Four triangles with bases of 12 centimeters and heights of 8 centimeters were used to form a parallelogram. Calculate the area of the parallelogram.

If [tex]b=\frac1a[/tex], then by rationalizing the denominator we can rewrite

[tex]b = \dfrac1{\sqrt3-\sqrt{11}} \times \dfrac{\sqrt3+\sqrt{11}}{\sqrt3+\sqrt{11}} = \dfrac{\sqrt3+\sqrt{11}}{\left(\sqrt3\right)^2-\left(\sqrt{11}\right)^2} = -\dfrac{\sqrt3+\sqrt{11}}8[/tex]

Now,

[tex]a^2 - b^2 = (a-b) (a+b)[/tex]

and

[tex]a - b = \sqrt3 - \sqrt{11} + \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{9\sqrt3 - 7\sqrt{11}}8[/tex]

[tex]a + b = \sqrt3 - \sqrt{11} - \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{7\sqrt3 - 9\sqrt{11}}8[/tex]

[tex]\implies a^2 - b^2 = \dfrac{\left(9\sqrt3 - 7\sqrt{11}\right) \left(7\sqrt3 - 9\sqrt{11}\right)}{64} = \boxed{\dfrac{441 - 65\sqrt{33}}{32}}[/tex]

Answer:

9

(Correct On Edgen)

The rewritten equation for the given equation is [tex]x=\frac{h+g}{-f}[/tex]. So, option C is correct.

A linear equation given in the form ax + b = c can be rewritten to solve for x as below:

ax + b = c

⇒ ax = c - b

∴ x = (c - b)/a

So, here the basic operations such as addition, subtraction, multiplication, and division are used on both sides to rewrite the given equation for solving x.

Given equation is -fx - g = h

Step 1: Adding 'g' on both sides

-fx - g + g = h + g

⇒ -fx = h + g

Step 2: Dividing by '-f' on both sides

-fx = h + g

⇒ -fx/-f = (h + g)/-f

∴ x = (h + g)/-f

Therefore, the rewritten equation to solve for x is x = (h + g)/-f.

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Disclaimer: The given question was incomplete in the portal. Here is the complete question.

Question: Select the correct answer. which equation is correctly rewritten to solve for x?

Equation: -fx = h + g

A. x = (g - h)/f

B. x = (h - g)/-f

C. x = (h + g)/-f

D. x = (h + g)/f

1) Quadrilateral PAST, TX=AX, [tex]\overline{TP} \parallel\overline{AS}[/tex] (given)

2) [tex]\angle XPT \cong \angle XSA[/tex] and [tex]\angle XTP \cong \angle XAS[/tex] (alternate interior angles theorem)

3) [tex]\triangle TXP \cong \triangle AXS[/tex] (AAS)

4) [tex]\overline{TP} \cong \overline{AS}[/tex] (CPCTC)

5) PAST is a parallelogram (a quadrilateral with two pairs of opposite congruent sides is a parallelogram)

(Adding to the other person's answer)

For the 5th step reason, put this: A quadrilateral is a parallelogram if a pair of opposite sides are parallel and congruent.

It won't work to just say something like the def. of parallelograms.

The equation in which b varies directly as the square root of c is b = 50 · √c. (Correct choice: B)

In this problem we have a case of direct variation between two variables, which is mathematically described by a direct proportionality model, whose form and characteristics are shown below:

b ∝ √c

b = k · √c      (1)

Where k is the proportionality constant.

First, we determine the value of the constant of proportionality by substituting on b and c and clearing the variable: (b = 100, c = 4)

k = b / √c

k = 100 / √4

k = 100 / 2

k = 50

Then, the equation in which b varies directly as the square root of c is b = 50 · √c. (Correct choice: B)

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Answer:

true

Step-by-step explanation:

mean we show up the distribution

Answer:

pretzel: 2

hotdog: 3

Step-by-step explanation:

Let h be the hotdog price and p the pretzel price.

