The number y of objects a machine produces is proportional to the time x (in minutes) that the machine runs. The machine produces five objects in four minutes.
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The pair of equations whose lines are perpendicular is (d) y = 1/6x + 3; y = -6x - 3

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

The pair of equations

By definition;

The slopes of perpendicular lines are opposite reciporcals

So, we have

(a) -1/3 and -3 false

(b) -3 and -6 false

(c) 3 and 3 false

(d) 1/6 and -6 true

Hence, the equations are (d) y = 1/6x + 3; y = -6x - 3

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Answer:

13:5

Step-by-step explanation:

Messy played 65 minutes while the substitute played 25 minutes. This ratio is 65:25 and can be simplified to 13:5.

Answer: Denominator ♥️

Step-by-step explanation:

Answer:

Either they converse s little more like if Kate asks "You came just at the right time! When did you get here?" or Alyiah says something like "Now come with me, I'm taking you to somewhere safe"

Step-by-step explanation:

This story sounds super cool, keep it up !!!

Answer:

99.75lbs.

Step-by-step explanation:

4 x 18.5=    74lbs

2  x6.75= 13.5

14x 7/8 =98/8=12.25

The straight line distance (meters) from sheehan lake (point a) to the small lake (point b) is 1700 m .

The sheehan lake (point A) is at 2000 m .

The small lake ( point B) is at 3700 m .

Distance between the two lake can be calculated by finding the difference between lakes .

To find the distance between sheehan lake and small lake = point B - point A .

Distance =  3700 - 2000

Distance = 1700 m .

The distance (meters) from sheehan lake (point a) to the small lake (point b) is 1700 m .

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The question is incomplete the complete question is :

Answer:

140 ml

Step-by-step explanation:

Let x be the amount of water in Beaker X and y be the amount of water in Beaker Y.

Then we get following equations:

First part

Second part

Substitute x in first equation:

Then finding x:

Initial amount of water in Beaker X is 140 ml, in Beaker Y is 160 ml

Answer:

f(x) = -1/2x² + 3/2x - 2

f(0) = (-1/2 × 0²) + (3/2 × 0) - 2

f(0) = 0 + 0 - 2

f(0) = -2

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Answer: 4.75%

Step-by-step explanation:

Answer:

44/15 converted into a mixed number   = 2(14/15)

Step-by-step explanation:

44/15 =     2.9333333...... = 2( 14/15)

so it is the number 2 and   (0.93333)

Lets see how is  the  decimal is in fraction

0.93333  is a mixed recurrent number  and in fraction is  14/15

14/15 = 0.93333.....

With recurring  mixed  decimal :

For the top part:

Take the non-repeating and the repeating(93) and subtract the non repeating(9)

93-9= 84

For the bottom part: for  every repeating decimal,you put a 9  And for every non repeating decimal,you put a zero

so one 9 and one zero (90)

84/90  = 14/15  = 0.93333....

The volume of the oblique pyramid with a square base edge length of 5 cm and height of 7 cm is  58.33 cubic centimeters.

To calculate the volume of this oblique pyramid,

We can use the formula V = (1/3) A h,

Where A is the area of the base and h is the height of the pyramid.

Since the base is a square with an edge length of 5 cm,

We can find its area by squaring the edge length:

A = 5²

  = 25 cm².

Plugging in the values we have:

V = (1/3) x25x7

V = (1/3)x175

V = 58.33 cm³ (rounded to two decimal places)

So the volume of the oblique pyramid is  58.33 cubic centimeters.

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The three solutions of the equation y = -2x - 1 are (–2, 3), (1, –3), and (2, –4).

To find the solutions, we substitute different values of x into the equation and solve for y.

For the first solution, when x is –2, we have y = -2(-2) - 1 = 3. Therefore, the first solution is (-2, 3).

For the second solution, when x is 1, we have y = -2(1) - 1 = -3. Thus, the second solution is (1, -3).

For the third solution, when x is 2, we have y = -2(2) - 1 = -4. Hence, the third solution is (2, -4).

These three points satisfy the equation y = -2x - 1, and therefore, they are the solutions of the equation. They represent coordinate pairs (x, y) where the equation holds true.

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The Number of sodas sold: 174,

The number of hot dogs sold: 58.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given a vendor sold a combined total of 232 sodas and hot dogs.

let S for the number of sodas sold and H for the number of hot dogs sold,

S + H = 232

The number of sodas sold was three times the number of hot dogs sold

S = 3H

substitute the values,

S + H = 232

3H + H = 232

4H = 232

H = 232/4

H = 58

and the number of sodas sold

S = 3H

S = 3*58

S = 174

Hence the number of sodas sold = 174,

and the number of hot dogs sold = 58.

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The number of students who watch between 1 - 2 hours is 9.

We have,

From the table,

Number of students who watch tv for 1 hour = 5

Number of students who watch tv for 1.5 hours = 3

Number of students who watch tv for 2 hours = 1

Now,

The number of students who watch between 1 - 2 hours.

= Number of students who watch tv for 1 hour + 1.5 hours + 2 hours

= 5 + 3 + 1

= 9

Thus,

The number of students who watch between 1 - 2 hours is 9.

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Let r be the common ratio. The correct answer is Rounding to the nearest dollar, the value of Madame Dumas's art collection 12 years after she started tracking its worth is $9,498,559.

A) Let the value of the collection three years ago be the first term, a = $450,000.

Then we can write:

Second term: \(ar = $810,000\)

Third term: \(ar^2 = $1,458,000\)

To find the common ratio r, we can divide the second term by the first term and the third term by the second term:

\(ar/a\)= \(\frac{810,000}{450,000}\)

\(r = 1.8\)

\(ar^2/ar\) = \(\frac{450000}{810000}\)

\(r = 1.8\)

So the explicit rule for the value of Madame Dumas's art collection n years after she started tracking its worth is:\(a_n = ar^(n-3)\)

B) To find the value of her collection 12 years after she started tracking its worth, we can use the explicit rule:

\(a_12 = ar^(12-3) = ar^9\)

We already know that \(a = $450,000\) and \(r = 1.8\), so we can substitute those values:\(a_12 = $450,000(1.8)^9 = $9,498,558.57\)

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Answer:

A

Step-by-step explanation:

Answer: \(y-3=\frac{3}{2}(x-2)\)

Step-by-step explanation:

The slope of AB is \(\frac{-1-7}{8-(-4)}=-\frac{2}{3}\)

Perpendicular lines have slopes that are negative reciprocals, so the slope of the line we need to find is 3/2.

So, the equation is \(y-3=\frac{3}{2}(x-2)\).

Answer:

Table 4 represents a function.

Step-by-step explanation:

Functions require that each x-value has a unique y-value. In the other tables you see a value repeated in the x column, with a different value in the y column.

Answer:1/11

Step-by-step explanation:

Let the yellow cubes be x

yellow = x

blue = 2x                // Blue cubes is twice of yellow

Green = 8x              // Green is four times of blue

Ratio:

Yellow : Blue : Green

  1       :   2    :     8

P(Yellow) = 1/11

Answer:

n can be a number less than 3

Step-by-step explanation:

Hope this helps!

Answer:

N<3

Step-by-step explanation:

The solutions to the given equation on the interval 0≤x<2π. −8sin(5x)=−4√ 3 The solutions to the equation -8sin(5x) = -4√3 on the interval 0 ≤ x < 2π are:

x = π/3 and x = 2π/3.

To find the solutions to the equation -8sin(5x) = -4√3 on the interval 0 ≤ x < 2π, we can start by isolating the sine term.

Dividing both sides of the equation by -8, we have:

sin(5x) = √3/2

Now, we can find the angles whose sine is √3/2. These angles correspond to the angles in the unit circle where the y-coordinate is √3/2.

Using the special angles of the unit circle, we find that the solutions are:

x = π/3 + 2πn

x = 2π/3 + 2πn

where n is an integer.

Since we are given the interval 0 ≤ x < 2π, we need to check which of these solutions fall within that interval.

For n = 0:

x = π/3

For n = 1:

x = 2π/3

Both solutions, π/3 and 2π/3, fall within the interval 0 ≤ x < 2π.

Therefore, the solutions to the equation -8sin(5x) = -4√3 on the interval 0 ≤ x < 2π are:

x = π/3 and x = 2π/3.

