Problem
Solve for x in the image below.
18
Solution
We can start with the pythagorean theorem:
(leg 1)² + (leg 2)² = (hypotenuse)²

The function that gives the value of tn for the geometric series is presented as follows;

[tex]t_n = 2 \times 3^{(n - 1)} [/tex]

The given geometric series is presented as follows;

2 + 6 + 18 + 54 +...

From the above series, we have;

The nth term of the geometric series is therefore;

[tex]t_n = a \cdot r^{(n - 1)} [/tex]

Which gives;

[tex]t_n = 2 \times 3^{(n - 1)} [/tex]

Where, tn is the nth term

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SOLUTION :

c² = 5² + 5²

c² = 25 + 25

c² = 50

c = √50 ft

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Answer:

Step-by-step explanation:

All pyramids have a volume as one-third of a prism with the same base area and the same height.

This will make the formula for the volume [tex]\frac{1}{3}(base*height)[/tex]. We already know the height of the pyramid is 10, but the area of the base for this rectangle would be its length and its width. Let's calculate this:

[tex]7*2.3=16.1\hspace{0.1cm}in^2[/tex]

Let's put these values back into the formula:

[tex]V=\frac{1}{3}(16.1*10)\\ V=\frac{1}{3}(161)\\ V= 53.7\hspace{0.1cm}in^3[/tex]

Answer:

3. 6 5. 3

Step-by-step explanation:

PEMDAS

3. 0.5 x (24) / 3 + 2

12/3 +2

4 + 2

6

5. (4 + 6/3) x 0.5

(4 + 2) x 0.5

6 x 0.5

3

Answer: number 3. is 6 and number 5. is 3

hope it helped

Answer:

B) 7/9

Step-by-step explanation:

          LCM of 3 and 9 is 9.

          [tex]\sf \dfrac{1}{3}=\dfrac{1*3}{3*3}\\\\[/tex]

              [tex]\sf =\dfrac{3}{9}[/tex]

      [tex]\sf \dfrac{4}{9}+\dfrac{1}{3}=\dfrac{4}{9}+\dfrac{3}{9}\\\\[/tex]

                 [tex]\sf =\dfrac{7}{9}[/tex]

The volume of the region in first octant is 9.

Given that the region in the first octant bounded by the cylinder r=3 and the plane z=y.

The graph is shown below.

we are given that first octant is bound by r=3  and z=y

We will use the conversion formula, i.e.

x²+y²=r² where x=rcos∅ and y=rsin∅

Firstly, we will find bound octant

0≤∅≤π/2

0≤r≤3

0≤z≤r sin∅

Now, we can set up integral

[tex]V=\int_{0}^{\frac{\pi}{2}}\int_{0}^{3}\int_{0}^{rsin(\theta)}rdzdrd\theta[/tex]

Further, we can solve it.

Firstly, we solve integral for z then we solve for r and after that we will solve for ∅, we get

[tex]\begin{aligned}V&=\int_{0}^{\frac{\pi}{2}}\int_{0}^{3}r^2 \sin (\theta)dr d\theta\\&=\int_{0}^{\frac{\pi}{2}}\frac{1}{3}r^3\sin \theta d\theta\left|_{0}^{3}\\ &=\int_{0}^{\frac{\pi}{2}}\left(\frac{1}{3}\sin\theta d\theta(27-0)\right)\\ &=\int_{0}^{\frac{\pi}{2}}9\sin \theta d\theta\\ &=0-(-9)\\ &=9\end[/tex]

Hence, the volume of the region in the first octant is bounded by the cylinder r=3 and the plane z=y is 9.

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The ordered pairs (5 , -2) , (3 , 1) , (4 , 2) are in the set of the solution (Option C)

An ordered pair is a composite of the x coordinate (abscissa) and the y coordinate (ordinate), with two values expressed between parenthesis in a predetermined order.

It aids visual comprehension by locating a point on the Cartesian plane.

The first line has negative slope and passing through points (0 , 0) and (4 , -2)

That is y > (-1/2)x

The second line has positive slope and passing through points (-2 , 0) and (2 , 2)

That is: y < (1/2)x + 1.

- Refer to the accompanying diagram to discover the common component of the solutions.

- The inequity is shown by the red shading.

