Indicate the method you would use to prove the two 's . If no method applies, enter "none".



SSS
ASA
SAS
AAS
None

On solving the provided question, we can say that Volume of cuboid - L X B X H=> volume = (x+6)*(x-2)*(x-1) => [tex]V = x^3 + 3x^2 - 16x + 12[/tex]

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

The dimensions are:

Length =(x + 6), Width = (x - 2) and Height = (x -1)

Volume of cuboid - L X B X H

volume = (x+6)*(x-2)*(x-1)

[tex]V = (x+6)(x^2 - 3x +2)[/tex]

[tex]V = x^3 - 3x^2 + 2x + 6x^2 - 18x + 12[/tex]

[tex]V = x^3 + 3x^2 - 16x + 12[/tex]

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Answer:

Cos A: [tex]\frac{15}{17}[/tex]

Tan A: [tex]\frac{8}{15}[/tex]

Sin C: [tex]\frac{8}{17}[/tex]

How I did it:

Cos A: [tex]\frac{Base}{Hypotenuse}[/tex] This is the basic " fraction "

Or in similar terms: = [tex]\frac{ab}{bc}[/tex]

Cos A = [tex]\frac{15}{17}[/tex]

Tan A = [tex]\frac{Perpendicular}{Base}[/tex]

Similar terms once again = [tex]\frac{ac}{ab}[/tex]

Tan A = [tex]\frac{8}{15}[/tex]

Sin A = [tex]\frac{Perpendicular}{Hypotnuse}[/tex]

Similar terms = [tex]\frac{ac}{bc}[/tex]

Since A = [tex]\frac{8}{17}[/tex]

Thus your answers are:

Cos A = [tex]\frac{15}{17}[/tex]

Tan A = [tex]\frac{8}{15}[/tex]

Sin A = [tex]\frac{8}{17}[/tex]

68.5% of Colton's gross pay is take-home pay. To find the percentage of Colton's gross pay that is take-home pay, we need to divide his net pay by his gross pay and then multiply by 100 to convert the resulting decimal to a percentage.

To find the percentage of Colton's gross pay that is take-home pay, we need to divide his net pay by his gross pay and multiply the resulting decimal by 100 to express it as a percentage. Colton's gross pay is $1421.50 and his net pay is $973.48. Dividing the net pay by the gross pay gives a result of 0.685, or 68.5% when converted to a percentage. This means that 68.5% of Colton's gross pay is take-home pay, or the amount of money that he receives after deductions are made. Therefore, Colton's take-home pay is $973.48, which is 68.5% of his gross pay.

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Answer:

[tex]8[/tex]

Step-by-step explanation:

[tex]x^2+12x+44=(x^2+12x+36)+8=(x+6)^2+8[/tex]

The equation y < - 4 · x - 1 represents the inequality seen in the figure.

According to analytic geometry, we can derive the equation of a line from the knowledge of two points along the line. In this problem we must determine an inequality of the form:

y < m · x - b

m = Δx / Δb

Where:

We know that points (x, y) = (- 1, 3) and (x, y) = (0, - 1) are points of the line. Now we proceed to determine the equation of the line:

m = (- 1 - 3) / [0 - (- 1)]

m = - 4

b = - 1

y < - 4 · x - 1

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40%=

5

2

​

5

2

​

⋅40=16 cars at 8000 each =128,000 in sales

40−16=

​

24 cars at 9000 each

​

=216,000 in sales

Total sales: 128,000+216,000=344,000

Total expense: 6500⋅40=260,000

Total profit: 344,000−260,000=84,000

Answer:

$84000

Step-by-step explanation:

40% of the cars would be 16 cars that are sold for $8000 each.

16×$8000=$128000

The remaining 60% of cars would be 24 cars to be sold at $9000 each.

24×$9000=$216000

The total profit = the sum - the amount he paid for all cars.

total profit = ($128000+$216000) - (40×$6500)

total profit = $344000 - $260000

total profit = $84000

Answer:

42 mi²

Step-by-step explanation:

Break it up into 2 shapes, top and bottom, then add the areas together.

Area 1 (top rectangle) = 12 x 3 = 36

Area 2 (bottom rectangle) = 2 x 3 = 6

Total area = 36 + 6 = 42 mi²

The pair of functions f(x) and g(x) below that equals 0 as the limit as x goes to infinity of the quotient of f of x and g of x will be C. f(x) = ln(x); g(x) = ex

For the limit of the quotient of f(x) and g(x) to equal 0 as x approaches infinity, it is necessary for f(x) to grow more slowly than g(x).

Out of the options given, the only pair of functions where this is true is f(x) = ln(x) and g(x) = ex. As x approaches infinity, ex grows much faster than ln(x), so the limit of the quotient of these two functions as x approaches infinity is 0.

