The number of Minghua's stamps is 1 1/2 times that of John's.

To make x² + 6x = 7 a perfect square, we add 16 to the equation.

In the question, we are asked for the term that must be added to the equation x² + 6x = 7, to make it into a perfect square.

The given equation can be shown as:

x² + 6x = 7,

or, x² + 6x - 7 = 0.

To make it a perfect square, we need to find the b² term as per the 2ab term for the formula, (a + b)² = a² + 2ab + b², where a is x.

This can be shown as:

x² + 6x - 7 = 0,

or, x² + 2(x)(3) - 7 = 0, where we get b = 3.

Thus, b² = 3² = 9, can be obtained by adding 16 to the equation, as -7 + 16 = 9.

Thus, we add 16 to both sides of the equation, to get:

x² + 2(x)(3) - 7 + 16 = 16,

or, x² + 2(x)(3) + 9 = 16,

or, (x + 3)² = 16, which gives us the required perfect square.

Thus, to make x² + 6x = 7 a perfect square, we add 16 to the equation.

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The end behavior of the given function (range) is x< 4 or x > 4. So, f(x) < 4 or f(x) > 4. The solution in interval notation is [tex]\mathbf{(-\infty, 4) \cup (4, \infty)}[/tex].

The last option is correct.

The end behavior of the given function f(x) = (8x+1)/2x-9 wants us to identify the range of the given function.

The range is the set of values of the dependent variable for which a function is defined. The function range is the combined domain of the inverse function.

From the information given:

[tex]\mathbf{f(x) = \dfrac{8x +1}{2x -9 }}[/tex]

Inverse of [tex]\mathbf{\dfrac{8x +1}{2x -9 }}[/tex] becomes [tex]\mathbf{f(x) = \dfrac{1+9x}{2(-4+x) }}[/tex]

The domain of the inverse is x< 4 or x > 4. So, f(x) < 4 or f(x) > 4. Now, representing the solution in interval notation, we have:

[tex]\mathbf{(-\infty, 4) \cup (4, \infty)}[/tex]

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Answer:Yes, it is possible to have the sum of square roots equal the square root of the sum of the radicands.

If either a or b equals zero, then the sums would be the same.

Since the square root of 0 is 0, adding it to a given radical would not change the radical. Also, adding zero to the radicand would not change its value.

Step-by-step explanation:

The statement √a + √b = √(a + b) is not possible since a ≠ b

The operation involving surd is most likely an algebraic expression where in the case of surd the value in the square root are like the alphabets in algebraic expression.

Some surd operations are given as shown below:

Now, let us consider the question given:

Since a and b are not equal, it means

√a + √b ≠ √(a + b)

Thus, we can conclude that the statement √a + √b = √(a + b) is not possible

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Answer:

Step-by-step explanation:

Step-by-step explanation:

15 r blue marbles

20- 5 = 15

Based on the given parameters, the midpoint of the line segment is (5, 1/2)

The complete question is added as an attachment

From the figure, we have the following coordinates

(5, 4) and (5, -3)

The midpoint of the segment is then calculated using

(x, y) = 0.5 * (x1 + x2, y1 + y2)

Substitute the known values in the above equation

(x, y) = 0.5 * (5 + 5, 4 - 3)

Evaluate the sum and the difference

(x, y) = 0.5 * (10, 1)

Evaluate the product

(x, y) = (5, 1/2)

Hence, the midpoint of the line segment is (5, 1/2)

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Check the picture below.

we could also look at it from the inscribed angle theorem, bearing in mind that the intercepted arc is 180°.

Answer:

2(7x + 2)

Step-by-step explanation:

Perimeter of a Rectangle = 2 x Length + 2 x Width.

Given Length = 4x, Width = 3x + 2,

Perimeter of Rectangle = 2(4x) + 2(3x + 2)

= 8x + 6x + 4

= 14x + 4 (Degree one polynomial)

= 2(7x + 2)

The first table is a quadratic function while the second table is a linear function.

1) For the first table, we have;

x y

0 5

1 0

2 -3

3 -4

4 -3

x = 2  and x = 4 have same value of y = -3  and as such it will be a Quadratic Function.

y = x²  - 6x + 5

2) For the second table, we have;

x y

2 5

5 14

6 17

8 23

10 29

This table is a Linear function because  slope is same and equal to 3 all through. Thus, the equation is y = 3x - 1  

3) For the third table, we have;

x y

-3 8

-2 4

-1 2

0 1

1 0.5

This is an exponential function because equation can be modelled by;

y = 2⁻ˣ

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The equation of the function is −3<x<1. See the explanation below.