- The inequity is shown by the blue shading.

- The two-colored shaded area reflects the common solutions to the two inequalities.

- Let's discover the ordered pairs in the system of linear inequalities' solution set.

- Points (-4, 2), (-3, 1), (4, -3) define the common shaded area.

- Points (5, -2), (3, 1), (3, -1) (4 , 2)

As a result, Point (5, -2) is in the darkened region.

As a result, Point (3, 1) is in the darkened area.

As a result, Point (4, 2) is in the darkened area.

As a result, the ordered pairings (5, -2), (3, 1), (4, 2) are in the solution set.

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The woman's shadow is moving away from the pole at the speed of 4 feet/sec.

The height of a pole-mounted street light = 18 ft

The height of a lady = 6 ft

The woman is moving quickly and directly away from the pole. Her speed = 4ft/sec.

The woman's distance from the pole at the precise moment question want to know the speed of the woman's shadow's leading edge = 45ft

A woman standing 6 feet tall moves away from the pole in a straight route at a pace of 4 feet per second. If we assume that t is the passing time in seconds and that x is the distance in feet between the pole and the lady, we are informed that dx/dt=4 ft/sec.

Therefore, it is concluded that the final answer is 4 ft/sec.

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Answer:

(3, - 6 )

Step-by-step explanation:

x - 2y = 15 ( add 2y to both sides )

x = 2y + 15 → (1)

2x + 4y = - 18 → (2)

substitute x = 2y + 15 into (2)

2(2y + 15) + 4y = - 18 ← distribute parenthesis and simplify left side

4y + 30 + 4y = - 18

8y + 30 = - 18 ( subtract 30 from both sides )

8y = - 48 ( divide both sides by 8 )

y = - 6

substitute y = - 6 into (1)

x = 2(- 6) + 15 = - 12 + 15 = 3

solution is (3, - 6 )

Answer:

x is 3 y is -6 I really hope this helps

In Wagnerian music drama, a basic recurring theme representing a person, object, event, or emotion is known as Leitmotif.

What is serious opera called?

What is Wagnerian leitmotif?

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Answer:

A = -8

You're welcome! :)

Answer: a = -8

Step-by-step explanation:

Combine multiplied terms into a single fraction

then find a Find common denominator for the fraction

then Combine fractions with common denominator,

Multiply the numbers, Multiply all terms by the same value to eliminate fraction denominators, Cancel multiplied terms that are in the denominator,

Multiply the numbers making your equation like this -5a+10=50

subtract 10 by both sides and then you will need to simplify making it

-5a + 40 then you divide them both by the same factor which is -5 then you simplify again making the answer to your question -8  

Answer:

Gavin has 19 nickels & 114 quarters

Step-by-step explanation:

N : D : Q

1 : 3 : 6 = 57

x : 57 : y

57 / 3 = 19

1 x 19 : 3 x 19 : 6 x 19

19 : 57 : 114

Answer:

Below in bold.

Step-by-step explanation:

f(x) = 2x^2 - 12x + 24

Convert to vertex form:

f(x) = 2(x^2 - 6x) + 24

     = 2[(x - 3)^2 - 9] + 24

     = 2(x - 3)^2 - 18 + 24

     = 2(x - 3)^2 + 6

So the vertex is at (3, 6) and the axis of symmetry is x = 3.

Answer: Graph provided below.

Step-by-step explanation:

Draw the graph of y = -2x and then shade the region below it because y is less than and equal to -2x. To draw the graph of y = -2x, plug in x values into the equation and plot the corresponding coordinates. See this video on how to graph linear equations:

https://www.khanacademy.org/math/in-in-grade-9-ncert/xfd53e0255cd302f8:linear-equations-in-two-variables/xfd53e0255cd302f8:graph-of-a-linear-equation-in-two-variables/v/graphs-of-linear-equations

The five rational numbers are 1/1729, 1/2, 3/2, 2/1, 1729/1 and the numbers should be of form p/q where p or q should be a taxicab number.

According to the question,

To represent 5 rational numbers on line, the numbers should be of form p/q where p or q should be a taxicab number.

A taxicab number is a smallest integer can be expressed as a sum of two positive integer cube.

