As a block of ice melts, its weight changes from 1.5 lbs to .25lbs. This change takes a half of an hour. At what rate does the weight of the ice change?

The equation showing y as a function of x is given as y = -x - 2

An equation is an expression relating two or more numbers and variables.

The standard form of a linear equation is:

Ax + By = C

where A, B and C are constants

The slope - intercept form of a linear equation is:

y = mx + b

Where m is the rate of change(slope) and b is the y intercept.

The graph passes through points (-2, 0) and (0, -2). Hence, the equation is::

y - 0 = [(-2-0)/(0 - (-2)](x - (-2))

y = -1(x + 2)

y = -x - 2

a) When the input is -3, that is x = -3:

y = -(-3) - 2 = 1

The output is 1 when the input is -3

b) When the output is 2, that is y = 2:

2 = -x - 2

-x = 4

x = -4

The input is -4 when the output is 2

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Answer:

16x+6

Step-by-step explanation:

5x+2+3x+1+5x+2+3x+1 =

16x+6

Answer:

16x + 2

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Perimeter of a rectangle}\\\\$P=2(w+l)$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width. \\\phantom{ww}$\bullet$ $l$ is the length.\\\end{minipage}}[/tex]

Given expressions:

To write an expression for the perimeter of the rectangle, substitute the given expressions for the width and length into the perimeter formula:

[tex]\begin{aligned}\implies \textsf{Perimeter} &=2\left(5x+2+3x-1 \right)\\ &= 2(5x+3x+2-1)\\&=2(8x+1)\\&=16x+2\end{aligned}[/tex]

The probability that a student studied for exactly 1 hour is 0.23.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It deals with the numerical estimates of the chance that an event will occur.

In this case the group of students was surveyed in a middle school class and they were asked how many hours they work on math homework each week.

The probability that a student studied for exactly 1 hour will be:

Number of students that studied for 1 hour / Total number of students

= 8 / 35

= 0.23

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The solution to the trigonometric equation is x = ( 3π/4 ) , x = ( 7π/4 )

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin (-θ) = -sin (θ)

csc (-θ) = -csc (θ)

cos (-θ) = cos (θ)

sec (-θ) = sec (θ)

tan (-θ) = -tan (θ)

cot (-θ) = -cot (θ)

In the first quadrant, sin, cos and tan are all positive.

In the second quadrant going anti-clockwise, only sin is positive.

In the third quadrant going anti-clockwise, only tan is positive.

In the fourth quadrant going anti-clockwise, only cos is positive

Given data ,

Let the trigonometric equation be represented as A

Now , the value of A is

cot ( x - π/2 ) = 1   be equation (1)

On simplifying the equation , we get

cot ( - ( π/2 - x ) ) = 1

Now , cot (-θ) = -cot (θ)

So , - cot ( π/2 - x ) = 1

And , the value of cot ( π/2 - θ ) = tan θ

Substituting the values in the equation , we get

-tan x = 1 over the interval [ 0 , 2π ]

The value of x for -tan x = 1 is given by x = ( 3π/4 ) + nπ

when n = 1

x = ( 7π/4 )

So , the values of x are ( 3π/4 ) and ( 7π/4 )

Hence , the solutions are ( 3π/4 ) and ( 7π/4 )

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(a) We know that 30% of the members of the club are female and 20% of these females own cars, and 30 female members own cars.

We can use this information to calculate the total number of female members in the club.

If 30% of the members are female and 20% of these females own cars,

then 20/100*30 female members = 6% of the total members own cars.

This means that 6% of the total members are female members who own cars.

Therefore, 30 female members / 6% = 500 female members.

So there are 500 female members in the club.

(b) If 30% of the members are female, then the total number of members is (100/30)*500 female members = 1666.67 members

(c) To increase the percentage of female members to 37.5%, we need to calculate the number of additional female members required to reach this goal. The current percentage of female members is 30% and we want to increase it to 37.5%. Therefore, we need an additional 37.5-30 = 7.5%. If the current number of female members is 500, to increase the percentage by 7.5%, we need an additional of 7.5/100*1666.67 = 125 additional female members.

I'm pretty sure the answer is 5280 feet

Answer: 5,280 Feet (1.609 km)

Step-by-step explanation: Why, the distance of 1 mile is equal to 5,280 feet (1.609 km).   It originated from the Roman mile passus, or “thousand paces,” which measured 5,000 Roman feet. I hope this helps!

Answer:

625, 125, 25, 5

Step-by-step explanation:

390625, 78125, 15625, 3125

We need to find out the relationship between a number and the previous number.

We can tell that there is no common difference since 78125 - 390625 cannot possibly equal 3125 - 15625.

We can try to check if this is a geometric sequence.

78125/390625 = 0.2

15626/78125 = 0.2

3125/15625 = 0.2

Each number is 1/5 of the previous number.

3125/5 = 625

625/5 = 125

125/5 = 25

25/5 = 5

Answer: 625, 125, 25, 5

The required inequality is x ≤ 5.09, where x is the number of outfits. Rashon can buy at most 5 outfits while staying within his budget.

To determine the number of biking outfits Rashon can buy while staying within his budget, you can set up an inequality using the information provided.

First, calculate the total cost of the reflectors and gloves:

3 reflectors × $10.78 + $32.64 = $38.34 + $32.64 = $71

Then, subtract the cost of the bicycle, reflectors, and gloves from Rashon's budget: $780 - $481.28 - $71 = $227.72

Now, you can use this remaining amount to determine the number of biking outfits Rashon can buy.

Let x be the number of outfits he can buy

You can set up an inequality as follows:

44.95x ≤ $227.72

Dividing both sides by 44.95:

x ≤ 5.09

However, since the number of outfits is an integer, he can only buy 5 outfits at most.

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When writing a number greater than or equal to 1 in scientific notation, the exponent of the power of 10 will be positive.

In scientific notation, a number is represented as a coefficient multiplied by a power of 10. For example, the number 12,000 can be written as 1.2 x 10⁴ in scientific notation.

When the number is greater than or equal to 1, the coefficient will be greater than or equal to 1 and less than 10. The exponent of the power of 10 will indicate the number of places the decimal point must be moved to the right to get the original number.

Since the number is greater than or equal to 1, the decimal point must be moved to the right, resulting in a positive exponent. So, when writing a number greater than or equal to 1 in scientific notation, the exponent of the power of 10 will always be positive.

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At 2.5 seconds the ball reach its maximum height.

And, Its maximum height will be 25 feet.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation that describes the height (h) of a ball that is thrown straight up as a function of the (t) that the ball has been in the air is,

⇒ h = 40t - 16t²

So, For the time does the ball reach its maximum height, we can put h = 0, so we get;

⇒ h = 40t - 16t²

⇒ 40t - 16t² = 0

⇒ 16t² - 40t = 0

⇒ t (16t - 40) = 0

⇒ 16t - 40 = 0

⇒ 16t = 40

⇒ t = 40/16

⇒ t = 2.5 seconds

Now, The height function is a quadratic function which has the zeroes at  t = 0 and t = 2.5.

So, It has the maximum at x = midpoint between the roots 0 and 2.5, i.e. 1.25 seconds.

Hence, Substitute this value t = 1.25 seconds into the given height function, we get;

⇒ h = 40t - 16t²

⇒ h = 40 × 1.25 - 16 (1.25)²

⇒ h = 50 - 25

⇒ h = 25 feet

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The equation showing the relation between shorter and longer skirt is 3s+4t = 140.

Given that the Scottish dance team used 140 yards of tartan to make dancing skirts.

The skirt pattern for the shorter members is 3- yards of fabric, and the skirt pattern for the taller members is 4 yards of fabric.

So, we need to find the equation represents the relationship between the number of short skirts and the number of long skirts that were made,

So, if there are s short skirts and t long skirts,

So,

The relation will be =

3s + 4t = 140

Hence the equation showing the relation between shorter and longer skirt is 3s+4t = 140.

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The expression that is equivalent to 2(b+3c) is C.

2(b) + 2(3c).

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

The expression 2(b + 3c) will be:

= 2b + 6c

3(b + 2c) will be:

= 3b + 6c

2(b) + 2(3c) will be:

= 3b + 6c

The correct option is C since they gave same value.

