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4 years ago

What is the volume of the triangular prism below?

Mathematics

1 answer:

worty [1.4K]4 years ago

8 0

Answer:

4.5 ft

Step-by-step explanation:

18 inches = 1.5 ft

$\frac{1}{2} \times 1.5 \times 2 \times 3 = 4.5$

Volume of triangular prism = Base Area x Length

Hope this helps

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If x = 1 is a common root of ax² +ax + 2 = 0 and x² + x + b = 0 , then ab =

vodka [1.7K]

Answer:

ab = 2

Step-by-step explanation:

Given equations

ax² +ax + 2 = 0

x² + x + b = 0

root of both the equation

x= 1

then we can plug in x = 1 in both the equation

ax² +ax + 2 = 0 x² + x + b = 0

a*1² +a*1 + 2 = 0 1² + 1 + b = 0

a +a + 2 = 0 1 + 1 + b = 0

2a + 2 = 0 2 + b = 0

2a = - 2 b = -2

a = -2/2 = -1

Thus,

a = -1

b = -2

a*b = -1*-2 = 2

ab = 2

6 0

3 years ago

How do I solve this equation to get the solution?<br><br> y= -2x - 1<br><br> -3x + 6y = 24

swat32

There are a few ways to solve this. The method I will use is the substitution method. Since they give us a "y = " statement, we can replace the y in the second equation with what it gives us to the right of the equal sign.

- 3x + 6(- 2x - 1) = 24

Simplify by using the distributive property.

- 3x + 6(- 2x) + 6(- 1) = 24
- 3x - 12x - 6 = 24.

Combine like terms

- 15x - 6 = 24

Add 6 to each side.

- 15x = 30

Divide both sides by - 15 to isolate variable X

x = 30 / - 15
x = - 2.

Now plug in the x-value we've found back into the first equation.

y = - 2( - 2) - 1
y = 4 - 1
y = 3

Your answer is (- 2, 3)

6 0

3 years ago

how is building a triangle with different side lengths given different than building a quadrilateral with given side lengths?

Mariana [72]

Answer:

there can only be one possibility for a triangle when given the lengths of all the sides but for a quadrilateral the measure of the angles could differ depending on the person building the,. this is because triangles are more stable than quadrilaterals meaning that their side lengths follow a lot more rules than quadrilaterals do, for example the length of the side lengths can indicate whether or not that triangle is an acute, obtuse, or right triangle, and this is also evident by considering that you can use the SSS theorem to indicate two triangles are congruent, but for quadrilaterals you cant do that

Step-by-step explanation:

8 0

4 years ago

Saeed bought 21 1/2 lb. of ground beef. He used 1/4 of the beef to make tacos and 2/3 of the remainder to make quarter-pound bur

blagie [28]

This may be a little complicated, but basically, you have to break everything down into decimals. 21.5 X .25 = 5.375. Subtract 5.375 from 21.5 and you should get 10.75 or 10 3/4. Divide 10 3/4 by 1/4, the answer should be 30 burgers.

7 0

3 years ago

1) Draw the arrow diagram and the matrix representation for the relation: R={(1, 2), (3, 4), (2, 3), (3, 2), (2, 1), (3, 1), (4,

tensa zangetsu [6.8K]

Answer:

The arrow diagram and the matrix representation for the relation is shown below.

Step-by-step explanation:

The given relation is

R={(1, 2), (3, 4), (2, 3), (3, 2), (2, 1), (3, 1), (4, 3)}

If a relation is defined as

$R=\{(x,y)|x\in R,y\in R\}$

Then the set of x values is domain and set of y values is range.

The domain of the function is

Domain={1, 2, 3, 4)

The range of the function is

Range={1, 2, 3, 4)

In arrow diagram, we have two sets first set represents the domain and second set represents the range. The arrow connecting the element represent the relation.

In matrix representation,

$M_{ij}=\begin{cases}1 & \text{ if } (x_i,y_j)\in R \\ 0 & \text{ if } (x_i,y_j)\notin R\end{cases}$

The arrow diagram and the matrix representation for the relation is shown below.

6 0

4 years ago