A gift-wrapping box is in the shape of an oblique triangular prism.

A triangular prism is shown. The bases are triangle A B C and triangle F E D. A bisector is drawn from point E to point G on side F D. Line F D is extended to point H outside of the figure. Another line is drawn from point C to point H to form a right angle. The length of E G is 10 inches, the length of F D is 15 inches, the length of C H is 8 inches, and the length of A F is 10 inches.

If EG = 10 in., FD = 15 in., CH = 8 in., and A F = 10 in., what is the height of the prism?


in.

What is the base area, B?


square inches

What is the volume of the prism?


cubic inches

Answer:

44.4 degrees

Step-by-step explanation:

Given the following

Hypotenuse = 7

Longer leg = 5 (adjacent])

Let the acute angle angle between both sides be x

According to SOH CAH TOA

Cos theta = adj/hyp

Cos x = 5/7

x= arccos (5/7)

x = arccos (0.7143)

x = 44.4degrees

Hence he measure of the acute angle that is included between the longer leg and the hypotenuse is 44.4 degrees

Answer:

perimeter = 30.56 units

Step-by-step explanation:

perimeter of full circle = 2(4)(3.14) = 25.12

perimeter of semi circle = (25.12)(0.5) = 12.56

perimeter = 12.56 + 10 + 8 = 30.56

Answer:

x = 60° (Alternate angles)

Step-by-step explanation:

a) x = 60°

b) Reason: Alternate angles

Answer:x=60

Step-by-step explanation: all angles in a triangle add up to 180 degrees, x is the same as the angle next to it, therefore x=60 degrees

Answer:

Down below

Step-by-step explanation:

The graph is attached to the answer.

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

Given is a function,

g(x) = -3, -8≤x-2

          1, -2≤x≤4

          5, 4≤x≤10

The function g(x) is a discrete function. It is continuous between -8 to -2, -2 to 4, and 4 to 10.

And the open circle at -8, -2, 4, and 10.

More about the function; click,

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Answer:

S.A. = 138.16

Step-by-step explanation:

S.A. = πrl+πr²

3.14 x 4 = 12.56

12.56 x 7 =87.92

3.14 x 4 = 12.56

12.56 x 4 = 50.24

87.92 + 50.24 = 138.16

Let me know if this helps!

Answer:

y=-7/4x+6

Step-by-step explanation:

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

m=(-1-6)/(4-0)

m=-7/4

y-y1=m(x-x1)

y-6=-7/4(x-0)

y-6=-7/4(x)

y-6=-7/4x

y=-7/4x+6

Answer:

5.670, 56.27,5.72.

Step-by-step explanation:

All you do is pay attention to that decimal and remember that the places where the numbers are present; they are invisible zero so,

56.72 is the same as 56.720000.

It's pretty clear for this question since the numbers are clear so all you do is look at the decimals.

Answer:

(b, -a)

Step-by-step explanation:

First note that the rule for a rotation by 270° about the origin is (x,y)→(y,−x)

Note that the coordinates were swapped and the x coordinates negated. Similarly;

Given the coordinate of the point U as (a, b), if the triangle is rotated 270degrees clockwise, the resulting coordinate will  be (b, -a)

Answer:

a) length of sides remain unchanged

Step-by-step explanation:

Given:  

Number 1X2Y6Z is divisible by 9.

To find:  

The least value of  X+Y+Z = ?

Solution:  

First of all, let us learn the divisibility rule of 9.  

A given number will be divisible by 9 if and only if the sum of digits of the given number is also divisible by 9.

For example:

Let us consider a number 923463.  

The sum of digits = 9 + 2 + 3 + 4 + 6 + 3 = 27  

27 is divisible by 9 so the number 923463 will also be divisible by 9.

Let us consider another example 8972.  

Sum of digits = 26  

26 is not divisible by 9 so the number 8972 will also be not divisible by 9.

Now, we are given the number 1X2Y6Z.  

Sum of digits = 1 + X + 2 + Y + 6 + Z = 9 + X+Y+Z

The number 1X2Y6Z will be divisible by if 9+X+Y+Z is divisible by 9.  

The least value of X+Y+Z can be zero, so the sum of digits = 9 + 0 = 9  

which will make the number 1X2Y6Z divisible by 9.

So, the answer is:

Least value of X+Y+Z = 0 so that the number 1X2Y6Z is divisible by 9.

9514 1404 393

Answer:

  0

Step-by-step explanation:

For a number to be divisible by 9, the sum of the digits must be divisible by 9. The given digits total 9, so x+y+z must be a multiple of 9. The least possible multiple of 9 is 0.

The least value of x+y+z is 0.

