How many unique triangles can be drawn with side lengths 8 in., 12 in., and 24 in.? Explain.

Answer:

10

Step-by-step explanation:

divide 140 by 14 and you get 10

Answer:

Area of rectangle: 256

Area of triangle 1: 24

Area of triangle 2: 16

Area of triangle 3: 96

Area of trapezoid: 120

Step-by-step explanation:

I just did the question on the thing so Ik I'm right.

-The graph measures by twos. To get the area of the rectangle get the base times height of it. That would be 16x16=256.

-Get base (8) times height (6) of triangle 1 then divide by 2, remember to count the squares by 2 for finding all areas. The formula would be 1/2(b)(h) because dividing by 2 is the same as multiplying times 1/2. Plug it in and     (8)(6)=48 then divide by 2 which equals 24.

-Same formula for triangle 2. Plug it in and (8)(4)=32 and divide by 2 and it equals 16.

-Same formula for triangle 3. Plugged in is (12)(16)=192 divide by 2 and it equals 96.

-To find the area of the trapezoid get your rectangle area (256) and subtract all the triangle areas. So 256 - 6 - 16 - 96 = 120.

The area of the given shapes are required.

256 square units

24 square units

16 square units

96 square units

120 square units

Area of the rectangle

[tex]A_r=(20-4)\times(20-4)\\\Rightarrow A_r=256\ \text{square units}[/tex]

The area of a right triangle is given by

[tex]\dfrac{1}{2}bh[/tex]

where

b = Base

h = Height

Every triangle here is a right triangle.

Triangle 1

[tex]b=20-14=6\ \text{units}[/tex]

[tex]h=12-4=8\ \text{units}[/tex]

[tex]A_1=\dfrac{1}{2}\times 6\times 8\\\Rightarrow A_1=24\ \text{square units}[/tex]

Triangle 2

[tex]b=20-16=4\ \text{units}[/tex]

[tex]h=20-12=8\ \text{units}[/tex]

[tex]A_2=\dfrac{1}{2}\times 4\times 8\\\Rightarrow A_2=16\ \text{square units}[/tex]

Triangle 3

[tex]b=20-4=16\ \text{units}[/tex]

[tex]h=16-4=12\ \text{units}[/tex]

[tex]A_3=\dfrac{1}{2}\times 16\times 12\\\Rightarrow A_3=96\ \text{square units}[/tex]

Area of trapezoid is Area of the rectangle minus Area of all the triangles.

[tex]A=A_r-(A_1+A_2+A_3)\\\Rightarrow A=256-(24+16+96)\\\Rightarrow A=120\ \text{square units}[/tex]

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Answer:

22

Step-by-step explanation:

The four-year-old brother can arrange the Legos in rows of 8.

To find the least number of rows the four-year-old brother can make with the black and yellow Legos, we need to determine the greatest common divisor (GCD) of 56 and 120. The GCD will represent the number of Legos in each row.

To find the GCD, we can use the Euclidean algorithm. Divide the larger number (120) by the smaller number (56). The remainder is 8. Then, divide the smaller number (56) by the remainder (8). The new remainder is 0.

Therefore, the GCD of 56 and 120 is 8. This means that the four-year-old brother can arrange the Legos in rows of 8, with 7 rows of black Legos and 1 row of yellow Legos, or vice versa.

Answer:

x=110 i think

Step-by-step explanation:

x+20+2x-70+x+x+20+x+90

=6x+60

6x+60=720

6x=(720-60)

6x=660

660/6=110

x=110

hope this helps!

Answer:

Step-by-step explanation:

sum of all angles of polygon = (n-2)*180   {n is no of sides}

= (6-2)*180 = 4*180 = 720

90 + 2x-70 + x+20 +x + x+20 + x = 720

Bring like terms together

90 - 70 + 20 + 20 + 2x + x + x + x + x =720

60 + 6x = 720

6x = 720 - 60

6x = 660

x = 660/6

x = 110

Answer:

its 7 for width and 3 and length

Step-by-step explanation:

L * W = 21

W= 4L-5

find the factors for 21 which is 21 and 1 or 7 and 3. Plug in which one is valified. 7 and 3 are correct.

