What is the sum of the measures of the exterior angles of the polygon shown below? If necessary, round to the nearest tenth.
like and 5 star

Answer:

TW = 9

Step-by-step explanation:

WY is the perpendicular bisector of TZ with TY ≅ ZY , then

Δ TWZ is isosceles with ZW ≅ TW , that is

3x = x + 6 ( subtract x from both sides )

2x = 6 ( divide both sides by 2 )

x = 3

Then

TW = x + 6 = 3 + 6 = 9

The value in the blank are: 12/18 =12/18 =14/9.3 =18/27.

To discover the unknown values in a mathematical equation, we cross multiply the numbers in the equation. The method of cross multiplication is frequently employed to identify the missing variable in an equation. We multiply both the numerator and denominator of the provided expression or fractions.

The given fractions are as follows:

12/18 =_/18 =14/_ =_/27

Taking the first two terms and applying cross multiplication we have:

12/18 =_/18

12(18)/ (18) = x

x = 12

Taking the next two terms:

12/18 =14/ y

Applying cross multiplication we have:

y = (14)(12)/ (18)

y = 9.3

Taking the third term and applying cross multiplication we have:

12/18 = z/27

z =12(27)/ 18

z = 18

Hence, the blanks are:

12/18 =12/18 =14/9.3 =18/27

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The measure of m∠EFG in triangle CDE is equal to 93 units.

In Mathematics, the midpoint theorem states that in a triangle, the line segment which joins the midpoints of any two (2) sides of the triangle must be parallel to the third side and congruent to half of the length of the third side.

By applying the midpoint theorem to triangle CDE, the measure of m∠EFG can be calculated as follows;

m∠ECD = m∠EFG

12 + 9x = −2x + 111

9x + 2x = 111 - 12

11x = 99

x = 99/11

x = 9.

For line segment m∠EFG, we have the following:

m∠EFG = −2x + 111

m∠EFG = −2(9) + 111

m∠EFG = −18 + 111

m∠EFG = 93 units.

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The quantity of butter that should be used is 120g. ii. The total quantity of flapjacks would be: 540g. b. The amount of oats would be: 75g.

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.

Given that the ratio of ingredients for the recipe is 1: 2: 2: 4.

Let us suppose the syrup has a ratio of 1x, then the ratio of other ingredients are:

sugar = 2x

butter = 2x

oats = 4x

a. Tiger uses syrup, x = 60g

i. The quantity of butter that should be used is 2x = 2(60) = 120g.

ii. The total quantity of flapjacks would be:

x + 2x + 2x + 4x = 60 + 120 + 120 + 240 = 540g

b. Given that:

150g syrup = 8 flapjacks

x = 1 flapjack

Using the cross multiplication method, we have:

x = 150/8

x = 18.75g

So, for one flap jack the syrup needed is 18.75g, then the amount of oats would be: 4x = 4(18.75) = 75g.

Hence, the quantity of butter that should be used is 120g. ii. The total quantity of flapjacks would be: 540g. b. The amount of oats would be: 75g.

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It take the man 19.83 seconds to fall to 130 feet

From the question, we have the following parameters that can be used in our computation:

h(t) = 12.5(0.2t − 1)^2 + 20

When the man reaches 130 feet, we have

h(t) = 130

Substitute the known values in the above equation, so, we have the following representation

12.5(0.2t − 1)^2 + 20 = 130

Using a graphing calculator, we have

t = 19.83

Hence, the time is 19.83 seconds

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Answer:

y= -4x+2

Step-by-step explanation:

diff in y / diff in x = slope

so the slope is (-2-2) /(1-0) = -4

intercept is whatever is on Y axis, it's 2

so y= -4x+2

Answer:

Step-by-step explanation:

Divide 100 by 16 and write the answer as a mixed number. Reduce the

fraction part of the mixed number.  6 1/4 here u go.

Answer: Y=5

8x5=40

40x5=200

200x5=1000

etc..

Answer: y=-7x-0 if solving for literal y or x=y+0/-7 if solving for literal x.

Step-by-step explanation:

-7x-y=0

add (+) 7x to both sides

-y=7x+0

then divide by -1

y=-7x-0

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

for literal X

-7x-y=0

add y to both sides

-7x=y+0

then divide by -7\

x=y+0/-7

Answer:

4x + 3 = y

Step-by-step explanation:

Answer:

4x+3

there is no actual explanation

Three added= +3

four times a number= 4*x=4x

Answer: D

Step-by-step explanation:

Srry, Im really bad at explaining but the answer is prob D

Answer:

the slope is -6

the y-intercept is 2

Step-by-step explanation:

y=mx+b where m is the slope and b is the y-intercept

a) Slope: -6;

b) y-intercept: 2, which means that the line touches the "y" axis on point (0, 2).

Given equation: [tex]y = -6x + 2[/tex].

