Write each expression in simplest form. (16 x¹/₄ y³/₃)⁻⁴

The coordinates of triangle ABC after a dilation centered at the origin with a scale factor of 2 are ( - 10 , - 14 ) , ( 12 , - 6 ) , ( 4 , 14 ) .

Let

OA vector = ( - 5 , - 7 )

OA' = 2 ( -5 , - 7 )

A' = ( - 10 , - 14 )

OB vector = ( 6 , - 3 )

OB' vector = 2 ( 6 , - 3 )

B' = ( 12 , - 6 )

OC vector = ( 2 , 7 )

OC' vector = 2 ( 2 , 7 )

c' = ( 4 , 14 )

Hence , the coordinates of triangle ABC after a dilation centered at the origin with a scale factor of 2 are ( - 10 , - 14 ) , ( 12 , - 6 ) , ( 4 , 14 ) .

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Answer: (2,-2 )

Step-by-step explanation: That's where U is located on the Graph.

There are 40128 peoples in the parade route by proportion.

According to the given question.

You can fit 19 people in a 5ft x 5ft square.

Here we need to find the number of peoples in the 10ft x 1 mile parade.

Since, we have to convert miles into feet then,

1 mile = 5280 feet

We know that the parade route is in the form of rectangle.

Also, the process of proportion reasoning involves understanding the multiplicative relationships between rational quantities.

Now we will find the number of peoples by proportions,

Let us consider the number of people in the rectangle as x.

Therefore,

19/25  = x/5280

⇒ (19/25)(5280) = x

⇒ x = 40128

Hence, there are 40128 peoples in the parade route by proportion.

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Answer: C

Step-by-step explanation:

Answer: C is the correct answer

Step-by-step explanation:

The simplified form of (2 + i)/(2 - i) is (3 + 4i)/5

A Simple Form or simplified form can be defined as When a fraction's numerator and denominator share only one common factor, it is said to be in its simplest form.

Consider the given complex number(2 + i)/(2 - i)

Multiply both numerator and denominator with the complex number (2 + i), and we get

{(2 + i) × (2 + i)} / {(2 + i) × (2 - i)}= {(2 + i) × (2 + i)} / (2² - i²)          

(using the formula (x + y)(x - y) = x² - y²)= {(2 + i) × (2 + i)} / (4 - (-1))= {(2 + i) × (2 + i)} / (4 + 1)= {(2 + i) × (2 + i)} / 5= (2² + 2i + 2i + i²)/5= (4 + 4i + (-1))/5= (3 + 4i)/5

Therefore, the simplified form of (2 + i)/(2 - i) is (3 + 4i)/5.

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Answer:

The answer is -2

Step-by-step explanation:

8-4 = 4

4÷-2 = -2

answer is  y ≤ [tex]\frac{1}{3}x (-4)[/tex]

Given that,

Area of shaded inequality below solid line is positive

and  y-intercept of the solid line is equal to  - 4

therefore,

The inequality must be

y ≤ [tex]\frac{1}{3}x (-4)[/tex]

In Mathematics, inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.

A system of linear inequalities in two variables includes at least two linear inequalities in the identical variables. When we solve linear inequality then we get an ordered pair. So basically, in a system, the solution to all inequalities and the graph of the linear inequality is the graph displaying all solutions of the system. Let us see an example to understand it.

the Linear inequality: 2x – y >1, x – 2y < – 1

The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.

here is given step to easily find the value of inequality:

Step 1: The inequality is already in the form that we want. That is, the variable y y is isolated on the left side of the inequality.

Step 2: Change inequality to equality. Therefore, y > x + 1y>x+1 becomes y = x + 1y=x+1.

Step 3: Now graph the y = x + 1y=x+1. Use the method that you prefer when graphing a line. In addition, since the original inequality is strictly greater than symbol, \Large{>}>, we will graph the boundary line as a dotted line.

Step 4: The original inequality is y > x + 1y>x+1. The greater than symbol implies that we are going to shade the top area or region.

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If Brad has $272 now and lent his friend Jorge $10, his monthly allowance is $47.00

What is the total monthly allowance over 6 months?

Brad total monthly allowance over 6 months is the sum of the amount lent to Jorge and the balance Brad has currently which is $272

total allowances for 6 months=$272+$10

total allowances for 6 months=$282

monthly allowance=total allowances for 6 months/6 months

monthly allowance=$282/6

monthly allowance=$47.00

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Answer:

The midpoint is (-1, 3)

Step-by-step explanation:

Given M = [tex]\sf \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} \right)[/tex]

[tex]M=\left(\frac{2+(-4)}{2}, \frac{5+1}{2} \right)\\M=(-1, 3)[/tex]

The image of point D after the transformation of the point A is

(6,3)

The complete question is added as an attachment

From the question, we have the coordinate of point A to be

A = (-4, 3)

The sequence of transformations is given as:

The rules of the above transformations are

reflection across the y-axis

(x, y)= (-x, y)

So, we have

A' = (4, 3)

translation two units to the right

(x, y)= (x + 2 , y)

So, we have

A'' = (6, 3)

This means that

D = (6,3)

Hence, the image of point D after the transformation of the point A is

(6,3)

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Employee: "with your discount you would only pay  $4.00 a month more for the upgraded plan."

What is the discounted cost per month with new upgraded version and employer's 20% discount?

The new price before considering the employer's discount is $80.00, which means that by deducting 20% of the new price, the employee is left to pay $64.00 every month and excess of that over the current monthly payment is $4.00 as shown explicitly below:

new upgraded price=$80.00

new upgraded after discount of 20%=$80*(1-20%)

new upgraded after discount of 20%=$64.00

The extra amount payable every month=new upgraded after discount of 20%-current charge

current monthly charge=$60.00

The extra amount payable every month=$64.00-$60.00

The extra amount payable every month(cost difference)=$4.00

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The distance ab between the point a (3,5) and b (-3,-3) is 8.54 units.

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

The points on the line is  a (3,5) and b (-3,-3).

According to given question we have

The distance ab between the point a (3,5) and b (-3,-3).

ab=

[tex]\sqrt{(x_{2}-x_{1})^{2} +(y_{2} -y_{1} )^{2} } \\\\=\sqrt{(-3-3)^{2} +(-3-5} )^{2} }\\\\=\sqrt{9+64} \\\\=\sqrt{73} \\\\=8.54 units[/tex]

Therefore, the distance ab between the point a (3,5) and b (-3,-3) is 8.54 units.

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all answers can be written multiple ways

7. 65/140, 13/28, or 46.43%

8. 18/140, 9/70, or 12.86%

9. 110/140, 11/14, or 78.57%

10. 95/140, 19/28, or 67.86%

The value of the given expression using PEDMAS is 0

The meaning of PEDMAS is expressed as shown below;

P is parenthesis

E is exponent

D is division

M is multiplication

A is addition

S is subtraction

Given the expression below;

1/6(6+18)-2²

Solve the parenthesis

1/6(6+18)-2²

1/6(24)-2²

Then exponent

1/6(24) - 4

Multiplication

(1/6*24) - 4

4 - 4

Then subtract to have:

4 -  4 = 0

Hence the value of the given expression using PEDMAS is 0

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The value of QR is 5

A line segment can be defined as the part of a straight line bounded by two different end points, and also contains every point on the line between its endpoints.

From the information given, the line QS has segments, line QR , RS and QS with R and the midpoint between Q and S

Given the points;

We have that;

QR + RS = QS

substitute the values

5x + x + 3 = 9

collect like terms

6x = 9 - 3

6x = 6

Make 'x' the subject

x = 6/ 6

x = 1

But QR = 5x = 5(1) = 5

Thus, the value of QR is 5

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The complete question;

If R is the midpoint of QS and QR = 5x, RS = x + 3, and QS = 9, what is QR?

