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3 years ago

Parallel lines in space are coplanar.

1 answer:

3 0

Coplanar lines are line witch lie on the same lie on the same plane. two parallel lines or two intersecting lines always lie in a plane. Thus, two line are coplanar, if and only if they are either parallel or intersecting. lines in three dimensional space are coplanar, only if they are not skewed lines.

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velikii [3]

Sometimes you just need to take a moment and really look for some hints that’ll help you. Rotate your page, maybe colour some lines.

Take a look at the picture, I coloured the lines and saw that the red and green angles are actually the same. And since the 90° angle is given, just subtract it from 140° to get your answer.

x = 50°

3 0

2 years ago

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Rewrite the expression without the negative exponent. 2x^−4

romanna [79]

Answer:

$\frac{2}{x^4}$

Step-by-step explanation:

The expression is $2x^{-4}$

We use the rule of exponents shown below to change the original to "positive" exponent form:

$a^-b=\frac{1}{a^b}$

Now we can change the original expression given into positive exponent:

$2x^{-4}\\=\frac{2}{x^4}$

8 0

2 years ago

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What is the equation of the midline for the function f(x) ?

Inessa05 [86]

let's recall the graph of sin(x), is simply a sinusoidal line waving about, but its midline is at the x-axis, namely y = 0.

this equation is simply a transformation of it, the 1/2 changes the amplitude by half, midline stays the same though, the +3, moves the whole thing upwards, a vertical shift of 3, meaning the midline went from 0 to 3, y = 3.

5 0

3 years ago

Part A

masya89 [10]

Answer:

Part A) The area of triangle i is $3\ cm^{2}$

Part B) The total area of triangles i and ii is $6\ cm^{2}$

Part C) The area of rectangle i is $20\ cm^{2}$

Part D) The area of rectangle ii is $32\ cm^{2}$

Part E) The total area of rectangles i and iii is $40\ cm^{2}$

Part F) The total area of all the rectangles is $72\ cm^{2}$

Part G) To find the surface area of the prism, we need to know only the area of triangle i and the area of rectangle i and the area of rectangle ii, because the area of triangle ii is equal to the area of triangle i and the area of rectangle iii is equal to the area of rectangle i

Part H) The surface area of the prism is $78\ cm^{2}$

Part I) The statement is false

Part J) The statement is true

Step-by-step explanation:

Part A) What is the area of triangle i?

we know that

The area of a triangle is equal to

$A=\frac{1}{2} (b)(h)$

we have

$b=4\ cm$

$h=1.5\ cm$

substitute

$A=\frac{1}{2} (4)(1.5)$

$Ai=3\ cm^{2}$

Part B) Triangles i and ii are congruent (of the same size and shape). What is the total area of triangles i and ii?

we know that

If Triangles i and ii are congruent

then

Their areas are equal

$Aii=Ai$

The area of triangle ii is equal to

$Aii=3\ cm^{2}$

The total area of triangles i and ii is equal to

$A=Ai+Aii$

substitute the values

$A=3+3=6\ cm^{2}$

Part C) What is the area of rectangle i?

we know that

The area of a rectangle is equal to

$A=(b)(h)$

we have

$b=2.5\ cm$

$h=8\ cm$

substitute

$Ai=(2.5)(8)$

$Ai=20\ cm^{2}$

Part D) What is the area of rectangle ii?

we know that

The area of a rectangle is equal to

$A=(b)(h)$

we have

$b=4\ cm$

$h=8\ cm$

substitute

$Aii=(4)(8)$

$Aii=32\ cm^{2}$

Part E) Rectangles i and iii have the same size and shape. What is the total area of rectangles i and iii?

we know that

Rectangles i and iii are congruent (have the same size and shape)

If rectangles i and iii are congruent

then

Their areas are equal

$Aiii=Ai$

The area of rectangle iii is equal to

$Aiii=20\ cm^{2}$

The total area of rectangles i and iii is equal to

$A=Ai+Aiii$

substitute the values

$A=20+20=40\ cm^{2}$

Part F) What is the total area of all the rectangles?

we know that

The total area of all the rectangles is

$At=Ai+Aii+Aiii$

substitute the values

$At=20+32+20=72\ cm^{2}$

Part G) What areas do you need to know to find the surface area of the prism?

To find the surface area of the prism, we need to know only the area of triangle i and the area of rectangle i and the area of rectangle ii, because the area of triangle ii is equal to the area of triangle i and the area of rectangle iii is equal to the area of rectangle i

Part H) What is the surface area of the prism? Show your calculation

we know that

The surface area of the prism is equal to the area of all the faces of the prism

The surface area of the prism is two times the area of triangle i plus two times the area of rectangle i plus the area of rectangle ii

$SA=2(3)+2(20)+32=78\ cm^{2}$

Part I) Read this statement: “If you multiply the area of one rectangle in the figure by 3, you’ll get the total area of the rectangles.” Is this statement true or false? Why?

The statement is false

Because, the three rectangles are not congruent

The total area of the rectangles is $72\ cm^{2}$ and if you multiply the area of one rectangle by 3 you will get $20*3=60\ cm^{2}$

$72\ cm^{2}\neq 60\ cm^{2}$

Part J) Read this statement: “If you multiply the area of one triangle in the figure by 2, you’ll get the total area of the triangles.” Is this statement true or false? Why?

The statement is true

Because, the triangles are congruent

8 0

3 years ago

Greg is in a car at the top of a roller-coaster ride. The distance, d, of the car from the ground as the car descends is determi

ANTONII [103]

Answer:

It takes 3 seconds over the interval [0,3]

Step-by-step explanation:

To find when the roller coaster reaches the ground, find when d=0.

$0=144-16t^2$

To solve divide each term by 16 and factor:

$\frac{0}{16}=\frac{144}{16} -\frac{-16t^2}{16} \\0= 9 - t^2\\0=(3-t)(3+t)$

Solve for t by setting each factor to 0.

t-3=0 so t=3

t+3=0 so t=-3

This means the car is in the air from 0 to 3 second.

8 0

3 years ago