Given the graph of function f is a parabola,

Thus, equation of parabola  is y=(x+3)(x+1)

⇒y=x² +4x+3

⇒y−3+2²

= x²+2× x ×2+2²

⇒y+1=(x+2)²

We can rewrite this as

 (x+2)² =4× (1/4) ×(y+1)

Comparing the above equation to the equation of a parabola, (x−h)² =4a(y−k), where (h,k) is the coordinates of vertex of parabola, we have,

(h,k)≡(−2,−1)

Hence, the x coordinate of the vertex is −2 which lies in the interval −3<x<1

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Answer:

[tex]m_{1} =1/2\\m_{2} =5[/tex]

Step-by-step explanation:

[tex]2m^{2} -11m+5=0[/tex]

[tex](2m-1)(m-5)=0[/tex]

[tex]2m-1=0\\2m=1\\m_{1} =1/2[/tex]

[tex]m-5=0\\m_{2} =5[/tex]

Hope this helps

The solution of the fraction given as -8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y² - 16) is determined as 4 or - 0.25.

A fraction represents a part of a whole or, more generally, any number of equal parts.

A fraction  can also be described as how many parts of a certain size there are, in a given whole.

The fraction given can be written as follows;

-8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y² - 16)

-8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y - 4)(y+4)

-8/(2y - 8)  = [5(y - 4) - (7y + 8)] /(y-4)(y + 4)

-8/(2y - 8)  = (5y - 20 + 7y + 8)/(y-4)(y + 4)

-8/(2y - 8)  = (12y - 12)/(y-4)(y + 4)

cross and multiply both sides of the equation;

-8((y-4)(y + 4)) = (12y - 12)(2y - 8)

-8(y² - 16) = 24y² - 96y - 24y + 96

-8y² + 128 =  24y² - 120y + 96

0 = 32y² - 120y - 32

solve the quadratic equation using formula method;

a = 32, b = -120, c = - 32

y = 4 or -0.25

Thus, the solution of the fraction given as -8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y² - 16) is determined as 4 or - 0.25.

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y=6

for the eqution

[tex]\frac{-8}{2y-8} =\frac{5}{y+4} -\frac{7y+8}{y^{2}-16 } \\[/tex]

Answer:

A' (-15, -5)

B' (10, -10)

C' (-5, -20)

Answer:

A ' (-15, -5)

B ' (10, -10)

C ' (-5, -20)

Step-by-step explanation:

The scale factor is [tex]K=5[/tex]. This tells us to multiply each coordinate, of each point, by the scale factor (5) to get the dilated points.

Point A is at [tex](-3,-1)[/tex] and moves to [tex]A ' (-15, -5)[/tex] after multiplying the x and y coordinates by 5. The same applies to points B and C as well.

Point B moves from [tex](2,-2)[/tex] to [tex]B' (10,-10)[/tex] because [tex]2*5=10[/tex] and [tex]-2*5=-10[/tex]. This also means that Point C moves from [tex](-1,-4)[/tex] to [tex]C' (-5,-20)[/tex] because  [tex]-1*5=-5[/tex] and [tex]-4*5=-20[/tex].

The dilation rule can be written as [tex](x, y)[/tex] → [tex](5x, 5y)[/tex]

As a result of the dilation, triangle A'B'C' has sides that are 5 times longer compared to the corresponding sides of triangle ABC.

The ordered pair (10,63) is a solution to the inequality y < -0.2x² + 9x - 7. This illustrates that the statement is true.

It should be noted that an inequality simply means a statement of an order relationship between two numbers and algebraic expressions.

From the information given, the equation illustrated is:

y < -0.2x² + 9x - 7.

63 < 0.2(10)² + (9 × 10) - 7

63 < 20 + 90 - 7.

63 < 103

In this case, the ordered pair (10,63) is a solution to the inequality y < -0.2x² + 9x - 7. This illustrates that the statement is true since sixty there is less than one hundred and three.

Therefore, this is true.

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Complete question:

The ordered pair (10,63) is a solution to the inequality y < -0.2x² + 9x - 7. Please select the best answer from the choices provided

True

False

The attached graph is the graph of the function f(x) = -2sin(x)

The function is given as:

f(x) = -2sin(x)

The above function is a sine function that has an amplitude of 2

Next, we plot the graph of the sine function f(x) = -2sin(x) using a graphing calculator

See attachment for the graph of f(x) = -2sin(x)

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Multiplying both sides of an inequality by a negative number reverses the inequality symbol.

