In the diagram below, m/CIH = 105° and m/BGD = 41°. Find m/AHF.
B.
D
41°
G
E
105
H
F
C

Answer: Ratio: 2:3

2 ==> 1st term

Step-by-step explanation:

22.78125/4.5=5.0625

5.0625^(1/(7-3))=

5.0625^(1/4)=1.5 ==> Ratio: 1:1.5 ==> 2:3

4.5 / 1.5^(3-1)=

4.5 / 1.5^2=

4.5 / 2.25 = 2 ==> 1st term

The first term (a) in the geometric progression is approximately 2.

The common ratio (r) is 1.5.

Here, we have to find the common ratio (r) and the first term (a) in the geometric progression, we'll use the formula for the nth term of a geometric sequence:

[tex]u_n = a * r^{(n-1)[/tex]

where:

[tex]u_n[/tex] is the nth term,

a is the first term,

r is the common ratio,

n is the position of the term in the sequence.

Given u3 = 4.5 and u7 = 22.78125:

For n = 3:

[tex]u_3 = a * r^{(3-1)}\\4.5 = a * r^2[/tex]

For n = 7:

[tex]u_7 = a * r^{(7-1)}\\22.78125 = a * r^6[/tex]

Now, we have two equations:

[tex]a * r^2 = 4.5\\a * r^6 = 22.78125[/tex]

Divide equation 2 by equation 1:

[tex](a * r^6) / (a * r^2) = 22.78125 / 4.5[/tex]

Simplify:

[tex]r^4 = 5.0625[/tex]

Now, take the fourth root of both sides to find the value of r:

r = √(5.0625)

r ≈ ± 1.5

Since r is the common ratio, it cannot be negative in a geometric progression.

So, the common ratio (r) is 1.5.

Now, we can find the first term (a) using equation 1:

[tex]a * r^2 = 4.5[/tex]

Substitute the value of r (1.5):

[tex]a * (1.5)^2 = 4.5[/tex]

a * 2.25 = 4.5

Divide by 2.25:

a ≈ 4.5 / 2.25

a ≈ 2

Therefore, the first term (a) in the geometric progression is approximately 2.

The common ratio (r) is 1.5.

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The first term of the arithmetic sequence so formed is $20 and the common difference is $10.

A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

Given:

To find: The first term and common difference of the arithmetic progression so formed.

Finding:

As the initial charge charged by the players is $20, it can be taken as the first term of the arithmetic sequence, at 0 hours; a₁ = 20

Now, since the hourly charge is $10, the given arithmetic sequence of the money charged will increase by $10 per hour; thus d = 10

The arithmetic sequence holds true for 5 hours maximum.

Thus the sequence so formed => [tex]a_n = 20 + (n - 1)10[/tex], 1 ≤ n ≤ 5.

Hence, The first term of the arithmetic sequence so formed is $20 and the common difference is $10.

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The expression that can be used to find the perimeter of the triangle is P = 12x^2 - 6 and the perimeter when x = 1.5 is 21 inches.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now it is given that,

Pablo folds a straw into a triangle with side lengths of 4x^2−3 inches, 4x^2−2 inches, and 4x^2−1 inches

Suppose the sides of the triangle are,

L = 4x^2−3 inches

B = 4x^2−2 inches

H = 4x^2−1 inches

Now since the perimeter is the sum of all the sides.

Thus, Perimeter of the given triangle is given as,

P = L + B + H

Putting the values we get,

P = (4x^2−3) + (4x^2−2) + (4x^2−1)

Expanding the brackets we get,

P = 4x^2 − 3 + 4x^2 − 2 + 4x^2 − 1

Taking alike terms together,

P = 4x^2 + 4x^2 + 4x^2 - 3 - 2 - 1

Now solving we get,

P = 12x^2 - 6

Thus is the expression for the perimeter of the triangle.

Now the perimeter when x  = 1.5

Put x  = 1.5 in the perimeter expression we get,

P = 12(1.5)^2 - 6

Solving we get,

P = 12*2.25 - 6

Solving we get,

P = 27 - 6

Thus we get,

P = 21 inches

this is the required perimeter when x = 1.5

Thus, the expression that can be used to find the perimeter of the triangle is P = 12x^2 - 6 and the perimeter when x = 1.5 is 21 inches.

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Answer:

12x2 −6; 21 inches

Step-by-step explanation:

Answer:

x = -2

Step-by-step explanation:

2x -5 = 3(4x + 5)  step 1

2x - 5 = 12x + 15  step 2

2x - 12x -5 = 15 Step 3

2x - 12x = 15 +5 simplify

      -10x/-10 = 20/-10 step 4

               x = -2

Making C the subject of the formula, we have: C = 5(F - 32)/9.

Given the formula, F = 9/5C + 32, we are asked to solve the equation for C, this means we would make C the subject of the formula.

F = 9/5C + 32

Subtract 32 from both sides

F - 32 = 9/5C + 32 - 32

F - 32 = 9/5C

Multiply both sides by 5/9

5/9(F - 32) = 9/5C(5/9)

5(F - 32)/9 = C

C = 5(F - 32)/9

Therefore, making C the subject of the formula, we have: C = 5(F - 32)/9.

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After solving each system, 2m = -4n - 4, 3m + 5n = -3, the values of m and n are calculated to be 4 and -3 respectively.

The two given equations, 2m = -4n - 4, and 3m + 5n = -3 are considered to be linear equations since the highest power of the variables in these equations is one.

By rearranging the second equation, the value of m is calculated to be,

3m + 5n = -3

3m = -3 - 5n

m = -3 - 5n / 3

Putting the calculated value of m in the first equation,

2m = -4n - 4

2(-3 - 5n / 3) = -4n - 4

-6 - 10n / 3 = -4n - 4

-6 - 10n = 3(-4n - 4)

-6 - 10n = -12n - 12

-10n + 12n = -12 + 6

2n = -6

n = -6/2

n = -3

To solve for m, put n = -3 in the first equation as follows,

2m = -4n - 4

2m = -4(-3) - 4

2m = 12 - 4

m = 8 / 2

m = 4

Thus the value of m and n in these systems are calculated to be 4 and -3 respectively.

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The corresponding area and perimeter of the shapes assuming all are unit squares are {5,5) units² and {16,15} units.

A square is a geometrical figure in which we have four sides each side must be equal and the angle between two adjacent sides must be 90 degrees.

Let's assume all blocks that exist in shape are square with dimension units or one.

Now the area of the square is given as ;

A = Side² = 1² = 1

Since the number of squares in 20 is 5

So,

A = 5 unit²

The number of squares in 21 is also 5

So,

A = 5 unit²

Now,

The perimeter of the square as given;

P = 4× side

Since side in 20 are 16 so 16 units.

The side in 21 is 15 so 15 units.

Hence "The corresponding area and perimeter of the shapes assuming all are unit squares are {5,5) units² and {16,15} units".

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Answer:  2.5 Hours. I hope I'm not sure but I think you just divide Miles Driven by MPH

Answer:

Step-by-step explanation:

Determine the two consecutive multiples of 10 that bracket 19.

19 is between 10 and 20.

15 is the midpoint between 10 and 20.

As illustrated on the number line, 19 is greater than the midpoint (15)

Therefore, 19 rounded to the nearest is 20

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The coordinate of points A, B, and C will be (0, a), (0, 0), and (a, 0), respectively.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

In an isosceles right triangle, the two legs of the triangle are congruent and intersect at right angles and their opposite angles are also equal.

The vertice C lies on the x-axis, then the coordinate of point C will be (a, 0).

The vertice A lies on the y-axis, then the coordinate of point C will be (0, a).

Then the coordinate of B will be at the origin which is (0, 0).

Thus, the coordinate of points A, B, and C will be (0, a), (0, 0), and (a, 0), respectively.

The diagram is attached below.

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Answer:

[tex]y = x \ln 2 +\left(\ln 2 \right)^2-2 \ln 2[/tex]

Step-by-step explanation:

Differentiation is an algebraic process that finds the gradient of a curve.

At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.

[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\If $y=f(u)$ and $u=g(x)$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{4.5 cm}\underline{Differentiating $x^n$}\\\\If $y=x^n$, then $\dfrac{\text{d}y}{\text{d}x}=nx^{n-1}$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{4.5 cm}\underline{Differentiating $\ln x$}\\\\If $y=\ln x$, then $\dfrac{\text{d}y}{\text{d}x}=\dfrac{1}{x}$\\\end{minipage}}[/tex]

Differentiate the given function using the chain rule:

[tex]\begin{aligned}f(x) & = \left(\ln x\right)^2\\\implies f'(x)& = 2\left(\ln x\right)^{2-1} \cdot \dfrac{\text{d}}{\text{d}x} \ln x\\& = 2\left(\ln x\right)^{1} \cdot \dfrac{1}{x}\\& = \dfrac{2}{x} \ln x \end{aligned}[/tex]

To find the gradient of the function at x = 2, substitute x = 2 into the differentiated function:

[tex]\implies f'(2) = \dfrac{2}{2} \ln 2 = \ln 2[/tex]

Therefore, the gradient of the function at x = 2 is ln(2).

Substitute x = 2 into the function to find the y-value of the point on the curve when x = 2:

[tex]\implies f(2)= \left( \ln 2\right)^2[/tex]

Slope-intercept form of a linear equation:

[tex]y=mx+b[/tex]

where:

Substitute the point (2, (ln 2)²) and the found gradient into the slope-intercept formula and solve for b:

[tex]\begin{aligned} y & = mx+b\\\implies \left(\ln 2 \right)^2 & = \ln 2 \cdot 2 + b\\\left(\ln 2 \right)^2 & =2\ln 2 +b\\b & = \left(\ln 2 \right)^2-2 \ln 2\end{aligned}[/tex]

Therefore, the tangent has the equation:

[tex]y = x \ln 2 +\left(\ln 2 \right)^2-2 \ln 2[/tex]

Answer:

najua unanijuki bait ni sawa Bora

The recursive definition for Q is Q(n) = Q(n-1) + 1.5

It refers to a "series where the deviations between every subsequent term are exactly the same" (or) "each term is acquired by adding a specific number (positive, negative, or zero) to its preceding term."

We have three values of sequence:

Q(1)=4

g(3)=7

Q(7)=13

Let us assume the sequence to be an arithmetic sequence

The n-th term of any arithmetic sequence is determined by:

[tex]a_{n}[/tex] = a+(n-1) d

Q(3)=Q(-1)+(3-1)d

7 =4+2d

2d = 3

d = 3/2

d = 1.5

Now, Q(7) = Q(1) + (-1)d

13 = 4+6 d

6d = 9

d = 9/3

d = 1.5

So, the d is the same for both terms.

Therefore, this is an arithmetic sequence.The recursive relation is given as [tex]a_{n}[/tex] = a(n-1)d.

Then, the recursive definition for Q is Q(n) = Q(n-1) + 1.5.

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The formula to calculate the 10th term of a Geometric Progression is :

                         => [tex]a_{10} = a.r^{9}[/tex]          

The formula to calculate [tex]n^{th\\}[/tex] term in a given Geometric progression is

                         =>  [tex]a_{n} = a.r^{n-1}[/tex]  

Where a1 = a, r is a common ratio defined by the ratio of any two successive terms r = a2/a1, and n is the term to be found.

In the given sequence, we have the first term i.e. a = -3, n = 10,  

common ratio  =>  r = a2/a1        =>    r = -2

Calculating using the G.P. formula for the 10th term

                        => [tex]a_{10} = a.r^{9}[/tex]

                        => [tex]a_{10} = (-3).(-2)^{(10-1)}[/tex]

                        => [tex]a_{10\\}[/tex] =  (-3)(-512)  = 1536

The 10th term for this sequence will be 1536.

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Answer:

Perimeter  = 9x+4x+18x+16

Perimeter = 31x+16

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The independent variable is time on the x axis and the dependent variable is distance on the y-axis.

When making a time graph, the independent variable is the variable that is shown by the x-axis. Time will usually be the independent variable because we cannot change time so we watch for the changes in other things as time goes on.

In this case therefore, the independent variable is time which will be shown as the x-values. The dependent variables would then be the distance which would be the y-values.

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The given sequence 2, 5, 9, 14,… is not an Arithmetic sequence.

The given sequence is 2, 5, 9, 14,…

Here, [tex] a_{1}[/tex] = 2, [tex] a_{2}[/tex] = 5 and [tex] a_{3}[/tex] = 9.

A sequence is considered as an Arithmetic sequence if their difference is equal. Represented as -

[tex] a_{2}[/tex] - [tex] a_{1}[/tex] = [tex] a_{3}[/tex] - [tex] a_{2}[/tex] = [tex] a_{4}[/tex] - [tex] a_{3}[/tex] and so on

Now, in the given sequence

⇒[tex] a_{2}[/tex] - [tex] a_{1}[/tex] = 5 - 3

[tex] a_{2}[/tex] - [tex] a_{1}[/tex] = 2

⇒ [tex] a_{3}[/tex] - [tex] a_{2}[/tex] = 9 - 5

[tex] a_{3}[/tex] - [tex] a_{2}[/tex] = 4

⇒ [tex] a_{4}[/tex] - [tex] a_{3}[/tex] = 14 - 9

[tex] a_{4}[/tex] - [tex] a_{3}[/tex] = 5

Since, the difference between the successive terms are not same.

∴ The given sequence 2, 5, 9, 14,… is not an Arithmetic sequence.

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Answer:

1 25/ 26

2 3/4

3 35/24

6 9/2

8 2/5

Step-by-step explanation:

[tex]r_{y = 2} r_{y - axis}[/tex] is  a glide reflection or composition of transformations that can be used to transform ΔABC to ΔDEF.

A glide translation is what?

When a figure is subjected to one transformation before another is applied?

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Using proportions, the coordinates of the point 3/10 of the way from (-3,-8) to (12,6) are: (1.5, -3.8).

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

We want a point C 3/10 of the way from A(-3,-8) to B(12,6), hence:

C - A = 3/10(B - A).

The x-coordinate of the point is found as follows:

x + 3 = 3/10(12 + 3)

x + 3 = 4.5

x = 1.5.

The y-coordinate of the point is found as follows:

y + 8 = 3/10(6 + 8)

y + 8 = 4.2

y = -3.8.

Hence the coordinates are: (1.5, -3.8).

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The segments joining the base vertices to the midpoints of the legs of an isosceles triangle will split into two equal triangles so they will be congruent.

If two figures are exactly the same in sense of their length side all things then they will be congruent.

If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent or to be in the relation of congruence.

ΔABC is isosceles where AB = AC

Now,

Line segment AD is intersecting at the midpoint of BC.

Now,

In ΔABD and ΔACD

AB = AC,AD = AD and BD = DC

Since all sides are equal so by SSS congruent property both will be congruent.

Hence "The segments joining the base vertices to the midpoints of the legs of an isosceles triangle will split into two equal triangles so they will be congruent".

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The sum of (6.9*10^6) and (5.9*10^5) is 7.49 * 10^6.

The arithmetically adding two or more numbers is called sum.

Scientific notation is a form of presenting a very small or very large number in simple form. it is in the form of multiplication of one digit with 10 raise to the power of respective exponent. plus power is used for huge number and minus power is used for tiny number.

Given numbers = 6.9 * 10^6 and 5.9 * 10^5

5.9 * 10^5 = 0.59 * 10^6

Sum of both numbers

= 6.9*10^6 + 0.59*10^6

= (6.9+0.59)*10^6

= 7.49*10^6

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The equation which can be used to represent the height of the door in centimeter is 900 = hb

Area of a rectangle = Height × width

900 = h × b

900 = hb

The door's height if its base is 25 centimeters wide?

Area of a rectangle = Height × width

900 = hb

900 = h × 25

900 = 25h

h = 900 /25

h = 36 centimeters

Therefore, the door's height if its base is 25 centimeters wide is 36 centimeters

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The measure of JL from the given parameters is 54

The midpoint of a line is the line that divides the line into two equal parts. If K is the midpoint of JL, then the measure of KK is equivalent to the measure of JK. Mathematically;

JK = KL

JK + KL = JL

Given the following parameters

JK=8x + 11 and

KL=14x- 1

Equate

8x+11 = 14x-1

-6x = -12

x = 2

Determine JL

JL = 2(8x+11)

JL = 2(16+11)

JL = 54

Hence the measure of JL from the given parameters is 54

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Answer:

g(x)=f(x-2)+3

Step-by-step explanation:

Answer:

f(x) = |x + 2| + 1

Step-by-step explanation:

The graph of f(x) is translated 2 units to the left and 1 unit up

A horizontal translation of 2 units results in the original function being f(x +2)

A vertical translation of 1 unit happens at f(x) + 1

Horizontal translation of 2 units left of f(x) = |x| is f(x+2) = |x + 2|

Vertical translation of 2 units up : f(x) = |x| + 1

Combined we get g(x) = |x + 2| + 1

Answer: 55

Step-by-step explanation

[tex]\sqrt{a^{2} + b^{2}}=c -- Pythagorean theorem[/tex]

[tex]\sqrt{14^{2} + 20^{2}}=c[/tex] ≈24.41 rounding up to whole number = 24

∠θ = [tex]tan^{-1} (opposite/adjacent) = tan^{-1} (20/14) = 55[/tex]

therefore, ∠θ = 55

Using Arithmetic progression(A.P.), the value of a22 will be 107

The formula to calculate A.P. is a + (n-1)d

The value of a5 = 5a1

a1 = 23

a5 = -5a1

a5 = 5 (23)

a5 =  115

a22 = a + (n-1)d

a22 = 23 + (22-1)d

a22 = 23 + 21d                                     ................(1)

a5 = 115

115 = a + (n-1)d

115 = 23 + (4)d                                    ...................(2)

from (1) and (2)

a5 = a + 4d

d = 23

a22 = 107

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Answer: Area= 804.248

Step-by-step explanation: