Which sequence of transformations can be used to show that triangle J is congruent to triangle P?

The number line that satisfies the inequality is option (B).

What are number lines?
Number lines are horizontal straight lines in mathematics where numbers are arranged in equal intervals. A numeric line can be used to represent every number in a sequence. The endpoints of this line go on infinitely. In other terms, it is an image of numbers on a straight line. It functions as a guide for distinguishing and organizing numbers. It can be used to represent any real number, including all whole numbers and natural numbers.

Solution Explained:
- (a+5) < 4/-2 <= -3-a

[tex]\left \{ {{- (a+5) < 4/-2} \atop { 4/-2 < -3-a}} \right.[/tex]

[tex]\left \{ {{-a - 5 < -2} \atop {-2 < = -a -3}} \right.[/tex]

[tex]\left \{ {{-a-5) +5 < -2+5} \atop {-2+3 < = (-a-3)+3}} \right.[/tex]

[tex]\left \{ {{-a- 5 +5 < 3} \atop {1 < = -a-3+3}} \right.[/tex]

[tex]\left \{ {{-a < 3} \atop {1 < = -a}} \right.[/tex]

[tex]\left \{ {a > -3} \atop {-a > = 1}} \right.[/tex]

[tex]\left \{ {{a > -3} \atop {a < = -1}} \right.[/tex]

[tex]-3 < a < = -1[/tex]

a ∈ (-3, -1]

Hence, the number line that satisfies the inequality -(a+5) < b/-2 <= -3-a is in option (B).

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At confidence, how large a sample should be taken to obtain a margin of error for the estimation of a population proportion? We now assume that past data are not available for developing a planning value for

Preliminary estimate for proportion (Not Known) is equal to 0.5

Margin of error = E = 0.03

Level of significance = 1-0.99 = 0.01

Z critical value is considered as (by using Z table) = 2.576

So, the sample size formula is taken as

n = [p(1 – p)][tex]\left[Z/E]^{2}[/tex]

=[0.5*(1-0.5)] [2.576/0.03][tex]^{2}[/tex]

=1,843.03                    

Hence, the sample size is approximately will be 1,844

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Answer:

120 minutes

Step-by-step explanation:

d=rt

D-distance

r-unit rate

T- time

14=7t

/7. /7

2=t

2 hours

2 x60=120

120 minutes

Hopes this helps please mark brainliest

Reflection is along line x = 1, using plotting of points.

What do you mean by reflection , rotation and translation?

An object can be reversed across a line through reflection without changing its size or shape.

Rotation is the movement of an item around a fixed point while maintaining its original size and shape.

A figure can be translated if it is moved in any direction without altering its size, form, or orientation.

An object is always translated, but it is never turned, flipped, or shrunk.

It is given that Jayden is drawing the top view of a square sandbox on a coordinate plane with vertices at D(1, 1), E(1, 6), F(6, 6) , and G(6, 1) .

On plotting these points on graph paper we get below graph, (1)

Now , to move the sandbox so that it is in the shade, he reflects it and the new  vertices of the image are at D′(1, 1), E′(1, 6), F′(−4, 6) , and G′(−4, 1)

On plotting these new coordinates we get below graph (2)  

Square box in the second graph shifted to left side of x = 1.

Therefore, reflection is along line x = 1.

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Answer:

314

Step-by-step explanation:

1. Divide 63 by pi (equals 20)

2. Divide 20 by 2 which equals 10.

3. Multiply 10 by itself to get the square. which would be 100

4. Multiply 100 by pi

3. Finally A=314

The expression 7⁻⁴/(7⁻⁴)⁶ in simplified form using positive exponents is (7)²⁰  .

In the question ,

it is given that ,

the expression is 7⁻⁴/(7⁻⁴)⁶ .

we need to find the simplified value of the expression .

So ,

= 7⁻⁴/(7⁻⁴)⁶

we know that (xᵃ)ᵇ = (x)ᵃˣᵇ

By using the above property , we get

= 7⁻⁴/(7)⁻⁴ˣ⁶

= 7⁻⁴/(7)⁻²⁴

we know that xᵃ/xᵇ = xᵃ⁻ᵇ

By using the above property , we get

= (7)⁻⁴×(7)²⁴

= (7)²⁴⁻⁴    ... by using the property xᵃ.xᵇ = xᵃ⁺ᵇ

= (7)²⁰

Therefore , The expression 7⁻⁴/(7⁻⁴)⁶ in simplified form using positive

exponents is (7)²⁰  .

The given question is incomplete , the complete question is

Simplify the following expression. Write your answer using positive exponents.

7⁻⁴/(7⁻⁴)⁶

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Answer:

Problem: 0.5(5-7x)=8-(4x+6)

Answer: x= -1

The equations that is true for the values x = -2 and x = 2 is x² – 4 = 0  and 4x² = 16.

