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k = 4 will make the polynomial a perfect square of a binomial.

A trinomial that factors into a perfect square binomial yields the square of a binomial. For instance, because it factors to (x + y)2, the trinomial x2 + 2xy + y2 is a perfect square binomial.

The perfect square formula looks like:

[tex]ax^{2} +2abx+b^{2} =(ax+b)^{2} \\ax^{2} -2abx+b^{2} =(ax-b)^{2}[/tex]

Given polynomial is,

kx² +12x + 9

We have to find the value of 'k' for which the given polynomial is a square of a binomial.

To find this we will use the formula,

(a +b)² = a² +2ab + b²

kx² + 12x + 9 = kx² + 2(6x) + 3²

                     = kx² + 2(3)(2x) + 3²

By comparing this with the formula of (a + b)²,

b = 3

a = 2x

(2x)²+2(2x)(3) + 3² = (2x + 3)²

4x² + 12x + 9 = (2x + 3)²

Therefore, k = 4 will make the polynomial a perfect square of a binomial.

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k = 4 will make the polynomial a perfect square of a binomial.

What is perfect square binomial?

A trinomial that factors into a perfect square binomial yields the square of a binomial. For instance, because it factors to (x + y)2, the trinomial x2 + 2xy + y2 is a perfect square binomial.

How perfect square formula looks like?
The perfect square formula looks like:
Given polynomial is,
kx² +12x + 9
We have to find the value of 'k' for which the given polynomial is a square of a binomial.
To find this we will use the formula,
(a +b)² = a² +2ab + b²
kx² + 12x + 9 = kx² + 2(6x) + 3²
                    = kx² + 2(3)(2x) + 3²
By comparing this with the formula of (a + b)²,
b = 3
a = 2x
(2x)²+2(2x)(3) + 3² = (2x + 3)²
4x² + 12x + 9 = (2x + 3)²
Therefore, k = 4 will make the polynomial a perfect square of a binomial.

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Answer: 34.5

Step-by-step explanation:

50 + 10 = 60 (birthday and dog walking)

60 - 7.50 = 53.5 (paid what she owed)

52.5 - 18 = 34.5 (bought a shirt)

Answer:

i think it is the bottom one

Step-by-step explanation:

Answer:

the length of the

rectangle when the width is 4 feet is 8

From the given picture of a triangle, we have come to find that variable x = 7 and y = 4

What is an isosceles triangle?

An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.

3x - 5 = y + 12  (if two angles of a triangle are equal, the sides opposite                    

                          them are also equal)   ------------(1)

Also, 3x - 5 = 5y - 4     (sides of a equilateral  triangle are equal)

So,  5y - 4 = y + 12

       5y - y = 12 + 4

         4y = 16

           y = 4

Now,

Put value of y in equation (1)

3x - 5 = y + 12

3x = 4 +12 + 5

3x = 21

x = 7

Hence, x = 7 and y = 4

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On solving the provided question, we get the following linear equation as the , that is  j = 6/20.

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

A mathematical equation is said to be linear if it has the formula y=mx+b, where m denotes the slope and b the y-intercept.

An algebraic equation is said to be linear if each term has an exponent of 1, and if the equation is graphed, it always produces a straight line. This is the basis for its designation as a "linear equation."

the linear equation:

[tex]17/20 = j + 11/20\\ 17/20 - 11/20 = j + 11/20 - 11/20\\ (17 - 11)/20 = j\\ 6/20 = j[/tex]

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Number of glasses Victoria need to buy for restaurant are at least 31 from the inequality given by 10x + 368 ≥ 673.

As given in the question,

Number of glasses required in the restaurant at least 673.

Number of glasses currently available in the restaurant = 368

Number of glasses in each set used to sale = 10

Let 'x' represent the number of sets of the glasses Victoria need to buy.

Required inequality is given by :

10x + 368 ≥ 673

⇒ 10x + 368 - 368  ≥ 673 - 368

⇒ 10x ≥ 305

⇒ x ≥ 30.5

Number of sets bought by Victoria = At least 31

Therefore, from the inequality 10x + 368 ≥ 673 the number of sets of glasses bought by Victoria is equal to at least 31.

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Answer:

-45 and - 16 has a difference of 29 b/c -16-(-45)= -16 +45 = 29

Answer:

135

Step-by-step explanation:

The vertex of y = |3x + 6| − 4 is (-2, -4) and the range of y = |3x + 6| − 4 is −4 ≤ y < ∞.

A parabola's vertex is the location at which it crosses its axis of symmetry. The vertex will be the lowest point on the graph, or the point at the base of the "U"-shape, if the coefficient of the x2 term is positive.

The point is called the vertex (h, k). As we are all aware, a parabola's conventional equation is y = ax2 + bx + c. The bottom of the U-shaped curve is where the vertex is located if the coefficient x2 is positive, and the top of the curve is where the vertex is located if it is negative.

Given,

y = |3x + 6| − 4

The vertex of y = |3x + 6| − 4 is,

We have to find the absolute values zeroes,

3x+6=0

x= -2

To find the value of y, substitute x value in the above,

y= -4

(x, y)=(-2, -4)

Therefore, the vertex of y = |3x + 6| − 4 is (-2, -4)

And now,

The range of y = |3x + 6| − 4 is,

It can be defined by f(x)≥k

k= -4

f(x)≥ -4

Therefore, the range of y = |3x + 6| − 4 is −4 ≤ y < ∞.

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Answer:

(−2, −4); −4 ≤ y < ∞

Step-by-step explanation:

When Akbar is 9 years older than Yasir and Hamid is 2 years younger than Yasir then, the expression for their sum of ages is 3x+7

A linear equation is a mathematical equation that describes a straight line. It is a first-degree polynomial equation, which means that the largest exponent of the variables is 1. Since a and b are constants and x and y are variables, linear equations have the general form ax+by=c. A straight line forms on a coordinate plane when the values of x and y fulfil the expression. The connection between two variables or the price of a product are two examples of real-world events that are frequently modelled using linear equations. Solving a linear equation entails determining the values of the variables that make the equation true. Different techniques, such graphing, substitution, or elimination, can be used to accomplish this.

How to solve?

Let x be Yasir's age

Akbar is x+9

Hamid is x-2

The sum of their ages is x+(x+9)+(x-2)

=3x+7

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Answer:

Is the question written correctly?  As written, the answer is 4.16 x [tex]10^{-8}[/tex].

Step-by-step explanation:

1+3+5+8+7+7+8= 39

39 = 937392920x

x = 39/(937392920)

x = 4.16 x [tex]10^{-8}[/tex]

The number of students who drive to school is 125.

What is  number ?

A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of expressing numbers that uses digits or symbols to represent them.

At Jefferson High School, there are 250 students who drive to school and 375 students who ride the bus to school. The number of students who drive to school is

=375-250

=125

Hence, the number of students who drive to school is 125.

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You should cast a shadow for a person or item at least three times and measure it each time to determine how the length of the shadow varies during the day.

The shape of an object always dictates the shape of its shadow. A shadow's size and shape can alter, though.

For instance, the location of the light source can induce these variations. The length of the shadow is influenced by the sun's position in the sky on a sunny day.

We can achieve the same effect indoors by adjusting the position of a flashlight reflecting on an object.

When the sun is low on the horizon, the shadows are lengthy, and when the sun is high, the shadows are considerably shorter.

So, To determine the change of length of object during the day, one should cast a shadow at least three separate times for a person or object and measure it each time

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Answer:

n=-30

Step-by-step explanation:

-4.5n=135

n=135/-4.5

n=-30

Answer:

I think someone who walks 60 feet in 10 seconds. Let me know if I'm wrong.

Step-by-step explanation:

10/60=.16667

6/42=0.1428

Possible length of the third side of the Triangle must be between 11 and 23.

As the third side of the triangle is between the sum of the sides and difference of the sides excluding both the numbers.

As triangle consist of three sides and it should must be in between two extreme values.

As by the property of Triangle

Third side should be less than sum of the sides and,

it should be greater than difference of the sides.

Sum of the sides = AB + BC = 6 + 17 = 23

Difference of the sides = 17 - 6 = 11

Then the third side will be between 11 and 23 excluding 11 and 23.

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The two column proof showing that AB ≅ CD and AD ≅ BC are congruent by CPCTC is as detailed below.

A two-column proof is defined as a geometric proof that consists of a list of statements, and the reasons that we know those statements are true.

The two column proof that shows AB ≅ CD and AD ≅ BC is as follows;

Statement 1; Parallelogram ABCD with diagonal AC

Reason 1: Given

Statement 2; AB ║ CD and AD ║ BC

Reason 2; Definition of Parallelogram

Statement 3; ∠1 ≅ ∠2 and ∠3 ≅ ∠4

Reason 3; Definition of angle bisector

Statement 4; AC ≅ AC

Reason 4; Reflexive Property of congruence

Statement 5; ΔABC ≅ ΔCDA

Reason 5; ASA Congruency postulate

Statement 6; AB ≅ CD and AD ≅ BC

Reason 6; CPCTC

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i dont now when i can help but this is my answer

Answer:

D. 50

Step-by-step explanation:

number to 49.13

Answer:

A

Step-by-step explanation:

Answer:

3/4>2/3

Explanation:

3/4 is the same as 3*3/4*3, which equals 9/12.

2/3 is the same as 2*4/3*4, which equals 8/12.

Thus, 3/4=9/12 and 2/3=8/12.