In conclusion, the correct option is C.

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If the well was 40 feet deep and the frog climbs 6 feet per hour, it would take the frog 40/6 = 6.67 hours to reach the top of the well.

However, the frog slips back 1 foot while resting for an hour, so the frog would only have covered 5 feet of the well after each hour of climbing. The frog would need to climb for a total of

40/5 = 8 hours

to reach the top of the well. Additionally, the frog would need to take 8 hours of rest to make up for the slipping back.

So the total time it would take the frog to get out of the well would be 8 hours + 8 hours = 16 hours.

If the well was 40 feet deep and the frog climbs 6 feet per hour, it would take the frog 40/6 = 6.67 hours to reach the top of the well.

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Using the normal curve to estimate the following percentages. The answer that is closes to being correct is 39.4%. So, the correct answer is C.

Since the distribution is approximately normal, we can use the empirical rule (also known as the 68-95-99.7 rule) to estimate the percentages.

a. 10.6%: This corresponds to the area under the curve that is more than 2 standard deviations below the mean. Using the rule, we know that about 2.5% of the area under the curve is more than 2 standard deviations below the mean. So 10.6% is too high. The answer is not a.

b. 89.4%: This corresponds to the area under the curve that is less than one standard deviation above the mean. Using the rule, we know that about 68% of the area under the curve is within one standard deviation of the mean. So 89.4% is too high. The answer is not b.

c. 39.4%: This corresponds to the area under the curve that is within one standard deviation of the mean. Using the rule, we know that about 68% of the area under the curve is within one standard deviation of the mean. So 39.4% is the closest to being correct. The answer is c.

d. 78.8%: This corresponds to the area under the curve that is less than two standard deviations above the mean. Using the rule, we know that about 95% of the area under the curve is within two standard deviations of the mean. So 78.8% is too high. The answer is not d.

e. 68.27%: This corresponds to the area under the curve that is within one standard deviation of the mean. This is the same as c. So e is not the correct answer.

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Answer:

∠ B = 121°

Step-by-step explanation:

ABCD is a cyclic quadrilateral

• opposite angles sum to 180°

∠ B and ∠ D are opposite angles , then

∠ B + 59° = 180° ( subtract 59° from both sides )

∠ B = 121°

The Original Price of helmet is $20.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

The helmet Clare plans to buy is on sale for 20% less than the original price.

let the sale price be x.

So, the Original price is (x+5).

Also, Sales price = Original price - 20% of Original price

x= x+ 5 - 0.20(x+5)

x = x+ 5 - 0.20x - 1

0.20x = 4

x= 4/ 0.20

x= $20

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Answer:

4 more laps to reach the goal of 14.4 km.

Step-by-step explanation:

First, let's find the total distance covered so far: 720 m x 16 laps = 11,520 m.

Next, let's convert the goal distance to meters: 14.4 km x 1000 m/km = 14,400 m.

Finally, let's subtract the total distance covered from the goal distance to find the remaining distance: 14,400 m - 11,520 m = 2,880 m.

Since a lap is 720 m long, the remaining distance can be divided by 720 m to find the number of laps left: 2,880 m ÷ 720 m = 4 laps.

Therefore, the runner needs to run 4 more laps to reach the goal of 14.4 km.

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If so far the George's string is 44 inches long , then his string is not long enough , so he need to make it longer .

To find whether George's string is long enough, we first convert both measurements to same unit of measurement.

that means we convert length of the string in inches to feet by dividing it by 12 ; because  there are 12 inches in a feet  ;

⇒ (44 inches)/(12 inches/feet)  

⇒ 3.67 feet  ;

The George's string is currently 3.67 feet long and he needs a string that is 4 feet long  .

So , his current string is not long enough and he needs to make it longer. He needs to add another 0.33 feet to his string  .

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The given question is incomplete , the complete question i

George needs a string that is 4 feet long. So far his string is 44 inches. Is it long enough or does he need to make it longer ?

The two numbers, then, are 86 and 61.The two numbers can be found by using basic algebra.

The two numbers can be found by using basic algebra. To solve for the two numbers, we can set up two equations, one for the sum and one for the difference. For the sum, we can set up the equation: x + y = 147. For the difference, we can set up the equation: x - y = 25. We can then solve for x by adding y to both sides of the equation for the difference, so x = 25 + y. We can then substitute this value for x in the equation for the sum, so 25 + y + y = 147, or 2y = 122, and y = 61. We can then substitute this value for y in the equation for x, so x = 25 + 61, or x = 86. The two numbers, then, are 86 and 61.