The value for f(g(1))  = 1

Given:

           g(x) =3 x+2 and f(x)= x-2 / 3

           f(x)  = x-2 / 3

substitute x =1  into the function f(x). Then:

           f(1)  = 1-2 / 3

           f(1)  =  -1/3

Now, the next step is to substitute  f(1) into the function g(x)

           g(x) = 3 x+2

        g(f(1)) = 3 (-1/3)+2

         g(f(1)) = 1

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The equation of the (g • h)(n) is (g • h)(n) = -4n³ - 8n² - 24n - 20 if the g(n)=-4n- 4 and h(n)=n² +5+n.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

g(n) = -4n - 4

h(n) =  n² +5+n

(g • h)(n) = g(n)h(n)

= (-4n - 4)(n² +5+n)

= -(4n + 4)(n² +5+n)

After simplification:

(g • h)(n) = -4n³ - 8n² - 24n - 20

Thus, the equation of the (g • h)(n) is (g • h)(n) = -4n³ - 8n² - 24n - 20 if the g(n)=-4n- 4 and h(n)=n² +5+n.

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Answer:

Equation: [tex]14x + 2 = 15x - 3[/tex]

Solution: [tex]x = 5[/tex]

Step-by-step explanation:

The two lines are parallel, therefore, the two given angles are equal alternate exterior angles.

[tex]14x + 2 = 15x - 3 \text{ / Subtract 14x}\\14x + 2 - 14x = 15x - 3 - 14x\\\to 2 = x - 3 \text{ / Add 3}\\2 + 3 = x - 3 + 3\\\to 5 = x[/tex]

Answer:

$ - 2

Step-by-step explanation:

$19 - $13 + 2 - $14  + 4 = - $2

Answer:

Step-by-step explanation:

DONT distribute the exponent

Instead, expand it to (x-2)*(x-2)

Multiply the First terms, Outer terms, Inner terms, then Last terms (FOIL)

Writing it out: (x*x) + (x*-2) + (-2*x) + (-2*-2)

Simplify: x^2 - 2x - 2x + 4

Answer: x^2 - 4x + 4

The expression equivalent to [tex]\frac{12x^{4} }{4x^{16} }[/tex] is 3[tex]x^{-12}[/tex] or 3[tex]x^{4-16}[/tex].that is option C) is correct.

According to the question the expression that we have been given to us is :

               [tex]\frac{12x^{4} }{4x^{16} }[/tex]

Note that we know the property of exponent which states that if teh exponents with same base and different power are divided then the powers are subtracted. That is,  

                 [tex]\frac{x^{m} }{x^{n} } = x^{m-n}[/tex]          (1)

Now using this rule we will evaluate the equation given that is

             = [tex]\frac{12}{4} * \frac{x^{4} }{x^{16} } \\\\[/tex]

First we will divide 12/4 which gives 3 then we will apply the property of exponent to the exponent function which gives,

             = 3 [tex]x^{4-16}[/tex]

             = 3 [tex]x^{-12}[/tex]

Hence the expression equivalent to [tex]\frac{12x^{4} }{4x^{16} }[/tex]  is 3[tex]x^{-12}[/tex]or 3[tex]x^{4-16}[/tex] that is option C) is correct.

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Based on the information, it should be noted that there be 67 adults and 733 students in the auditorium.

Let adults tickets = a

Let students tickets = s

The auditorium at McCaskey East High School in Lancaster, PA has 800 seats. This will be:

a + s = 800 ..... i

Therefore, suppose that the drama club has a goal of making $3400. This will be:

7a + 4s = 3400 ..... ii

From equation i, a = 800 - s.

7a + 4s = 3400

7(800 - s) + 4s = 3400

5600 - 7s + 4s = 3400

Collect like terms

-7s + 4s = 3400 - 5600

3s = -2200

s = 2200 / 3

s = 733

a = 800 - 733 = 67

Therefore, there'll be 67 adults and 733 students.

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The length of AC and AB is 19 and 11.

It is the measurement of something from end to end or along its longest side or a measurement of a particular part of something:

We have,

BC = 8

AC = 3x - 8

AB = 2x - 7

We can  make the line as:

A______B______C

We can write as:

AC = AB + BC

3x - 8 = 2x - 7 + 8

Simplify all the like terms together.