9/12 > 8/12, and since 3/4=9/12 and 2/3=8/12, 3/4>2/3.

Hope this helps.

Answer:

%10

Step-by-step explanation:

If the gold steadily increased $400 over a four-month period, we need to figure out how much the gold increased each month.

400 ÷ 4 = 100

Now that we figured out that the gold steadily increased $100 every month, we now need to figure out what percent it grew.

1000 ÷ 100 = 10

The price grew %10 every month.

The graph has 2 x-intercepts.

What is the quadratic function?

In mathematics, a polynomial of degree two in one or more variables is referred to as a quadratic polynomial. A quadratic polynomial defines the polynomial function known as a quadratic function.

We have,

f(x) = -3(x-3)² + 1

by simplifying the equation above

-3(x² -6x + 9) + 1 = 0

-3x² + 18x - 27 + 1 = 0

-3x² + 18x - 26 = 0

By calculating the quadratic equation we get

[tex]x=\frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

[tex]x=\frac{ -18 \pm \sqrt{18^2 - 4(-3)(-26)} }{2(-3)}[/tex]

[tex]x= 3 \pm \frac{\sqrt{3} }{3}[/tex]

x = 2.42265,      x = 3.57735

so the points are (0, 0) and (2.4, 3.6)

The graph crosses the x-axis at (2.4, 3.6)

Hence, the graph has 2 x-intercepts.

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The equation that used to determine the dimension is 2(2x+10) = 300 and the dimensions of the rectangular yard is 80 foot and 70 foot

Total length of the fence = 300 foot

Consider the width of the rectangular yard = x

The length of the rectangular yard = x + 10

The perimeter of the rectangle = 2(l + w)

Where l is the length and w is the width

Substitute the values in the equation

300 = 2(x+10 + x)

300 = 2(2x + 10)

4x + 20 = 300

4x = 300 - 20

4x = 280

x = 280/4

x = 70 foot

The length = x + 10

= 70 + 10

= 80 foot

Therefore, the equation is 2(2x+10) = 300 and dimensions are 80 foot and 70 foot

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Answer:

1. Yes

2. No

3. No

4. Yes

Step-by-step explanation:

To find out whether or not 3/5 will make each equation true, simply input 3/5 in the missing slots and solve to see if they equal to the value intended.

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below

[tex](\stackrel{x_1}{15}~,~\stackrel{y_1}{545})\qquad (\stackrel{x_2}{44}~,~\stackrel{y_2}{864}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{864}-\stackrel{y1}{545}}}{\underset{run} {\underset{x_2}{44}-\underset{x_1}{15}}} \implies \cfrac{ 319 }{ 29 } \implies \text{\LARGE 11}[/tex]

Hence, the slope of the line is [tex]m=11[/tex].

What is the slope of line?

The slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says  [tex](x_1,y_1)[/tex]  and [tex](x_2,y_2)[/tex]can be easily determined by finding the difference between the coordinates of the points.

As we know that,

The slope has several names

(1) average rate of change

(2)rate of change

(3)delta[tex]Y[/tex] over delta[tex]X[/tex]

(4)Δ[tex]y[/tex]over Δ[tex]x[/tex]

(5)rise over run

(6)gradient

(7)constant of proportionality

So, the same cat wearing the different costumes to get the slope of the straight line, the two points are

[tex](x_1,y_1)=(15,545)\\(x_2,y_2)=(44,864)[/tex]

[tex]m=\frac{864-545}{44-15}\\\\m=\frac{319}{29}\\\\m=11[/tex]

Hence, the slope of the line is [tex]m=11[/tex].

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The area of the resulting shape if a circle with a 12-inch diameter is folded in half and then folded in half again is 28.26 square inches

If a circle with a 12-inch diameter is folded into half and then folded into half again the circle will become a quadrant.

So,

The area of a quadrant is area of a circle divided by 4

Area of a quadrant = πr² / 4

Diameter of a circle = 2r

12 = 2r

divide both sides by 2

r = 6 inch

Area of the quadrant = 3.14 × (6)²/4

Area of the quadrant = (3.14 × 36) /4

Area of the quadrant = 113.04 / 4

Area of the quadrant = 28.26 square inches

In conclusion, the area of the quadrant is 28.26 square inches

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Answer: 178.25

Step-by-step explanation:

124.25 + 223.56 - 89.56 - 80.00

Answer: $178.25

Step-by-step explanation: Your balance on May 15 is $124.25. On May 20, you deposit $223.56, which increases your balance to $124.25 + $223.56 = $347.81. You then write a check for $89.56, which decreases your balance to $347.81 - $89.56 = $258.25. Finally, you withdraw $80.00 from an ATM on May 25, which decreases your balance to $258.25 - $80.00 = $178.25. Therefore, your current balance is $178.25.