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The required, 68.2 divided by 0.4 is equal to quotient 170.5, as per the given condition.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
68.2 divided by 0.4 is given as,

To divide a decimal value by another decimal value, you can use the same process as dividing whole numbers, but you need to make sure that the decimal points are lined up correctly.

= 68.2 / 0.4

= 682/4
= 170.5

Therefore, 68.2 divided by 0.4 is equal to 170.5.

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If a 12-ft-by-15-gt rectangular swimming pool has a 3-ft-wide no-slip surface around it. The outer perimeter of the no-slip surface around the rectangular swimming pool is 78 feet.

The key idea in this problem is to recognize that the no-slip surface around the pool consists of a rectangular strip of uniform width that runs parallel to the edges of the pool. To find the outer perimeter of this strip, we need to add up the lengths of all four sides of the rectangle formed by the outermost edges of the no-slip surface.

Let's start by finding the length of the no-slip surface that runs along the length of the pool. Since the pool is 12 feet long and the no-slip surface extends 3 feet beyond each end of the pool, the total length of the no-slip surface is:

12 + 2(3) = 18 feet

The "2(3)" term in this equation represents the 3-foot-wide extension on each end of the pool. Next, we need to find the length of the no-slip surface that runs along the width of the pool. Since the pool is 15 feet wide and the no-slip surface extends 3 feet beyond each side of the pool, the total width of the no-slip surface is:

15 + 2(3) = 21 feet

Now we have the lengths of the two parallel sides of the rectangle formed by the outermost edges of the no-slip surface. To find the lengths of the other two sides, we simply add up the lengths of the corresponding sides of the pool.

Therefore, the length of the rectangle is 12 + 2(3) = 18 feet, and the width of the rectangle is 15 + 2(3) = 21 feet.

Finally, we can add up the lengths of all four sides of the rectangle to find the outer perimeter of the no-slip surface:

2(18) + 2(21) = 36 + 42 = 78 feet.

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The indirect speech version of the given sentence would be:

She said that her mother was cooking food.

Indirect speech (also known as reported speech) is a way of expressing what someone else said, without using their exact words. In indirect speech, we usually report the statement or question using a reporting verb like "say", "tell", "ask", or "explain", followed by a conjunction such as "that". We also need to change the tense and sometimes the pronouns to reflect the new context.

Indirect speech is often used in writing and speaking to convey someone else's message, opinion or idea. It helps us to paraphrase or summarize what someone else said, without quoting them directly. It is important to learn how to use indirect speech correctly, as it is a common feature of both formal and informal communication.

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The probability of selecting a jury composed of 12 women from a pool of 30 people that includes 12 men and 18 women is extremely low, only 0.0657%.

The probability of an event happening is the measure of how likely that event is to occur.

In this case, we need to find the probability of selecting a jury of 12 women from a pool of 30 people. To calculate this probability, we can use the formula:

Probability = Number of favorable outcomes / Total number of outcomes

The total number of outcomes is the number of ways in which we can select 12 people from a pool of 30. We can calculate this number using the combination formula:

Total number of outcomes = C(30,12) = 30! / (12! * (30-12)!) = 28,238,760

Now, we need to calculate the number of favorable outcomes, which is the number of ways in which we can select 12 women from a pool of 18. We can calculate this number using the combination formula as well:

Number of favorable outcomes = C(18,12) = 18! / (12! * (18-12)!) = 18,564

Therefore, the probability of selecting a jury composed of 12 women is:

Probability = Number of favorable outcomes / Total number of outcomes

Probability = 18,564 / 28,238,760

Probability = 0.000657 or 0.0657%

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On solving the provided question we can say that the equations are  y = 3x - 6 and y = -2x + 8

A mathematical equatiοn is a fοrmula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is known as an equation in algebra. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relatiοnship between the twο sentences οn either side of a letter is described by a mathematical formula. Often, there is οnly one variable, which alsο serves as the symbοl, fοr instance, 2x – 4 = 2.

the equations are

y = 3x-6

y = -2x+8

3x - 6 = -2x+8

5x -6 = 8

5x = 14

x = 14/5

Now solve for y:

y = 3(14/5) - 6

y = 42/5 - 6

y=42/5 - 30/5

y = 12/5

The position 12/5 is where these two lines cοnverge. The triangle created by these two lines and the x-axis has a height equal to this.

So that we can identify the triangle's base, let's lοcate the roots of these equations (where they contact the x-axis).

Put a 0 in both equations.

(I) 0 = 3x - 6  

6 = 3x

x = 2  

Set the second equation equal to 0.

(II)  y = -2x+8

2x = 8

x = 8/2

x = 4

The triangle has a base between the numbers (2, 0) and (4, 0), giving it a length of two units.

The triangle has a height of 12/5 units.

