rate of change between (-4,-12)and (2,4)

Answer:

BF×BA= DF×CF

9×2=3x

x = 6

AB=9

CD=11

Rounding 473,615 to the nearest hundred gives us 473,600.

We have,

Rounding a number to the nearest hundred means that you are looking at the digit in the tens place of the number.

If that digit is 5 or greater, you round up the digit in the hundreds place, and if it is less than 5, you keep the digit in the hundreds place the same.

In the case of 473,615, the digit in the tens place is 1, which is less than 5. So we keep the digit in the hundreds place (3) the same and round the remaining digits to zero.

Thus,

Rounding 473,615 to the nearest hundred gives us 473,600.

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Answer:

Step-by-step explanation:

slope is rise over run or y over x

Let m be the slope

On this case, simply count the units for both x and y from tip to tip of the line segment

m = y/x

direction of the line is up and right so the sign is both positive

m = 4/1

m = 4

m = y/x

direction of the line is down and right so y is negative and x is positive

m = -3/4

Daisy would be paid $155 if she works 13 hours in a day.

If Daisy works for up to 8 hours in a day, she is paid a flat rate of $10 per hour, so her earnings for the day would be:

Earnings = 10 × 8 = $8

If Daisy works for more than 8 hours in a day, then her earnings for the extra hours are calculated at a rate of 1.5 times her hourly wage, which is $15 per hour.

So, if Daisy works x hours in a day, where x is greater than 8, then her net earnings for the day can be expressed as:

Earnings = 80 + (x - 8) × 15

This expression takes into account the first 8 hours of work, which are paid at a flat rate of $10 per hour, and the extra hours, which are paid at a rate of $15 per hour

If Daisy works 13 hours in a day, then her net earnings for the day would be:

Earnings = 80 + (13 - 8) × 15 = 80 + 5 × 15 = $155

So Daisy would be paid $155 if she works 13 hours in a day.

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The required heat energy required to boil 75.25 g of ethanol is 62.1835 kJ.

The heat energy required to boil a substance can be calculated using the formula:

Q = m × Hv

where Q is the heat energy, m is the mass of the substance, and Hv is the heat of vaporization. From the given, we have m = 75.25 g and Hv = 0.826 kJ/g

Substituting the given values, we get:

Q = 75.25 g × 0.826 kJ/g

Q = 62.1835 kJ

Where kJ (kilojoule) is the unit of heat.

Therefore, the heat energy required to boil 75.25 g of ethanol is 62.1835 kJ.

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Find three additional polar representations of the point, using −2π<θ<2π. (Enter your answers in order from smallest to largest first by r-value, then by θ-value.) (r,θ)= ( (r,θ)r= ( (r,θ)= ( Question: That's it! Find three additional polar representations of the point, using −2π<θ<2π.

Answer:

where do you live

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

To solve this problem, we can use the following formula:

(amount of solution 1) + (amount of solution 2) = total amount of mixture

We can also set up equations for the amount of acid in each of the solutions:

0.25(amount of solution 1) + 0.65(amount of solution 2) = 0.4(total amount of mixture)

We have two equations and two unknowns, so we can solve for the amounts of each solution. Let's set x to be the amount of the 25% acid solution and y to be the amount of the 65% acid solution. Then we have:

x + y = 80                (equation 1)

0.25x + 0.65y = 0.4(80)   (equation 2)

We can simplify equation 2 by multiplying everything by 100, to get rid of the decimals:

25x + 65y = 3200

Now we can solve this system of equations. One way to do this is to solve equation 1 for one of the variables, and substitute it into equation 2. We get:

x = 80 - y

25(80 - y) + 65y = 3200

2000 - 25y + 65y = 3200

40y = 1200

y = 30

So we need 30 liters of the 65% acid solution. To find the amount of the 25% acid solution, we can substitute y = 30 into equation 1:

x + 30 = 80

x = 50

So we need 50 liters of the 25% acid solution. Therefore, we need 50 liters of the 25% acid solution and 30 liters of the 65% acid solution to produce 80 liters of a 40% acid solution.

An exponential function that best models the data include the following: A. [tex]r(x) = 223.06(1.09)^x[/tex]

In this scenario, the Company Time, x (months) would be plotted on the x-axis (x-coordinate) of the scatter plot while the Net Revenue, r(x (millions of dollars) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an exponential equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the Company Time, x (months) and the Net Revenue, r(x (millions of dollars), an exponential equation for the line of best fit is given by:

[tex]r(x) = 223.06(1.09)^x[/tex]

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The volume of the rectangular pyramid is 20800 m³.

