for each triangle list the sides in order from shortest to longest explain your reasoning with words or numbers for the order

We need to solve the next expressions:

17. 19yd. 28in.- 16yd. 31in

We need to solve subtract each expression.

Then:

19yd. 28in.- 16yd. 31in =

19yd - 16yd and 28in-31in

3yd -3in

Then, we have the next equivalent.

1 yard = 36 in

So:

36 in - 3 in = 33 in

Therefore

19yd. 28in.- 16yd. 31in = 2 yard 33

18 61wk. 4da.- 18wk. 6da.

We need to subtract both expression:

Then

61wk - 18wk = 43kw

4da-6da = -2da

Where 1 week = 7 days

Then

7 da - 2da = 5 da

Hence, 43kw -1 wk = 42 wk.

The result is:

42 wk 5 da

21. 8tbsp. 2tsp. * 15

We need to convert 2ts into tbsp and then multiply the result by 15.

If

1 tsp ------- 0.333tbsp

Then

2tp ------ 2(0.333tbsp)= 0.66666 tbsp

Now

(8tbsp + 0.6666 ) * 15 = 130 tbsp

Given two equations,

Comapring both equations,

Therefore, x = 1/3.

Answer:

Explanation:

What we want to answer in this question is simply, the area of the room that will be painted blue if he decides he would paint exactly have the room blue

So, we need to simply get the area of the room and divide this by half

Mathematically, the area of a rectangle is the product of its two sides

Thus, we have it that the area of the room is:

Now, to get the area painted blue, we divide this by 2 as follows or multiply by 1/2

We have this as:

One can decide which rational number operations to use to solve problems based on the context of the information.

Studying rational numbers is significant because they illustrate how the world is so complex that we will never be able to comprehend it.

A rational number is defined as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively. Every integer and 3/7, for example, are rational numbers.

A rational number is defined as the quotient of the fraction p/q of two integers, a numerator p and a non-zero denominator q. Every integer is a rational number since q might be equal to 1.

In this case, the operation include addition, subtraction, division, etc. This will be based on the context.

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SOLUTION:

Step 1:

In this question, we are asked to calculate Chandler's gross pay from the statement of bi-weekly earnings.

Step 2:

To get the Gross pay, we need to do the following:

Now, we need to calculate Total Deductions:

Now, we have that the Net Pay = $ 780. 63

Then,

CONCLUSION:

Chandler's Gross Pay = $ 974. 54

Given:

The function used to compute the probability of x successes in n trials, when the trials are dependent.

Required:

To choose the correct option for the given statement.

Explanation:

The hypergeometric distribution is a discrete probability distribution. It is used when you want to determine the probability of obtaining a certain number of successes without replacement from a specific sample size.

Therefore the option c is correct.

Final Answer:

c ) hypergeometric probability function.

Question:

Draw a right triangle with a leg that has a length of 10 and the angle opposite to that side is 55 degrees. find the length of the hypotenuse. round your answer to the nearest tenth.​

Solution:

A right triangle with a leg that has a length of 10 and the angle opposite to that side is 55 degrees is given by the following picture:

In this case, the appropriate trigonometric identity is:

where y is the opposite side, and h is the hypotenuse. Now, replacing the given data in the previous equation we obtain:

and solving for h, we get:

then, the correct answer is:

Step-by-step explanation:

since M is the midpoint, it means that AM = MB.

so,

b² + 5b = 3b + 35

b² + 2b - 35 = 0

the general solution to such a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case (x is called b, don't get confused, as this is not the factor of x) this gives us

b = (-2 ± sqrt(2² - 4×1×-35))/(2×1) =

= (-2 ± sqrt(4 + 140))/2 = (-2 ± sqrt(144))/2 =

= (-2 ± 12)/2 = -1 ± 6

b1 = -1 + 6 = 5

b2 = -1 - 6 = -7

therefore, we have 2 solutions

b = 5

AM = 5² + 5×5 = 25 + 25 = 50

b = -7

AM = (-7)² + 5×-7 = 49 - 35 = 14

control, as AM = MB

MB = 3×5 + 35 = 15 + 35 = 50

or

MB = 3×-7 + 35 = -21 + 35 = 14

AM = MB in both cases, so, all is correct.