We know that:

h + p = 5

and

2h + 3p = 12

We can solve this system of equations:

h = 5-p

2(5-p) + 3p = 12

So the second eq. becomes:

10 - 2p + 3p = 12

10 + p = 12

p = 2

Sub in the first:

h = 5 - p = 5-2 = 3

So p = 2, h = 3

Answer: $3 / hot dog

Step-by-step explanation:

Given information:

1 hot dog + 1 pretzel = $5

2 hot dogs + 3 pretzels = $12

Set variables:

Let x be the price per hot dog

Let y be the price per pretzel

Set system of equations:

x + y = 5

2x + 3y = 12

Multiply the first equation by 3:

3x + 3y = 15

2x + 3y = 12

Subtract the second equation from the first equation (Elimination):

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

3x + 3y - 2x - 3y = 3

(3y - 3y) + 3x - 2x = 3

0 + x = 3

[tex]\boxed{x=3}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The computation shows that the amount will be 44.70 Dollars.

The options are missing: Here are the missing options:

A. 44.70 US dollars

B. 73.06 US dollars

C. 136.87 US dollars

D. 140.41 US dollars

For solving this question first we will convert the USD to euros.

The conversion rate we have is:

1 euro = 1.3687 USD

250/1.3687 = 182.655 euros

Now we will subtract it from what he has spent:

= 182.655 - 150

= 32.655 euros

Now we will again convert it back to USD. This will be:

32.655 euros * 1.3687 = 44,695 us dollars

Therefore, the answer is 44.70.

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The best option that would be used to show the data would be the line graph.

The reason  I chose the line graph is that it would show us the trend in the data. This is in a way that we would see the periods there was a high bills.

Also the line graph is very simple to understand. The relationship and the changes in the data is easily seen.

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The height of the mountain from a point a sea level is approximately 1496.650 meters.

First, we construct the geometric diagram of the situation and find all needed angles and sides to determine the height of the mountain. First, we determine the missing side x by the law of sines:

Law of sines

1000 m/sin 3° = x/sin 14.261°

x ≈ 4706.886 m

Now we determine the height of the mountain by trigonometric functions:

h = 100 m + (4706.886 m) · sin 17.261°

h ≈ 1496.650 m

The height of the mountain from a point a sea level is approximately 1496.650 meters.

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what help? how can i help you?

Answer:

1. 3 terms; degree 5

2. 2 terms; degree 3

3. 9mn³ + 14mn²

4. 9a^4b^3

Step-by-step explanation:

Problems 1 - 2:

Each product of a number and variables is a term. The number may be 1, so it is not written. Also, a term may not have a variable.

The degree of a term is the sum of the exponents of all the variables of the term. A plain variable, such as x has an exponent of 1 which is not written but must be added to determine the degree.

The degree of the polynomial is the same as the degree of the term with the highest degree.

1.

3 terms

degree 5

2.

2 terms

degree 3

Problems 3 - 4:

Combine like terms. Like terms have the same variables and exponents.

3.

6mn³ - mn² + 3mn³ + 15mn² =

= 6mn³ + 3mn³ - mn² + 15mn²

= 9mn³ + 14mn²

4.

a^4b^3 + 8a^4b^3 =

= 1a^4b^3 + 8a^4b^3

= 9a^4b^3

The relationship of the data can be classified as a fairly strong positive correlation.

Correlation is a statistical measure used to measure the relationship that exists between two variables.

Positive correlation is when two variables move in the same direction. If one variable increases, the other variable also increases. When there is a positive correlation, the graph of the variables is upward sloping

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The boat speeds of 15 km/h and 18 km/h, directions, and the time of travel of 45 minutes gives the angle between their paths as approximately 68°.

The given parameters are;

Direction of the first boat = Northeast

Speed of the first boat = 15 km/h

Direction of the second boat = Northwest

Speed of the second boat = 18 km/h

Distance between the boats after 45 minutes = 14.0 km.

45 minutes = 0.75 × 1 hour

Distance traveled by the first boat in 45 minutes, d1, is therefore;

d1 = 15 km/h × 0.75 hr = 11.25 km

For the second boat, we have;

d2 = 18 km/h × 0.75 hr = 13.5 km

Using cosine rule, we have;

14² = 11.25² + 13.5² - 2 × 11.25 × 13.5 × cos(A)

Where A is the angle between the paths of the two boats.

Which gives;

[tex]cos(A) = \frac{361}{972} [/tex]

[tex] A= \mathbf{ arccos\left(\frac{361}{972} \right) }\approx 68^\circ [/tex]

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The chance or chance that the lawn mower will hit a chunk of glass that is already cracked is calculated with the aid of dividing the variety of glasses that are cracked by way of the full quantity of glasses. on this item, the unknown may be calculated through . The solution is, therefore,  0.20.

Opportunity is a measure of the chance of an event to arise. Many occasions cannot be predicted with overall reality. We are able to are expecting only the danger of an event to arise i.e. how likely they're to manifest, using it.

The possibility is the branch of arithmetic regarding numerical descriptions of how in all likelihood an occasion is to arise, or how possibly it's miles that a proposition is actual. The possibility of an occasion various between 0 and 1, where, roughly talking, 0 indicates the impossibility of the event and 1 shows reality.

The probability of an event can be calculated by possibility components via surely dividing the favorable range of effects through the full range of possible outcomes.

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Answer: 1/8

Step-by-step explanation:

The value of x in x^yz = y^2 is [tex]x = \sqrt[yz]{y^2}[/tex]

The equation is given as:

x^yz = y^2

Rewrite the equation properly as follows

[tex]x^{yz} = y^2[/tex]

Take the yz root of both sides

[tex]\sqrt[yz]{x^{yz}} = \sqrt[yz]{y^2}[/tex]

Apply the law of indices

[tex]x^{\frac{yz}{yz}} = \sqrt[yz]{y^2}[/tex]

Divide yz by yz

[tex]x = \sqrt[yz]{y^2}[/tex]

Hence, the value of x in x^yz = y^2 is [tex]x = \sqrt[yz]{y^2}[/tex]

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Answer:

e

Step-by-step explanation:

Using euler's identity we can see that e^ipi=-1 and considering that i=y and  i^2=-1 we can conclude that x=e

Step-by-step explanation:

we have given

l=10m

b=8m

h=5m

volume =?

area=?

volume =l*b*h

= 10*8*5

=400

area=2(lb+lh+bh)

=2(10*8+10*5+8*5)

=2(80+50+40)

=2(170)

=340

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Answer:

76,200 mm

Step-by-step explanation:

1 meter = 1000 mm, by definition.  Make that a conversion factor:

(1 meter)/(1000 mm), or (1000 mm)/(1 meter).  Both are equal to 1, since 1 meter = 1000 mm.  We can multiply anything by 1, so take the original measurement of length of 76.2 meters, and multiply it by (1000 mm)/(1 meter).

(76.2 meters)*((1000 mm)/(1 meter)) = 76,200 mm.  The meters cancels, leaving just mm, the desired unit.

Answer: B, D, E

Step-by-step explanation:

a. The function that models the situation is  F(t) = 48(1.08)ˣ

b. The price of the stock 6 years from now is $76.17

c. Find the graph in the attachment

d. I receive a dividend of $0.026.

Since the stock price increases at a rate of 8% every year, and is initially $48, it follows exponential growth.

So, the current price [tex]F(t) = A(1 + r)^{t}[/tex] where

So,  [tex]F(t) = A(1 + r)^{t}[/tex]

[tex]F(t) = 48(1 + 0.08)^{t} \\= 48(1.08)^{t}[/tex]

So, the function that models the situation is F(t) = 48(1.08)ˣ

The price of the stock 6 years from now is gotten when t = 6.

So,

[tex]F(t) = 48(1.08)^{t} \\= 48(1.08)^{6} \\= 48(1.5869)\\= 76.17[/tex]

So, the price of the stock 6 years from now is $76.17

Find the graph in the attachment

Since every quarter, the company pays a dividend of 1.5 %, the rate per year would be r = 1.5 % ÷ 1/4 year = 1.5 % × 4 = 6 % per year.

Since they pay at a rate, r = 6 % = 0.06 of the stock price, F(t) as dividend.

After n years, the dividend is D = (r)ⁿF(t)

= (0.06)ⁿF(t)

So, [tex]D = (0.06)^{t}F(t) \\= (0.06)^{t}[4.8(1.08)^{t}][/tex]

So, after 3 years when t = 3,

[tex]D = (0.06)^{t}[4.8(1.08)^{t}]\\D = (0.06)^{3}[4.8(1.08)^{3}]\\D = 0.000216 \times 48 \times 1.2597\\D = 0.013[/tex]

Since there are 3 shares, the total dividend would be D' = 3D

= 3 × 0.013

= 0.026

So, i receive a dividend of $0.026

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Answer:

-6, -15

Step-by-step explanation:

Each term is 9 less than the previous term.

The angle between their paths to the nearest degree is 68⁰.

first displacement, a = 15 km/h  x (45/60)

first displacement, a = 11.25 km

second displacement, b = 18 km/h  x (45/60)

                                     b = 13.5 km

c² = a² + b² - 2ab(cosθ)

2ab(cosθ) = a² + b² - c²

cosθ =  (a² + b² - c²)/(2ab)

cosθ = (11.25² + 13.5² - 14²) / (2 x 11.25 x 13.5)

cosθ = 0.371

θ = arc cos(0.371)

θ = 68.22 ⁰

Thus, the angle between their paths to the nearest degree is 68⁰.

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The probability of having, at most, 9 girls, is 0.9515

The probability that a random baby is a girl is:

p = 0.5

And the probability that a random baby is a boy is:

q = 0.5

Then the probability that, at most, 9 out of 11 babys are girls, is given by:

1 - p(10) - p(11)

Where P(10) is the probability that 10 of the babies are girls and p(11) is the probability that the 11 babies are girls.

p(10) = C(11, 10)*(0.5)^10*(0.5)^1 = C(11, 9)*(0.5)^11

Where C(11, 10) is the combinations of 10 elements that we can make with a set of 11 elements, such that:

C(11, 10)=  11!/(11 - 10)!*10! = 11

Replacing that, we get:

P = 11*(0.5)^11 = 0.0054

p(11) = C(11, 11)*0.5^11 = 1*0.5^11 = 0.0005

Then the probability is:

P = 1 - 0.0054 - 0.0005 = 0.9515

The probability of having, at most, 9 girls, is 0.9515

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Answer:

x=1/3

Step-by-step explanation:

The perimeter of a rectangle is the sum of its side lengths.

A rectangle is special in that sides opposite one another have equal length. So if [tex]x[/tex] is the length of the horizontal sides, the total perimeter of the rectangle is

[tex]4\,\mathrm{cm} + 4\,\mathrm{cm} + x\,\mathrm{cm} + x\,\mathrm{cm} = (8+2x)\,\mathrm{cm}[/tex]

We're given the perimeter is actually 18 cm, so

[tex]8+2x = 18[/tex]

Solve for [tex]x[/tex].

[tex](8 + 2x) - 8 = 18 - 8[/tex]

[tex]2x = 10[/tex]

[tex]\dfrac12 \cdot 2x = \dfrac12 \cdot 10[/tex]

[tex]\boxed{x = 5}[/tex]

Answer:

21

Step-by-step explanation:

(69.8-32)×(5/9)=21