Find the surface area of the prism below.



SA= square meters

Answer:

a) [tex]y = -\frac{2}{3}x + \frac{5}{6}[/tex]

b) [tex]y = 2x - \frac{1}{2}[/tex]

These two paths are not perpendicular to each other.

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

[tex]y = mx + b[/tex]

In which m is the slope of the line and b is the y-intercept.

If two lines are perpendicular, the multiplication of their slopes is -1.

(a) the engineering lab and the computer center

Coordinates (3.5,-1.5) and (0.5,0.5)

The slope is given by the change in y divided by the change in x.

Change in y: 0.5 - (-1.5) = 0.5 + 1.5 = 2

Change in x: 0.5 - 3.5 = -3

Slope: [tex]m = \frac{2}{-3} = -\frac{2}{3}[/tex]

So

[tex]y = -\frac{2}{3}x + b[/tex]

Now, to find the y-intercept, we replace one of these points into the equation.

(0.5,0.5) means that when [tex]x = 0.5 = \frac{1}{2}, y = 0.5 = \frac{1}{2}[/tex]

So

[tex]y = -\frac{2}{3}x + b[/tex]

[tex]0.5 = -\frac{2}{3}(0.5) + b[/tex]

[tex]b = \frac{1}{2} + \frac{1}[3}[/tex]

[tex]b = \frac{5}{6}[/tex]

So

[tex]y = -\frac{2}{3}x + \frac{5}{6}[/tex]

(b) the engineering lab with the library.

(0.5,0.5) and (-1,-2.5).

First, we find the slope:

Change in y:-2.5 - 0.5 = -3

Change in x: -1 - 0.5 = -1.5

The slope is: [tex]m = \frac{-3}{-1.5} = 2[/tex]

So [tex]y = 2x + b[/tex]

Now we find b

[tex]y = 2x + b[/tex]

[tex]0.5 = 2(0.5) + b[/tex]

[tex]b = -0.5 = -\frac{1}{2}[/tex]

So

[tex]y = 2x - \frac{1}{2}[/tex]

The multiplication of their slopes, is

[tex]2*\frac{-2}{3} = -\frac{4}{3}[/tex]

Since it is different of one, these paths are not perpendicular to each other.

Answer:

a. 7 units

b. 5 units

c. 24 units

d. 35 units

a) The length of this rectangle is, 5 units.

b) The width of this rectangle is, √74 units

c) The perimeter of the rectangle is,

⇒ 2 (5 + √74)

d) The area of the rectangle is,

⇒ 5√74 units²

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

The coordinates of a rectangle are,

⇒ (3, 0), (3, -5), (-4, 0) and (-4, -5)

Now, The length of this rectangle is,

⇒ Distance between (3, 0) and (3, - 5).

⇒ √ (- 5 - 0)² + (3 - 3)²

⇒ √25

⇒ 5 units

And, The width of this rectangle is,

⇒ Distance between (3, - 5) and (- 4, 0).

⇒ √ (- 4 - 3)² + (0 + 5)²

⇒ √49 + 25

⇒ √74 units

And, The perimeter of the rectangle is,

⇒ 2 (Lenght + Width)

⇒ 2 (5 + √74)

And, the area of the rectangle is,

⇒ Length × Width

⇒ 5 ×√74

⇒ 5√74 units²

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Answer:

[tex]E \approx \exp(0.31)[/tex]

Step-by-step explanation:

From the question we are told that

Occurrence of volcanoes[tex]x=37 times[/tex]

The number year

[tex]N= 1832-1950\\N=118 years[/tex]

Generally the number  of volcanoes occurring is mathematically modeled as

[tex]X \approx Poisson(0.31)[/tex]

Generally the waiting time of the earthquakes will also be modeled with exponential distribution with the same parameters

[tex]E \approx \exp(0.31)[/tex]

Answer:

Step-by-step explanation:

Answer:

88.5

Step-by-step explanation:

formula = ab ×(sin∅)/2

= 18×12 × (sin 55)/2

= 88.5

Answer:

2m3np−6p−4p

Step-by-step explanation:

That is the answer

Answer:

2√3

Step-by-step explanation:

Given the following information,

Long = 3 = Adjacent

Angle of elevation =30 degrees

Required

Hypotenuse

Using SOH CAH TOA identity

Cos theta = adj/hyp

Cos 30 = 3/hyp

hyp = 3/cos30

hyp = 3/√3/2

hyp = 3* 2/√3

hyp = 6/√3

hyp = 6/√3 * √3/√3

hyp = 6√3/3

hyp = 2√3

Hence the hypotenuse is 2√3

Answer:

2v3

Step-by-step explanation:

Answer:

the first option

Step-by-step explanation:

for a number to be rational, it should be able to be expressed as a fraction.  Non terminal decimals must have a repeating pattern. Square roots of random numbers aren’t rational. Just like the first rule with decimals, the third number cannot be expressed as a fraction

Answer:

Step-by-step explanation:

it’s the first one

9514 1404 393

Answer:

  A.  57 7/9 ft³

Step-by-step explanation:

The volume of a rectangular prism (cuboid) is the product of its dimensions.

  V = LWH

  V = (4 1/3 ft)(3 1/3 ft)(4 ft)

If you drop the fractions, this becomes ...

  V = (4 ft)(3 ft)(4 ft) = 48 ft³

You know the fractions add some amount to this, so you know the volume will be somewhat larger than 48 ft³. The only reasonable choice is A: 57 7/9 ft³.

__

If you feel the need to compute the volume exactly, you can do so using improper fractions.

  V = (13/3 ft)(10/3 ft)(4 ft) = 520/9 ft³ = 57 7/9 ft³

Answer:

The answer is C.[1,0]

Step-by-step explanation:

HIJK is a parallelogram because the midpoint of both diagonals is (1, 0), which means the diagonals bisect each other.

The midpoint is the middle of a line projecting from one end to another.

Given the parallelogram HIJK with the coordinate points

H(-2,2), I(4,3), J (4, -2), and K (-2, -3)

The diagonals are HJ and IK.

Determine the midpoint

M(x, y) = [(-2+4)/2, (2-2)/2]

M(x, y) = (2/2, 0/2)
M(x, y) = (1, 0)

This shows that HIJK is a parallelogram because the midpoint of both diagonals is (1, 0), which means the diagonals bisect each other.

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Answer:

19 is the answer .......explanation is in image.

Answer:

8.01 Is the answer your welcome

Answer:

(a)

x cubed is

=x^3=x3

5 times the cube of x is

=5x^3=5x3

4 times x is

=4x=4x

the quotient of 4 times x and 3 is

=\frac{4x}{3}=34x

so,

the difference of 5 times the cube of x cubed and the quotient of 4 times x and 3 is

=5x^3-\frac{4x}{3}=5x3−34x ..........Answer

(b)

5 times cube of x is

=5x^3=5x3

5 times cube of x divided by 4 times x is

=\frac{5x^3}{4x}=4x5x3 ..........Answer

(c)

difference of 5 times x cube and 4 is

=5x^3 -4=5x3−4

so,

the quotient of the difference of 5 times x cube and 4 and x is

=\frac{5x^3-4}{x}=x5x3−4 ...........Answer

(d)

difference of 5 times x and 4 is

=5x-4=5x−4

so,

the cube of the difference of 5 times x and 4 is is

=(5x-4)^3=(5x−4)3 ............Answer

Answer:

$63.20

Step-by-step explanation:

first we have to find how much the sweater is marked down in money. we do this by converting the percentage to decimal form and multiply by the original price.

79•0.2= 15.8

so the sweater is marked down $15.80. now we subtract that markdown from the original price to find the new price

$79-$15.8= $63.20

hope this helps chu <3

Answer:

When the lines are parallel, there are no solutions, and sometimes the two equations will graph as the same line, in which case we have an infinite number of solutions.

Step-by-step explanation:

Answer:

[tex]\frac{1}{25} =0.04[/tex] (Unusual)

Step-by-step explanation:

1/5 for one drawing

1/5 chance to win once, if there is only one game.

Then multiply them together to get 1/25.

If you need in decimal form 1/25 = 0.04 (unusual)

If an individual makes seven draws, what is the probability the individual will win a prize exactly two times is 0.2753

A permutation is an act of arranging the objects or numbers in order.