The table of values is given as:

A: (-16 > -4) (-16 < -4) (-16 = -4)

B: (40 > 8) (40 < 8) (40 = 8

C: (-45 > 15) (-45 < 15) (-45 =15)

D: (35 > -20) (35 < -20) (35 = -20)

In the above list of inequalities, the true inequalities are

-16 < -4 --- because -16 is less than -4

40 > 8 --- because 40 is greater than 8

-45 < 15 --- because -45 is less than 15

35 > -20 --- because 35 is greater than -20

Lastly, when an inequality is multiplied or divided by a negative number, the inequality sign changes

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Answer:

-16 < -4

40 > 8

-45 < 15

35 > -20

Reverses

Step-by-step explanation:

hope this helps

Answer:

C. 7

Step-by-step explanation:

The answer is 7. Use the power of a power property. To use it you have to multiply the power inside the parenthesis to the one outside of the parenthesis. 1/5 * 5 = 1. Since the power is 1, you do not need to write the power.

Hope this helps!

The volume of the solid is 900 cubic unit given that the solid lies between planes perpendicular to the x-axis at x = 0 and x = 19, the cross sections perpendicular to the x-axis on the interval 0 ≤ x ≤ 15 are squares with diagonals that run from the parabola y = - 2√x to the parabola y = 2√x. This can be obtained by finding the area of the square using the length of the diagonal.

Given that, diagonals that run from the parabola y = - 2√x to the parabola   y = 2√x

D = 2√x - (-2√x)

D = 4√x

D² = s² +  s², where s is the side of the square

(4√x)² = 2s²

16x = 2s²

s² = 8x

s² is the area

Thus,

V = [tex]\int\limits^{15}_0 {8x} \, dx[/tex]

V =  [tex]8\int\limits^{15}_0 {x} \, dx[/tex]

V = 4 (15² - 0)

V = 4×225

⇒ V = 900 cubic unit

Hence the volume of the solid is 900 cubic unit given that the solid lies between planes perpendicular to the x-axis at x = 0 and x = 19, the cross sections perpendicular to the x-axis on the interval 0 ≤ x ≤ 15 are squares with diagonals that run from the parabola y = - 2√x to the parabola y = 2√x.

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Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: A solid lies between planes perpendicular to the x-axis at x = 0 and x = 19. The cross sections perpendicular to the x-axis on the interval         0 ≤x ≤ 15 are squares with diagonals that run from the parabola y = - 2√x to the parabola y = 2√x. Find the volume of the solid.

Answer:

B, cos(0)=1

Step-by-step explanation:

cos(0)=1

Coordinate A is at point (1,0)

Question 4

[tex]\sin 30^{\circ}=\frac{y}{14\sqrt{3}}\\\\\frac{1}{2}=\frac{y}{14\sqrt{3}}\\\\\boxed{y=7\sqrt{3}}\\\\\\\\\cos 30^{\circ}=\frac{x}{14\sqrt{3}}\\\\\frac{\sqrt{3}}{2}=\frac{x}{14\sqrt{3}}\\\\\boxed{x=21}[/tex]

Question 5

[tex]\cos 45^{\circ}=\frac{x}{28}\\\\\frac{1}{\sqrt{2}}=\frac{x}{28}\\\\x=\frac{28}{\sqrt{2}}\\\\\boxed{x=14\sqrt{2}}\\\\\\\\\sin 45^{\circ}=\frac{y}{28}\\\\\frac{1}{\sqrt{2}}=\frac{y}{28}\\\\y=\frac{28}{\sqrt{2}}\\\\\boxed{y=14\sqrt{2}}[/tex]

F(x)= 2(x-2)^2 + 2 is the correct equation of F(x)

A quadratic function is a polynomial function of the second degree. The general form of a quadratic function is this: f (x) = ax^2 + bx + c, where a, b, and c are real numbers and a≠ 0.

Graphs of quadratic functions

The term "parabola" refers to the graph of a quadratic function. A parabola essentially resembles the letter "U," yet it can be inverted or exactly this shape depending on the situation. The leading coefficient determines whether the graph of a quadratic function opens up or down; if it is more than zero, the parabola opens up; if it is less than zero, the parabola opens down.

It is given that graph of F(x), shown below, resembles the graph of G(x) = x^2, but it has been changed somewhat.

We need to find the equation of F(x)

In the figure, parabola opens up, the leading coefficient is greater than zero ,So option (d) is correct

Hence the equation of F(x) is 2(x-2)^2 + 2

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What is a Venn Diagram?

Explain : A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science.