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Answer:it is 900 because that’s a number that is irrational

Step-by-step explanation:

No, these measurements do not form a triangle. The sum of any two sides of a triangle must be greater than the third side. In this case, 7 cm + 8 cm = 15 cm, which is not greater than the third side, 9 cm.

A triangle is a three-sided polygon, and all three sides must meet certain criteria in order to form a triangle. Specifically, the sum of any two sides must be greater than the third side. In this case, the given measurements are 7 cm, 8 cm, and 9 cm. When adding the 7 cm and 8 cm together, the sum is 15 cm, which is not greater than the third side, 9 cm. Therefore, these measurements do not form a triangle. To determine if a triangle can be formed with any given measurements, one must sum any two sides and ensure that the sum is greater than the third side. If the sum is not greater than the third side, then the measurements do not form a triangle.

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Answer: is A

Step-by-step explanation:

The value of x in the quadrilateral is 23°

Geometry is a branch of mathematics that deals with shapes, angles, dimensions and sizes of different things we see in everyday life

The interior angles of the quadrilateral are :

180 - (x+16)°          (sum of angles on a straight line)

180 - (3x-1)°           (sum of angles on a straight line)

180 - 6x°              (sum of angles on a straight line)

180 - 5x°              (sum of angles on a straight line)

Since the sum of the interior angles of a quadrilateral is 360°. We have:

180-(x+16)° + 180-(3x-1)° + 180-6x° + 180-5x° = 360°

180 - x - 16 + 180 - 3x + 1 + 180 - 6x + 180 -5x = 360

705 - 15x = 360

15x = 705 - 360

15x = 345

x = 345/15

x = 23°

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The communicable diseases that are known for targeting the human respiratory system are C. I, II, and III.

There are several diseases that target the human respiratory system and a lot of them are communicable . One of the most popular of these is the Coronavirus infection which forced the world into various lockdowns to prevent its spread.

Then there is Influenza II which is one of the most communicable diseases in existence. It also attacks the human respiratory system much like Tuberculosis III.

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Answer:

4^3

Step-by-step explanation:

4x4 would be squared aka 4^2 but since theres three itd be cubed aka 4^3

These sides also follow the same ratio a/2 : (a√3)/2: a

We get 1:√3:2. This is the 30-60-90 triangle theorem.

Now, According to the question:

Let's consider an equilateral triangle ABC with a side length equal to 'a'.

Now, draw a perpendicular from vertex A to side BC at point D of the triangle ABC. The perpendicular in an equilateral triangle bisects the other side.

Triangle ABD and ADC are two 30-60-90 triangles. Both the triangles are similar and right-angled triangles. Hence, we can apply the Pythagoras theorem to find the length AD.

[tex](AB)^2 = (AD)^2 + (BD)^2[/tex]

[tex]a^2 = (AD)^2 + (a/2)^2[/tex]

[tex]a^2 - (a/2)^2 = (AD)^2[/tex]

[tex]3a^2/4 = (AD)^2[/tex]

(a√3)/2 = AD

AD = (a√3)/2

BD = a/2

AB = a

These sides also follow the same ratio a/2 : (a√3)/2: a

Multiply by 2 and divide by 'a',

(2a)/(2a) : (2a√3)/(2a): (2a/a)

We get 1:√3:2. This is the 30-60-90 triangle theorem.

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The required values of u = 21° and v = 2 units in the given triangle.

A triangle is a closed shape composed of three angles, three sides, and three vertices. It is one of the most fundamental geometric forms and is represented by the symbol Δ.

The triangle is given in the shown figure, as follows:

We have to determine the value of u and v

In ΔHGF,

∠G = 67°

∠F = 92°

As we know that the sum of interior angles is always 180 degrees in the triangles.

So, ∠u + ∠G + ∠F = 180°

u +  67° + 92° = 180°

u + 159° = 180°

u = 21°

We can see that the bisector HF divides into equal parts EF and FG.

So, EF = FG

This means v = 2

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The graph of the reflected function: g(x) = 3^(-x) can be seen in the image at the end.

