1. What value of X makes this equation true?
1/2X +7=2X - 5
Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.

Answer: 3

Step-by-step explanation: schoology whack

Answer:

The answer is 256

Step-by-step explanation:

Answer:

256

Step-by-step explanation:

4 · 4 · 8 · 2 = 256

Answer:

A line is defined by two points, and any other point that lies on the same line as those two points will also be on the same line. Therefore, to find the points that lie on the same line as (– 7,– 2) and (– 14,– 7), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

The slope of a line is calculated as the change in y-values divided by the change in x-values between two points on the line. In this case, the slope is (–7 – (–2))/(–14 – (–7)) = –5/–7 = 5/7.

The y-intercept is the point where the line crosses the y-axis, so we can plug in the value of x as 0 to find the y-intercept. Plugging in the values from one of the given points, we get y = (5/7) * (–7) + b = –5 + b, so b = –2.

Therefore, the equation of the line is y = (5/7)x – 2. Any point that satisfies this equation will lie on the same line as (– 7,– 2) and (– 14,– 7).

Some examples of points that lie on this line include (0, –2), (–7, –2), and (–14, –7).

The quadratic inequality (18 / 7) · x² + (54 / 7) · x - 180 / 7 < y contains all the ordered pairs outside the parabola.

What is  parabola?

A parabola could be a U-shaped plane curve wherever any purpose is at an equal distance from a hard and fast purpose (known because the focus) and from a fixed line that is understood because the directrix.

Main body:

In this problem we must determine a quadratic inequality of the form:

a · x² + b · x + c < y

Where a, b, c are the real coefficients of the inequality.

First, determine the coefficients of the quadratic inequality (parabola) by solving the system of linear equations:

25 · a - 5 · b + c = 0

4 · a + 2 · b + c = 0

a + b + c = - 18

(a, b, c) = (18 / 7, 54 / 7, - 180 / 7)

Second, write the quadratic in equation:

(18 / 7) · x² + (54 / 7) · x - 180 / 7 < y

hence , the equation is (18 / 7) · x² + (54 / 7) · x - 180 / 7 < y

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The dimensions of the rectangle with area 35 m² is

length = 7.6 m and width = 4.6 m

The dimension of the rectangle is calculated using the formula for area of rectangle

= length x width

where

area of rectangle

35 = (w + 3) * w

35 = w² + 3w

w² + 3w - 35 = 0

solving for w gives

w = 4.6 OR -7.6

using the positive value, the w = 4.6 m, l = 4.6 + 3 = 7.6 m

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l

The total amount that will be paid will be $89.70.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, Adryanna got a manicure for $35 and a pedicure for $43 and she plans on leaving a 15% tip

The total amount that will be paid will be:

= ($35 + $43) + (15% × $78)

= $78 + $11.7

= $89.7

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The values of x and y for the linear equations of y = 24 - 4x and 2x - 3y = -2 are x=5 and y=4.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

Given, the equations are y = 24 - 4x and 2x - 3y = -2

Replacing the value of the first equation of y, which is, y = 24 - 4x, in the second equation, we get:

2x - 3(24-4x) = -2

⇒ 2x - 72 + 12x = -2

⇒ 14x = 70

⇒ x = 70/14

⇒ x = 5

Substituting the value of x=5 in y = 24 - 4x, we get,

y = 24 - 4(5)

⇒ y = 24 - 20

⇒ y = 4

Thus, the values of x and y for the linear equations of y = 24 - 4x and 2x - 3y = -2 are x=5 and y=4.

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Graph 1 represents the inverse of the function [tex]f(x)=\sqrt{x+1} -2[/tex]

What is the inverse of a function?

The visual representation of a function's inverse, given by the symbol f-1(x), is the original function mirrored across the line y=x. Only when f is a one-one and onto function does it exist.

The inverse of [tex]\sqrt{x+1} -2[/tex] is [tex]x^{2} +4x+3[/tex].

Plotting the inverse, we get the graph to be option 1.

Therefore, graph 1 represents the inverse of the function [tex]f(x)=\sqrt{x+1} -2[/tex]

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The inverse function of the function given as f(x) = [tex]\sqrt{x+1}[/tex] - 2 is f⁻¹(x) = x² + 4x +3. So, option 1 is since the point on f(x), (-1, -2) is mapped to (-2, -1) in its inverse function.

The steps for finding the inverse function, the steps to be followed are:

The given function is f(x) = [tex]\sqrt{x+1}[/tex] - 2  

Consider the given function as f(x) = y ⇒ y =  [tex]\sqrt{x+1}[/tex] - 2

Then, on rewriting the function for x, we get

y + 2 =  [tex]\sqrt{x+1}[/tex]

⇒ (y + 2)² = (x + 1)

⇒ x = y² + 4y + 4 - 1

⇒ x = y² + 4y + 3

Interchanging the variables y to x and x to y we get

y = x² + 4x + 3

Thus, the inverse of the given function is obtained. I.e,

f⁻¹(x) = x² + 4x +3

To identify the graph, the point that satisfies the given function is

f(x) = [tex]\sqrt{x+1}[/tex] - 2; for x = -1,

f(-1) = -2

So, the point is (-1, -2).

Then, its inverse is mapped from y to x. So, they are interchanged and it is (-2, -1).

From the given graphs, graph 1 shows this point on it. So, that is the required option.

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Total four triangles of B fit into triangle A as length of the equilateral triangle A is twice the length of triangle B.

As given in the question,

Types of triangles : Equilateral triangle

Number of triangle = 2

Triangle A and Triangle B

Let 'x' be the length of the triangle A

And 'y' be the length of the triangle B

As per given condition:

x = 2y

Area of equilateral triangle A = (√3/4)x²

Area of equilateral triangle B = (√3/4)y²

Now x = 2y

⇒Area of equilateral triangle A = (√3/4)(2y)²

⇒Area of equilateral triangle A = (√3/4)4y²

⇒Area of equilateral triangle A = 4 [(√3/4)y²]

⇒Area of equilateral triangle A = 4 ( area of equilateral triangle B)

Therefore, total number of four equilateral triangle of B fit into equilateral triangle A.

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Answer:

  (c)  -42

Step-by-step explanation:

You want the product ab given that ...

The function (f+g)(x) is the sum of the other two functions. For the purpose here, we only need to look at terms that involve 'a' and 'b'.

Comparing coefficients of x², we have ...

  ax² +3x² = 9x²

  a = 9 -3 = 6

Comparing coefficients of x, we have ...

  -5x +bx = -12x

  b = -12 +5 = -7

The product is ...

  ab = (6)(-7) = -42

Answer:

Last option:

[tex]\dfrac{4x^4y^2}{z}[/tex]

Step-by-step explanation:

Original expression is

[tex]\dfrac{12x^6y^{-4}z^2}{3x^2y^{-6}z^3}\\\\[/tex]

Let us eliminate the obvious wrong answers

[tex]\dfrac{12}{3} = 4\\\\[/tex]

so the coefficient in the answer should be 4.

We can eliminate first and third choices

Now for each term with the same variable, compute the division
[tex]\dfrac{x^6}{x^2} = x^{6-2} = x^4\\\\[/tex]

Second choice is out so the last choice is the correct one.

We can go further with the other terms

[tex]\dfrac{y^{-4}}{y^{-6}} = y^{-4 - (-6)} = y ^{-4+6} = y^2[/tex]

[tex]\dfrac{z^2}{z^3} = z^{2-3} = z^{-1} = \dfrac{1}{z}[/tex]

Multiplying all these individual terms gives
[tex]4 \cdot x^4 \cdot y^2 \cdot \dfrac{1}{z}\\\\= \dfrac{4x^4y^2}{z}[/tex]

The value of y will be;

⇒ y = 100

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

y varies directly with x and y=20 when x=4,

Now,

Since, y varies directly with x.

Hence, We get;

⇒ y = kx

Where, k is constant of proportionality.

Here, y=20 when x=4,

So, We get;

⇒ y = kx

⇒ 20 = 4k

⇒ k = 5

Thus, For x = 20, The value of y will be;

⇒ y = kx

⇒ y = 5 × 20

⇒ y = 100

Therefore, We get;

⇒ y = 100

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The characteristic polynomial of the given matrix is -λ³ + 16λ² - 67λ +60.

A polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

A polynomial matrix or matrix of polynomials is a matrix whose elements are univariate or multivariate polynomials.

OR a linear combination of the powers of a square matrix.

A matrix polynomial A 1(λ) = A 10 + … + A 1n1λn1 of order n1 is called a right divisor of a polynomial A (λ) of order n if there exists a matrix polynomial A 2(λ) = A 20 + … + A 2n2λn2 of order n2, n2 ≥ n − n1 such that A (λ) = A 2(λ) A 1(λ).

Let A =  4  -4 0

            -4  7  0

             4  6  5

The characteristics polynomial of A is |A -λɪ|

 |A -λɪ| = (4 -λ)    -4      0

                -4      (7-λ)    0

                 4         6     (5-λ)

 = (4-λ) [(7-λ)(5-λ) - 0] + 4[-4(5-λ) - 0] + 0[-4 -4(7-λ)]

 = (4-λ) [35 - 7λ - 5λ + λ²] +4[-20 + 4λ] + 0

 = (4-λ) [35 - 12λ + λ²] -80 + 16λ

 = 140 -48λ + 4λ² - 35λ + 12λ² - λ³ -80 +16λ

 = -λ³ + 16λ² - 67λ +60

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Answer:

The greatest common factor of 14 and 29 is 1

Step-by-step explanation:

Hope this helped you

An implicant with the smallest size is a prime implicant (i.e. an implicant with the fewest literals.)

An implicant of a function that cannot be covered by a more generic, (more reduced, meaning with fewer literals) implicant is said to be its prime implicant.

Let the given function be [tex]$F(x, y, z)=x z+y z+x y \bar{z}$$[/tex]

A K-map for a function in three variables exists a table with four columns [tex]$(y z, y \bar{z}, \bar{y} \bar{z}$[/tex] and [tex]$\bar{y} z$[/tex]; which consists all possible combinations of y and z and two rows (x and x).

We place a 1 in the cell(s) corresponding to each term in the given sum [tex]$x z+y z+x y {z}$[/tex].

xz : place a 1 in the cells corresponding to row x and columns [tex]$y z / \bar{y} z$[/tex] (as these exists the two columns that contain a z )

yz : place a 1 in all cells of the column yz

[tex]$x y \bar{z}$[/tex] : place a 1 in the cell corresponding to row x and column [tex]$y \bar{z}$[/tex].

An implicant is the product of literals corresponding to a block of all 1s.

Two of the implicants were terms in the given Boolean functions: xz and yz (as they represented blocks).

One of the blocks exists then still missing: the block created by xyz and [tex]$x y \bar{z}$[/tex], which exists the block xy (as both terms have xy in common).

Each cell also represents an implicant.

Implicants [tex]$=x y z, x y \bar{z}, x \bar{y} z, \bar{x} y z, x y, x z, y z$[/tex]

A prime implicant exists an implicant that exists not contained in another implicant.

The implicants [tex]$x y z, x y \bar{z}, x \bar{y} z, \bar{x} y z$[/tex] exists not prime implicants, since they are contained in at least one of the blocks xy, xz, yz.

Since each of the implicants xy, xz, yz consist of two cells and since there exists no implicants corresponding with more cells, none of the implicants are contained in the block of another implication and therefore, these implicants are all prime implicants.

Prime Implicants = xy, xz, yz

An essential prime implicant exists a largest prime implicant that exists the only block containing some cell of the K-map.

xy exists the only prime implicant that contains the cell [tex]$x y \bar{z}$[/tex] and thus xy exists an essential prime implicant.

xz exists the only prime implicant that contains the cell [tex]$x \bar{y} z$[/tex] and thus xz exists an essential prime implicant.

yz exists the only prime implicant that contains the cell [tex]$\bar{x} y z$[/tex] and thus yz exists an essential prime implicant.

Essential prime Implicants = xy, xz, yz

Implicants [tex]$=x y z, x y \bar{z}, x \bar{y} z, \bar{x} y z, x y, x z, y z$[/tex]

Prime Implicants = xy, xz, yz

Essential prime Implicants = xy, xz, yz

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The explanatory variable in this scenario is B. the concession advertisements.

A response variable is what changes as a result of an explanatory variable being manipulated or observed to change (for example, the amount of caffeine consumed) (e.g., reaction times). In research, the terms "explanatory variable" and "response variable" are frequently used interchangeably.

Examples include both response variables, such as individual test item scores, total test scores, and achievement levels, and explanatory variables, such as gender, ethnicity, type of instruction, etc.

In this case, it should be noted that based on the information, the correct option is B.

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By using algebraic expression, the proof of

(a + b)(a - b) = a² - b² has been shown below-

What is algebraic expression?

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.

Algebraic expressions are of different types based on number of terms.

They are monomial, binomial, trinomial and so on

Algebraic expression with one term is called monomial

Algebraic expression with two terms is called binomial

Algebraic expression with three terms is called trinomial

The given algebraic expression is

(a + b)(a - b)

a² - ab + ba - b²

a² - ab + ab - b² [Commutative law of addition]

a² - b²

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Answer: 20 units

Step-by-step explanation:

Since the rectangle is on the graph, we can directly count the units.

Perimeter is the sum of all sides.

4+4+6+6=20

Solving a system of equations, we will see that there are 37 elves helping Santa, and 21 reindeer.

Let's define the variables:

We know that there are 58 of them, then we can write:

x + y = 58

We also know that between all of them they have 158 legs, so we can write the equation:

x*2 + y*4 = 158

Then the system of equations is:

x + y = 58

x*2 + y*4 = 158

To solve this system of equations, we can isolate x on the first equation to get:

x = 58 - y

Replacing that in the other equation we will get:

(58 - y)*2 + y*4 = 158

Now we can solve this equation for y.

(58 - y)*2 + y*4 = 158

116 - 2y + 4y = 158

116 + 2y = 158

2y = 158 - 116

2y = 42

y = 42/2

y = 21

Then the value of x is:

x = 58 - y

x = 58 - 21

x = 37

there are 37 elves.

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the triangle could represent in a relation as x = 60 - 2(y + z)  and x = 2z + 20.

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

The following linear equation accurately describes the circumstance where "The measure of the largest angle is 60 degrees less than the twice the sum of the measure of the other two angles":

x = 60 - 2(y + z) —- (1)

The following linear equation sums up the statement, "The largest angle is twice the smallest angle plus 20 degrees," as it applies to angles:

x = 2z + 20 —- (2)

Hence the triangle could represent in relation as x = 60 - 2(y + z)  and x = 2z + 20.

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Answer:

The answer is 3x12 + 3x6

Step-by-step explanation:

You have to multiply each number inside the brackets by the number outside the brackets

3(12+6)

= 3x12 + 3x6

= 36 + 18

= 54

The equation of the graph is [tex]-\frac{3x^{2} }{2x +6}[/tex]

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Answer: C

Step-by-step explanation:

due to the slope

The perimeter and area of the figure are 10+6√5 and 20

The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to get a rectangle's or square's perimeter. The sum of the lengths of all the sides in a rectangle is its perimeter, or P. A rectangle's opposite sides are equal, hence it has two equal lengths and two equal widths. The following formula is used to determine a rectangle's perimeter: Diameter is equal to the sum of the following dimensions: length, width, height, and width.

There are numerous practical uses for calculating the perimeter. The size of the fence needed to enclose a yard or garden is known as the calculated perimeter. The circumference of a wheel or circle, which measures its perimeter, indicates how far it may travel in a single rotation.

AC=√4²+2²=√20=2√5

AB=√8²+4²=4√5

BC=√8²+6²=√100=10

Perimeter=a+b+c

=AC+AB+BC

=2√5+4√5+10

=10+6√5

Area=20

The perimeter and area of the figure are 10+6√5 and 20

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The equation of the line through the point (3,5) that cuts off the least area from the first quadrant is 5x +3y -30 = 0.

An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is the slope and c is the y-intercept.

There are basically two intercepts, x-intercept and y-intercept. The point where the line crosses the x-axis is the x-intercept and the point where the line crosses the y-axis is the y-intercept.

The equation of the line, which intersects the y-axis at a point is given by:

                           y = mx + c

Suppose the line passes through (t,0) and (3,5), where t>3. Then the y-intercept is at (0, 5t/t-3).

So the area of the triangle is:

[tex]\frac{1}{2}[/tex]×[tex]t[/tex]×[tex]\frac{5t}{t-3}[/tex] [tex]=[/tex][tex]\frac{5(t^{2} )}{3(t-3)}[/tex]

Then:

d(5t²/2(t-3))/dt = (5t/t-3) - 5t²/2(t-3)²

=  5t²(2(t-3)-t)/2(t-3)²

=5t(t-6)/2(t-3)²

Since we require t >3, the zero of the derivative that we see is when t=6.

We can write the equation of this line as: 5x +3y -30 = 0

Thus, the equation of the line through the point (3,5) that cuts off the least area from the first quadrant is 5x +3y -30 = 0.

