Solve the triangle by finding the missing sides and angles. Round the sides to the nearest 10th and angle to the nearest degree 15 yd 13yd

Answer: 3x+6=9

3x=3

x=1

Step-by-step explanation:

Answer:

x = 1

Step-by-step explanation:

To solve this, we must first isolate the variable 'x':

3x + 6 = 9

      -6   -6

3x = 9 - 6

Combine like terms

3x = 3

Isolate 'x' fully

3x = 3

/3    /3

x = 1

Hope this helps :)

Answer:

\(\huge\boxed{x=3\dfrac{1}{5}\to x=3.2}\)

Step-by-step explanation:

\(\dfrac{8}{15}=\dfrac{x}{6}\quad|\text{cross multiply}\\\\15\cdot x=8\cdot6\\\\15x=48\qquad|\text{divide both sides by 15}\\\\\dfrac{15x}{15}=\dfrac{48}{15}\\\\x=\dfrac{48:3}{15:3}\\\\x=\dfrac{16}{5}\\\\x=3\dfrac{1}{5}\to x=3.2\)

Answer:

3 1/5

Step-by-step explanation:

8/15 = x/6

cross multiplication

8*6    15*x

48/15x

x = 3 1/5

The perimeter of the field is 380m

What is perimeter?

A perimeter is a closed path that encloses, surrounds, or delimits a one-dimensional length, a two-dimensional shape, or both. The circumference of a circle or an ellipse is its perimeter. There are numerous practical uses for calculating the perimeter.

Let, a rectangular field is 30m longer than wide.

The area of the field is 8800m².

Suppose the width of the rectangular field is x.

So, length of the rectangular field becomes x + 30.

As the area of the field is 8800m².

Since,

        Area of rectangle = length x width

                            8800 = (x + 30) x x

                            8800 = x^2 + 30x

         x^2 + 30x - 8800 = 0

x^2 + 110x - 80x - 8800 = 0

  x(x + 110) - 80(x + 110) = 0

            (x + 110) (x - 80) = 0

⇒ (x + 110) =0,  (x - 80) = 0

⇒ x = -110,  x = 80

Since, the length is not negative.

Hence, the width of the rectangle is 80m and the length of the rectangle is (x + 30) = (80 + 30) = 110m

Now to find the Perimeter of the rectangle.

Perimeter = sum of all sides

                 = 80 + 80 + 110 + 110

Perimeter = 380m

Therefore, the perimeter of the rectangle is 380m.

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Answer:

35 degrees.

Step-by-step explanation:

It's a reflective sideway triangle.

Answer:

x = 35° :)

Step-by-step explanation:

x is 35° because of the vertical angle

To find the exact length of the curve given by x = et − 9t, y = 12et/2, 0 ≤ t ≤ 3, we can use the arc length formula:
L = ∫(a to b) √[dx/dt]^2 + [dy/dt]^2 dt
Substituting the given values, we get:
L = ∫(0 to 3) √[e^t - 9]^2 + [6e^(t/2)]^2 dt
Simplifying the expression under the square root, we get:
L = ∫(0 to 3) √(e^(2t) - 18e^t + 81 + 36e^t) dt
L = ∫(0 to 3) √(e^(2t) + 18e^t + 81) dt
L = ∫(0 to 3) (e^t + 9) dt
L = [e^t + 9t] from 0 to 3
L = [e^3 + 9(3)] - [e^0 + 9(0)]
L = e^3 + 27 - 10.99
L ≈ 25.5
Therefore, the exact length of the curve is approximately 25.5 units.

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Hey there!

