A student is constructing a pair of perpendicular lines using a compass and ruler. Here are her first steps:

Step 1: The student draws her first line and labels it l. She marks a point A (not on the first line) for the second line to pass through.

Step 2: She puts the compass point on A and draws an arc that intersects l at two points. She labels the points B and C.

Step 3: Without changing the compass setting, she puts the compass point on B and draws a large arc.

What should be her next step?

Answer:

see explanation

Step-by-step explanation:

basically Gauss' method simplifies to

Sum = (number of terms) ÷ 2 × (1st term + last term)

43

S₂₀₀ = 200 ÷ 2 × (1 + 200) = 100 × 201 = 20,100

44

S₄₀₀ = 400 ÷ 2 × (1 + 400) = 200 × 401 = 80,200

45

S₈₀₀ = 800 ÷ 2 × (1 + 800 ) = 400 × 801 = 320,400

46

S₂₀₀₀ = 2000 ÷ 2 × (1 + 2000) = 1000 × 2001 = 2,001,000

Answer:

Sum = (number of terms) = 2 x (1st term + last term) 43

43. S200 = 200 = 2 × (1+200) = 100 201 = X 20,100

44 400 400 = 2 × (1+400) = 200 × 401 = 80,200

45 S800 = 800 = 2 × (1+800) = 400 × 801 = 320,400

46 S2000 = 2000 2 × (1+ 2000) = 1000 × 2001 = 2,001,000

Using derivatives, it is found that the x-values in which the slope belong to the interval (-1,1) are in the following interval:

(-15,-10).

It is given by the derivative at x = x0, that is:

[tex]m = f^{\prime}(x_0)[/tex].

In this problem, the function is:

[tex]f(x) = 0.2x^2 + 5x - 12[/tex]

Hence the derivative is:

[tex]f^{\prime}(x) = 0.4x + 5[/tex]

For a slope of -1, we have that:

0.4x + 5 = -1

0.4x = -6

x = -15.

For a slope of 1, we have that:

0.4x + 5 = 1.

0.4x = -4

x = -10

Hence the interval is:

(-15,-10).

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For function k(x, y) = -x² - y² + 4x + 4y,

the absolute minimum is 0 and the absolute maximum is 6

For given question,

We have been given a function k(x, y) = -x² - y² + 4x + 4y

We need to find the absolute maximum and minimum values of the function, subject to the constraints 0 ≤ x ≤ 3, y ≥ 0, and x + y ≤ 6

First we find the partial derivative of function k(x, y) with respect to x.

⇒ [tex]k_x=-2x+4[/tex]

Now, we find the partial derivative of function k(x, y) with respect to y.

[tex]\Rightarrow k_y=-2y+4[/tex]

To find the critical point:

consider    [tex]k_x=0[/tex]     and      [tex]k_y=0[/tex]

⇒       -2x + 4 = 0     and    -2y + 4 = 0

⇒          x = 2            and       y = 2

This means, the critical point of function is (2, 2)

We have been given constraints 0 ≤ x ≤ 3, y ≥ 0, and x + y ≤ 6

Consider k(0, 0)

⇒ k(0, 0) = -0² - 0² + 4(0) + 4(0)

⇒ k(0, 0) = 0

Consider k(3, 3)

⇒ k(3, 3) = -3² - 3² + 4(3) + 4(3)

⇒ k(3, 3) = -9 - 9 + 12 + 12

⇒ k(3, 3) = -18 + 24

⇒ k(3, 3) = 6

Therefore, for function k(x, y) = -x² - y² + 4x + 4y,

the absolute minimum is 0 and the absolute maximum is 6

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The general solution of the given system of odes is

m=1 ; m=4    (real roots)

In arithmetic, a system of odes equations is a finite set of differential equations. Any such device may be either linear or non-linear. Also, such a machine can be both a machine of normal differential equations or a system of partial differential equations.

the compatibility conditions of an overdetermined system of odes equations may be succinctly stated in terms of differential forms (i.e., a shape to be specific, it needs to be closed). See integrability situations for differential systems for more.

It is an elaborately based poem praising or glorifying an event or character, describing nature intellectually as well as emotionally. A traditional ode is dependent on three essential parts: the strophe, the antistrophe, and the epode. Distinct forms together with the homostrophic ode and the abnormal ode also enter.

dx/dt = 2x+2y =   x^1 = 2x+2y     1

dy/dt = x+3y =    y^1 = x+ 3y        2

differentiating 1 with respect to 't'

x^11 = 2x^1+ 2y^1

y^1 = x+3y

x^11 = 2x^1= 2(x+3y)

x^11 = 2x^1+ 2x+ 6y

x^11 = 2x^1+ 2x+ 6(x^1-2x/2)

x^11 = 2x^1+ 2x+ 3x^1- 6x

x^11 = 5x^1 - 4x

x^11 -5x^1 - 4x

x^11 - 5x^1 -4x =0

Auxillary equation is m^5- 5m+4=0

m^2 - m - 4m + 4 = 0

m(m-1) -4 (m-1) =0

(m-1) (m-4) = 0

m=1 ; m=4    (real roots)

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The options C and E is a correct options which are

C. The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°.

E. The length of the minor arc between 6 and 7 is approximately 5.2 inches.

According to the statement

we have given that the radius of the clock face is 10 inches and the face of a clock is divided into 12 equal parts.

And we have to choose the three statements which are correct from the given options.

So,

Check the all given options to find the correct options.

So, OPTION A :

360/12=30 degrees between each number

3-1 = 2 2*30 = 60 degrees so A is FALSE

Now, OPTION B:

C=2 x π x r

r=10

using 3.14 for PI = 10*3.14 =31.4 x 2 = 62.8 so B is TRUE

Now OPTION C:

30 x 4 = 120 degrees = TRUE

Now, OPTION D:

10-3 = 7

7/12 x 62.8 = 0.5833*62.8 = 36.63 inches = FALSE

Now, OPTION E:

1/12=0.0833 x 62.8 = 5.23 rounded to 5.2 = TRUE

So, The options C and E is a correct options which are

C. The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°.

E. The length of the minor arc between 6 and 7 is approximately 5.2 inches.

Disclaimer: This question was incomplete. Please find the full content below.

Questions:

The face of a clock is divided into 12 equal parts. The radius of the clock face is 10 inches. Assume the hands of the clock will form a central angle.

Which statements about the clock are accurate? Check all that apply.

A. The central angle formed when one hand points at 1 and the other hand points at 3 is 30°.

B. The circumference of the clock is approximately 62.8 inches.

C.The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°.

D. The length of the major arc between 3 and 10 is approximately 31.4 inches.

E. The length of the minor arc between 6 and 7 is approximately 5.2 inches.

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Answer: 10xy-12+15x-8y=(5x-4)*(2y+3).

Step-by-step explanation:

[tex]10xy-12+15x-8y=(10xy-8y)+(15x-12)=\\=2y*(5x-4)+3*(5x-4)=(5x-4)*(2y+3).[/tex]

Answer: 42.99

Step-by-step explanation:

42.988. Since 8 is close to ten and is in the hundredth we round it hence 42.99.

In the given diagram, the value of the dashed side of rhombus OABC is 5

From the question, we are to determine the length of the dashed line (OA), in rhombus OABC

In the diagram, we can observe that the length of OA is the distance between point A and the origin (O).

Using the formula for calculating distance between two points,

d =√[(x₂-x₁)² + (y₂-y₁)²]

In the diagram,

The coordinate of the origin is (0, 0)

The coordinate of point A is (3, 4)

Thus,

x₁ = 0

x₂ = 3

y₁ = 0

y₂ = 4

Putting the parameters into the formula, we get

OA =√[(3-0)² + (4-0)²]

OA =√(3² + 4²)

OA =√(9+16)

∴ OA =√25

OA = 5

Hence, in the given diagram, the value of the dashed side of rhombus OABC is 5

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Answer: (-4, 0) and (4, 8)

Step-by-step explanation:

Looking at the graph, we can see where the line passes the parabola and can tell the solutions are (-4, 0) and (4, 8)

Answer:

A = 20%

B = 33.33%

C = 46.67%

Step-by-step explanation:

Ok we need to add up 3, 5, and 7

3+5+7 = 15

405/15 = 27.