Equations:

Equation is an an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations.

For example, 3x² − 2x + 9 is an algebraic expression.

Given,

Here we have the following equations

x² – 4 = 0

x² = –4

3x² + 12 = 0

4x² = 16

2(x – 2)² = 0

Now, we need to find which of these equations are tur for the values x = -2 and x = 2.

In order to find the true equation, we have to apply the given values on each of these to find which one is correct,

When x = 2 then,

(2)² – 4 = 0 => 4 - 4 = 0 (True)

(2)² = –4 => 4 ≠ -4 (Not true)

3(2)² + 12 = 0 => (3x4) + 12 = 0 => 12 + 12 = 0 => 24 ≠ 0 (Not true)

4(2)² = 16 => (4 x 4) = 16 => 0 = 0 (True)

2(2– 2)² = 0 => 2(0) = 0 = 0 = 0 (True)

Similarly, when we apply the value of x = -1, then we get,

(-2)² – 4 = 0 => 4 - 4 = 0 (True)

(-2)² = –4 => 4 ≠ -4 (Not true)

3(-2)² + 12 = 0 => (3x4) + 12 = 0 => 12 + 12 = 0 => 24 ≠ 0 (Not true)

4(-2)² = 16 => (4 x 4) = 16 => 0 = 0 (True)

2(-2– 2)² = 0 => 2(-4)² = 0 => 32 ≠ 0 = 0 (Not true)

Therefore, the resulting equations are x² – 4 = 0  and 4x² = 16.

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An equation of the line that began with a y-intercept of (0, 4), shifted up 3 units, and is perpendicular to y = 3/4(x) - 2 is: A. y = -4/3(x) + 7.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

In Mathematics, the condition for perpendicularity of two lines is given by m₁ × m₂ = -1. Next, we would determine the slope of this equation that began with a y-intercept of (0, 4):

3/4 × m₂ = -1

3m₂/4 = -1

3m₂ = -4

m₂ = -4/3

In order to determine the new y-intercept, we would translate the equation by shifting it 3 units up:

Translation = y + 3 = 4 + 3 = 7.

Now, we can write this equation in slope-intercept form as follows:

y = mx + c

y = -4x/3 + 7 or y = -4/3(x) + 7.

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Complete Question:

What is the equation of the line that began with a y-intercept of (0,4), was shifted up 3 units, and is perpendicular to y = 3/4x-2?

answer choices:

A. y = -4/3(x) + 7

B. y=-3/4(x)+7

C. y=-3/4(x)+4

D. y =-4/3(x)+4

The required rate of annual decay rate is given as 11.70%.

Given that,
The half-life of Radium-228 is 5.75 years. What is the annual decay rate is to be determined.

The half-life of the element is defined as the time span in which the element grows or decays half of its whole composition of growth and decay.

Here,
According to the question,
[tex]1/2 = (1 - r)^{5.57}\\(1/2)^{1/5.57} = (1 -r)\\r = 0.1170\\r = 11.70%[/tex]

Thus, the required rate of annual decay rate is given as 11.70%.

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For the given inequality –3(2x – 5) < 5(2 – x) the correct way of representation is x > 5 which means an open circle is at 5 and bold line starts at 5 and is pointing to the right.

As given in the question,

Given inequality is given by:

–3(2x – 5) < 5(2 – x)

Simplify the given inequality to get the correct way of representation,

Open the parenthesis we get,

-3(2x) + 3(5) < 5(2) -5(x)

⇒-6x +15 < 10 -5x

Take like terms on the same side we get,

⇒15-10< 6x -5x

⇒ x > 5

This means value of x starts from 5 move towards right direction excluding 5.

Therefore, for the given inequality –3(2x – 5) < 5(2 – x) the correct way of representation is x > 5 which means an open circle is at 5 and bold line starts at 5 and is pointing to the right.

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Answer:

The lines through the given points are parallel

Step-by-step explanation:

The given lines can be evaluated as follows

The first step is to calculate the slope [tex]m_{1}[/tex] of the first line using the slope formula as follows

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

Take two coordinates on the first line

[tex](10,5)~\text{and}~(-8,9)[/tex]

Substitute [tex]9[/tex] for [tex]y_{2}[/tex], [tex]-8[/tex] for [tex]x_{2}[/tex] , [tex]5[/tex] for [tex]y_{1}[/tex] , [tex]10[/tex] for [tex]x_{1}[/tex]  in the slope formula

[tex]m_{1}=\frac{9-5}{-8-10}[/tex]

Simplify the numerator and the denominator at the right side of the equation

[tex]m_{1}=\frac{4}{-18}[/tex]

Simplify the fraction at the right side of the equation

[tex]m_{1}=-\frac{2}{9}[/tex]

The slope of the first line is [tex]-\frac{2}{9}[/tex]