How to draw a Venn Diagram?

Explain : To create an intersecting Venn diagram, draw three circles that overlap in the middle. You'll be able to show which attributes are unique to each circle, which overlap between two, and which are common characteristics of all three groups. Two circles overlapping is a classic venn diagram

What is a venn Diagram mostly used for?

Explain : A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items. Often, they serve to graphically organize things, highlighting how the items are similar and different.

Set notations: The concepts illustrated in Venn ...

Scaled Venn Diagram: Also called Area Propo...

Reuleaux Triangle: Shape formed from the int...

Intersection: The items that overlap in the sets. ...

Here's some question for Venn Diagrams!

A. What's the first step creating a Venn Diagram? https://www.math-only-math.com/practice-test-on-Venn-diagrams.html

B. What's the last step to create a Venn Diagram? https://www.purplemath.com/modules/venndiag4.htm

C. What does a Venn Diagram looks like?

( Try using those questions to partice more about Venn Diagrams! )

( Also, thank you for the points! )

Answer:

7a + b

Step-by-step explanation:

5a + 2a + 3b - 2b

= 7a + 3b - 2b

= 7a + b

Answer: Read the explanation

Step-by-step explanation:

If the points of a figure are all moved the same, they are congruent.

Point A is moved 9 points right, and 7 points down.

Point B is moved 9 points right, and 7 points down.

Point C is moved 9 points right, and 7 points down.

So, they are congruent.

Answer:

5.373 cm

Step-by-step explanation:

Divide the volume by the length to find the area of the equilateral triangle

100/8 = 12.5

Area of equilateral triangle = sqrt(3) / 4  *  s^2   = 12.5

   s^2 = 12.5 *4  / sqrt3

    s = 5.373 cm

Answer: [tex]\frac{\sqrt{6}}{2}[/tex]

Step-by-step explanation:

By the Pythagorean theorem,

[tex]2^2 + (MN)^2 = (\sqrt{10})^2\\\\4+(MN)^2 = 10\\\\(MN)^2 = 6\\\\MN=\sqrt{6}\\\\\implies \tan L=\frac{\sqrt{6}}{2}[/tex]

The linear regression method seeks to predict values of a(n) dependent variable based on values of a(n)  independent variable.

According to the statement

we have to explain the linear regression method and explain the way by which this method is used to predict the values.

So, For this purpose we know that the

Linear regression is the most basic and commonly used predictive analysis. Regression estimates are used to describe data and to explain the relationship.

And

Linear regression analysis is used to predict the value of a variable based on the value of another variable. The variable you want to predict is called the dependent variable. The variable you are using to predict the other variable's value is called the independent variable.

from these definitions it is clear that the there is a presence of two types of variables which are dependent and independent variables.

So, The linear regression method seeks to predict values of a(n) dependent variable based on values of a(n)  independent variable.

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Answer:

1000xm

Step-by-step explanation:

1 meter = 3.2808 feet, hence. 9.8424 x 10^8 feet in 1 second. 1 foot in x seconds. hence it takes 1 / (9.8424 x 10^8) = 0.10168 x 10^(-8) seconds. ➡️1km = 1000xm⬅️

It will take light approximately 3.0 x 10⁻⁵ seconds to travel one meter.

To find out how long it will take light to travel one meter, we need to convert the given distance of 10,000 km to meters and the time of 3.0 x 10² seconds to seconds.

Given:

Distance traveled by light = 10,000 km

Time taken by light = 3.0 x 10² seconds

To convert km to meters, we know that 1 km = 1 x 10³ m, so:

10,000 km = 10,000 x 1 x 10³ m = 1 x 10⁷ m

Now, we can find the time taken to travel one meter by dividing the total time by the total distance:

Time taken to travel one meter = Total time / Total distance

Time taken to travel one meter = (3.0 x 10² seconds) / (1 x 10⁷ m)

To simplify the expression, we can cancel out one factor of 10 from the numerator and denominator:

Time taken to travel one meter = (3.0 x 10) / (1 x 10⁶ m)

Now, we get the final answer:

Time taken to travel one meter = 3.0 x 10⁻⁵ seconds

So, it will take light approximately 3.0 x 10⁻⁵ seconds to travel one meter.

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Answer:

f(t)=250(1-0.12)^t

or

f(t)=250(0.88)^t

Step-by-step explanation:

Use the formula f(t)=P(1+b)^t

Plug in the information.

f(t)=250(1-0.12)^t

or

f(t)=250(0.88)^t

The only thing I did in the second equation is I subtract 0.12 from 1.

Hope this helps!