The perimeter p of the rectangle equals 30. Find the value of X?

The angle is increased in approximately 0.095 radians (5.443°) for [tex]x = 0.45\,m[/tex].

Based on the statement we construct the geometric diagram, by definition of tangent we have expressions for the initial and final angles ([tex]\theta_{1}[/tex], [tex]\theta_{2}[/tex]), in radians, of the figure:

Initial triangle

[tex]\tan \theta_{1} = \frac{y_{1}}{x_{1}}[/tex] (1)

Final triangle

[tex]\tan \theta_{2} = \frac{y_{2}}{x_{2}}[/tex] (2)

By using (2), the equivalence [tex]\theta_{2} = \theta_{1}+\Delta \theta[/tex] and trigonometric identities we have the following expression:

[tex]\frac{y_{2}}{x_{2}} = \frac{\tan \theta_{1}+\tan \theta_{2}}{1-\tan \theta_{1}\cdot \tan \theta_{2}}[/tex] (3)

By (1), we simplify the expression:

[tex]\frac{y_{2}}{x_{2}} = \frac{\frac{y_{1}}{x_{1}} + \tan \Delta \theta}{1-\frac{y_{1}}{x_{1}}\cdot \tan \Delta \theta}[/tex] (3b)

If [tex]0 \le \Delta \theta \le \frac{\pi}{6}[/tex], then we can use the following approximation:

[tex]\tan \Delta\theta \approx \Delta \theta[/tex] (4)

Then, we reduce (3b) into an entirely algebraic expression:

[tex]\frac{y_{2}}{x_{2}} = \frac{\frac{y_{1}}{x_{1}}+\Delta \theta }{1-\frac{y_{1}}{x_{1}}\cdot \Delta \theta }[/tex] (3c)

Where [tex]y_{2} = \sqrt{r^{2}-x_{2}^{2}}[/tex].

Now we clear [tex]\Delta \theta[/tex] within the formula:

[tex]\Delta \theta = \frac{\frac{y_{2}}{x_{2}}-\frac{y_{1}}{x_{1}}}{\frac{y_{1}}{x_{1}}\cdot \left(1+\frac{y_{2}}{x_{2}} \right) }[/tex]  (5)

If we know that [tex]x_{1} = y_{1} = 0.5[/tex], [tex]r = 0.707[/tex] and [tex]x_{2} = 0.45[/tex], then we estimate the angle change:

[tex]y_{2} = \sqrt{0.707^{2}-0.45^{2}}[/tex]

[tex]y_{2} \approx 0.545[/tex]

[tex]\Delta \theta = \frac{\frac{0.545}{0.45}-1 }{1\cdot \left(1+\frac{0.545}{0.45} \right)}[/tex]

[tex]\Delta \theta = 0.095[/tex]

As [tex]\Delta \theta < \frac{\pi}{6}[/tex], then the result seems to be reasonable. The angle is increased in approximately 0.095 radians (5.443°) for [tex]x = 0.45\,m[/tex].

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Answer:

Salami: $3.00

Ham: $ 8.00

Step-by-step explanation:

12 * 1/4 = 12/4 = $3.00

12 * 2/3 = 24/3 = $8.00

Answer:

She thought the multiplication symbol was the addition symbol

actual answer: 1.39 x 10^12

Step-by-step explanation:

If it was addition, then she’d be correct;

6.75x10^6 + 0.2x10^6

= (6.75 + 0.2)x10^6

= 6.95x10^6

But really, it was a multiplication, meaning the answer really is;

(6.95x10^6)x(0.2x10^6)

= 1.39 x 10^12

Step-by-step explanation:

10y - 3(y + 2) > 2y + 4

10y - 3y - 6 > 2y + 4

(10 - 3 - 2)y > 4 + 6

5y > 10

y > 10/5

y > 2

[tex] \: [/tex]

Solution → y > 2

Interval Notation → [tex] \lang 2 , \infty\rang[/tex]

The solution in interval notation is: (2, ∞)

To solve the inequality 10y - 3(y + 2) > 2y + 4, follow these steps:

Step 1: Distribute the -3 on the left side of the inequality:

10y - 3y - 6 > 2y + 4

Step 2: Combine like terms:

(10y - 3y) - 6 > 2y + 4

7y - 6 > 2y + 4

Step 3: Get all the y terms on one side by subtracting 2y from both sides of the inequality:

7y - 2y - 6 > 2y - 2y + 4

5y - 6 > 4

Step 4: Get the constant term on the other side by adding 6 to both sides of the inequality:

5y - 6 + 6 > 4 + 6

5y > 10

Step 5: Finally, solve for y by dividing both sides by 5:

y > 10/5

y > 2

The solution to the inequality is y > 2. Now, let's write it in interval notation.

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Answer:

Girls are   4/5 of the students.

Step-by-step explanation:

boys + girls = 100% of students.

