please answer and explain how to get it.

To show that the angle bisector of an equilateral triangle is perpendicular to the base​, we can assume an equilateral triangle with sides ABC. Next, we can get an angle bisector in the middle represented by BD which becomes perpendicular to the base BC.  

After getting the angle bisector, we would see that the line segment BD, divides angle BAC into two equal angles, each measuring 30 degrees. Now, we can draw a perpendicular line from point D to the base BC.

We could also draw a line E, which is the perpendicular line that intersects the base BC. We want to show that BD is perpendicular to BC, which means we need to show that angle BDE is a right angle.

Since the sum of angles BDA and ADE is 90 degrees (they form a right angle), and the sum of angles BAD, ABD, and BDA is 180 degrees, it follows that angle BDE must be a right angle.

Therefore, we have shown that the angle bisector of an equilateral triangle is perpendicular to the base.

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The formula for the nth term of the arithmetic sequence is an = 4n + 2

Let d be the common difference of the arithmetic sequence, and let a1 be the first term. Then we have:

a4 = a1 + 3d = 10

a6 = a1 + 5d = 18

We can solve this system of equations to find a1 and d. Subtracting the first equation from the second, we get:

2d = 8

d = 4

Substituting this into either of the original equations, we get:

a1 + 12 = 18

a1 = 6.

So the arithmetic sequence is:

6, 10, 14, 18, ...

To find the nth term of this sequence, we can use the formula:

an = a1 + (n - 1)d

Substituting in the values of a1 and d, we get:

an = 6 + 4(n - 1)

Simplifying, we get:

an = 4n + 2

Therefore, the formula for the nth term of the arithmetic sequence whose fourth term is 10 and sixth term is 18 is:

an = 4n + 2

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Answer: The answer is D

Answer:

The equation x - y = 7 represents a linear equation with two variables, x and y. To find three ordered pairs (x, y) that satisfy this equation, we can arbitrarily choose values for one variable and solve for the other.

Ordered Pair 1:

Let's choose x = 0:

x - y = 7

0 - y = 7 (Substituting x = 0)

y = -7

So, the first ordered pair is (0, -7).

Ordered Pair 2:

Let's choose y = 0:

x - y = 7

x - 0 = 7 (Substituting y = 0)

x = 7

So, the second ordered pair is (7, 0).

Ordered Pair 3:

Let's choose x = 5:

x - y = 7

5 - y = 7 (Substituting x = 5)

y = -2

So, the third ordered pair is (5, -2).

Therefore, three ordered pairs (x, y) that satisfy the equation x - y = 7 are: (0, -7), (7, 0), and (5, -2).

Answer:8%

Step-by-step explanation:

you divide 25 by 32 and round to nearest tenth

hope this helps :)

The equation of exponential function of following table is represented by the table below is y = A(Bˣ).

An exponential function is a mathematical function denoted by f(x) = eˣ (where the argument x is written as an exponent). Unless otherwise stated, the term usually refers to positive-valued functions of real variables, but can be extended to complex numbers and generalized to other mathematical objects such as matrices and Lie algebras. Although the exponential function arose from the notion of exponentiation (iterative multiplication), its modern definition (which has several equivalent characterizations) allows it to be extended exactly to any real argument, including irrational numbers. Its ubiquitous appearance in pure and applied mathematics has led mathematician Walter Rudin to believe that the exponential function is "the most important function in mathematics."

To find the equation of exponential form:

For case 1,

Exponential form: y = A(Bˣ)

y = 0.1, x = 0

[tex]0.1 = A(B^{0})[/tex]

0.1 = A(1)

A = 0.1

For case 2,

Exponential form: y = A(Bˣ)

y = 0.05, x = 1

[tex]0.05 = 0.1(B^{1})[/tex]

B = 0.5

For case 3,

y = 0.025, x = 2

[tex]A = 0.1(B^{2})[/tex]

[tex]0.025 = 0.1(0.5^{2})[/tex]

0.025 = 0.025

For case 4,

y = 0.0125, x = 3

0.0125 = 0.1(0.5³)

0.0125 = 0.1(0.125)

0.0125 = 0.0125

We calculated the value of A and B, and proved it in case 3 and case 4.

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The complete question is as follows:

Find the equation of the exponential function represented by the table below:

Answer: 13 units

Step-by-step explanation:

If you look at the corresponding side on the other triangle, it is also 13, and in the question it say the side on the other triangle has the same length as the one you are finding.

Answer:

Angle 1 = 51.6°

Angle 2 = 38.4°

Step-by-step explanation:

All complimentary angles add up to 90°.

If two complimentary angles were congruent then their measures would both be 45°.

Since one angle's measure is 6.6° more than the other's measure, it's measure is 6.6° more than 45°

Vice versa for the second angle, its measure will be 6.6° less than 45°

The better prediction for y, when x = 74, based on the scatter plot, can be found to be 57.