The most famous taxicab number is 1729. Thus,

1729 = 1³ + 12³

1729 = 9³+ 10³

Now, 2 = 1³ + 1³ so, 2 is the first taxicab number. Therefore, five rational numbers are  1/1729, 1/2, 3/2, 2/1, 1729/1.

In 1/1729 -> 1729 is taxicab number

In 1/2 -> 2 is taxicab number

In 3/2 -> 2 is taxicab number

In 1/1729 -> 2 is taxicab number

In 1729/1  -> 1729 is taxicab number

Hence, five rational numbers are 1/1729, 1/2, 3/2, 2/1, 1729/1 and the numbers should be of form p/q where p or q should be a taxicab number.

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The measure of the seventh interior angle of the heptagon is 124°. (Correct choice: C)

Heptagons are polygons with seven sides, seven vertices, seven interior angles and seven central angles. Herein we know the value of the sum of six interior angles and we need to know the measure of the seventh interior angle. We can determine the measure of the seven interior angles by using the following expression:

θ = (n - 2) · 180°, where n is the number of sides of the polygon.     (1)

If we know that n = 7, then sum of the internal angles in the heptagon is:

θ = (7 - 2) · 180°

θ = 900°

And the measure of the final interior angle is found by subtraction:

θ₇ = 900° - 776°

θ₇ = 124°

The measure of the seventh interior angle of the heptagon is 124°. (Correct choice: C)

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The next step Javier needs to take in order to evaluate the expression is to simplify it to it's lowest term. Details below

From the question given, we were told that Javier submitted 2 for a

Thus, the new expression becomes

2 × 2³ - 1

Recall

Aⁿ × Aᵐ = Aⁿ⁺ᵐ

Thus,

2 × 2³ = 2¹⁺³ = 2⁴

Therefore,

2 × 2³ - 1 = 2⁴ - 1

But

2⁴ = 16

Thus,

2⁴ - 1 = 16 - 1

2⁴ - 1 = 15

Therefore,

2 × 2³ - 1 = 15

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The probability P(ANB), that is, P(A ∩ B), given that A and B are independent events and P(A) = 0.25 and P(B) = 0.333 is 0.08325. Hence, option C is the right choice.

For any two events A and B, the probability of event A and B, that is, P(A ∩ B) is given as:-

In the question, we asked the probability P(ANB), that is, P(A ∩ B), given that A and B are independent events and P(A) = 0.25 and P(B) = 0.333.

We know that when the events are independent, P(A ∩ B) = P(A).P(B).

Thus, P(A ∩ B) = (0.25)*(0.333),

or, P(A ∩ B) = 0.08325.

Thus, the probability P(ANB), that is, P(A ∩ B), given that A and B are independent events and P(A) = 0.25 and P(B) = 0.333 is 0.08325. Hence, option C is the right choice.

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The average force exerted on the ball during the serve is 57 N the resistive force is -1125 N.

a. Average force

Using  this formula

Force (F) = Mass ×Acceleration

Where:

Mass (m) = 57 g = 57 / 1000= 0.057 Kg

Acceleration (a) = u / t = 50 / 0.05 = 1000 m/s²

Let plug in the formula

Force (F) = 0.057 × 1000

Force (F) = 57 N

b. Resistive force

F = m(v – u) / t

Where:

Force (F) = ?

Mass (m) = 3000 Kg

Initial velocity (u) = 72 Km/h = 72 / 3.6 = 20 m/s

Final velocity (v) = 18 Km/h = 18 / 3.6 = 5 m/s

Time (t) = 40s

Let plug in the formula

Force = 3000(5 – 20) / 40

Force = 3000(-15) / 40

Force=-45,000/40

Force = -1125 N

Therefore the average force exerted on the ball during the serve is 57 N the resistive force is -1125 N.

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Answer:

Rotation, Reflection, Dilation.