The volume of the pyramid can be found as follows:

The pyramid is a rectangular base pyramid. Therefore,

volume of the pyramid = 1 / 3 Bh

where

Therefore,

B = 52 × 30

B = 1560 m²

volume of the pyramid = 1 / 3 × 1560 × 40

volume of the pyramid = 62400 / 3

volume of the pyramid = 20800 m³

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When C = 20, F is equal to 68, and when F = 100, C is approximately 37.78.

Given the equations:

C = (5/nine) * (F - 32)

F = (9/5) * C + 32

If we replace specific values for F or C, we will locate the corresponding price for the opposite variable. Here are some examples:

Let's expect C = 20. Substituting this fee into the second equation:

F = (9/five) * 20 + 32

F = 36 + 32

F = 68

Therefore, when C = 20, F is equal to sixty-eight.

Let's expect F = a hundred. Substituting this cost into the primary equation:

C = (five/9) * (100 - 32)

C = (5/9) * 68

C = 340/9

C ≈ 37.78

So, whilst F = one hundred, C is approximately 37.78.

These examples exhibit how you may locate the values of F and C by using substituting one variable into the equations and fixing for the alternative variable. Remember, you could choose any unique values for F or C and perform the calculations consequently.

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The correct question is:

"C=5/9 (f -32)

F= 9/5C + 32

Solve for F and C"

Answer:

Let x be the cost of the pass.

Then the cost of the souvenir is (2/3)x.

The cost of the burger is (1/4) of the cost of the souvenir, which is (1/4)(2/3)x = (1/6)x.

The total cost of the items is x + (2/3)x + (1/6)x = (11/6)x.

Tim had $2.00 left over after buying these items, so we can set up the equation:

(11/6)x + 2 = 40.50

Solving for x, we get:

x = 18

Therefore, the cost of the pass is $18, the cost of the souvenir is (2/3)($18) = $12, and the cost of the burger is (1/6)($18) = $3.

The value of the y-intercept of the graph of the function h(x) = 12.3(4.9)^x is 12.3.

To determine the value of the y-intercept of the graph of the function[tex]h(x) = 12.3(4.9)^x,[/tex] we need to find the value of h(0) since the y-intercept corresponds to the point where the graph intersects the y-axis (x = 0).

Substituting x = 0 into the function, we have:

[tex]h(0) = 12.3(4.9)^0[/tex]

Since any number raised to the power of 0 is equal to 1, we have:

h(0) = 12.3(1)

Multiplying 12.3 by 1 gives us:

h(0) = 12.3

Therefore, the value of the y-intercept of the graph of [tex]h(x) = 12.3(4.9)^x[/tex] is 12.

The y-intercept represents the value of the function when x = 0, which in this case is 12.3.

It is the point where the graph crosses the y-axis.

This means that when there is no exponential growth or decay (x = 0), the value of the function is 12.3. As x increases or decreases, the function will grow or decay exponentially, but at x = 0, it starts with a value of 12.3.

The graph of this function would start at the point (0, 12.3) and then either increase or decrease exponentially depending on the value of the base (4.9 in this case).

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Using the formula of compound interest, the number of years is 7.6 years

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.

The formula of compound interest is given as;

[tex]A = P(1 + \frac{r}{n} )^n^t[/tex]

But in this case, the interest was compounded continuously

[tex]A = Pe^r^t[/tex]

Substituting the values into the formula;

[tex]7450 = 5500e^(^0^.^0^5^2^5 ^* ^t^)[/tex]

Solving for t;

t = 7.6 years

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Once we have those values, we can plug them into the formula and calculate the area of trapezium PQRS. And that's it!

To start, let's quickly review what a trapezium is. A trapezium, also known as a trapezoid, is a four-sided geometric shape with two parallel sides (called the bases) and two non-parallel sides (called the legs). The distance between the two parallel sides is known as the height.
In order to find the area of a trapezium, we use the formula:
Area = (sum of bases x height) / 2
So for trapezium PQRS, we need to identify the length of its two bases and its height in order to use this formula.
Without any specific measurements given in your question, I'll assume we don't have any numerical values to work with. Instead, let's use variables to represent the length of each base and the height.
We can call the shorter base PQ, and the longer base SR. Let's say PQ has a length of 'a' units, and SR has a length of 'b' units. For the height, let's call it h.
So, the formula for the area of trapezium PQRS becomes:
Area = ((a + b) x h) / 2
This means that to find the area of the trapezium, we simply need to know the lengths of the two bases (a and b) and the height (h).
Once we have those values, we can plug them into the formula and calculate the area of trapezium PQRS. And that's it!

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Answer:

First, let's calculate the total cost of buying the shares:

1000 shares * $15.23/share = $15,230

Next, we need to calculate the commission paid to the broker for buying the shares:

$15,230 * 0.0075 = $114.23

So, the total cost of buying the shares including the commission is:

$15,230 + $114.23 = $15,344.23

Now, let's calculate the total revenue from selling the shares:

1000 shares * $18.78/share = $18,780

We also need to calculate the commission paid to the broker for selling the shares:

$18,780 * 0.0075 = $140.85

So, the total revenue from selling the shares after the commission is:

$18,780 - $140.85 = $18,639.15

The total profit from buying and selling the shares is:

$18,639.15 - $15,344.23 = $3,294.92

The rate of return is the profit divided by the total cost, expressed as a percentage:

($3,294.92 / $15,344.23) * 100% = 21.5%

Therefore, Omar's rate of return is 21.5%.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since the given figure is a right triangle, we can use Pythagorean Theorem

where c² = a² + b²

c = 15

15² = a² + b²

Since 15 is the hypotenuse, we can then say that the possible legs of the triangle are less than 15.

225 - a² = b²

we will do trial and error

let a be 14

225 - 14² = b²

b = √29

a = 14cm, b = √29cm, c = 15cm

let a be 13

225 - 13² = b²

b = 2√14

a = 13cm, b = 2√14cm, c = 15cm

let a be 12

225 - 12² = b²

b = 9

a = 12cm, b = 9cm, c = 15cm

You can solve for other possible values using the same process as above. Since there are no conditions whether the lengths of the legs should be a whole number or not then the above dimensions can be considered. If you're looking for an answer that consists of whole numbers then the answer would be a = 12cm, b = 9cm and c = 15cm

Answer:

720 m^2

Step-by-step explanation:

Solution:

The formula for the surface area of a triangular prism is:

Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)

= (S1 +S2 + S3)L + bh

where,

Given:

side 1 (S1) : 5 m

side 2(S2): x m

side 3(S3): 12 m

length (l)=22m

Here we need to find side 2, we can easily find it using Pythagoras' theorem.

a^2+b^2=c^2

5^2+12^2=x^2

x^2=169

x=[tex]\sqrt{169}=13 m[/tex]

therefore, side 2 is 13 m.

Substituting value in the formula

Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)

= (S1 +S2 + S3)L + bh

Surface Area=(5+13+12)*22+5*12= 720 m^2

Answer:

720 m²

Step-by-step explanation:

The given diagram shows a triangular prism.

A triangular prism consists of two congruent triangular bases and three rectangular faces connecting these bases.

To calculate the surface area of the triangular prism, we first need to calculate the length of the hypotenuse of the right triangular base. To do this, we can use Pythagoras Theorem:

[tex]\begin{aligned}\sf Hypotenuse\;of\;triangular\;base&=\sqrt{5^2+12^2}\\&=\sqrt{25+144}\\&=\sqrt{169}\\&=13\; \sf m\end{aligned}[/tex]

The surface area of a triangular prism is the sum of the areas of all its faces. Therefore:

[tex]\begin{aligned}\sf Total\;surface\;area&=2\left(\dfrac{1}{2} \cdot 5 \cdot 12\right)+12\cdot 22+5 \cdot 22+13 \cdot 22\\\\&=60+264+110+286\\\\&=720\; \sf m^2\end{aligned}[/tex]

Therefore, the total surface area of the given triangular prism is 720 m².

The appropriate measure of variability for this data is the IQR, and its value is 250.

We have,

The range is not the best measure of variability for this data since it only takes into account the maximum and minimum values and does not consider the other values in the dataset.

The IQR (interquartile range) is a better measure of variability since it gives a measure of the spread of the middle 50% of the data.

To find the IQR, we first need to find the median:

Arranging the data in order, we get:

200, 450, 600, 650, 700, 800

The median is the middle value, which is 650.

The first quartile (Q1) is the median of the lower half of the data:

Q1 = median(200, 450, 600) = 450

The third quartile (Q3) is the median of the upper half of the data:

Q3 = median(700, 800, 650) = 700

The IQR is the difference between Q3 and Q1:

IQR = Q3 - Q1

= 700 - 450

= 250

Therefore,

The appropriate measure of variability for this data is the IQR, and its value is 250.

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The table that represents a linear function is the second table.

A linear function is written as:

y = ax + b

We can see that for each increase of 1 unit in the value of x, the value of y increases by a units.

Then we need to identify the table where the increases in the y-value are constant.

With that in mind we can discard options 1, 3 and 4.

Wher particularly options 1 and 4 show that sometimes the y-value increases and sometimes decreases, that is why we discard these.

Then the remainign option must be the correct one, which is the second option.

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Melissa will drink 7/32 gallons more water than Holden after hiking 14 miles.

Holden drinks 1/8 gallon of water every 2 miles, so after hiking 14 miles, he would have drank (14/2) * (1/8) = 7/16 gallons of water.

Melissa drinks 3/8 gallon of water every 2 miles, so after hiking 14 miles, she would have drank (14/2) * (3/8) = 21/32 gallons of water.

The difference in the amount of water they drink is:

21/32 - 7/16 = 21/32 - 14/32 = 7/32 gallons

Therefore, Melissa will drink 7/32 gallons more water than Holden after hiking 14 miles.

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Answer:

11.49

Step-by-step explanation:

a^2+b^2=c^2

think of this as a triangle, we are going to use Pythagorean theorem.

the hypotenus is 14 ft and one of the legs is 8 ft. so the other leg is x

8^2 + x^2 = 14^2

64 + x^2 = 196

subtract the 64 on both sides

x^2 = 132

to counter the square we square root it

so x = the square root of 132 which comes out to a decimal

11.489....

rounded it would be 11.49

hope this helped

The value of y at the indicated point is √3.

In Mathematics and Geometry, a square root function refers to a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.

In this scenario and exercise, we would determine the y-value by substituting the x-value into the given square root function as follows;

y² = x - 3

By taking the square root of both sides of the square root function, we have:

y = √(x - 3)

When x = 6, the y-value is given by;

y = √(6 - 3)

y = √3

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The large box weighs 18.75 kg, and the small box weighs 15.75 kg.

We have,

Let's assume the weight of a large box is L kg, and the weight of a small box is S kg.

According to the given information, we can create the following equations:

Equation 1: 3L + 5S = 135 (1st delivery)

Equation 2: 9L + 7S = 279 (2nd delivery)

To solve these equations, we can use a method called "elimination" or "substitution."

Multiply Equation 1 by 3 and Equation 2 by 1, so that the coefficients of L will be the same:

Equation 1: 9L + 15S = 405

Equation 2: 9L + 7S = 279

Now, we can subtract Equation 2 from Equation 1 to eliminate L:

(9L + 15S) - (9L + 7S) = 405 - 279

Simplifying:

8S = 126

Divide both sides of the equation by 8:

S = 126/8 = 15.75

So, the weight of a small box (S) is 15.75 kg.

Now,

substitute the value of S into Equation 1 to find the weight of a large box (L):

3L + 5(15.75) = 135

3L + 78.75 = 135

3L = 135 - 78.75

3L = 56.25

Divide both sides of the equation by 3:

L = 56.25/3 = 18.75

So,

The weight of a large box (L) is 18.75 kg.

Thus,

The large box weighs 18.75 kg, and the small box weighs 15.75 kg.

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From the given statements, the first statement which states, the melting point of mercury is 32 degrees cooler than the melting point of bromine is correct.

Given that, the melting point of mercury = -39

the melting point of bromine = -7

the difference between both melting points = -39 - (-7) = -32

In math, as we go to the negative values, the value of the number decreases.  [-7 > -39]

From the above analysis, we can conclude that the melting point of mercury is 32 degrees cooler than the melting point of bromine. So, the option A which is the first statement is correct from the given image.

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Answer: 29.9986-----30.0 degrees

Step-by-step explanation:

x = [tex]tan^-^1(5.6/9.7)\\\\toa[/tex]

[tex]\tan(x )=\cfrac{\stackrel{opposite}{5.6}}{\underset{adjacent}{9.7}} \implies \tan^{-1}(~~\tan( x )~~) \approx \tan^{-1}\left( 0.58 \right) \\\\\\ x \approx\tan^{-1}\left( 0.58 \right)\implies x \approx 30.0^o[/tex]

Answer:

121

Step-by-step explanation:

firstly you arrange the numbers in ascending order the number in the middle is considered to be the median

The image polygon P'S'R'T' has vertices P'(-5, 1), S'(0, -1), R'(3, -2), and T'(-2, -4).

To determine the image vertices of P' when the preimage is rotated 90° counterclockwise, we can use the following formula:

(x', y') = (-y, x)

where (x, y) are the coordinates of the preimage vertex, and (x', y') are the coordinates of the image vertex after rotation.

Using this formula for each vertex of the polygon PSRT, we get:

For P(1, 5), rotating 90° counterclockwise gives us P'(-5, 1).

For S(1, 0), rotating 90° counterclockwise gives us S'(0, -1).

For R(-2, -3), rotating 90° counterclockwise gives us R'(3, -2).

For T(-4, 2), rotating 90° counterclockwise gives us T'(-2, -4).

Therefore, the image polygon P'S'R'T' has vertices P'(-5, 1), S'(0, -1), R'(3, -2), and T'(-2, -4).

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