A certain right triangle with integer side lengths has perimeter $72$. What is its area?

Answer:

[tex]\Large \boxed{x=\frac{-9}{13} \ \ \mathrm{or} \ \ x = -1}}[/tex]

Step-by-step explanation:

[tex]13x^2 + 13x + 9x + 9 = 0[/tex]

Factor the expression.

[tex]13x(x+1)+9(x+1)=0[/tex]

Take (x + 1) as a common factor.

[tex](13x+9)(x+1)=0[/tex]

Set factors equal to 0.

First possibility:

[tex]13x + 9 = 0[/tex]

[tex]13x=-9[/tex]

[tex]\displaystyle x=\frac{-9}{13}[/tex]

Second possibility:

[tex]x+1=0[/tex]

[tex]x=-1[/tex]

Answer: 12.25miles.

Step-by-step explanation:

This is a simple proportion.

                       20 miles   = 3.5miles

      ∴                1 mile     = 3.5/20

      ∴  1hour 10minutes  which is equivalent to 70minutes will be

                                        =  (3.5/20 x ⁷⁰/₁ ) miles

                                        = 12.25miles

Answer:

D. 16

Step-by-step explanation:

[tex] GH^2 = GF \times GE[/tex]

[tex] 12^2 = 9 \times (9+x - 2)[/tex]

[tex] 144= 9 \times (7+x)[/tex]

[tex] \frac{144}{9}= (7+x)[/tex]

[tex] 16= 7+x [/tex]

[tex] 16-7=x [/tex]

[tex] 9=x [/tex]

GE = 9 + x - 2 = 9 + 9 - 2 = 18 - 2

GE = 16

Answer: Plane

Step-by-step explanation: A plane is a flat surface that has no thickness.

Think of a plane as a wall or a floor of a room.

Another important characteristic of a plane is that it has no edges.

So it extends forever in all directions.

Answer:

-9

Step-by-step explanation:

x+2=-7

x+2-2=-7-2

x=-9

Answer:

-9

Step-by-step explanation:

i took this assignment

Answer:

1,200

Step-by-step explanation:

1020 divided by 0.85= 1200

x < -3 or x > 1

=====================================================

Work Shown:

Solve the first inequality for x

3x+2 < -7

3x < -7-2 .... subtract 2 from both sides

3x < -9

x < -9/3 .... divide both sides by 3

x < -3

Do the same for the second inequality

-4x+5 < 1

-4x < 1-5

-4x < -4

x > -4/(-4) .... note the inequality sign flips

x > 1

So either x < -3 or x > 1. This points to choice A as the answer.

Answer:

y = (-3/2)x + 7/2

Step-by-step explanation:

Find the slope of this line first.

As you move from the first point to the second, x (the 'run') increases by 6 and y (the 'rise') decreases by 4 (from 3 to -1).  Thus the slope is

m = rise/run = -6/4 or -3/2.

Find b for this situation, using y = mx + b, m = -3/2, y = -1 and x = 3:

-1 = (-3/2)(3) + b.  Multiply all three terms by 2:

2(-1) = -9 + 2b, or 7 = 2b.  Then b = 7/2, and the desired equation is

y = (-3/2)x + 7/2

Answer:

Part I: 2πr*X/360

Part II: 2.5 radians

Part III: 143.24°

Step-by-step explanation:

Part II: and Part III: 2π(6)*x/360 = 15, x = 143.24°

143/360 = x/2π, x = 2.5 radians

Answer:

The possible coordinates of the midpoint are -10.5 and 10.5

Step-by-step explanation:

The given parameters are;

The coordinate of A = 0

The distance from A to R which is the same as AR = 21

Given that R is on the number line, we have;

When R is on the left side of A, which is = 0 - 21 = -21, we have;

The coordinates of the midpoint, M from -21 to 0 is given as follows;

M = (A + R)/2 = (0 - 21)/2 = -10.5

When R is on the right side of A, which is = 21 - 0 = 21, we have;

The coordinates of the midpoint, M from 21 to 0 is given as follows;

M = (A + R)/2 = (0 + 21)/2 = 10.5

Therefore, the possible coordinates of the midpoint are -10.5 and 10.5.

Answer:

[tex]y=-\frac{12}{7}x-\frac{80}{7}[/tex]

Step-by-step explanation:

In order to find the slope-intercept form of a line when given two points, we need to first put it into point-slope form. The point-slope form is given by the equation:

[tex]y-y_1=m(x-x_1)[/tex]

Where m is the slope and x₁ and y₁ is one of the two points.

Anyways, let's first find the slope. Let's designate (-2,-8) as x₁ and y₁ and (-9,4) as x₂ and y₂ (it doesn't really matter). The formula for slope is:

[tex]m=\frac{y_2-y_1}{x_2-x_1} =\frac{(4)-(-8)}{(-9)-(-2)}=12/-7=-12/7[/tex]

So, the slope is -12/7.

Now, pick a point for the point-slope form. To keep things consistent, I'm going to use the point (-2,-8) as x₁ and y₁. Plug in -12/7 for m. Therefore:

[tex]y-(-8)=-\frac{12}{7}(x-(-2))\\[/tex]

Now, simplify, distribute, and isolate the y:

[tex]y+8=-\frac{12}{7}(x+2)\\y+8=-\frac{12}{7}x-\frac{24}{7}\\y=-\frac{12}{7}x-\frac{24}{7}-8\\y=-\frac{12}{7}x-\frac{24}{7}-\frac{56}{7} \\y=-\frac{12}{7}x-\frac{80}{7}\\y=-\frac{12}{7}x-\frac{80}{7}[/tex]

Answer:

40%

Step-by-step explanation:

First, we must find out how many perfect squares are between 1 and 10.

1, 2, 4, 9,

Now, we put that quantity over 10.

4              2

--      =      --

10            5

Answer:

x < -3

Step-by-step explanation:

First we simplify:

-5x - 5 > 7x + 31

-12x > 36

x < -3.

We reverse the sign because we divided by a negative number on both sides.

That should be easy to graph.

Answer:

Step-by-step explanation:

-4x - 8 + 6 = 5 -3x - 3

-4x - 2 = -3x + 2

-x - 2 = 2

-x = 4

x = -4

For the expression 2(-2x - 4) + 6 = 5 – 3(x + 1) the value of x is -4.

Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.

The given expression is,

2(-2x - 4) + 6 = 5 - 3(x + 1)

To find the value of x, simplify the expression,

-4x - 8 + 6 = 5 - 3x - 3

-4x - 2 = 2 - 3x

-4 = 4x - 3x

x = -4

The required value of x is -4.

To know more about Algebra on:

https://brainly.com/question/24875240

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Answer:

1) Debit Depreciation expenses for $1,200; and Credit Accumulated depreciation for $1,200.

2) Debit Unearned Rent Revenue for $3,400; and Credit Rent Revenue for $3,400.

3) Debit interest expenses for $500; Credit Interest payable for $500.

4) Debit Supplies expenses a/c for $1,900; and Credit Cost of goods sold for $1,900.

5) Debit Insurance expense for $600; Credit Insurance prepaid for $600.

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided for answering the question. See the attached pdf file for the complete question.

The explanation to the answer is now provided as follows:

The adjusting entries at March 31 will look as follows:

Perez Rental Agency

Date        Accounts Name                                         Dr($)            Cr($)    

Mar 31    Depreciation exp. ($400 * 3monts)           1,200

                Accumulated depreciation                                          1,200

             (To record depreciation expenses.)                                              

Mar 31     Unearned Rent Revenue                           3,400

                 Rent Revenue (1/3 * $10,200)                                    3,400

              (To record earned unearned rent revenue.)                                

Mar 31   Interest  expenses a/c                                    500

               Interest payable                                                              500

              (To record accrued interest on note payables.)                      

Mar 31    Supplies  expenses a/c ($2,800 - 900)      1,900

                 Supplies on hand                                                       1,900

              (To record supplies expenses.)                                                    

Mar 31     Insurance exp. ($200 * 3 months)               600

                 Prepaid insurance                                                         600

               (To record expired prepaid insurance.)                                      

Answer:The answer is OD 10.125

Step-by-step explanation:

Add all the lengths of the fish (6+8+9+10+11+12+12+13) = 81

Divide by 8

81/8

=10.125

Answer:

32/13

Step-by-step explanation:

Please include the instructions when you post a problem.

Let's assume you re to simplify this expression.

We get:

-4+2(-2+5)^2        -4 + 2(3)^2        -4 + 36

__________  = ------------------- = ----------------- = 32/13

5-(2-4)^3               5 - (-2)^3            5 + 8

Answer:

60/11

Step-by-step explanation:

tan A = 60/11

Answer:

tan A = 60/11

Answer:

3.3

Step-by-step explanation:

7-7=0

-3+-7=-10

10 divided by 3 is 3.3

Answer: y < (-1/4)*x + 1.

Step-by-step explanation:

The first thing you need to notice is that the line is not solid and that the shaded part is under the line, so our inequality will be strictly smaller than a linear equation.

y < a*x + b.

Now let's find the equation of the line.

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

In the graph, we can see that the line passes through the points: (0,1) and (4. 0)

Then the slope is:

a = (0 - 1)/(4 -0) = -1/4.

Now we know that the line is:

y = (-1/4)*x + b

To find the value of b, just replace the value of one of the points in the equation.

We know that (0,1) is a solution of the equation (x= 0, y = 1)

1 = (-1/4)*0 + b = b

1 = b

Then our inequality is:

y < (-1/4)*x + 1.