1) Radius (r) = 23.9846

Circumference (c) = 150.7in

Area = 1,807.243in

2) Radius (r) = 34.98226

Circumference (c) = 219.8

Area = 3,844.55m²

3) Radius (r) = 40.9824cm

Circumference (c) = 257.5cm

Area = 5,276.48cm²

4) Radius (r) = 36.9876ft

Circumference (c) = 232.4ft

Area = 4,297.96

5) Radius (r) = 56.9775m

Circumference (c) = 358m

Area = 10,198.97m²

6) Radius (r) = 39.9797in

Circumference (c) = 251.2in

Area = 5,021.45in²

Answer:

add two and  take the remaining    5/2

Step-by-step explanation:

Answer:

the question is probably wrong

Step-by-step explanation:

10 - -6 = 16

-6 - -6 = 0

16/0= undefined?

i) The dispersion relation for the given equation is ± (v / 6) * k.

ii) The group velocity for the given equation is ± v / 6.

iii) The phase velocity is ± v / 6.

To find the dispersion relation, as well as the group and phase velocities for the given equation, let's start by rewriting the equation in a standard form:

82y(x, t) - 8\(t^2\) + 84y(x,t) = -2 * 8\(x^4\)

Simplifying the equation further:

8(2y(x, t) - \(t^2\) + 4y(x,t)) = -16\(x^4\)

Dividing both sides by 8:

2y(x, t) - \(t^2\) + 4y(x,t) = -2\(x^4\)

Rearranging the terms:

6y(x, t) = \(t^2\) - 2\(x^4\)

Now, we can identify the coefficients of the equation:

Coefficient of y(x, t): 6

Coefficient of \(t^2\): 1

Coefficient of \(x^4\): -2

(i) Dispersion Relation:

The dispersion relation relates the angular frequency (ω) to the wave number (k). To determine the dispersion relation, we need to find ω as a function of k.

The equation given is in the form:

6y(x, t) = \(t^2\) - 2\(x^4\)

Comparing this with the general wave equation:

A * y(x, t) = B * \(t^2\) - C * \(x^4\)

We can see that A = 6, B = 1, and C = 2.

Using the relation between angular frequency and wave number for a linear wave equation:

\(w^2\) = \(v^2\) * \(k^2\)

where ω is the angular frequency, v is the phase velocity, and k is the wave number.

In our case, since there is no coefficient multiplying the y(x, t) term, we can set A = 1.

\(w^2\) = (\(v^2\) / \(A^2\)) * \(k^2\)

Substituting the values, we get:

\(w^2\) = (\(v^2\) / 36) * \(k^2\)

Therefore, the dispersion relation for the given equation is:

ω = ± (v / 6) * k

(ii) Group Velocity:

The group velocity (\(v_g\)) represents the velocity at which the overall shape or envelope of the wave propagates. It can be determined by differentiating the dispersion relation with respect to k:

\(v_g\) = dω / dk

Differentiating ω = ± (v / 6) * k with respect to k, we get:

\(v_g\) = ± v / 6

So, the group velocity for the given equation is:

\(v_g\) = ± v / 6

(iii) Phase Velocity:

The phase velocity (\(v_p\)) represents the velocity at which the individual wave crests or troughs propagate. It can be calculated by dividing the angular frequency by the wave number:

\(v_p\) = ω / k

For our equation, substituting the dispersion relation ω = ± (v / 6) * k, we have:

\(v_p\) = (± (v / 6) * k) / k

\(v_p\) = ± v / 6

Therefore, the phase velocity for the given equation is:

\(v_p\) = ± v / 6

To summarize:

(i) The dispersion relation is ω = ± (v / 6) * k.

(ii) The group velocity is \(v_g\) = ± v / 6.

(iii) The phase velocity is \(v_p\) = ± v / 6.

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Answer:

6:4

Step-by-step explanation:

Answer:

3:2

Step-by-step explanation:

For every 3 bananas, there are 2 cookies.

Answer:

it would also be 3/4x (in terms of y=mx+c)

Step-by-step explanation:

parallel lines have the same slope/gradient

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

8x-12=6x+2

8x-6x=2+12

x=7

Multiply 4 with 2x - 3

Take 6x to LHS and make it negative. And take -12 to RHS and make it positive. This process is called transposition.

Now subtract 6x from 8x, we get 2x. And on the RHS, it will be 14.

Now divide both sides with 2.

2 and 2 gets cancelled out in LHS.

Answer:

x = 7

Hope you could understand.

If you have any query, feel free to ask.

Answer:

A number is a multiple of 3 if the sum of the digit equal to a number divided by 3

so, 3+7+0+9=19

21, 24, 27 are numbers that is a multiple of 3

So, the number are

19+x=21

x=2

19+x=24

x=5

19+x=27

x=8

Answer:

1110

Step by step explanation:

370×9=3330

in the question it's said that 370 ×9 is a multiple of 3

i.e,3330 is a multiple of 3.

3 multiplied with x = 3330

x = 3330/3

=1110

Step-by-step explanation:

The 20° angle is equal to the angle next you friend.

since they are interior alternate angles

The height of the ballon is 600 feet

Let x be the missing distance we are looking for

so the missing distance is 1754 feet

Here I represented the situation to visualize the problem

Let h be L be the length of the ladder

so the ladder is 14 ft

If Ridgewood Savings Bank charges a $27 per check overdraft protection fee. The amount she will owe the bank after July 12 is: $1,071.42.

Total obligation can be defined as the amount a person owe another person or the debt amount a borrower  is expected to payback to a lender.

Balance $1,400

July 9 check ($1,380.15)

Balance $19.85

July 10 check ($765.67)

($670 + $95.67)

Balance -$745.82 (Overdraft)

Now let find the amount she owe

Balance -$745.82

July 11 check $130

Balance -$875.82

July 12 check $87.60

Ending balance -$963.42

Overdraft fee $108

($27 ×4)

Total obligation -$1,071.42

Therefore her total obligation is $1,071.42.

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Answer:

3 workbooks 5 dry earase markers

Step-by-step explanation:

seems to me like you need help offten

Answer:

9.987 × 10^-3

Step-by-step explanation:

Answer: 28°

Step-by-step explanation:

First set up an equation using the fact that a horizontal line has an angle of 180°

140+x+12=180

Solve: 152+x=180

Subtract 152 from both sides: x=28

x=28°

Step-by-step explanation:

Hope it will help you ❤❤

Answer:

(-5,8)

Step-by-step explanation:

The given equation y = -3x - 7 holds true for the ordered pair, so (-5, 8) is a solution. Thus, option third is correct.

To determine whether each ordered pair is a solution to the equation y = -3x - 7, we substitute the x and y values into the equation and check if it holds true.

For the ordered pair (8, -56):

y = -3x - 7

-56 = -3(8) - 7

-56 = -24 - 7

-56 = -31

The equation does not hold true for this ordered pair, so (8, -56) is not a solution.

For the ordered pair (-5, 8):

y = -3x - 7

8 = -3(-5) - 7

8 = 15 - 7

8 = 8

The equation holds true for this ordered pair, so (-5, 8) is a solution.

For the ordered pair (-9, -23):

y = -3x - 7

-23 = -3(-9) - 7

-23 = 27 - 7

-23 = 20

The equation does not hold true for this ordered pair, so (-9, -23) is not a solution.

For the ordered pair (4, 19):

y = -3x - 7

19 = -3(4) - 7

19 = -12 - 7

19 = -19

The equation does not hold true for this ordered pair, so (4, 19) is not a solution.

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The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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Daniella and her friends collected a total of 44 shells.

What is linear equation ?

Linear equation can be defined as equation in which highest degree is one.

Given ,

Daniella and her 10 friends are collecting shells on the beach to make crafts.

After they have collected the shells and put them in a pile, they split them evenly among the group. Each person gets 4 shells.

The correct equation for this problem is:

s = 11 x 4

where s is the total number of shells collected.

Simplifying this equation, we have:

s = 44

Therefore, they collected a total of 44 shells.

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Answer:

15 different sums.

Step-by-step explanation:

1+2

1+3

1+4

1+5

1+6

2+3

2+4

2+5

2+6

3+4

3+5

3+6

4+5

4+6

5+6

There is 15 different sums.

Answer:

In this section we will discuss the method of graphing an equation in two variables. In other words, we will sketch a picture of an equation in two variables.

Step-by-step explanation:

Answer:

4.8x345+338283

Step-by-step explanation:

The exact value of sinθ in simplest radical form is sinθ = 1.

The terminal side of an angle in standard position is a line passing through the point (x,y).

To find the exact value of sinθ, use the trigonometric identity sinθ = y/r, where r is the distance or length of the line segment from the origin

r = √(x² + y²)

Given the point (-20, 21), the value of sinθ is 21/√(20² + 21²).

Simplifying, 21/√(441), sinθ = 21/21 = 1.

Therefore, the exact value of sinθ in simplest radical form is sinθ = 1.

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Answer:

x = (-3+√15)/2 or, x = (-3-√15)/2

Step-by-step explanation:

2x²+6x-3=0

Standard quadratic formula,

ax²+bx+c = 0

where,

x =(-b±\(\sqrt{b^{2}-4ac }\))/2a       ...............................(i)

Here,

a = 2

b = 6

c = -3

Putting the values in equation(i), we get,

x = (-6±\(\sqrt{6^{2} -4.2.(-3)}\))/2.2

=(-6 ± √60)/4

=(-6 ± 2√15)/4

= (-3 ± √15)/2

Therefore, x = (-3+√15)/2 or x = (-3-√15)/2 :)

The solid line on the graph has a positive slope that will be 2y - 3x ≥ 7. Then the correct option is C.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)

The points that are on the line are given below.

(-9, -10), (-3, -1), and (3, 8)

The inequality of the line is given as,

(y - 8) ≥ [(8 + 1) / (3 + 3)] (x - 3)

y - 8 ≥ (3/2)(x - 3)

2y - 16 ≥ 3x - 9

2y - 3x ≥ 7

The solid line on the graph has a positive slope that will be 2y - 3x ≥ 7. Then the correct option is C.

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Answer: c

Step-by-step explanation:

Answer:

3z^2

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

The pair of functions that are not inverses of each other is (A).

To determine if two functions, g(x) and h(x), are inverses of each other, we need to check if the composition of the two functions, g(h(x)) and h(g(x)), both result in x.

A. g(x) = 2 + 9 = 11, h(x) = 1/2x - 9

g(h(x)) = g(1/2x - 9) = 2 + 9 = 11

h(g(x)) = h(11) = 1/2(11) - 9 = -3/2

Since g(h(x)) ≠ x and h(g(x)) ≠ x, the functions g(x) and h(x) are not inverses of each other.

B. g(x) = x - 1, h(x) = x + 1

g(h(x)) = g(x + 1) = (x + 1) - 1 = x

h(g(x)) = h(x - 1) = (x - 1) + 1 = x

Since g(h(x)) = x and h(g(x)) = x, the functions g(x) and h(x) are inverses of each other.

C. g(x) = 3x - 6, h(x) = 1/3x + 2

g(h(x)) = g(1/3x + 2) = 3(1/3x + 2) - 6 = x

h(g(x)) = h(3x - 6) = 1/3(3x - 6) + 2 = x

Since g(h(x)) = x and h(g(x)) = x, the functions g(x) and h(x) are inverses of each other.

D. g(x) = 3x + 4, h(x) = x - 4/3

g(h(x)) = g(x - 4/3) = 3(x - 4/3) + 4 = 3x - 4

h(g(x)) = h(3x + 4) = (3x + 4) - 4/3 = 3x + 8/3

Since g(h(x)) ≠ x and h(g(x)) ≠ x, the functions g(x) and h(x) are not inverses of each other.

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