QUESTION SIX Solve the following problems: (a) Find the gradient, x and y intercepts of 3x + 4y + 12 = 0. Sketch the graph. (6 Marks) (b) Find the gradient, x and y intercepts of the line I, passing through the points P (-1,4) and Q (3,0). Sketch the graph. (6 Marks) (c) A line 1₂ is perpendicular to 4. Find its gradient. (2 Marks) (14 Marks)​

1. Cost is proportional to Area includes;

-Carpeting that cost $22 for every 3 square yard

-Cost ($) and Area (ft^2) table

-Mulch that cost a set amount to cover a square foot

2.    Cost is not proportional to Area;

- Linear graph

-  Asphalt sealant that is quoted at a set price per square foot, plus a labor fee

3. Not enough information

- A wood deck quoted at a bulk cost for 25 square feet.

The Linear graph is not proportional to the area looking at the coordinates that has been provided. The cost to the yard area does not have a consistent progression. By this, $1,600 should cove 60 yd² instead of 80

The above answer is based on the information provided in the picture as seen below;

Drag each object to show whether cost is proportional to area in the situation represented.

Cost is proportional to Area       Cost is not proportional to Area               Not enough information

a. A wood deck quoted at a bulk cost for 25 square feet.

d. Asphalt sealant That is quoted at a set price per square foot, plus a labor fee.

c. Carpeting that cost $22 for every 3 square yard

d. Mulch that cost a set amount to cover a square foot

e.   Cost ($)                 Area (ft^2)

       500                        400

       750                         600

     1000                        800

f. A cost ($) and area (yd^2) that has coordinates (0, 0), (20, 1200) (80, 1600)

Find more exercises on Cost proportional to Area;

https://brainly.com/question/30170974

#SPJ1

Answer:Transpolar Drift Stream y el anticiclónico Beaufort Gyre

Step-by-step explanation:

Answer:

88

Step-by-step explanation:

The distance traveled by a rider on a Ferris wheel can be calculated by finding the circumference of the wheel and then multiplying it by the number of complete laps.

The formula for the circumference of a circle is:

C = πd

where C is the circumference, d is the diameter, and π is a constant approximately equal to 3.14.

In this case, the diameter of the Ferris wheel is 14 meters, so the radius (half the diameter) is 7 meters.

C = πd = π(14) = 43.9823 meters (rounded to 4 decimal places)

To find the distance traveled after 2 complete laps, we need to multiply the circumference by 2:

distance = 2C = 2(43.9823) = 87.9646 meters

Rounding to the nearest meter, the distance traveled by a rider after 2 complete laps is 88 meters.

it will take approximately 6.8 minutes until there are 50 grams of the element remaining.

We can use exponential decay formula to solve this problem:

A = A₀ ×e²(-rt)

where A is the amount of the element remaining, A₀ is the initial amount, r is the decay rate (as a decimal), t is the time elapsed.

We know that the initial mass of the element is 640 grams, the decay rate is 19.3% per minute, and we want to find the time it takes for there to be 50 grams of the element remaining. So we can write:

50 = 640 ×e²(-0.193t)

Dividing both sides by 640, we get:

0.078125 = e²(-0.193t)

Taking the natural logarithm of both sides, we get:

ln(0.078125) = -0.193t

Solving for t, we get:

t = ln(0.078125) / (-0.193)

t ≈ 6.8 minutes

Therefore, it will take approximately 6.8 minutes until there are 50 grams of the element remaining.

learn more about logarithm here:

https://brainly.com/question/30085872

Answer:

Please mark me the brainliest

Let's denote the time in minutes by t, and the mass of the element at time t by m(t). Then we can write an exponential decay equation:

m(t) = m(0) * (1 - r)^t

where m(0) is the initial mass of the element, r is the decay rate as a decimal (19.3% = 0.193), and t is the time in minutes.

We know that the initial mass is m(0) = 640 grams, and we want to find the time t when the mass has decreased to 50 grams. So we can set up the following equation:

50 = 640 * (1 - 0.193)^t

Simplifying:

0.07796875 = 0.807^t

Taking the natural logarithm of both sides:

ln(0.07796875) = ln(0.807^t)

Using the property of logarithms that ln(a^b) = b * ln(a):

ln(0.07796875) = t * ln(0.807)

Dividing both sides by ln(0.807):

t = ln(0.07796875) / ln(0.807)

Using a calculator, we get:

t ≈ 24.9

Therefore, to the nearest tenth of a minute, it will take 24.9 minutes until there are 50 grams of the element remaining.