Combinations are the way of selecting the objects or numbers from a group of objects or collection, in such a way that the order of the objects does not matter.

An individual can win a prize by drawing the highest numbered card out of five cards.

Given that an individual makes 7 draws

p = 1/5  =  0.2

q = 1-P =0 .5

5 times corresponds to B( 7 , 0.2)

P(x = 2) = 7 C₂ (0.7)² (0.8)⁵

= 21 * 0.04 * 0.3277

= 0.2753

Therefore If an individual makes seven draws, what is the probability the individual will win a prize exactly two times is 0.2753

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Answer:

6

Step-by-step explanation:

Answer:

1759.52cm^3

Step-by-step explanation:

Given data

Cylinder E

h = 30 cm and

r = 4 cm

The expression for the volume is

V= πr^2h

V= 3.142*4^2*30

V= 3.142*16*30

V=1508.16 cm^3

Cylinder F

h=5 cm

r = 4 cm

The expression for the volume is

V= πr^2h

V= 3.142*4^2*5

V= 3.142*16*5

V=251.36 cm^3

Hence the total volume is

=251.36+1508.16

= 1759.52cm^3

Answer:

14,96

Step-by-step explanation:

Answer:graph d

Step-by-step explanation:

I just took the test on a p# x and yea I'm dum and got it wrong

Answer:It’s graph B

Step-by-step explanation:

Answer:

7 wedges

Step-by-step explanation:

=60% of 126g

=60 ÷ 100 × 126g

=75.6g

=75.6 g ÷ 10g

=7.56 = 7 wedges

Answer:

Each Pizza will cost $12.55

Step-by-step explanation:

we first going to subtract the following

$47.60 - 5 - 4.95 = $37.65

$37.65 / 3 (the number of pizza ) = $12.55

$12.55

Step-by-step explanation:

Amount spent on 3 pizzas= Total —( amount spent on salad + tip)

=460—(4.95+5)

= $37.65

cost of each pizza= 37.65÷3

= $12.55

Answer:

See explanation

Step-by-step explanation:

cos(θ)= 18/30 = 3/5

sin(θ)= 24/30 = 4/5

tan(θ)= 24/18 = 4/3

cos(ϕ)= 24/30 = 4/5

sin(ϕ)= 18/30 = 3/5

tan(ϕ)= 18/24 = 3/4

The value of the trigonometric ratios have been determined.

In a Right angled triangle , the trigonometric ratios are used to determine the value of angles and sides.

The side length of the triangle as given in the figure is 18 , 24 , 30

The value of the trigonometric ratios are

cos θ = Base / Hypotenuse

sin θ =  Perpendicular / hypotenuse

tan θ =  Perpendicular / Base

cos(θ)= 18/30 = 3/5

sin(θ)= 24/30 = 4/5

tan(θ)= 24/18 = 4/3

cos(ϕ)= 24/30 = 4/5

sin(ϕ)= 18/30 = 3/5

tan(ϕ)= 18/24 = 3/4

Therefore the value of the trigonometric ratios have been determined.

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Answer: look at the picture

Step-by-step explanation: Hope this help :)

Answer:

I think it's 40 . I'm not sure

Answer:

0.6 liter per kilo

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Both triangles have three angles of the same value.

Remember that the angles in all triangles add up to 180°.

Let's use that to find out the unknown angles.

For the first triangle:

180 - 82 - 43 = 55°

55° is also in the second triangle.

Let's check with the second triangle:

180 - 82 - 55 = 43°

43° is also in the first triangle.

Therefore, both triangles are similar as the angles in both triangles are the same - 82°, 43° and 55°.

Hence, C.

Answer:

Step-by-step explanation:

To factorise

3x² - 6x

3x² - 6x

[Taking common term out]

= (3x × x) - (3x × 2)

= 3x ( x - 2)

Hence, factorised answer of 3x² - 6x is 3x (x-2) (Ans)

Answer:

oo nvjfdifhdkvcbjkggnnvv

Step-by-step explanation:

please mark me answer banilist

Answer:

pentagon

Step-by-step explanation: