Describe how you can use compatible numbers to estimate 17 x 27

Answer:

I think it's rotated 90 degrees clockwise

Step-by-step explanation:

The transformation of circle K to circle K' is a translation, specifically a movement of 4 units to the right and 10 units down, represented by T(4, -10).

The transformation that maps circle K to circle K' is a translation. In a translation, every point of the object moves the same distance in the same direction. For circle K to circle K', this would be a shift 4 units to the right and 10 units down. The coordinates of the center of the circle move from (3,7) to (7,-3). We can calculate this movement by subtracting the initial coordinates from the final ones: (7-3, -3-7) = (4, -10). Therefore, the transformation would be written as T(4, -10).

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Answer:

x = -3/7

Step-by-step explanation:

We are given the following equation for which we have to solve for x:

[tex]3(3x - 1) + 2(3 - x) = 0[/tex]

So we will start by expanding the equation by multiplying the common factor with the brackets to get:

[tex]9x-3+6-2x=0[/tex]

Arranging the like terms together (variables on one side of the equation and constants on the other side) to get:

[tex]9x-2x=3-6\\\\7x=-3\\\\x=-\frac{3}{7}[/tex]

Therefore, x = -3/7.

Answer:

81

Step-by-step explanation:

45% × 180 = [tex]\frac{45}{100}[/tex] × 180 = 81

Answer:

The answer is  81

Step-by-step explanation:

You can do it following the next steps

1.- Place the the "45" by 100 = 0.45

2.- Multiply 0.45 times 180= 81

Answer:

The answer is 1/square root 2

Step-by-step explanation:

The correct measure of angle 2 is [tex]\( m\angle2 = 130\°\)[/tex].

To find the measure of angle 2, we need to use the properties of parallel lines and the angles formed when a transversal intersects them. When a transversal intersects two parallel lines, corresponding angles are equal, and alternate interior angles are also equal.

In the given scenario, lines b and c are parallel, and we assume that the transversal intersects these parallel lines at points not shown in the conversation. Let's denote the angles formed by the intersection of the transversal with line b as angles 1, 2, 3, and 4, and with line c as angles 5, 6, 7, and 8, respectively.

Since lines b and c are parallel, we have the following relationships:

1. [tex]\( m\angle1 = m\angle5 \)[/tex] (corresponding angles)

2. [tex]\( m\angle2 = m\angle6 \)[/tex] (corresponding angles)

3. [tex]\( m\angle3 = m\angle7 \)[/tex] (corresponding angles)

4. [tex]\( m\angle4 = m\angle8 \)[/tex] (corresponding angles)

5. [tex]\( m\angle1 = m\angle8 \)[/tex] (alternate interior angles)

6. [tex]\( m\angle2 = m\angle7 \)[/tex] (alternate interior angles)

7. [tex]\( m\angle3 = m\angle6 \)[/tex] (alternate interior angles)

8. [tex]\( m\angle4 = m\angle5 \)[/tex] (alternate interior angles)

From the given options, we can eliminate [tex]\( m\angle2 = 31\° \)[/tex] and [tex]\( m\angle2 = 50\° \)[/tex] because these options would imply that [tex]\( m\angle6 \) and \( m\angle7 \)[/tex] are also [tex]\( 31\° \) and \( 50\° \)[/tex], respectively. This would mean that the sum of the angles in the triangle formed by the transversal and line c would be less than [tex]\( 180\° \)[/tex], which is impossible.