Step-by-step explanation:

To show that Sk - ku is a martingale, we need to show that it satisfies the two properties of a martingale:

Sk - ku is integrable for all k.

For any k, E[Sk+1 - ku+1 | E0,...,Ek] = Sk - ku.

First, we show that Sk - ku is integrable for all k:

E[|Sk - ku|] = E[|(X1 + ... + Xk) - k|]

= E[|X1 + ... + Xk| - k] (using linearity of expectation)

≤ E[|X1| + ... + |Xk|] + k (by triangle inequality)

= kE[|X1|] + ... + kE[|Xk|] + k (using linearity of expectation)

= kE[|X1|] + ... + kE[|X1|] + k (since Xi are IID)

= kE[|X1|] + k (since there are k terms)

< ∞ (since E[|X1|] is finite)

Therefore, Sk - ku is integrable for all k.

Next, we show that for any k, E[Sk+1 - ku+1 | E0,...,Ek] = Sk - ku:

E[Sk+1 - ku+1 | E0,...,Ek] = E[(X1 + ... + Xk+1) - (k+1) | E0,...,Ek]

= E[(X1 + ... + Xk) + Xk+1 - (k+1) | E0,...,Ek]

= E[(X1 + ... + Xk) - k | E0,...,Ek] + E[Xk+1 | E0,...,Ek]

= Sk - ku + E[Xk+1] (by the martingale property of Sk - ku)

= Sk - ku + u (since the mean of X1, X2, ... is u)

Therefore, Sk - ku is a martingale.

Now, we can use the optional stopping theorem to prove that E[ST] = uE[T]:

By the optional stopping theorem, we have:

E[ST] = E[(Sk - ku)(T - k) + Sku]

= E[(Sk - ku)(T - k)] + E[Sku]

= E[E[(Sk - ku)(T - k) | E0,...,Ek]] + E[Sku] (using law of total expectation)

= E[(Sk - ku)E[T - k | E0,...,Ek]] + E[Sku] (using linearity of expectation)

= E[(Sk - ku)(E[T | E0,...,Ek] - k)] + E[Sku] (using law of total expectation)

= E[(Sk - ku)(T - k)] + E[Sku] (since T is a bounded stopping time)

= E[SkT - kuT - kS + ku] + E[Sku]

= E[SkT] - uE[KT] - kE[S] + ku + E[Sku] (using linearity of expectation)

= uE[KT] - uE[KT] - kE[S] + ku + E[Sku] (using the optional stopping theorem)

= ku + E[S(T-k)]

= ku + E[Sk - k^2] (since T is a stopping time)

To learn more about stopping visit:

https://brainly.com/question/29825115

#SPJ11

32 is the number of teams took less than 20minutes to complete the game

Given that Isaac measured the time it took for some teams to complete an escape room game.

The times were recorded in the table

We have to find the number of teams which are  less than 20minutes to complete the game

Number of teams took less than 20 minutes

=8+24

=32

Hence, 32 is the number of teams took less than 20minutes to complete the game.

To learn more on Statistics click:

https://brainly.com/question/30218856

#SPJ1

Answer:

To go from ABC to DEF, you have to multiply by 8/9

Step-by-step explanation:

40/45 = 8/9

88/99 = 8/9

80/90 = 8/9

Yes, of course!

Ricardo has made 4 out of the 12 recipes in his cookbook.

To find out what fraction of the recipes he has made, you can write it as a fraction:

4/12

To simplify this fraction, you can divide both the numerator and denominator by 4, which gives:

4/12 = 1/3

Therefore, Ricardo has made 1/3 of the recipes in his cookbook.

Answer:

x = 6 feet

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 8² = 10²

x² + 64 = 100 ( subtract 64 from both sides )

x² = 36 ( take square root of both sides )

x = [tex]\sqrt{36}[/tex] = 6 feet

10 pounds of milk chocolate, 15 pounds of dark chocolate, and 25 pounds of almond chocolate.

We have,

A grocer sells milk chocolate at $2.60 per pound, dark chocolate at $4.80 per pound, and dark chocolate with almonds at $5.50 per pound.

Let x be the pounds of milk chocolate and y is the number of pounds of of dark chocolate.

So, x + y + (x+y)= 50

2(x+y)= 50

x+y = 25

x = 25 - y

Now, 2.6x + 4.8y + 5.5(x+y)= 50(4.71)

2.6x + 5.5x + 4.8y + 5.5y = 235.5

8.1x+ 10.3y = 235.5

8.1(25-y) + 10.3y = 235.5

202.5 - 8.1y + 10.3y = 235.5

2.2y = 33

y = 15

and, x = 10

Thus, 10 pounds of milk chocolate, 15 pounds of dark chocolate, and 25 pounds of almond chocolate.

Learn more about Equation here:

https://brainly.com/question/14012550

#SPJ1

The calculated value of r ihe lateral area of the cylinder is 512π square units is 16 units

From the question, we have the following parameters that can be used in our computation:

The lateral area of the cylinder is 512π square units

The lateral area of the cylinder is 2πrh

So, we have

2πrh = 512π

Substitute r for h

2πr^2 = 512π

Divide both sides by 2π

So, we have

r^2 = 256

Take the square roots

r = 16

Hence, the radius is 16 units

Read more about area at

https://brainly.com/question/24487155

#SPJ1

Answer:

Step-by-step explanation:

1

Therefore, for the equation y=x+5 , the slope is 1 , and the y-intercept is 5 .

Answer:

A,C,E

Step-by-step explanation:

Answer:

a and c and e

Step-by-step explanation:

got it right on my home work

Answer:

5.45

Step-by-step explanation:

literally do 10.9/2

Answer:

tanx

Step-by-step explanation:

If it has 2 complex zeros, then it must have 2 real zeros.

Remember that the number of zeros that a polynomial of degree N has is also N.

For example in functions like:

f(x) = x^N

We can say that the zero x = 0 has a multiplicity of N, so we have N equal zeros.

Then a polynomial of degree 4 has 4 zeros, if two are complex, then the other two are real zeros.

So we conclude that the answer is 2.

Learn more about polynomials at:

https://brainly.com/question/4142886

#SPJ1

The  scale factor of the dilation is 30:1.

We have,

A superhero action figure has a volume of 1500 cm³.

The volume of the dilated figure is 45,000 cm³

Now, the scale factor should be

= 45000/ 1500

= 30 /1

Thus, the scale factor of the dilation is 30:1.

Learn more about Scale Factor here:

https://brainly.com/question/21844975

#SPJ1

The measure of the angles are:

∠1 = 90

∠2 = 90

∠3 = 132

We have,

The angle between the tangent and the radius of a circle is 90.

So,

∠1 = 90

∠2 = 90

And,

48 + 90 + 90 + ∠3 = 360 ______(1)

Solve for ∠3 from (1).

48 + 90 + 90 + ∠3 = 360

48 + 180 + ∠3 = 360

∠3 = 360 - 228

∠3 = 132

Thus,

The measure of the angles are:

∠1 = 90

∠2 = 90

∠3 = 132

Learn more about Circle here:

https://brainly.com/question/11833983

#SPJ1

The point on the number line that is 7/9 of the way from -3.6 to 10 is approximately 6.97777777778.

To find the point on the number line that is 7/9 of the way from -3.6 to 10, we can use the following formula:

Point = Starting point + (Fraction of distance) x (Total distance)

In this case, the starting point is -3.6, the total distance is the distance from -3.6 to 10 (which is 10 - (-3.6) = 13.6), and the fraction of distance is 7/9.

Plugging in these values, we get:

Point = -3.6 + (7/9) x (13.6)

Simplifying,

Point = -3.6 + (7/9) x (13.6)

Point = -3.6 + 9.9556

Point = 6.97777777778

To learn more about fractions;

https://brainly.com/question/10354322

#SPJ1

The line of reflection of the given image is:

A reflection across y = -3

A line of reflection is a line that lies between two identical mirror images, so the distance of any point of one figure from the line will equal the distance of the same point of the mirror image (flipped figure).

The definition above tells us that if we are given two images, such as mirror images of each other, the line of reflection can be determined by calculating the midpoint from any two points of the figures.

Looking at the given image, the center point of the mirror images is seen as y = -3

Read more about Line of reflection at: https://brainly.com/question/26642069

#SPJ1

We can see that the triangle has two equal angles, then it is an isosceles triangle.

Here we have a triangle where we know that the interior angles are:

x°, 4x°, and 4x°

remember that the sum of the interior angles of any triangle is 180°, then we can write the linear equation:

x + 4x + 4x = 180

Solving that for x we will get:

9x = 180

x = 180/9

x = 30

Then the angles are:

x° = 20°

4x° = 80°

4x° = 80°

We can see that we have two equal angles, then the triangle is an isosceles triangle.

