What is the value of n in the numerical sentence below?

√16 ÷ 4³ = 4ⁿ

n = ?

The value of x in 5(x + 1) = 4(x + 8) is 27.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

5(x + 1) = 4(x + 8)

Now, applying distributive property

5x+ 5 = 4x+ 32

5x - 4x = 32- 5

x= 27

Hence, the value of x is 27.

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Answer:

1.16 in

2.24 in

3.12.8 in

Step-by-step explanation:

We are given that

Width of photo=5 in

Length of photo=8 in

We have to find the length of new photo in each case.

1. Let x represent the width and y represents the length of photo.

When width increase then length of photo is also increases then it is direct proportion.

[tex]\frac{x_1}{y_1}=\frac{x_2}{y_2}[/tex]

Substitute the values then we get

[tex]\frac{5}{8}=\frac{10}{y}[/tex]

[tex]y=\frac{10\times 8}{5}=16[/tex]

Hence, the length of photo=16 in

2.Width=x=15 in

Again using the formula

[tex]\frac{5}{8}=\frac{15}{y}[/tex]

[tex]y=\frac{15\times 8}{5}=24[/tex]

Hence, the length of new photo=24 in

3. Width =x=8 in

Substitute the values in the given formula

[tex]\frac{5}{8}=\frac{8}{y}[/tex]

[tex]y=\frac{8\times 8}{5}=\frac{64}{5}=12.8[/tex]

Hence, the length of new photo=12.8 in

Final answer:

An independent system of linear equations has two lines that intersect at exactly one point. If the slope of one line is the negative reciprocal of the other, the lines are perpendicular, indicating they intersect once and the system is independent.

Explanation:

If the slope of one line in a system of linear equations is the negative reciprocal of the slope of the other line, this indicates that the two lines are perpendicular to each other. Perpendicular lines intersect at one point and therefore, the system of equations is independent. An independent system has a single unique solution, meaning that there is exactly one point where the two lines cross.

In terms of graphs and equations, the slope or 'm' in the equation y = mx + b represents the rate at which the dependent variable changes with respect to the independent variable. The negative reciprocal relationship between slopes of two lines means that one will rise (positive slope) and fall (negative slope) at the same rate but in opposite directions, ensuring they intersect just once unless the y-intercepts (b) are also identical, which would make them the same line (dependent system) rather than intersecting lines.

this is the question...

Answer:

the answer is d

Step-by-step explanation:

everybody else keeps getting it wrong, the answer is d

Answer:

  2√42 ≈ 12.961

Step-by-step explanation:

All of the right triangles are similar, so ...

  short leg/long leg = BC/AC = AC/CD

  AC² = BC·CD = 7·24 = 168

  AC = √168 = 2√42

Final answer:

To divide 6.4 by 43.52, the approximate quotient is 0.09238.

Explanation:

To divide 6.4 by 43.52, you can simply perform the division operation. Here are the steps:

Therefore, 6.4 divided by 43.52 is approximately 0.09238.

Answer:

[tex]ln(8y^{6})[/tex]

Step-by-step explanation:

3ln(2)+6ln(y)

= [tex]ln(2^{3} )+ln(y^{6})[/tex]

= [tex]ln(8 )+ln(y^{6})[/tex]

=  [tex]ln(8*y^{6})[/tex]

= [tex]ln(8y^{6})[/tex].

Final answer:

The expression 3√54−4√24 simplifies to √6 after factoring out the perfect squares under the radicals and combining like terms.

Explanation:

The student's question requires simplifying the expression 3√54−4√24. To simplify a square root, we look for perfect squares that are factors of the number under the root. For √54, we can notice that 54 = 9 * 6, and since √9 is a perfect square, we have 3√54 = 3*√9*√6 = 3*3*√6 = 9√6. Similarly, for √24, it is 24 = 4 * 6, so √24 = √4*√6 = 2*√6, and thus -4√24 = -4*2*√6 = -8√6. Combining these two results, we have 9√6− 8√6, which simplifies to √6. Therefore, the simplified expression is √6.

Answer:                                  

The answer is trade association.                

Step-by-step explanation:              

Such organizations are founded to encourage trade and collaboration between companies. These are also known as industry trade group or business association and is funded by businesses that operate in a particular industry.          

An angle bisector is a ray, segment, or line that divides a given angle into two angles of equal measure. Therefore, the correct answer is option C.

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

An angle bisector is defined as a ray, segment, or line that divides a given angle into two angles of equal measures.

Steps to Construct an Angle Bisector:

Step 1: Draw any angle, say ∠ABC.

Step 2: Taking B as the center and any appropriate radius, draw an arc to intersect the rays BA and BC at, say, E and D respectively. (Refer to the figure below)

Step 3: Now, taking D and E as centers and with the same radius as taken in the previous step, draw two arcs to intersect each other at F.

Step 4: Join B to F and extend it as a ray. This ray BF is the required angle bisector of angle ABC.

Step 2: Taking B as the center and any appropriate radius, draw an arc to intersect the rays BA and BC at, say, E and D respectively. (Refer to the figure below)

Therefore, option C is the correct answer.