Area of a Triangle:

A = 1/2bh

A = (1/2) · (2) · (12/5)

A = 12/5

The region between the x-axis that is enclosed by the lines y = 3x - 6 and y = -2x + 8 has a 12/5 unit area.

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Answer: 7/10

Step-by-step explanation:

multiply 4/5 by 7/8=28/40 or 7/10

Players A and B withdraw balls from the urn consecutively until a read ball is selected, the probability that player A selects the red ball is approximately 0.408.

To find the probability that player A selects the red ball, we can use the law of total probability and consider all the possible ways the game could end. A selects the red ball on the first draw. The probability of this is simply the proportion of red balls in the urn, which is 3/10.

A selects a black ball on the first draw, followed by B selecting a black ball on their turn, and so on, until A finally selects the red ball. The probability of this is:

(7/10) * (6/9) * (5/8) * ... * (1/4) * (3/7)

Notice that the probability of selecting a black ball decreases by one after each turn, since the total number of balls in the urn decreases by one and the number of black balls decreases by one.

The probability of selecting the red ball on the last turn (after all the black balls have been selected) is 3/3 = 1. We multiply all these probabilities together to get the total probability of this sequence of events.

A selects a black ball on the first draw, followed by B selecting a black ball on their turn, and so on, until B finally selects the red ball. The probability of this is:

(7/10) * (6/9) * (5/8) * ... * (2/4) * (3/6)

Notice that the probability of selecting a black ball decreases by one after each turn, just like in the previous case. However, the probability of B selecting the red ball on their turn is now 3/6, since there are only six balls left in the urn at this point. We multiply all these probabilities together to get the total probability of this sequence of events.

Adding up these three probabilities, we get:

3/10 + (7/10) * (6/9) * (5/8) * ... * (1/4) * (3/7) + (7/10) * (6/9) * (5/8) * ... * (2/4) * (3/6) ≈ 0.408

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The length x of the right triangle is 8.66 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the side of the right triangle can be found using trigonometric ratios as follows:

Hence,

tan 60° = opposite / adjacent

where

opposite side = x

adjacent side = 5

Therefore,

tan 60° =  x  / 5

cross multiply

x = 5 tan 60°

x = 5 × 1.73205080757

x = 8.66025403784

x = 8.66 units

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If radius of circle is tripled then area of circle will be increased by:9 times.

If the radius of a circle is tripled, then the new radius is three times the original radius, or R' = 3R, where R is the original radius and R' is the new radius. The area of a circle is given by the formula A = πR^2, where A is the area and R is the radius.

Substituting R' = 3R into the formula for the area of a circle, we get:

A' = πR'^2

= π(3R)^2

= 9πR^2

Therefore, the new area A' is 9 times the original area A. In other words, if the radius of a circle is tripled, the area of the circle will be increased by a factor of 9. This is because the area of a circle is proportional to the square of its radius.

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Answer: no it does not

Step-by-step explanation: Because 1,007 squared is 1,014,049 and the sum of 911 squared is 829,921 and then 829 squared is 687,241 then add 829,921+687,241=1,517,162 when it should equal 1,014,049 which is the amount of 1,007 squared to make it a right triangle.

The solution is : no, it does not form a right triangle.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

given that,

A triangular shaped region has side lengths of 829 miles, 911 miles, and 1,007 miles.

now, we get,

Because 1,007 squared is 1,014,049

and the sum of 911 squared is 829,921

and then 829 squared is 687,241

then add 829,921+687,241=1,517,162

when it should equal 1,014,049

which is the amount of 1,007 squared to make it a right triangle.

as we know that,

in right triangle,

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a^2 + b^2 = c^2.

so, we get,

The solution is : no, it does not form a right triangle.

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The value of x in the triangle is equal to: A. 21.

In Mathematics, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the sides are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side).

Note: x is the side opposite to the 60° angle.

The side opposite to the 60° angle, x = 7√3 × √3

The side opposite to the 60° angle, x = 7 × 3

The side opposite to the 60° angle, x = 21 units.

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The value of x and y in the quadratic and linear equation are (0.37, -137) and (-3.26 , -6.74) respectively

In the problem given;

2x² + 4x - y = -3 ..eq(i)

-2x + y = -4 ..eq(ii)

From equ(ii)

Using the linear equation;

y = 2x - 4 ...eq(iii)

Put eq(iii) into eq(i)

2x² + 4x - (2x - 4) = -3

2x² + 4x - 2x - 4 = -3

2x² + 2x - 4 = -3

Rearrange the equation;

2x² + 2x - 4 + 3 = 0

2x² + 2x - 1 = 0

Solving the quadratic equation;

x = 0.37 or -1.37

Put the value of x into eq(ii)

-2(0.37) + y = -4

y  = -3.26

or

-2(-1.37) + y = -4

y = -6.74

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