27*3 = A

27*5 = B

27*7 = C

A = 81 / 20%

B = 135 / 33.33%

C = 189 / 46.67%

The reverse number of the three-digit number is 732

Let the three-digit number be xyz.

So, the reverse is zyx

This means that

Number = 100x + 10y + z

Reverse = 100z + 10y + x

From the question, we have the following parameters:

y = x + 1

z = 1 + 2y

The sum is represented as:

100x + 10y + z + 100z + 10y + x = 10^3 - 31

100x + 10y + z + 100z + 10y + x = 969

Evaluate the like terms

101x + 101z + 20y = 969

Substitute y = x + 1

101x + 101z + 20(x + 1) = 969

101x + 101z + 20x + 20 = 969

Evaluate the like terms

101x + 101z + 20x = 949

121x + 101z = 949

Substitute y = x + 1 in z = 1 + 2y

z = 1 + 2(x + 1)

This gives

z = 2x + 3

So, we have:

121x + 101z = 949

121x + 101* (2x + 3) = 949

This gives

121x + 202x + 303 = 949

Evaluate the sum

323x = 646

Divide by 323

x = 2

Substitute x = 2 in z = 2x + 3 and y = x + 1

z = 2*2 + 3 = 7

y = 2 + 1 = 3

So, we have

x = 2

y = 3

z = 7

Recall that

Reverse = 100z + 10y + x

This gives

Reverse = 100*7 + 10*3 + 2

Evaluate

Reverse = 732

Hence, the reverse number of the three-digit number is 732

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Answer:

Step-by-step explanation:

x+3y=1

From the representation, the point H and F on the rectangle are H(-3,3) and F(2,-2).

According to the statement

we have given that the a rectangle on the graph with the two given points and we have to find the another points of the graph.

So, to find the points of the rectangle

firstly the given points are:

E(2,3) And G(-2,-2) and we have to find the point H and F.

So, The point H :

For the point H the lines of rectangle meet with each other at the 3 from origin on the x axis to the negative side and at the 3 from origin on the y axis.

So, the point H become H(-3,3)

And for point F:

For the point F the lines of rectangle meet with each other at the 2 from origin on the x axis to the positive side and at the 2 from origin on the y axis on the negative side.

So, the Point F become F(2,-2).

So, From the representation, the point H and F on the rectangle are H(-3,3) and F(2,-2).

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Answer:

D. 25pi

Step-by-step explanation:

"circumscribed" means the rectangle is inside the circle and just the corners (vertices) of the rectangle are touching the circle. This means the diagonal of the rectangle is the diameter of the circle. See image. If the sides of the rectangle are 6 and 8 then the third side that makes the triangle(half the rectangle) is 10. You can find this using Pythagorean Theorem or Pythagorean triples (shortcut)

6^2 + 8^2 = d^2

36 + 64 = d^2

100 = d^2

d = 10

This is the diameter of the circle. The radius would then be 5.

Area of a circle is:

A = pi•r^2

= pi•5^2

= 25pi

Answer:

Step-by-step explanation:

We know a total of 6000 is being turned into 510, in two accounts which equal to 15%, to find how much is in each account we can create the following equation:

[tex]5x+10x=510[/tex]

Solve for x

[tex]15x=510\\x=34[/tex]

Now multiply x by the corresponding percentages to find how much was invested into each percentage.

[tex]34*5=170[/tex]

[tex]34*10=340[/tex]

Therefore we now know that 170 dollars was invested into the 5% division, and 340 dollars was invested into the 10% division.

We can of course check our answer by adding 170+340 which equals our original investment of 510.

$1800 is invested at 5% and the remainder, $4200, is invested at 10%.

percentage, a relative value indicating hundredth parts of any quantity.

Let us consider the amount invested at 5% x.

The amount invested at 10% is then the remainder, which is:

$6000 - x

Now we can set up an equation for the total interest earned:

0.05x + 0.10($6000 - x) = $510

Simplifying and solving for x:

0.05x + $600 - 0.10x = $510

-0.05x + $600 = $510

-0.05x = -$90

Divide both sides by 0.05

x = $1800

Hence, $1800 is invested at 5% and the remainder, $4200, is invested at 10%.

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The polynomial that should be subtracted from the dividend first is; x³ + 2x²

The long division we are given is;

        __________

x + 2 ) x³ + 3x² + x

Now, when we divide the polynomial by (x + 2), it means that the first quotient will be x².

Then by the multiplication of (x + 2) and x², we get a polynomial which will be subtracted from the dividend. Thus, we have;

(x + 2) * (x²) = x³ + 2x²

Thus, the polynomial to be subtracted is x³ + 2x²

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For a bedroom measuring 6 3/4" by 4 1/2" on the drawing, the dimensions of the bedroom are 18 ft. by 27 ft.

Option (C) is correct.

In mathematics, a dimension is the length or width of an area, region, or space in one direction. It is just the measurement of an object's length, width, and height.

According to the question,

The scale of an architectural sketch is 1/4" = 1'. If, according to the drawing, a bedroom has the dimensions 6 3/4 by 4 1/2 inches.

Then, the dimensions of the bedroom in feets are calculated as follows:

As 1/4" = 1'

6 3/4" = 27'= 27 ft.

Similarly,

4 1/2" = 18' =18 ft.

Thus, the dimensions of the bedroom are: 18 ft. by 27 ft.

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Answer:

-3/(b-6) = 3/(-b+6) = 3/(6-b)

Step-by-step explanation:

7/(b-6) + 10/(6-b)

= 7/(b-6) + 10/(-b+6)

= 7-10/(b-6)

= -3/(b-6) = 3/(-b+6) = 3/(6-b)

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{7}{b - 6} + \cfrac{10}{6 - b} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{7}{b - 6} + \cfrac{10}{ - (b - 6)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{7}{b - 6} - \cfrac{10}{ b - 6} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ - 3}{ b - 6}\:\:\: or \:\:\: \dfrac{3}{6-b} [/tex]

The number that has to fill the blank to make the trinomial a perfect square is 72x

From the question, we are to determine the number that makes the given trinomial a perfect square

The given trinomial is

9x² + ___+ 144

For any given trinomial ax² + bx + c, the trinomial is a perfect square if

b² = 4ac

In given trinomial,

a = 9, c = 144, b = ?

Now, we will determine the value of b

Putting the values into the equation,

b² = 4ac

b² = 4×9×144

b² = 5184

b = √5184

b = 72

Thus,

The trinomial will become 9x² + 72x+ 144

Hence, the number that has to fill the blank to make the trinomial a perfect square is 72x

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The valid prediction for the mean of the population possible using these samples is C. Yes, the variation of the sample means is small

It should be noted that a sample mean is an average of a set of data . Also, the sample mean can be used to calculate the standard deviation, central tendency, and the variance of a data set.

The sample mean can be applied to a variety of uses, including calculating population averages.

Here, the sample variance is a measure of the degree to which the numbers in a list are spread out. Here, the numbers given are close to each other.

If the numbers in a list are all close to the expected values, the variance will be small and if they are far away, the variance will be large.

Therefore, the correct option is C.

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Answer:

C: Yes, the variation of the sample means is small.

Step-by-step explanation:

Correct answer on edge

The equation that could represent a linear combination of the system 2/3x + 5/2y = 15 and 4x + 15y = 12 is 0 = 26

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

2/3x + 5/2y = 15

4x + 15y = 12

Multiply the first equation by 6, to eliminate the fractions.

