A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.

A polygon with a horizontal top side labeled 45 yards. The left vertical side is 20 yards. There is a dashed vertical line segment drawn from the right vertex of the top to the bottom right vertex. There is a dashed horizontal line from the bottom left vertex to the dashed vertical, leaving the length from that intersection to the bottom right vertex as 10 yards. There is another dashed horizontal line that comes from the vertex on the right that intersects the vertical dashed line, and it is labeled 12 yards.

What is the area of the playground?

900 square yards
855 square yards
1,710 square yards
1,305 square yards

Answer:

j + 3 ≤ 12

Hope this helps :)

Solution, Explanation, & Check part below

Step-by-step explanation:

1. Isolate variable by doing the inverse operation which is subtracting 3 on both sides of the equation.

j + 3 ≤ 12

- 3 - 3

j ≤ 9

j can be any number that is less than 9 or equal to 9.

Check:

9 + 3 ≤ 12

12 ≤ 12

12 is equal to 12 ✓

Answer:

------------------------

After 3 half-lives the remaining amount becomes:

Convert 1/8 to percent:

Answer:

A. $450 + 0.05x ≥ 600

B. she needs at least $3,000 in sales.

Step-by-step explanation:

You know that she gets paid 450 a week, she gets plus a 5% commission on her sales as well.

We know she hopes to earn $600 a week but we dont know the amount of sales.

X represents the amount of sales (since we dont know)

divide the 5% by 100 = 0.05x

She wants to AT LEAST earn $600 which is why ≥ is used as it means greater than or equal to and we do not know.

Answer:

A. $450 + 0.05x ≥ 600

B. she needs $3,000 in sales.

Step-by-step explanation:

Answer:

5,056.5 is the answer of 20226 /4

The formula to find  the total number of shaded triangles in the first 10 sierpinski triangles is Sn = (1 - 310)/(-2).

The Sierpiski triangle, also known as the Sierpiski gasket or Sierpiski sieve, is a fractal appealing fixed set with the general shape of an equilateral triangle that is subdivided recursively into smaller equilateral triangles. The name Sierpiski is derived from the Polish language. This is one of the simplest instances of self-similar sets, meaning it is a mathematically generated pattern that can be replicated at any magnification or reduction. It was initially built as a curve.

The Sierpinski triangle can be divided into three self-similar sections (n=3), each of which can then be enlarged by a factor of two (m=2) to produce the full triangle. N = md, where n is the number of self-similar pieces and m is the magnification factor, is the formula for dimension d.

The formula to find  the total number of shaded triangles in the first 10 sierpinski triangles is Sn = (1 - 310)/(-2).

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The work done by the electrostatic force on a particle of charge q is calculated by the equation W = qE·(b-a), where E is the electric field and a and b are the starting and ending points of the particle's movement.

The work done by the electrostatic force on a particle of charge q can be calculated using the equation W = qE·(b-a), where q is the charge of the particle, E is the electric field, and a and b are the starting and ending points of the particle's movement. This equation states that the work done by the electrostatic force is equal to the charge of the particle multiplied by the electric field multiplied by the difference between the starting and ending points. This equation is useful when calculating the amount of work done by an electrostatic force on a particle, and is a core concept of electrostatics. In order for the equation to be applicable, it is important that the electric field remains constant over the distance between a and b. If the electric field changes, then the work done is calculated by integrating the equation over the entire path of the particle's movement.

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Answer: y - $50 = $5*(x - 3)

Step-by-step explanation:

We know that each ticket is sold at $5.00

The band initially had an amount of money M.

We know that after selling 3 tickets, the band had $50

We can write this as:

M + 3*$5.00 = $50

M + $15 = $50

M = $50 - $15 = $35

We want to write the equation for the account in the point-slope form.

We know that the slope will be equal to the cost of a single ticket, and we already have the point:

x = 3

y = $50

Then we can write:

y - $50 = $5*(x - 3)

This is the equation we wanted to find.

Answer:

ok what is thepromblem

Step-by-step explanation:

Answer:

whats up? whats tha questionn :)

Step-by-step explanation:

The scalar projection is 42/13, and the vector projection is 42/169⟨-5,12⟩.

The scalar projection of b onto a can be calculated using the formula \(\frac{a.b}{|a|}\), and the vector projection of b onto a can be calculated using the formula \(\frac{a.b}{|a|^{2} } .a\). The formula for finding the magnitude of a is |a| = √c²+d² if a = ⟨c,d⟩.

a = ⟨−5, 12⟩, b = ⟨4, 6⟩

a⋅b = ⟨−5, 12⟩⟨4, 6⟩

= -20 + 72

= 42

|a| = √[(-5)² + (12)²]

= √25 + 144

= √169

= 13

The scalar projection is

\(\frac{a.b}{|a|}\) = [⟨−5, 12⟩⟨4, 6⟩]/√[(-5)² + (12)²]

= [-20 + 72]/√25 + 144

= 42/√169

= 42/13

The vector projection is

\(\frac{a.b}{|a|^{2} } .a\) = [42/(13)²] ⟨−5, 12⟩

= 42/169⟨−5, 12⟩

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The height of the flagpole is 12.9 feet to the nearest tenth.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

The boy is 5' 3" tall and his shadow is 4 feet.

