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2 years ago

Use a net to find the surface area of the right triangular prism shown:

Mathematics

1 answer:

erma4kov [3.2K]2 years ago

3 0

Answer:

256 ft²

Step-by-step explanation:

Net comprises: 2 equal triangles, 2 equal rectangles and 1 smaller rectangle

Area of a triangle = 1/2 x base x height

⇒ area of one triangle = 1/2 x 10 x 7 = 35 ft²

Area of a rectangle = width x length

⇒ area of larger rectangle = 6 x 12 = 72 ft²

⇒ area of smaller rectangle area = 6 x 7 = 42 ft²

⇒ Total area = (2 x 35) + (2 x 72) + 42 = 256 ft²

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The product of a whole number and unit fraction 2/3

anastassius [24]

Can you add the whole question I think it may be 6/4

5 0

2 years ago

The sum of 5 consecutive integers is 110, what is the fourth number in this sequence?

Xelga [282]

The answer is: " 23 " .

→ The fourth number in the sequence is: " 23 " .

_____________________________________

Explanation:

To solve:

" x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 110 " ;

in which:

"x" = The first number in these sequence;

"(x + 1 )" = the second number in the sequence;

"(x + 2)" = the third number in the sequence;

"(x + 3)" = the fourth number in the sequence;

"(x + 4)" = the fifth number in the sequence;

_____________________________________

Solve for the "fourth number in the sequence" ; or: "(x + 3)" ;

_____________________________________

Given: " x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 110 " ;

↔ " x + x + 1 + x + 2 + x + 3 + x + 4 = 110 " ;

→ Solve for "x" ;

→ then, solve for "(x + 3)" ;

→ which is the fourth number in this sequence;

_____________________________________

→ " x + x + 1 + x + 2 + x + 3 + x + 4= 110 " ;

"5x + 1 + 2 + 3 + 4= 110 " ;

" 5x + 10 = 110 " ;

Solve for "x" :

Subtract "10" from EACH SIDE of the equation; as follows:

" 5x + 10 - 10 = 110 - 10 " ;

to get :

" 5x = 100 " ;

Now, divide EACH SIDE of the equation by "5" ;

to isolate "x" on one side of the equation; & to solve for "x" ; as follows:

5x / 5 = 100 / 5 ;

to get:

" x = 20 " .

_____________________________________

Now, to find the fourth number in the sequence:

→ " (x + 3) " ;

→ Substitute "20" for "x" ;

" x + 3 = 20 + 3 = 23" ;

_____________________________________

The answer is: " 23 " .

The fourth number in the sequence is: " 23 " .

_____________________________________

Let us check our work:

If there are five "5" numbers in the sequence, and "23" is the "fourth number" , then: "24" is the "fifth number" .

As such: "22" is the "third number" ; "21" is the "second number" ; and "20" is the "first number" . Is this consistent with: "x = 20" as the "first number" ? Yes!

Thus, "20 + 21 + 22 + 23 + 25 = ? 110 ? ? ;

→ 20 + 21 = 41 ;

→ 41 + 22 = 63 ;

→ 63 + 23 = 86 ;

→ 86 + 24 = 110 . Yes!

_____________________________________

Hope this answer is helpful!

Best wishes in your academic pursuits—

and within the "Brainly" community!

_____________________________________

5 0

3 years ago

There is a 10% off sale on laptop computers. If someone saves $35 on a laptop, what was its original cost?

IceJOKER [234]

Answer:

The original cost is $350

Step-by-step explanation:

Let's assume

original cost of computer is x

There is a 10% off sale on laptop computers

So, amount saved is

$=\frac{10}{100}x=0.10x$

now, we are given

someone saves $35 on a laptop

so, we can set them equal

and then we can solve for x

$0.10x=35$

we can divide both sides by 0.10

and we get

$x=350$

So,

The original cost is $350

4 0

2 years ago

Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇f. (If the vector field is

kodGreya [7K]

We're looking for a scalar function $f(x,y)$ such that $\nabla f(x,y)=\vec F(x,y)$ . That is,

$\dfrac{\partial f}{\partial x}=2x-6y$

$\dfrac{\partial f}{\partial y}=-6x+6y-7$

Integrate the first equation with respect to $x$ :

$f(x,y)=x^2-6xy+g(y)$

Differentiate with respect to $y$ :

$-6x+6y-7=-6x+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=6y-7$

Integrate with respect to $y$ :

$g(y)=3y^2-7y+C$

So $\vec F$ is indeed conservative with the scalar potential function

$f(x,y)=x^2-6xy+3y^2-7y+C$

where $C$ is an arbitrary constant.

6 0

2 years ago

Solve for x: −1 < x + 3 < 5

MA_775_DIABLO [31]

Answer:

Step-by-step explanation:

Subtract 3 from all sides.

-4 < x < 2

6 0

3 years ago