What is the value of the expression?
-16+12

We simplify the expression -2√15(-8 + 10√15) = 150 + 16√15

To answer the question, we need to know what surds are

Surds are square roots of positive integers.

Since we have  -2√15(-8 + 10√15), we simplify the expression

So, -2√15(-8 + 10√15) = -2√15 × (-8) + 10√15 × √15 (expanding the bracket)

= -2× (-8) × √15 + 10 × √(15 × 15)

=  16 × √15 + 10 × √15²

=  16 × √15 + 10 × 15

=  16√15 + 150

=  150 + 16√15

So, we simplify the expression -2√15(-8 + 10√15) = 150 + 16√15

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The required, expression for the perimeter of the wood deck is 4w + 76 + 8c.

The length of the rectangular region will be the original length of the pool plus twice the width of the walkway since the walkway will extend out from both sides of the pool:

Length of rectangular region = 24 + 2c

Similarly, the width of the rectangular region will be the original width of the pool plus twice the width of the walkway:

Width of rectangular region = 14 + 2c

Now, to find the perimeter of the wood deck, we need to add up the lengths of all four sides of the rectangular region. Each side will have a length of w, since the wood deck extends w feet on all sides:

Perimeter of wood deck = 2(w + Length of rectangular region) + 2(w + Width of rectangular region)

Substituting the expressions we found for the length and width of the rectangular region, we get:

Perimeter of wood deck = 2(w + 24 + 2c) + 2(w + 14 + 2c)

= 4w + 76 + 8c

Therefore, the expression for the perimeter of the wood deck is 4w + 76 + 8c.

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Answer:

a) Prepare a frequency table for the data

Step-by-step explanation:

Answer:

a

2

​

=9a+b

2

​

Step-by-step explanation:

Answer:

Step-by-step explanation:

(a²+b²)²=(a²-b²)²+4a²b²=(a²-b²)²+4(ab)²=9²+4×3²=9²(1+4)

a²+b²=3√5

(a+b)²=a²+b²=2ab=3√5+2(3)=3(2+√5)

a+b=√3√(2+√5)

Answer:

a=π-3/5,B =π-2/5

Step-by-step explanation:

product of roots

sum of roots

Answer:

No

Step-by-step explanation:

You should only use t procedures when the sample sizes are less than 30, as that is when the Central Limit Theorem kicks in.

Essentially, t procedures are good for small samples while z procedures are better for larger samples.

Formula for finding mean:

Mean = (a1 + a2 + ... + an) / n

Mean is another word for  average; average number of a data set.

Problems with steps:

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

1) 9, 3, 6

Average =  Sum/Count

Sum =   18/6

Count = 3

2) 14, 12, 17, 9

52/4

Mean = 13

3) 15,8,10,5,7

= 45/5

Mean = 9

4) 18,19,11

= 48/3

Mean = 16

5) 4,20,16,4

= 44/4

Mean = 11

6) 12,11,12,20,15

= 70/5

Mean= 14

7) 19,8,3

= 30/3

Mean = 10

8) 7,13,6,2

= 28/4

Mean = 7

9) 12,15,17,2,14

60/5

Mean = 12

10) 10,18,8

= 36/3

Mean = 12

11) 5,2 ,0,1

= 8/4

= 2

12) 3,9,5,16,7

= 40/5

Mean = 8

SOLVED !

Hope this helps!

- ROR

The correct statement about the center of both box plots is the median for Town A, 30° is greater median for Town B, 25°

A box plot is used to study the distribution of a dataset. The box plot consists of two lines and a box. The two lines are known as whiskers. The whiskers represent the minimum and maximum numbers.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.

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In the polygon ABCD, the production of point A' and point D' is (-2,-2)  and (4,-2) respectively.

In coordinate planes, the rule of transformation involves interchanging the x and y values on the plane such that:

[tex]\mathbf{(x,y) \to (k_x, k_y)}[/tex]

where;

From the given information:

Now, using the coordinate vertices:

The corresponding coordinate of the image vertices is as follows:

A(-1,-1) → A'(2 × (-1), 2 × (-1))

A' = (-2,-2)

D(2,-1) → A'(2 × (2), 2 × (-1))

D' = (4,-2)

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The function C(g) that represents the total daily cost, C, of producing x golf clubs is C = 1671 + 60g

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

A plant can manufacture 50 golf clubs per day at a total daily cost of $4671 and 70 golf clubs per day for a total cost of $5871.

Let's suppose x is the fixed cost and y is the variable cost.

4671 = 50y + x …(1)

5871 = 70y + x …(2)

1200 = 20y

y = 60

x = 1671

Total cost:

C(g) = 1671 + 60g

g is the number of golf per day.

Slope = 60

y- Intercept = 1671 (from the graph)

Thus, the function C(g) that represents the total daily cost, C, of producing x golf clubs is C = 1671 + 60g

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(50, 22.5) is the solution of the system of equations, therefore, the true statement would be: Both plans cost the same when 50 texts are sent.

A solution to the system of linear equations is the point of intersection where both line of each equation meet.

The solution to the system of linear equations given in the graph attached below is (50, 22.5).

(50, 22.5) implies that both plans will cost the total amount when 50 text are sent.

The true statement using the graph would be: Both plans cost the same when 50 texts are sent.

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Answer:

Both plans cost the same when 22 texts are sent

Step-by-step explanation:

on edge

Answer:

Step-by-step explanation:

The given equations are:

1) 2y = -x + 9

⇒ x = 9-2y

2) 3x - 6y = -15

⇒3x = 6y - 15

x = 2y - 5

Equating the values of x, we get:

9 - 2y = 2y - 5

9 + 5 = 4y

14 = 4y

y = 3.5

Using this value of y in equation 1 we get:

x = 9 - 2(3.5) = 2

So, the solution set is (2, 3.5)

Answer:

I think it is c

Step-by-step explanation:

I graphed it

Applying the leg rule, the value of x in the given right triangle is: A. 6.

The leg rule for solving a right triangle having an altitude is expressed as:

hypotenuse/leg = leg/part.

In the image given we have the following:

Hypotenuse = 4 + 5 = 9 units

Leg = x

Part = 4

Plug in the values into the leg rule formula:

9/x = x/4

(x)(x) = (9)(4)

x² = 36

x = √36

x = 6 units.

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Answer: Answer is In the step-by-step EXPLANATION.

Step-by-step explanation: Let's Begin,

Amanda and Ndiba are selling flower bulbs for a school fundraiser. Customers can buy packages of tulip bulbs and bags of daffodil bulbs. Amanda sold 6 packages of tulip bulbs and 12 bags of daffodil bulbs for a total of $198.

6t + 12d = 198

Ndiba sold 7 packages of tulip bulbs and 6 bags of daffodil bulbs for a total of $127.

7t + 6d = 127

So when you find, the cost of each package of tulips bulbs and one bag of daffodil bulbs.  

Use elimination here, multiply the 2nd equation by 2, subtract the 1st equation

14t + 12d = 254

Then, 6t + 12d = 198 -subtraction eliminates d, find t

8t + 0 = 56

t = 56/8

t = $7 for tulips

Find d using the 1st equation, t=7

6(7) + 12d = 198

42 + 12 d = 198

12d = 198 - 42

d = 156/12

d = $13 for daffodils

And I think that's it.

Answer:

y = [tex]\frac{1}{2}[/tex] x

Step-by-step explanation:

the equation of a line passing through the origin is

y = mx ( m is the slope )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (6, 3) ← 2 points on the line

m = [tex]\frac{3-0}{6-0}[/tex] = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]

y = [tex]\frac{1}{2}[/tex] x ← equation of line

The transformation of A is A' = (8, -3)

From the graph, we have:

A = (3,1)

The scale factor and the center of dilation are given as:

k = 2

(a,b) = (-2,1)

The rule of reflection across the axis is:

(x,y) ⇒ (x,-y)

So, we have:

A' = (3,-1)

The rule of dilation is represented as:

(x,y) ⇒ (k(x - a) + a, k(y - b) + b)

So, we have:

A' = (2(3 + 2) - 2, 2(-1 - 1) + 1)

Evaluate

A' = (8, -3)

Hence, the transformation of A is A' = (8, -3)

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Answer:

110 / 360  * 40 pi

Step-by-step explanation:

Give circumference = 40 pi     (NOT 40 cm as posted)

AB covers a fraction of 360 complete circle   110/360 ths

  110/360   *  40 pi      units

The interval at which the function decrease is (-2,0) and the number of tulip bulb in the garden is 12.8

From the table, we can see that the value of the function decreases from 12 to 3 and finally to 0, when the values of x increase from -2 to 0

Hence, the interval at which the function decrease is (-2,0)

The square garden has a side length x.

So, the area (A) of the garden is:

A = x²

From the question, we understand that 5 tulip bulbs are to be planted per unit area.

This means that the number of bulb in the garden is:

n = 1/5 * x²

Evaluate

n = 0.2x²

When the side length of the garden is 8, we have:

n = 0.2 * 8²

Evaluate

n = 12.8

Hence, the number of tulip bulb in the garden is 12.8

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Answer:

1.89 x 5.42 x 5.2 inches

Step-by-step explanation:

Use your calculator or multiply it yourself, times all of them together.

I'm going to assume you start with

[tex]\dfrac{6^2 - 4 (3 - \sqrt{25})^2}{|4 - 8|}[/tex]

Let's simplify some pieces of this:

[tex]6^2 = 6\times6 = 36[/tex]

[tex]\sqrt{25} = \sqrt{5^2} = 5[/tex]

[tex](3 - \sqrt{25})^2 = (3 - 5)^2 = (-2)^2 = (-2)\times(-2) = 4[/tex]

[tex]|4 - 8| = |-4| = 4[/tex]

So as a first step we can reduce this to

[tex]\dfrac{6^2 - 4 (3 - \sqrt{25})^2}{|4 - 8|} = \dfrac{36-4\times4}4[/tex]

Now,

[tex]36 = 9\times4[/tex]

so every term contains a factor of 4 that we can cancel:

[tex]\dfrac{36-4\times4}4 = \dfrac{9\times4-4\times4}4 = \dfrac{9-4}1 = 9-4 = \boxed{5}[/tex]

as expected.

The solution to the equation one-third (x + 9) = negative 12 is  x = -45

The equation is given as:

one-third (x + 9) = negative 12

Rewrite properly as:

1/3 (x + 9) = -12

Multiply both sides by 3

x + 9 = -36

Subtract 9 from both sides

x = -45

Hence, the solution to the equation one-third (x + 9) = negative 12 is  x = -45

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Answer

36 units

Step-by-step explanation:

UW = UV + VW

9x-9 = 2x - 4 + 4x + 10

9x - 9 = 6x + 6

3x = 15

x = 5

UW = 9(5) - 9 = 45 - 9 = 36

answer is  36 units

Answer:

4×(x+1)(3x-8)(x+4)= (4x²+4)(3x-8)(x+4)= (12x³-32x²+12x²-32)(x+4)= (12x³-20x²-32)(x+4)= 12x⁴+48x³-20x³-80x²-32x²-128x= 12x⁴+28x³-112x²-128x

The correct answer is option C.Which is the inequalities that show the graphs are y < x and y > 2.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The inequality which is shown in the figure is y < x and y > 2.We can see in the graph when you plot y > 2 then it will cover all the values greater than 2 in the graph.

Similarly, if we plot the inequality y < x on the graph it will cover all the values of y which are less than x and intersect at the point ( 2, 2).

Therefore the correct answer is option C.Which is the inequalities that show the graphs are y < x and y > 2. The graph is attached with the answer below.

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Answer:

this is your answer

[tex] {9}^{4} [/tex]

[tex]\large{\sf \boxed{(\sf -3)^8}}[/tex]

[tex]\rightarrow \sf ((-3)^2)^4[/tex]

apply exponent rule: [tex]\sf \bf \left(a^b\right)^c=a^{bc}[/tex]

[tex]\rightarrow \sf (-3)^8[/tex]