Answer:

x = 3

Step-by-step explanation:

2x = 6

x = 3 (Because we divide on both sides by 2 so that the x is by itself, 6/2 = 3)

Answer:

Please see the attached pictures for full solution

Answer:

[tex]A = 40w-w^2[/tex]      

Step-by-step explanation:

We are given the following in the question:

Perimeter of rectangle = 80 inches.

Let l be the length and w be the width of rectangle.

Perimeter of rectangle =

[tex]P= 2(l+w)[/tex]

Putting values, we get,

[tex]80 = 2(l+w)\\40 = l+w\\\Rightarrow l = 40 - w[/tex]

Now, we have to find the area of the rectangle in terms of w.

Area of rectangle =

[tex]A = l\times w[/tex]

Putting values, we get

[tex]A = (40-w)w\\A = 40w-w^2[/tex]

is the required expression of area of rectangle in terms of w.

Yes, the perimeter is used to calculate the length of the rectangle in the term of w.

Answer:second one should be correct I took this last year

Step-by-step explanation:

Answer:

x = 2.564 ( to 3 dec. places )

Step-by-step explanation:

Using the rule of logarithms

log[tex]x^{n}[/tex] ⇔ n logx

Given

[tex]5^{x}[/tex] = 62 ( take the ln of both sides )

ln[tex]5^{x}[/tex] = ln 62, that is

x ln5 = ln 62 ( divide both sides by ln 5 )

x = [tex]\frac{ln62}{ln5}[/tex] ≈ 2.564

Answer:

2.5

Step-by-step explanation:

ln(5^x)=ln(62)

[tex]x=\frac{ln62}{ln5}[/tex]

≈2.56433

Option A(9,4,9,4) shows the most likely side lengths for a parallelogram because opposite sides of parallelogram are always equal.

Hope it will help u...

Answer:

2-1

Step-by-step explanation:

Given two points we can find the slope using

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

    = (-2 -5)/(2-1)

     = -7/1

   = -7

The denominator is 2-1

Answer:

2 - 1

Step-by-step explanation:

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

= (-2 - 5)/(2 - 1)

= -7

[tex]V=a^3[/tex]

[tex]2,460.375=a^3\\a=\sqrt[3]{2,460.375} \\a=13.5[/tex]

Answer: length is equal to 13.5

Answer: 8.21 in by 7.02 in

Step-by-step explanation: You would divide 345 by 42 AND 295 by 42, you would get 8.21 from 345 by dividing with 42 and you would get 7.02 by dividing by 7.02 and before you make your final answer MAKE SURE ITS IN INCHES!!!

Answer:

  (x -8)^2 +(y +3)^2 = 36

Step-by-step explanation:

The equation of a circle with center (h, k) and radius r is ...

  (x -h)^2 +(y -k)^2 = r2

Putting your numbers into this form gives ...

  (x -8)^2 +(y +3)^2 = 36

Answer:

The answer is 2881

Step-by-step explanation:

Look at the attached picture ⤴

I have shown the steps there....

So,Hope it will help u ....:)

✴Have a great day✴

Answer:

if the probability of a 6 is 1/5, the probability of “not six” is 4/5. The probability of a 6 on the first roll and not on the second is 1/5 x 4/5 = 4/25. The six could come on the second roll so that probability must be doubled. The overall probability of exactly one six is 8/25 or 0.32.

Step-by-step explanation:

Answer:

Cylinder Volume   =   π • r² • height

radius = 4 cm

Volume   =   π • 4^2 * 20

Volume   =   PI * 320

Volume   =   1,005.3096491487 which rounds to

1,005 cubic centimeters

Actually ALL those answers should say CUBIC CENTIMETERS.

