Which statements are always true
about ABCD? Select all that apply.

The equation for the relation of sides of triangle can be obtained by similar triangle property.

Consider triangle ABC and triangle DBE.

Determine the ratio of corresponding sides of simillar triangle.

Thus similar triangle property is used to set up the equation.

The common ratio of the resulting sequence is 1.4.

Given that, the three terms are 60, 100 and 180.

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.

Let the same constant is added to the given number is x.

60+x, 100+x and 180+x

Now, the common ratio is

(100+x)/(60+x) = (180+x)/(100+x)

⇒ (100+x)(100+x)=(180+x)(60+x)

⇒ (100+x)²=10800+180x+60x+x²

⇒ 10000+200x+x²=10800+180x+60x+x²

⇒ 10000+200x=10800+180x

⇒ 20x=800

⇒ x=40

The three number are 100, 140 and 220

The common ratio is 140/100 =1.4

Therefore, the common ratio of the resulting sequence is 1.4.

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The correct statement regarding the measure of variability used to represent the data is given as follows:

The IQR of 10 is the most accurate to use, as the data is skewed.

The interquartile range of a data-set is given by the difference of the third quartile by the first quartile of the data-set.

It is the measure of variability to be used when a data-set contains outliers, or is skewed, as is the case for this problem.

The charity received 18 donations, hence the quartiles are given as follows:

Hence the IQR is given as follows:

IQR = 22.5 - 12.5

IQR = 10.

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The line's slope is \(\frac{1}{2}\) and the distance increases by 1 mile every 2 hours.

What is a good example of a line's slope?

The proportion of the increase in the y-value to the increase in the x-value may also be used to determine slope. For instance: We can get the slope of a line given two locations, P = (0, -1) & Q = (4,1) on the line.

A. Since the line's slope is 2, it follows that the y-variable, which is most likely distance, grows by 2 units for every increment in the x-variable, which is most likely time. The accurate statement is thus: speed is increased by Two miles per hour.

B. Since the line's slope is 2, it follows that the y-variable will drop by 2 units for every unit rise in the x-variable, which is most likely time. The accurate description is thus: speed drops by Two miles per hour.

C. If the line's slope is 1/2, the y-variable will rise by 1/2 unit for every increment in the x-variable, which is probably time. The precise description is that the distance grows by a mile every two hours.

D. If indeed the line's slope is 1/2, the y-variable will drop by 1/2 unit for every unit rise in the x-variable, which is probably time. The precise description is: distance shrinks by a mile every two hours.

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Answer: (3y² * dy/dx + 3x² * dy/dx - 9y) / 9.

Step-by-step explanation: To find dy/dx for the relation x³ + y³ = 9xy, we can use the chain rule. The chain rule states that if y is a function of x and x is a function of t, then the derivative of y with respect to t is equal to the derivative of y with respect to x times the derivative of x with respect to t.

In this case, we are given that y is a function of x and we want to find the derivative of y with respect to x. To do this, we can rewrite the given equation as follows:

x³ + y³ = 9xy

y³ = 9xy - x³

We can then take the derivative of both sides of the equation with respect to x to find dy/dx as follows:

3y² * dy/dx = 9y + 9x * dy/dx - 3x² * dy/dx

3y² * dy/dx = (9y + 9x * dy/dx) - 3x² * dy/dx

0 = (9y + 9x * dy/dx) - (3y² * dy/dx + 3x² * dy/dx)

0 = 9y + 9x * dy/dx - 3y² * dy/dx - 3x² * dy/dx

We can then solve this equation for dy/dx as follows:

0 = 9y + 9x * dy/dx - 3y² * dy/dx - 3x² * dy/dx

9x * dy/dx = 3y² * dy/dx + 3x² * dy/dx - 9y

9x * dy/dx = 3y² * dy/dx + 3x² * dy/dx - 9y

dy/dx = (3y² * dy/dx + 3x² * dy/dx - 9y) / 9x

dy/dx = (3y² * dy/dx + 3x² * dy/dx - 9y) / 9x

Therefore, the derivative of y with respect to x for the given equation is equal to (3y² * dy/dx + 3x² * dy/dx - 9y) / 9.

Answer

\(\frac{dy}{dx}\)

Step-by-step explanation:

Your welcome ;)

Answer:

9

Step-by-step explanation:

First, find x. Since x is the average of the three number, add the three up and then divided by three. Thus:

\(x=\frac{13+-16+6}{3}=3/3=1\)

y is the cube root of 8. Thus:

\(y=\sqrt[3]{8}=2\)

So:

\(x^2+y^3\\=(1)^2+(2)^3\\=1+8=9\)

Answer:

ljih

Step-by-step explanation:

Answer:

2/5 or the third one

Step-by-step explanation:

The first two are 1/2 after they are simplified and the second two are just below or just above one half, the last one is above and the third one is below.

Answer:

2/5

Step-by-step explanation:

Convert all fractions to have a common denominator

4, 10, and 5 can all be multiplied to equal 20

As a result, we will use 20 for the common denominator

What multiplied by 4 equals 20? 5 × 4 = 20

What multiplied by 10 equals 20? 2 × 10 = 20

What multiplied by 5 equals 20? 4 × 5 = 20

If we multiply this to the denominator, we must also multiply the same number to the numerator

Starting from left to right:

2 × 5 / 4 × 5 = 10/20

5 × 2 / 10 × 2 = 10/20

2 × 4 / 5 × 4 = 8/20

3 × 5 / 4 × 5 = 15/20

Compare: 10/20, 10/20, 8/20, 15/20

Which fraction has the smallest numerator?

8/20 as 8 is less than 15 and 10

Which fraction was 8/20? Check back to our work.

8/20 = 2/5

2/5 is the least

[~S & (R V S)] ≡ (Q ⊃ S) is true when A = T, S = F, R = F, and Q = T by substituting the propositional variables.

A truth table is a table used to determine the truth values of a compound proposition, which is a logical statement made up of simpler propositions using logical operators such as "and" (represented by "&"), "or" (represented by "V"), "not" (represented by "~"), conditional (represented by "⊃"), and biconditional (represented by "≡").

Let's substitute the given truth values for the propositional variables in the given statement:

[~F & (F V F)] ≡ (T ⊃ F)

Using the truth table for conjunction (represented by "&") and disjunction (represented by "V"), we can simplify the left-hand side of the equivalence:

[T & F] ≡ (T ⊃ F)

Using the truth table for conditional (represented by "⊃"), we can simplify the right-hand side of the equivalence:

F ≡ F

Since both sides of the equivalence have the same truth value, the statement is true.

Therefore, [~S & (R V S)] ≡ (Q ⊃ S) is true when A = T, S = F, R = F, and Q = T.

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Answer:

$1,422.87

Step-by-step explanation:

Answer: 1422.9

Step-by-step explanation:

Answer: 1%

Explanation: sorry if I’m wrong.

Answer:

6.12

Step-by-step explanation:

The work required to pump the water out of the spout is approximately 64,307,077 ft-lb

To find the work required to pump the water out of the spout, we need to calculate the weight of the water in the tank and then convert it to work using the formula: work = force × distance.

First, let's calculate the volume of water in the tank. The frustum of a cone can be represented by the formula: V = (1/3)πh(r1² + r2² + r1r2), where r1 and r2 are the radii of the two bases and h is the height.

Given r1 = 3 ft, r2 = 6 ft, and h = 12 ft, we can calculate the volume:

V = (1/3)π(12)(9 + 36 + 18) = 270π ft³

Now, we can calculate the weight of the water using the density of water:

Weight = density × volume = 62.5 lb/ft³ × 270π ft³ ≈ 53125π lb

Next, we convert the weight to force by multiplying it by the acceleration due to gravity (32.2 ft/s²):

Force = Weight × acceleration due to gravity = 53125π lb × 32.2 ft/s² ≈ 1709125π lb·ft/s²

Finally, we can calculate the work by multiplying the force by the distance. Since the water is being pumped out of the spout, the distance is equal to the height of the frustum, which is 12 ft:

Work = Force × distance = 1709125π lb·ft/s² × 12 ft ≈ 20509500π lb·ft ≈ 64307077 lb·ft

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The pair of corresponding angles in the image given at the end of the answer is of:

B. 1 and 5.

Corresponding angles appear when there are two parallel lines being cut by a transversal line.

The corresponding angles are the angles that are in the same position relative to the transversal and also relative to different parallel lines.

From the image given at the end of the answer, the lines are given as follows:

Then the corresponding angles are listed as follows:

Meaning that option B is correct.

