What is the contrapositive of the following statement?
If two triangles are congruent, then their corresponding angles are congruent.

A) If the corresponding angles of two triangles are congruent, then the triangles are congruent.

B) If two triangles are congruent, then their corresponding angles are congruent.

C) If two triangles are not congruent, then their corresponding angles are not congruent.

D) If the corresponding angles of two triangles are not congruent, then the triangles are not congruent.

The value x= -2 makes the inequality  true.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

12 > 2x + 4

Now, if we put x= 8 then

= 2x+ 8

= 2(8)+8

= 16+ 8

= 24 > 12

So, x=8 is not true

Now,  if we put x= 4 then

= 2x+ 8

= 2(4)+8

= 8+ 8

= 16 > 12

So, x=4 is not true

Now,  if we put x= 12 then

= 2x+ 8

= 2(12 )+8

= 24 + 8

= 32 > 12

So, x=12 is not true

and,  if we put x= -2 then

= 2x+ 8

= 2(-2)+8

= -4+ 8

= 4 < 12

So, x=-2 is true.

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Answer:

1/4 cup and 4 tablespoons

The missing sides of the triangles are:

NUMBER 6 and 7: x = 12√2 units, y = 12√2 units

NUMBER 8 and 9: x = 25 units, y = 25√3 units

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

NUMBER 6 and 7

sin 45° = x/24

x = 24 * sin 45°

x = 24 * (√2)/2

x = 12√2 units

sin 45° = y/24

y = 24 * sin 45°

y = 24 * (√2)/2

y = 12√2 units

NUMBER 8 and 9

sin 30° = x/50

x = 50 * sin 30°

x = 50 * 1/2

x = 25 units

sin 60° = y/50

y = 50 * sin 60°

y = 50 * (√3)/2

y = 25√3 units

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Answer:

y=40x+35

Step-by-step explanation:

After 0 months, she still needs to pay the first $35. This means that this is her y-intercept, and in the formula “y=mx+b”, it would go in the “b” place. Then x would mean how many months have passed, so therefore 40 would go into the “m” place. If you put that together, it looks like “y=40x+35”.

The correct statement comparing the values of the 8s in 2,7812 and 94894 is that the 8 in 2,7812 has a greater value than the 8 in 94894.

This is because the value of a digit in a number is determined by its place value. In the number 2,7812, the 8 is in the hundreds place, meaning it has a value of 800. In the number 94894, the 8 is in the tens place, meaning it has a value of 80.

Therefore, the 8 in 2,7812 has a greater value (800) than the 8 in 94894 (80).

Here is the answer in HTML format:

The correct statement comparing the values of the 8s in 2,7812 and 94894 is that the 8 in 2,7812 has a greater value than the 8 in 94894.

This is because the value of a digit in a number is determined by its place value. In the number 2,7812, the 8 is in the hundreds place, meaning it has a value of 800. In the number 94894, the 8 is in the tens place, meaning it has a value of 80.

Therefore, the 8 in 2,7812 has a greater value (800) than the 8 in 94894 (80).

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The measure of each Angle is 80, 50 and 50 degree.

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Given:

<H= 4x- 20

and, <G = 2x

and, <I = 2x

Now, In triangle GHI using Angle Sum Property

<G+ <H+ <I= 180

4x- 20 + 2x+ 2x = 180

8x - 20 = 180

8x = 200

x= 25

So, the measure of <G = 4x- 20 = 100 -20 = 80 degree.

and, <H = <I= 2x= 2(25)= 50 degree

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the fractions with the same denominator will be 14/16 and 13/16.

What is a fraction?

It can also be written as a mixed number, which is a whole-number quotient with a proper-fraction residual, if the numerator is larger. This type of expression is used when the numerator is larger.

Divided by its denominator, any fraction can be converted to a decimal. The outcome may end at some point or one or more digits may repeat continuously.

The given fraction is given are 7/8 and 13/16.

Taking lcm of the denominator will be 16

So the fraction will be 7*2 = 14

So the fractions will be 14/16 and 13/16.

Hence the fractions with the same denominator will be 14/16 and 13/16.

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The simplification of the given polynomial is az-bz+3b²-6ab+3a².

The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.

The given polynomial (a-b)·z+3(b-a)².

Here, (a-b)·z+3(b²-2ab+a²)

= z·(a-b)+3b²-6ab+3a²

= az-bz+3b²-6ab+3a²

Therefore, the simplification of the given polynomial is az-bz+3b²-6ab+3a².

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The equation which can be used to represent the situation is 396 = x - 0.2x

The original price of the love seat was $495.

Let

Original price of the love seat= x

New price= $396

Percentage discount= 20%

396 = x - (20% of x)

396 = x - 0.2x

396 = 0.8x

divide both sides by 0.8

x = 396 / 0.8

x = $495

Hence, the equation 396 = x - 0.2x is used to solve the question and the original price is $596

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Since BD is a diameter of circle A, the slope of BD is equal to -2/3.

In Mathematics and Geometry, perpendicular lines can be defined as two (2) lines that intersect or meet each other at an angle of 90° (right angles).

By critically observing the geometric shape, we can reasonably infer and logically deduce that line segment BD is perpendicular to line segment BE.

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

3/2 × m₂ = -1

3m₂ = -2

Slope, m₂ = -2/3.

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Complete Question:

In the diagram, BD is a diameter of circle A. If the slope of BE is 3/2, what is the slope of BD?

Answer: x = 8, x = -2

Step-by-step explanation:

(x - 3)² = 25

Step 1: Take the square root on each side of the equation.

(x - 3)² = 25

√(x - 3)² = ±√25

Step 2: After taking the square root on each side of the equation, this allows you to solve for x.

x - 3 = ±5

Solution 1

x - 3 = 5

x = 5 + 3

x = 8

Solution 2

x - 3 = - 5

x = -5 + 3

x = -2

Another way to solve this problem is to multiply (x - 3)² using the FOIL methods (first, outer, inner, last) and then set it equal to 25.

(x - 3) (x - 3) = 25

x² - 3x - 3x + 9 = 25

The next step is to add like terms. After adding like terms, solve for x.

x² - 3x - 3x + 9 = 25

x² - 6x + 9 - 25 = 25 - 25

x² - 6x - 16 = 0

Last step is to factor x² - 6x - 16 = 0 so you can solve for the two solutions.

(x - 8) (x + 2) = 0

Solution 1

x - 8 = 0

x = 8

Solution 2

x + 2 = 0

x = -2

Reflect it across the x-axis, then translate it up 6 units and left 1 unit before reflecting it across the y-axis.

You should be aware that a collection of numbers, or "terms," is referred to as a sequence. Examples of terms include 2, 5, and 8. Some sequences can be made endlessly long by taking advantage of a particular pattern they follow. Use the example of 2,5,8 and add 3 to continue the series. There are formulas that demonstrate where to look for words within a sequence. A collection of objects that are in some order is known as a sequence in mathematics (or events). It resembles a set in that it has pieces (also called elements or terms). The total, perhaps infinite number of ordered objects are referred to as the sequence's length. the act of placing two or more objects in a logical order.

We are given the following

Δ DOG and ΔCAT

According to Chanel, the series of transformations that maps triangle ABC onto triangle DEF is as follows:

Reflect it across the x-axis, then translate it up 6 units and left 1 unit before reflecting it across the y-axis.

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Answer:

(x + 7)/(x - 3)

Step-by-step explanation:

To simplify this expression, we first factor the numerator and denominator, and then cancel any common factors:

x² + 3x - 28 = (x + 7)(x - 4)

x² - 7x + 12 = (x - 3)(x - 4)

So the expression simplifies to:

(x + 7)(x - 4) / (x - 3)(x - 4)The (x - 4)

factor in both the numerator and denominator cancels out, leaving:

x + 7 / x - 3

Therefore, the simplified expression is (x + 7)/(x - 3)

Answer: C

Step-by-step explanation:

Again, let's use elimination.

Does it suggest a different interpretation than the rest of the article? Yes, because it indicates there is a flaw in saying that the data shows human and chimp similarities.

Is it a reason for pursuing DNA Research? Nope.

Does it specifiy the extent of similarity? Yup.

SO now we are down to A and C as possible choices.

C is the answer, because while the data can be used to produce a different interpretation, its purpose in developing the main idea is purely specification.

The area of the shaded region is 24x² - 78x + 33.

A square is a two-dimensional figure that has four sides and all four sides are equal.

The area of a square is side².

We have,

Two squares:

Smaller square:

Side = x + 4

Larger square:

Side = 5x - 7

Now,

Area of the shaded region.
= Area of the bigger square - Area of the smaller square

= (5x - 7)² - (x + 4)²

= 25x² - 70x + 49 - x² - 8x - 16

= 24x² - 78x + 33

Thus,

24x² - 78x + 33 is the area of the shaded region.

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Answer: 7

Step-by-step explanation:

We know that the base sides of the triangular prism are 6cm, 5cm, and

[tex]x[/tex] cm. We also know that the length of the prism is 20.

To calculate the lateral surface area of the triangular prism, we need to use the following equation:

[tex](a + b + c)[/tex] x [tex]length[/tex]

So we can input our values, to get this:

[tex](6 + 5 + x) 20 = 360[/tex]

Then we solve the equation by the following steps:

[tex]= > 6+5+x = \frac{360}{20} = 18\\= > 11 + x = 18\\= > x = 7[/tex]

Hope this helps, if you have any further inquiries about this, please reply back. :)

Answer:

12 lb of seed.

Step-by-step explanation:

We need to determine the amount of seed required for a 4800 sq ft lawn.

First, we need to find out how many 1200 sq ft portions the 4800 sq ft lawn is:

4800 sq ft / 1200 sq ft/portion = 4 portions

Next, we can use the seed manufacturer's recommendation of 3 lb of seed per 1200 sq ft:

3 lb/portion * 4 portions = 12 lb

Therefore, the architect will need 12 lb of seed.

The estimate of the product, using rounding, is given as follows:

0.67 x 322 = 216.

The product in the context of this problem is defined as follows:

0.67 x 322.

Multiplying the two numbers, the result is given as follows:

0.67 x 322 = 215.74.

We want to round the product to the nearest integer, hence we add one to the integer part, as the decimal part has a first digit which is greater than 4.

Thus the rounded result is given as follows:

216.

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The final amount momentum of the t-shirt is 17.5 kg⋅m/s, which is the sum of the initial momentum of the t-shirt (2 kg⋅m/s) and the change in momentum (15.5 kg⋅m/s) due to the force applied.

The final amount momentum of the t-shirt is 17.5 kg⋅m/s, which is calculated by summing the initial momentum of the t-shirt (2 kg⋅m/s) and the change in momentum (15.5 kg⋅m/s) due to the force applied. Momentum is a vector quantity which is equal to the product of the mass and velocity of an object. In this case, the t-shirt has a mass of 4 kg and a velocity of 4 m/s. The force of 15 N applied to the t-shirt for 3 seconds causes the t-shirt to accelerate, increasing its velocity from 4 m/s to 8 m/s. This increase in velocity results in an increase in the momentum of the t-shirt from 2 kg⋅m/s to 17.5 kg⋅m/s. Thus, by calculating the change in momentum due to the applied force, we can determine the final momentum of the t-shirt.

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Answer:

17 years & 9 months

Step-by-step explanation:

annual rate 3.9%

every quarter = 3.9%/4 = 0.98%

compounding every quarter = (1+0.98%)

how long = assuming t quarters

2000 * (1+0.98%) ^t = 4000

solve for t

t= 71

so 71/4 = 17 years & 9 months

Answer: 22v-4

Step-by-step explanation: four less than means subtract and product means multiply

Answer: The expression inside the parentheses can be simplified as follows:

24/16 + 3/3 = 3

So, the expression becomes:

6/11 - 3/12 = 6/11 - 1/4

Now we can subtract the two fractions:

6/11 - 1/4 = 6/11 - 4/11 = 2/11

So the final answer is 2/11.

Step-by-step explanation:

The company produce each month to maximize their profit be (50, 100000).

To ensure the best output and price levels are realized in order to maximize returns, business firms engage in the process of profit maximization. In order to achieve its profit objectives, the company modifies important variables including sale price, production costs, and output levels.

"Profit maximization" emphasizes the location of this critical point, or the optimal output at which your company is most profitable. An educational non-profit organization called Khan Academy states that "a corporation striving to maximize profit will produce the quantity where 'marginal cost' and 'marginal income' are equal to each other."

Let x be the number of ceiling fans

If the price per fan when you sell x fans exists (300 - 2x), then the amount received for selling x fans exists x(300 - 2x)

The cost for producing x fans is (20x + 100).

Profit = x(300 - 2x) - (20x + 100)

y = (1000 + 20x)(300 - 2x)

simplifying the equation, we get

y = 300000 - 2000x + 6000x - 40x²

y = -40x² + 4000x + 300000

simplifying the above equation, we get

y = -40(x² - 100x + 2500) + 100000

y = -40(x - 50)² + 100000

vertex: (50, 100000).