Looking at the scatter plot, the better prediction of y when the value of x is 74 can be found by looking for the values of y that have a value of x that is around 74.

From the scatter plot, we see that the value of x of 74, would correspond with the value of y of 57. We can therefore infer that y = 57 is the better prediction for x = 74.

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Step-by-step explanation:

you remember the priorities of mathematical operations :

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

it is irrelevant how close or how far apart the operands are written.

I think, missing operators are multiplications.

so, by writing really everything

(7 × 6) ÷ 2 × [{45 + 3 × (7 × 2 - 15 + 6)} + 4]

we get in a first step :

(42) ÷ 2 × [{45 + 3 × (14 - 15 + 6)} + 4]

second step

21 × [{45 + 3 × (5)} + 4]

third step

21 × [{45 + 15} + 4]

fourth step

21 × [60 + 4]

fifth step

21 × 64

sixth step

1,344

Using the power reducing formulas the expression [tex]5cos^4(x) = 5(1 + cos(2x))^{2/4}[/tex].

We can define higher powers of a trigonometric function in terms of lower powers of the same function using the power-reducing formulas, which are trigonometric identities. Higher powers of cosine can be expressed using this formula in terms of sine and cosine's initial powers. For the other trigonometric functions, such as sine and tangent, there are equivalent formulas. These formulas can be used to solve trigonometric equations and to simplify trigonometric expressions.

The given function is 5cos^4(x).

Now, the power reducing formulas are given by:

[tex]cos(2x) = cos^2(x) - sin^2(x) = 2cos^2(x) - 1\\cos^2(x) = (1 + cos(2x))/2[/tex]

Substituting the value of second equation in 1 we have:

cos(2x) = 2(1 + cos(2x))/4 - 1

[tex]cos(2x) = (2cos^2(x) - 1) = cos^2(x) - sin^2(x)[/tex]

Now we have:

[tex]cos^2(x) = (1 + cos(2x))/2[/tex]

Thus,

[tex]cos^4(x) = (1 + cos(2x))/2)^2[/tex]

Now multiplying by 5:

[tex]5cos^4(x) = 5(1 + cos(2x))^{2/4}[/tex]

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If piece of cake has area of 100 in² and sweeps angle of 50°, then the radius of the cake is 15.13 inches.

The area of the piece of cake is given as 100 square inches and

The piece of cake sweeps out an angle of 50 degrees, we have to find the radius of the cake;

We know that "Area" of a sector of a circle is given as : A = (θ/360)πr²,

where A = area of the sector, θ is = angle swept by sector, and r is radius of circle,

We know that area of "piece-of-cake" is = 100 square inches and

The "angle-swept' by the piece is = 50 degrees.

Substituting the values in area of sector formula,

We get,

⇒ 100 = (50/360)πr²,

⇒ r² = (100 × 360)/(50π)

⇒ r ≈ 15.13,

Therefore, the radius of the cake is approximately 15.13 inches.

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The cube's volume can be expressed as V = s³ = x³ since the height of the cube is x and all sides have equal length. The surface area of the cube can be expressed as SA = 6s² = 6x².

b. The sphere's volume can be expressed as V = (4/3)πr³, where r is half the diameter or x/2. Therefore, V = (4/3)π(x/2)³ = (1/6)πx³.

The surface area of the sphere can be expressed as SA = 4πr² = 4π(x/2)² = πx².

c. The ratio of the cube's volume to its surface area can be expressed as V/SA = (x³)/(6x²) = x/6, with the restriction that x > 0.

d. The ratio of the sphere's volume to its surface area can be expressed as V/SA = [(1/6)πx³]/(πx²) = x/6, with the restriction that x > 0.

e. Since the ratios of the volumes to the surface areas of the containers are the same, the efficiency of the packaging will depend only on the amount of material required for each shape. The cube will require less material since it has a smaller surface area, making it the more efficient choice.

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The values of x, y and z are given as follows:

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The bases for the triangle in this problem are given as follows:

6 and 19.

Hence the segment x is obtained as follows:

x² = 6 x 19

x = sqrt(6 x 19)

x = 10.68.

Applying the Pythagorean Theorem, the value of y is given as follows:

y² = 6² + 10.68²

y = sqrt(6² + 10.68²)

y = 12.25.

The value of z is given as follows:

z² = 10.68² + 19²

z = sqrt(10.68² + 19²)

z = 21.8.

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The rectangle with largest area has length 3 and width 3/2, with an area of 9/2.

What is a rectangle?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. As a result, it is sometimes referred to as an equiangular quadrilateral. Because the opposing sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

The equation for the area of a rectangle is length * width. For us here, it would be x * y. We can substitute the equation of the line for y and get

A = x * (6-x)/2

A = 3x - x2/2

To find the maximum of this equation, we first need to find a critical point. So we take the derivative and find the zeros:

A' = 3 - x = 0

x = 3

So we have a critical point at 3, which happens to be the maximum of the area equation. We plug this back into the line equation to get y:

y = (6 - 3)/2 = 3/2

So the rectangle with largest area has length 3 and width 3/2, with an area of 9/2.

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Answer:

955 11 7 11

3101 thats my answer

Step-by-step explanation:

10 and 3 thank you

The volume of the triangular prism will be 400 cubic feet.

Given that:

Width, W = 15 feet

Height, h = 8 feet

Base length, b = 6²/₃ feet

Volume is a measurement of three-dimensional space that is utilized. The concept of length is linked to the notion of capacity.

The volume of the triangular prism is calculated as,

V = 1/2 · b · h · W

V = 0.5 · 6²/₃ · 8 · 15

V = 400 cubic feet

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The equation for the best fit of the scatter plot is y = x - 3

What is the scatter plot?

In a scatter plot, dots are used to represent the values of two different numerical variables. The values of each data point are represented by the position of each dot on the horizontal and vertical axes. Use scatter plots to see how different variables are related to one another.

Given data,

Let the scatter plot be represented as A

Now, the value of A is plotted below

where the slope of the plot is given by

m = y / x

m = 1

And, the y-intercept of the plot is when x = 0

So , when x = 0 , y = -3

Hence, the scatter plot is y = x - 3

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The ratios of each type are:

1/4 has big beak (BB)

2/4  has big short beak (Bb)

1/4 has short beak (bb)

A Punnett square is a diagram used to predict the possible outcomes of a genetic cross between two individuals.

               B          b

B            BB        Bb

b             Bb        bb

We have 1 BB, this implies that we have one bird with big beak.

We have 2 Bb, this implies that we have two bird with big short beak.

We have 1 bb, this implies that we have one bird with short beak.

The ratios of each type are:

1/4 (i.e. 25%) has big beak (BB)

2/4 (i.e. 50%) has big short beak (Bb)

1/4 (i.e. 25%) has  short beak (bb)

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Answer:

Step-by-step explanation:

You want the equations for the lines shown on the graph.

The slope-intercept form of the equation for a line is ...

  y = mx + b

where m is the slope, and b is the y-intercept.

The slope of a line is the ratio of its "rise" to its "run". The rise and run are the vertical distance and horizontal distance between two points, respectively. We usually want to choose points that are where the line crosses grid intersections, as this gives the most exact value for the slope.

Red line: There is no rise for any value of run. The slope is ...

  m = rise/run = 0/1 = 0

Green line: The green line crosses the y-axis at y = 1, and crosses the next grid intersection to the right at (1, -1). The rise between those points is -2 (2 grid squares down), and the run is 1 (1 grid square to the right). The slope is ...

  m = -2/1 = -2

Blue line: The blue line crosses the y-axis at y = -1, and crosses the next grid intersection to the right at (1, 1). The rise between those points is +2 (2 grid squares up), and the run is 1 (1 grid square to the right). The slope is ...

  m = 2/1 = 2

Yellow line: The yellow line crosses the y-axis at y = -1, and crosses the next grid intersection to the right at (2, -2). The rise between those points is -1 (1 grid square down), and the run is 2 (2 grid squares to the right). The slope is ...

  m = -1/2

Y-Intercept.

The y-intercept is the value of y where the line crosses the y-axis. In the slope-intercept form equation (y=mx+b), this is the value of 'b'. In the previous section, we used those crossings as one of the grid intersections for finding the slope. They are ...

Using the slope and y-intercept for each line, we can now write the equations:

__

Additional comment

The slope-intercept form of the equation is not the only possible way to write an equation for a line. There are more than half a dozen other ways an equation for a line can be written. Each will have its use.

Other forms include ...

  ax +by = c . . . . . . . standard form

  ax +by -c = 0 . . . . . general form

  x/a +y/b = 1 . . . . . . . intercept form

  y -k = m(x -h) . . . . . point-slope form

Intercept forms don't work well when one of the intercepts is missing. For the red line, the x-intercept is missing. Essentially, the x-terms disappear from the standard, general, and intercept form equations. In the point-slope form, the equation of the red line is y-5=0, since the slope is 0.

Answer:

Using the Pythagorean theorem, the length of the rope can be found as follows:

c^2 = a^2 + b^2

where c is the length of the rope, a is the height of the fence (8 feet), and b is the distance from the fence to the point where the rope is attached to the ground (6 feet).

Plugging in the values, we get:

c^2 = 8^2 + 6^2

c^2 = 64 + 36

c^2 = 100

c = √100

c = 10

Therefore, the length of the rope is 10 feet.

Answer:

The length of the rope is 10 feet.

Step-by-step explanation:

To find the length of the rope attached to the top of an 8-foot-tall fence and fastened to the ground 6 feet away, we can use the Pythagorean theorem, which states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. In this case, the vertical leg is the height of the fence (8 feet) and the horizontal leg is the distance from the base of the fence to where the rope is fastened (6 feet). Therefore, the length of the rope (the hypotenuse) is given by:

hypotenuse^2 = vertical leg^2 + horizontal leg^2

Substituting the values, we get:

hypotenuse^2 = 8^2 + 6^2

hypotenuse^2 = 64 + 36

hypotenuse^2 = 100

Taking the square root of both sides, we get:

hypotenuse = 10

So the length of the rope is 10 feet.

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Answer:

$525

Step-by-step explanation:

To calculate the sales commission for this employee, we need to first calculate the total sales made by the employee for the week. The employee made sales of 800 on Monday, 600 on Tuesday, 1300 on Wednesday, 800 on Thursday and 800 on Friday. The total sales made by the employee for the week is:

800 + 600 + 1300 + 800 + 800 = 4500

Since the employee does not earn sales commission for the first $1000 of sales but earns a 15% sales commission on all sales made thereafter, we need to calculate the commission earned on sales above $1000.

The total sales above $1000 is:

4500 - 1000 = 3500

The commission earned on sales above $1000 is:

3500 x 15% =$525

Therefore, the employee earned a sales commission of $525 this week.

Therefore, the expected value of the event P(2k) for 2 ≤ k ≤ 6, given the event E, is 96/1 or simply 96.

Probability theory is widely used in many fields, including mathematics, statistics, physics, engineering, economics, and social sciences. It provides a framework for analyzing and understanding uncertain events and making predictions based on available information. Probability theory is also used in decision-making, risk management, and game theory, among other applications.

Here,

We can start by calculating the probability of each event in the sample space:

P(1) = 1/32

P(4) = 1/8

P(8) = 1/4

P(16) = 1/2

P(32) = 1

P(64) = 1

Next, we can calculate the probability of the event E by summing the probabilities of the individual outcomes in E:

P(E) = P(1) + P(8) + P(32) + P(64)

= 1/32 + 1/4 + 1 + 1

= 33/32

Now, we can calculate the expected value of the event P(2k) for 2 ≤ k ≤ 6:

E[P(2k)] = Σ[2 ≤ k ≤ 6] P(2k) * ΘS(2k)

= P(4)*ΘS(4) + P(8)*ΘS(8) + P(16)*ΘS(16) + P(32)*ΘS(32) + P(64)*ΘS(64)

= (1/8)*4 + (1/4)*8 + (1/2)*16 + (1)*32 + (1)*64

= 4/8 + 8/4 + 16/2 + 32 + 64

= 1/2 + 2 + 8 + 32 + 64

= 106.5

Therefore, the expected value of the event P(2k) for 2 ≤ k ≤ 6, given the event E, is 106.5. However, since the event E has a probability greater than 1, this result does not make sense. So, we need to normalize the probabilities of the events by dividing them by P(E) to obtain the correct expected value:

P'(1) = P(1)/P(E) = (1/32)/(33/32) = 1/33

P'(8) = P(8)/P(E) = (1/4)/(33/32) = 8/33

P'(32) = P(32)/P(E) = 1/(33/32) = 32/33

P'(64) = P(64)/P(E) = 1/(33/32) = 32/33

Now, we can calculate the normalized expected value:

E[P(2k)] = Σ[2 ≤ k ≤ 6] P'(2k) * ΘS(2k)

= P'(8)*ΘS(8) + P'(32)*ΘS(32) + P'(64)*ΘS(64)

=(8/33)*8 + (32/33)*32 + (32/33)*64

= (64/33) + (1024/33) + (2048/33)

= 3136/33

= 96/1

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Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4 using trigonometric ratio.

We know that the point (-3, 4) is on the terminal side of the angle θ, and we can use the Pythagorean theorem to find the value of the hypotenuse:

r² = x² + y²

r² = (-3)² + 4²

r² = 9 + 16

r² = 25

r = 5

Now we can find the values of sin θ, csc θ, and cot θ:

sin θ = y/r = 4/5

csc θ = r/y = 5/4

cot θ = x/y = -3/4

Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4.

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Since 260 is close to 264, our answer of 264 is reasonable.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.

The sum of 401-137 can be found by subtracting 137 from 401:

401 - 137 = 264

Therefore, the sum of 401-137 is 264.

To estimate whether this answer is reasonable, we can use rounding. We can round 401 to 400 and 137 to 140, which makes the subtraction easier to estimate mentally:

400 - 140 ≈ 260

Since 260 is close to 264, our answer of 264 is reasonable.

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Step-by-step explanation:

slope,   m = ( y1-y2) / (x1-x2)   = ( 6-8) / (12-28) =  -2 / -16 = 1/8