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3 years ago

What is the height of a triangular prism that has a height of 9 meters and a base with the following deminsions 4m 14m

Mathematics

1 answer:

Andrew [12]3 years ago

6 0

Answer:

252m^3

Step-by-step explanation:

A solid having a triangular base is what we call a triangular prism. For every prism, its volume is always equal to the area of its base times its height. In other words:

V = AxH

V - volume

A- area

H - height of prism

We know that:

h = 4 m (side of base)

b = 14 (other base side)

A = bh/2 = 14x4/2 = 28 m^2

And then: V = A x H = 28 x 9 = 252 m^3

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2x - 3y = 14<br> 5x - 3y = -10

pshichka [43]

Answer:

x = -8

y = -10

Step-by-step explanation:

Elimination

2x - 3y = 14

5x - 3y = -10

__________--

-3x = 24

x = 24/-3

x = -8

Subsitution

2x - 3y = 14

2(-8) - 3y = 14

-16 - 3y = 14

-3y = 14 + 16

-3y = 30

y = 30/-3

y = -10

5 0

3 years ago

S KM ∥ JN? Why or why not?

bixtya [17]

Given: We have the given figure through which we can see

LK=16,

KJ=10,

LM=24,

MN=15

To Find: Whether KM || JN and the reasoning behind it.

Solution: Yes, KM || JN because $\frac{16}{10}= \frac{24}{15}$

Explanation:

For this solution, we use the concept of Similar Triangles.

Now, KM || JN if ΔLKM ~ ΔLJN (i.e., if ΔLKM is similar to ΔLJN).

Now, ∠MLK=∠NLJ

To prove similarity of the two triangles, we have to show that the sides are proportional. In other words, LK:KJ = LM:LN

$LK:KJ=LM:LN\\\\ \frac{LK}{KJ} =\frac{LM}{LN}\\\\\frac{16}{26}= \frac{24}{39}\\\\$

which is true as both sides simplify to $\frac{8}{13}$

Thus, we see that ΔLKM ~ ΔLJN (i.e., if ΔLKM is similar to ΔLJN).

Therefore, KM || JN.

To come to the reasoning, notice that

$\frac{LK}{LJ} =\frac{LM}{LN}\\\\\frac{LK}{LK+KJ} =\frac{LM}{LM+MN}\\\\\frac{LK+KJ}{LK} =\frac{LM+MN}{LM}\\\\1+\frac{KJ}{LK}=1+ \frac{MN}{LM}\\\\\frac{LK}{KJ} =\frac{LM}{MN}$

In other words, $\frac{16}{10}= \frac{24}{15}$

4 0

4 years ago

Read 2 more answers

We are going to fence in a rectangular field that encloses 75 ft2. Determine the dimensions of the field that will require the l

pychu [463]

Answer:

For width W and length L, we have:

W = L = √(75ft^2) = 8.66ft

Step-by-step explanation:

For a rectangle of length L and width W, the area is:

A = L*W

and the perimeter is:

P = 2*L + 2*W

First, we know that the area of our rectangle is:

A = 75ft^2 = L*W

And we want to minimize the perimeter of our rectangle, then we need to minimize:

P = 2*L + 2*W

From the equation:

75ft^2 = L*W

We can isolate one of the variables, let's isolate L

L = (75ft^2)/W

We could replace this in the perimeter equation:

P(W) = 2*( (75ft^2)/W) + 2*W

P(W) = (150 ft^2)/W + 2*W

To find the minimum of the perimeter we need to look at the zero of the first derivative of P(W).

P'(W) = dP(W)/dW = -(150ft^2)/W^2 + 2

Now we need to find the value of W such that:

P'(W) = 0

0 = -(150ft^2)/W^2 + 2

(150 ft^2)/W^2 = 2

(150ft^2) = 2*W^2

(150ft^2)/2 = W^2

75 ft^2 = W^2

√(75ft^2) = W = 8.66ft

And remember that:

L = (75ft^2)/W

replacing with W = √(75ft^2)

L = (75ft^2)/√(75ft^2) = √(75ft^2)

Then:

W = L = √(75ft^2) = 8.66ft

6 0

3 years ago

Can someone please help me with these 2 problems? I’m confused

saveliy_v [14]

Answer:

7) $\dfrac{25c^2}{d^4}$

8) $4w^6r$

Step-by-step explanation:

You must use the laws of exponents.

$(\dfrac{5c}{d^2})^2 =$

When you raise a fraction to an exponent, raise the numerator and the denominator to that exponent.

$= \dfrac{(5c)^2}{(d^2)^2}$

When you raise a product to an exponent, raise each factor to that exponent.

When you raise an exponent to an exponent, multiply the exponents.

$= \dfrac{5^2c^2}{d^4}$

$= \dfrac{25c^2}{d^4}$

$\dfrac{-16w^7r^2}{-4wr} =$

To divide powers with the same base, subtract the exponents. Remember that a plain variable, such as w is the same as w^1.

$=\dfrac{-16}{-4}w^{7-1}r^{2-1}$

$= 4w^6r$

8 0

3 years ago

Which system of equations is equivalent to the following system? 3x + 5y = 29 x + 4y = 16 3x + 5y = 29 −x − 4y = 16 3x + 5y = 29

sp2606 [1]

Answer:

Option 3x+5y=29 and -3x-12y=-48 is the system of equations equivalent to the given system of equations 3x+5y=29 and x+4y=16

Step-by-step explanation:

Given system of equations is 3x+5y=29 and x+4y=16

To find the equivalent system of equations to the given system of equations :

Option 3x+5y=29 and -3x-12y=-48 is the system of equations represents the given system of equations.

Because we can write the given equations as below

3x+5y=29 and x+4y=16

x+4y=16 rewritting as below

When multiply the above equation into (-3) we get

$(-3)\times (x+4y)=16\times (-3)$

$-3x-4y=-48$ as same as the equation x+4y=16 so we can say that they are equivalent

Therefore Option 3x+5y=29 and -3x-12y=-48 is the system of equations represents the given system of equations

Therefore 3x+5y=29 and -3x-12y=-48 is the system of equations equivalent to the given system of equations 3x+5y=29 and x+4y=16

3 0

3 years ago