The equation of circle is given by,

The equation of line is given by,

The points of intersection of the circle and line is,

A=(Xa, Ya)=(10, 0)

B=(Xb, Yb)=(-8, 6)

The length of chord AB can be calculated using distance formula as,

Let (Xc, Yc) be the coordinates of point C on the circle. Hence, using equation (1), we can write

Using distance formula, the expression for the length of chord AC is given by,

Since (Xa, Ya)=(10, 0),

It is given that chords AB and AC have equal length. Hence, we can write

Squaring both sides of above equation,

Subtract equation (4) from (3) and solve for Xc.

Put Xc=-8 in equation (3) to find Yc.

So, the coordinates of point C can be (Xc, Yc)=(-8, 6) or (Xc, Yc)=(-8, -6).

Since (-8, 6) are the coordinates of point B, the coordinates of point C can be chosen as (-8, -6).

Therefore, the coordinates of point C is (-8, -6) if chords AB and AC have equal length.

To find the solution to the system of equation

we will use the elimination method

3x - y = - 5 ----------------------------(1)

2x + 3y = 4 -------------------------------(2)

We will eliminate y and solve for x

multiply equation (1) through by 3

9x - 3y = - 15 ------------------------------------(3)

add equation (2) and equation (3)

11x = -11

divide both-side of the equation by 11

x = -1

substitute x = -1 in equation (1) and solve for y

3x - y = - 5

3(-1) - y = -5

-3 - y = -5

add 3 to both-side of the equation

- y = -5 +3

-y = -2

multiply through byb -1

y = 2

Hence, the correct option is B

Answer: 82 R1 or decimal form 82.031

Step-by-step explanation:

0082

. --------

-0

26

. - 0

. 262

. -256

65

-64

. 1

Given:

Jim baked 48 cookies with 4 scoops of flour.

So, the unit rate will be = 48/4 = 12 cookies/scoop of flour

So, for 96 cookies, the number of scoops of flour will be =

96/12 = 8

So, the answer will be 8 scoops of flour

Given:

The ship is moved from (-10,9) to (-1,-5) in the coordinate plane.

To find:

The transformation rule

Explanation:

The initial point can be written to obtain the terminal point as follow,

In general,

We write,

Final answer: Option C.

Given:

Principal - $12,000

Annual Interest Rate = 5.5% or 0.055 in decimal form

Time in years = 10 years

Find: simple interest and future value

Solution:

The formula for getting the simple interest is:

Let's replace the variables in the formula with their corresponding numerical value.

The interest after 10 years is $6, 600.

So, if the interest is 6,600, the future value of the money is:

The future value of the deposited money after 10 years is $18, 600.

We have to find the linear relationship for the cost of tuition in function of the year after 1990.

The cost in 1990 was $104, so we can represent this as the point (0, 104).

The cost in 1998 was $184, so the point is (8, 184).

We then can calculate the slope as:

We can write the equation in slope-point form using the slope m = 10 and the point (0,104):

We can then write the cost c as:

We then can estimate the cost for year 2002 by calculating c(x) for x = 12, because 2002 is 12 years after 1990.

We can calculate it as:

Now we have to calculate in which year the tuition cost will be c = 254. We can find x as:

As x = 15, it correspond to year 1990+15 = 2005.

Answer:

a) c = 10x + 104

b) $224

c) year 2005.

To answer this we have to apply the simple interest formula:

I =P x r x t

Where:

I= interest

P= Principal

R= Interest rate ( in decimal form)

t = time (years)

Replacing with the values given:

Interest= I

Principal = ?

Interest rate = 2/100 =0.02

time= 5 years

I = P x 0.02 x 5

I= 0.1P

Amount= P+I

A = P+0.1P

5,000= P+0.1P

5,000= 1.1P

5,000/1.1 =P

4,545.45 =P

Eliana can drive 198 km with 22 liters of fuel.

If Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km then she would need 15.5 liters of fuel

In this question, we have been given Eliana drove her car 81 km and used 9 liters of fuel.

81 km=9 liters

9 km= 1 liter

She wants to know the distance she can drive on 22 liters of fuel. She assumes her car will continue consuming fuel at the same rate.

By unitary method,

22 liters = 22 × 9 km

              = 198 km

Also, given that  if Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km.

We need to find the amount of fuel she would need.

Let 139.4 km = x liters

By unitary method,

x = 139.4 / 9

x = 15.5 liters

Therefore, Eliana can drive 198 km with 22 liters of fuel.

If Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km then she would need 15.5 liters of fuel

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1)

2)

3)

4)

Answer: 22

Step-by-step explanation:

The first step is to define the daily rates of each pump

From the information given,

First pump can empty the pool in 7 days. This means that

Daily rate of first pump = 1/7

The first pump's rate is 1/7 per day

Second pump can empty the pool in 14 days. This means that

Daily rate of second pump = 1/14

The second pump's rate is 1/14 per day

Let t be the number of days it will take both pumps, working together to empty the pool. Thus,

combined daily rate of both pumps = 1/t

The rates are additive. It means that

1/7 + 1/14 = 1/t

Simplifying the left side, we have

3/14 = 1/t

The combined pumps rate is 3/14 per day

By taking reciprocal of both sides,

t = 14/3 = 4.67

It will take the two pumps 4.67 days to empty the pool together

Given:

Required:

To determine the possibilities for the nature of the roots of the given equation.

Explanation:

(A)

we have that

K is the center of circle

J -----> point of tangency

segment IK is a radius

segment JL is a chord

segment GI is a secant

segment JI is a diameter

segment GJ is a tangent

arc JIL is a major arc

arc JL is a minor arc

arc JLI is a half circle (180 degrees)

Part 2

we have that

arc ST

Remember that

arc ST+87+72=180 degrees ------> by half circle

so

arc ST=180-159

arc WV

we have

arc WV+arc UV=180 degrees -----> by half circle

arc UV=72 degrees

so

arc WV=180-72

arc VUT

arc VUT=arc VU+arc UT

substitute given values

arc VUT=72+87

Constant of variation ( k ):

• y = 2/3

• x = 1/4

k = 8/3

Based on k we can find the value of y when x =3/4 as follows:

Answer:

• k = 8/3

• When ,x, = ,3/4,,, y = 2

An angle in standard position has the vertex at the origin and the initial side is on the positive x-axis.

Thus, the initial side of the angle is:

Now, half the circumference measures pi, thus, pi/2 is a quarte of the circumference. As we want to find the angle -pi/2, then we need to rotate the terminal side clockwise:

Find the sine and the cosine.

The sine and the cosine in the unit circle are given by the coordinates as follows:

As can be seen in the given unit circle, the terminal side is located at:

Thus, the values of cosine and sine are:

Given:

200 lottery tickets are sold for $6 each.

The person with the single winning ticket will get $71.

So, The probability of winning = 1/200

The probability of losing =

Answer: the expected value is. aroud 1-2

Step-by-step explanation:

With each additional tree , the estimated time increases by 10 minutes .

in the question ,

a table with number of trees and time required to plant them is given .

For planting 1 tree 30 minutes is required to plant them .

for planting 2 trees 40 minutes is required to plant them .

increase in number of tree = 2 tree - 1 tree = 1 tree

change in time required = 40 min - 30 min = 10 min

for planting 3 trees , 50 minutes is required to plant them .

increase in number of tree = 3 trees - 2 trees = 1 tree

change in time required = 50 min - 40 min = 10 min

So, we can see that for every additional tree planted the time increases by 10 minutes .

Therefore , with each additional tree , the estimated time increases by 10 minutes .

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Work Shown:

5 blue + 4 red = 9 total

A = P(1st is red, 2nd is red)

A = P(1st is red)*P(2nd is red, given 1st is red)

A = (4/9)*(3/8)

A = 12/72

B = P(1st is blue, 2nd is red)

B = P(1st is blue)*P(2nd is red, given 1st is blue)

B = (5/9)*(4/8)

B = 20/72

C = P(2nd is red)

C = A+B

C = 12/72 + 20/72

C = 32/72

C = 4/9

The change of base formula states that:

this means that we can caculate any logarithm using the natural logarithm if we make the quotient of the natural logarithm of the original value and the natural logarithm of the original base.

In this case we have:

Then, using the change of base formula, we have:

Once we have the expression we just evaluate the expression on the right to get the appoximation we need:

Currently

Let Amy's current age be x. Since Dianne is 23 years older than her daughter, then she is (x + 23) years old.

In 5 years

Amy's age will be (x + 5) years.

Dianne's age will be:

The sum of their ages in 5 years is 91. Therefore, we have:

Solving, we have:

Amy is 29 years old. Therefore, Dianne will be:

ANSWER:

Amy is 29 years old, and Dianne is 52 years old.