For a beach trip, Sarai spends $9 on sunscreen, $18 on beach towels, $22 on food, $9 on a first aid kit, and $11 on sand toys.

Which of the following equations is in equation formed when completing the square on y^2 - 12 y= -27

bogdanovich [222]

Answer:

$(y-6)^2=9$

Step-by-step explanation:

Given

$y^2 - 12y = -27$

Required

Get equivalent expression using completing the square

<em>Follow these steps:</em>

<em>Take the coefficient of y; That is -12</em>

<em>Divide it by 2; That is (-12/2)</em>

<em>Square it: (-12/2)^2</em>

<em />

Add to both sides of the equation

$y^2 - 12y + (\frac{-12}{2})^2= -27 + (\frac{-12}{2})^2$

$y^2 - 12y + (-6)^2= -27 + (-6)^2$

$y^2 - 12y + 36= -27 + 36$

$y^2 - 12y + 36= 9$

Expand the right-hand side

$y^2 - 6y - 6y + 36= 9$

Factorize:

$y(y-6)-6(y-6) =9$

$(y-6)(y-6)=9$

$(y-6)^2=9$

5 0

3 years ago

A spool of rope contains 65 yards of rope. How many 4-foot pieces of rope can be cut from the spool? How much rope is left ov

Thepotemich [5.8K]

So there is 65 yards and one yard is 3 feet so you multiple 65 by 3 which is 195 . Then you divide by 4 as you have to see how many four foot pieces can be cut which you end up with 48.75 which means that you can have 48 four foot pieces. So since you have 48 four foot pieces you multiply 48 by 4 and you have 192 and if you subtract 195 which is how many feet there is in the 65 yards you get three feet and that is how much of the rope that is left over.

5 0

3 years ago

In a trapezoid the lengths of bases are 11 and 18. The lengths of legs are 3 and 7. The extensions of the legs meet at some poin

Mademuasel [1]

Answer: $7\frac{5}{7}$ unit and 18 unit

Step-by-step explanation:

Let ABCD is a trapezoid where AB and CD are the bases. ( In which AB is greatest base which shown in below figure)

AD and BC are the legs of the trapezoid ABCD.

Now, we have ( According to the question ),

AB = 18 unit, BC = 7 unit, AD = 3 unit and DC = 11 unit.

Here the leg AD extends from point D.

Similarly leg BC extends from point C.

Let they meet at point P ( shown in below diagram)

Since In triangles PAB and PDC,

∠PDC ≅ ∠PAB ( because DC ║ AB )

And, ∠ PAB ≅ ∠ PBA

∠DPC ≅ ∠ APB ( reflexive)

Therefore, By AAA similarity postulate,

$\triangle PDC \sim \triangle PAB$

Thus, By the definition of similarity,

$\frac{PD}{PA} = \frac{DC}{AB}$

$\frac{PD}{PD+3} = \frac{11}{18}$ ( because PA = PD+DA)

⇒ 18 PD = 11 PD +33

⇒7PD = 33

⇒ PD = 33/7

Again by the definition of similarity,

$\frac{PC}{PB} = \frac{DC}{AB}$

$\frac{PC}{PC+7} = \frac{11}{18}$ ( because PB = PC + CB)

⇒ 18 PC = 11 PD +77

⇒7PC = 77

⇒ PC = 11

Thus, PA = PD+DA = 33/7 + 3 = $7\frac{5}{7}$

And, PB = PC + CB = 11 + 7 = 18

8 0

3 years ago

PLSSS HELPpPP URGENT

lozanna [386]

Answer:

A.

Step-by-step explanation:

as u can see,the other acute angle is 43° and the other is also an acute angle and acute angles must not surpass until 80° meaning, the other acute angle is 47°

4 0

3 years ago

Read 2 more answers

What is the value of x when Rq=3x+2 ,QN =2x and SM=3x?

Andru [333]

The value of x is 2 because the centroid of the triangle divides each median in the ratio of 2:1 option (C) is correct.

<h3>What is the triangle?</h3>

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

RQ = 3x+2 ,QN = 2x and SM=3x

In the figure, the TM, Rn, and SL are medians of the triangle SRT and Q is the centroid.

The centroid of the triangle divides each median in the ratio 2:1

RQ/QN = 2/1

(3x+2)/2x = 2/1

After solving:

3x + 2 = 4x

x = 2

Thus, the value of x is 2 because the centroid of the triangle divides each median in the ratio of 2:1 option (C) is correct.

Learn more about the triangle here:

brainly.com/question/25813512

#SPJ1

5 0

2 years ago