In order to solve by completing the square, what value needs to be added to both sides of the equation:

Answer:

  a) 9^2

  b) 9^(1/2)

  c) 9^(3/2)

Step-by-step explanation:

It is perhaps easier to start by using 3^n.

  3 = 3^1

  27 = 3^3

  81 = 3^4

Recognize that 3 = 9^(1/2) and replace 3 in each of the above. The applicable rule of exponents is (a^b)^c = a^(bc).

a) 81 = (9^(1/2))^4 = 9^2

b) 3 = 9^(1/2)

c) 27 = (9^(1/2))^3 = 9^(3/2)

Answer:

(a) 9^2

(b) 9^0.5

(c) 9^1.5

Step-by-step explanation:

We need to find n such that 9^n = value indicated.

Recall that n=2 is a square, so

(a) 9^2=9*9=81

Recall that n=0.5 (or 1/2) is a square root, because 9^0.5 * 9^0.5 = 9^1 = 9, so

(b) 9^0.5 = 3, because 3*3 = 9

Recall that multiplication of two powers with the same base is the sum of the exponents, e.g. 9^a * 9^b = 9^(a+b).

Therefore,

(c) 27 = 9*3 = 9^1 * 9^0.5 = 9^(1+0.5) = 9^1.5

This is the same as saying 27 cubic inches

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

Explanation:

We get the volume of a cube by using the formula

V = s^3

where the cubed exponent is directly tied together with the idea of volume being in cubic units. In this case, s = 3 which leads to

V = s^3

V = 3^3

V = 3*3*3

V = 27 cubic inches

As another example, let's say s = 4. That means

V = s^3

V = 4^3

V = 4*4*4

V = 64

We multiply the side length by itself having three copies total. This formula only applies to cubes. A more generalized formula for rectangular blocks is V = L*W*H where L,W,H are the length width and height in that order. This generalized formula allows for side lengths to be different, but if L = W = H, then it makes more sense to go with the first formula instead.

Answer:

∠ A ≈ 44.42°

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos A = [tex]\frac{adjacent}{hypotenuse}[/tex]  = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{5}{7}[/tex] , then

∠ A = [tex]cos^{-1}[/tex] ([tex]\frac{5}{7}[/tex] ) ≈ 44.42° ( to the nearest hundredth )

PR / Sin(Q) = QR / Sin(P)

53 / Sin(90) = 45 / Sin(P)

53 / 1 = 45 / Sin(P)

Sin(P) = 45 / 53

Sin(P) = 0.8490566038

P = 58.11 degrees

Answer:

58.11°

Step-by-step explanation:

tan P = 45/28 = 1.607

< P = tan`¹ 1.607 = 58.11°

Answer:

the temperature is above zero

Step-by-step explanation:

hope it helps

Answer:

solved graphically,

it's just the point where the two lines intersect

Answer:

A = 388.58 cm^2

Step-by-step explanation:

For a cone whose base has a radius R, and a hypotenuse S, the area is:

A = pi*R^2 + pi*R*S

Where pi = 3.14

In this case, we can see that the diameter is: 15cm

Then the radius, half of the diameter, is:

R = 15cm/2 = 7.5cm

The hypotenuse is 9cm, then S = 9cm

A = 3.14*(7.5cm)^2 + 3.14*(9cm)*(7.5cm) = 388.575 cm^2

Rounding to two decimal places, we need to look at the third one, which is a five, so we need to round up:

A = 388.58 cm^2

Answer: 26

Step-by-step explanation:

I dont know if this was the right answer, I just divided

Answer:

26 smaller bags

Step-by-step explanation:

Answer:

A. AB≈ DE

is the answer to this question

Answer:

[tex] {5}^{2x + 1} \div 25 = 125[/tex]

[tex] {5}^{2x + 1} \div 5² = 5³[/tex]

doing crisscrossed multiplication

[tex] {5}^{2x + 1}=5³×5²[/tex]

In multiplication common numbers is added

[tex] {5}^{2x + 1}=5^{3+2}[/tex]

If there is a same term than it can be add ,subtract .

;.

2x+1=5

2x=5-1

x=[tex] 4\div 2 [/tex]

x=2 is a required answer.

Answer:

I think it's C and E am not sure

Answer:

5

Step-by-step explanation:

4x-9y= -1

so change 4x-9y to 1 in

6+(-1) = 5

Answer:

4x-9y=-1

4x=-1+9y

Step-by-step explanation:

6+4x-9y

6+(-1+9y)-9y

6-1+9y-9y

5+0

5

Answer:

It's B , or #2

2x-3y<7

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

it just is lol k

12345678]

Answer:

A=28

Step-by-step explanation:

A^2+21^2=35^2

A^2+441=1225

A^2=784

A=28

Given:

Consider the below figure attached with this question.

To find:

The conclusion that can be determined from the dot plot.

Solution:

The number of dots in the dot plot is 15. So, the number of observations is 15 and option D is correct.

The data set represented by the dot plot is:

2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6

Number of observations is 15, which is an odd number. So, the median of the data set is:

[tex]Median=\dfrac{15+1}{2}\text{th term}[/tex]

[tex]Median=\dfrac{16}{2}\text{th term}[/tex]

[tex]Median=8\text{th term}[/tex]

[tex]Median=4[/tex]

The median of the data set is 4. So, option A is incorrect.

Mean of the data set is:

[tex]Mean=\dfrac{\text{Sum of all observations}}{\text{Number of observations}}[/tex]

[tex]Mean=\dfrac{2+2+3+3+3+4+4+4+4+4+5+5+5+6+6}{15}[/tex]

[tex]Mean=\dfrac{60}{15}[/tex]

[tex]Mean=4[/tex]

The mean of the data set is 4. So, option B is incorrect.

