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2 years ago

Can someone please help me I will give brainliest

Mathematics

1 answer:

Darina [25.2K]2 years ago

8 0

Part A

<h3>Answer: Net A</h3>

Reason:

This is something you'll have to draw out on paper (or print it out), then fold up the diagram to represent the 3D prism.

Net A has the middle rectangle as the floor. The other rectangles form the vertical left side and the right slanted side. The triangles form the remaining walls.

Folding up net B will have the triangle ABC oriented in the wrong way, and things won't match up perfectly.

==============================================================

Part B

<h3>Answers: AB = 3, BC = 5, CD = 8.6</h3>

Reason:

When folded up, side AB goes from the floor to the highest point on the prism. This would be the 3 inches marked.

Side BC is the slanted part, and it is 5 inches in length. Note that AB = 3 and AC = 4, so BC = 5 helps make up a 3-4-5 right triangle (refer to the pythagorean theorem).

Lastly, CD = 8.6 is the length or depth of the prism.

==============================================================

Part C

<h3>Answer: 115.2 square inches</h3>

Reason:

To find the surface area of the 3D prism, we will find the area of each region on the 2D net. This is because the surface area is the amount of wrapping paper needed to enclose the 3D figure.

Let's find the area of triangle ABC

area = base*height/2 = 4*3/2 = 6

Each triangle has an area of 6 square inches. That gives an area of 2*6 = 12 square inches so far for the triangles combined.

Now let's find the perimeter of either triangle:

AB+BC+AC = 3+4+5 = 12

Multiplying this perimeter with the depth of the prism will determine the lateral surface area

12*8.6 = 103.2

Add this lateral area onto the previously calculated triangle combined area (12 square units) and we get 12+103.2 = 115.2 square inches

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Given cosα = −3/5, 180 < α < 270, and sinβ = 12/13, 90 < β < 180

torisob [31]

I got

$- \frac{6 3}{65}$

What we know

cos a=-3/5.

sin b=12/13

Angle A interval are between 180 and 270 or third quadrant

Angle B quadrant is between 90 and 180 or second quadrant.

What we need to find

Cos(b)

Cos(a)

What we are going to apply

Sum and Difference Formulas

Basics Sine and Cosines Identies.

1. Let write out the cos(a-b) formula.

$\cos(a - b) = \cos(a) \cos(b) + \sin(a) \sin(b)$

2. Use the interval it gave us.

According to the given, Angle B must between in second quadrant.

Since sin is opposite/hypotenuse and we are given a sin b=12/13. We. are going to set up an equation using the pythagorean theorem.

${12}^{2} + {y}^{2} = {13}^{2}$

$144 + {y}^{2} = 169$

$25 = {y}^{2}$

$y = 5$

so our adjacent side is 5.

Cosine is adjacent/hypotenuse so our cos b=5/13.

Using the interval it gave us, Angle a must be in the third quadrant. Since cos is adjacent/hypotenuse and we are given cos a=-3/5. We are going to set up an equation using pythagorean theorem,

$( - 3) {}^{2} + {x}^{2} = {5}^{2}$

$9 + {x}^{2} = 25$

${x}^{2} = 16$

$x = 4$

so our opposite side is 4. sin =Opposite/Hypotenuse so our sin a =4/5.Sin is negative in the third quadrant so

sin a =-4/5.

Now use cosine difference formula

$- \frac{3}{5} \times \frac{5}{13} + - \frac {4}{5} \times \frac{12}{13}$

$- \frac{15}{65} + ( - \frac{48}{65} )$

$- \frac{63}{65}$

Hope this helps

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3 years ago

In order to make the expression below equivalent to 1 2 x 6, which additional operation should be included in the expression? Us

marysya [2.9K]

The additional operation which needed to make the expression equivalent to given expression is $-\dfrac{3}{4} x$ . Thus the option 3 is the correct option.

<h3>What is equivalent expression?</h3>

Equivalent expression are the expression whose result is equal to the original expression, but the way of representation is different.

Given information-

The equation given in the problem is,

$\dfrac{5}{4} x+6$

Let the equation is equation number 1.

This expression is to convert in the expression, which is,

$\dfrac{1}{2}x+6$

Let the above equation is equation number 2.

Let the additional operation which needed to make the expression equivalent to given expression is $f(x)$ .

As the addition of $f(x)$ and equation 1 is equal to the equation 2. Therefore,

$f(x)+\dfrac{5}{4} x+6=\dfrac{1}{2}x+6$

Solve the equation as,

$f(x)=\dfrac{1}{2}x+6-\dfrac{5}{4} x-6\\f(x)=\dfrac{1}{2}x-\dfrac{5}{4} x\\f(x)=\dfrac{2-5}{4} x\\f(x)=\dfrac{-3}{4} x$

Hence, the additional operation which needed to make the expression equivalent to given expression is $-\dfrac{3}{4} x$ . Thus the option 3 is the correct option.

Learn more about the equivalent expression here;

brainly.com/question/2972832

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Answer:

Step-by-step explanation:

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3 years ago

Can someone please help me I will give brainliest ​

Can someone please help me I will give brainliest