The image is given at the end of the answer.

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Emily funded $6000 in stocks and $12,000 in bond funds. She also funded the remaining  $2,000 in her savings account.

Future value = $20,000

Simple interests rate = 1.5%

The return rate on bonds= 4.5%

The return rate on stocks = 6.2%

Total amount made on invests =  $942

Time period = 1 year

Let us assume that the amount of money Emily invested = x

Amount invested in stock = y

If the amount is twice = 2y

The interest earned = x * 0.015

Interest on bond = 2y * 0.045

Interest on stocks = y * 0.062

The equation will be:

(x * 0.015) + (2y * 0.045) + (y * 0.062) = 942

0.015x + 0.152y = 942  ------ Equation 1

Total future value is given as $20,000

x + 2y + y = 20000

x + 3y = 20000

x = 20000 - 3y

Substituting the x value in the first equation:

0.015(20000 - 3y) + 0.152y = 942

300 - 0.045y + 0.152y = 942

0.107y = 642

y = 6000

Therefore, we can conclude that Emily funded $6000 in stocks and $12,000 in bond funds.

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The volume of air of a sphere with diameter 9 centimeters is 381.51 cubic centimeters

The formula for the volume of a sphere is:

V = (4/3)πr³

where r is the radius of the sphere.

The diameter of the sphere is 9 cm, which means the radius is half of that:

r = 9/2 = 4.5 cm

Substituting this value into the formula, we get:

Volume = (4/3)π(4.5)³

Volume = (4/3)×3.14 × 91.125

Volume = 381.51 cubic centimeters

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Answer:

The man

Step-by-step explanation:

Let's say the hotel cost $12400(just an example...)

So the website will show $12400. And the man needs to pay $12400.

Since one pound is 1.24 dollars, 12400 dollars will be 12400/1.24=10000 pounds.

12400>10000, so the man is right, the number of pounds will be less than the number of dollars shown.

The man is right about the Exchange rate.

The rate at which one currency will be exchanged for another is known as the exchange rate. The most frequent types of currencies are national currencies,

A currency's relative value expressed in terms of another currency is called an exchange rate (or group of currencies). The exchange rate is a significant economic variable for nations with active international trade, like Australia.

Given:

The Situation is The man's friend told him that " It will actually cost more

pounds than the price shown, because of the exchange rate."

This means the price in pounds is more than dollar.

But the exchange rate is found to be

£1 = $1.24

So, the price in dollar is more than in pounds.

Hence, the Men is correct.

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Answer:

See below

Step-by-step explanation:

Here is one possible mistake:

Let y= u = ( 2ax^2 +c)^2          expand

        4 a^2 x^4  + 4 a x^2 c   + c^2

  dy/ dx   then becomes  

16 a^2 x^3 + 8 a x c  <====== you have  8 a^2x^3 + 8axc  

   MAYBE ??

\(y = (2ax^2 + c)^2 (bx^2 - cx)^{-1}\)

By the product rule,

\(\dfrac{dy}{dx} = \dfrac{d(2ax^2+c)^2}{dx} (bx^2-cx)^{-1} + (2ax^2+c)^2 \dfrac{d(bx^2-cx)^{-1}}{dx}\)

For the first derivative on the right side, let \(u=2ax^2+c\). Then by the chain rule,

\(\dfrac{d(2ax^2+c)^2}{dx} = \dfrac{du^2}{dx} \\\\ ~~~~~~~~~~~~~~~~~~ = \dfrac{du^2}{du}\dfrac{du}{dx} \\\\ ~~~~~~~~~~~~~~~~~~ = 2u \dfrac{du}{dx} \\\\ ~~~~~~~~~~~~~~~~~~ = 2(2ax^2+c) \dfrac{d(2ax^2+c)}{dx}\)

and by the power rule, this reduces to

\(\dfrac{d(2ax^2+c)^2}{dx} = 2 (2ax^2+c) (4ax) \\\\ ~~~~~~~~~~~~~~~~~~ = 8ax (2ax^2 + c)\)