If 20% of the students are boys then 80% are girls

80% = 80/100 =  4/5

9514 1404 393

Answer:

  4.82 m

Step-by-step explanation:

The mirror reflects light at the same angle the light hits it, so the triangles formed by the line of sight, the ground, and the objects involved are similar. This means corresponding lengths are proportional.

  height/mirror distance = T/12.15 = 1.35/3.4

Multiplying by 12.15, we find the top of the goalpost to have a height of ...

  T = 12.15(1.35/3.4) ≈ 4.82 . . . meters

The goalpost is about 4.82 meters high.

Answer:

Step-by-step explanation:

45 divided by two

Answer:

x>2

Step-by-step explanation:

1) 6x+3 > 15

2) 6x > 15-3

3) 6x > 12

4) x > 12÷6

5) x > 2

Answer:

Hundred thousands - 7

Ten Thousands- 4

Step-by-step explanation:

Answer:

42 sweets

Step-by-step explanation:

The ratios are 5 : 3 : 2 = 5x : 3x : 2x (x is a multiplier )

June gets 42 more sweets than Alex , then

5x = 2x + 42 ( subtract 2x from both sides )

3x = 42 ( divide both sides by 3 )

x = 14

Gavyn = 3x = 3 × 14 = 42 sweets

Answer:

42 sweets.

Step-by-step explanation:

First work out the number of parts:

5 + 3 + 2 = 10.

So June gets 5/10 = 1/2 of the sweets.

Alex gets 2/10 = 1/5.

Gavyn gets 3/10.

If the total number of sweets was x, then:

1/2 x - 1/5 x = 42

5/10x - 2/10 x = 42

3/10 x = 42

x = 42*10/3 = 140.

So Gavyn has 3/10 * 140 = 42.

Answer:

k=0.023

Step-by-step explanation:

[tex]r \alpha {t }^{2} \\ r = k {t}^{2} \\ 144 = k \times {72 }^{2} \\ k = \frac{144}{ {72 }^{2} } \\ k = 0.023 \\ the \: eqn \: is \: therefore \\ r = 0.023 \times {t}^{2} [/tex]

The equation that expresses the relationship between the variables is r=kt and the variation constant k=2.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

Given that, the variable r is directly proportional to the square of t

Now, r∝t

r=kt

Here, r =144 when t =72

Thus, 144=k×72

k=2

Therefore, the equation that expresses the relationship between the variables is r=kt and the variation constant k=2.

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Answer:

1.5 songs/minutes

Step-by-step explanation:

30÷20 = 1.5

Answer:

1/8

Step-by-step explanation:

Answer:

$180

Step-by-step explanation:

y = 30x +150

30(1) + 150

= 180

Answer:

5³

Step-by-step explanation:

5³ is the answer since it's the greater between the two numbers

Answer:

125

Step-by-step explanation:

This is because 5^2 *5 is 125 and 5^3 * 1 = 125   and the findings are both numbers have to be multiplied by a whole number to quantify a same identical multiple total number - we can check this by dividing by the smallest 125/5^2  = 5  and then the largest is 125/5^3 = 1 and we know there could not be a smaller whole number  - The other workings would be to do a prim e factor tree   of 125  =  5  25  5 and 5 =  5^3 and here we are told 5^3 is a multiple of 125 and 5^2 is also a multiple of 5^3 as it square fits 5 times into 125 as 5*25 is 125  

Answer:

35

Step-by-step explanation:

Answer:

add 6 time 8 and get the answer like that.

Step-by-step explanation:

just keep adding that what you need to do ok.

Answer:

B

Step-by-step explanation:

hope it helps, and im finding another question

Answer:

B. a German citizen

Step-by-step explanation:

I think I'm not sure.

Answer:

1,000

Step-by-step explanation:

10 x 10 x 10 = 1,000

1000

Step-by-step explanation:

10³

=10×10×10

1000

Answer:

first I need to know what your question is to be able to answer this question sorry

Answer:

Ummm what is the question?

Step-by-step explanation:

Answer:

31, the five halves of is 6.2

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

3x+15+4x-5=180

7x+10=180

7x=170

x=10

Answer:

Step-by-step explanation:

5x + 2 - 3x - 1 = 3x + 2

5x - 3x - 3x = - 2 + 1 + 2

5x - 6x = 1

-1x = 1

x = 1 / -1

x = -1

Answer: Yes

Step-by-step explanation: Depends on what x equals.

Answer:

I would assume it is c. 1, because of rounding, but I'm only 70% sure.

Answer:

3,168 cal= 2lbs of Ice Cream

Step-by-step explanation:

I need to fin how many calories are in two pounds of that ceratin ice cream.

594cal/6=99cal

99cal=1 oz

16oz x 2 = 32oz

99 x 32 = 3,168 cal

There is 3,168 cal in two pounds of ceratin ice cream.

Answer: The amount budgeted for Auto Expenses is $18,200

Step-by-step explanation:

13 Percent of $140,000 is $18,200

0.13 times 140,000 :-)