Which are steps in the process of completing the square used to solve the equation? 1 = 2(x2 + 2x) 1 = 2x2 + 4x 2 = 2(x2 + 2x + 1) 3 = 2(x + 1)2 2 = 2(x + 1)2

Answer:

Perimeter of square = [tex]12\sqrt{2}\,\,inches[/tex].

None of the given options is correct

Step-by-step explanation:

Given: Length of diagonal of the square = 6 inches

To find: perimeter of square

Solution:

Let x denotes side of square

Diagonal of square = [tex]\sqrt{2}x[/tex]

Also,  length of diagonal of the square = 6 inches

So,

[tex]x=\frac{6}{\sqrt{2}}\\=\frac{6}{\sqrt{2}}\left ( \frac{\sqrt{2}}{\sqrt{2}} \right )\\=3\sqrt{2}[/tex]

Perimeter refers to the distance around a two-dimensional shape.

Perimeter of square = 4×side

=[tex]4(3\sqrt{2})=12\sqrt{2}\,\,inches[/tex]

So, none of the given options is correct.

Answer:

A': (2, 8)

Step-by-step explanation:

I have attached the work to your problem below.

I hope this helps.

Answer:

B. 63°

Step-by-step explanation:

The distance around a circle is 360°

This means that 297° + n = 360°

Equation:

297 + n = 360

We can find the value of n by subtracting:

297 + n = 360

-297        -297

n = 63

Therefore, the value of n is 63 degrees.

Answer:PPlEASeee

Step-by-step explanation:

Answer:

Step-by-step explanation

(a) 1/10 × 750g=75g

(b)1/10 ×45g=4.5g

(c)1kg=1000g

=1/10×1000g=100g

(d)1/10×1259g=125.9g

Hope it helps you!!

Answer:

Step-by-step explanation:

a) Amount of Sugar = (1/10) of 750 g

                                 [tex]\frac{1}{10}*750\\\\[/tex]

                                = 75 g

b)Amount of Sugar = (1/10) * 45

                                = 4.5 g

c) Amount of Sugar = (1/10) * 1000 g   {1 kg = 1000g}

                                = 100 g

d) Amount of Sugar = (1/10) *1259

                                = 125.9 g

Answer:

Step-by-step explanation:

I hope it helps

Answer:

1

Step-by-step explanation:

3/11 / 3/11

=3/11 * 11/3

=1

Answer:

D. He distributed Negative one-fourth over (8 x + 12), distributed –1 over (Negative 2 x + 5), and then combined like terms.

Step-by-step explanation:

We know that when using the distributive property, you have to multiply the outside value with the inside value and then either subtract or add.

You can combine like terms first, but that is only if there are like terms inside the parentheses. In this case, there are not, so you would distribute first.

So, to do that, you have to first distribute -1/4 to the 8x+12 and then distribute the -1 to the -2x+5. (note that they did not include the 1, but it is still there)

So, it is D

Answer:

= 100 km

Step-by-step explanation:

Total length = 5/5

Covered length = 2/5

Remaining length = 5/5 - 2/5 = 3/5

If 3/5 = 60 km

What about 5/5 = ?

= 5/5 x 60 x 5/3 (reciprical)

= 60 x 5/3

= 300/3

= 100 km

Covered distance = 100 - 60 = 40 km

Answer:

area of shaded portion=56 - 1/2 ×3×4=56-6= 50 yd^2

Answer:

D

Step-by-step explanation:

on edge

Answer:

D

Step-by-step explanation:

Answer:

14,130 feet³

Step-by-step explanation:

2r=d

2r=30

r=15

Formula for the volume of a cone is: [tex]\frac{1}{3} *b*h[/tex]

[tex]\frac{1}{3} *[/tex]π[tex]*r[/tex]²[tex]*h[/tex]=

[tex]\frac{1}{3} *3.14*15^{2} *60=\\[/tex]

[tex]\frac{1}{3} *3.14*225*60=[/tex]

[tex]\frac{1}{3} *3.14*13,500=\\[/tex]

[tex]\frac{13,500}{3} *3.14=\\[/tex]

[tex]4500*3.14=[/tex]

14,130 feet³

Answer: -2

Step-by-step explanation: This equation is written in y = mx + b form.

