given: m||n, angle 1 is congruent to angle 3
prove: k||L

[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{ \cfrac{1}{4}}(x-\stackrel{x_1}{8}) \implies {\large \begin{array}{llll} y +2= \cfrac{1}{4} (x -8) \end{array}}[/tex]

For the quadratic equation 2x² - 4x - 48 = 0 value of x is 6 and -4.

What is quadratic equation?

The second-degree equation is a quadratic equation. This indicates that it has at least one (1) squared phrase. Ax2 + bx + c = 0 is one of the most used formulas for solving quadratic equations. Here, a, b, and c are constants or numerical coefficients. Here, the variable "X" is unknowable.

ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

We have a quadratic equation;

2x² - 4x - 48 = 0

To find the value of x we have to follow these steps ;

(2x^2 -  4x) -  48  = 0

Pull out like factors :

2x^2 - 4x - 48  =   2 • (x^2 - 2x - 24)

x2 multiplied by 2x and 24

x^2 is the initial term, and it has a coefficient of 1.

The coefficient of the middle term, which is -2x, is 2.

"The constant," the final term, is -24.

⇒ x^2 - 6x + 4x - 24

⇒   (x+4)  •  (x-6)

⇒ 2 • (x + 4) • (x - 6)  = 0

therefore x+4 = 0

 x = -4

and   x-6 = 0

Add  6  to both sides of the equation :

                     x = 6

Hence, for the quadratic equation 2x² - 4x - 48 = 0 value of x is 6 and -4.

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Answer: 32082.2

Step-by-step explanation:

Based on the given conditions, formulate:: 341300 * (2.3% + 4.4% + 2.7%)

Calculate the sum or difference: 341300 * 0.094

Calculate the product or quotient: 32082.2

Step-by-step explanation:

Answer:

In a rhombus, all sides are equal. Therefore, you can set WV (s+12) and UV (3s) equal to each other.

s+12 = 3s

Subtract s from both sides, so the variables are all on one side.

12 = 2s

Divide both sides by 2 to isolate the variable.

6 = s

UV = 3s

UV = 3(6)

UV = 18

The number of algae after 7 days is approximately 70.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

Given that,

Initial population of algae = 50

Percentage increase = 5%

To calculate the number of algae at any day, we need to find a formula.

Initial population = 50

After 1 day, population = 50 + (5% × 50) = 50 + (0.05 × 50) = 50 (1 + 0.05)

After 2 days, population = 50 (1 + 0.05)²

So, population after n days = 50 (1 + 0.05)ⁿ

Population of algae after 7 days = 50 (1 + 0.05)⁷

                                                      = 50 (1.05)⁷

                                                      = 70.355 ≈ 70

Hence there will be approximately 70 algae after 7 days.

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If there is 200 feet of fencing available, the maximum possible area of the corral is 5000 Feet.

In the question, if there is 200 feet of fencing available, then we have to find the maximum possible area of the corral.

The formula of area of rectangle is:

A = L × B, where L is the length of the rectangle and B is the breadth of the rectangle.

The A = 200 feet and rectangular area is enclosed using the creek as one side and fencing for the other three sides, to create a corral.

So, L + 2B = 200

Subtract L on both side, we get

2B = 200 - L

Divide by 2 on both side, we get

B = 100 - L/2

A = f(L)

A = L·(100 - L/2)

A = 100L - [tex]L^2[/tex]/2

Now finding the derivative.

A' = [tex]\frac{df(L)}{dL}[/tex]

A' = -L + 100

Let A' = 0

-L + 100 = 0

Subtract 100 on both side, we get

-L = -100

L = 100 feet

Now putting the value of L in B = 100 - L/2.

B = 100 - 100/2

B = 100 - 50

B = 50 feet

The maximum possible area of the corral = 100 × 50

The maximum possible area of the corral = 5000 Feet

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Answer:20

Step-by-step explanation:

you do it

Answer:

36 = 2 x 18

Step-by-step explanation:

Answer:

3(x-5)

Step-by-step explanation:

Answer:

3(x - 5)

Step-by-step explanation:

Make terms..

x + 2x - 15 =

3x - 15

Now lets find a common factor of them..

3x - 15

3(x - 5)

Thus,

3(x - 5), Is your answer

The triangle DEF's section EF measures 24 units in length.

As per the data given in the above question are as bellow,

The provided details are as follow,

Procedure: Calculating the length that results from distorting a triangle by a scale factor

The triangle mentioned in the previous sentence is summarised in the diagram below. Using a trigonometric relationship, we discover that the following formula best describes the length of the section EF:

[tex]$\sin a^{\circ}=\frac{E F}{D E}$[/tex]

If we know that DE=30 and [tex]$\sin a^{\circ}=\frac{4}{5}$[/tex], then the length of the segment EF is:

[tex]E F=D E \cdot \sin a^{\circ} \\& E F=30 \cdot\left(\frac{4}{5}\right) \\[/tex]

EF=24

Sine (sin), cosine (cos), and tangent (tan), which are defined in terms of the ratios of the sides of a right triangle, are the fundamental trigonometric functions.

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Note: The correct question would be as bellow,

A triangle was dilated by a scale factor of 6. If sin a° = four fifths and segment DE measures 30 units, how long is segment EF?triangle DEF in which angle F is a right angle, angle D measures a degrees, and angle E measures b degrees

15.5 units

24 units

30 units

37.5 units

Answer:

  -9/8

Step-by-step explanation:

You want a full simplification of ...

  [tex]3\cdot\log_{\frac{4}{9}}{\sqrt[4]{\dfrac{27}{8}}}[/tex]

The relevant rules of logarithms are ...

  log(ab) = log(a) +log(b)

  log(a/b) = log(a) -log(b)

  log(a^b) = b·log(a)

  logₐ(b) = log(b)/log(a)

  [tex]3\cdot\log_{\frac{4}{9}}{\sqrt[4]{\dfrac{27}{8}}}=\dfrac{3}{4}\log_{\frac{4}{9}}\left(\dfrac{27}{8}\right)=\dfrac{3}{4}\cdot\dfrac{\log\dfrac{27}{8}}{\log\dfrac{4}{9}}\\\\\\=\dfrac{3(\log(3^3)-\log(2^3))}{4(\log(2^2)-\log(3^2))}=\dfrac{3(3\cdot\log(3)-3\cdot\log(2))}{4(2\cdot\log(2)-2\cdot\log(3))}\\\\\\=\dfrac{9(\log(3)-\log(2))}{8(\log(2)-\log(3))}=\boxed{-\dfrac{9}{8}}[/tex]

__

Additional comment

We have reduced everything to the difference of the logs of 2 and 3. You could stop the reduction to smallest parts at any point where you recognize things that will cancel. You could write numerator and denominator in terms of powers of (3/2), for example.

Answer:

84

Step-by-step explanation:

x/2=3*28/2=3*14 = 42

x=84

Answer: No solution

Step-by-step explanation:

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

Expand the right side:

6x + 12 = 6x + 6

Subtract 6x from both sides:

12 = 6

This is obviously not true, so there are no solutions to this equation :>

Answer:42 miles

Step-by-step explanation: She runs 3 times a week so 2  1/3 times 3 is equal to 7.

7x6=42

To solve the triangle, or identify unknown portions in terms of known portions, we can apply the Pythagorean theorem and the properties of sines, cosines, and tangents. The x is  8 .

To solve the triangle, or identify unknown portions in terms of known portions, we can apply the Pythagorean theorem and the properties of sines, cosines, and tangents.

Pythagorean theorem: a2 + b2 = c2.

Sine: sin A=a/c, sin B=b/c.

Cosines: cos A = b/c, cos B = a/c.

Identity based on trigonometry

cos x sin (90-x)

therefore, if we have

(4x plus 10) o = Cos (6x)

(4x plus 10) o = Sin (90- 6x)

4x + 10 = 90 - 6x

4x+6x = 90 - 10

10x = 80

x = 80/10

x = 8

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The time it takes for the wave to travel from point A to point B is 0.0086 seconds.

Assuming the question is referring to a sinusoidal wave with a frequency of 50 Hz, we can use the wave speed formula to calculate the time it takes for the wave to travel from point A to point B.

Wave speed (v) = frequency (f) x wavelength (λ)

Since the frequency is given as 50 Hz, we need to determine the wavelength to find the wave speed.

To calculate the wavelength, we can use the distance between two consecutive points on the wave that is in phase, such as points A and D or B and C. From the given information, we know that the distance between A and D or B and C is one wavelength. Therefore, we can calculate the wavelength as follows:

wavelength (λ) = distance between A and D or B and C = 10 m - 3 m = 7 m

Using the wave speed formula and the calculated wavelength, we can find the wave speed:

v = f x λ = 50 Hz x 7 m = 350 m/s

Now we can use the wave speed formula to find the time it takes for the wave to travel from point A to point B:

v = d / t

where d is the distance between A and B (which is 3 m) and t is the time it takes for the wave to travel that distance.

Rearranging the formula, we get:

t = d / v = 3 m / 350 m/s = 0.0086 s

Therefore, the time it takes for the wave to travel from point A to point B is 0.0086 seconds.

To find the amplitude of the wave, we would need additional information, as the amplitude is the maximum displacement of the wave from its equilibrium position.

As for whether points A and B are in phase, we need to compare the phase difference between the two points to the wave period. The period of a wave is the time it takes for one complete oscillation, and it is given by:

period (T) = 1 / frequency (f) = 1 / 50 Hz = 0.02 s

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The following type of study can be concluded as an observational study.

An observational study is a type of study that is used to gather data on the characteristics and behaviors of a particular group of people or subjects without actively manipulating or interfering with the subjects.

This study can be used to suggest a causal relationship between increased stress and muscle cramps, but it cannot conclusively prove causality.

There are several reasons why this study design cannot be used to conclude a causal relationship. First, the study is a non-randomized, uncontrolled experiment, which means that there may be other factors that could be influencing the results.

For example, the subjects in the stress group may have other characteristics or preexisting conditions that are related to muscle cramps. Additionally, the study does not have a control group for comparison, so it is not possible to determine if the muscle cramps are caused by stress or by some other factor.

Second, the study design is a single-blind study, which means that only the subjects are not aware of their group assignment, but the experimenter knows which group the subjects are in. This can lead to bias in data collection, analysis, or interpretation.

Therefore, The following type of study can be concluded as an observational study.

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Answer:

11/20

Step-by-step explanation:

Add 1/5 and 1/4. You get 9/20.

Subtract that from 1 and you get 11/20 :)

Answer:

11/20

Step-by-step explanation:

1/5+1/4

4/20+5/20= 9/20

20/20-9/20=11/20

The length of the base of the triangle is 40ft

A triangle is a polygon with three sides, three angles, three vertices, and sum of angles is s 180 degrees

The given parameters that will help us to solve the problem are

The area of the triangle is given as

Area = 1/2 *b*h

Area = 1/2*b*5 = 100

Area = 5b/2 = 100

Area = 5b = 200

Making b the subject of the relation

b= 200/5 =40 ft

Therefore the response for 40 ft is correct

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The coordinates of the centroid of triangle ABC are given as follows:

(-1, 4).

The coordinates of the centroid of a triangle are obtained finding the mean of the coordinates of the three vertices of the triangle.

This means that the x-coordinate of the centroid of triangle ABC is given as follows:

(-1 + 2 - 4)/3 = -1.

(mean of the x-coordinates of each of the three vertices).

The y-coordinate of the centroid of triangle ABC is given as follows:

(10 + 1 + 1)/2 = 4.

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The required interest rate would be 6.9% to the nearest tenth of a percent.

We can use the formula A = P(1+r/n)^nt, where A is the amount of money at the end of the investment, P is the principal, r is the interest rate, n is the number of times the interest is compounded, and t is the time period.

In this case: A = $14,000, P = $11,000, n = 1 (continuous compounding), and t = 9.

Plugging these values into the percent formula, we get: 14,000 = 11,000(1+r)^9. Solving for r, we get: r = 0.069 or 6.9%.

We can use the formula A = P(1+r/n)^nt, where A is the amount of money at the end of the investment, P is the principal, r is the interest rate, n is the number of times the interest is compounded, and t is the time period.

In this case: A = $14,000, P = $11,000, n = 1 (continuous compounding), and t = 9.

Plugging these values into the formula, we get: 14,000 = 11,000(1+r)^9. Solving for r, we get: r = 0.069 or 6.9%.

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Answer:

There is a difference of 51 degrees

Step-by-step explanation:

-13 to zero is 13 degrees

zero to 38 degrees is 38 degrees

13 + 38 is an increase of 51 degrees

Answer:

113.04

Step-by-step explanation:

see attached

Answer:

11 and 12

Step-by-step explanation:

Solving this would be the case of finding that square root of 131, then rounding both up and down.

First, to solve

The square root of 131 is 11.45

Now we take that 11.45 and round both up and down

Rounding down is 11 and rounding up is 12.

11 and 12 are next to each other, making them consecutive.

Answer:

I think its 11 and 12

Step-by-step explanation:

The graph does not represent y as a function of x, as each value of x is mapped to two outputs.

The portion that could be removed to make it a function is given as follows:

y < 0.

Hence the domain and the range are given as follows:

A relation represents a function when each input value is mapped to a single output value.

On the circle, a vertical line through the circle would cross the line twice, meaning that each input is mapped to two outputs, hence the relation is not a function.

We have to remove one of the outputs for the relation to be a function, hence, removing y < 0, the domain and the range are given as follows:

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The initial battery charge was of:

19%.

The time it takes for the battery to be full is of:

32.4 minutes.

The linear function in slope-intercept format is given as follows:

y = mx + b

In which:

Each minute , the percentage of battery’s capacity that was charged increased by 2.5 percent, hence the slope m is given as follows:

m = 2.5.

Hence:

y = 2.5x + b.

After 17 minutes of charging the battery was 61.5 percent full, hence when x = 17, y = 61.5, and the intercept b is obtained as follows:

61.5 = 2.5(17) + b

b = 61.5 - 2.5 x 17

b = 19.

The battery is fully charged when y = 100, hence the time is obtained as follows:

2.5x + 19 = 100

2.5x = 81

x = 81/2.5

x = 32.4 minutes.

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