Here's a little tip that will help you quickly find the slope and y-intercept.

First, solve the equation for "y". This equation is already solved for "y", this is called "slope-intercept form". Now, take a look at the attached image and identify the values. As you can tell, for the given equation, values are:

a) Slope: -6;

b) y-intercept: 2, which means that the line touches the "y" axis on point (0, 2).

You may verify this information using the algebraic methods (slope formula and substituting "x" by 0 and calculate "y"). It'll give you the same answer, this is just a faster way to find the values.

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Answer:

JN = 16

Step-by-step explanation:

Since diagonals in parallelograms bisect each other, JN = [tex]\frac{1}{2}[/tex]JL

Answer:

To find JN in parallelogram JKLM when JL is 32, you can draw a line from J to L, and then extend the line to find JN. The length of JN will be equal to 32.

Answer:

student tickets cost $4.50

adult tickets cost $7.00

Step-by-step explanation:

a = cost of an adult ticket

s = cost of a student ticket

(1)  68a + 136s = 1088

(2) 79a + 140s = 1183

solve (1) for a:

68a = 1088 - 136s

a = 16 - 2s    substitute this into (2):

79(16-2s) + 140s = 1183

1264 - 158s + 140s = 1183     solve for s:

-18s = -81

s = -81/-18 = 4.50   plug this into either equation 1 or 2 to solve for a:

68a + 136(4.50) = 1088

68a = 1088 - 612 = 476

a = 476/68 = 7.00

Answer:

a.

The growth rate (k) can be calculated using the exponential growth formula: P = P0 * e^(kt), where P0 is the initial population, t is the time in years, and e is the natural logarithm base.

From the information provided, the initial population of elves in 2000 was 23, and in 2003, the population was 34. By substituting the values into the formula and solving for k, we get:

34 = 23 * e^(k * 3)

Taking the natural logarithm of both sides:

ln(34) = ln(23 * e^(k * 3))

Using the logarithmic identity:

ln(34) = ln(23) + ln(e^(k * 3))

Solving for k:

k = (ln(34) - ln(23)) / (3) = 0.175

Therefore, the growth rate (k) for the population of elves is 0.175.

b.

To find the population of elves in 2020, we can use the exponential growth formula:

P = P0 * e^(kt)

Substituting the initial population of elves in 2000, which was 23, and the growth rate (k), which we found to be 0.175, we get:

P = 23 * e^(0.175 * 20)

Calculating the exponential function:

P = 23 * e^3.5

Therefore, there will be approximately 51 elves in 2020.

c.

To find the year when there will be 543 elves, we can use the exponential growth formula and solve for t:

543 = 23 * e^(0.175 * t)

Dividing both sides by 23 and taking the natural logarithm of both sides:

ln(543/23) = 0.175 * t

Solving for t:

t = (ln(543/23)) / 0.175

Therefore, there will be 543 elves in the year 2027.

i am not sure

(a) The perimeter of the rectangle in centimeter is 2,800 cm.

(b) The area of the rectangle is 450,000 cm².

The perimeter of the rectangle in centimeter is calculated as follows;

P = 2 ( L + B )

where;

The length of the rectangle = 9 m = 900 cm

The breadth of the rectangle = 5 m = 500 cm

Perimeter = 2 ( 900 cm + 500 cm ) = 2,800 cm

The area of the rectangle is calculated as follows;

A = LB

A = 900 cm  x  500 cm

A = 450,000 cm²

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Answer:

The first one is 76°, second one is 38°, third one is 66°

Step-by-step explanation:

Suppose the second one is x, given the first one is twice of the second one, so the first one is 2x.

2x+x+(28°+x)=180°

4x=152°

x=38

So, the first one is 76°, second one is 38°, third one is 66°

Answer:

The length of a is 36 mm.

Step-by-step explanation:

Similar rectangles have the same shape, but can have different sizes. The ratio of the lengths of corresponding sides of similar rectangles is always the same.

Given that b = 18 mm, c = 24 mm, and d = 36 mm, the ratio of the lengths of corresponding sides of the two rectangles is c/d = 24/36 = 2/3.

So, the length of a is equal to b * (c/d) = 18 * (2/3) = 36 mm.

The number of gems that Hector will get if he plays for 10.5 hours is given as follows:

84 gems.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

From the table, the constant is given as follows:

k = 48/6 = 32/4 = 16/2 = 8.

Hence the equation giving the number of gems after playing for x hours is given as follows:

y = 8x.

After 10.5 hours, the number of gems is then given as follows:

y = 8 x 10.5

y = 84 gems.

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Answer:

84

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the difference A - B', we need to first find the complement of B, denoted by B', which is the set of all elements in U that are not in B.

Given that U = {1, 2, 3, 4, 5, 6, 7, 8, 9},

B = {1, 4, 6, 9},

then B' = {2, 3, 5, 7, 8}.