_____

102060/9 = 11340

64 cm

(Pls brainliest)

Answer:

c times m

Step-by-step explanation:

hope this helps :b

=- No way

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

use Pythagoras theorem

Answer:

5 units

Step-by-step explanation:

It says round to the nearest 10th so it cant be 5.1 or 4.99, and 25 is to big for that side, so 5 units

Answer:

D) 6^5 · 3^5

Step-by-step explanation:

(6 · 3)^5 = 1889568

A) WRONG

(5 · (6 · 3)) = 90

B) WRONG

9^5 = 59049

C) WRONG

6 · 3^5 = 1458

D) CORRECT

6^5 · 3^5 = 1889568

Answer:

everything is in the picture

Answer:

175%

Step-by-step explanation:

The first one is a whole=1

the second one is cut in four but only 3 are shaded so 1/4=0.25    0.25*3=0.75

3/4/0.75 is shaded

so 1+0.75=1.75

1.75=175%

Answer:

C. [tex] \sqrt{x + 2} - \sqrt{x}[/tex]

Step-by-step explanation:

[tex] \frac{2}{ \sqrt{x} + \sqrt{x + 2} } \\ \\ = \frac{2}{ (\sqrt{x} + \sqrt{x + 2}) } \times \frac{(\sqrt{x} - \sqrt{x + 2})}{(\sqrt{x} - \sqrt{x + 2})} \\ \\ = \frac{2( \sqrt{x} - \sqrt{x + 2}) }{ ({ \sqrt{x} )}^{2} - {( \sqrt{x + 2} )}^{2} } \\ \\ = \frac{2( \sqrt{x} - \sqrt{x + 2}) }{ x - {( x + 2)} } \\ \\ = \frac{2( \sqrt{x} - \sqrt{x + 2}) }{ x - x - 2 } \\ \\ = \frac{2( \sqrt{x} - \sqrt{x + 2}) }{ - 2 } \\ \\ = - ( \sqrt{x} - \sqrt{x + 2}) \\ \\ \frac{2}{ \sqrt{x} + \sqrt{x + 2} } = \purple{ \bold{\sqrt{x + 2} - \sqrt{x} }}[/tex]

Answer:

I believe 31 dollars and 95 cents

Step-by-step explanation:

Marie would earn $37.2 in 4 1/2 hour.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas. This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Marie charges a $10.75 base fee for each dog she walks,

and, additional $7.10 per hour that she walks the dog.

Each day she spends $5.50 on dog treats.

So, if Marie works for 4 1/2 hour then she can earn

= 10.75 + 4 1/2 x 7.1 - 5.5

= 10.75 + 4.5 x 7.1 - 5.5

= $37.2.

Hence, Marie would earn $37.2.

Learn more about Unitary Method here:

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Answer:

V≈5.23×10-7m³

Step-by-step explanation:

V=π(d

2)2h=π·(0.014

2)2·3.4×10-3≈5.23389×10-7m³

Answer: 523.1 mm^2

You first want to find the radius for the volume of cylinder formula. You first do 14 divided by 2 to get the radius. You should get 7. Then after you find the radius you then put it into the formula which is v=3.14 x radius^2 x height. The equation with all the numbers from the problem is 3.14 x 7^2 x 3.4. After you put the equation into your calculator you should get 523.1 mm^2.

a) 3x + 5y =  26  

b) 2x + 2y = 12

First, we need to find a way to equate either the x terms or the y terms in each equation. a)  6x + 10y = 52

                          b) 6x + 6y = 36

Then take equation b) from the equation a) to eliminate the x component.

a) 6x + 10y = 52

- b) 6x + 6y = 36

   0x    + 4y = 16

            y = 4 ?

Then substitute the value of y into either equation to find the value of x.

b) 2x + 2y = 12

   2x + (2x4) =12

   2x + 8 = 12

   2x = 4

   x = 2

I hope this new information i read helps you maybe understand it and as an example!

Answer:

solution given:

B.

CE=2×2=4[base side is double to the line of mid point]

AB=15/2=7.5[b is a mid point]

m<AEC=75°[ corresponding angle]

5.

given:

BD=x+1

CE=x+10

we have

2BD=CE

2(x+1)=x+10

2x+2=x+10

2x-x=10-2

x=8

Answer:

Q1; 124.72

Sorry I don’t understand the second one

Step-by-step explanation:

Answer:

a = - 24 ; n =25

a = 28 ; n = 25

Step-by-step explanation:

n = l - a/d + 1

d = common difference = 4

Last term = l = 72

n = 72 - a/4 + 1

4n = 72 - a + 4

4n = 76 - a

a = 76 - 4n - - - (1)

Sum of terms :

Sn = n/2(a + l)

Sn = 600

600 = n/2(a + 72)

1200 = n(76-4n +72)

1200 = 148n - 4n

4n² - 148n + 1200

Solving the quadratic equation :

Roots of n are :

12 and 25

From (1)

n = 12

a = 76 - 4(12) = 28

n = 25

a = 76 - 4(25) = - 24

Hence,

a = - 24 ; n =25

a = 28 ; n = 25

Answer:

25

Step-by-step explanation:

Answer:

Maria needs to start at 9:20 in order to make it to the terminal.

Step-by-step explanation:

2:30 + 0:20 = 2:50. 12:10 - 2:50 = 9:20.