Apply the properties of operations to multiply the expression

The required rotation of the 180° is given by, (X,y) -> (-X,-y), option A is correct and the required translation is given by (x + 6, y - 2), option D is correct.

Given that,
To determine which option shows the rotation of 180°, and translation of right 6 units and down 2 units.

Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.

Here,
For the rotation of the 180°, the given coordinate undergoes the change in direction so the required coordinate after 180° rotation is given as (-x, -y).
Now, for the translation of 6 units right we must add x with 6 and for 2 units down we must subtract y by 2, the required translation is given as(x + 6, y -2).

Thus, the required rotation of the 180° is given by, (X,y) -> (-X,-y), and the required translation is given by (x + 6, y - 2).

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Each pair of angles should be matched with the correct property (theorem) as follows:

e. Vertical Angles: Angles 7 and 6.

a. Alternate Exterior Angles: Angles 1 and 8.

g. Alternate Interior Angles: Angles 4 and 5.

h. Corresponding Angles: Angles 2 and 6.

d. Supplementary Angles: Angles 6 and 8.

Parallel lines simply refers to two (2) lines that always have the same or equal distance apart and never meet.

The alternate exterior angle theorem states that when two (2) parallel lines are cut through by a transversal, the alternate exterior angles that are formed are congruent or angles of equal measure and magnitude such as Angles 1 and 8.

The alternate interior angles theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent such as Angles 4 and 5.

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The hypotenuse of the right triangle is 7.93 inches.

According to the question,

We have the following information:

A right triangle has a leg that measures 7 in. The angle opposite this side measures 62°.

Now, the hypotenuse can be easily found using the trigonometric function.

(More to know: in a right triangle, we can use the Pythagoras theorem. This theorem can not used in any other triangle.)

We will use sin 62 to find hypotenuse.

Sin 62 = perpendicular/hypotenuse

Hypotenuse = perpendicular/sin 62

Hypotenuse = 7/0.88295

Hypotenuse = 7.93 inches

Hence, the hypotenuse of the right triangle is 7.93 inches.

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To find x, you would do 180-36-63, which would be 81.

Then you would do 180-81 to find z, which is 99.

To find y, would do do 180-99-13, which is 68.

Answer:

x=81

y=68

Z=99

Step-by-step explanation:

to find x we have to remember the rule that all 3 angles sum up to be 180 in a triangle

So we use this to find x

180-(63+36)=x

180-99=x

81=x

Now to find z since it is on a flat plane you just subtract 81 from 180 to find z

180-81=z

99=z

Now to find y we add all the angles of the second triangle and then subtract that sum by 180

180-(13+99)=y

180-112=y

68=y

Hopes this helps please mark brainliest

{3, 4} are the values which make up the solution set of the inequality

2b ≥ 6.

Given, an inequality

2b ≥ 6.

Now, we have to find the solution set of the given inequality,

2b ≥ 6

On dividing both the sides by 2, we get

2b/2 ≥ 6/2

b ≥ 3

So, the solution set of the given inequality, be

the values of b must be greater than or equal to 3.

So, Option (3) i.e. {3 , 4} is the solution set of the inequality.

Hence, {3, 4} are the values which make up the solution set of the inequality 2b ≥ 6.

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The simplified form of the expression, [tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } }[/tex] after evaluating is equal to [tex]\sqrt[3]{2}[/tex]

What are Powers?

Steps to Combine and Simplify Exponents

The three basic rules of exponents used to combine the exponents and simplify the expression are as follows:

Here, we have to simplify and evaluate the given expression using the rules of exponents.

We have the given expression, [tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } }[/tex]  -------(4)

Using the exponents rules, [tex](a^{m})^{n} =a^{m \times n}[/tex] and [tex](a \times b)^{m}=a^{m} \times b^{m}[/tex] in the above expression, we get

[tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } = \frac{2^{\frac{2}{3} } \times 3^{\frac{2}{3} } \times 2^{3 \times \frac{1}{3} } }{2^{\frac{2}{3} } \times 2^{\frac{2}{3} } \times 3^{\frac{2}{3} }}[/tex]

Simplifying further using (1) and (2), we get (4) as,

[tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } = \frac{2^{\frac{2}{3}}}{2^{\frac{2}{3}+\frac{2}{3} }} \times \frac{3^{\frac{2}{3} } }{3^{\frac{2}{3} }} \times 2^{1} \\\implies \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } =\frac{2^{\frac{2}{3}}}{2^{\frac{4}{3} }} \times 2^{\frac{2}{3}-\frac{2}{3} } \times 2\\\implies \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } =2^{\frac{2}{3}-\frac{4}{3} } \times 2^{0} \times 2[/tex]

We know that, [tex]a^{0} =1[/tex]

So, further simplifying we get

[tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } =2^{-\frac{2}{3} } \times 1 \times 2\\\imples \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } = 2^{-\frac{2}{3}+1 } \\\imples \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } }=2^{\frac{1}{3}}\\ \imples \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } }=\sqrt[3]{2}[/tex]

Therefore, the simplied form of the given expression is [tex]\sqrt[3]{2}[/tex]

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The new price of the car is $25441.

Given that the $26,000 car is on sale for 5% off with 3% tax.

The discount will be:

= 5% × $26000

= $1300

The tax will be:

= 3% × ($26000 - $1300)

= 3% × $24700

= $741

The new price will be:

= Amount - Discount + Tax

= $26000 - $1300 + $741

= $25441

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The number is 17

Let the number = x

From the question, we have

(x*100)/10*1000 = 170000

x = 17

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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Answer:

-3/22

Step-by-step explanation:

Hope this helps!

Answer: [tex]-\frac{3}{22}[/tex]

Step-by-step explanation:

To find the product, multiply the two fractions:

[tex]-\frac{2}{11} *\frac{3}{4} =-\frac{2*3}{11*4} =-\frac{6}{44} =-\frac{3}{22}[/tex]

Inverse of the function is -2+x

What do you mean by inverse function?

A function that returns the initial value for which a function has produced an output is known as an inverse function. If f(x) is a function that produces the value y, then [tex]f^{-1}(y)[/tex] the inverse function of y, will provide the value x.

The function's inverse, represented by ,  [tex]f^{-1}[/tex] returns the original value that was used to create the output (x).

Given function is  y = x² + 4x + 4

To find the inverse function, we need to express x as a function of y:

Substitue y=x

⇒ x = [tex]y^{2}+4y+4[/tex]

Substract x from the above equation we get,

[tex]y^{2}+4y+4[/tex] - x = 0

Solve the above equation using quadratic formula we get,

y = [tex]\frac{-4+\sqrt{16-4(4-x)} }{2}[/tex]   [tex]=\frac{-4+\sqrt{16-16+4x} }{2}[/tex]  = [tex]\frac{-4+2x}{2}=-2+x[/tex]

Similarly, y = -2-x

Therefore, [tex]f^{-1}=[/tex] -2+x , -2-x

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Answer:

Step-by-step explanation:

Ok:

Area of circle:

A=πr^2

1. Apply to question!

5^2π=

25π/4: Since it is a 1/4 of the circle

6.25π

Answer: 6.25π or 6.25 pie

Answer:

about 19.63496 m^2

Step-by-step explanation:

this is 1/4 of a circle so we find the are of the full circle

pi(r)^2

pi(5)^2

pi25

78.53982

Divide by 4

78.53982/4

19.63496

Hopes this helps please mark brainliestC

Answer:

Part A

[tex](x-r)^2+(y-s)^2=t^2[/tex]

where:

Part B

Domain = [-3, 17]

Range = [-14, 6]

Part C

Point (9, 1) is inside the border of the circle.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

From inspection of the given triangle:

Substitute these values into the formula to derive the standard equation of the circle:

[tex]\boxed{ (x-r)^2+(y-s)^2=t^2}[/tex]

where:

Given the center of the circle (r, s) is (7, -4) and the radius (t) is 10.

The domain of the circle is the x-value of the center minus and plus the radius:  

[tex]\begin{aligned}\implies \textsf{Domain}&=[r-t,r+t]\\&= [7-10, 7+10] \\&= [-3, 17]\end{aligned}[/tex]

The range of the circle is the y-value of the center minus and plus the radius:

[tex]\begin{aligned}\implies \textsf{Range}&=[s-t,s+t]\\&=[-4-10, -4+10]\\& = [-14, 6]\end{aligned}[/tex]

Substitute (r, s) = (7, –4) and t = 10 into the derived equation from part A:

[tex]\implies (x-r)^2+(y-s)^2=t^2[/tex]

[tex]\implies (x-7)^2+(y-(-4))^2=10^2[/tex]

[tex]\implies (x-7)^2+(y+4)^2=100[/tex]

Substitute the given point (9, 1) into the equation:

[tex]\begin{aligned}\implies (9-7)^2+(1+4)^2&=2^2+5^2\\&=4+25\\&=29\end{aligned}[/tex]

As 29 < 100, the point (9, 1) is inside the border of the circle.

Answer:

No solution.  The lines are parallel

Step-by-step explanation:

I graphed with Desmos.  It is a free.

Step-by-step explanation:

what is the problem to solve ?

I assume we need to calculate the area of the whole figure ?

in any case, we have a problem :

a rhombus is a tilted square, a special parallelogram, as it has 4 equal sides.

that would mean all 4 sides of that central rhombus are 5 in.

that would make both triangles equilateral triangles (all 3 sides are equally long : 5 in).

but in order for a right-angled triangle to have the Hypotenuse = 5 in and the height (= left leg) = 4 in, that must make the right leg

5² = 4² + leg²

25 = 16 + leg²

9 = leg²

leg = 3 in

and so, the baseline of the large triangle 2×3 = 6 in.

and not 5 in, which must be the top and base line of the rhombus.

so, the whole problem definition is wrong.

the only solution when accepting the given lengths, is that the triangle sides are NOT a straight extension of the rhombus sides.

the triangle side is the Hypotenuse of the smaller internal right-angled triangle

side² = 4² + (5/2)² = 16 + 6.25 = 22.25

side = 4.716990566... in

anyway, the area of each of the large triangles is

baseline×height / 2 = 5×4/2 = 10 in²

we have 2 triangles = 2×10 = 20 in²

the area of the rhombus is

baseline×height = 5×4 = 20 in²

please note that the area of a rhombus is also

diagonal1 × diagonal2 / 2

but that applies only, when we have the lengths of the diagonals. both approaches give the same result, of course.

so, the whole area is

20 + 20 = 40 in²

Answer:

value of stock =1.5% × 420?= 6.3

The pairs of numbers given, (1, 2) is not a solution.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

y= 2x+1 /3

Now, First value of x = 0

y= 2(0)+1 /3

y= 1/3

i.e., (0, 1/3)

and, Second value of x = 1

y= 2(1)+1 /3

y= 5/3

i.e., (1, 5/3)

and, Third value of x = 4

y= 2(4)+1 /3

y= 9/3

y=3

i.e., (4, 3)

Hence, from the pairs of numbers given, (1, 2) is not a solution.

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The roots of the equation x³ + 2x² + 36x + 72 = 0 are ( -2 , -6i , +6i )

What is Factorizing?

Brackets should be expanded in the following ways:

For an expression of the form a(b + c), the expanded version is ab + ac, i.e., multiply the term outside the bracket by everything inside the bracket

For an expression of the form (a + b)(c + d), the expanded version is ac + ad + bc + bd, in other words everything in the first bracket should be multiplied by everything in the second.

Given data ,

Let the equation be x³ + 2x² + 36x = -72

Adding 72 on both sides , we get

x³ + 2x² + 36x + 72 = 0

Now , on simplifying we get

Take the common factor x² in first two terms and 36 in last two terms

So ,

x² ( x + 2 ) + 36 ( x + 2 ) = 0

Now , taking ( x + 2 ) as common factor , we get

( x² + 36 ) ( x + 2 ) = 0

So , for the equation to be 0 , either ( x + 2 ) = 0 or ( x² + 36 ) =0

And , we can find the solutions to the equation as

x + 2 = 0

Subtracting 2 on both sides , we get

x = -2

So , one solution is -2

Now ,

( x² + 36 ) =0

Subtracting 36 on both sides , we get

x² = -36

x = √ ( -36 )

x = ± 6i

So , we got two more solutions as -6i and +6i

Hence , the roots of the equation are -2 , -6i and +6i

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THE LENGTH AND WIDTH WILL BE = length: 5.7 yd

width: 1.7 yd.

According to our question-

 w(w +4) = 10

 w² +4w = 10 . . . . . eliminate parentheses

 w² +4w +4 = 14 . . . . . . add the square of half the w-coefficient to complete the square

 (w +2)² = 14 . . . . . . . . . rewrite as a square

 w +2 = √14 . . . . . . . . . take the square root

 2 = -2 +√14 ≈ 1.7 . . . . yards (width)

Then the length is 4 more yards than this, so is ...

 length = 1.7 +4 = 5.7 . . . yards

The length and width are 5.7 and 1.7 yards, respectively.

In the attached graph, we let x represent the length. As you can see, the magnitudes of the two zeros are width and length.

HENCE,THE LENGTH AND WIDTH WILL BE = length: 5.7 yd width: 1.7 yd.

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The solution of linear programming problem is the maximum value is 2, x_1 = 1, x _2 =0.

What is linear programming problem?

The goal of the Linear Programming Problems (LPP) is to determine the best value for a given linear function. The ideal value may be either the highest or lowest value. The specified linear function is regarded as an objective function in this situation. The objective function may have a number of variables that must meet a set of linear inequalities known as linear constraints. These variables may also be subject to conditions. The following scenarios, such as manufacturing difficulties, diet problems, transportation challenges, allocation problems, and so on, can be solved optimally using the linear programming problems.

After first iteration,

Negative minimum Z_j-C_j is -2 and its column index is 1. So, the entering variable is x_1.