For the other derivative, let \(v = bx^2-cx\). Then

\(\dfrac{d(bx^2-cx)^{-1}}{dx} = \dfrac{dv^{-1}}{dx} \\\\ ~~~~~~~~~~~~~~~~~~~~ = \dfrac{dv^{-1}}{dv}\dfrac{dv}{dx} \\\\ ~~~~~~~~~~~~~~~~~~~~ = -v^{-2} \dfrac{dv}{dx} \\\\ ~~~~~~~~~~~~~~~~~~~~ = -(bx^2-cx)^{-2}\dfrac{d(bx^2-cx)}{dx}\)

which reduces to

\(\dfrac{d(bx^2-cx)^{-1}}{dx} = -(bx^2 - cx)^{-2} (2bx - c)\)

So one expression for the derivative we want is

\(\dfrac{dy}{dx} = 8ax (2ax^2 + c) (bx^2-cx)^{-1} - (2ax^2+c)^2 (bx^2 - cx)^{-2} (2bx - c)\)

The value of y is 18

Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.

Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.

Therefore;

14/21 = 12/y

14y = 21 × 12

14y = 252

divide both sides by 14

y = 252/14

y = 18

Therefore the value of y is 18.

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Step-by-step explanation:

Based on the information given, we have a diagram with two sides labeled as 13.3 mm and 5.5 mm, and another side labeled as X mm.

To find the length of X, we can use the fact that the sum of the lengths of the sides of a triangle is equal to the perimeter.

Perimeter = 13.3 mm + 5.5 mm + X mm

The perimeter is the total distance around the triangle. Since we have three sides, the perimeter is the sum of the lengths of those sides.

To find X, we can subtract the sum of the known sides from the perimeter:

X mm = Perimeter - (13.3 mm + 5.5 mm)

Since the value of X is not given, we cannot calculate it without the perimeter value. If you provide the perimeter value, I can help you find the length of X.

Answer:

Sample

Step-by-step explanation:

The term that represents the description in the question is called sample.

Take for instance:

In the above descriptions:

40 and 1000 represent the samples while 100 and 100000 represent the populations, respectively.

Another example is when 10 cats are picked from an animal farm in order to study their eating pattern.

All these and many more represent sample.

Using simple interest, it is found that the monthly payments are of $739.00.

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

\(A(t) = A(0)(1 + rt)\)

In which:

In this problem:

Then, the total amount will be of:

\(A(t) = A(0)(1 + rt)\)

\(A(t) = 85000[1 + 30(0.071)]\)

\(A(t) = 266050\)

In 30 x 12 = 360 monthly payments, hence:

266050/360 = 739.

The monthly payments are of $739.00.

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Answer:

x is 60⁰ because 180 - 40 is 120 divide it by 2 because the bottem angles are equal and u get 60

Answer:

C

Step-by-step explanation:

The fraction of girls among the members that play sports is equal to the fraction of boys among the members that do not play sports.

Answer:

Your correct answer is option C. which is The fraction of girls among the members that play sports is equal to the fraction of boys among the members that do not play sports.

Answer:

4

Step-by-step explanation:

Answer:

$4.00

Step-by-step explanation:

I used a calculator.

Answer:

Gradient of parallel line= 7

Gradient of perpendicular line \( = - \frac{1}{7} \)

Step-by-step explanation:

The equation of the line is already in slope-intercept form (y= mx +c). This means that the coefficient of x is the gradient and the constant -3 is the y-intercept of the line.

y= 7x -3

Gradient= 7

Parallel lines have the same gradient.

Thus, the slope of the line parallel to this line is also 7.

The product of the gradients of 2 perpendicular lines is -1.

(Gradient of perpendicular line)(7)= -1

Gradient of perpendicular line

= -1 ÷7

\( = - \frac{1}{7} \)

Hello! :)

Parallel lines have the same slope.

If one line has a slope of 7, then the line parallel to it has a slope of 7 as well.

Now, perpendicular lines have slopes that are opposite reciprocals. It means we take the slope of one line, make it negative, and flop it over:

\(7\\-7\\-\frac{1}{7}\)

Hope it helps. Feel free to ask me if you have any questions.

~A determined teen

\(MagicalNature\)

Answer:

A

Step-by-step explanation:

Answer:  (10m-3)/5

Step-by-step explanation:

Convert 1 2/5 into an improper fraction

Simplify  5+25+2  to  7

Simplify 2/3m to 2m/3

Simplify 7/5m to 7m/5

Expand and remove the parenthesis

Collect the like terms

Simplify