Answer:

See Attachment for number line

Step-by-step explanation:

Given

Temperatures: 5°C, -1°C,- 3°C, 2°C, and 0°C

Required

Order from least to greatest using number line

First, we have to order the temperatures:

In order from least to greatest, we have: -3°C     -1°C     0°C    2°C    5°C

Next, we calculate the range;

Range = Highest - Least

Range = 5°C - 3°C

Range = 2°C

See Attachment for number line

Answer:

The third angle is 180-(49+75)=56 degrees

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Answer:

56

Step-by-step explanation:

Answer:

Almonds = 400grams

Cashew = 300 grams

Step-by-step explanation:

Let the grams of cashew be represented by = C

the grams of almonds be represented by = A

A 700 g dry fruit pack costs ₹216 .It contains some almonds and the rest cashew kernel

C + A = 700g ......Equation 1

C = 700 - A

If almonds cost ₹288 per kg and cashew kernel cost ₹336 per kg

Let's convert them to grams

1 kg = 1000grams

For almonds

= 288/1000 = 0.288g

For cashew

= 336/1000 = 0.336g

Hence,

0.288 × A + 0.336g × C = ₹216

0.288A + 0.336C = 216

From Equation 1, substitute 700 - A for C in Equation 2

0.288A + 0.336(700 - A) = 216

0.288A + 235.2 - 0.336A = 216

Collect like terms

0.288A - 0.336A = 216 - 235.2

- 0.048A = -19.2

A = -19.2/-0.048

A = 400 grams

Substitute 400g for a in Equation 1

C + A = 700g ......Equation 1

= C + 400g = 700g

C = 700g - 400g

C = 300g

Therefore, the number of grams of Almonds = 400grams

Cashew = 300 grams

Answer:

Step-by-step explanation:

[tex]m = 7\\(8,9)=(x_1 , y_1)\\\\y-y_1=m(x-x_1)\\\\y - 9=7(x -8)\\y-9=7x-56\\\\Collect\:like\:terms\\\\y = 7x-56+9\\\\y = 7x-47[/tex]

Answer:

Hey there!

Expand (2+i)(3-i). You should get 7+i

Expand (7+i)(1+2i). You should get 5+15i

Expand (5+15i)(1-i). You should get 20+10i

Expand (20+10i)(3+i). You should get 50+50i as your final answer.

Let me know if this helps :)

Answer:

Step-by-step explanation:

P(1, -2) ;Q(4,3)

Let R(x1,y1)

Midpoint=[tex](\frac{x_{1}+x_{2}}{2},\frac{y_1+y_2}{2})\\[/tex] = (4,3)

[tex](\frac{1+x_1}{2},\frac{-2+y_1}{2})=(4,3)\\[/tex]

Compare x coordinates and y coordinates

[tex]\frac{1+x_1}{2}=4 ; \frac{-2+y_2}{2}=3[/tex]

1+x1 = 4*2   ; -2+y2 = 3*2

1+x1 = 8       ;  -2 +y2 = 6

   x1= 8-1     ;        y2 = 6+2

    x1 = 7     ;         y2 = 8

R(7 , 8)

Answer:

32

Step-by-step explanation:

Use the correct order of operations.

40 + 8 × 2 - 8 × 3​ =

= 40 + 16 - 24​

= 56 - 24

= 32

Answer:

y = 6

Step-by-step explanation:

Given a parallelogram ABCD with diagonals AC and BD.

Kindly refer to the diagram attached for the given parallelogram.

[tex]AE=2x\\BE=y+10\\CE=x+2\\DE=4y-8[/tex]

To find:

The value of y = ?

Solution:

First of all, let us consider a property of parallelogram and its diagonals.

The intersecting point of diagonals of a parallelogram bisect the diagonals in two equal parts.

Let us consider the given parallelogram ABCD which has its diagonals BD and AC intersecting at point E.

As per the property stated above:

AE = CE and

DE = BE

Putting the values of AE, CE, DE and BE as given in the question statement and solving for [tex]x[/tex] and [tex]y[/tex]:

[tex]2x = x+2\\\Rightarrow \bold{x = 2}[/tex]

and

[tex]y+10=4y-8\\\Rightarrow 4y-y = 10+8\\\Rightarrow 3y=18\\\Rightarrow y =\dfrac{18}{3}\\\Rightarrow \bold{y= 6}[/tex]

So, the answer is:

y = 6

Answer: 8 liters  can.

Step-by-step explanation:

First we need to find the volume of the cart tank . Since it is in the shape of a rectangular prism we have to multiply the length by the width by the height to find the volume.

V= 40 * 25 * 8  

V =  8000  

Which means that the volume is 8000 cubic centimeters.  

Now convert 8000 cubic centimeters to liter.

It gives us a hint that 1 liter is equal to 1000 cm^3

So to convert 8000 cubic centimeters to liters we will have to divide it by 1000.

8000/1000 = 8 liters.

Answer:

A) A

Step-by-step explanation:

The square root of 7 is just over two and a half.

Answer:

A. A

Step-by-step explanation:

Step 1: Find closest perfect roots near √7

We know that √4 = 2

We also know that √9 = 3

√7 is between √4 and √9, so √7 is between 2 and 3.

Therefore, our answer is A.