Next, we consider [tex]\( m\angle2 = 120\° \)[/tex]. If this were true, then [tex]\( m\angle7 \)[/tex] would also be [tex]\( 120\° \)[/tex]. However, this would imply that the sum of the angles in the triangle formed by the transversal and line c would be [tex]\( 120\° + 60\° \)[/tex] (since [tex]\( m\angle6 \) and \( m\angle8 \)[/tex] would be supplementary, adding up to [tex]\( 180\° \)[/tex]), which again is impossible because the sum of angles in any triangle is [tex]\( 180\° \).[/tex]

Finally, we consider [tex]\( m\angle2 = 130\° \)[/tex]. This option is possible because if [tex]\( m\angle2 = 130\° \)[/tex], then [tex]\( m\angle7 \)[/tex] would also be [tex]\( 130\° \)[/tex]. The remaining angle in the triangle formed by the transversal and line c (which is [tex]\( m\angle6 \) or \( m\angle8 \)[/tex]) would be [tex]\( 180\° - 130\° = 50\° \)[/tex]. This satisfies the triangle angle sum property, as [tex]\( 130\° + 50\° = 180\° \)[/tex].

Therefore, the correct measure of angle 2 is [tex]\( m\angle2 = 130\° \)[/tex].

The complete question is:

Lines b and c are parallel. What is the measure of 2?

m2 = 31°

m2 = 50°

m2 = 120°

m2 = 130°

Answer:

The correct answer is (−4, −8)

Step-by-step explanation:

You have to substitute!!! :)

−3x + 4y = −20                y = x − 4

-3(4) + 4(8) = -20             8 = 4 - 4

-12 + 32 = -20                  8 = 0

20 = 20

−3x + 4y = −20                y = x − 4

-3(0) + 4(-5) = -20           -5 = 0 - 4

0 + 20 = -20                    -5 = -4

20 = -20

−3x + 4y = −20                y = x − 4

-3(-2) + 4(-6) = -20          -6 = -2 - 4

6 - 24 = -20                    -6 = -6

-18 = -20      

−3x + 4y = −20                y = x − 4

-3(-4) + 4(-8) = -20         -8 = -4 - 4

12 - 32 = -20                  -8 = -8

-20 = -20

Answer:

(-4,-8)

Step-by-step explanation:

This a system of equation that have two variables x and y and we have two equations that we have to solve simultaneously

−3x+4y=−20 ....(1)

y=x−4 ....(2)

We can substitute equation (2) and (1)

-3x+4y = −20

-3x+4(x−4) = −20

-3x + 4x -16 = -20

x = -4

Now we need to find the value of y

y=x−4 = -4 - 4 = -8

(-4,-8)

Final answer:

To find the value of p when c = 3.2, substitute c = 3.2 into the expression for p. The value of p is 2. To find the value of c when p = 85, substitute p = 85 into the expression for p and solve for c. The value of c is -30.

Explanation:

To find the value of p when c = 3.2, we substitute c = 3.2 into the expression for p.

Substituting c = 3.2 into p = 10 - 2.5c, we get p = 10 - 2.5 * 3.2 = 10 - 8 = 2.

So, p = 2 when c = 3.2.

To find the value of c when p = 85, we substitute p = 85 into the expression for p.

Substituting p = 85 into p = 10 - 2.5c, we get 85 = 10 - 2.5c.

Then, we solve for c: 2.5c = 10 - 85 = -75.

Dividing both sides by 2.5, we get c = -75/2.5 = -30.

So, c = -30 when p = 85.

Answer:

- 4x² + 10x

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

= - x² + 6x - 1 - (3x² - 4x - 1) ← distribute

= - x² + 6x - 1 - 3x² + 4x + 1 ( collect like terms )

= - 4x² + 10x

Final answer:

To find f-g (x), subtract g(x) from f(x) and combine like terms. The resulting function is f-g (x) = -4x² + 10x.

Explanation:

To find the difference of the functions f(x) and g(x), denoted as f-g (x), we simply subtract the function g(x) from f(x). In the given problem:

f(x) = -x² + 6x - 1

g(x) = 3x² - 4x - 1

We subtract the expressions:

f-g (x) = (-x² + 6x - 1) - (3x² - 4x - 1)

Removing the parentheses and simplifying, we get:

f-g (x) = -x² + 6x - 1 - 3x² + 4x + 1

Combine like terms:

f-g (x) = -4x² + 10x

Thus, the function f-g (x) is -4x² + 10x.