6 * (2/3x + 5/2y = 15)

This gives

4x + 15y = 90

Subtract the equation 4x + 15y = 90 from 4x + 15y = 12

4x - 4x + 15y - 15y = 12 - 90

Evaluate the difference

0 + 0 = -78

Evaluate the sum

0 = -78

The above equation is the same equation as option (b) 0 = 26

This is so because they both represent that the system of equations have no solution

Hence, the equation that could represent a linear combination of the system is 0 = 26

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Complete question

The system of equations below has no solution.

2/3x + 5/2y = 15

4x + 15y = 12

Which equation could represent a linear combination of the system?

The terms through degree four of the Maclaurin series is [tex]f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....[/tex].

In this question,

The function is f(x) = [tex]\frac{sin(x)}{1-x}[/tex]

The general form of Maclaurin series is

[tex]\sum \limits^\infty_{k:0} \frac{f^{k}(0) }{k!}(x-0)^{k} = f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^{2} +\frac{f'''(0)}{3!}x^{3}+......[/tex]

To find the Maclaurin series, let us split the terms as

[tex]f(x)=sin(x)(\frac{1}{1-x} )[/tex] ------- (1)

Now, consider f(x) =  sin(x)

Then, the derivatives of f(x) with respect to x, we get

f'(x) = cos(x), f'(0) = 1

f''(x) = -sin(x), f'(0) = 0

f'''(x) = -cos(x), f'(0) = -1

[tex]f^{iv}(x)[/tex] = cos(x), f'(0) = 0

Maclaurin series for sin(x) becomes,

[tex]f(x) = 0 +\frac{1}{1!}x +0+(-\frac{1}{3!} )x^{3} +....[/tex]

⇒ [tex]f(x)=x-\frac{x^{3} }{3!} +\frac{x^{5} }{5!}+.....[/tex]

Now, consider [tex]f(x) = (1-x)^{-1}[/tex]

Then, the derivatives of f(x) with respect to x, we get

[tex]f'(x) = (1-x)^{-2}, f'(0) = 1[/tex]

[tex]f''(x) = 2(1-x)^{-3}, f''(0) = 2[/tex]

[tex]f'''(x) = 6(1-x)^{-4}, f'''(0) = 6[/tex]

[tex]f^{iv} (x) = 24(1-x)^{-5}, f^{iv}(0) = 24[/tex]

Maclaurin series for (1-x)^-1 becomes,

[tex]f(x) = 1 +\frac{1}{1!}x +\frac{2}{2!}x^{2} +(\frac{6}{3!} )x^{3} +....[/tex]

⇒ [tex]f(x)=1+x+x^{2} +x^{3} +......[/tex]

Thus the Maclaurin series for [tex]f(x)=sin(x)(\frac{1}{1-x} )[/tex] is

⇒ [tex]f(x)=(x-\frac{x^{3} }{3!} +\frac{x^{5} }{5!}+..... )(1+x+x^{2} +x^{3} +......)[/tex]

⇒ [tex]f(x)=x+x^{2} +x^{3} - \frac{x^{3} }{6} +x^{4}-\frac{x^{4} }{6} +.....[/tex]

⇒ [tex]f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....[/tex]

Hence we can conclude that the terms through degree four of the Maclaurin series is [tex]f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....[/tex].

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The graph that matches the polynomial function that has x-Intercepts at -2, ;, and 2 and a relative maximum at x = -1 is: graph A.

We are given that the polynomial function has the following characteristics:

Relative maximum at x = -1, this implies that the peak point of the graph has an x-value that is equal to -1. In order words, the "mountain" is at x = -1.

Graph A has a "mountain" that is at x = -1.

We are given the x-intercepts of the polynomial function as:

-2, 1/2, and 2. This means that the graph intercepts the x-axis at -2, 1/2, and 2.

Graph A in the image attached has x-intercepts of -2, 1/2, and 2.

Therefore, we can conclude that the graph that matches the polynomial function that has x-Intercepts at -2, ;, and 2 and a relative maximum at x = -1 is: graph A.

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The number of ways there are to move from (0, 0) to (7, 7) in the coordinate plane with movements of only one unit right or one unit up accordingly is; 49 while that such that y =x is; 7.

It follows from the task content that the movement intended on the coordinate plane is; from (0, 0) to (7, 7).

The number of ways to move such that movements of only one unit right or one unit up is; 7 × 7 = 49.

The number of ways for which y= x is therefore is; 7 as the movement is diagonal.

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Answer:

Step-by-step explanation:

The expression is:

Find its value when n = 3, substitute n with 3 in the expression:

The matching answer choice is B.

Answer:

  (-∞, ∞)

Step-by-step explanation:

Unless there are restrictions on the domain, the range of any odd-degree polynomial function is "all real numbers."

The given function is a linear function, degree 1. This is an odd degree, so the range of the function is "all real numbers."

  -∞ < f(x) < ∞

  (-∞, ∞) . . . . . in interval notation

Answer:

w = -11

Step-by-step explanation:

[tex]\sqrt{3 - 2w} = w + 6[/tex]

[tex](\sqrt{3 - 2w})^2 = (w + 6)^2[/tex]

[tex] 3 - 2w = w^2 + 12w + 36 [/tex]

[tex] w^2 + 14w + 33 = 0 [/tex]

[tex] (w + 11)(w + 3) = 0 [/tex]

[tex] w + 11 = 0 [/tex]   or   [tex] w + 3 = 0 [/tex]

[tex] w = -11 [/tex]   or   [tex] w = -3 [/tex]

When you square both sides of an equation, you must check all solutions for extraneous solutions.

Check w = -11.

[tex]\sqrt{3 - 2w} = w + 6[/tex]

[tex] \sqrt{3 - 2(-11)} = -11 + 6 [/tex]

[tex] \sqrt{3 + 22} = -5 [/tex]

[tex] \sqrt{25} = -5 [/tex]

[tex] 5 = -5 [/tex]

This is a false statement, so the solution w = -11 is extraneous since it does not satisfy the original equation.

Check w = -3.

[tex]\sqrt{3 - 2w} = w + 6[/tex]

[tex] \sqrt{3 - 2(-3)} = -3 + 6 [/tex]

[tex] \sqrt{3 + 6} = 3 [/tex]

[tex] \sqrt{9} = 3 [/tex]

[tex] 3 = 3 [/tex]

This is a true statement, so the solution w = -3 is valid.

Answer: w = -11

Answer:

Step-by-step explanation: P(x 3), Q(7, -1) and PQ= 5 .

To Find :

The possible value of x.​

Solution :

We know, distance between two points in coordinate plane is given by :

Therefore, the possible value of x are 10 and 4.

The value of x from the given set of values is 5

A rectangle is a 2 dimensional shape with 4 sides and angle. The formula for calculating the area and perimeter is given as:

Area = length * width

Perimeter = 2(length + width)

If the length of a rectangle is 2 inches more than its width and the perimeter of the rectangle is 24 inches, the resulting equation will be:

2x + 2(x + 2) = 24,

Expand and determine the value of "x"

2x+ 2x + 4 = 24

4x + 4 = 24

Subtract 4 from both sides

4x = 24 - 4

4x = 20

Divide both sides by 4

4x/4 = 20/4

x = 5

Hence the value of x from the given set of values is 5

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Complete question

The length of a rectangle is 2 inches more than its width. The perimeter of the rectangle is 24 inches. The equation 2x + 2(x + 2) = 24, where x is the width in inches, represents this situation. The value of x from the set {1, 3, 5, 7} that holds true for the equation is . So, the width of the rectangle is inches and its length is inches.

The last digit of the product of all the numbers between 11 and 29 is 0.

A product is something that has undergone one or more multiplications.

Here, we're looking for the final digit of the product of all whole numbers greater than 11 and less than 29.

Next, we have the product as: 12*13*14*15*16*17*18*19*20*21*22*23*24*25*26*27*28

Now take note of the 20 that is present.

Any number multiplied by 20 will result in a zero, so:

Product = 20*(12*13*14*15*16*17*18*19*21*22*23*24*25*26*27*28)

Using only that, we can infer that 0 represents the final digit in the product of all the numbers between 11 and 29.

Learn more about product here:

https://brainly.com/question/10873737

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