What does reflection across x =- 2 mean?

k = 4 value of k will roots of the equation be real and equal if kx² + 4x + 1 = 0. The given problem can be solved using the concepts of quadratic equations.

The equation of the second degree is a quadratic equation. This indicates that it contains a phrase that is squared, at least once. ax² + bx + c = 0, which uses constants or numerical coefficients for the variables a, b, and c, is one of the classic formulae for solving quadratic equations. Unknown variable 'x' is used here. For an equation to have equal roots the value of the discriminant is 0. The discriminant of a quadratic equation ax² + bx + c = 0 is given by the formula.

The given quadratic equation is :

kx² + 4x + 1 = 0

Here, a = k, b = 4, c = 1

Now, D = b² - 4ac

or, D = (4)² - 4 × k × 1

or, D = 16 - 4k

We know that a quadratic equation has real and equal roots, if D = 0

16 - 4k = 0

or, 16 = 4k

or, k = 4

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Answer:

Step-by-step explanation:

To find x, you first need to find the length of the base. The total length of the base is 8, so the length of the base for one triangle is 4 meaning 8/2

Pythagoras theorem = [tex]a^2 + b^2 = c^2[/tex]

In this case, a will be 4 and c will be 5. Remember that c will always be the longest side of a right-angle triangle.  

[tex]5^2 + x^2 = 4^2 \\25 +x^2 = 16 \\x^2 = 25 -16 \\x^2 = 9 \\x \sqrt{9}\\ x = 3[/tex]

Graph b is correct and Shows the proportionality of the given dataset.

the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Given, A dataset

x:       1       2      3      4      

y:       2      4      6      8

Since in the given data for all the values of x, the value of y is consistently getting twice.

Thus Give data is proportional

and Only graph b is Correct in the term of given values

Therefore, The given dataset's proportionality is shown in Graph B, which is accurate.

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Answer:

117

Step-by-step explanation:

7/30 like mystery  

into a decimal this is 0.2333

times this by 500 and you get 116.65

which rounds to 117

Models with gaps, openings, and edges that have only one face merging with them are examples of non-manifold geometry.

Non-manifold geometry is a type of geometry in which some points have neighborhoods that are not topologically equivalent to a ball. This means that some points have neighborhoods that are not locally homeomorphic to a small disk. This can happen when there are gaps, openings, or edges that have only one face merging with them. In these cases, the model is not "watertight" and it is considered non-manifold geometry.

On the other hand, manifold geometry is a type of geometry in which every point has a neighborhood that is topologically equivalent to a ball. This means that every point has a neighborhood that is locally homeomorphic to a small disk. In other words, every point has a neighborhood that is topologically equivalent to a small disk. This is the case in most "smooth" or "watertight" 3D models, where every edge is shared by exactly two faces.

Non-manifold geometry can occur in many 3D modeling scenarios, such as when creating a model with a hole, an edge that is not shared by any faces or when merging two or more models with different topologies.

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The triangle's angles would be 15 degrees smaller than they originally were

If each angle of a triangle is reduced by 15 degrees, the triangle's angles would be 15 degrees smaller than they originally were. For example, if a triangle had angles of 60, 90, and 30 degrees, they would become 45, 75, and 15 degrees after being reduced by 15 degrees.

Triangles can be divided into various categories based on the size of their angles and the breadth of their sides. One of the most typical shapes, the triangle is utilised in building due to its stability and stiffness. Applying the concepts in a variety of real-world issues is made possible by understanding these properties.

Triangles are divided into the following sorts according to their side lengths:

Equilateral Triangle: When all three sides of a triangle are the same length, the triangle is said to be equilateral.

Isosceles triangle: An isosceles triangle is one in which each of its sides are equal or congruent.

Scalene triangle: A scalene triangle is a triangle in which none of the sides are equal.

