w is directly proportional to y
w is inversely proportional to x?
(a) When y = 4, w = 14
Work out the value of w when y = 9

Answer:

x=2

Step-by-step explanation:

Hi there!

Whenever we're solving an algebraic equation, our goal is always to isolate the variable, which in this case is x. We would do this by performing inverse operations on both sides of the equal sign to cancel values out.

[tex]10-2x + 3 = 5x-9 + 4x[/tex]

Combine like terms on both sides of the equal sign

[tex]10+ 3-2x = 5x+ 4x-9 \\13-2x = 9x-9[/tex]

Add 2x to both sides to cancel out -2x (addition is the inverse of subtraction)

[tex]13-2x +2x = 9x-9 +2x\\13 = 11x-9[/tex]

Add 9 to both sides to cancel out -9 and isolate 11x (addition is the inverse of subtraction)

[tex]13+9 = 11x-9+9\\22=11x[/tex]

Divide both sides by 11 to isolate x (division is the inverse of multiplication)[tex]\frac{22}{11} =\frac{11x}{11} \\2=x[/tex]

Therefore, x=2.

I hope this helps!

Answer:

x = 19°

Step-by-step explanation:

We know that ∠UTV and ∠RTS are vertical angles, therefore is the measure of ∠UTV = 85, then the measure of ∠RTS would also be 85, by the "Vertical angles are congruent theorem.

=> ∠UTV ≅ ∠RTS

=> ∠UTV = 85°

=> ∠RTS = 85°

Now that we know all three angles of within the triangle, we can say that the sum of all three angles within the triangle is 180, we can conclude;

∠R + ∠T + ∠S = 180°

(3x) + (85°) + (2x) = 180°

5x + 85° = 180°

5x = 180° - 85°

5x = 95

x = 95/5

x = 19°

Hence, there is you're answer! x = 19°

Hope this helps!

Answer:

1/4¹⁰

Step-by-step explanation:

this is the the simplified version for the question

Answer:

[tex]22[/tex]

Step-by-step explanation:

Similar shapes must have corresponding sides in a constant proportion. Therefore, we can set up the following equation and solve for [tex]?[/tex]:

[tex]\frac{28}{42}=\frac{?}{33}[/tex] (divide corresponding sides)

[tex]\frac{28}{42}=\frac{?}{33},\\\\?=\frac{28\cdot 33}{42}=\boxed{22}[/tex]

Answer:

Step-by-step explanation:

table3 represents exponential function

Answer:

t + c = 623

t = c + 135

thomas has 379 songs downloaded, and carl has 244

Step-by-step explanation:

togheter they have 623 songs, aka the sum of thomas (t) and carl (c) is 623.

t + c = 623

thomas has 135 more than Carl. so Carl plus 135 is equal to thomas

t = c + 135

now you can solve it:

t + c = 623

(c+135) + c = 623

c + c = 488

2c = 488

c = 244

carl has 244 songs downloaded

t  + 244 = 623

t = 379

thomas has 379 songs downloaded

The system of equations represents t + c = 623 and t = c + 135 and Tomas has 379 while Carl has 244 downloaded.

An equation can be defined in numerous ways. Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.

As per the given,

Together they have 623 songs downloaded.

t + c = 623

Tomas has 135 more songs downloaded than Carl.

t = c + 135

By substitution,

c + 135 + c = 623

2c = 488

c =244

And , t = 244 + 135 = 379

Hence "The equations in the system show that Tomas has 379 while Carl has 244 downloaded and that t + c = 623 and t = c + 135 are represented".

For more about the equation,

brainly.com/question/10413253

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Answer:

x = 21

Step-by-step explanation:

For a pentagon, n = 5.

Each angle measures:

(n - 2)180/5 = (5 - 2)(180)/5 = 108

5x + 3 = 108

5x = 105

x = 21

Answer:

D. Axis of symmetry: x = –0.5; Vertex: (–0.5, 0.75); f(x) = x2 + 2x + 1

Step-by-step explanation:

A. Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Down

Vertex:  

( 1 /2 , 1 /4 )

Focus:  

( 1 /2 , 0 )

Axis of Symmetry:  

x

=

1

2

Directrix:  

y

=

1

2

x

y

− 2

− 6

− 1

− 2

1

2

1

4

1

0

2

− 2

B. Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex:  

( − 1 /2 , 3 /4 )

Focus:  

( − 1 /2 , 1 )

Axis of Symmetry:  

x

=

−

1

2

Directrix:  

y

=

1

2

x

y

− 2

3

− 1

1

− 1

2

3

4

1

3

2

7

C. Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex:  

( 1 /2 , 3 /4 )

Focus:  

( 1 /2 , 1 )

Axis of Symmetry:  

x

=

1

2

Directrix:  

y

=

1

2

x

y

− 2

7

− 1

3

1

2

3

4

1

1

2

3

D. Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex:  

( − 1 , 0 )

Focus:  

( − 1 , 1 /4 )

Axis of Symmetry:  

x

=

− 1

Directrix:  

y

=

− 1

4

x

y

− 3

4

− 2

1

− 1

0

0

1

1

4

Answer:

$1182.65

Step-by-step explanation:

Given :

Fortnight gross pay = $1300

Given :

PAYE: $31.85 FNPF: 5% HEALTH INSURANCE: $20.50 calculate her fortnightly net pay

FNPF = 5% = 0.05 * $1300 = $65

PAYE = $31.85 ; HEALTH INSURANCE = $20.50

Total deduction = $(65 + 31.85 + 20.50) = $117.35

Net pay :

Gross pay - deduction

$1300 - $117.35 = $1182.65

Answer:

5w-8/3=4w+2

-8/3=-1w+2

-8=-1w+6

-14=-1w

14=w

Hope this helps, have a great day :)

Answer:

13

Step-by-step explanation:

3h - j

3(8) - 11

24 - 11

13

Answer: [tex]9\ ft[/tex]

Step-by-step explanation:

Given

Height of the cylinder [tex]h=5\ ft[/tex]

Volume of the cylinder [tex]V=1271.7\ ft^3[/tex]

The volume of the cylinder is given by [tex]V=\pi r^2h[/tex]

Consider r be the radius of the circle

[tex]\Rightarrow 1271.7=\pi r^2\cdot 5\\\\\Rightarrow r^2=\dfrac{1271.7}{3.142\times 5}\\\\\Rightarrow r^2=80.948\\\Rightarrow r=8.99\approx 9\ ft[/tex]

Thus, the radius of the cylinder is [tex]9\ ft[/tex]

Answer:

16/3

Step-by-step explanation:

Answer:

David=$8.8

Jo=$13.2

Mary=$22

Step-by-step explanation:

2+3+5=10

44/10=4.4

David=4.4x2=$8.8

Jo=4.4x3=$13.2

Mary=4.4x5=$22

8.8+13.2+22=44

Answer:

12y = -7

Step-by-step explanation:

Answer:

0.47

Step-by-step explanation:

0.47

47 hundredths is equal to 0.47.

If this helps please mark as brainliest

Answer:

The standard form of forty-seven hundredths is 0.47.

Step-by-step explanation:

Have a nice day! :-)

TeamRocket3

Answer:

The Richter scale and how it measures earthquake magnitude. The Richter scale calculates an earthquake's magnitude (size) from the amplitude of the earthquake's largest seismic wave recorded by a seismograph. ... (That is, an earthquake measuring 5.0 releases 31 times more energy than an earthquake measuring 4.0.)

Answer:

11,25

Step-by-step explanation:

Answer: 120

Step-by-step explanation:

Answer:

120°

Step-by-step explanation:

Answer:

convert km into m

1 km=1000m

360 km=1000*360m

=360000m

again,convert 3 hours into seconds

3 hours=60*60*3

=10800 second

average spped=total distance /time taken

=360000/10800

=33.33 m/s

Step-by-step explanation:

Answer:

The volume of the hollow ball will be equal to the difference between the volume of a sphere with the outer radius and the volume of a sphere with the inner radius.

Remember that the volume of a sphere of radius R is given by:

V = (4/3)*pi*R^3

where pi = 3.14

Then if R is the outer radius, and r is the inner radius, the volume of the hollow ball is:

V = (4/3)*pi*( R^3 - r^3)

In this case, we have:

R = 200m

r = 100m

Then the volume of the hollow ball is:

V = (4/3)*3.14*( (200m)^3 - (100m)^3)

V = 29,306,666.67 m^3

Now, if this hollow ball is made of iron, we want to find the mass.

Remember the relation:

Mass = Density*Volume.

We know that the density of the iron is:

D = 7300 kg/m^3

Then the mass of this hollow ball is:

M = (7300 kg/m^3)*(29,306,666.67 m^3) = 213,938,666,666.6 kg

Answer:

A. -8x⁴y³ - 6x³y⁴ + 10x²y^6

Step-by-step explanation:

Given:

– 2x²y³ ( 4x² + 3xy – 5y³)

Open the parenthesis

= (– 2x²y³ * 4x²) + (– 2x²y³ * 3xy) - (– 2x²y³ * 5y³)

= -8x⁴y³ + (-6x³y⁴) - (- 10x²y6^6)

= -8x⁴y³ - 6x³y⁴ + 10x²y6^6

The correct answer is

A. -8x⁴y³ - 6x³y⁴ + 10x²y^6

Answer:

19.5 dollars

Step-by-step explanation:

9.75% of 200 is 19.5

Answer:

After 7 steps, co-ordinate would be  (35, 21) in the N-E direction

Step-by-step explanation:

Complete question

Testing a robot. The robot is 17 inches tall and weighs 4 pounds. The employees of the company marked a grid on the floor and set the robot at (5,3). They programmed the robot to walk 2 yards east and 6 yards north each minute. What will the co-ordinate after 7 steps

Solution

The grid on the floor is (5, 3)

5 is the X -co-ordinate and 3 is the y co-ordinate

Since the robot is walking in the north and east direction , it will be in the first co-ordinate only

After seven steps, in east direction, the co-ordinate would be 7 * 5 = 35

After seven steps, in north direction, the co-ordinate would be 7 * 3 = 21

So the co-ordinate would be (35, 21)

Answer:

B. √3/2.

Step-by-step explanation:

If we follow the circle from (1,0) clockwise through 240 degrees we end up at 120 degrees.

sin(120)

= √3/2

Answer:

4

Step-by-step explanation:

Answer:

[tex]98.28\:\mathrm{ft^3}[/tex]

Step-by-step explanation:

The volume of a rectangular prism is given by [tex]V=l\cdot w\cdot h[/tex], where [tex]l[/tex] is the length of the prism, [tex]w[/tex] is the width of the prism, and [tex]h[/tex] is the height of the prism.

Substituting given values, we get:

[tex]V=2.5\cdot 4.25\cdot 9.25=98.28125\approx \boxed{98.28\:\mathrm{ft^3}}[/tex]

Since "Simplify your answers" is very subjective, I've rounded to the nearest hundredth as that is reasonably universal, but you may need to adjust the rounding as desired.

Answer:

420

Step-by-step explanation:

just multiply all the numbers together

Answer: 420 cubic inches

Step-by-step explanation:

Use the formula V = lwh to solve.

V = L * W * H

V = 6 * 7 * 10

V = 420 cubic inches

Answer:

hope this will help you more