This scale drawing shows a reduction in a figure.
What is the value of x?
Enter your answer as a decimal in the box.
X=

a) find that x = 140/2 = 70.

b) side length \(x\) the maximum area that the playground can have is x = 70

c)  The maximum area that the playground can have is 980 square meters

a. The playground is a rectangle, and the perimeter of a rectangle is given by 2(l + w) = 2x. The given information is that the perimeter is 280 meters, so we can set up the equation 2x = 280. Solving for x, we find that x = 140/2 = 70.

Now that we know the perimeter, we can find the area of the playground by using the formula A = lw. Since the perimeter is fixed at 280 meters, we can express the area of the playground as a function of x:

A(x) = lw = (x/2)(280 - x) = 140x - x^2

b. To find the side length x that gives the maximum area, we need to take the derivative of the area function and set it to zero.

A'(x) = 140 - 2x = 0

x = 70

c. Plugging x = 70 back into the area function, we get:

A(x) = 140x - x^2 = 140 * 70 - 70^2 = 140 * 70 - 4900 = 980.

The maximum area that the playground can have is 980 square meters.

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Answer:

64 is the area!

- love bri <3

Answer:

A and C

Step-by-step explanation:

Using the statistical tool, the following were arrived at:

It should be noted that when arranged from lowest to highest, the IQR represents the central 50% of values.

Find the median (middle value) of the lower and higher half of the data to get the interquartile range (IQR).

These are the quartile 1 (Q1) and quartile 3 (Q3) values (Q3). The difference between Q3 and Q1 is the IQR.

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Answer:

382^2 mod

Step-by-step explanation:

To determine the shared secret key, we need to use the formula (g^a mod p)^b mod p = (g^b mod p)^a mod p, where g is the generator, p is the prime, a is our secret number, and b is the value sent by Aisha. Plugging in the values, we get (7^227 mod 437)^308 mod 437 = (7^308 mod 437)^227 mod 437.

To solve for the shared secret key, we first need to calculate (7^308 mod 437). This can be done by raising 7 to the 308th power and then taking the remainder when divided by 437. We can do this by repeatedly squaring 7 and taking the remainder each time. This results in the following sequence:

7^2 mod 437 = 49

7^4 mod 437 = 161

7^8 mod 437 = 267

7^16 mod 437 = 9

7^32 mod 437 = 49

7^64 mod 437 = 161

7^128 mod 437 = 267

7^256 mod 437 = 9

7^512 mod 437 = 49

Since 512 is greater than 308, we can stop here and use the value 49 as the result of 7^308 mod 437. We can now plug this value into the formula to calculate the shared secret key: (49^227 mod 437)^308 mod 437 = (49^308 mod 437)^227 mod 437.

To solve for the shared secret key, we need to find the value of 49^308 mod 437. This can be done using the same method as before, by repeatedly squaring 49 and taking the remainder each time. This results in the following sequence:

49^2 mod 437 = 67

49^4 mod 437 = 382

49^8 mod 437 = 221

49^16 mod 437 = 67

49^32 mod 437 = 382

49^64 mod 437 = 221

49^128 mod 437 = 67

49^256 mod 437 = 382

Since 256 is greater than 308, we can stop here and use the value 382 as the result of 49^308 mod 437. We can now plug this value into the formula to calculate the shared secret key: 382^227 mod 437 = 382^227 mod 437.

To find the shared secret key, we need to calculate 382^227 mod 437. This can be done using the same method as before, by repeatedly squaring 382 and taking the remainder each time. This results in the following sequence:

9514 1404 393

Answer:

  500

Step-by-step explanation:

The PIN code has 3 unknown digits, so 10^3 = 1000 possible combinations of digits. Of those, half will be odd numbers.

There are 500 sets of digits that Alan's PIN code could be.

Answer:

Step-by-step explanation:

To find the area of the shaded region, we need to first find the x-coordinates of the points where the two functions intersect. We can set f(x) = g(x) and solve for x:

x^4 - 12x^3 + 48x^2 = 44x + 105

x^4 - 12x^3 + 48x^2 - 44x - 105 = 0

We can use a numerical method, such as the Newton-Raphson method, to approximate the roots of this equation. Using a graphing calculator or computer algebra system, we can find that the roots are approximately:

x = -1.932, x = 0.695, x = 4.149

Note that the root x = -1.932 is outside the given interval [3, 4], so we can ignore it.

The shaded region is bounded by the x-axis, the line y = 340, and the graphs of f(x) and g(x) between x = 3 and x = 4. To find the area of this region, we can integrate the difference between the two functions over this interval:

A = ∫3^4 [g(x) - f(x)] dx

A = ∫3^4 [44x + 105 - (x^4 - 12x^3 + 48x^2)] dx

A = ∫3^4 [-x^4 + 12x^3 - 48x^2 + 44x + 105] dx

We can integrate term by term using the power rule:

A = [-x^5/5 + 3x^4 - 16x^3 + 22x^2 + 105x]3^4

A = [-1024/5 + 192 - 192 + 22 + 105] - [-81/5 + 108 - 192 + 66 + 105]

A = 347.2

Therefore, the area of the shaded region is approximately 347.2 square units.

Answer:

Step-by-step explanation:

\(h(x) = - 49x - 125\)

To find h(-67) , substitute the value of x that's - 67 into h(x). That is for every x in h(x) , replace it with - 67

We have

\(h( - 67) = - 49( - 67) + 125 \\ = 3283 - 125\)

We have the final answer as

Hope this helps you

Given:

In  ΔKLM, l = 48 inches, ∠K=55° and ∠L=46°.

To find:

The length of k, to the nearest inch.

Solution:

According to Law of sine,

\(\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

In ΔKLM, using law of sine, we get

\(\dfrac{k}{\sin K}=\dfrac{l}{\sin L}\)

\(\dfrac{k}{\sin (55^\circ)}=\dfrac{48}{\sin (46^\circ)}\)

\(k=\dfrac{48\times \sin (55^\circ)}{\sin (46^\circ)}\)

On further simplification, we get

\(k=\dfrac{48\times 0.819152}{0.7193398}\)

\(k=\dfrac{39.319296}{0.7193398}\)

\(k=54.66025 \)

Approximate the value to the nearest inch.

\(k\approx 55 \)

Therefore, the length of k is 55 inch.

The length of k, to the nearest inch is  ∠K=55°.

Since

In ΔKLM, l = 48 inches, ∠K=55° and ∠L=46°.

Now here we apply law of sine

\(a\div sin\A = b\div sin\ B = c\div sin\c \\\\k\div sin \ k = l\div sin\ L\\\\k\div sin\ 55 = 48\div sin\ 66\)

k = 54.66

k = 55 degrees

hence, The length of k, to the nearest inch is  ∠K=55°.

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 2545.10\\ P=\textit{original amount deposited}\dotfill &\pounds 2000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{each year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}\)

\(2545.10 = 2000\left(1+\frac{\frac{r}{100}}{1}\right)^{1\cdot 4} \implies \cfrac{2545.10}{2000}=\left( 1+\cfrac{r}{100} \right)^4 \\\\\\ \cfrac{2545.10}{2000}=\left( \cfrac{100+r}{100} \right)^4\implies \sqrt[4]{\cfrac{2545.10}{2000}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[4]{\cfrac{2545.10}{2000}}=100+r\implies 100\sqrt[4]{\cfrac{2545.10}{2000}}-100=r\implies \boxed{6.2\approx r}\)

Answer:

Exactly 1.30725 bags are needed to cover the garden.

Step-by-step explanation:

We have a yard with a surface of 1307.25 square feet.

We know that one bag of fertilizer covers 1000 square feet.

We want to know how many bags are needed to cover the garden. We can calculate the number of bags as:

\(B=S\cdot b=1307.25\;\text{sq.ft.}\cdot \dfrac{1\,\text{bag}}{1000\,\text{sq.ft.}}=1.30725\,\text{bags}\)

B: number of bags needed for the yard.

S: surface of the yard.

b: number of bags per square foot.

Answer

Explanation

There are 12 spacings around the entire

a)The value of  ∠b=64°.

b)The values of angles q, r, s, t are ∠q= 65°, ∠r=65°, ∠s=50°, ∠t=65°.

c)The value of  ∠B=72 degrees.

The same-side interior angles are additional if a transversal connects two parallel lines. Alternate interior angles are equivalent if a transversal connects two parallel lines. Corresponding angles are equal.

a) Given line PQ is parallel to ST.

   One of the theorems of parallel lines is, Corresponding angles are equal.

Here the corresponding angles are ∠a, ∠b.

so, ∠a=∠b

∴∠b=64°

b) It is given that lines B and C are parallel, according to one of the theorems of parallel lines, vertically opposite angles are equal. So, the angle opposite to 65° is also equal to 65°. Sum of the angles suspended by a line on another line is 180°. Therefore the other angle in the triangle is 180°-130°=50°.

Since the sum of interior angles in a triangle is 180°, the angle q will be:

   ∠q= 180°-(65°+50°)

    ∠q= 65°.

Vertically opposite angles are equal, therefore ∠q=∠r=65°.

∠s=180°-(65°+65°)

∠s=50°.

Corresponding angles are equal, therefore

130°=65°+∠t

∠t=65°.

c) Given lines A, and B are parallel. We know that the Corresponding angles are equal, therefore

3m=4m-24

⇒m=24

Therefore ∠B=4(24)-24

∠B=72 degrees.

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1 mile = 5,280 feet.

60 miles x 5,280 = 316,800 total feet.

1 hour = 3,600 seconds.

316,800 feet / 3,600 seconds = 88 feet per second.

The answer is 88 ft/s

Answer:

8

Step-by-step explanation:

After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:

Amount remaining = Initial amount × (1/2)^(number of half-lives)

In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.

So, the equation becomes:

Amount remaining = Initial amount × (1/2)^4

Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.

Simplifying the equation:

Amount remaining = Initial amount × (1/16)

Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

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By adding 3 to both sides of the equation (6+3)-3=9-3, this demonstrates the addition property of equality. This results in the equation being simplified to 6+3=9.

The properties of equality describe the relationship between two sides of an equation and state that the two sides remain equal even after the same arithmetic operation is performed on each side. a = a, according to the reflexive property of equality. For example, 5 = 5, because the number's value is equal to itself.

As per the addition property of equality, when we add the same number to both sides of an equation then the two sides remain equal. This can be written as, if a = b, then a + c = b + c.

Translated question "Draw a line from each equation to the property of equality it illustrates. (6+3)−3=9−3 Addition Property of Equality"

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Answer:

60'' × 52'' or a 79.4'' TV

Step-by-step explanation:

Leaving a room of 2 inches on all sides means we subtract 4 inches from the height and length to find the maximum dimensions of the TV.

With this, we get 60'' × 52''. To find the diagonal length of the TV, use the Pythagorean Theorem which simply states the length of the diagonal is equal to the square root of the sum of the squared dimensions.

\(\sqrt{a^2+b^2} =c\)

\(\sqrt{60^2+52^2}=79.4\)

Therefore your TV can have a maximum size of 79.4 inches.

Answer: 2/9 = 0.22

Step-by-step explanation: This is rounded to the nearest hundredth which is in the 2nd place after the decimal point.

Answer:

5:6

Step-by-step explanation:

the ratio before would be 10/12 so you would have to divide both sides by 2 so you would get 5/6.Hope this helped

Answer:

  a13 = 20,480

Step-by-step explanation:

The first term is a1 = 5, and the common ratio is ...

  r = 10/5 = 2

The generic term is ...

  an = a1·r^(n-1)

  an = 5·2^(n-1)

Then the 13th term is ...

  a13 = 5·2^(13 -1) = 5·4094

  a13 = 20,480

Kala spun the spinner 1000 times and got the following results:

- Yellow: 400 times

- Red: 300 times

- Blue: 300 times

1. Calculate the amount of sales tax:

  - The item costs $350 before tax.

  - The sales tax rate is 14%.

  - To find the sales tax amount, multiply the cost of the item by the tax rate:

    Sales tax = $350 * 0.14 = $49.

2. Determine the total cost of the item including tax:

  - Add the sales tax amount to the original cost of the item:

    Total cost = $350 + $49 = $399.

3. Analyze the spinner results:

  - The spinner has 10 equal-sized slices.

  - There are 4 yellow slices, 3 red slices, and 3 blue slices.

  - Kala spun the dial 1000 times.

4. Calculate the frequency of each color:

  - Yellow: Kala got 400 yellow results out of 1000 spins.

  - Red: Kala got 300 red results out of 1000 spins.

  - Blue: Kala got 300 blue results out of 1000 spins.

5. Calculate the probability of landing on each color:

  - Yellow: Probability = Frequency of yellow / Total spins = 400 / 1000 = 0.4.

  - Red: Probability = Frequency of red / Total spins = 300 / 1000 = 0.3.

  - Blue: Probability = Frequency of blue / Total spins = 300 / 1000 = 0.3.

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Answer:

48/13

Step-by-step explanation:

To make this into an improper fraction, convert the integer into a fraction using the denominator of the fraction

3 * 13/13 = 39/13

Then add it to the rest of the fraction

39/13 + 9/13

= 48/13

Answer: 48/13

Step-by-step explanation: first multiply 3 x 13 to get 39. do this because you get the fraction for the whole number, 3. then, add 39 to the numerator (9). you will get 48/13. you do this because you are adding the whole number (3) to the fraction so that way it is an improper fraction.

Okay, here we have this:

Considering the provided graph, we are going to calculate the requested equation, so we obtain the following:

So let's remember that to obtain the equation of a straight line of the form y=mx+b, we need to know the slope and the y-intercept, so we have:

Slope=(y2-y1)/(x2-x1)

Slope=(3-2)/(3-0)

Slope=1/3

And we can see that the y-intercept is y=2, so we finally get the following equation of the line:

y=mx+b

y=1/3x+2

Finally we get that the correct answer is the third option.

Step-by-step explanation:

\(x = 3 + t\)

\(y = - t {}^{2} \)

\(x - 3 = t\)

\(y = - (x - 3) {}^{2} \)

This is the answer or

\(y = - {x}^{2} +6x - 9\)

They are both parabola with a vertex at 3,0 , facing downwards.

Answer:

I just need points.

Step-by-step explanation:

Answer:

$179,000 - $94,000 = annual salary for the Governor of Tennessee

The value of the function at x = 2 will be 5.

A function is a statement, tenet, or rule that establishes a connection between two variables. Mathematics is replete with functions, which are necessary for the construction of intricate relationships.

The result of the calculation that the mathematical model depicts is the expression's result when the necessary parameters and natural laws are given values.

The table represents a function.

x     f(x)

-1     5

0     10

2     8

9     14

In the above table, we can see that at the value of x = 2 in the function the value of the whole function is 5.

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