Find the area of the following Triangle.

The algebraic rule that best describes the translation of quadrilateral ABCD to quadrilateral A'B'C'D' is P'(x, y) = (x + 8, y + 7). (Correct answer: A)

According to the image attached we understand that the quadrilateral ABCD is transformed into quadrilateral A'B'C'D' by applying pure translation. Translations are a kind of rigid transformation, defined as a transformation applied on a geometric locus such that Euclidean distance is conserved at every point of the construction.

Vectorially speaking, translations are described by the following formula:

P'(x, y) = P(x, y) + T(x, y)     (1)

Where:

By direct comparison, we conclude that the quadrilateral ABCD is translated 8 units in the +x direction and 7 units in the +y direction. Hence, the algebraic rule that describes the translation of quadrilateral ABCD to quadrilateral A'B'C'D' is:

P'(x, y) = (x, y) + (8, 7)

P'(x, y) = (x + 8, y + 7)

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The perimeter and area of this minor circle are equal to 32.857 units and 88.345 units² respectively.

First of all, we would determine the circumference of this circle by using this formula:

C = πD

C = 22/7 × 14

C = 44 units.

For the length of an arc of the circle:

Arc length/Circumference = 3/7

Arc length = 3/7 × C

Arc length = 3/7 × 44

Arc length = 18.857 units.

Now, we can calculate the perimeter:

Perimeter = 2r + arc length

Perimeter = 2(14/2) + 18.857

Perimeter = 14 + 18.857

Perimeter = 32.857 units.

Mathematically, the area of a minor circle is given by this formula:

Area = θr²/2

But, we would have to find the angle in radians:

18.857/32.857 = θ/360

θ = 3.6059 radians.

Substituting the given parameters into the formula, we have;

Area = (3.6059 × 7²)/2

Area = 88.345 units².

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Answer:

E. 38°

Explanation:

A rhombus has 360° interior angle.

Half of the other side has 180° angle.

Solve for x:

sum of interior angles = 180°

x + 14 + x + 14 + x + x = 180°

4x + 28° = 180°

4x = 180° - 28°

4x = 152°

x = 152°/4 = 38°

Sum of half interior angles=180°

So

Option E

The x-intercept is 4, and the asymptote is located at y = 3 , Option C is the correct answer.

An asymptote is a line that a curve approaches but it never reach.

The given equation

y = log₅(x-3)

To find the asymptote

Set the argument of the logarithm equal to zero.

x - 3 = 0

The vertical asymptote occurs at

x = 3

The equation can also be written as

[tex]\rm 5^y = x-3[/tex]

To find the x intercept we will put the value of y = 0 ;

therefore

5⁰ = x -3

1=x-3

x = 4

Therefore ,The x-intercept is 4, and the asymptote is located at y = 3 , Option C is the correct answer.

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Answer:

The x-intercept is 4, and the asymptote is located at x = 3.

Step-by-step explanation:

I got it right on the test.

Answer:

Choice C:   [tex]m=\frac{1}{2}; y=\frac{1}{2} x+4[/tex]

Step-by-step explanation:

To find your slope do:

[tex]\frac{y^2-y^1}{x^2-x^1}[/tex]

[tex]\frac{3-4}{-2-0}=\frac{-1}{-2} =\frac{1}{2}[/tex]

that's how you get 1/2

4 is just the y-int.

The required equation of line passes through (0, 4) and (-2, 3),  has slope of m = 1/2 , is y = 1/2x + 4. Option C is correct.

The equation is the values of two expressions that are equal.

The slope of the line is the tangent angle made by the line with horizontal. i.e. m =tanx where x in degrees.

The slope of the equation line passing through (0, 4) and (-2, 3)
[tex]m=\frac{y_2-y_1}{x_2-x_1} \\m = (3 - 4) / (-2-0)\\m = -1/-2\\m = 1/2[/tex]

Strand form of the equation of the line,
[tex]y-y_1 = m(x-x_1)[/tex]
Putting values in the standard form of the equation of the line.

y - 4 = 1/2 * (x - 0)
y = 1/2 * x + 4
[tex]y = \frac{1}{2} x + 4[/tex]

Thus, the required equation of line passes through (0, 4) and (-2, 3),  has slope of m = 1/2 , is y = 1/2x + 4. Option C is correct.

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Assets are the goods you possess that can generate future economic advantage. The correct option is D.

Assets are the goods you possess that can generate future economic advantage. Liabilities are amounts owed to other parties. In a nutshell, assets put money in your pocket, while liabilities take money out!

Given Over the period of a year, Julie’s net worth decreased. Therefore, the statement that is true is Julie’s assets decreased by more than her liabilities.

Hence, the correct option is D.

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Answer:

ok umm this looks hard can u give mor info?

Step-by-step explanation:

The solution to the equations are:

The equation is given as:

[tex]9x\² - 36x + 36 = 0[/tex]

The above equation is a quadratic equation which can be represented as:

[tex]ax\² + bx + c = 0[/tex]

The discriminant (d) is calculated as:

[tex]d = b\² - 4ac[/tex]

So, we have:

[tex]d = (-36)\² - 4 * 9 * 36[/tex]

[tex]d = 0[/tex]

A discriminant of 0 means that the equation has two equal real solutions

Hence, 9x² - 36x + 36 = 0 has two equal real solutions

The equation is given as:

[tex]x\² - x + 4 = 0[/tex]

The above equation can be represented as:

[tex]ax\² + bx + c = 0[/tex]

The discriminant (d) is calculated as:

[tex]d = b\² - 4ac[/tex]

So, we have:

[tex]d = (-1)\² - 4 * 1 * 4[/tex]

[tex]d = -15[/tex]

A discriminant of -15 means that the equation has no real solutions

Hence, x² - x + 4 = 0 has no real solutions

We have:

[tex]4x\² + 23 - 35[/tex]

Evaluate the difference

[tex]4x\² -12[/tex]

Factor out 4

[tex]4(x\² -3)[/tex]

Hence, the factored expression of 4x² + 23 – 35 is 4(x² -3)

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Answer:

X=3+-√5/3

Step-by-step explanation:

x=-b+-√b^2-4ac/2

=3+-√(-3)^2-4(1)(1)/2

The formula that can be used to find the area of the figure shaded green is 9² - 4². The correct option is c 9² - 4²

From the question, we are to determine the formula that could be used to find area of the figure shaded green

From the formula for calculating area of a square

A = s²

Where A is area

and s is the side length

Then, the area of the bigger square will be

A = 9²

NOTE: Side length of the bigger square is 9m

Then,

For the smaller square, which is not shaded green

A = 4²

NOTE: Side length of the smaller square is 4m

∴ Area of the figure shaded green = 9² - 4²

Hence, the formula that can be used to find the area of the figure shaded green is 9² - 4². The correct option is c 9² - 4²

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The equation of the circle with center at (2,-4) and tangent to the line x = -2 is given by:

(2) (x - 2)² + (y + 4)² = 16

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The circle has center at (2,-4), hence [tex]x_0 = 2, y_0 = -4[/tex].

The center is tangent to the line x = -2, hence it has a point at x = -2, since |-2 - 2| = 4, r = 4 -> r² = 16.

Hence the equation of the circle is given by:

(2) (x - 2)² + (y + 4)² = 16

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Why?

Notice that f(x) is positive when -2 < x < 1. In other words, f(x) is positive when x = -1 and when x = 1.

This interval of -2 < x < 1 translates directly to the interval notation of (-2, 1)

Unfortunately this interval notation looks identical to ordered pair notation. Be sure not to mix the two concepts up.

The parenthesis in interval notation tell the reader "do not include the endpoints". We cannot include x = -2 nor x = 1 because these values make f(x) zero, but we want f(x) > 0.

Something like choice D is a non-answer because the value x = 2 is in the interval (1,4), but f(2) = -8 which isn't positive. We can rule choice D out because of it. Choices A and C are similar situations.

Answer:

3

Step-by-step explanation:

pls mark brainliest

Answer: B

Step-by-step explanation:

The ratio of the areas of similar figures is the square of the scale factor.

So, the ratio of the areas is 16, and thus the area of DEF is (16)(90)=1440

Answer:

I guess, A is the wanted answer, but

A and D together are the really correct answer.

Step-by-step explanation:

if I understand this correctly, then

g(x) = sqrt(x - 3)

the domain of a function is the definition of all valid x (input) values.

the range of a function is the definition of all valid y (result) values.

well, the content (the arguments) of a square root cannot be negative (at least not while dealing with real numbers).

so, the answer options B and D are automatically out, because the domain contains values that would make the arguments of the square root negative.

I guess your teacher wants to focus only on the positive results of the square root, so A is the correct number.

BUT formally, without designated restrictions, a square root has always 2 solutions : a positive and a negative one.

because (-x)² = (x)² = x².

so, I would have to say that the really correct answer is

A + D, because the range contains both, the positive and the negative numbers.

Step-by-step explanation:

spending 3 parts and saving 2 parts means that there are 3+2 = 5 parts in the whole.

the whole being $100.

one of the 5 parts is then 100/5 = $20.

so, she spent 3×20 = $60 and saved 2×20 = $40.

Answer:

[tex]2\sqrt{5}[/tex] is an irrational number.

[tex](\sqrt{3} )^2[/tex] is a rational number.

Step-by-step explanation:

Answer:

none of the above

Step-by-step explanation:

4x + 7 = x + 2

4x - x + 7 = x - x + 2

3x + 7 = 2

3x + 7 - 7 = 2 - 7

3x = -5

3x / 3 = -5 / 3

x = -5 / 3 = -1.667

5x - 8 = x + 4

5x - x - 8 = x - x + 4

4x - 8 + 8 = 4 + 8

4x = 12

4x / 4 = 12 / 4

x = 3

3x + 2 = 5x + 2

3x - 5x + 2 = 5x - 5x + 2

-2x + 2 = 2

-2x + 2 - 2 = 2 - 2

-2x = 0

x = 0

Integers, As a whole number that can be written without a remainder,

x = 3

x = 0

(Mixed) Fraction

x = -5 / 3 = -1.667

The sentence "Four times the sum of a number and 17 is at least −26" translated to an inequality is 4(x+17) ≥ -26

From the question, we are to translate the given sentence into an equality.

The given sentence is

Four times the sum of a number and 17 is at least −26

Let the unknown number be x

Then,

The sum of a number and 17 will be

x + 17

Then,

Four times the sum of a number and 17 can be written as  

4(x+17)

Now,

"At least -26" means it is greater than or equal to -26

Thus,

Four times the sum of a number and 17 is at least −26 becomes

4(x+17) ≥ -26

Hence, the sentence "Four times the sum of a number and 17 is at least −26" translated to an inequality is 4(x+17) ≥ -26.

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Answer:

18

Step-by-step explanation:

The value of n = 1 , 2 , 3. Find the first 3 term and add them.

3*1 + 3*2 + 3*3 = 3 + 6 + 9

                         = 18

The perimeter of the base of the right pentagonal prism is 30 units

The given parameters are:

The volume of a right pentagonal prism is:

V = 0.5Pah

Where P represents the perimeter of the base.

So, we have:

0.5 * P * 14 * 4 = 840

Divide both sides by 0.5 * 14 * 4

P = 30

Hence, the perimeter of the base is 30 units

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The true statements are; A. Both graphs have exactly one asymptote. C. Both graphs are exponential functions. B. Both graphs have been shifted and flipped.

When the expression of function is such that it involves the input to be present as an exponent (power) of some constant, then such function is called exponential function.

There usual form is specified below. They are written in several such equivalent forms.

For example, y^x

, where a is a constant is an exponential function.

The graphs are exponential functions because as x increases, the y approaches infinity.

Here, the graphs have exactly one asymptote.

we can see that both graphs appear to have been shifted and flipped especially when at their respective coordinates.

The true statements are;

A. Both graphs have exactly one asymptote.

C. Both graphs are exponential functions.

B. Both graphs have been shifted and flipped.

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Answer:

13/32 Susan

5/16 Enrique

9/32 Martin

Step-by-step explanation:

26+20+18=64

26/64=13/32

20/64=5/16

18/64=9/32

Answer:

x = [tex]-\frac{1}{9}[/tex]

Step-by-step explanation:

FOIL what is in the parentheses by multiplying terms by -4.

[tex]-4(3x+\frac{2}{6})[/tex]

-4(3x) = -12x and -4(2/6) = -4/3

now add these products: [tex]-12x-\frac{4}{3}[/tex]

That is the simplified product ^, but assuming you're supposed to set the equation to equal 0...

Set equation to 0 and add the fraction to both sides. Rewrite as [tex]-12x=\frac{4}{3}[/tex]

Divide both sides by -12 to get variable, x, alone. Multiplying 4/3 by -1/12 is the same as dividing 4/3 by -12. The negative sign from the -12 make the quotient negative.

x = [tex]-\frac{1}{9}[/tex]

Answer:

x = -1/9

Step-by-step explanation:

FOIL what is in the parentheses by multiplying terms by -4.

-4(3x) = -12x and -4(2/6) = -4/3

now add these products:

That is the simplified product ^, but assuming you're supposed to set the equation to equal 0...

Set equation to 0 and add the fraction to both sides. Rewrite as

Divide both sides by -12 to get variable, x, alone. Multiplying 4/3 by -1/12 is the same as dividing 4/3 by -12. The negative sign from the -12 make the quotient negative.

x= 1/9

The inequality T/5 > 20 represents and T is the total number of points Kylee earned for five games situation option fourth is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

Kylee is playing a game she has to receive more than 20 points on average of five games to move onto the next level.

T is representing the total number of points Kylee earned for five games

The average is 20.

T/5 is also representing the average points of five games.

She has to receive more than 20 points on average in five games:

T/5 > 20

Thus, the inequality T/5 > 20 represents and T is the total number of points Kylee earned for five games situation option fourth is correct.

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Answer:

12.5

Step-by-step explanation:

divide 43.75 by 3.5 to get your answer

The equation written in slope-intercept form is y = (1/3)x -9

A linear equation is that which can be represented in the form of y =mx +c , m is the slope and c is the intercept.

The given equation is

y+6 = 1/3(x-9)

To determine the slope and the intercept this equation needs to be solved

y+6 = (1/3)x - 3

y = (1/3)x -9

Therefore this is the slope intercept format , here

the slope = 1/3

intercept = -9

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The exterior angles in the given triangle are angles 4 and 5.

The given shape is a triangle. A triangle is a three-sided polygon that has angles that sum up to 180 degrees. The exterior angle is the angle that is formed when a line is extended from the next side and the other side of the triangle. Simply put, it is the angle that is not inside the triangle.

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