What is the area of the following figure: A) 30 cm 2 B) 36 cm 2 C) 18 cm 2 D) 15 cm 2

The length that can be cut off from the three given pieces of wood equally to form a right triangle is 5 cm

Given parameters:

dimension of the three pieces of wood = 20 cm, 41 cm and 44 cm

To find:

let the length that is cut off from each of the wood = y

From Pythagoras theorem, we will have the following equation.

[tex](44-y)^2 = (20-y)^2 + (41-y)^2\\\\expand \ the \ equation \ as \ follows;\\\\1936 - 88y + y^2 = 400 - 40y + y^2 + 1681 - 82y + y^2\\\\simplify \ by \ collecting \ similar \ terms \ together\\\\(1936 - 400- 1681) + (-88y + 40y+ 82y) + (y^2 - 2y^2) = 0\\\\-145 +34y - y^2 = 0\\\\multiply \ through \ by \ (-1)\\\\y^2-34y + 145 = 0\\\\factorize \ the \ above \ quadratic\ equation\\\\y^2 -5y - 29y + 145 = 0\\\\y(y - 5) -29(y - 5)=0 \\\\(y -5)(y-29) = 0\\\\y = 5 \ \ \ or \ \ \ \ y = 29[/tex]

Since the least measurement of one of the pieces of the wood is 20 cm, we cannot cut off 29 cm.

Thus, the highest amount we can cut off equally is 5 cm

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Answer:

x=6

Step-by-step explanation:

The crocodile river is y = 4

The road will intersect at ( 6,4)

We have two points on the line

(6,7) and (6,4)

The slope is

m = (y2-y1)/(x2-x1)

   = (4-7)/ (6-6)

  = -3/0

The slope is undefined

That means the equation is in the form

x=

Since the x coordinate is 6

x=6

Answer:

70

Step-by-step explanation:

8 choose 4

= (8!)/(4!*4!)

=(8*7*6*5)/(4*3*2*1)

=1680/24

=70

Answer:

4/8 simplified=1/2

Step-by-step explanation:

i hope this is right sorry if not

Answer:

its a mnemonic

Oh  Heck  Another  Hour Of  Algebra

(O = opposite side, H = hypotenuse ) = sine

(A = adjacent side,  H = hypotenuse ) = cosine

(O = opposite side,  A = adjacent ) = tangent

Answer:

star or asterisk if you are talking about (*)

Answer:

(*) is similar to (×)

and it means multiply

Answer:

252

Step-by-step explanation:

The conversion factor is

180/pi

7pi/5 * 180/pi = 7 *180/5 = 252 degrees

Answer:

20x+4

Step-by-step explanation:

In this question, we have to find an equation for two lines, depending on the input x, which creates the following piecewise function for this graph:

[tex]y = t, 0 \leq t \leq 10, -t + 20, 10 \leq t \leq 20[/tex]

Equation of a line:

The equation of a line is given by:

[tex]y = mt + b[/tex]

In which m is the slope and b is the y-intercept(value of y when x = 0).

This situation:

x between 0 and 10:

From here, we can take two points (t,y). I will take (0,0) and (10,10).

From point (0,0), we get that when [tex]x = 0, y = 0[/tex], which means that the y-intercept is [tex]b = 0[/tex], thus:

[tex]y_1 = mt[/tex]

To find the slope, when we have two points, it is given by change in y divided by change in t, so:

Change in t: 10 - 0 = 10

Change in y: 10 - 0 = 10

Slope: [tex]m = \frac{10}{10} = 1[/tex]

Thus, the first definition is:

[tex]y_1 = t, 0 \leq t < 10[/tex]

x between 10 and 20:

I will take the points (10,10) and (20,0).

First, we find the slope:

Change in t: 20 - 10 = 10

Change in y: 0 - 10 = -10

Slope: [tex]m = \frac{-10}{10} = -1[/tex]

Thus:

[tex]y_2 = -t + b[/tex]

For the intercept, we have point (20,0), which means that when [tex]t = 20, y = 0[/tex]. So

[tex]0 = -20 + b[/tex]

[tex]b = 20[/tex]

Thus, the second definition is:

[tex]y_2 = -t + 20, 10 \leq t \leq 20[/tex]

Write an equation for the graph.

We use the two definitions, that is:

[tex]y = y_1, 0 \leq t \leq 10, y_2, 10 \leq t \leq 20[/tex]

So

[tex]y = t, 0 \leq t \leq 10, -t + 20, 10 \leq t \leq 20[/tex]

A similar question can be found at https://brainly.com/question/16024991

Answer:

{ 11, -4, -29}

Step-by-step explanation:

5(-2) + y = 1

-10 + y = 1

y = 11

5(1) + y = 1

y = -4

5(6) + y = 1

30 + y = 1

y = -29

Answer:

The Range is the set: { -29, -4, 11 }

Step-by-step explanation:

You need to apply the given function to the x-values of the Domain, to find what values of the Range they are associated with. So let's start by isolating y on one side of the expression:

y = 1 - 5 x

Now let's find what values they result when x = -2, 1, and 6:

y = 1 - 5 (-2) = 1 + 10 = 11

y = 1 - 5 (1) = 1 - 5 = -4

y = 1 - 5 (6) = 1 - 30 = -29

Therefore the Range is the set: { -29, -4, 11 }

Answer:

1.68

Step-by-step explanation:

log723.7=2.86

multiplication in log is addition so 2.86+

log0.0667=-1.18

so 2.86+-1.18=1.68

Answer:

Commutative property

Step-by-step explanation:

You can switch the places of -2 and 3 without changing the output.

This property is called the commutative property

Answer:

(5, 2)

Step-by-step explanation:

(5, 6) go down 4 units means subtract 4 from the y

(5, 2)

The point to end up will be (5, 2).

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

In the first quadrant you start at (5, 6 ) and move 4 units down.

Now,

Since, In the first quadrant you start at 5, 6 and move 4 units down.

Hence, The end up point = (5, 6 - 4)

                                       = (5, 2)

Thus, The point to end up will be (5, 2).

Learn more about the coordinate visit:

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Answer:

1093 tickets

Step-by-step explanation:

Take the total amount and divide by the amount per ticket to determine the number of tickets

6558/6

1093 tickets

Answer:

The band have to sell 1093 Ticket to meet its goal

Step-by-step explanation:

Total cost = $6,558

Per Ticket cost =$6

formula:

No of Tickets = Total cost of Ticket ÷  Per Ticket Cost

                       = 6558 ÷ 6

No of Tickets = 1093

Check:

Total Cost = No of Ticket × Per ticket cost

                 = 1093 × 6

Total Cost =$6558

Answer:

b. vertical shrink

Step-by-step explanation:

Answer:

D. Testing the null hypothesis that the mean difference equals 0 is not equivalent to determining whether the confidence interval includes 0

Step-by-step explanation:

Dependent samples are samples that are related to one another.

In a hypothesis test, the hypothesis test and the confidence interval are equivalent in the sense that they result in the same conclusion.

However, in an hypothesis test , we fail to reject the null hypothesis if the rejection region is greater than the t-test statistics. It is therefore crucial to understand that if the true mean is zero. the confidence interval level for the mean of differences within the lower limit and the upper limits must contain zero , which implies the mean difference and the confidence interval  are equivalent.

Answer:

D. 1 real; 4 complex  

Step-by-step explanation:

1. Calculate the total number of roots

The fundamental theorem of algebra states that any polynomial of degree n has n roots.

Your polynomial is fifth degree, so it has five roots.

2. Calculate the number of real roots

We can use Descartes' rule of signs to determine the number of real roots:

The number of positive real roots is the same as the number of changes in the sign of the coefficients of ƒ(x) or less than by an even number.

The number of negative real roots is the same as the number of changes in sign of the coefficients of the terms of f(-x) or less than this by an even number.

(a) Number of positive real roots

The coefficients of ƒ(x) are

+1 +3 +8 +14 +16 + 8  

There are no changes of sign, so there are no positive real roots.

(b) Number of negative real roots

(i) Find f(-x)

f(-x) = -x⁵+ 3x⁴ - 8x³ + 14x² - 16x + 8

(ii) Count the changes of sign

The coefficients of f(-x) are

-1 ∥ +3 ∥ -8 ∥+14 ∥ -16 ∥ +8

There are five changes of sign.

Thus, the number of negative roots is five, three, or one.

So far, we know that we have five roots. None is positive, and there could be one, three, or five negative real roots.

3. Confirm by sketching the graph

The real roots are the points at which the graph crosses or touches the x-axis.

The graph (see below) crosses the x-axis at only one point.

Thus. we have

Answer:

[tex]\boxed{ x \geq 0}[/tex]

Step-by-step explanation:

Hey there!

Well we can cross out A. x is all real numbers because,

it’s not it only has all the positive numbers.

B. Is correct because the domain is every number greater than or equal to 0.

x ≥ 0

Hope this helps :)

The domain of the graph of a function is x ∈ [0, ∞) or x ≥ 0 option (B) x ≥ 0 is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

A function is shown in the graph which is plotted on the two-dimensional coordinate plane.

From the graph, we can see the graph of a function exists in the first quadrant only and it is increasing.

The interval in which the graph exists is [0, ∞)

or

The domain of a graph of a function is:

x ≥ 0

Thus, the domain of the graph of a function is x ∈ [0, ∞) or x ≥ 0 option (B) x ≥ 0 is correct.

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Answer:

A, B, C

Step-by-step explanation:

none of the 4 options changes the shape.

but D changes the size.

C is the only one that also maintains the orientation of the triangle - it only shifts its position.

A and B maintain size and shape, but they do change its orientation.

1 hour = 60 minutes.

Convert the minutes to decimals by diving by 60

30/60 = 0.5

2 hours and 30 minutes = 2.5 hours

45/60 = 0.75

5 hours 45 minutes = 5.75 hours

15/50 = 0.25

3 hours 15 minutes = 3.25 hours

Ow add all the hours:

2.5 + 5 + 5.75 + 3.25 = 16.5 hours

Answer: B. 16.50

Answer:

Outside temperature at 2 A.M = -33.2°C

Step-by-step explanation:

Given:

Temperature at 12:00 midnight (outside) = -30.9°C

Rate of decreases = - 2.3°C per two hour

Find:

Outside temperature at 2 A.M

Computation:

Outside temperature at 2 A.M = Temperature at 12:00 midnight (outside) + Rate of decreases

Outside temperature at 2 A.M = -30.9°C + (- 2.3°C)

Outside temperature at 2 A.M = -33.2°C

Answer:

First opening all the bracet

-8*-8*5*5*-8

- and -will be + so,

64*25*-8

64*-200

-12800

Answer:H2+Br2-->2HBr

Step-by-step explanation:

The amount of atoms on the left side must be equal to the amount of atoms on the right side for each element.

On the left you got 2xH and 2xBr.

This means you must have the same amount on the right.

2HBr =2xH + 2xBr

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{3x - 9x + 3y = 1}\\\huge\text{\boxed{\rightarrow} -6x + 3y = 1}\\\huge\text{\boxed{\rightarrow} -6x + 3(3.2) = 1}\\\huge\text{\boxed{\rightarrow} -6x + 9.6 = 1}[/tex]

[tex]\huge\textsf{SUBTRACT \underline{\underline{9.6}} to BOTH SIDES}\\\huge\text{-6x + 9.6 - 9.6 = 1 - 96}\\\\\\\huge\textsf{DIVIDE \underline{\underline{-6}} to BOTH SIDES}\\\\\huge\boxed{\dfrac{-6\mathsf{x}}{-6}= \dfrac{-8.6}{-6}}[/tex]

[tex]\huge\textsf{SIMPLIFY ABOVE \& YOU HAVE YOUR}\\\huge\textsf{RESULT OF THE X-VALUE}\\\\\\\boxed{\huge\boxed{\huge\textsf{x = \bf 1.433333 or } \mathsf{x = \bf \dfrac{8.6}{6}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}\\\\\\\\\boxed{\huge\boxed{\frak{Amphitrite1040:)}}}[/tex]

Answer:

yes it is correct it is not the first one

because the lines are not the same size and are in the right direction

Answer:

The last one

Step-by-step explanation:

All the other tables have repeating x values

I hope this helps!

pls ❤ and give brainliest pls

Answer:

x = 6

Step-by-step explanation:

no slope means vertical line x = ?

Answer:

282.7 ft^2

Step-by-step explanation:

Surface area=2*pi*r(r+h)

2*pi*3*(15)=282.7 ft^2

Hey there!

I believe your answer would be 282.7.

The formula should be 2πrh+2πr^2. So, 2·π·3·12+2·π·3^2.

Round the answer to the nearest tenth, and you will get 282.7!

Hope this helps!

Have a great day!

Answer:

30 gallons of tea

Step-by-step explanation:

We are looking at the average of cups of tea per minute but we are given the time frame of lunch in hours, so first, we have to convert the hours to minutes:

There are 60 minutes in 1 hour and lunch is 2 hours long.  So, multiply 60 by 2 to get 120 minutes total.

Next, we have to find out the number of cups of tea poured during the lunch.  We have been told already that an average of 4 cups of tea are poured a minute.

Therefore, multiply 4 by the total number of minutes for lunch.  You will multiply 4 by 20 to get 480 cups of tea poured in total during the catered lunch.

Finally, we have to see how many gallons of tea the caterer should bring.  We should know that there are 16 cups in one gallon.

That means we have to divide the total number of cups poured by 16.  Divide 480 by 16 to get 30 gallons of tea that the caterer should bring.

Answer:

[tex]19.79 - 2.8 = 16.99gallons[/tex]