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All the three figures given in the problem cannot be squares.

A parallelogram is a type of quadrilateral of which the opposite sides are equal and parallel. A diagonal of a parallelogram divides it into two congruent triangles.

Given that,

There are an equiangular rhombus, an equilateral rectangle, and a parallelogram with four right angles.

They can be explained one by one as follows,

(a) A rhombus has all the four sides as equal and its opposite sides are parallel.

When all the angles of a rhombus becomes equal, its each angle is a right angle.

It implies that it will have all angles equal to right angle and all sides are equal as well.

Thus, an equiangular rhombus is a square.

(b) A rectangle has all its angle equal to right angle.

Opposite sides are equal and parallel.

When all the sides become equal, it will be a square.

(c) A parallelogram has its opposite sides as  equal and parallel.

When all the angles become right angles, it can be a rectangle.

Hence, an equiangular rhombus and an equilateral rectangle can be a square but a parallelogram with four right angles cnnot be so.

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Final answer:

The coefficient of the fourth term in the expansion of (x + 3)⁴ is calculated using the binomial theorem, which results in a coefficient of 108.

Explanation:

To find the coefficient of the fourth term in the expansion of (x + 3)⁴, we can use the binomial theorem. The binomial theorem states that when a binomial is raised to a power, the expansion consists of terms in the form of [tex]C(n, k) \times a^{n-k} \times b^k[/tex], where C(n, k) is the binomial coefficient. In our case a = x and b = 3, and n = 4.

For the fourth term where k = 3, the term would be [tex]C(4, 3) \times x^{4-3} \times 3^3[/tex]. The binomial coefficient C(4, 3) is equal to 4 because there are four ways to choose three items out of four. Therefore, the coefficient is 4 × 3³ = 4 × 27 = 108. So, the coefficient of the fourth term in the expansion of (x + 3)⁴ is 108.

If two chords are the same distance from the center of a circle then they are congruent.

Given that, two chords are the same distance from the center of a circle.

The chord of a circle is a line that connects two points that are located on the circumference of the circle. These two points can be located anywhere on the same circumference.

Chords are equidistant from the center if and only if their lengths are equal. Equal chords are subtended by equal angles from the center of the circle.

Hence, if two chords are the same distance from the center of a circle then they are congruent.

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Answer:

slope of perpendicular line = [tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

Find  the slope of a line that is perpendicular to the line shown on the graph

To find slope of the given line , we pick two points from the graph

(0,1) and (1,3)

[tex]slope = \frac{y_2-y_1}{x_2-x_1} =\frac{3-1}{1-0} = 2[/tex]

Slope of given line = 2

slope of perpendicular line = negative reciprocal of slope of given line

slope of perpendicular line = [tex]-\frac{1}{2}[/tex]

the average rate of change for the given graph from x = -2 to x = 0  is:

                                    3

We know that the average rate of the graph of the function f(x) form x=a to x=b is calculated by the formula:

[tex]Average\ Rate\ of\ change=\dfrac{f(b)-f(a)}{b-a}[/tex]

Here we have:

a= -2 and  b=0

Also, from the graph of the function we have:

f(a)=0  and  f(b)=6

Hence, the average rate of change of the graph from x= -2 to x=0 is:

[tex]Average\ Rate\ of\ change=\dfrac{6-0}{0-(-2)}\\\\i.e.\\\\Average\ Rate\ of\ change=\dfrac{6}{2}\\\\i.e.\\\\Average\ Rate\ of\ change=3[/tex]

              Hence, the answer is:  3

The reasonable conjecture for Kathryn to make by recognizing a pattern and using inductive reasoning is:

  When a pair of lines intersect, the vertical angles are congruent.

The vertical angles are the opposite angles that are formed by the intersection of two lines. They are also known as Vertically opposite angles.

We know that when a pair of lines intersect then the vertical angles are always congruent.

However the measure of the angles may be acute or obtuse or right angle.

The same could be seen with the help of the figure attached to the answer.

Unit rate is the quantity of an amount of something at a rate of one of another quantity.

584 units = 8 hours

1 hour = 73 units

2 hours = 146 units

The number of units produced in 2 hours is 146 units.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

A machine produces 584 units in 8 hours.

This means,

584 units = 8 hours

Divide both sides by 8.

1 hour = 73 units

Now,

1 hour = 73 units

Multiply 2 on both sides.

2 hours = 146 units

Thus,

The number of units produced in 2 hours is 146 units.

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1. where is the y intercept of any direct variation equation?

A direct variation equation is one in which the general form is:

y = k x

where k is the constant of proportionality

The y-intercept in this case is therefore zero so it is located on the origin (0, 0)

2. The equation which is a direct variation is:

                3) 3x-7y=0

                Because we can write this as:

                y = (3/7) x

3. what is the direct variation equation if y=8 and x = 4?

We solve for the value of k since we know that:

k = y/x

k = 8/4 = 2

So the equation is:

y = 2x

4. what is the direct variation equation if y =-5 and x = 7?
We also solve for the value of k since we know that:

k = y/x

k = -5/7

So the equation is:

y = (-5/7) x