Take two coordinates on the second line

[tex](2,-4)~\text{and}~(11,-6)[/tex]

Substitute [tex]-6[/tex] for [tex]y_{2}[/tex], [tex]11[/tex] for [tex]x_{2}[/tex] , [tex]-4[/tex] for [tex]y_{1}[/tex] , [tex]2[/tex] for [tex]x_{1}[/tex]  in the slope formula

[tex]m_{2}=\frac{-6-(-4)}{11-2}[/tex]

Take out the brackets in the numerator at the right side of the equation

[tex]m_{2}=\frac{-6+4}{11-2}[/tex]

Simplify the numerator and the denominator at the right side of the equation

[tex]m_{2}=\frac{-2}{9}[/tex]

The slope of the second line is [tex]-\frac{2}{9}[/tex]

Since the slope of both lines are equal, then the lines through the given points are parallel

Hence the lines through the given points are parallel

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Answer:

7/5

Step-by-step explanation:

12x - 15 = 6 - 3x

15x = 21

x = 7/5

Answer:

Step-by-step explanation:

it is 2

The equation of the parabola from the vertex is f(x) = -3(x - 5)² + 9

The equation of the function is given as

f(x) = 3x²

Also, we have

Vertex = (5, 9)

The form of the equation is given as

f(x) = a(x - h)² + k

Where

Vertex = (h, k)

This means that

Vertex = (h, k) = (5, 9)

Substitute (h, k) = (5, 9) in the equation f(x) = a(x - h)² + k

So, we have

f(x) = a(x - 5)² + 9

This also means that

f(x) = -3(x - 5)² + 9

The -3 is gotten from f(x) = -3x²

Hence, the equation of the parabola is f(x) = -3(x - 5)² + 9

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The expression using distributive property becomes 7n - 35

The distributive property is also known as the distributive law of multiplication over addition and subtraction.

The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC. This distributive law is also applicable to subtraction and is expressed as, A (B - C) = AB - AC. This means operand A is distributed between the other two operands.

Using this distributive law, A × (B + C) = AB + AC. to re-write the expression -7(5 - n), A = -7, B = 5 and C = -n

we have -7(5 - n) = (-7 x 5) + (-7 x -n)

which is further simplified as (-35) + (7n) = 7n - 35

In conclusion, the re-written form of -7(5 - n) in distributive form is 7n - 35

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Answer:

um well fierst da answer is proberly yes and no

Step-by-step explanation:

i tried to do da work

Answer:

The total amount of college students enrolled part-time that year would be approximately 2 million.

Step-by-step explanation:

In order to find out the amount of college students enrolled part-time that year, we need to convert the 23% into 0.23, and then use a calculator, with this equation:

0.23 x 6,600,000 = 1,518,000

Now, it says to "round your answer to the nearest million."

1.518 million is closer to 2 million than 1 million, so our answer would be 2 million.

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Denise got $30 for her birthday, spending $6 on lunch, and having $24 left.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the money that Denise get for her birthday.

Denise split her birthday money with her two sisters. the spent 6$ on lunch, so he has $24 left. Hence:

Amount gotten for birthday = $6 + $24

y = $6 + $24 = $30

Denise had $30

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The volume of a drill bit with a radius of 3 centimeters is of:

16.32 cm³.

To obtain the numeric value of a function or of an expression, each instance of the input variable of the function has to be replaced by the value at which we want to find the numeric value.

The volume of a drill bit with a radius of r centimeters is given by the equation presented as follows:

[tex]V = \frac{\sqrt{3}}{9}\pi r^3[/tex]

Hence, for a radius of 3 centimeters, as is the case in this problem, the lone instance of r is replaced by 3, and the volume is obtained as follows:

[tex]V = \frac{\sqrt{3}}{9}\pi (3)^3 = 16.32[/tex]

The unit of the volume is in cubic centimeters, as the radius is measures in centimeters and then it is cubed.

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The solution set of 'b' for the given compound inequality is

-2 < b < 4.

Given, a compound inequality 6b < 24 and 4b + 12 > 4.

Now, solving the first inequality,

6b < 24

On dividing both the sides by 6, we get

6b/6 < 24/6

b < 4.

Now, solving the second inequality,

4b + 12 > 4

On subtracting 12 from both the sides, we get

4b + 12 - 12 > 4 - 12

4b > -8

On dividing both the sides by 4, we get

4b/4 > -8/4

b > -2.

So, the solution set of b to satisfy the compound inequality be,

greater than -2 and less than 4 i.e.

-2 < b < 4.

Hence, the solution set of 'b' is -2 < b < 4.

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Option (A) is the correct option and on simplifying the expression by combining like terms we get,

24 - 3p.