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Step-by-step explanation:

The charge of Company B is $65.50 + 0.14x and the charge of Company A is $45.50 + 0.11x.

So, the difference is $65.50 + 0.14x - ($45.50 + 0.11x) = $20 + 0.03x dollars more than Company A.

Answer: The transformation matrix R for a rotation of 120° about an axis from the origin through the point (1,1,1) can be calculated using the formula:

R = I + (sin(θ))U + (1-cos(θ))UU'

where θ is the angle of rotation (120° in this case), I is the identity matrix, U is a skew-symmetric matrix, and U' is its transpose. The skew-symmetric matrix can be calculated as follows:

U = [0, -z, y; z, 0, -x; -y, x, 0]

where x, y, and z are the components of the vector (1,1,1) that defines the axis of rotation.

Plugging in the values and simplifying, the transformation matrix R is:

R = [ cos(120°), -sin(120°), 0; sin(120°), cos(120°), 0; 0, 0, 1 ]

Note: cos(120°) = -1/2 and sin(120°) = √(3)/2.

Step-by-step explanation:

The unit vectors that are orthogonal to both i+j and i+k are

± (-1/√3, 1/√3,1/√3 )

What are vector equations ?

Vector equations allow for the creation of parametric curves. That is, points in space are formed for each value of the parameter by the equation of a vector, where each of its elements has a function with an independent variable that we refer to as a parameter.

a=i+j = < 1,1,0 > , b=i+k = < 1,0,1>

Let c= + < (  cos α,cos β ,cos γ )>

be the unit vectors (in opposite directions) orthogonal to a and b

the scalar product :

c.a =  cos α +cos β = 0

c.b =  cos α + cos γ = 0

It follows that ,

c= ± (  -cos α,cos α ,cos α )

cos α = ±1/√3

c= ± (-1/√3, 1/√3,1/√3 )

The unit vectors that are orthogonal to both i+j and i+k are

± (-1/√3, 1/√3,1/√3 )

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The unit vectors that are orthogonal to both i+j and i+k are

± (-1/√3, 1/√3,1/√3 )

What are vector equations ?

Vector equations allow for the creation of parametric curves. That is, points in space are formed for each value of the parameter by the equation of a vector, where each of its elements has a function with an independent variable that we refer to as a parameter.

a=i+j = < 1,1,0 > , b=i+k = < 1,0,1>

Let c= + < (  cos α,cos β ,cos γ )>

be the unit vectors (in opposite directions) orthogonal to a and b

the scalar product :

c.a =  cos α +cos β = 0

c.b =  cos α + cos γ = 0

It follows that ,

c= ± (  -cos α,cos α ,cos α )

cos α = ±1/√3

c= ± (-1/√3, 1/√3,1/√3 )

The unit vectors that are orthogonal to both i+j and i+k are

± (-1/√3, 1/√3,1/√3 )

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The completed entries is added as an attachment

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

3,723 ÷ 51

Express 3,723 as 2295 + 1428

So, we have the following representation

3,723 ÷ 51 = (2295 + 1428) ÷ 51

Expand the expression

So, we have the following representation

3,723 ÷ 51 = 2295 ÷ 51 + 1428 ÷ 51

Evaluate the quotients

3,723 ÷ 51 = 45 + 28

Next, we complete the blanks (see attachment) for the completed entries

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Line 1 and line 3 are parallel and line 1 and line 2 are perpendicular.

What is a System of Equations?

A system of equations in algebra is made up of two or more equations that are solved together. "A group of equations satisfied by the same set of variables are called a system of linear equations. Finding the values of the variables employed in the system of equations is the first step towards solving it. While maintaining the balance of the equations on both sides, we compute the values of the unknown variables. Finding a variable whose value makes the condition of all the given equations true is the primary goal of solving an equation system.

y = -5/2 x -1

4x-10y = 8

2y = -5x+7

line 1, m = -5/2

line 2, m = 2/5

line 3, m -5/2

Hence, Line 1 and line 3 are parallel and line 1 and line 2 are perpendicular.

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Answer & Step-by-step explanation:

To get the range of the function y = 2x + 1, we need to determine the set of all possible output values (y) that the function can produce for the given domain.

When x = -2, y = 2(-2) + 1 = -3.

When x = 4, y = 2(4) + 1 = 9.

When x = 6, y = 2(6) + 1 = 13.

So, the output values (y) for the given domain { -2, 4, 6 } are -3, 9, and 13.