Answer:

4/3 or D

Step-by-step explanation:

Let's get this equation into y=mx+b form.

m=slope b=y-int

Subtract 5 from both sides to isolate y on a side.

4x-6=3y

Divide both sides by 3 to isolate y on one side.

(4/3)x-2=y

y=(4/3)x-2

m=4/3

b=-2

So our slope is 4/3

Answer:

B. (2, 0) - True, True, True

Step-by-step explanation:

A. (2, 3) - False

y ≤ 6x - 12 (False)

y ≤ 1/2x + 6 (False)

y ≥ -x - 4 (True)

B. (2, 0) - True, True, True

y ≤ 6x - 12 (True)

y ≤ 1/2x + 6 (True)

y ≥ -x - 4 (True)

C. (-3, 0) - False

y ≤ 6x - 12 (False)

y ≤ 1/2x + 6 (False)

y ≥ -x - 4 (True)

D. (1,1) - False

y ≤ 6x - 12 (False)

y ≤ 1/2x + 6 (False)

y ≥ -x - 4 (True)

Brainliest?

Answer:

The graph shifts 3 units left and 15 down. It narrows by a factor of 2 and is right side up.

Step-by-step explanation:

There are two ways of doing this. You can graph it, or you can put it in the vertex form by completing the square.

A quick way of putting this into the vertex form is write the general equation

y = a(x - h)^2 + k

h= - b/2a = - 12/4 = - 3

So the equation in vertex form is

y = 2(x + 3)^2 - 15

Description

y = 2(x + 3)^2 - 15

shifts 3 units to the left and 15 units down. It also narrows by a factor of 2. Finally, it is right side up.

Graph

Since you have seen the graph before, there is not much more to add. It just shows what has been written above.

30 minutes is half an hour.

so in 30 minutes is 16 commercials, so in 1 hour is twice as many, 32 commercials.

there are 24 hours in a day, so 32 commercials 24 times, 32 * 24.

Answer:

€16.40

Step-by-step explanation:

First, we need to divide £12.30 by 3 to find out how many groups of 3 there is:

12.3 ÷ 3 = 4.1

Now we can multiply this by 4 to find the euro equivalent:

4.1 * 4 = 16.4

So £12.30 is €16.40

If x and y are proportional, then y : x = constant.

[tex]\dfrac{y}{x}=a\to y=ax[/tex]

We have (4, 3) and (x, 9). Substitute:

[tex]\dfrac{9}{x}=\dfrac{3}{4}[/tex]        cross multiply

[tex]3x=(9)(4)[/tex]

[tex]3x=36[/tex]       divide both sides by 3

[tex]\boxed{x=12}[/tex]

Answer:

Step-by-step explanation:

The first four terms of geometric series is:

[tex]a,ar,ar^2,ar^3[/tex]

Since, we have given information that the third number is greater than 44 that means:

[tex]ar^2=a+44[/tex]

Above equation can be rewritten as:

[tex]a(r^2-1)=44[/tex]

Now, using:

[tex]a^2-b^2=(a+b)(a-b)[/tex]

Here, a=r,b=1

[tex]a(r+1)(r-1)=44[/tex]        (1)

The sum of first four terms is:

[tex]a+ar+ar^2+ar^3=220[/tex]

[tex]a(1+r+r^2+r^3)=220[/tex]

[tex]a(1(1+r)+r^2(1+r))=220[/tex]

[tex]a((1+r)(1+r^2))=220[/tex]      (2)

Divide equation (2) by (1) we get:

[tex]\frac{r^2+1}{r-1}=\frac{220}{44}[/tex]

[tex]r^2+1=5r-5[/tex]

[tex]\Rightarrow r^2-5r+6=0[/tex]

[tex]\Rightarrow r^2-3r-2r+6=0[/tex]

[tex]\Rightarrow r(r-3)-2(r-3)=0[/tex]

[tex]\Rightarrow (r-2)(r-3)=0[/tex]

[tex]\Rightarrow r=2,3[/tex]

CASE1: When r=2 in [tex]ar^2=a+44[/tex]

[tex]a(4)=a+44[/tex]

[tex]3a=44[/tex]

[tex]a=\frac{44}{3}[/tex]

CASE2:When r=3 in [tex]ar^2=a+44[/tex]

[tex]a(3)^2=a+44[/tex]

[tex]\Rightarrow 9a=a+44[/tex]

[tex]\Rightarrow 8a=44[/tex]

[tex]\Rightarrow a=\frac{44}{8}=\frac{11}{2}[/tex]

The series becomes:

From CASE1: [tex]\frac{44}{3},\frac{44\cdot 2}{3},\frac{44\cdot 2^2}{3},\frac{44\cdot 2^3}{3}[/tex]

[tex]\Rightarrow \frac{44}{3},\frac{88}{3},\frac{176}{3},\frac{352}{3}[/tex]

From CASE2: [tex]\frac{11}{2},\frac{11\cdot 3}{2},\frac{11\cdot 3^2}{2},\frac{11\cdot 3^3}{2}[/tex]

[tex]\Rightarrow \frac{11}{2},\frac{33}{2},\frac{99}{2},\frac{297}{2}[/tex]

A geometric progression is characterized by a common ratio.

The terms of the progression are: [tex]\mathbf{T_n =5.5, 16.5, 49.5,148.5}[/tex] or [tex]\mathbf{T_n =\frac{44}{3}, \frac{88}{3}, \frac{176}{3},\frac{352}{3}}[/tex]

The given parameters are:

[tex]\mathbf{S_4 = 220}[/tex]

[tex]\mathbf{T_3 = T_1 + 44}[/tex]

The third term is represented as:

[tex]\mathbf{T_3 = ar^2}[/tex]

The first term is:

[tex]\mathbf{T_1 = a}[/tex]

So, we have:

[tex]\mathbf{ar^2 = a + 44}[/tex]

Subtract a from both sides

[tex]\mathbf{ar^2 - a = 44}[/tex]

Factor out a

[tex]\mathbf{a(r^2 - 1) = 44}[/tex]

Express as difference of two squares

[tex]\mathbf{a(r + 1)(r - 1) = 44}[/tex]

Make r + 1 the subject

[tex]\mathbf{r +1 = \frac{44}{a(r -1)}}[/tex]

Recall that:

[tex]\mathbf{S_4 = 220}[/tex]

This gives:

[tex]\mathbf{a + ar + ar^2 + ar^3 = 220}[/tex]

Factor out a

[tex]\mathbf{a(1 + r + r^2 + r^3) = 220}[/tex]

Factor out r^2

[tex]\mathbf{a(1 + r + r^2(1 + r)) = 220}[/tex]

Rewrite as:

[tex]\mathbf{a(1(1 + r) + r^2(1 + r)) = 220}[/tex]

Factor out 1 + r

[tex]\mathbf{a((1 + r^2)(1 + r)) = 220}[/tex]

Substitute [tex]\mathbf{r +1 = \frac{44}{a(r -1)}}[/tex] in [tex]\mathbf{a((1 + r^2)(1 + r)) = 220}[/tex]

[tex]\mathbf{a((1 + r^2)\times \frac{44}{a(r -1)} = 220}[/tex]

[tex]\mathbf{((1 + r^2)\times \frac{44}{(r -1)} = 220}[/tex]

Divide both sides by 44

[tex]\mathbf{(1 + r^2)\times \frac{1}{(r -1)} = 5}[/tex]

Multiply through by r - 1

[tex]\mathbf{1 + r^2 = 5r - 5}[/tex]

Collect like terms

[tex]\mathbf{r^2 - 5r + 5 +1 = 0}[/tex]

[tex]\mathbf{r^2 - 5r + 6 = 0}[/tex]

Expand

[tex]\mathbf{r^2 - 2r - 3r + 6 = 0}[/tex]

Factorize

[tex]\mathbf{r(r - 2) - 3(r - 2) = 0}[/tex]

Factor out r -2

[tex]\mathbf{(r - 3)(r - 2) = 0}[/tex]

So, we have:

[tex]\mathbf{r = 3\ or\ r = 2}[/tex]

Calculate a using: [tex]\mathbf{a(r^2 - 1) = 44}[/tex]

When r = 3

[tex]\mathbf{a(3^2 -1) = 44}[/tex]

[tex]\mathbf{a(9 -1) = 44}[/tex]

[tex]\mathbf{8a = 44}[/tex]

[tex]\mathbf{a = 5.5}[/tex]

When r = 2

[tex]\mathbf{a(2^2 -1) = 44}[/tex]

[tex]\mathbf{a(4 -1) = 44}[/tex]

[tex]\mathbf{3a = 44}[/tex]

[tex]\mathbf{a = \frac{44}{3}}[/tex]

The nth term of a GP is:

[tex]\mathbf{T_ = ar^{n-1}}[/tex]

So, the terms of the progression are:

[tex]\mathbf{T_n =5.5, 16.5, 49.5,148.5}[/tex]

or

[tex]\mathbf{T_n =\frac{44}{3}, \frac{88}{3}, \frac{176}{3},\frac{352}{3}}[/tex]

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To ensure Trisha has at least 5 times as many key chains as thumb drives in each gift bag, the inequality x ≥ 5y can be used, where x is the number of key chains and y is the number of thumb drives. Considering she needs to make at least 50 bags, the inequality x + y ≥ 50 is also relevant.

For Trisha to satisfy the condition of having at least 5 times as many key chains as thumb drives in each gift bag, the following inequality can represent her situation:

x ≥ 5y

Here, x is the number of key chains and y is the number of thumb drives. Trisha must also create at least 50 gift bags, so another inequality to consider is the total number of gift bags:

x + y ≥ 50

Since Trisha has 25 thumb drives (y) and 200 key chains (x), she is limited by the number of thumb drives. The maximum number of gift bags she can create with one thumb drive in each is 25 bags, which means she can use up to 125 key chains (5 times 25). Thus, Trisha can satisfy the requirement by using all 25 thumb drives and up to 125 key chains, ensuring there's a minimum of one thumb drive or key chain per bag.

Answer:

1,250 drinks

Step-by-step explanation:

Woody spends $0.05 to make a glass of lemonade and makes $0.25 when he sells one, so his net gain is $0.20. 250 / .20 is 1,250.

Final answer:

Woody needs to sell 1,250 glasses of lemonade to earn the $250 required to buy a bicycle. Calculated by dividing the goal ($250) by the profit per glass ($0.20), which is the difference between the selling price ($0.25) and the cost price ($0.05).

Explanation:

Woody is operating a small business of selling lemonade and seeks to achieve a certain amount of total revenues to purchase a bicycle. To solve this, one must determine the profit per glass of lemonade sold, which is the selling price minus the cost to make it. Since Woody sells a glass for $0.25 and it costs $0.05 to make, the profit per glass is $0.25 - $0.05 = $0.20.

To calculate the total number of glasses Woody needs to sell to earn $250, divide his goal by the profit per glass. Thus:

Total number of glasses = ($250 / $0.20 per glass) = 1250 glasses

Hence, Woody must sell 1,250 glasses of lemonade to earn enough money to buy the bicycle.

Answer: 9

Step-by-step explanation:

The factors of 18: 1, 2, 3, 6, 9, 18

The factors of 27: 1, 3, 9, 27

The GCF of 18 and 27 is 9. This means that 9 is the largest number that can evenly divide both 18 and 27 without leaving any remainder.

Step 1: Find the Factors of Each Number

To find the factors of a number, you identify all the whole numbers that divide that number without leaving a remainder. Here are the factors of 18 and 27:

Factors of 18: 1, 2, 3, 6, 9, 18

Factors of 27: 1, 3, 9, 27

Step 2: Identify the Common Factors

Next, we look for the common factors between the two sets of factors. These are the numbers that appear in both lists:

Common factors of 18 and 27: 1, 3, 9

Step 3: Determine the Greatest Common Factor (GCF)

The GCF is the greatest or largest number among the common factors. In this case, the greatest common factor among 1, 3, and 9 is 9.

Therefore, the GCF of 18 and 27 is 9. This means that 9 is the largest number that can evenly divide both 18 and 27 without leaving any remainder.

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Answer:

y = 10  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

The angles of this triangle should all add up to 180 degrees.

There are 3 angles so 180 ÷ 3 = 60.  Each angle will = 60 degrees.

To find y:

5y + 10 = 60

5y = 60 - 10

5y = 50

y = 50 ÷ 5

y = 10

The distance of line AB if A(3, 5) and B(-3,-3) is D.10.

[tex]\sqrt[/tex] (5--3)^2 + (3-(-3))^2 = V100 = 10.

To calculate the distance AB between points A (x1, y1) and B (x2, y2), first draw a right triangle with segment ¯AB in the hypothalamus. AC is a horizontal distance, so it's just a difference in x-coordinates: | (x2-x1) |. Similarly, BC is the vertical distance | (y2-y1) |. ..

The vertical distance of the line (Ax + By + c = 0) from point

is equal to | Ax'+ By' + c√A2 + B2 |. Where (x', y') are the coordinates of the point. Since we need the distance of the line from the origin, the coordinates will be (0,0), which is the vertical distance of the line from the origin.

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Answer:

Possible number of outcomes = 24

Number of outcomes have an 'a' and an odd number = 3

Step-by-step explanation:

The total outcomes are as follows:

S = {(a, 1), (a, 2), (a, 3), (a, 4), (a, 5), (a, 6),

      (b, 1), (b, 2), (b, 3), (b, 4), (b, 5), (b, 6),

      (c, 1), (c, 2), (c, 3), (c, 4), (c, 5), (c, 6),

      (d, 1), (d, 2), (d, 3), (d, 4), (d, 5), (d, 6)}

n(S) = 24

Hence, possible number of outcomes = 24

The outcomes have an 'a' and an odd number are:

E = {(a, 1), (a, 3), (a, 5)}

n(E) = 3

Hence, there are 3 outcomes have an 'a' and an odd number.

Answer:

The set of all points on a plane equidistant to a given point

Step-by-step explanation:

"following"?

Answer:

The collection of all points in a plane that are the same distance from a given point.

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

2 x √3 = 3.46410161514 , which is a rational number, because it is a real nomber

Answer: [tex]\frac{27}{125}[/tex]

Step-by-step explanation:

Here the total numbers are 1,  4,  3,  7,  6

Since the total number of possible arrangement = [tex]5\times 5 \times5 \times 5 \times 5=5^5[/tex]

The total number of the odd numbers in the given numbers = 3

Thus the possible arrangement that the first three digits will be odd numbers = [tex]3\times 3\times 3\times 5\times 5=3^3\times 5^2[/tex]

Thus, the probability that the first three digits of Irvings ID number will be odd numbers = the possible arrangement that the first three digits will be odd numbers / total possible arrangement =  [tex]\frac{3^3\times 5^2}{5^5} = \frac{3^2}{5^{5-2}}[/tex]

= [tex]\frac{3^3}{5^3} = \frac{27}{125}[/tex]

Hello from MrBillDoesMath!

Answer:

 80,100  (which is NONE of the provided answers)

Discussion:

-225 * -356 =

+ (225 * 356)   =            as the product of two negative numbers is positive

 80,100

Regards,  

MrB

P.S.  I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!

The answer should be D. 9 1/5

Answer:

Step-by-step explanation:

Given equation [(x-1)/3]=(x+3)/4

Let us first get rid denominators from both sides.

On cross multiplying both sides, we get

4(x-1) = 3(x+3)

4x-4 = 3x+9

Adding 4 on both sides, we get

4x-4+4 = 3x+9+4

4x = 3x +13

Subtracting 3x on both sides, we get

4x-3x = 3x-3x +13

x = 13.

Now, we need to find the value of [ ] fraction We have [(x-1)/3] in given equation.

Plugging x= 13 in (x-1)/3, we get

13-1/3 = 12/3 = 4.

Answer:

The length is 81 feet.

Step-by-step explanation:

If you plot the equations for both length and width on a graph, making them both equal to y of course, you find that they cross each other in two places. The places they cross are (81, 11) and (70, 0). It is impossible for the answer to have the width as 0 feet, so the answer is 81 feet.

Answer:

depends on the how many fee your talking

Step-by-step explanation:

Answer: 615= 140 + 19x

Step-by-step explanation:

19x represents the price per guess (x) how many people are coming. Good Luck!

To solve for the number of guests Taryn can invite, set up the inequality 140 + 19x < 615 and then solve for x.

To solve for the number of guests Taryn can invite, we need to set up an inequality. Let x represent the number of guests. The total cost, C, can be calculated by adding the cost to rent the space, $140, to the cost per guest, $19, multiplied by the number of guests. So, the inequality can be written as 140 + 19x < 615.

To solve for x, we need to isolate it by subtracting 140 from both sides: 19x < 475. Finally, divide both sides by 19 to get the solution: x < 25.

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This is classic Pythagorean solving:

Side^2 + Side^2 = Hypotenuse^2

The hypotenuse is the longest side of a triangle, and it connects the leg and the base usually. In this triangle, 18 is the hypotenuse -- so since we are solving for the unknown side, the equation is:

a^2 + 5.7^2 = 18^2 -- now solve

a^2 = 18^2 - 5.7^2

a^2 = 291.51

a = sqrt(291.51)

a = 17.07 -- because height is the square root of the difference of the squares of 18 and 5.7

The answer is choice B.

The correct answer is b. 17.07 centimeters, because height = Square root of the difference of the squares of 18 and 5.7.

To find the approximate height of the cone-shaped hat, we need to use the Pythagorean theorem. The height of the cone (h) can be found using the formula:

[tex]\[ h = \sqrt{r^2 - a^2} \][/tex]

 where r is the slant height of the cone and a is the radius of the base of the cone.

Given that r = 18 cm and a = 5.7 cm, we substitute these values into the formula:

[tex]\[ h = \sqrt{18^2 - 5.7^2} \][/tex]

[tex]\[ h = \sqrt{324 - 32.49} \][/tex]

[tex]\[ h = \sqrt{291.51} \][/tex]

 Now, we can approximate the square root of 291.51 to find the height:

[tex]\[ h \approx 17.07 \text{ cm} \[/tex]]

 Therefore, the approximate height of the hat is 17.07 centimeters. The other options are incorrect because they do not correctly apply the Pythagorean theorem:

 a. 3.51 centimeters: This is the square root of the difference of 18 and 5.7, which does not use the correct formula for the height of a cone.

c. 18.88 centimeters: This is the square root of the sum of the squares of 18 and 5.7, which would be the length of the slant height, not the height of the cone.

d. 4.87 centimeters: This is the square root of the sum of 18 and 5.7, which is not a correct application of the Pythagorean theorem for finding the height of a cone."

Jaimie swims 12 the length of the swimming pool every 14 of a minute. Then in one minute, he will swim = 14/12=1.16  So, he will be able to swim 1.16 length in 1 minute.