Minimum ratio is 1 and its row index is 2. So, the leaving basis variable is S_2.

∴ The pivot element is 2.

Entering =x_1, Departing =S_2, Key Element =2

After second iteration:

Since all Z_j-C_j≥0

Hence, optimal solution is arrived with value of variables as :

x_1=1,x_2=0

Max Z=2

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Step-by-step explanation:

g(x) = the original function at x-2.

just means it is the same function as the original function, just moved 2 units to the right.

just think about it :

e.g.

g(3) is the same as the originated function at x=1.

g(4) is the same as the original function at x=2.

...

so, everything that happened for the original function at x, happens now for g at x+2.

therefore, again, things move 2 units to the right (positive x direction) .

that means the vertex "moves" from

(-5, 6) to (-3, 6)

the vertex of g(x) = (-3, 6)

Answer:

The answer to this problem is 1401.

Step-by-step explanation:

By using the order of operations listed here, we can solve the problem very easily.

EVALUATE IN PARENTHESES [tex]40-9[/tex]: 40 minus 9 is 31, so now the problem is 15(31) x 3 + 6

MULTIPLY/DIVIDE [tex]15(31)*3[/tex]: X times Y can be [tex]X*Y[/tex] or [tex]X (Y)[/tex]. This evaluates to [tex]15*31*3[/tex] which is 1395.

ADD/SUBTRACT: The problem now is just [tex]1395+6[/tex] which evaluates to a total of [tex]1401[/tex].

Check the picture below.

Every second, 44 megabytes of files will be transferred to her hard drive.

The size of the files on her external hard drive in megabytes is given F, where F = 38 + 6t and t is the time in seconds since the transfer began.

The function is below

F = 38 + 6t   ....(i)

To determine the number of megabytes of files transferred to her hard drive every second

Substitute the value of t = 1 in the equation (i), and solve for F

F = 38 + 6(1)

F = 38 + 6

F = 44

So the number of megabytes of files = 44

Therefore, every second, 44 megabytes of files will be transferred to her hard drive.

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Answer:

2

Step-by-step explanation:

6w is a term

7x is a term

Answer:

ft HD st he do it to we if do ks do just bc

Answer:

y = 4 sin(2x/3)

Step-by-step explanation:

The parent function for sine functions is:   y = a sin b(x - c) + d

"a" defines amplitude/vertical dilation

"b" defines the change to the period/horizontal dilation

"c" defines the phase shift/horizontal translation

"d" defines the midline/vertical translation  

We can already set "a = 4" because 4 is the amplitude.

However, to include the period into the function, we have to take note of the parent sine function already having a period of 2π.

This means: 2π/b = period

                    2π/period = b

                    2π/3π = b

                    2/3 = b

Knowing the "a" and "b" values, we can set up the equation:

y = 4 sin(2x/3)

No horizontal/vertical translations were applied, so "c" and "d" are both zero.

Answer: y-9 = 17(x+7)

Step-by-step explanation:

We will use the second coordinate point to use in the equation and the first coordinate (-8, -8) to figure out the slope of this line.

Answer:

y-9=17x+119

Step-by-step explanation:

given points (-8,-8) & (-7,9)

let's take (-7,9) as (x1,y1) and (-8,-8) as (x2,y2)  

now for finding out equation through two points, we use

[tex] \frac{x-x_{1} }{x_{1}-x_{2}  } =\frac{y-y_{1} }{y_{1}-y_{2}  } [/tex]

So accordingly, we input the values

[tex] \frac{x-(-7) }{-7-(-8)}  } =\frac{y-9 }{9-(-8)  } [/tex]

[tex] \frac{x+7 }{-7+8}  } =\frac{y-9 }{9+8  } [/tex]

[tex] \frac{x+7 }{1}  } =\frac{y-9 }{17 } [/tex]

[tex] 17(x+7) = y-9 [/tex]

[tex] 17x+119 = y-9 [/tex]

A 32% mark up means that the price goes up by 32 percent. The way to find this is by finding 132% of $400.

1.32 x 400 = $528.

I hope this helps!

The price of the microscope after the markup of 32% at the store will be equal to $528.

The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.

As per the given data in the question,

Price of microscope = $400

Markup percentage = 32%

Increase in price = 400 × 32/100

= $128.

Price after markup will be,

$400 + $128 = $528.

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The graph of the function g(x) after putting the value in function f(x) is attached with the answer.

What is function?

A relation b/w a collection of inputs and outputs is known as a function. A function is a relationship between inputs in which each input is connected to precisely one output.

Given function:  f(x) = x-1

we have to find: g(x)=f(3/4x)

Putting the value of f(x) in g(x),

g(x) = 3/4x - 1

Now, the graph of the function (3/4)x - 1 is attached in the question.

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