Consider a rectangle of 13 x 26 dimension with and side of square at corner be x.

(Refer the attachment)

Now,

Formulating the volume equation for the box

So corner square sides we are going to fold up which makes height of the box

and remaining part will be length and breadth

As shown in fig,

Length=26-x

breadth=13-x

And height will be x

$V(x)=x*(26-x)*(13-x)$

To get maximum volume differentiate the above equation,

$V(x)=x*(26*13-26*x-13*x+x^2)$

$V(x)=x^3-39x^2+338x\\$

$V'(x)=3x^2-78x+338$

$V''(x)=6x-78$

Now ,Solve the Quadratic Equation to get x values,

$3x^2-78x+338$ =0

x=[-b±(b^2-4ac)^1/2]/2a

x=[78±Sqrt[(78)^2-4*338*3)]/2*3

x=[78±Sqrt(3028)]/6

x=[78±55.027]/6

x=78+55.027/6 or x=78-55.027/6

x=22.17 or x=3.8288

Use these values in 6x-78 to know which value posses the max and min value for the function.

So when x=22.17

6x-78=6*22.17-78

=55.02>0 i.e function will have minimum value .

When x=3.8288

6*3.8288-78

=-55.0272<0 i.e. Function will have maximum value

Now, the function will defines the maximum volume

$V(x)=x^3-39x^2+338x$

$V(x)=3.8288^3-39*(3.82883)^2+338*3.8288$

$V(x)=56.13-571.73+1294.13$

$V(x)=778.53 C.C$

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3 years ago

A7-ft ladder is placed against a wall with its base 3 ft from the wall. How high above the ground is the top of the ladder? Roun

Firdavs [7]

Answer:

6.3 feet

Step-by-step explanation:

use pythagorean theorem

a² + b² = c²

a² + 3² = 7²

a² + 9 = 49

Subtract 9 from both side

a² = 40

Take the square root of both sides

a = 6.324555320336759

Rounded

a = 6.3

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3 years ago

(Pls help i need this ASAP I got 5 min left) If ΔSTU is reflected over the y-axis, what are the coordinates of the vertices of Δ

Svetradugi [14.3K]

Answer:

T(2,4) S(3,2) U(1,1)

Step-by-step explanation:

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3 years ago

Which inequality represents all values of x for which the product below is defined?

Vedmedyk [2.9K]

Step 1 ) Separate the 4 and x.

$\displaystyle\sqrt{4x} * \sqrt{x+2}$

↓

$\displaystyle\sqrt{4} \sqrt{x} \sqrt{x+2}$

Step 2 ) Simplify the square root of 4.

$\displaystyle\sqrt{4} \sqrt{x} \sqrt{x+2}$

↓

$\displaystyle\ 2 \sqrt{x} \sqrt{x+2}$

Step 3 ) Simplify.

$\displaystyle\ 2 \sqrt{x} \sqrt{x+2}$

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$\displaystyle\ 2 \sqrt{x(x+2)}$

This is now in its simplest form, so the final answer is...

$\displaystyle\ 2 \sqrt{x(x+2)}$

or it could be...

$\displaystyle\ 2 \sqrt{x} \sqrt{x+2}$

Either one is correct. Only difference is one is in simplest form and one isn't.

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- Marlon Nunez

7 0

3 years ago

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