In the diagram Shown a 2 foot wide flower border surrounds the heart shaped pond.What is the area of the border?

Final answer:

The measure of each of the four exterior angles of the hexagon is 21 degrees, and the measure of the remaining two exterior angles is 138 degrees each. This was determined by setting up an equation based on the sum of exterior angles of a polygon, which is always 360 degrees, and solving for x.

Explanation:

To solve this problem, we start by understanding that the sum of the exterior angles of any polygon is always 360 degrees. For a hexagon, this sum is divided among six exterior angles. According to the problem, four of these angles are each x degrees, and the remaining two are each twice the sum of x and 48.

Let's set up the equation reflecting this information:
4x + 2(2x + 96) = 360.

Simplifying this equation, we get:
4x + 4x + 192 = 360,
which combines to:
8x + 192 = 360.

Now, we'll solve for x:
8x = 360 - 192,
8x = 168,
x = 21.

Therefore, each of the four exterior angles is 21 degrees, and each of the remaining two exterior angles is twice the sum of 21 and 48, which is:
2(21 + 48) = 2(69) = 138 degrees.

Answer:

The perimeter of the figure is [tex]114.24\ in[/tex]

Step-by-step explanation:

we know that

The perimeter of the figure is equivalent to the perimeter of a square plus the perimeter of a semicircle

step 1

Find the perimeter of square

The perimeter of square is equal to

[tex]P=4b[/tex]

where

b is the length side of the square

we have

[tex]b=16\ in[/tex]

substitute

[tex]P=4(16)=64\ in[/tex]

step 2

Find the circumference of a semicircle

The circumference of a semicircle is equal to

[tex]C=\pi r[/tex]

we have

[tex]r=16\ in[/tex]

[tex]\pi=3.14[/tex]

substitute

[tex]C=3.14(16)=50.24\ in[/tex]

step 3

Find the perimeter of the figure

[tex]64\ in+50.24\ in=114.24\ in[/tex]

The answer is:           " [tex]\frac{1}{2}[/tex] x  −  6 "  .

_______________________________________________

      →   in which "x" represents the "unknown number" .        

_______________________________________________

The expression written for: "Half of a number decreased by 6"  is:

               →      " [tex]\frac{1}{2}[/tex] x  −  6 "   ;  

_____________________________________________

               →   in which "x" represents the "unknown number" .

________________________________________

Explanation:

Let "x" represent the "unknown number".

→   "One-half" of a number , decreased by "6" ;

              →  is written as:   "1/2 of "x" ,  minus "6" .

Note that:  " 1/2 of x "  =  " [tex]\frac{1}{2}[/tex]  * x "   =   " [tex]\frac{1}{2}[/tex]  x "  .

Then, we subtract "6" ; from that value;  to write the expression:

________________________________________

The expression written for:  "Half of a number decreased by 6"  is:

                    "  [tex]\frac{1}{2}[/tex] x  −  6 " ;  

                     →            in which "x" represents the "unknown number" .

________________________________________

Hope this helps!

Best wishes in your academic endeavors — and within the "Brainly" community!

________________________________________

Final answer:

The number of infected people can be determined by doubling the number of infected people for each day that passes.

Explanation:

The number of infected people can be determined by doubling the number of infected people for each day that passes. Let's say that on the first day, there is 1 infected person. On the second day, the number of infected people doubles to 2. On the third day, it doubles again to 4, and so on. We can represent this pattern with an exponential equation: y = 2ˣ, where y is the number of infected people and x is the number of days that have passed.

For example, if 5 days have passed, we can plug in x = 5 into the equation: y = 2⁵ = 32. So, there would be 32 infected people.

Final answer:

The number Chris wrote, considering the values and conditions provided for each digit, is 40353.

Explanation:

To solve this problem, let's identify each digit based on the clues provided:

Now we start assigning values:

So the number Chris wrote is 40353.

The number Chris wrote appears to be 43031.

To determine the 5-digit number that Chris wrote, we need to analyze the values of each digit based on the clues given.

One digit has the value of 3:

One digit has a value of 4000:

One digit has a value that is 10 times the digit in the ones place:

One digit has a value that is 10 times the digit in the tens place:

One digit has a value that is 10 times the thousands place:

Based on the second and first clues:

So, we could set:

Therefore the representation of the number combining these values might just happen to yield:

[tex]40000 + 300 + 10 + 1 = 43031[/tex]

Answer:

median; The outlier has a large effect on the sum.

Step-by-step explanation:

Final answer:

The median is the preferred measure of central tendency for the given data set due to the presence of outliers, which can skew the mean.

Explanation:

For the given data set, we should consider the presence of outliers in determining the preferred measure of central tendency. This data set contains values such as 95, which is considerably higher than the rest of the values. This can skew the mean to a higher value, making it less representative of the data set. The median is the middle value when all the numbers are arranged in order, which makes it robust to the effect of outliers. In contrast, the mode represents the most frequently occurring number in the data set, which might not be the best central value in this case. Given the outlier's effect on the mean, the median would be a more accurate reflection of the central tendency for this data set.

Han is around a distance of 40 feet away from Clare, Clare is around -50 feet away from Han and both would be -10 feet far away from the meeting point.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

Given that Han's velocity is 4 feet per second, and their meeting point is 0 feet and 0 seconds. Clare's speed is -5 feet per second.

We can calculate their distance in 10 seconds by multiplying their velocity.

Han is around (10× 4)40 feet away from Clare.

Clare is around (10× -5)-50 feet away from Han.

Han and Clare would be -10 feet faraway from the meeting point.

Learn more about Arithmetic operations here:

brainly.com/question/25834626

#SPJ2

Final answer:

The measure of each base angle in an isosceles triangle with a 28-degree vertex angle is 76 degrees, which is the result of subtracting the vertex angle from 180 and dividing by 2.

Explanation:

To find the measure of each base angle of an isosceles triangle when the vertex angle is given, you can use the fact that the sum of all angles in a triangle is 180 degrees. Since in an isosceles triangle the two base angles are congruent (equal in measure), you can subtract the vertex angle from 180 degrees and then divide the result by 2 to find the measure of each base angle.

For the given triangle with a vertex angle of 28 degrees:

Thus, the measure of each base angle in the given isosceles triangle is 76 degrees.

To arrange the six numbers into three pairs so that the sum of each pair is equal, you could create the pairings of 4 and -2, -1 and 5, and 6 and 8. Each of these pairs has a sum of 2, 4, and 14 respectively.

The six number cards provided are 4, -2, -1, 5, 6 and 8. The task is to arrange these into three pairs, such that the sum of each pair is equal. Based on these conditions, our possible pairs are:

These pairs are obtained by adding the numbers together. For example, the pair 4 and -2 results in a sum of 2 (4 + -2 = 2). Similarly, -1 and 5 also results in a sum of 4 (-1 + 5 = 4), and 6 and 8 results in a sum of 14 (6 + 8 = 14). Two pairs have the same sum of 4 while one pair has the sum of 14.

https://brainly.com/question/34289844

#SPJ2

Therefore, the complete question is

Here are six number cards

-4, -2, -1, 5, 6, 8

Arrange the cards into three pairs with the same total.

• Please write each pair on separate lines and use the word 'and' between the numbers (eg. 7 and -3)

Answer:If

x – 5 ≠ 10, then 4x + 1 ≠ 61.

Step-by-step explanation:

I just completed the test

Using the principle of inclusion-exclusion, it was determined that out of 66 surveyed students, 15 do not like banana peppers on their pizza.

The number of students who do not like banana peppers on their pizza can be calculated as follows:

Students who like pepperoni pizza only = 25 - 5 = 20

Students who like banana peppers pizza only = 31 - 5 = 26

Students who do not like banana peppers = Total students surveyed - Students who like banana peppers - Students who like only pepperoni = 66 - 31 - 20 = 15 students

The unknown length, a, in this triangle can be found using the formula in the first option, a² + 15² = 17².

Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.

Given is a right angled triangle.

We know the Pythagoras Theorem which states that,

Hypotenuse² =  Base² + Altitude²

Hypotenuse is the side opposite to the right angle.

Here length of hypotenuse = 17 m

Length of base = 15 m

Length of altitude = a

Using the theorem,

17² = 15² + a²

Or,

a² + 15² = 17²

Hence the correct formula is a² + 15² = 17².

Learn more about Pythagoras Theorem here :

https://brainly.com/question/21926466

#SPJ6

Answer:

yup 4 cages

Step-by-step explanation:

Answer:

C. An athlete drinks 3.85 L per day when the temperature is 80°F

Step-by-step explanation:

Y-intercept of a linear model, equation or a straight line refers the point at which a line crosses the y-axis of a graph. It generally indicates a point on the graph where x equals 0.

For the equation y = 3.85 + 0.55x

At y-intercept, x = 0. Substitute x into the equation, we have:

y = 3.85 + 0.55 (0)

y = 3.85 + 0

y = 3.85

This implies that the value of fluid drank by an athlete at the starting temperature of 80°F (at x=0) is 3.85 L per day

Final answer:

Ellen should use approximately 18.98 pounds of the more expensive candy worth $3.74 per pound to achieve a 27-pound mixture worth $3.06 per pound when mixed with candy worth $1.45 per pound.

Explanation:

To solve the problem of mixing candies to achieve a specific price per pound, we can use the method of weighted averages. Ellen wants to mix candy worth $1.45 per pound with candy worth $3.74 per pound to create a 27-pound mixture that will be worth $3.06 per pound. Let's denote the amount of the more expensive candy as x pounds and the amount of the less expensive candy as 27 - x pounds.

The total value of the expensive candy is x times $3.74, and the total value of the less expensive candy is (27 - x) times $1.45. The total value of the mixture should equal 27 times $3.06, which gives us the equation:

(x × $3.74) + ((27 - x) × $1.45) = 27 × $3.06

Expanding the equation:

$3.74x + $1.45 × 27 - $1.45x = $82.62

Combining like terms:

$3.74x - $1.45x = $82.62 - $1.45 × 27

$2.29x = $82.62 - $39.15

$2.29x = $43.47

Dividing both sides by $2.29 gives us the amount of the more expensive candy:

x = $43.47 / $2.29

x ≈ 18.98 pounds

Ellen should use approximately 18.98 pounds of the more expensive candy to achieve the desired mixture.

To solve this problem, set up a system of equations using the weight and price information. Then solve the system of equations to find the number of pounds of the more expensive candy. Ellen should use 19 pounds of the more expensive candy, which is worth $3.74 per pound.

To solve this problem, we can set up a system of equations. Let x represent the number of pounds of candy worth $1.45 per pound and y represent the number of pounds of candy worth $3.74 per pound. We know that the total weight of the mixture is 27 pounds, so we have the equation x + y = 27. We also know that the average price of the mixture is $3.06 per pound, so we can set up the equation (1.45x + 3.74y)/27 = 3.06.

We can solve this system of equations using substitution or elimination methods. Let's use substitution.

So, Ellen should use 19 pounds of the more expensive candy, which is worth $3.74 per pound.

Using the property of exterior angles, mK is found by adding the measures of the non-adjacent interior angles mF and mH, resulting in mK being equal to 131°.

The student is asking to find the measure of exterior angle mK in triangle FGH. To find mK, which is the exterior angle adjacent to G, we need to use the property of exterior angles in a triangle. This property states that the measure of an exterior angle is equal to the sum of the measures of the two non-adjacent interior angles.

To find mK we add the measures of angles mF and mH:

mK = mF + mH

mK = 94° + 37°

mK = 131°

Therefore, the measure of the exterior angle K is 131°, which corresponds to answer choice D.

The median is 6.

This median is easy to find-- you place all your numbers in numerical order and choose the number(s) in the middle-- for this question the median is 6.

I believe your line plot looks like this [Screenshot was taken on K12]:

Please forgive me if this is wrong, and please tell me the correct answer if this  incorrect.

Final answer:

To solve the equation ((5x−16)^3−4)^3=216,000, one must apply the rules of exponents and algebraic manipulation step by step, isolating x and using mathematical operations to simplify the expression.

Explanation:

Solving an Equation with Powers

The problem ((5x−16)^3−4)^3=216,000 involves understanding the rules of exponents and algebraic manipulation. When you're dealing with expressions raised to a power, it's important to remember that the power affects everything inside the parentheses, including the number. This is evident in expressions like (5³)* which is equivalent to 5⅜⅓ and results in 5 multiplied by itself 12 times, giving 5⁼.

When approaching the given equation, you would first look to isolate the base of the cube on one side, leading to the cube root to undo the cube power. You would continue simplifying step by step until you isolate x, the variable in question. The key here is to perform operations that counteract the powers and other mathematical operations presented.

In some cases, you might encounter a polynomial long division such as dividing S=9x⁵ +4x⁴ - 5x³ +6x² + 2x - 3 by another polynomial. This requires knowledge of the long division algorithm adapted for polynomials. Each term is divided individually to find the quotient.