The range of the data set is:

[tex]Range = Maximum - Minimum[/tex]

[tex]Range = 6-2[/tex]

[tex]Range = 4[/tex]

The range of the data set is 4. So, option C is incorrect.

Therefore, the correct option is D.

Answer:

x=24   2x=48

Step-by-step explanation:

We first do 112-64 which will give us 2x.

So, we know 48=2x.

divide both sides by two and we get:

x=24

Answer:

B

Step-by-step explanation:

2x and 48 are opposite from each other, making them equal

if you put them into an equation to solve for x, you get:

2x=48

/2    /2

x=24

now that you have x, you can plug it back into the original equation to get: 48

Answer:

Step-by-step explanation:

the answer is d

b/c when you see the parabola lie in -3<x>1

it is down ward because the function is negative

Answer:

-0.5

Step-by-step explanation:

Slope (m) = [tex]\frac{1.3 - 3.8}{0.18 + 4.82}[/tex]

or, m = -2.5/ 5

or, m = -1/2 = -0.5

∴Slope is -0.5

Answer:

58

Step-by-step explanation:

The center line in a box plot represents the median

33517

Method 1

Given:

374F in base 16

To convert to octal;

(i) convert each digit in the number to binary

3 = 0011

7 = 0111

4 = 0100

F = 1111

(ii) join the bits together starting from the first i.e

374F = 0011 0111 0100 1111

(iii) starting from the right to left, group the bits together, each group having 3 bits

374F = 0 011 011 101 001 111

(iv) the group with number of bits less than 3 should be padded with zero.

374F = 000 011 011 101 001 111

(v) convert each of the groups in (iv) above to decimal as follows:

000 = 0

011 = 3

011 = 3

101 = 5

001 = 1

111 = 7

(vi) combine the result above to get;

033517

The first zero can be removed

33517

Therefore, the number in octal is 33517₈

Method 2

Given:

374F in base 16

To convert to octal;

i) convert the number to decimal as follows;

a. Multiply each digit by 16 raised to the power of one less than their position starting from the leftmost digit.

=> 3 is at position 4, so we have

3 x 16⁴ ⁻ ¹ = 3 x 16³

=> 7 is at position 3, so we have

7 x 16³ ⁻ ¹ = 7 x 16²

=> 4 is at position 2, so we have

4 x 16² ⁻ ¹ = 4 x 16¹

=> F is at position 1, so we have

F x 16¹ ⁻ ¹ = F x 16⁰

b. Add each of the terms found in (a) together.

(3 x 16³) + (7 x 16²) + (4 x 16¹) + (F x 16⁰)

c. Remember that F = 15 in decimal. Therefore, substitute F = 15 into the result in (b)

(3 x 16³) + (7 x 16²) + (4 x 16¹) + (15 x 16⁰)

d. Solve the result in (c)

(3 x 4096) + (7 x 256) + (4 x 16) + (15 x 1)

12288 + 1792 +64 + 15

14159

Therefore,

374F in decimal is 14159

(b) Now convert the decimal to octal by dividing by 8 and noting the remainder.

8 | 14159

8 | 1769 r 7

8 | 221 r 1

8 | 27 r 5

8 | 3 r 3

  | 0 r 3

Taking the remainders from bottom up gives

33517₈

Therefore, the number in octal is 33517₈

Answer: C 1.6 K cents

Step-by-step explanation:

8 divided by 5 equals 1.6. 1.6 times 1 aka K equals 1.6 1.6 K cents or C is your answer.

Answer:

200

Step-by-step explanation:

Answer:

5 postcards

Step-by-step explanation:

65/100 + 30/100 (change it) = 95/100

Answer:

x = -8, y = 6

Step-by-step explanation:

x + 2y = 4 ------(1)

x + y = - 2

y = - x - 2 ----------(2)

Substitute y in (1)

x + 2(- x - 2) = 4

x - 2x - 4 = 4

- x = 4 + 4

x = -8

Substitute x in (2)

y = - (- 8) - 2 = 8 - 2 = 6

Answer:

x = - 1

Step-by-step explanation:

Given

4x = x^2 - 5               Transfer 4x to the right side.

Solution

x^2 - 4x - 5 = 0          Factor

(x - 5)(x + 1)

You want the negative solution. That means that the middle sign must be plus.

x + 1 = 0                   Subtract 10 from both sides

x = - 1                       Ten on the left disappears by the subtraction process.

Is that correct?

4x = x^2 - 5

x = - 10

4*(-1) = (-1)^2 - 5

-4  = ? 1 - 5

-4 = - 4

and it does work.  

Answer:

slope = 3/7

Step-by-step explanation:

To find slope we need two coordinates from the line.

Let it be (-7, 0) and (3, 0)

[tex]slope, m = \frac{y_2-y_1}{x_2-x_1}= \frac{3-0}{0--7} = \frac{3}{7}[/tex]

Answer:15

Step-by-step explanation:

Answer:

because it has the words "less than", the "-2" is after the multiplication which is "2n" so the answer is...

D.) 2n-2

Step-by-step explanation:

Step-by-step explanation:

a) the ratio between their altitudes = 3:5

b) the ratio between their base areas = 9:25

c) the ratio between their lateral edges = 3:5

d) the ratio between their volumes = 27:125

e) the ratio between their lateral areas =9:25

Answer:

7 = The y-intercept of the exponential function

1 = The y-intercept of the linear function

2 = The number of points of intersection

5 = The y-value of the solution in Quadrant I

Tell me if i'm wrong