Given, the expression 6(4 - 2p) + 9p

On simplifying, we get

24 - 12p + 9p

24 - 3p

So, on simplifying the given expression, we get

24 - 3p

Hence, Option (A) is the correct option and on simplifying the expression by combining like terms we get,

24 - 3p

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The amount of water left in the tub after 5 minutes is; 24 gallons

The given recursive formula is expressed as;

aₙ = aₙ ₋ ₁ - 12

We are told that a₀ represents the amount of water left, in gallons, in a bathtub n after the drain stopper was pulled.

Thus, when n = 1, we have;

a₁ = a₁ ₋ ₁ - 12

a₁ = a₀ - 12

a₁ = 84 - 12

a₁ = 72

Then;

a₂ = a₁ - 12

a₂ = 72 - 12

a₂ = 60

It will seem that it follows a sequence pattern of;

aₙ = 84 - 12n

Thus;

a₅ = 84 - 12(5)

a₅ = 24 gallons

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Answer:

the answer is 99 because the difference between the numbers is 11 and if you do 9 ×11 you get 99

Answer: The nth term of this sequence is a n= 11n-2

Step-by-step explanation:

Sequence : 9, 20, 31, 42

Difference : +11, +11, +11

The formula for nth term of an arithmetic progression is a n= d.n+a1-d

The formula for nth term of an arithmetic progression is d= 11 and a1=9

so.

a n=d.n+a 1-d

a n=11.n+9-11

a n=11n-2

Hope it helps :)

The value of x is .[tex]\sqrt{170}[/tex]

What is Pythagorean Theorem?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the other two sides.

Here, the two sides of the triangle are, 7 and 11.

By Pythagorean theorem,

[tex]7^2 + 11^2 = x^2\\49 + 121 =x^2 \\170 = x^2\\x = \sqrt{170} \\[/tex]

Hence, the value of x is [tex]\sqrt{170}[/tex].

Here, the sum of two sides of triangle is not a perfect square.

Therefore, the side lengths is not a Pythagorean triple.

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Answer:

b < 8

Step-by-step explanation:

Given inequality:

[tex]\dfrac{3}{2}b+5 < 17[/tex]

Subtract 5 from both sides:

[tex]\implies \dfrac{3}{2}b+5-5 < 17-5[/tex]

[tex]\implies \dfrac{3}{2}b < 12[/tex]

Multiply both sides by 2:

[tex]\implies 2 \cdot \dfrac{3}{2}b < 2 \cdot 12[/tex]

[tex]\implies3b < 24[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3b}{3} < \dfrac{24}{3}[/tex]

[tex]\implies b < 8[/tex]

Using the distance, 5/4 far distance that they ride in all.

In the given question,

Carlos and his mom went out on a bike ride.

They rode 5/8 of a mile to the park and then rode 5/8 of a mile back home.

We have to check how far did they ride in all.

We have to find the total distance that he ride to park and from the park.

We can find the total distance by adding the whole distance that he ride.

Total distance = Distance to the park + Distance back home

Total distance = 5/8+5/8

Since the denominator is same. So

Total distance = (5+5)/8

Total distance = 10/8

Now simplifying.

Total distance = 5/4

Hence, 5/4 far distance that they ride in all.

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Answer:

Step-by-step explanation:

y=-x-7........(1)

5y+3x=-13..........(2)

(2) - 3x(1)=>

5y+3x= -13

3y + 3x = - 21

(-)    (-)      (+)

-----------------------

2y+0=8

=>y=4

  (1)=>

  y= -x-7

=>x= -y-7

=>x= -4-7

=>x= -11 .

Answer:

x=-11 & y= 4

Step-by-step explanation:

y=-x-7

5y+3x=-13

y+x=-7—eqn i

5y+3x=-13—eqn ii

multiply eqn i by 5

5y+5x=-35

multiply eqn Ii by 1

5y+3x=-13

put eqn I and Ii together

5y+5x=-35

5y+3x=-13

subtract

2x=-35--13

2x=-35+13

2x=-22

divide both sides by 2

2x/2 = -22/2

x=-11

put x=-11 into eqn i

y+x=-7

y-11=-7

y=-7+11

y=4

A company's profit is determined by its revenue less its cost of operations.Subtract costs from revenue to get the profit function.

Let P(x) stand for the profit, R(x) for the revenue, and C(x) for the expense.Profit thus equals P(x) = R(x) -C. (x).The revenue and expense can be modeled as fixed values or as functions,

Profit = Revenue - Cost

We need to find an equation for the revenue R(x).

R(x) = number of units * unit price = x * p(x) = x(72-x) = 72x - x2

Therefore: Profit P(x) = 72x - x2 - (20 + 52x) =  - x2 + 20x -20

To find max profit, run the 1st derivative test, so set P'(x) = 0 and solve for x:

P'(x) = -2x + 20

set P'(x) = 0 ----> -2x+20 = 0 ----> -2x = -20 -----> x = 10

The number of units, x, that produces the maximum profit is 10.

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