which of these is right

The length of the zip wire is approximately 25.42 meters.

To calculate the length of the zip wire, we can use trigonometry and the given information about the angle and the distance between the two posts.

Given:

Distance between the two posts: 25m

Angle of the zip wire to the horizontal: 10°

We can use the trigonometric function cosine (cos) to find the length of the zip wire. Cosine relates the adjacent side to the hypotenuse of a right triangle.

In this case, the adjacent side is the distance between the two posts (25m) and the hypotenuse is the length of the zip wire that we want to calculate.

Using the cosine function:

cos(angle) = adjacent/hypotenuse

cos(10°) = 25m/hypotenuse

To find the hypotenuse (length of the zip wire), we can rearrange the equation:

hypotenuse = 25m / cos(10°)

Using a calculator or trigonometric tables, we can find the value of cos(10°) to be approximately 0.9848.

Therefore, the length of the zip wire is:

hypotenuse = 25m / 0.9848 ≈ 25.42m

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Answer:

it is inscribed in the circle.

Step-by-step explanation:

A) The value of x in log₄(x² - 12x + 48) = 2, is x = 4 OR x = 8

B) The value of x in 27^(4x-6) =(1/9)^(2x-7), is x = 2

From the question, we are to solve the given equations

The given equation is log₄(x² - 12x + 48) = 2

From one of the laws of logarithm, we have that

logₐ x = n ⇒ x = aⁿ

Thus,

log₄(x² - 12x + 48) = 2 becomes

(x² - 12x + 48) = 4²

x² - 12x + 48 = 16

x² - 12x + 48 - 16 = 0

x² - 12x + 32 = 0

Solve the quadratic equation

x² - 12x + 32 = 0

x² - 8x - 4x + 32 = 0

x(x - 8) -4(x - 8) = 0

(x - 4)(x - 8) = 0

x - 4 = 0 OR x - 8 = 0

x = 4 OR x = 8

B) 27^(4x-6) =(1/9)^(2x-7)

Solve for x

27^(4x-6) =(1/9)^(2x-7)

Express the bases in index form

3^3(4x-6) =(3)^-2(2x-7)

Equate the powers

3(4x - 6) = -2(2x - 7)

12x - 18 = -4x + 14

12x + 4x = 14 + 18

16x = 32

Divide both sides by 16

16x/16 = 32/16

x = 2

Hence, the value of x is 2

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Answer:

p=88

Step-by-step explanation:

(20*2)+(24*2)=

40+48=

88

Answer:

88cm

Step-by-step explanation:

Perimeter of a rectangle = 2 ( l + b )

Perimeter of Picture frame = 2 ( 24 + 20 )

= 48 + 40

= 88

Answer:Therefore, the equation of the line with a slope of 9/7 and containing the midpoint of the line segment with endpoints (2, -3) and (-6, 5) is:

y = (9/7)x + 25/7.

Step-by-step explanation:Step 1: Find the midpoint of the line segment.

The midpoint formula is given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Given the endpoints of the line segment as (2, -3) and (-6, 5), we can find the midpoint as follows:

Midpoint = ((2 + (-6)) / 2, (-3 + 5) / 2)

Midpoint = (-4 / 2, 2 / 2)

Midpoint = (-2, 1)

So, the midpoint of the line segment is (-2, 1).

Step 2: Write the equation of the line using the slope-intercept form.

The slope-intercept form of a line is given by:

y = mx + b

where m is the slope and b is the y-intercept.

Given the slope as 9/7, we have:

y = (9/7)x + b

Step 3: Substitute the coordinates of the midpoint to find the value of b.

Using the coordinates of the midpoint (-2, 1), we can substitute these values into the equation:

1 = (9/7)(-2) + b

1 = -18/7 + b

To find the value of b, we can solve this equation:

1 + 18/7 = b

25/7 = b

Step 4: Write the final equation of the line.

Using the value of b, the equation becomes:

y = (9/7)x + 25/7

Answer:

The correct choice is option a. 2520

Step-by-step explanation:

LCM of 40, 30, and 126 is as followed:

= 2 × 2 × 2 × 3 × 3 × 5 × 7

= 2520

Answer:

a)2520 is correct

Answer:

option c is the correct answer

first take y raised to the power 4 common then cancel its power by y raised to the power 3

you get your answer

0.0405 is the number that contains the digit 2 once, the digit 3 twice, the digit 4 thrice, and more 5s than threes, leading 0s are allowed.

based on data gathered from the sources

Suppose the information as shown by

How many eight-digit numbers have more 5s than 3s and contain the digits 2 exactly once, 3 exactly twice, and 4 precisely three times

Let there be more 5s than 3s and more 8-digit numbers with the digits 2 once, 3 twice, 4 three times, and 5s than 3.

2,3,3,4,4,4

after that:

= 8!/2!3!3!4!4!4!

= 8.7.6.5.4!/2×6×6×24×24×4!

= 35/864

Now, 0.405, followed by a digit 2 and 3 make up the eight-digit number.

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the correct answer is,

\(x = \frac{121}{25} \)

if you want me to solve without the parentheses then the answer would be,

\(x = \frac{1609}{100} \)

Answer:

What they said

Step-by-step explanation:

By the substitution property of equality, measure of ∠ABC ≅ measure of ∠GHI (m∠ABC=m∠GHI)

The substitution property of equality states that if x = y, then x can be substituted in for y in any equation, and y can be substituted for x in any equation

From the given information, we have that

∠ABC ≅ ∠DEF

and

∠GHI ≅ ∠DEF

By the substitution property, ∠ABC can be substituted for ∠DEF in the second equation

That is,

∠GHI ≅ ∠ABC

∴  ∠ABC ≅ ∠GHI

Hence, measure of ∠ABC ≅ measure of ∠GHI (m∠ABC=m∠GHI)

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Answer:

First one : <ABC ≅ <DEF //// Given

Second one : <GHI ≅ <DEF ///// Given

Third one : <DEF ≅ <ABC //// Symmetric property

Fourth one : <GHI ≅ <ABC //// Transitive property

Fifth one : m<GHI = m<ABC /// Definition of ≅ angles

Sixth one : m<ABC = m<GHI /// Symmetric property

Step-by-step explanation:

The Vertex is : (-6, -30)

The X-intercepts are : Approximately (-10.89, 0) and (-1.11, 0)

The Y-intercept is : (0, 6)

The Axis of symmetry is : x = -6

The functions Domain: is All real numbers

The Range is : All real numbers greater than or equal to -30.

To sketch the graph of the quadratic function \(f(x) = x^2 + 12x + 6,\) we can start by identifying the vertex, x-intercepts, y-intercept, axis of symmetry, domain, and range.

To find the vertex, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation in standard form\((ax^2 + bx + c).\)

In this case, a = 1, b = 12, and c = 6.

Applying the formula, we get x = -12/(2 \(\times\) 1) = -6.

To find the y-coordinate of the vertex, we substitute this x-value into the equation:\(f(-6) = (-6)^2 + 12(-6) + 6 = 36 - 72 + 6 = -30.\)

So, the vertex is (-6, -30).

To determine the x-intercepts, we set f(x) = 0 and solve for x. In this case, we need to solve the quadratic equation \(x^2 + 12x + 6 = 0.\)

Using factoring, completing the square, or the quadratic formula, we find that the solutions are not rational.

Let's approximate them using decimal values: x ≈ -10.89 and x ≈ -1.11. Therefore, the x-intercepts are approximately (-10.89, 0) and (-1.11, 0).

The y-intercept is obtained by substituting x = 0 into the equation: \(f(0) = 0^2 + 12(0) + 6 = 6.\)

Thus, the y-intercept is (0, 6).

The axis of symmetry is the vertical line that passes through the vertex. In this case, it is the line x = -6.

The domain of the function is all real numbers since there are no restrictions on the possible input values of x.

To determine the range, we can observe that the coefficient of the \(x^2\) term is positive (1), indicating that the parabola opens upward.

Therefore, the minimum point of the parabola occurs at the vertex, (-6, -30).

As a result, the range of the function is all real numbers greater than or equal to -30.

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Answer:

It could be two unique triangles (the 7 inch length could be either of the two nonincluded sides.)

Step-by-step explanation:

Answer:36.7

Step-by-step explanation:

Answer:

$3.20/gallon

Step-by-step explanation:

to fill up your tank at $3.20/gallon only costs $38.40

Answer:

Y =4x^4 + 4x^3 − 37x^2 + 41x −12

Step-by-step explanation:

Y = (2x - 1 ) (x + 4) (2x - 3) (x - 1)

Using commutative property we can re-arrange RHS,

Y= (2x - 1) (2x - 3) (x + 4) (x - 1)

Using the property

[(x+a) (x+b) = x^2 + (a+b)*x +ab],

Y =

[(2x)^2 + (-1 - 3)*2x + (-1 )*(-3)] [x^2 + (4 - 1)*x + 4*(-1)]

From here onwards I would recommend u to do the calculation by your own bc I might have made mistakes

in the steps but I got right but still just check yourself if u copy all the steps as it is

Y = (4x^2 -8x + 3) (x^2 + 3x -4)

Y = 4x^4 + 12x^3 - 16x^2 -8x^3 -24x^2 + 32x + 3x^2 + 9x - 12

Y = 4x^4 + 4x^3 -37x^2 + 41x - 12

Here I got the answer right so my calculations will also might be right

I checked my answer if it's right using an app called "MathPapa" and it's a great app to solve algebra questions like urs. The screenshot of the answer using this app is here on the top. This is the longest question I have solved for anyone, bye and have a nice day ahead!

Answer:

5 cans

Step-by-step explanation:

First multiply 15 by 3 to see how many ounces are needed in total: 15x3=45

Then divide 45 by 9 to see the amount of cans: 45/9=5

Answer:

Step-by-step explanation:

side AB is congruent to side AX

this means that the angle ∠A = 4x is the same angle as ∠Z

therefore ∠A = ∠Z = 4x

inside angle of a triangle = 180

∠A + ∠B + ∠Z = 180

4x + 7x + 4x = 180

15x = 180

x = 180/15

x = 12

now substitute x = 12 into angle B

∠B = 7x

∠B = 7 (12)

∠B = 84

Answer:

Step-by-step explanation:

Tienes que multiplicar 10 ×7

The final answer is (f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

To find the composite functions (f o g)(x) and (g o f)(x), we need to substitute one function into the other.

(f o g)(x):

To find (f o g)(x), we substitute g(x) into f(x):

(f o g)(x) = f(g(x))

Let's substitute g(x) = x^2 - 8 into f(x) = x^2 + 8:

(f o g)(x) = f(g(x)) = f(x^2 - 8)

Now we replace x in f(x^2 - 8) with x^2 - 8:

(f o g)(x) = (x^2 - 8)^2 + 8

Simplifying further:

(f o g)(x) = x^4 - 16x^2 + 64 + 8

(f o g)(x) = x^4 - 16x^2 + 72

Therefore, (f o g)(x) = x^4 - 16x^2 + 72.

(g o f)(x):

To find (g o f)(x), we substitute f(x) into g(x):

(g o f)(x) = g(f(x))

Let's substitute f(x) = x^2 + 8 into g(x) = x^2 - 8:

(g o f)(x) = g(f(x)) = g(x^2 + 8)

Now we replace x in g(x^2 + 8) with x^2 + 8:

(g o f)(x) = (x^2 + 8)^2 - 8

Simplifying further:

(g o f)(x) = x^4 + 16x^2 + 64 - 8

(g o f)(x) = x^4 + 16x^2 + 56

Therefore, (g o f)(x) = x^4 + 16x^2 + 56.

(f o g)(2):

To find (f o g)(2), we substitute x = 2 into the expression (f o g)(x) = x^4 - 16x^2 + 72:

(f o g)(2) = 2^4 - 16(2)^2 + 72

(f o g)(2) = 16 - 64 + 72

(f o g)(2) = 24

Therefore, (f o g)(2) = 24.

In summary:

(f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

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Answer:

y = 20x + 200

Step-by-step explanation:

The 200 is the constant.  It is only added once, but the monthly deposits are added at 20 every month.  

After 1 month:

y = 20x + 200

y = 20(1) + 200

y = 20 + 200

y =220       money deposited.

After 2 months:

y = 20x + 200

y = 20(2) + 200

y = 40 + 200

y =240 money deposited.

After 3 months:

y = 20x + 200

y = 20(3) + 200

y = 60 + 200

y = 260  money deposited

And so on, and so on, and so on...

Answer:

e3x

Step-by-step explanation:

(a) The area of a trapezium is given by the formula:

Area = (1/2) × sum of parallel sides × distance between them

Substituting the given values, we get:

10 = (1/2) × (AB + DC) × h

where h is the perpendicular distance between AB and DC.

We can express h in terms of AB and DC using the Pythagorean theorem, since AD is the height of the right triangle ACD:

AD² + h² = DC²

(x - 1)² + h² = (x + 3)²

x² - 2x + 1 + h² = x² + 6x + 9

h² = 8x + 8

Substituting this value of h² in the equation for the area, we get:

10 = (1/2) × (AB + DC) × (sqrt(8x + 8) / sqrt(1))

10 = (1/2) × (AB + DC) × sqrt(8x + 8)

Substituting the given values of AB and DC in terms of x, we get:

10 = (1/2) × ((3x + 2) + (x + 3)) × sqrt(8x + 8)

10 = (2x + 5) × sqrt(8x + 8)

(2x + 5)² × (8x + 8) = 100

(2x + 5)² × 2(x + 1) = 25

4x² + 4x + 25 = 25

4x² + x - 25 = 0

(b) We can solve the quadratic equation 4x² + x - 25 = 0 using the quadratic formula:

x = [-b ± sqrt(b² - 4ac)] / 2a

where a = 4, b = 1, and c = -25.

Substituting the values, we get:

x = [-1 ± sqrt(1² - 4(4)(-25))] / 2(4)

x = [-1 ± sqrt(401)] / 8

x = (-1 ± 20.025) / 8

x = -3.128 or x = 1.628

Since the length of a side cannot be negative, we reject the negative value of x and take x = 1.628.

Substituting this value of x in the expression for AB, we get:

AB = 3x + 2 = 3(1.628) + 2 = 7.884 ≈ 7.88 cm

Therefore, the length of AB is approximately 7.88 cm, correct to 2 significant figures.

Answer:

\( \frac{1}{12} \)

Step-by-step explanation:

\( \frac{2}{9} \div \frac{8}{3} \\ = \: \frac{1}{12}\)

So, if you divide 2/9 by 1/12, you'll get 8/3

Answered by GAUTHMATH

Answer: 22

Step-by-step explanation: 65 divided by 3 is 22

Answer:

21or22

Step-by-step explanation:

65/3

Answer: 36˚

Step-by-step explanation:

180 - 3x = 2x

180 = 5x

.: x = 36˚

Answer:

111

Step-by-step explanation:

The sum for a 7-sided interior polygon is 900

126+158+120+125+121+139=789

900-789=111

Answer:

x = 111°

Step-by-step explanation:

x + 120+158+126+125+121+139= 900°

x + 789 = 900

x = 900 - 789

x = 111

Answer:

Amount that Brian has after 2 years = £6932.53

Step-by-step explanation:

To find, the amount that Brian will have after 2 years:

Formula for amount where compound interest is applicable:

\(A = P \times (1+\dfrac{R}{100})^t\)

Where A is the amount after t years time

P is the principal.

R is the rate of interest.

In the question, we are given the following details:

Principal amount,P = £6300

Rate of interest,R = 4.9%

Time,t = 2 years

Putting the values in formula:

\(A = 6300 \times (1+\dfrac{4.9}{100})^2\\\Rightarrow 6300 \times (\dfrac{104.9}{100})^2\\\Rightarrow 6932.53\)

Hence, Amount that Brian has after 2 years = £6932.53

Answer:

THE ANSWER IS ABOVE

Step-by-step explanation:

hahahaha