Simplify each numerical expression.
1) 6 + 2 x 8 - 12 + 9 - 3

Answer:

4/63

Step-by-step explanation:

20/315 = (20÷5)/(315÷5)

Step-by-step explanation:

Against the wind, the wind works against the speed. With the wind, the wind aids the speed.

4(p - w) = 2416

4(p + w) = 2896

p - w = 604

p + w = 724

2p = 1328

p = 664 mph

664 + w = 724

w = 60 mph

[tex]\huge{\sf \left[{x-2y\atop 6x-2z}\:\:\:{4y-3\atop 2y-z}\right]=\left[{-3\atop 4}\:\:\:{5\atop 3}\right]}[/tex]

Creating equations

[tex]\\ \sf\longmapsto x-2y=-3\dots(1)[/tex]

[tex]\\ \sf\longmapsto 4y-3=5\dots(2)[/tex]

[tex]\\ \sf\longmapsto 6x-2z=4\dots(3)[/tex]

[tex]\\ \sf\longmapsto 2y-z=3\dots(3)[/tex]

[tex]\\ \sf\longmapsto 4y-3=5[/tex]

[tex]\\ \sf\longmapsto 4y=5+3[/tex]

[tex]\\ \sf\longmapsto 4y=8[/tex]

[tex]\\ \sf\longmapsto y=\dfrac{8}{4}[/tex]

[tex]\\ \bf\longmapsto y=2[/tex]

[tex]\\ \sf\longmapsto x-2y=-3[/tex]

[tex]\\ \sf\longmapsto x=-3+2y[/tex]

[tex]\\ \sf\longmapsto x=-3+2(2)[/tex]

[tex]\\ \sf\longmapsto x=-3+4[/tex]

[tex]\\ \bf\longmapsto x=1[/tex]

[tex]\\ \sf\longmapsto 2y-z=3[/tex]

[tex]\\ \sf\longmapsto z=2y-3[/tex]

[tex]\\ \sf\longmapsto z=2(2)-3[/tex]

[tex]\\ \sf\longmapsto z=4-3[/tex]

[tex]\\ \bf\longmapsto z=1[/tex]

Answer:

arc length = 4π units

Step-by-step explanation:

The arc length is calculated as

arc = circumference of circle × fraction of circle

     = 2πr × [tex]\frac{90}{360}[/tex]

     = 2π × 8 × [tex]\frac{1}{4}[/tex]

     = 2π × 2

    = 4π units ← exact answer

Answer:

Sunil = 3000 and raj = 2000

Step-by-step explanation:

there are total 5000 and if it will be divided into 5 parts( total of ratio ) then 3 will be equal to 3000 and 2 equal to 2000

Answer:

2^5

Step-by-step explanation:

2x2x2x2x2

Count the number of 2's, that is the power

The base is 2

2^5

Answer:

2 to the power of 5

Step-by-step explanation:

there are 5 2's being multiplied by each other and that can be shortened to the power of 5.

Answer:

13 is answer

Step-by-step explanation:

hope it helps

supplementary angles = the sum of those angles will equal to 180 degrees

so,

2x + 3 + 3x + 2 = 180

5x + 5 = 180

5x = 175

x = 35

angle 1 -> 2x + 3 = 70 + 3 = 73

angle 2 -> 3x + 2 = 105 + 2 = 107

if you want to check, 107 + 73 = 180

hope it helps :)

Answer:

(2,-7)

Step-by-step explanation:

The point moves down 3 units resulting in (2,-7)

Answer:

Trinomial, 2

Step-by-step explanation:

Answer:

Trinomial, 2

Step-by-step explanation:

Answer:

(i) 3.438159 kg

(ii) 5.336803297 cm

Step-by-step explanation:

the external diameter = 12 cm, => the radius = 6 cm.

the internal diameter = 12 - 2×2 = 8 cm, radius = 4 cm.

I assume the mass of 1 cm³ (not cm) is 5.4 g (very, very light metal).

the material is in the volume of external sphere minus internal (empty) sphere.

the volume of a sphere is

4/3 × pi×r³

V-e = 4/3 × pi×6³ = 4/3 × pi×216 = 4×pi×72 = 904.7786842 cm³

V-i = 4/3 × pi×4³ = 4/3 × pi×64 = 268.0825731 cm³

V-e - V-i = 4/3 × pi×(216-64) = 4/3 × pi×152 = 636.6961111 cm³

1cm³ = 5.4g

636.6961111 cm³ = 5.4×636.6961111 = 3438.159g = 3.438159 kg

for (ii) we need to work with the volume of the material and calculate backwards to find the radius of the sphere with the full volume of that size.

636.6961111 = 4/3 × pi×r³ = 4/3 × pi×152

152 = r³

r = 5.336803297

[tex]\huge\mathsf\green{ANSWER}:—[/tex]

[tex]option \: \: c \: \: \: \frac{3}{4} \: is \: the \: correct \: option[/tex]

Rational numbers are numbers which can be represent in the form of p/q where p and q are integers and q≠0 that's why 3/4 is the correct option

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Value of n:

[tex]5n - 17 = 2n + 1[/tex]

[tex]5n - 2n = 1 + 17[/tex]

[tex]3n = 18[/tex]

[tex]n = \frac{18}{3}[/tex]

[tex]n = 6[/tex]

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Lengths:

The lengths are given as functions of n, since n = 6:

The length of the sides are: 13 cm, 13 cm and 6 cm.

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Perimeter:

The perimeter is the sum of the lengths of all sides, so: 13 + 13 + 6 = 32 cm.

A similar question is given at https://brainly.com/question/6139098

Step-by-step explanation:

using the slope formula, we can see that the slope is 0

Now

[tex]\\ \sf\longmapsto 160\times \dfrac{1}{60}[/tex]

[tex]\\ \sf\longmapsto \dfrac{160}{60}[/tex]

[tex]\\ \sf\longmapsto 2.6miles/min[/tex]

Answer:

Totally number of coaches needed is 12

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

Step-by-step explanation:

Question 5

Part A

if Sin(x) = - 3/5  and tan(x) < 0

you are told 3 things

tan(x) = Sin(x)/cos(x)

tan(x) = -3/5 // 4/5

Tan(x) = -3/4

Part B

cos(2x) = cos^2(x) - sin^2(x)

cos(2x) = (4/5)^2 - (-3/5)^2

cos(2x) = 16/25 - 9/25

cos(2x) = 7/25

Part B

x + y = 90

sin(x +y) = 1

Sin(x - y) =

Sorry can't do this part. I don't know what this is equal to.

Answer:

0.5

Step-by-step explanation:

k = y/x

k = 0.5/1

k = 0.5

Answer:

2.5

Step-by-step explanation:

Function

It is a function

Answer:

6 inches

Step-by-step explanation:

A=b1+b2/2*h

Fill in the equation with what we know

21=8+x/2*3

Isolate x

Quick steps: 21/3=7*2=14-8=6

x=6

Answer:

[tex]f^{-1}[/tex](x) = 0.5x + 2

Step-by-step explanation:

let y = f(x) and rearrange making x the subject , that is

y = 2x - 4 ( add 4 to both sides )

y + 4 = 2x ( divide both sides by 2 )

[tex]\frac{y+4}{2}[/tex] = x

Change y back into terms of x with x = [tex]f^{-1}[/tex] (x)

[tex]f^{-1}[/tex] (x) = [tex]\frac{x+4}{2}[/tex] = 0.5x + 2

Answer: F -1(x)  = 0.5 x + 2

Step-by-step explanation:

Just took the test on edmentum and got a 100

Answer:

I got that AE^2 = 8EC^2

Step-by-step explanation:

Here's what I did. I probably did this wrong, but this might give you an idea on how to solve it.

First, create equations:

AB = BC = AC = DE = 2EC

BD= BC = EC

Then, I used pythagorean theorem (since AD is perpendicular to BC): AD^2 + DE^2 = AE^2

Substitute: (2EC)^2 + (2EC)^2 = AE^2

Simplify: 4EC^2 + 4EC^2 = AE^2

AE^2 = 8CE^2

Answer:

I think the answer is 2

Step-by-step explanation:

Between 30 and 60 is double b so just divide 4 by 2.

Answer:

Step-by-step explanation:

Answer:

Option c points at (-2,0) (-1, 0.5) and (1,1)

Step-by-step explanation:

Answer:

y=-4x

Step-by-step explanation:

Parallel to the line, slope is - 4. The equation of line is y=-4x