Step-by-step explanation:

Question 11

1) [tex]\overline{BA} \cong \overline{FA}[/tex], [tex]\angle 1 \cong \angle 2[/tex] (given)

2) [tex]\angle A \cong \angle A[/tex] (reflexive property)

3) [tex]\triangle AEB \cong \triangle ACF[/tex] (ASA)

4) [tex]\overline{AC} \cong \overline{AE}[/tex] (CPCTC)

Question 12

1) Isosceles [tex]\triangle ACD[/tex] with [tex]\overline{AC} \cong \overline{AD}[/tex], [tex]\overline{BC} \cong \overline{ED}[/tex] (given)

2) [tex]\angle ACD \cong \angle ADC[/tex] (angles opposite congruent sides in a triangle are congruent)

3) [tex]\angle ACB[/tex] and [tex]\angle ACD[/tex] are supplementary. [tex]\angle ADC[/tex] and [tex]\angle ADE[/tex] are supplementary (angles that form a linear pair are supplementary)

4) [tex]\angle ACB \cong \angle ADE[/tex] (supplements of congruent angles are congruent)

5) [tex]\triangle ABC \cong \triangle AED[/tex] (SAS)

6) [tex]\overline{AB} \cong \overline{AE}[/tex] (CPCTC)

7) [tex]\triangle ABE[/tex] is an isosceles triangle (a triangle with two congruent sides is isosceles)

Note: I changed the names of the segments in Question 11 because of the word filter.

the operation:

[tex]2*10^1 - 4*10^0 = 20 - 4 = 16[/tex]

Gives a square number.

A perfect square is the product of a number and itself.

As you can see in the example, 16 is a square number. Then let's try to get 16.

To get 16 we can use the difference:

20 - 4

So the first therm needs to be equal to 20, and the second equal to 4.

To write 20 in scientific notation we have:

[tex]2*10^1[/tex]

To write 4 in in scientific notation:

[tex]4*10^0[/tex]

Then the operation:

[tex]2*10^1 - 4*10^0 = 20 - 4 = 16[/tex]

Gives a square number.

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The possible outcomes are WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL

The given parameters are:

Coin = Head (H) and Tail (T)

Marble = W, B, B, B, R, R

See attachment for the tree diagram

From the tree diagram, we have the following possible outcomes

WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL

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The value of 'k' in the quadratic Equation    [tex]4x^{2}+kx+4=0[/tex] having one rational solution is k is 8.

Here, the given equation is  [tex]4x^{2}+kx+4=0[/tex]

By comparing the given equation with the standard form of the quadratic equation we get,

a = 4

b = k

c = 4

The given quadratic is having one rational solution, which means [tex]b^{2} -4ac=0[/tex]

Therefore,

[tex]k^{2} -4 \times 4\times4=0\\k^{2} -64=0\\k^{2} =64\\k=\sqrt{64} \\k=8[/tex]

Therefore, the value of k is 8.

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The angle subtended at the centre of the circle by a 2.9 centimeter arc is  equal to 15° 38.46'/15° 38' 27.6''.

In this problem we have to determine the measure of a central angle of a circular section in DMS (Degrees - Minutes - Seconds) system, in which a degree is equal to 60 minutes and a minute to 60 seconds. First, we must calculate the radius of the circle by the area formula:

r = √ (A / π)     (1)

r = √ (354 / π)

r ≈ 10.615 cm

Then, the measure of the central angle in radians is found by the equation of circular arc:

θ = s/r

θ = 2.9 cm / 10.615 cm

θ = 0.273 radians

Finally, we convert the angle into DMS system:

θ = 0.273 rad × 180°/π

θ = 15.641°

Degrees: 15°

Minutes and seconds: 0.641° (38.46')

Minutes: 38'

Seconds: (0.46' = 27.6'')

The angle subtended at the centre of the circle by a 2.9 centimeter arc is  equal to 15° 38.46'/15° 38' 27.6''.

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The value of n in 1/5n+3/5n=7/9 is 35/36

The equation is given as:

1/5n+3/5n=7/9

Multiply through by 5

n + 3n = 35/9

Evaluate the sum

4n = 35/9

Divide both sides by 4

n = 35/36

Hence, the value of n in 1/5n+3/5n=7/9 is 35/36

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Answer: Y-intercept: (0,5) X-intercept: (3,0)

Step-by-step explanation: Set x and y equal to 0.

The missing letter is p. The correct option is B. p

From the question, we are to determine the missing letter in the given pattern

The given pattern is

t, s, r, q, _, o, n, m,...

Consider the English alphabet

a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z.

If we study the pattern, we will realize that the alphabets are in the reverse order.

Hence, the missing letter is p. The correct option is B. p

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