Next, we find A - B' by looking for the elements that belong to A and not to B':

A - B' = {2, 4, 6, 8} - {2, 3, 5, 7, 8} = {4, 6, 8}.

Reid found 1 quarter, 3 dimes, 1 nickel and 1 penny coins.

Currency is anything that is generally accepted to have value as a medium of exchange so that it can be traded for goods and services.

Given that, Reid found 6 coins that totaled 61 cents in all.

Since, in total he got 6 coins that value 61 cents in total.

So, wd know that,

1 quarter = 25 cents

1 dime = 10 cents

1 nickel = 5 cents

1 penny = 1 cents,

Adding them = 25 + 10 + 5 + 1

= 41 cents

We need 20 cents and 2 coins more,

So, add 3 coins more in nickel, so, that,

3 nickels = 30 cents

Now, Reid in total will have 6 coins and that will value 61 c.

Hence, Reid found 1 quarter, 3 dimes, 1 nickel and 1 penny coins.

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An equation that models the total number of hours which Laura babysits is l = d + 5.

In order to write an equation that model this situation, we would assign variables to the number of hours Delilah babysits and the number of hours Laura babysits respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into an algebraic equation based on the fact that Laura babysits 5 hours more per week than Delilah as follows;

l = d + 5

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The relative frequency of rolling a three is 14/40 or 0.35.

Answer14/40 or 0.35

Step-by-step explanation:

Number of times dice is rolled= 40

Number of times three comes up= 14

Relative frequency(Probability) = 14/40 or 0.35

The period of the sinusoidal function in this problem is given as follows:

5 units.

A periodic function is a function that has the behavior repeating in intervals over the domain.

Then the period of the function is defined as the shortest difference between two points in which the function has the same behavior.

One of the examples of the shortest difference in this problem is between x = 1 and x = 6, hence the period is calculated as follows:

6 - 1 = 5 units.

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Answer:

[tex]3\sqrt{1201}[/tex]

Step-by-step explanation:

assuming the missing side was the long side or the c side

[tex]a^{2} +b^2=c^2\\72^2+75^2=c^2\\5184+5625=10809\\\sqrt{10809}=3\sqrt{1201}[/tex]

Answer: The amount invested at 6% was $1393.57, the amount invested at 9% was $306.13, and the amount invested at 15% was $1393.57 + $306.13 + $100 = $1800.70.

Step-by-step explanation:

Let's denote the amount invested at 6% as "x". Then, the amount invested at 9% would be "y", and the amount invested at 15% would be "z".

According to the problem, we have the following information:

x + y + z = $7500 (the total amount invested)

0.06x + 0.09y + 0.15z = $867 (the total annual income)

And,

z = x + y + $100 (the amount invested at 15% was $100 more than the amounts invested at 6% and 9% combined)

We can substitute the third equation into the first equation to get:

x + y + x + y + $100 = $7500

Simplifying:

2x + 2y + $100 = $7500

2x + 2y = $7400

Next, we can substitute "z = x + y + $100" into the second equation:

0.06x + 0.09y + 0.15(x + y + $100) = $867

Expanding:

0.06x + 0.09y + 0.15x + 0.15y + 0.15 * $100 = $867

0.21x + 0.24y + $15 = $867

0.21x + 0.24y = $852

Finally, we can solve for x and y using the equations "2x + 2y = $7400" and "0.21x + 0.24y = $852".

We can use elimination method to find x:

2x + 2y = $7400

0.21x + 0.24y = $852

Multiplying the first equation by 0.21:

0.42x + 0.42y = $1557.8

Subtracting the second equation from the first:

0.42x + 0.42y - 0.21x - 0.24y = $1557.8 - $852

0.21x - 0.03y = $705.8

Dividing both sides by 0.21:

x = $705.8 / 0.21 + 0.03y / 0.21

x = $3357.14 / 0.24 + y

Finally, substituting x back into the equation "2x + 2y = $7400":

2($3357.14 / 0.24 + y) + 2y = $7400

Expanding:

$6714.29 + 2.24y = $7400

Solving for y:

2.24y = $7400 - $6714.29

y = $685.71 / 2.24

y = $306.13

And finally, substituting y back into the equation "x = $3357.14 / 0.24 + y":

x = $3357.14 / 0.24 + $306.13

x = $1393.57

Therefore, the amount invested at 6% was $1393.57, the amount invested at 9% was $306.13, and the amount invested at 15% was $1393.57 + $306.13 + $100 = $1800.70.

Answer:

PLACEHOLDER SRRY BRB

Step-by-step explanation:

Answer:

1) x=1/4Y-1/2   2) x=1/4Y-1/2

Step-by-step explanation:

x=1/4Y-1/2       x=1/4Y-1/2

-4x=2-Y           2x=-4-Y

x=-1/2+1/4Y     x=-2-1/2Y

x=1/4Y-1/2        x=1/4Y-1/2