3x - 2x = 8 - 7 + 8

x = 16 - 7

x = 9

Now,

AC = 3x - 8 = 3 x 9 - 8 = 27 - 8 = 19

AB = 2x - 7 = 2 x 9 - 7 = 18 - 7 = 11

Thus the length of AC and AB is 19 and 11.

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The complete question is:

AC = 3x - 8, BC = 2x + 7, and AB = 8. Find AC and AB.

[tex]range = 119.1 - 78 .4 = 40.7[/tex]

First determine the mean average:

[tex]mean = \frac{119.1 + 95.2 + ... + 90.1}{10} = 99.76[/tex]

[tex]stdev = \sqrt{ \frac{ \sum(x - mean) {}^{2} }{n - 1} } = \sqrt{ \frac{(119.1 - 99.76) {}^{2} + ... }{10 - 1} } = 15.285[/tex]

Using the sine ratio, the value of x is: A. 26°.

Sine ratio is:

Sin ∅ = opposite side length / hypotenuse length of a right angle.

Given the following:

Reference angle (∅) = x

Opposite side length = 11

Hypotenuse side length = 25

Plug in the values

Sin x = 11/25

x = sin^(-1)(11/25)

x ≈ 26°

Thus, using the sine ratio, the value of x is: A. 26°

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Answer:

294 - 150 divided by 8 = A

Step-by-step explanation:

So, we already know, that we have $294 as our total. If we subtract $150, we get $144. The final step would be to divide it by $8 and that would be 18. There is 18 guests at the party.

Hope it helped!

The factorization of the given expression 3(a-b)(3r-T)+9(b-a)(2t-5s) will be equal to 3(a-b){[3r-T]-392t-5s]}.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Given expression is 3(a-b)(3r-T)+9(b-a)(2t-5s) the factorization will be done as below:-

E = 3(a-b)(3r-T)+9(b-a)(2t-5s)

E =  3(a-b)(3r-T)- 9(a-b)(2t-5s)

E = 3(a-b){[3r-T]-392t-5s]}.

Therefore, the factorization of the given expression 3(a-b)(3r-T)+9(b-a)(2t-5s) will be equal to 3(a-b){[3r-T]-392t-5s]}.

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Answer:

[tex]2 \times 10^{-4}[/tex]

Step-by-step explanation:

[tex]5 \times 10^{-2} \times 4 \times 10^{-3} \\\to 20 \times 10^{-2 + -3} \\\to 2 \times 10 \times 10^{-5} \\\to 2 \times 10^{1 + -5} \\\to 2 \times 10^{-4}[/tex]

[tex] \large \bf \implies{2 \times {10}^{ - 4} }[/tex]

[tex] \bf(5 \times {10}^{ - 2} )(4 \times {10}^{ - 3} )[/tex]

Step 1) : Rewrite the expression

[tex] \bf \longrightarrow(5 \times 4) \times( {10}^{ - 2} \times {10}^{ - 3} )[/tex]

Step 2) : Calculate the product or quotient

[tex] \bf \longrightarrow20 \times ( {10}^{ - 2} \times {10}^{ - 3} )[/tex]

Step 3) : Simplify using exponent rule with same base

[tex] \bf {a}^{n} . \: {a}^{m} = {a}^{n + m} [/tex]

[tex] \bf \longrightarrow20 \times {10}^{ - 2 - 3} [/tex]

Step 4) : Calculate the sum or difference

[tex] \bf \longrightarrow20 \times {10}^{ - 5} [/tex]

Step 5) : Express the number in scientific notation

[tex] \bf \longrightarrow2 \times {10}^{ - 4} [/tex]

Answer: The first one is 15 and the second one is 1.

Step-by-step explanation: I plugged in -4 where x is so the equation was (-4)^2-1 which equals 15.For other one i did the same thing except with the 2 so the equation was 3(2)-5 which equals 1.