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Answer:

45

Step-by-step explanation:

5✖y=225

225÷5 =45

B=45

Answer:

45

Step-by-step explanation:

5y=225

÷5. ÷5

y=45

divide 225 by 5 to get y , hope i helped xx

Answer: 4

Step-by-step explanation:

Answer: C

Step-by-step explanation:

By expanding and combining like terms, you get 4x^4+6x^3+9x^2-4x+3, which is C. (Too complex, I don't want to type all the work I did on paper onto this)

The value of a₆ is -128, which matches the result we obtained using the recursive definition of the sequence.

What is meant by geometric?

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. Its general term is. aₙ= a₁ r⁽ⁿ⁻¹⁾. The value r is called the common ratio. It is found by taking any term in the sequence and dividing it by its preceding term.

The nth term of a geometric sequence is given as:

aₙ= a₁ r⁽ⁿ⁻¹⁾.

In which a1 is the first term.

For this problem, we have :

The first term is  a1 = 4 and aₙ = -2aₙ₋₁.

Therefore, the common ratio is q = -2.

To solve the sequence using the geometric sequence formula, we need to first recognize that the sequence is a geometric sequence with a common ratio of -2.

a₁ = 4

a₂ = -2a₁ = -8 = 4 * (-2)

a₃ = -2a₂ = 16 = 4 * (-2)²

a₄ = -2a₃ = -32 = 4 * (-2)³

a₅ = -2a₄ = 64 = 4 * (-2)⁴

a₆ = -2a₅ = -128 = 4 * (-2)⁵

The formula for a geometric sequence is aₙ= a₁ r⁽ⁿ⁻¹⁾., where a is the first term, r is the common ratio, and n is the index of the term.

In this case, a=4 and r = -2, so the formula for the nth term is aₙ=4*(-2)⁽ⁿ⁻¹⁾.

To find a6, we substitute n = 6 into the formula:

a₆ = 4 * (-2)⁽⁶⁻¹⁾

= 4 * (-2)⁵

= -128

Therefore, the value of a₆ is -128, which matches the result we obtained using the recursive definition of the sequence.

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Answer:

12=4. (-6y) = -24y

Step-by-step explanation:

The shape of the object is revealed in its pre-image, while its final form and position are revealed in the image following transformation.

Changes to the graph of a parent function are referred to as transformations. Transformations can be divided into three categories: translations, reflections, and dilations.

Four distinct approaches to modify the position and/or shape of a point, line, or geometric figure are collectively referred to as transformations. The Pre-Image of the object is its initial shape, while the Image, after transformation, is the final shape and location of the thing.

Imaging or duplicating an object is a part of transformation geometry. Transform geometry, which incorporates translation, reflection, dilation, and rotation, is covered in the ninth-grade curriculum. You will apply these concepts or notes up till grade 12.

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The probability of students chosen at random does not study chemistry is  [tex]\frac{20}{41}[/tex].

What is probability?

The likelihood of an event happening is gauged by probability. Many things are impossible to completely predict in advance. Using it, we can only make predictions about how probable an event is to happen, or its chance of happening. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

Total number of student = 6+7+2+5+4+8+6+3 = 41

Now number of chemistry students = 8+3+4+6 = 21

Then Non chemistry students = 41-21 = 20

So required probability = Non chemistry student/ Total number of students

=> probability = [tex]\frac{20}{41}[/tex]

Hence the probability of students chosen at random does not study chemistry is  [tex]\frac{20}{41}[/tex].

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[tex]\sqrt{252\\[/tex] = 6[tex]\sqrt{7}[/tex]

We have to find the equivalent of [tex]\sqrt{252\\[/tex] so first find.

Prime factorization of 252= 2² × 3² × 7²

now, Prime factors of 252 in pairs: (2×2) × (3×3) × 7

Now, the square root of 252: [tex]\sqrt{252\\[/tex] = [tex]\sqrt{((2*2) *(3*3) *7}[/tex]

So, the square root of 252 =   (2*3)[tex]\sqrt{7}[/tex]  = 6[tex]\sqrt{7}[/tex]

Factorization of an algebraic expression means writing the given expression as a product of its factors. These factors can be numbers, variables, or an algebraic expression.

There are a few methods or tricks to remember. Reduce the expression by the greatest common factor. Check if there are perfect squares or differences of squares. Use the algebraic formulas or identities to factorize the expression.

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The system of inequality is 0 ≤ y ≤ 20.

Inequality in math is when two expressions, equations, or values are not equal to each other. Inequalities are represented by symbols such as "<" (less than), ">" (greater than), and "≠" (not equal to). Inequalities can be used to represent real-world situations where values or expressions can be greater than, less than, or not equal to each other. For example, the inequality “x > 5” means that x is greater than 5.

The system of inequalities that Nicholas needs to solve is:

10x + 25y ≤ 500

0 ≤ x ≤ 20

0 ≤ y ≤ 20

The first equation states that the total pay from both of his jobs must be less than or equal to $500. The second and third equations state that the number of hours he works at each job must be between 0 and 20.

Solving this system of inequalities will tell Nicholas how many hours he needs to work at each job in order to meet his obligations of $500 per week.

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A box-and-whisker plot is a graphical representation of a data set that uses quartiles and quartile boundaries to identify and display the distribution of the data.

|   |

|---|

|   |   __7___   __14__   __23__   __29__   __34__

|   |  |     | |     | |     | |     | |     |

|   |  |  24 | |  30 | |     | |     | |     |

|   |  |_____| |_____| |_____| |_____| |_____|

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The total number of books in the library's collection is; 350.

The equation mb = 70 can be used to find the total number of books in the library's collection. To solve for the total number of books, we need to divide both sides of the equation by m.

So;

70 / m = b

Where b is the total number of books in the library's collection, and m is the proportion of historical fiction books in the library's collection (expressed as a decimal).

To find the total number of books in the library's collection, we need to divide the number of historical fiction books (70) by the proportion of historical fiction books in the library's collection (expressed as a decimal).

Example: If historical fiction books make up 20% of the library's collection, m = 0.2 (20% expressed as a decimal).

Therefore, 70 / 0.2 = 350.

Thus, the library has 350 books in total.

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a)  We will cut the wire [tex]$=60-4\left(\frac{60}{4+\pi}\right)$[/tex] =26.3940

b) For the maximum area, we can not cut the wire anywhere.

Length of wire =Perimeter of circle +Perimeter of square

[tex]$$\begin{aligned}& 2 \pi r+4 x=60 \\& r= \frac{60-4 x}{2 \pi}=\frac{30-2 x}{\pi}\end{aligned}$$[/tex]

Let the side of squares x and r is the radius of the circle.

[tex]$$\begin{aligned}\text { Area } & =\pi r^2+x^2 \\& =\pi\left[\frac{30-2 x}{\pi}\right]^2+x^2 \\A(x) & =\frac{1}{\pi}[30-2 x]^2+x^2 \\A^{\prime}(x) & =\frac{2}{\pi}(30-2 x)(-2)+2 x \\A^{\prime}(x) & =0 \Rightarrow \frac{2}{\pi}(30-2 x)(-2)+2 x=0 \\& x=\frac{60}{4+\pi} \approx 8.40\end{aligned}$$[/tex]

A'(5) = -15.464, A'(9)=2.72

Since [tex]$A^{\prime}(x)$[/tex] the change negtive to positive at [tex]$x=\frac{60}{4+\pi}$[/tex], so its minima.

[tex]r=\frac{30-2\left(\frac{60}{4+\pi}\right)}{\pi}=\frac{30}{4+\pi}[/tex]

a) for the minimum area the side of the square should be [tex]$\frac{60}{4+\pi}$[/tex] which is  approximately equal to 8.40.

We will need to cut the wire 4 times the side of the square

So we will cut the wire [tex]$=60-4\left(\frac{60}{4+\pi}\right)$[/tex] =26.3940

b) for the maximum area the problem is defined into [tex]0 \leqslant x \leqslant 15[/tex]

So, when x=0 the square shrinks to 0 and the whole 60 wire is made into a circle.

When x=15 making the parameter of the. square 60 and the whole circle shrink to 0

So for the maximum area, we can not cut the wire anywhere.

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The length of the hypotenuse if the legs are 6 and 8 is 10.

What is right triangle ?

A right triangle consists of two legs and a hypotenuse. The two legs meet at a 90° angle and the hypotenuse is the longest side of the right triangle and is the side opposite the right angle. There are a couple of special types of right triangles, like the 45°-45° right triangles and the 30°-60° right triangle.

Have given ,

Let legs are a , b and hypotenuse is c.

then a = 6 , b = 8 and c = ?

We know that for a right triangle ,

[tex]a^{2} + b^{2} = c^{2}[/tex]

∵ [tex]6^{2} + 8^{2} = c^{2}[/tex]

[tex]c^{2}[/tex] = 36 + 64

[tex]c^{2}[/tex] = 100

c = 10

Hence , The length of the hypotenuse if the legs are 6 and 8 is 10.

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Answer: 77

Step-by-step explanation:

alright average just means the sum of all the items in a set divided by the number of items in a set.

So, if you have an average of 70 for 6 tests, your scores added up shall be 70x6 = 420.

Now, to solve this we need to first at 60+78+65+68+72 which is equal to 343. Subtracting 343 from 420 we have 420-343 = 77. So, for her last test the student needs to get a 77.

You will need to deposit $27,914.02 now in order to have a $194,888 retirement fund after 37 years at an APR of 7% compounded daily.

PV = Future Value / (1+r/n)^nt

PV = 194,888 / (1+0.07/365)^(365*37)

PV = 27,914.02

To calculate the present value of a future amount, you need to know the future value, the annual percentage rate (APR), and the number of compounding periods. In this case, the future value is $194,888, the APR is 7%, and the number of compounding periods is 37 years (365 days per year). The present value is calculated by dividing the future value by (1+r/n)^nt, where r is the APR, n is the number of compounding periods, and t is the number of years. Plugging in the numbers, we get 27,914.02, which is the amount you need to deposit now to have a $194,888 retirement fund after 37 years at an APR of 7% compounded daily.

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True: On the graph above, f(1) = 4.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the line and passes through the points (-1, -2) and (1, 4) by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-2) = (4 - (-2))/(1 - (-1))(x - (-1))

y + 2 = 6/2(x + 1)

y = 3(x + 1) - 2

y = 3x + 3 - 2

y = 3x + 1

When x = 1, the value of y is given by;

y = 3x + 1

y = f(1) = 3(1) + 1

y = f(1) = 4.

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The inverse of the logarithmic function f(x) = log2x is the exponential function f(x) = 2^x

The inverse of a logarithmic function is an exponential function. To find the inverse of the logarithmic function f(x) = log2x, we need to switch the x and y values of the function and solve for the y. This will give us the inverse function in the form y = 2^x.

The inverse of the logarithmic function f(x) = log2x is the exponential function f(x) = 2^x.

The inverse of a logarithmic function is an exponential function, which is a function of the form y = b^x, where b is a constant. To find the inverse of the logarithmic function f(x) = log2x, we need to switch the x and y values of the function and solve for the y. This will give us the inverse function in the form y = 2^x, where 2 is the constant. This inverse exponential function expresses the relationship between the x and y values of the logarithmic function in reverse, with the x values now being the exponents and the y values being the result of the exponential function.

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The solution of the inequality is x ≥ 0 or x ≤ -20

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4

|(1/5)x + 2| + 4 ≥ 6

Due to the absolute sign | |, the inequality can be written as:

(1/5)x + 2 + 4 ≥ 6  or -[(1/5)x + 2] + 4 ≥ 6

For (1/5)x + 2 + 4 ≥ 6:

(1/5)x + 2 + 4 ≥ 6

(1/5)x + 6 ≥ 6

(1/5)x ≥ 6 - 6

(1/5)x ≥ 0

x ≥ 0

For -[(1/5)x + 2] + 4 ≥ 6:

-[(1/5)x + 2] + 4 ≥ 6

-(1/5)x - 2 + 4 ≥ 6

-(1/5)x + 2 ≥ 6

-(1/5)x  ≥ 6 - 2

-(1/5)x  ≥ 4

-x  ≥ 4 × 5

-x  ≥ 20

x ≤ -20

Thus, the solution is x ≥ 0 or x ≤ -20

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A horizontal shift is a transformation in which a graph is shifted either left or right along the x-axis. A positive shift indicates a movement to the right and a negative shift indicates a movement to the left.

A horizontal shift is a transformation of a graph in which the graph is shifted either left or right along the x-axis. This is in contrast to a vertical shift, which shifts the graph up or down along the y-axis. A positive horizontal shift indicates that the graph has been shifted to the right. This means that the x-coordinates of any point on the graph will be increased by the same amount. On the other hand, a negative horizontal shift indicates that the graph has been shifted to the left. This means that the x-coordinates of any point on the graph will be decreased by the same amount. Horizontal shifts can also be referred to as translations or x-translations. This transformation can be used to move a graph in order to better compare its shape to another graph. It can also be used to more clearly show a pattern in the data, or to adjust the range of values that are shown on the graph.

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The probability x is odd 0[Φ(1.5+2k)−Φ(0.5+2k)].

Let Y first follow the normal distribution described by N. (0,1). Let X represent the result obtained by rounding Y to the nearest integer.

Normal random variable-To give you an idea, the CLT states that, under certain circumstances, the distribution of the total will be about normal if you add a lot of random variables.

The standard normal random variable is initially defined. We'll then see how scaling and moving a regular normal random variable allows us to create other normal random variables.

2∑∞k=0P(0.5+2k≤Y≤1.5+2k)

=2∑∞k=0[Φ(1.5+2k)−Φ(0.5+2k)]

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9÷0.001 is greater than 8÷0.001.

7÷0.001 is less than 8÷0.001.

8÷0.002 lie between 8÷0.001 and 8÷110.

Division expressions are mathematical expressions using division.

The division expression which is greater than 8÷0.001 is:

9÷0.001

Since, the numerator of the number 9÷0.001 is greater than 8÷0.001. and as their denominator is same.

so, the number whose numerator is greater than the other will result in the overall number to be greater.

The division expression which is less than 8÷0.001 is 7÷0.001.

Since, for two numbers with same denominator the number whose numerator is smaller is smaller than the other.

The division expression that lie between 8÷0.001 and 8÷110 is: 8÷0.002.

Since 8÷0.002 is greater than 8÷110, as for two numbers with same numerator but different denominator the number whose denominator is greater is a smaller number.

similarly 8÷0.002 is smaller than 8÷0.001

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The sum is B. 11c -14

How to determine this

By using the rule of BODMAS

Where B = Bracket off

O =  Order

D = Division

M = Multiplication

A = Addition

S = Subtraction

By following this given,

(9c - 8) + (2c - 6)

Using the first order,

By removing the Bracket

9c - 8 + 2c - 6

So, by order addition

9c + 2c - 8 - 6

11c - 8 - 6

And then, Subtraction

= 11c - 14

Therefore, the sum = 11c - 14

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Round to 35, the nearest 10th is 40. This process is called Round off.

Round-off is the process by which we simplify the number by writing to its nearest number it can be written on the place value of  10th, 100, or 1000, etc. In round-off, the numbers 0,1,2,3,4 are considered as nearest to the "0" and the numbers 5,6,7,8,9,10 are considered as nearest to the "10" similarly in this question 35 is considered as nearest to the "40". The number can also be used for numbers as well as decimal numbers so that we can write the decimal number in simplified form. The use of round-off facilitates the number so that we can easily calculate them.

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