T
15
the
2
-2
y
0
(4.3)
2
(4.-2),
**
Which is the equation of the given line?

D = M/12 + N/4 represents the relationship between Elena's distance in miles, D, and her biking speed.

Speed = distance/ time

Here, we are given that Elena bikes 20 minutes each day for exercise. She bikes at a constant speed of M miles per hour for the first 5 minutes, then at N miles per hour for the last 15 minutes.

Therefore, distance covered by her in the first 5 minutes = speed x time

time = 5 minutes = 5/60 hours

= 1/12 hours

Thus, distance = M(1/12)

= M/12

Now, similarly, distance covered by her in the last 15 minutes = N(15/60)

=N/4

Thus, the total distance in miles, D, covered by her in the last 15 minutes = N(15/60)

= N/4

Thus, the total distance in miles, D, covered by her is D = M/12 + N/4

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Answer:

Perimeter  = 9x+4x+18x+16

Perimeter = 31x+16

Give Brainliest please :)

Answer:

40%

Step-by-step explanation:

To start off, we are going to place the number of movies he thought were very good, over the movies he watched over the entire year into a fraction (or a certain number over the total amount)!

18/45 or [tex]\frac{18}{45}[/tex]

Next, we are going to place this into our calculator and will get a decimal value.

18/45 → 0.40

Last, we are going to change this number into a percentage, by multiplying our decimal by 100.

0.40 → 40%

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer: 26,000

Step-by-step explanation:

26 000

See the pictures attached

Step1: Underline the place value spot you are rounding off to

Step2:circle the next door neighbour

Step3: if the number you circled is bigger than 5 it will stay the same. if it is smaller than 5 it will become a 0 and so will all the numbers that follow

The perimeter of the smaller of the two similar trapezoids is 14 yards.

Similar polygons are polygons that have equal corresponding angles and proportional corresponding sides.

The ratio of one side of a polygon to the corresponding side of the other is called the scale factor.

The ratio of the perimeters is the same as the scale ratio, while the ratio of the areas is the square of its scale ratio.

If two similar trapezoids have a scale factor of 3 : 2, then the ratio of their perimeters is also 3 : 2.

If the perimeter of the larger trapezoid is 21 yards, solve for the perimeter of the smaller trapezoid using the ratio for the perimeter.

3 : 2 = 21 yards : perimeter of the smaller trapezoid

perimeter of the smaller trapezoid = 2(21 yards)/3

perimeter of the smaller trapezoid = 14 yards

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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

Answer: Area= 804.248

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

The circumference is the perimeter of a circle or ellipse in geometry.

The circumference of the ride is about 138.23 feet.

The circumference is the perimeter of a circle or ellipse in geometry. That is, the circumference would be the circle's arc length if it were opened up and straightened out to a line segment. In general, the perimeter is the length of the curve around any closed figure.

The radius is half the diameter.

So, the radius of the circular ride is 22 feet.

Circumference of a circle = [tex]\pi[/tex] d

Where the value of d = 44, then

substitute the value of d in the above equation

Circumference of a circle = [tex]\pi[/tex] d

Circumference of a circle = [tex]\pi[/tex]44

Circumference of a circle = 138.33

Therefore, the circumference of the ride is about 138.23 feet.

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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:

g) 10 tickets and 8 snacks = 32

h) 7 tickets and 5 snacks = 21.5

i) x tickets and y snacks = 53.5

Step-by-step explanation:

Each ticket cost $2 and the snacks, cost $1.50 so we multiply them by the number of tickets and snacks.

g) 10 tickets and 8 snacks = 32

    Explanation: 10x2=20 ,  8x1.50 = 32

h) 7 tickets and 5 snacks = 21.5

  Explanation:7x2=14  ,  5x1.50 = 21.5

i) x tickets and y snacks = 53.5

     Explanation: x=17 and y=13

You add the number of tickets for (Question g,h - tickets, and snacks so

the total cost is $53.5

But the question says you do not use the unit $ so don´t use it.

Sorry If I got it wrong

Answer: G. $20 for tickets and $12 for snacks

H.$14 for tickets and $7.50 for snacks

I. Probably $2 for ticket and $1.50 for snack

Step-by-step explanation: G is $20 and $12 because you first have to multiply 10 tickets by $2 to get the cost of 10 tickets and then multiply $1.50 by 8 snacks to get the cost of 8 snacks.

H is $14 and $7.50 because you also have to multiply 7 tickets by $2 to get the cost of 7 tickets and multiply $1.50 by 5 snacks to get the cost of 5 snacks.

I is probably $2 and $1.50 because the variables x and y are unknown so you would have to put how much each raffle tickets and snacks cost for x and y. Hope this makes sense!

The recursive formula for the given sequence: 1,5,14,30, . . . is a(n) = a(n-1) + n². It can also be expressed as a(n) = 4a(n-1) -6a(n-2) +4a(n-3) -a(n-4), with a(1) = 1.

A recursive formula of a sequence tells us how to find the nth term, a(n), from the preceding terms, a(n-1), a(n-2), ....

The sequence is:

    1,5,14,30, . . . .

Here:

a(1) = 1, a(2) = 5, a(3) = 14, and a(4) = 30.

Let us write:

a(1) = 1

a(2) = 1 + 4 = a(1) + 2²

a(3) = 5 + 9 = 5 + 3² = a(2) + 3²

a(4) = 14 + 16 = 14 + 4² = = a(3) + 4²

So we can conclude the recursive formula is:

a(n) = a(n-1) + n²

However, we can find another recursive formula.

We have:

a(n) = a(n-1) + n²   ........ (1)

For n -1 this becomes:

a(n-1) =  a(n-2) + (n-1)²

a(n-1) = a(n-2) + n² - 2n + 1 ........ (2)

Subtract (1) - (2):

a(n) - a(n-1) = a(n-1) + n²  - a(n-2) - n² + 2n - 1

a(n) - a(n-1) = a(n-1) -a(n-2) + 2n - 1

⇒ a(n) = 2a(n-1) -a(n-2) + 2n - 1  ...(3)

Equation (3) applies for any n, therefore for n -1, eq.(30 becomes:

a(n-1) = 2a(n-2) -a(n-3) + 2(n-1) - 1   ....(4)

Subtract Eq.(3) - Eq.(4).

a(n) - a(n-1) =  2a(n-1) -a(n-2) + 2n - 1 - (2a(n-2) -a(n-3) + 2n - 3)

a(n) - a(n-1) = 2a(n-1) - 3a(n-2) + a(n-3) + 2

⇒ a(n) = 3a(n-1) - 3a(n-2) + a(n-3) + 2   ....(5)

Substitute for n-1 again into Eq.(5):

a(n-1) = 3a(n-2) - 3a(n-3) + a(n-4) + 2 .....  (6)

Subtract Eq.(6) - Eq.(5)

a(n) - a(n-1) =  3a(n-1) -3a(n-2) +a(n-3) +2 -3a(n-2) +3a(n-3) -a(n-4) -2

a(n) - a(n-1) =  3a(n-1) -6a(n-2) +4a(n-3) -a(n-4)

⇒ a(n) = 4a(n-1) -6a(n-2) +4a(n-3) -a(n-4)

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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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A compound function is when the output of one function is used as the input of another function. If we have a function ff and another function gg, the function fg(x)fg(x) is called "ff of gg of xx" or "fgfg of xx" and is a composition of the two functions.

The order in which functions are applied is important. Find the function of the function. If you have two or more functions, there can be many different permutations of those functions, giving you many different composite functions.

fg(x)fg (x) can be written f[g(x)] f[g(x)] to indicate that the inner function should be applied before the outer function.

Solution:

Your problem → f(x)=x/2, g(x)=-2x+4, Find f(g(x))

f(x)=x2, g(x)=-2x+4, fog(x)=?

g(x)=-2x+4, f(x)=x2

fog(x)=f(g(x))

=f(-2x+4)

=-2x+42

=-x+2

fog(x)=-x+2

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Answer:

he descends only 57 feet ,as the mine is 10 feet below the surface befor descending

Answer:

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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 From the list of numbers presented ( 1,0.5,0.25,0.125,0.0625)  we can determine that this is a finite sequence.

      A sequence is an order of elements that are governed by a pattern, that is, it has variations between each element that remain constant and allow us to determine values before or after the known elements.

 A sequence maintains an order, and this numerical order can be finite or infinite, in the given case we have the following list:

1, 0.5, 0.25, 0.125, 0.0625

1/2ⁿ

  We can clearly notice that we have a limit number and it is 0.0625, as we know the beginning of the sequence and the exact end we can know that we are in the presence of a finite sequence.

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7th term of the series = 27.5

Here the series is in arithmetic sequence

Now we have to find the common difference between the series,

common difference (d) = 15- 12.5 = 17.5 - 15 = 2.5

To find the nth term of an arithmetic series we have a formula,

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

So by this we can find the 7th term of the series

[tex]t_{7}[/tex] = 12.5 + (7-1) 2.5

  = 12.5 + 6 × 2.5

  = 12.5 + 15

 = 27.5

So the 7th term of the series is 27.5

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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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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:

1 25/ 26

2 3/4

3 35/24

6 9/2

8 2/5

Step-by-step explanation:

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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[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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The slope of the line containing (8,-3) and (-6,-2) is (1/14).

The slope of a straight line can be written as follows,

m =  [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex]                 equation1

The line is containing the points (-3,3) and (4,3). So, we can write

[tex]y_{2}[/tex] = -2 , [tex]y_{1}[/tex] = -3 , [tex]x_{2}[/tex] = -6 , and [tex]x_{1}[/tex] = 8 .

On substituting the values of variables in equation1, we will get

m = ( (-2)-(-3) ) / ( (-6)-(8) ) = (1/14).

As the slope of a line is (1/14), so we can conclude that the given line is a straight line.

Here:

m = the slope of the line

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.

The slope of the line containing (8,-3) and (-6,-2) is (1/14).

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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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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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Answer:

3 and 4

Step-by-step explanation:

Since complementary angles add up to 90,

and 1 is a right angle while 3 and 4 are vertical angles

The position and label of the given right angle triangle ΔX Y Z whose hypotenuse will be 3.16 b have been plotted.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

In a triangle, the sum of all three angles is 180°

Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.

Given the right-angle triangle ΔX Y Z

XY = b(base) and XZ = 3b(perpendicular).

By Pythagoras theorem,

Hyp² = Base² + Perp²

Hyp² = b² + (3b)²

Hyp² = 10b²

Hyp = 3.16b

Hence "The position and label of the given right angle triangle ΔX Y Z whose hypotenuse will be 3.16 b have been plotted".

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