Learn more about triangles at:

https://brainly.com/question/1058720

#SPJ1

The required two pairs of polar coordinates for the point (0, -10) are:

(10, π/2) and (10, -π/2)

To convert from Cartesian coordinates (x, y) to polar coordinates (r, θ), we can use the following formulas:

[tex]r = \sqrt{(x^2 + y^2)}\\\theta = \tan^{-1}(y/x)[/tex]

Since the x-coordinate of the point (0, -10) is 0, we can directly say that the angle θ is either π/2 or -π/2, depending on whether y is positive or negative.

For y = -10, we get:

[tex]r = \sqrt{(0^2 + (-10)^2)} = 10[/tex]

Therefore, two pairs of polar coordinates for the point (0, -10) are:

(10, π/2) and (10, -π/2)

Both of these pairs have the same distance from the origin (r = 10) but different angles (π/2 and -π/2).

Learn more about polar coordinates here:

https://brainly.com/question/11657509

#SPJ1

There are 125 sheets in the sale package.

If a regular package of graph paper contains 100 sheets, then a package with 25% more sheets would contain:

100 + (25/100) x 100 = 100 + 25 = 125

So a package with 25% more sheets would contain 125 sheets.

During the sale, the store is offering a package with 25% more sheets for no additional cost.

This means that the sale package contains the same number of sheets as a regular package, plus an additional 25% of that same number of sheets.

To find the number of sheets in the sale package, we can set up an equation:

Number of sheets in sale package = Number of sheets in regular package + 25% of the Number of sheets in the regular package

or

Number of sheets in sale package = 100 + 0.25 x 100

Simplifying,

Number of sheets in the sale package = 100 + 25

Number of sheets in the sale package = 125

To learn more about the percentage;

https://brainly.com/question/24159063

#SPJ1

Gus will need to fill the bucket 3 times to completely fill the fish tank, assuming he doesn't spill any water.

To find how many times Gus will need to fill the bucket to completely fill the fish tank, we first need to calculate the volume of the bucket. The formula for the volume of a cylinder is:

V = πr²h

where V is the volume, r is the radius, and h is the height.

Substituting the given values into the formula gives:

V = 3.14 x 5² x 20

V = 3.14 x 25 x 20

V = 1570 inches³

Therefore, each time Gus fills the bucket, he will add 1570 inches³ of water to the fish tank. To calculate how many times he needs to fill the bucket to fill the entire fish tank, we can divide the total volume of the fish tank by the volume of the bucket:

4710 / 1570 = 3

To learn more about cylinder click on,

https://brainly.com/question/12221568

#SPJ1

Complete question is:

Gus has a fish tank that holds 4710 inches³ of water. He is using a cylinder shaped bucket with a radius of 5 inches and a height of 20 inches to fill the tank. How many times will Gus need to fill the bucket to completely fill the fish tank if he doesn't spill a drop?

Answer:

[tex]28 + y + 36 = 180[/tex]

[tex]64 + y = 180[/tex]

[tex]y = 116[/tex]

Using the triangle proportionality theorem, the length of side PB in the given triangle is 10

From the question, we are to determine what the length of PB is in the given triangle

From the Triangle Proportionality Theorem which states that "If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally".

Thus,

From the given diagram, we can write that

AP / PB = AQ /QC

From the given information,

AP = 4

AQ = 6

QC = 15

4 / PB = 6 / 15

6 × PB = 4 × 15

6 × PB = 60

Divide both sides by 6

PB = 60 / 6

PB = 10

Hence, the length of PB is 10

Learn more on Calculating the length of a side of a triangle here: https://brainly.com/question/20833563

#SPJ1

Answer:

Step-by-step explanation:

7x+2.50y=600

The directed line segment PQ is divided at this point at a 3:1 ratio (1, 8)

According to the section formula, the coordinates of a point R may be determined by dividing a line segment PQ by that point in the ratio m:n as follows:

[tex]R_x = (n * Px + m * Qx) / (m + n)\\R_y = (n * Py + m * Qy) / (m + n)[/tex]

where [tex]P_x, P_y[/tex] are the coordinates of point P, and [tex]Q_x, Q_y[/tex] are the coordinates of point Q.

In this case, we want to divide the line segment PQ in a ratio of 3:1. This means that m = 3 and n = 1.

Using the formula, we can find the coordinates of the point R that divides PQ in a 3:1 ratio:

Rx = (1 * (-8) + 3 * 4) / (3 + 1) = 1

Ry = (1 * (-4) + 3 * 12) / (3 + 1) = 8

Therefore, the point that partitions the directed line segment PQ in a ratio of 3:1 is (1, 8).

Learn more about the section formula here:

https://brainly.com/question/30242641

#SPJ1