Step-by-step explanation:

Answer:

No, They are not equivalent

Step-by-step explanation:

The two expressions are only said to be equivalent if they are the same regardless of whatever value the variable(s) is.

The variable in this question is x.

To prove this, we equate both expressions:

[tex]10x + 6 = 5x + 11[/tex]

[tex]10x - 5x = 11 - 6\\\\\\5x = 5\\\\\\x = 1[/tex]

This shows that they have the same value ONLY when x is 1.

This is why Andre says that they are equivalent, but they are not.

No, I do not agree with Andre because the two equations 10x + 6 and 5x + 11 are indeed equivalent.

No, I do not agree with Andre. Two equations are considered equivalent if they have the same solution for all values of x.

Let's check if 10x + 6 and 5x + 11 are equivalent by substituting x = 1 into both equations:

For 10x + 6: 10(1) + 6 = 10 + 6 = 16

For 5x + 11: 5(1) + 11 = 5 + 11 = 16

We can see that both equations indeed equal 16 when x is 1, so Andre is correct in this case. 10x + 6 and 5x + 11 are equivalent equations.

Answer:  

P(red then green) = 5/8 * 3/7 = 15/56

Step-by-step explanation: Since this is a logical "and" case, we have to multiply the separate events' probabilities...thus  P(red then green) = 5/8 * 3/7 = 15/56

Answer:

3/28

Step-by-step explanation:

3 red+ 5 green = 8 marbles in the jar

1st marble:

P(red) = number of red/ total = 3/8

We keep the marble

2 red+ 5 green = 7 marbles in the jar

P(green) = number of green/ total = 2/7

P (red,keep,green) = P(red)* P(green) = 3/8*2/7 = 6/56 = 3/28

Answer:

2700!

Step-by-step explanation:

hope that helped <3

Answer:

3/2

Step-by-step explanation:

So for the x it increases by +2. For the y it increases by +7. We do rise over run which is y over x. So it will be 3/2.

Answer: 3.5 or 7/2

Step-by-step explanation: use the slope formula y2-y1 / x2-x1

I chose 14-7 / 6-4

9514 1404 393

Answer:

  $70

Step-by-step explanation:

The excess amount is 20% of the goal. The given amount is 120% of the goal, so the proportion of the given amount that is excess is ...

  (20% of goal)/(120% of goal) = 1/6

Then the excess is (1/6)($420) = $70.

You raised $70 more than the $350 goal.

The original fundraising goal was $350, and since $420 was raised, which is 120% of the goal, $70 more was raised than the goal.

To find out how much more was raised than the goal during the fundraising event, start by understanding the percentage given. The $420 raised is 120% of the goal, which means the goal amount represents 100%. To calculate the original goal, you should divide the amount raised by the percentage raised (expressed as a decimal), so you divide 420 by 1.2 (since 120% as a decimal is 1.2).

Now, calculate the goal amount:
420 / 1.2 = $350

Therefore, the original goal was $350. Since the amount raised was $420, we subtract the goal from the amount raised to determine how much more was raised:
420 - 350 = $70.

Thus, the amount raised exceeded the goal by $70.

Answer:

its round

Step-by-step explanation:

Answer: The correct answer is mean and range.

Answer:

-7a^2 b^3

Step-by-step explanation:

-7(- a^2 )( -b^3 )

-7 * -a^2

A negative times a negative is a positive

7a^2

7a^2 * -b^3

A positive times a negative is a negative

-7a^2 b^3

Answer:

this is because of two diagonals which lie in the interior of the rectangle.

Answer:

A = 3 units^2

Step-by-step explanation:

The area of a triangle is

A  = 1/2 bh where b is the length of the base and h is the height

b = the distance from B to C = 4 units = 2  ( watch the scale)

h = the distance from A to C along the x axis =6 units = 3  (watch the scale)

A = 1/2 (2)(3)

A = 3 units^2