The slope is the multiplier or the coefficient of

the x-term whcih in this case is -2/

Answer:

-2

Step-by-step explanation:

slope is number next to x in equation y = mx + b

Answer:

x ≈ - 0.7 ≈ 0.7; Option A

Step-by-step explanation:

Let us substitute f ( x ) with 0, as to find the " real zero value( s ) " of the function;

0 = 3x^4 + x^2 - 1 ⇒ Swap sides, as such,

3x^4 + x^2 - 1 = 0 ⇒ Rewrite equation with u being = x^2, u^2 = x^2,

3u^2 + u - 1 = 0 ⇒ And solve for u by completing the square,

3u^2 + u = 1 ⇒ Divide either side by 3,

u^2 + u / 3 = 1 / 3 ⇒ Write equation in the form x^2 + 2ax + a^2 = ( x + a )^2, solving for a,

2au = 1 / 3u,

a = ( 1 / 3u ) / 2u,

a = 1 / 6 ⇒ Add value of a^2 to either side of equation,

u^2 + u / 3 + ( 1 / 6 )^2 = 13 / 36,

( u + 1/ 6 )^2 = 13 / 36 ⇒ Solve for u,

u = ( √13 - 1 ) / 6, and u = ( - √13 - 1 ) / 6 ⇒ Substitute value of u back into first equation to solve for x,

x = √( - 1 + √13 ) / 6 ), x = - √( - 1 + √13 ) / 6 ), x = √( - 1 - √13 ) / 6 ), x = - √( - 1 - √13 ) / 6 ) ⇒ Convert to approximate decimal form,

x = 0.6589.... = - 0.6589....

Answer; x ≈ - 0.7 ≈ 0.7; Option A

Step-by-step explanation:

4 + 3x -20 = 0

3x - 16 = 0

3x = 16

x = 16/3

Answer:

3 vases chipped.

Step-by-step explanation:

Let's use a ratio:

chipped : all

     2      :   12

     1       :    6

     3      :    18

We can expect 3 out of 18 vases to be chipped.

Answer:

1

Step-by-step explanation:

First, write the experimental probability as a fraction in simplest form.

P(chipped)

=

chipped

total

=

2

20

=

1

10

The experimental probability is

1

10

.

We can predict the outcome of the second set of trials by assuming that the ratio will be the same as in the first set of trials. Write a proportion by setting the two ratios equal to each other, then solve.

1

10

=

n

10

1

10

(1010)

=

n

10

(1010) Multiply both sides by (1010)

110

= 10n Simplify

10

= 10n Simplify

1

= n Divide both sides by 10

You would expect 1 of the next 10 vases to be chipped.

Answer:

[tex]l \approx 15.455\,ft[/tex]

Step-by-step explanation:

The length of the ramp is computed with the help of the following trigonometric function:

[tex]\sin \theta = \frac{h}{l}[/tex]

[tex]l = \frac{h}{\sin \theta}[/tex]

[tex]l = \frac{4\,ft}{\sin 15^{\circ}}[/tex]

[tex]l \approx 15.455\,ft[/tex]

Answer:

A. Figure A

Step-by-step explanation:

The protractor on the top left has an arrow halfway inbetween 50° and 60, making the angle 55°.

Therefore, the answer is Figure A.

Answer:

Rectangles, squares, and rhombus are quadrilaterals that have attributes of a parallelogram.

Step-by-step explanation:

Answer:

f(1) =2

Step-by-step explanation:

f(x) = 4^x- 2

Let x=1

f(1) = 4^1 -2

     =4-2

     =2

Answer: ab + bc + ac = 155

Step-by-step explanation:

Given: a² + b² + c² = 90      and     a + b + c = 20

Square the second equation, subtract it from the first equation, then simplify.

Square the second equation:

(a + b + c)² = 20²

a² + b² + c² + 2ab + 2bc + 2ac = 400

Subtract the equations:

   a² + b² + c² + 2ab + 2bc + 2ac = 400

- (a² + b² + c²                                 = 90)

                         2ab + 2bc + 2ac = 310

Simplify:

2(ab + bc + ac) = 310

÷2                      ÷2    

  ab + bc + ac = 155

Answer:

Paul can drive 162.14 miles a day for the budget of 120 dollars.

OB. C=38.93+0.50x

Step-by-step explanation:

120=C

120=38.93+0.50x

81.07=0.50x

162.14=x

Answer:

Median: 11

Range: 12

25% percentile: 9

75% percentile: 14

IQR: 5

Step-by-step explanation:

Least: 7

Q1: 9

Q2: 11

Q3: 14

Max: 19

Median: 11

Range: 19 - 7 = 12

25% percentile: 9

75% percentile: 14

IQR: 14 - 9 = 5

Step-by-step explanation:

Step 1:  Find the median

The median on the box-and-whisker plot is the line that is inside of the box.  On this plot, the median is 11 since it is where the line is.

Step 2:  Find the range

The range on a box-and-whisker plot is the difference from the largest point and the smallest point.  On this plot, the largest point is 19 and the smallest point is 7.  So, subtract 7 from 19 and you get that the range is 12.

Step 3:  Find the 25th percentile

The 25th percentile on a box-and-whisker plot is the left side of the box object.  On this plot, the 25th percentile is 9.

Step 4:  Find the 75th percentile

The 75th percentile on a box-and-whisker plot is the right side of the box object.  On this plot, the 75th percentile is 14.

Step 5:  Find the inter-quartile range

The inter-quartile range on a box-and-whisker plot is the difference between the 75th percentile or right side of the box and the 25th percentile or the left side of the box.  On this plot, the 75th percentile is 14 and the 25th percentile is 9.  So, subtract 9 from 14 and you get that the inter-quartile range is 5.

Q 5) No. of boys = 20

Answer:

Q 6) Total time taken to answer both the quizzes = 90 minutes

Step-by-step explanation:

Q 5.

Let the number of boys = x

Therefore, number of girls = x - 5

Since,

No. of boys + No. of girls = 35

hence,

x + x- 5 = 35

2x-5 = 35

2x = 35 + 5

2x = 40

x = 40/2

x = 20

Hence 20 boys participated in the activity.

Let the time taken to answer history quiz= x min

Therefore, time taken to answer geography quiz = (x + 30) min

According to the given information:

x = 1/2(x + 30)

2x = x + 30

2x - x = 30

x = 30 min

Hence, x + 30 = 30 + 30 = 60 min

Total time taken to answer both the quizzes = 30 + 60 = 90 minutes

Answer:

[tex]\cos \theta=-\dfrac{8}{17}[/tex]

Step-by-step explanation:

Coordinates of Point b[tex]=(-8,15)[/tex]

b lies on the circle whose equation is [tex]x^2+y^2=289[/tex]

[tex]x^2+y^2=17^2[/tex]

Comparing with the general form a circle with center at the origin: [tex]x^2+y^2=r^2[/tex]

The radius of the circle =17 which is the length of the hypotenuse of the terminal ray through point b.

For an angle drawn in standard position through point b,

x=-8 which is negative

y=15 which is positive

Therefore, the angle is in Quadrant II.

[tex]\cos \theta=\dfrac{Adjacent}{Hypotenuse} \\$Adjacent=-8\\Hypotenuse=17\\\cos \theta=\dfrac{-8}{17} \\\cos \theta=-\dfrac{8}{17}[/tex]

Answer:

x = 6

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

1+3 is 4

16÷4 is 4

4+4 is 8

Answer:

8

Step-by-step explanation:

16

4

+1+3

=4+1+3

=4+4

=8

Answer:

x=-1      x=5

Step-by-step explanation:

f(x) =−3(x+1)(x−5)

0 = −3(x+1)(x−5)

Using the zero product property

x+1 = 0     x-5=0

x=-1      x=5