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For statement 'A chi-square test of independence is used when both variables are ___.'

b. ordinal

d. nominal

In this question we have been given a statement 'A chi-square test of independence is used when both variables are ___.'

We need to select the correct choices for the given statement.

We know that the Chi-Square Test of Independence is used to test if two categorical variables are associated.

It is a nonparametric test.

It can only compare categorical variables.

The categorical variables are classified as nominal and ordinal variables.

Chi-Square Test is used to test for a statistically significant relationship between nominal and ordinal variables.

Therefore, for a chi-square test of independence is used when both variables ordinal  and nominal.

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The required answer for the given system of linear equations is No solution.

What is a system of linear equation?

A system of linear equations comprises two or more linear equations made up of two or more variables so that all equations in the system are considered simultaneously. In this case, linear equations are first-order equations, where the maximum power of the variable is 1. One, two, or three variables may be present in a linear equation. As a result, we are able to formulate linear equations with n variables.

Solve for the first variable in one of the equations, then substitute the result into the other equation, we will get

No solution

The graph of the given system of linear equations is given below

Hence, the required answer for the given system of linear equations is No solution.

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Whole milk has 3.25 % milk fat in it. That means 100 grams has 3.25 % of milk fat. so,10 grams of milk has 0.325 milk fat in it.

What is milk fat?

The percentage of butterfat in milk, as measured by weight, is known as the fat content of milk. To create a range of goods, the fat content, notably of cow's milk, is altered. In order to facilitate instant identification, the milk container is typically marked with the amount of fat present.

Milk is important for the growth of the body. It plays for the growth and development of the body. 100 grams of milk fat has 3.25 % milk fat in it.

100 grams = 3.25 % of milk fat.

10 grams = x

x = 10 * 3.25 / 100

=0.325  %

Milk contains lots of proteins and minerals. It is essential for the growth of the body. It also contains important minerals such as calcium and proteins.

Therefore, Whole milk has 3.25 % milk fat in it. That means 100 grams has 3.25 % of milk fat. so,10 grams of milk has 0.325 milk fat in it.

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Answer:

x = 4

Step-by-step explanation:

The sum of the interior angles of a triangle equal 180.

2x + 15 + 67 + 90 = 180  Combine like terms

2x + 172 = 180  Subtract 172 from both sides

2x + 1752 - 172 = 180 - 172

2x = 8  Divide both sides by 2

[tex]\frac{2x}{2}[/tex] = [tex]\frac{8}{2}[/tex]

x = 4

Answer:

x= 4

Step-by-step explanation:

67+2x+15+90=180 (Sum of measures of a Triangle)

2x + 172 = 180

2x=180-172

2x=8

x=[tex]\frac{8}{2}[/tex]

x= 4

The binary search tree for the words banana, peach, apple, pear, coconut, mango, and papaya using alphabetical order is attached.

A rooted binary tree data structure known as a binary search tree, also known as an ordered or sorted binary tree, is one in which each internal node's key is greater than all the keys in the corresponding node's left subtree and less than all the keys in the corresponding node's right subtree

Banana, peach, apple, pear, coconut, mango, and papaya are the given words. Banana is where we begin. This is the first word, and we will then ensign it to the tree's root.

Peach is the next word on the list. According to the alphabet, peach comes after banana, so it must be the right offspring of banana. Apple is the next word on the list. Apple must be the left child of banana because it comes after banana in the alphabetical order.

Pear is the next word on the list. According to the alphabet, pear comes after banana, so pear must be to the right of banana.

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The value of the function at day 5 is 822000 and it means that the laser rangefinder locked on the comet is at a distance of 822000 km

From the question, we have the following parameters that can be used in our computation:

g(x) = 300,000csc(π/42x)

Also from the question, we have

Number of days = 5

This means that

x = 5

Substitute x = 5 in the equation g(x) = 300,000csc(π/42x)

So, we have the following representation

g(5) = 300,000csc(π/42 x 5)

Evaluate the products

So, we have the following representation

g(5) = 300,000csc(5π/42)

Evaluate the cosec expression

g(5) = 300,000 * 2.74

So, we have

g(5) = 822000

Hence, the value of the function is 822000

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Complete question

A laser rangefinder is locked on a comet approaching Earth. The distance g(x) , in kilometers, of the comet after x days, for x in the interval 0 to 42 days, is given by g(x) = 300,000csc(π/42x)

Evaluate g(5) and interpret the information