6. Find the values of x and y. 30° 17

Answer: y = -1/4x + 4

Step-by-step explanation:

slope intercept form = y = mx + b

since you are given m and b, plug in the points into the formula

-1/4 goes in for m and 4 goes in for b

leaving us with:

[tex]y=-\frac{1}{4} x+4[/tex]

Answer:

[tex]y=-\frac{1}{4}x+4[/tex]

Step-by-step explanation:

Ok, so the slope-intercept form is generally expressed as: [tex]y=mx+b[/tex]

y-intercept:

Let's start by explaining why the "b" value represents the y-intercept. So I attached a graph to make this a bit more understandable, but the gist is that anywhere on the y-axis, is going to have x=0, any point on the y-axis can generally be expressed as (0, y).

This means, if we want to find the y-intercept, using the slope intercept form, we simply plug in 0 as x, since that's what x will always be equal to at the y-intercept.

We get the following equation: [tex]y=m(0) + b[/tex], and since anything times zero is just zero, we can simplify this to: [tex]y=b[/tex], meaning the y-intercept will be the "b" value in any slope-intercept form equation.

The slope:

By definition the slope is just how much the y-value changes as x increase by one. Whenever we increase the x-value by one, in the equation y=mx+b, we have one more "m", or the value is increasing by m.

Let's look at an example:

[tex]y=m(1) +b\implies m+b[/tex]

[tex]y=m(2) + b \implies m + m + b[/tex]

[tex]y = m(3) + b \implies m + m + m +b[/tex]

See how each time we increase the value "x" by one, the value of "y" increases by m. So by definition "m" is the value of the slope.

So putting this all together with your example, we get the following equation:

[tex]y=-\frac{1}{4}x+4[/tex]

The correct answer which represents the quotient of 20√z⁶ ÷ √16z⁷ in simplest radical form is; (5√z)/z.

The quotient given can be evaluated by means of the laws of indices as follows;

20√z⁶ ÷ √16z⁷

= 20√z⁶ ÷ 4√z⁷

= 5 √(z⁶/z⁷)

= 5 √z^(-1)

= 5 × z^(-1/2)

= 5/√z

Hence, by rationalisation; we have;

= (5√z)/z.

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If Caisse can download a maximum of 1000 mb of songs or movies then the inequality that represents the number of movies and songs that Caisse downloads each month is 85x+4y<1000.

Given that Caisse can download a maximum of 1000 mb of songs or movies to her smartphone each month. the file of each movie is 85mb, and the file of each song is 4mb.

We are required to find the inequality that represents the number movies and songs that Caisse downloads each month.

Inequality is like an equation that shows the relationship between variables that are expressed in greater than, less than , greater than or equal to , less than or equal to sign.

let the number of movies be x and the number of songs be y.

According to question Caisse cannot download more than 1000 mb, so we will use less than towards equation.

It will be as under:

85x+4y<1000.

Hence if Caisse can download a maximum of 1000 mb of songs or movies then the inequality that represents the number of movies and songs that Caisse downloads each month is 85x+4y<1000.

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The feasible reason for inequality y>2 is attached.

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Answer:

150.8 in³

Step-by-step explanation:

The volume of the 5 inch ball is

[tex]\frac{4}{3}\pi (5/2)^{3}[/tex]

The volume of the 13 inch ball is

[tex]\frac{4}{3}\pi (13/2)^{3}[/tex]

Subtracting these volumes, we get about 150.8 in³.

The amount of space (volume) that is in the larger spherical ball than the smaller will be 1,084.8 in.³

To find the volume of a sphere, which is the amount of space the solid contains, the formula used is given as: 4/3 πr³,

where r is the radius of the sphere, which is half the measure of the diameter.

Diameter of the smaller spherical ball = 5 inches

Radius = 5/2 = 2.5 inches

Volume of the smaller spherical ball = 4/3 πr³ = 4/3 × π × 2.5³

Volume ≈ 65.5 in.³

Diameter of the larger spherical ball = 13 inches

Radius = 13/2 = 6.5 inches

Volume of the larger spherical ball = 4/3 πr³ = 4/3 × π × 6.5³

Volume of the larger spherical ball ≈ 1,150.3 in.³

The amount of space (volume) that is in the larger spherical ball than the smaller.

= 1,150.3  - 65.5

The amount of space (volume) that is in the larger spherical ball than the smaller will be 1,084.8 in.³

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Answer:

39916800

Step-by-step explanation:

1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10 × 11

The probability that a person in this income bracket will be audited this year is of 3%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that 30 out of 1000 people are audited, hence the probability that a person in this income bracket will be audited this year is given by:

p = 30/1000 = 0.03 = 3%.

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Answer:

I think it would be D

0.7 is the new probability of the event being sold out given that total number of events is 7 and 5 events are sold out. This can be obtained by using the formula for probability.

Probability is the chance of occurrence of an event.

⇒ The formula for finding probability,

Probability = [tex]\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ outcomes}[/tex]

Here it is given in the question that,

Therefore by using the formula of probability we get,

⇒ Probability (Junior Athletics being sold out) = [tex]\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ outcomes}[/tex]

Probability (Junior Athletics being sold out) = [tex]\frac{Number\ of\ events\ sold\ out}{Total\ number\ of\ events}[/tex]

Probability (Junior Athletics being sold out) = 5/7

⇒ Probability (Junior Athletics being sold out) = 0.7

Hence 0.7 is the new probability of the event being sold out given that total number of events is 7 and 5 events are sold out.

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[tex]f(x)=\left( \cfrac{3x^2-2}{2x+3} \right)^3\implies \cfrac{df}{dx}=\stackrel{\textit{\LARGE chain~ ~~ rule}}{3\left( \cfrac{3x^2-2}{2x+3} \right)^2\underset{quotient~rule}{\left( \cfrac{6x(2x+3)~~ - ~~(3x^2-2)2}{(2x+3)^2} \right)}} \\\\\\ \cfrac{df}{dx}=3\left( \cfrac{3x^2-2}{2x+3} \right)^2\left( \cfrac{12x^2+18x-6x^2+4}{(2x+3)^2} \right) \\\\\\ \cfrac{df}{dx}=3\left( \cfrac{3x^2-2}{2x+3} \right)^2\left( \cfrac{6x^2+18x+4}{(2x+3)^2} \right)[/tex]

[tex]\cfrac{df}{dx}=3 \cfrac{(3x^2-2)^2}{(2x+3)^2} \left( \cfrac{2(3x^2+9x+2)}{(2x+3)^2} \right)\implies \cfrac{df}{dx}=\cfrac{6(3x^2-2)^2(3x^2+9x+2)}{(2x+3)^4}[/tex]

now, we could expand the polynomials, but there isn't much simplification, so no much point doing so.

Answer:

none

Step-by-step explanation:

A. -7 <= x < 0

B. x <= -7 or x > 0

C. -7 < x <= 0

D. x < -7 or x >= 0

To create a graph to represent -7 < x < 0, draw empty circles at -7 and 0, then connect the two with a line.

Answer: x = -1 or x = 5/3

Step-by-step explanation:

|3x - 1| = 4

=> 3x - 1 = 4 or 3x - 1 = -4

=>x = 5/3 or x = -1

The value of the expression 2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 is 400000

The equation is given as:

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000

From the question, we understand that the expression is to be solved from left to right (without using the pemdas mathematical rule)

So, we start by multiplying 2 and 4

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 8 + 48000 / 8 - 1 x 30 x 2 + 40000

Add 8 and 48000

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 48008 / 8 - 1 x 30 x 2 + 40000

Divide 48008 by 8

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 6001 - 1 x 30 x 2 + 40000

Subtract 1 from 6001

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 6000 x 30 x 2 + 40000

Multiply 6000 and 30

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 180000 x 2 + 40000

Multiply 180000 by 2

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 360000 + 40000

Evaluate the sum

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 400000

Hence, the value of the expression 2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 is 400000

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Answer:

10 m/s

Step-by-step explanation:

Let x = speed of fish and y = speed of current. When swimming with current, the fish's speed is x + y. When swimming against it, the speed is x - y. Therefore, we can set up a system of linear equations to solve for x, the speed of fish.

x + y = 14

x - y = 6

2y = 8

y = 4

x - 4 = 6

x = 10

The speed of fish in still water is 10 m/s, and the speed of current is 4 m/s.

Answer:

Speed of fish in still water = 10 m/s

Speed of current = 4 m/s

Step-by-step explanation:

Let the speed of the fish in still water = x m\s

Let the speed of the current  = y m/s

Speed of the fish with the current = x + y

 x +y = 14 m/s ------------------(I)

Speed of the fish against current = x -y

 x - y = 6 m/s ----(II) &

Add the equations (I) & (II) and 'y' will be eliminated and we can find the value of 'x'.

     x + y = 14

     x - y =  6      {Now, add)

     2x    = 20

           x = 20/2

          x = 10

[tex]\sf \boxed{\text{\bf Speed of fish in still water = 10 \ m / s}}[/tex]

Plugin x = 10 in equation (I)

    10 + y = 14

            y = 14 - 10

           y = 4

[tex]\sf \boxed{\text{\bf Speed of the current = 4 \ m/s}}[/tex]

Answer:

correct

Step-by-step explanation:

dividing both quantities in a ratio by the same non zero number does indeed find an equivalent ratio.

for example

60 : 36 ( divide both parts by 6 )

= 10 : 6 ← equivalent ratio ( divide both parts by 2 )

= 5 : 3 ← equivalent ratio in simplest form

in fact dividing the original by the HCF of the 2 quantities gives the ratio in simplest form immediately , that is

60 : 36 ( divide both parts by 12 )

= 5 : 3

Answer:

1.24

Step-by-step explanation:

because 1.24>1.215>0.365>0.095

The inequalities are matched with the respective graphs as shown in the attached image.

In mathematics, inequality is the relationship between two non-equal expressions, denoted by a sign such as 'not equal to,' > 'greater than,' or 'less than.'

Roads feature speed limits, some movies have age limitations, and the time it takes to go to the park are all instances of inequalities in the real world.

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The function position of the particle is s(t) = (1 / 12) · t⁴ + (7 / 6) · t³ + 3 · t² + (63 / 4) · t.

By mechanical physics we know that the function velocity is the integral of function acceleration and the function position is the integral of function velocity. Hence, we need to integrate twice to obtain the function position of the particle:

Velocity

v(t) = ∫ t² dt - 7 ∫ t dt + 6 ∫ dt

v(t) = (1 / 3) · t³ - (7 / 2) · t² + 6 · t + C₁

Position

s(t) = (1 / 3) ∫ t³ dt - (7 / 2) ∫ t² dt + 6 ∫ t dt  + C₁ ∫ dt

s(t) = (1 / 12) · t⁴ + (7 / 6) · t³ + 3 · t² + C₁ · t + C₂

Now we find the values of the integration constants by solving the following system of linear equations:

0 = C₂

63 / 4 = C₁ + C₂

The solution of the system is C₁ = 63 / 4 and C₂ = 0. The function position of the particle is s(t) = (1 / 12) · t⁴ + (7 / 6) · t³ + 3 · t² + (63 / 4) · t.

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Answer:

(the figure is poorly drawn)

Step-by-step explanation:

find y

180 - 120 = 60°

find x

180 - 60 - 30 = 90°

Answer:

2

Step-by-step explanation:

Use pemdas

4a*(3-2b)

4(1/2)*(3-2(-1))

4* 1/2 = 2

2*(3-2(-1)

-2*-1 = 2

2(3-2)

3 -2 = 1

2(1) = 2

The number of times Ken visits, given the £3.6 pool charge, and 1/3 savings per visit is 5 times.

The entry fee = £3.60

Amount saved on entry fee by having a membership card = 1/3 of the entry fee

Amount Ken spends on the membership card and the reduced entry fee = £5

Therefore;

Reduced entry fee = £3.60×(1 - 1/3) = £2.4

Amount saved per visit = £3.6 - £2.4 = £1.2

The number of visits, n, before he gets back his £5 is therefore;

Ken has to visit the swimming pool more than 4 times to get his £5 back.

Rounding to the next larger whole, therefore;

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Answer:

$78.60

Step-by-step explanation:

0.14x + 31 = 0.14*340 + 31 = 78.6

Step-by-step explanation:

it's 2x²+8x

and I cannot understand your question

Answer:

x = - 6, x = - 1

Step-by-step explanation:

[tex]\frac{2x}{x+2}[/tex] = - [tex]\frac{6}{x+4}[/tex] ( cross- multiply )

2x(x + 4) = - 6(x + 2) ← distribute parenthesis on both sides )

2x² + 8x = - 6x - 12 ( subtract - 6x - 12 from both sides )

2x² + 14x + 12 = 0 ( divide through by 2 )

x² + 7x + 6 = 0 ← in standard form

(x + 6)(x + 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

x + 1 = 0 ⇒ x = - 1

[tex]given \: that \: its \: linear \\ m = \frac{15 - 3}{3 - 0} = \frac{12}{3} = 4 [/tex]

[tex]b = y(0) = 3 \\ y = 4x + 3 \: [/tex]

Answer:

D) y = 4x + 3

Step-by-step explanation:

   [tex]\sf \boxed{\bf y = mx +b}[/tex]

Here, m is the slope and b is y intercept.

At y intercept, x = 0

         From the table, y intercept  = 3

Choose any two points from the table to find the slope.

(0 ,3)  & (3,15)

[tex]\sf \boxed{\bf Slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

           [tex]\sf =\dfrac{15-3}{3-0}\\\\=\dfrac{12}{3}\\\\=4[/tex]

m = 4 ; b = 3

 Equation of line:

                 y = 4x  + 3

Answer:

108

Step-by-step explanation:

11+61=72

We use 180 and subtract it by 72 because we know that all angles in a triangle add up to 180.

180-72=108

By applying trigonometric expressions and algebra properties, the trigonometric equation 1 - cos 12x is equivalent to the trigonometric equation 2 · sin² 6x. (Correct choice: D)

Herein we have a trigonometric equation which has to be simplified. Simplification procedure consists in applying trigonometric expressions and algebra properties to transform the function from the form f(cos 12x) to the form f(cos 6x). Now we present the solution in detail:

By applying trigonometric expressions and algebra properties, the trigonometric equation 1 - cos 12x is equivalent to the trigonometric equation 2 · sin² 6x. (Correct choice: D)

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See attachment for the graph of the function y = 5 sin(4x)

The trigonometry function is given as:

y = 5 sin(4x)

To plot the graph, we use the following domain:

x > 0

This represents the minimum value of x

Also, we use

x < π/2

This represents the maximum value of x

When the domain are combined, we have:

0 < x < π/2

This means that the domain that gives a complete cycle is 0 < x < π/2

See attachment for the graph of the function

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Answer:

18 miles

Step-by-step explanation:

hihihihihiuijihihihi