The shadow of the flagpole is 17 feet.

The boy is 5.25 feet tall.

Let the height of the flagpole is h feet.

So,

17/h = 5.25/4

h = 68/5.25

h = 12.95

h = 12.9 to one decimal place.

Therefore, h = 12.9 to one decimal place.

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Answer:

im not sure but i think the answer is 1,983.31

Step-by-step explanation:

The gun will need to turn at a rate of approximately 0.32 radians per second to accurately track the aircraft.

To determine the rate at which the gun needs to turn to track the aircraft, we can use the concept of angular velocity. Angular velocity is defined as the rate of change of the angle with respect to time.

In this scenario, the gun needs to track the aircraft, which is moving in a straight-line path directly overhead. The gun needs to match the angular position of the aircraft to ensure accurate tracking.

The angle between the gun and the vertical axis can be calculated using trigonometry. We can use the fact that the elevation of the aircraft from the ground remains constant at 160 ft.

The tangent of the angle between the gun and the vertical axis is given by the ratio of the vertical displacement (160 ft) to the horizontal displacement (the distance covered by the aircraft per unit time, which is 500 ft/s).

Tangent of the angle = vertical displacement / horizontal displacement

Tangent of the angle = 160 ft / 500 ft/s

Using inverse tangent (arctan) function, we can find the angle in radians:

Angle = arctan(160/500) ≈ 0.3198 radians

Since the gun needs to track the aircraft as it moves, it needs to turn at the same angular velocity as the aircraft. Therefore, the gun needs to turn at a rate of approximately 0.32 radians per second to accurately track the aircraft.

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Answer: Length = 15 meters

Width = 2 meters

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

Area of a rectangle = l × w

where l = length

w = width

Therefore,

2l + 2w = 34 ...... i

l × w = 30 ........ ii

From equation i

2l + 2w = 34

Divide through by 2.

l + w = 17 ...... iii

Then, l = 17 - w ........ iv

Put equation iv into ii

l × w = 30

(17 - w) × w = 30

17w - w² = 30

w² - 17w + 30 = 0

w² - 15w - 2w + 30 = 0

w(w - 15) - 2(w - 15) = 0

(w - 2) = 0

w = 0 + 2 = 2

w - 15 = 0

w = 0 + 15 = 15

Length = 15 meters

Width = 2 meters

The value of m<2 = 107

Given:

m<SOX = 160

m<1 = x+14

m<2 = 3x - 10

x + 14 + 3x - 10 = 160

4x + 14 - 10 = 160

4x + 4 = 160

4x = 160 - 4

4x = 156

divide by 4 on both sides

4x/4 = 156/4

x = 39

m<2  = 3*39 - 10

= 117 - 10

= 107

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A buffer solution is a aqueous solution

The pH of a solution can be calculated using the expression:

pH = -log[H+]

where [H+] is the concentration of hydrogen ions in the solution.

To find the concentration of hydrogen ions in the given solution, we need to first calculate the concentration of acetate ions ([ac-]), since acetic acid (HAc) and sodium acetate (NaAc) form a buffer solution.

The dissociation of acetic acid can be represented by the equation:

HAc ⇌ H+ + Ac-

The equilibrium constant expression for this reaction is:

Ka = [H+][Ac-] / [HAc]

We know the concentration of acetic acid (HAc) is 4.5 x 10^-3 M. We also know that, for a buffer solution, the concentration of the acid and the conjugate base (Ac-) are related by the equation:

Ka = [H+][Ac-] / [HAc]

= [H+][Ac-] / (4.5 x 10^-3)

Solving for [Ac-], we get:

[Ac-] = Ka x [HAc] / [H+]

= (1.8 x 10^-5) x (4.5 x 10^-3) / [H+]

= 8.1 x 10^-8 / [H+]

Now we can use the fact that the dissociation of sodium acetate (NaAc) is 100% to find the concentration of hydroxide ions ([OH-]) in the solution:

NaAc → Na+ + Ac-

Since NaAc dissociates 100%, [Ac-] = [Na+] = 4.5 x 10^-3 M.

Now we can use the fact that the solution is a buffer solution to calculate the concentration of hydrogen ions ([H+]). For a buffer solution, the Henderson-Hasselbalch equation can be used:

pH = pKa + log([Ac-] / [HAc])

where pKa is the dissociation constant of the acid.

The pKa of acetic acid is 4.76, so:

pH = 4.76 + log([Ac-] / [HAc])

= 4.76 + log(4.5 x 10^-3 / (8.1 x 10^-8 / [H+]))

= 4.76 + log(5.56 x 10^4 [H+])

= 4.76 + 4.74 + log[H+]

= 9.50 + log[H+]

Finally, we can solve for [H+]:

[H+] = 10^(-pH)

= 10^(-9.50)

= 3.16 x 10^-10 M

Therefore, the pH of the solution is:

pH = -log[H+]

= -log(3.16 x 10^-10)

= 9.50

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Answer: x=8

Step-by-step explanation:

10+5x=50

5x=50-10

5x=40

40/5

simplify then it’s 8.

Answer:

4hours + 1hour = $2.50

Step-by-step explanation:

four hours free= 0 charge

1 hour = $2.50

therefore 4 + 1 = $2.50

Answer:

69740

Step-by-step explanation:

To determine the total value

There is a 350 per month insurance plan and a 45 per month insurance plan for a total 395 per month

There are 12 months

395 * 12 =4740

Add this to the yearly compensation

65000+4740= 69740

Answer:

Step-by-step explanation:

[(350 + 45) * 12] + 65000 =

(395 * 12) + 65000 =

4740 + 65000 =

69740

The impulse response function is obtained as h(t) = 2f_m * Sinc[2f_m(t - t_o)]. The output signal y(t) is obtained by convolving the input signal x(t) = S(t - 4t_o) with h(t).

4a. The magnitude response function is plotted based on the given complex-valued spectrum, indicating a value of 1 for frequencies within a cutoff frequency f_m and 0 for frequencies beyond it. The phase response function is linear and equal to -π/2 for frequencies within f_m and 0 for frequencies beyond.

4b. The impulse response function (IRF) h(t) is derived as 2f_m * Sinc[2f_m(t - t_o)], where f_m is the cutoff frequency and t_o is the time delay. The output signal y(t) is obtained by convolving the input signal x(t) = S(t - 4t_o) with h(t) using the convolution integral.

A sketch of the resulting output signal y(t) would depend on specific values of f_m and t_o, and the considered time interval. It represents the response of the filter to the input signal x(t), considering the characteristics of the IRF h(t) and the convolution operation.

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(a) Find the dual of the LP.Primal problem isminimize \($b_1y_1+C_1x_1+...+C_nx_n$\) subject to \($a_{11}x_1+a_{12}x_2+...+a_{1n}x_n \leq\) \(b_1$...$a_{m1}x_1+a_{m2}x_2+...+a_{mn}x_n \leq b_m$ and $x_1, x_2,\)..., x_n\(\geq 0$\)

Let us find the dual of the above primal problem.

Dual problem ismaximize \($b_1y_1+...+b_my_m$\)subject to \($a_{11}y_1+a_{21}y_2+...+a_{m1}y_m \leq\)\(C_1$...$a_{1n}y_1+a_{2n}y_2+...+a_{mn}y_m \leq C_n$\)

and\($y_1, y_2, ..., y_m \geq 0$\)

(b) Find the standard form of the LP and dual.Standard form of the primal problem isminimize \($b_1y_1+C_1x_1+...+C_nx_n$\)subject to \($a_{11}x_1+a_{12}x_2+...+a_{1n}x_n +s_1 = b_1$...$a_{m1}x_1+a_{m2}x_2+...+a_{mn}x_n +s_m = b_m$\) and\($x_1, x_2, ..., x_n, s_1, s_2, ..., s_m \geq 0$\)

Standard form of the dual problem ismaximize \($b_1y_1+...+b_my_m$\)subject to \($a_{11}y_1+a_{21}y_2+...+a_{m1}y_m \leq 0$...$a_{1n}y\)

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10 is the number that belongs to the green box in the triangle.

Let us find the third interior angle in the triangle

By angle sum property the sum of three angles is 180 degrees

78+56+x=180

134 + x =180

Subtract 134 from both sides

x=180-134

x=46

So sin 56 /12 = sin 46/x

0.829/12=0.7193/x

0.069=0.7193/x

x=0.7193/0.069

The number in green box x=10.42

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Answer:

P=a+b+c

Step-by-step explanation:

Answer:

4.295cm

Step-by-step explanation:

Here,

Circumference = 27cm

We know,

C=2πr

or, 27 = 2×22×r

7

or, 44×r = 27

7

27

or, r = 44

7

or, r = 27×7

44

Therefore, r = 4.295cm

18) If two parallel lines are cut by a transversal, the alternate interior angles are congruent.

19) Given

20) A midpoint splits a segment into two congruent parts. (I assume it's supposed to say \(\overline{VX} \cong \overline{XY}\))

21) Vertical angles are congruent.

22) ASA

23) CPCTC

The primary characteristic of a probability sample is that each element or unit in the population has a known and nonzero chance of being selected for inclusion in the sample.

In other words, every member of the population has a measurable probability of being chosen as part of the sample, and the selection is based on a random process. This characteristic ensures that the sample is representative of the population and allows for statistical inference and generalization of the findings from the sample to the larger population.

what is the mean of non zero?

The term "non-zero" refers to values that are not equal to zero. To find the mean of non-zero values, you need a set of data that contains both zero and non-zero values. From this set of data, you would exclude the zero values and calculate the mean using only the non-zero values.

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Answer:

3x - y = 22

Step-by-step explanation:

The abcisssa is known as the x coordinate while the ordinate is the y coordinate

abcissa = x

ordinate = y

“three times the abscissa = 3x

“three times the abscissa decreased by ordinate is expressed as;

3x - y

Is the result is 22, hence;

3x - y = 22

this gives the required expression