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Answer:

See below

Step-by-step explanation:

Bi-conditional statement:

The associated conditional statements are:

Answer:

See below.

Step-by-step explanation:

Length * width

4 * 3 = 12 ft\(^2\)

Answer:

24 square feet

Step-by-step explanation:

Area = area of triangle - area of rectangle

\(Area \ of \ triangle = \frac{1}{2} \times base \times height =\frac{1}{2} \times(4 +5) \times (5+3) = 9 \times 4 = 36 \ ft^2\\\\Area \ of \ rectangle = Length \times Breadth = 3 \times 4 = 12 \ ft^2\\\\\\Area \ of \ the\ shaded \ region = 36 - 12 = 24 \ ft^2\)

Answer:

86

Step-by-step explanation:

= 200 +142 -28

=342-28

=314

= 1000

Answer:

\(z=\frac{s}{h-4c^4}\)

Step-by-step explanation:

Switch the subject

\(s=zh-4zc^4\\zh-4zc^4=s\)

Factor

\(zh-4zc^4\\=z\left(h-4c^4\right)\\z\left(h-4c^4\right)=s\)

Divide: remember that h - 4c^4 is not equal to zero

\(\frac{z\left(h-4c^4\right)}{h-4c^4}=\frac{s}{h-4c^4}\)

Simplify your solution where z is the redefined subject

\(z=\frac{s}{h-4c^4}\)

Step-by-step explanation:

s=zh-4zc^4

we will factorise

s=z(h-4c^4)

we will divide both sides by (h-4c^4)

s/(h-4c^4)=z

z=s/(h-4c^4)

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Answer:

Step-by-step explanation:

-3/8y = -24

-3y = -24 (8)

y = -192 / -3

y = 64

Add up the number of students within the random sample data:
32+26+28+22 = 108

We can then use proportional fractions / cross-multiply to answer the question.

In a sample size of 108 students, 32 of them preferred Movie A.
There are 900 students in total.

\(\frac{32}{108} =\frac{x}{900}\)

32*900 = 28800

108*x = 108x

108x = 28800

x = \(266\frac{2}{3}\) or \(\frac{800}{3}\)

In decimal form that is approximately 266.667 and round that to the nearest whole number, you get 267 students who would prefer Movie A.

The number of days took by Rita to travel the distance of 1,875 miles is 4.5 days.

We will learn how to calculate the value of such a unit from value of a multiple and thus the value of a multiple from value of a unit using the unitary method.

Now, as per the given question;

The total day taken by Rita to cover 1,250 miles is 3.

Thus,  1250 miles ----> 3 days

Let number of days taken by Rita to cover 1875 miles is 'x'.

So, 1875 miles ----> x

Then, the total distance will be

1875×(3) = 1250x

x = (1875×3)/1250

x = 4.5 days

Therefore, the total time taken by Rita to finish the distance of 1,875 miles is 4.5 days.

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The distance between Earth and the moon is 3.8 x 10^3 Kilometers. The time taken to travel this distance was 2.1 x 10^3 Minutes.

The formula to calculate speed is Speed = distance/time.

So, the speed of Luna I was 3.6 x 10^3 / 2.1 x 10^3 Kilometers/Mintues.

Answer:

Part a =

The distance between Earth and the moon is 3.8 x 10^5  kilometers. The time taken to travel this distance was 2.16 x 10^3 minutes.

The formula to calculate speed is speed = distance/time.

So, the speed of Luna I was 3.8 x 10^5/2.16 x 10^3  kilometers/meters.

Part b =

The expression from part A is 3.8 x 10^5/2.16 x 10^3 kilometers/meters. Break the expression into the product of two fractions, one fraction for the first factors and the other for the powers of 10.

3.8/2.16 x 10^5/10^3

Part c =

3.8/2.16 x 10^5/10^3

Using division, the value of the first fraction is 3.8/2.16 = 1.759 = 1.76.

Using the properties of exponents, the value of the second fraction is 10^5/10^3 = 10^5 x 10^-3 = 10^ 5 - 3 = 10^2.

3.8/2.16 x 10^5.10^3 = 1.76 x 10^2

Part d =

The value 1.76 x 10^2 is written in scientific notation. So, the average speed of Luna I was 1.76 x 10^2 kilometers/minute.

Step-by-step explanation:

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