First, for any function y = f(x), a reflection across the y-axis is written as:

g(x) = f(-x)

So we only change the sign of the argument of the function.

The graphed function is the parent function:

f(x) = 3^x

A reflection across the y-axis, will give the new function:

g(x) = f(x) = 3^(-x)

The graph of this will be like the graph of f(x) but reflected across the y-axis, like the graph below.

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The statements that are true about the data in the graph include the following:

B. If 200 students were surveyed, 28 would choose art as their favorite subject.

C. If 400 students were surveyed, 64 would chose social studies as their favorite subject.

In Mathematics, a pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors or sections.

Assuming 200 students were surveyed at 14%, the number of students who would choose art as their favorite subject can be calculated as follows;

Number of students for arts = 14/100 × 200

Number of students for arts = 0.14 × 200

Number of students for arts = 28 students.

Assuming 400 students were surveyed at 16%, the number of students who would choose social studies as their favorite subject can be calculated as follows;

Number of students for social studies = 16/100 × 400

Number of students for social studies = 0.16 × 400

Number of students for social studies = 64 students.

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When a linear force works, it produces In the domain of rotation, work is accomplished by a torque delivered through an angle . work = (torque) * (angle).

A linear equation is one that has the form y=mx+b in algebra.The slope is B, and the y-intercept is m. Since y and x are variables, the previous sentence is frequently referred to as a "linear equation with two variables." Bivariate linear equations are linear equations with two variables. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.

given

When a linear force works, it produces In the domain of rotation, work is accomplished by a torque delivered through an angle .

work = (torque) * (angle). Work is defined as force times distance.

The angle of rotation is calculated by dividing the length of the arc by the radius of curvature. 360° is equal to two revolutions, or two rad.

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Answer:

L.S = R.S ( see below)

Step-by-step explanation:

[tex]7x + 28 = -6x-24\\13x = -52\\x = -4[/tex]

L.S

[tex]7(-4)+28 = 0[/tex]

R.S

[tex]-6(-4) - 24 = 0[/tex]

L.S = R.S

x = -4 is correct

The shorter side of the tile is 12.5 inches and the longer side is 15 inches.

Answer: To find point Q on the line segment PR that partitions it into the segments PQ and QR in the ratio 4:5, we need to use the concept of proportion.

We can set up the proportion as:

PQ / QR = 4 / 5

To find the actual point Q on the line segment PR, we need to know the coordinates of points P and R. Without them, it is not possible to find the point Q. Once we have the coordinates of P and R, we can use the proportion above to find the coordinates of Q.

Alternatively, we can use the concept of a "partitioned ratio" which is a way to split a line segment into a certain ratio. It is found by adding the two ratios together and then dividing the length of the line segment by that number. In this case (4+5 =9) and then PQ = (4/9) * PR and QR = (5/9) * PR.

Step-by-step explanation:

Answer:

17/20

Step-by-step explanation:

3/5 + 1/4

The common factor is 20, so we have

12/20 + 5/20 = 17/20

We can't simplify 17/20 any further, so the answer is 17/20

Answer:

10^2

Step-by-step explanation:

I hope this helps you

The volume of the step and the surface area of the steps are 120000 cm³ and 26,400 cm² respectively.

What is a Rectangular Prism?

A rectangular prism is a three-dimensional shape that consists of six faces. The two faces are at the top and bottom and the other faces are lateral faces.

The given steps can be divided into 3 rectangular boxes each with length, l = 1 m = 100 cm, width, w = 20 cm, and height, h = 20 cm.

The volume of a rectangular box = l × w × h

= 100 × 20 × 20

= 40000 cm³

Volume of 3 rectangular boxes = 3 × 40000 cm³

= 120000 cm³

Surface area of a rectangular box = 2 (lw + lh + wh)

= 2 [(100 × 20) + (100 × 20) + (20 × 20)]

= 2 [2000 + 2000 + 400]

= 2 [4400]

= 8800 cm²

The surface area of 3 rectangular boxes = 3 × 8800

= 26,400 cm²

Hence, the volume of the steps is 120000 cm³ and the surface area of the steps is 26,400 cm².

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the 1srt one

Step-by-step explanation: