help....
delta math questions...

Answer:

x=15

Step-by-step explanation:

Use the Pythagorean Theorem: a^2+b^2=c^2

1. a = 20, b = x, c = 25

2. 20^2+b^2= 25^2

3. Expand: 400+b^2= 625

4. Subtract + Simplify: b^2= 625-400

5. Fully Solve: b^2 = 225 -> Square root of b^2 = Square root of 225

6. Last Step: Simplify: b = 15.

Here is a similar problem for you to solve, put your answer in the comments.

a= 12, b=5, c=?

Solve for c using the Pythagorean theorem.

The probability that each guest of each type m+n will receive a roll is 79.

Given that the breakfast should have consisted of three types of rolls, one each of the nut, cheese and fruit rolls, and the cook should have wrapped each of the nine rolls.

The denominator of m/n equals the total number of possible role configurations assigned to the three people. It [tex]${9 \choose 3}{6 \choose3}$[/tex] is the same as the number of ways to choose three roles out of 9 to give to the first person [tex]${9 \choose 3}$[/tex], and three rolls of 6 [tex]${6 \choose3}$[/tex]. After that, the remaining three roles have no more configurations.

The numerator is the number of ways to assign a roll of each type to each of the three people, which can be done by defining the three types of roles such as flavored x, flavored y and flavored z.

xxx, yyy, zzz

So we have to choose one x, one y and one z to give to the first person. There are 3x, 3y and 3z to choose from, resulting in 3³ combinations. Multiply that by the combinations of xs, ys and zs for the second person, which is clearly 2³ since there are two of each letter left. simplify to our fraction m / n, which is 9/70. If you add them together, you get 9 + 70 = 79.

Thus, the probability that each guest has obtained a roll of each type is m / n, where m and n are relatively prime, so m + n is 79.

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The angle formed by the line of sight and the horizontal line can best be described as an angle of elevation.

The angle of elevation is an angle that is formed between the horizontal line and the line of sight.

The angle of elevation is says to be the angle made between a horizontal plane and a straight line to a given object that is elevated off the ground.

Therefore, the angle formed by the line of sight and the horizontal line can best be described as an angle of elevation.

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⊰___________________ ___________________________________ __⊱

Answer:

Yes, it is a polynomial

Step-by-step explanation:

This polynomial is a trinomial, since it has 3 terms (the prefix tri means three) and its degree is 3 (the degree of a polynomial is the largest exponent in that particular polynomial).

Done !! Hope this made sense to you !!

⊰________________________________________________________⊱

[tex]\small{\pmb{\tt{CALLIGRAPHY}}[/tex]

Answer: (2, 18)

Step-by-step explanation:

When x=2, [tex]f(2)=2(3)^{2}=18[/tex].

So, it should pass through (2, 18).

Answer:

  a) payment: $1677.99

  b) total repaid: $604,076.40

  c) saved: $168,231.60

Step-by-step explanation:

The amortization formula can be used to find the monthly payment on the loan. The total repaid will be the sum of payments made. The amount saved will be the difference between the total repaid amounts for the different loans.

The payment A on a loan of principal P at annual rate r for t years is given by ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

The loan of interest is for $425,000 × (1 -30%) = $297,500. Then the payments on a 30 year loan are ...

  A = $297,500(0.0544/12)/(1 -(1 +0.0544/12)^-360) ≈ $1677.99

For a 15-year loan, the payments are ...

  A = $297,500(0.0544/12)/(1 -(1 +0.0544/12)^-180) ≈ $2421.36

The above calculation shows the monthly payment is $1677.99.

The total repaid is the sum of 360 monthly payments:

  360×$1677.99 = $604,076.40

The total repaid is the sum of 180 monthly payments:

  180×$2421.36 = $435,844.80

and the savings is ...

  $604,076.40 -435,844.80 = $168,231.60

__

Additional comment

We are asked to round to the nearest cent. The payment amounts here are accurately calculated to that precision. The total repaid on an actual loan will be slightly different, because the final payment will be slightly different.

The 30-year mortgage will have a slightly lower final payment because the monthly amount is rounded up. The 15-year mortgage will have a slightly higher final payment because the monthly amount is rounded down.

Overall, this means the totals of payments shown here, and their difference, vary slightly from the reality of loans of this kind. (They're probably not accurate to the nearest cent.)

Even using the "exact" payment value may not give the actual loan values. This is because the actual amortization schedule is rounded to the nearest cent each month. The cumulative effect of this rounding seems to be calculable only by figuring the 360 (or 180) actual monthly balance amounts.

We have calculated the answers in the manner we suppose is expected. Producing an actual amortization spreadsheet is a bit more work.

We have proven that ∠BEC ≅ ∠BCE by using the alternate interior angles theorem

From the question, we are to write a proof to prove that ∠BEC ≅ ∠BCE

From the given information, we have that

BC || EF

Note that line DE is a transversal

Thus, by the alternate interior angles theorem, we have that

∠BCE ≅ ∠FEC

Also, we were given that line EC bisects ∠BEF

That is,

Line EC divides ∠BEF into two equal angles.

Therefore,

∠BEC ≅ ∠FEC

By the substitution property of equality, we get

∠BEC ≅ ∠BCE

Hence, we have proven that ∠BEC ≅ ∠BCE by using the alternate interior angles theorem

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There is a total of 10 games played.

There are 5 players, If we select a given player, then that player will play one game with each of the other 4 players.

So we have 4 games at the moment.

Now we select one of the other 4 players, (we don't count the one we choose before). The one that we choose now will play one game wich each one of the remaining 3, so we add 3 more games.

Now we do the same with the remaining 3, this time we add 2 more games.

Now we do that with the remaining 2, now we add 1 more game.

Adding all the games we have:

4 + 3 + 2 + 1 = 10

There is a total of 10 games played.

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Answer:

856.5ft^2

Step-by-step explanation:

I took the test.

Answer:

53.7

Step-by-step explanation:

The area of the rectangular base is 7(2.3)=16.1.

So, the total volume is (1/3)(16.1)(10), which is about 53.7

The slope of the line is - 3 / 2 .

The slope of a line is the change in y coordinate with respect to the change in x coordinate.

Therefore, using (0, 6)(4, 0)

Hence,

m = slope = y₂ - y₁ / x₂ - x₁

slope = 0 - 6 / 4 - 0

slope = -6 / 4

slope = - 3 / 2

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No she is not correct 1/3 is great that 1/4

Answer:

No, she isn't correct because if the numerator are same but if denominators is different,then the fraction with smaller denominator is greater.

The possible outcomes are WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL

The given parameters are:

Coin = Head (H) and Tail (T)

Marble = W, B, B, B, R, R

See attachment for the tree diagram

From the tree diagram, we have the following possible outcomes

WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL

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52.94% of the viewers prefer videos on a mobile or laptop device

The given parameters are

Viewers that prefer videos on a mobile or laptop device = 18

Total number of viewers = 34

The percentage of voters in this category is then calculated as

Percentage = 18/34 * 100%

Evaluate the expression

Percentage = 52.94%

Hence, 52.94% of the viewers prefer videos on a mobile or laptop device

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Answer:

impossible

Step-by-step explanation:

a scalene triangle is a triangle in which all three sides are in different lengths, and all three angles are of different measures.

because all 3 angles must be different, they cannot be congruent.

because if angles are congruent, it means that they are of equal size.

the desired definition is a paradox or oxymoron. it contradicts itself and can never be true.

Answer:

it cannot have all angles congruent: impossible.

Step-by-step explanation:

by the definition scalene, it means no angle is the same length. meaning, to have all the sides congruent (the same length) that would be impossible and it can never happen. if you would like a congruent triangle, an isosceles or equilateral is the triangle you're looking for.

17.32 the number of units in the length of diagonal $DA$ of the regular hexagon.

Six equilateral triangles can be formed from the hexagon. The equilateral triangle has an equal length on each side. The diagonal of the hexagon is formed by joining two of the sum of the lengths of the equilateral triangles. As a result, the hexagon's diagonal is twice as long as its sides.

For a polygon, the SUM of the internal angles is:

(n-2) * 180 (n=6 for hexagon)

(6-2)*180 = 720   Thus EACH angle is :   720/6 = 120 degrees

Therefore, the triangle's main angle is 120 degrees, and its other two angles are equal.

There are 180 degrees in any triangle:  

(180-120) / 2 = 30 degrees for each of the smaller angles.

Now use the law of sines:

10/sin30 = x/(sin120)

10/(.5)  × (sqrt3 )/ 2 = x

10 sqrt 3

10/sin30  ×  sin 120  =  17.32

17.32 is the number of units in the length of diagonal $DA$ of the regular hexagon.

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The domain of the function is [1,  ∞) and the range is [0,  ∞)

The equation of the function is given as:

g(x) = 3√x - 1

The domain is the possible values of x.

Set the radicand to greater than or equal to 0

x - 1 >= 0

Add 1 to both sides

x >= 1

This can be rewritten as:

[1,  ∞)

Breakdown

g(x) = 3√x - 1

x - 1 >= 0

x >= 1

[1,  ∞)

The range is the possible values of y.

Set the radicand to 0

g(x) = 3 * 0

Evaluate the product

g(x) = 0

This can be rewritten as:

[0,  ∞)

Breakdown

g(x) = 3√x - 1

g(x) = 3 * 0

g(x) = 0

[0,  ∞)

Hence, the domain of the function is [1,  ∞) and the range is [0,  ∞)

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Answer:

Correct answer is D: [1, ∞) and R: (-∞, 0]

Step-by-step explanation:

Insert the given function on desmos to observe the following explanation.

The domain (x values) begin at 1, and go on to positive infinity (the squared bracket indicates a stop/start at that certain point). The range goes into negative infinity (y values) and begins at the y value of 0, so it does not go above that point on the y axis (hence the squared bracket).

The biotic factors of an ecosystem are arranged in feeding levels known as trophic levels.

The trophic level of an organism is the position it occupies in a food web. The trophic level of an organism is the number of steps it is from the start of the chain.

Below are the list of the trophic levels:

The biotic factors of an ecosystem are arranged in feeding levels known as trophic levels.

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Used formula

Answer:

6x+5

Step-by-step explanation:

the derivative of a sum is equal to the sum of derivatives:

(3x^2 + 5x + 2)' = (3x^2)' + (5x)' + (2)' = 6x + 5

Q.E.D.

The volume will be one-eighth times the volume.

The scale factor k is given as

k = 1/2

Let the initial volume be v

When each side is multiplied by the scale factor, we have the new volume to be

V = k^3 * v

Substitute 1/2 for k in the above equation

V = (1/2)^3 *v

Evaluate the exponent

V = 1/8 *v

This gives

V = 1/8v

Hence, the volume will be one-eighth times the volume.

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Answer:

x ≤ 135/2

Step-by-step explanation:

x is the cost per night. You have to pay for 2 nights, and you do not want to spend more than $135 total. Another way to say that, is you want to spend less than or equal to $135.

x = cost per night

2 = number of nights

2x = total cost

Total cost must be less than or equal to $135.

2x ≤ 135

Divide each side by 2.

x ≤ 135/2

Point [tex](1,5)[/tex] is a solution of the equation [tex]g(x)=3x+2[/tex] and point [tex](1,5)[/tex] is not a solution of equation [tex]f(x)=|x-1|+1[/tex]

Why point [tex](1,5)[/tex] is solution of the equation [tex]g(x)=3x+2[/tex] ?

If point [tex](1,5)[/tex] is solution of the equation then they must satisfy the equation.

So we need to check one by one

[tex](x,y)=(1,5)[/tex]

equation [tex]g(x)=3x+2[/tex]

We can write as

[tex]y=3x+2\\5=3*1+2\\5=5[/tex]

So  point [tex](1,5)[/tex] is solution of this equation.

Equation [tex]f(x)=|x-1|+1[/tex]

We can write as

[tex]y=|x-1|+1\\5=|1-1|+1\\5=0+1\\5\neq 1[/tex]

So point [tex](1,5)[/tex] is not solution of equation [tex]f(x)=|x-1|+1[/tex]

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A relationship between two variables in which the variables vary in the opposite direction (i.e., one increases while the other decreases, or vice versa) is referred to as a negative correlation.

When two variables move in opposite sizes and directions from one another, so that when one increases, the other drops, and vice versa, this is referred to as having a negative correlation or inverse correlation.

In order for investors to profit from price increases in some assets when others decline, negative correlation is used when building diverse portfolios.

Over time, the correlation between two variables might change significantly. Bonds and stocks typically have negative correlation.

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Using the Factor Theorem, the expression 3x² + 2 is factored as follows:

[tex]3x^2 + 2 = (\sqrt{3}x + i\sqrt{2})((\sqrt{3}x - i\sqrt{2}))[/tex]

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

In this problem, the expression is:

3x² + 2.

The roots are found as follows:

[tex]3x^2 + 2 = 0[/tex]

[tex]x^2 = -\frac{2}{3}[/tex]

[tex]x = \pm \sqrt{-\frac{2}{3}}[/tex]

[tex]x_1 = -i\sqrt{\frac{2}{3}}[/tex]

[tex]x_2 = i\sqrt{\frac{2}{3}}[/tex]

Hence the factored expression is:

[tex]3x^2 + 2 = \left(x + i\sqrt{\frac{2}{3}}\right)(x - 1\sqrt{\frac{2}{3}}\right) = (\sqrt{3}x + i\sqrt{2})((\sqrt{3}x - i\sqrt{2}))[/tex]

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The green mathematics tells about the impulse response of an in homogeneous linear differential operator.

According to the statement

we have to explain the green mathematics.

In mathematics, Actually there is a Green Function which was founded by a mathematician George Green.

In this function, a Green's function is the impulse response of an in homogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions.

The example of green function is the Green's function G is the solution of the equation LG = δ, where δ is Dirac's delta function; the solution of the initial-value problem Ly = f is the convolution (G ⁎ f), where G is the Green's function.

Actually in this function, it gives the relationship between the line integral of two dimensional vector over a closed path by a integral.

In this there is a green theorem, which  relates a line integral around a simply closed plane curve C and a double integral over the region enclosed by C.

So, The green mathematics tells about the impulse response of an in homogeneous linear differential operator.

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The terms that explains the value of Sin(pi/3) on the unit circle would be Sin(pi/3) = Opposite side of angle.

According to the statement

we have to give the terms which explain the sin (pi/3) perfectly.

And we have choose these terms from the these below written conditions like From Right Triangle, Hypotenuse, and unit circle.

And Now we explain all terms below

So,

"Right Triangle is a triangle whose one of the angle measures 90° "

And "The hypotenuse is a longest side of the right triangle.

And"Unit Circle is a circle with radius 1."

For given question,

We have been  given a unit circle.

So, We need to find the sin (pi/3)

We know, in a right triangle for any angle , θ

Sinθ = Opposite side of angle / Hypotenuse

So, for , Sin(pi/3) = Opposite side of angle / 1

Sin(pi/3) = Opposite side of angle

Therefore, The terms that explains the value of Sin(pi/3) on the unit circle would be Sin(pi/3) = Opposite side of angle.

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Using an exponential equation, supposing a rate of 5%, it is found that it will take about 2.9 years for Emma's balance to reach $450.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1+r)^t[/tex]

In which:

A(0) is the initial value.

r is the growth rate, as a decimal.

In this problem:

Her initial balance is of $300, hence . A(0)=300

The growth rate is of 15%, hence R =0.15

Then,

[tex]A(t) = A(0)(1+r)^t[/tex]

[tex]A(t) = 300(1+0.15)^t\\A(t) = 300(1.5)^t\\[/tex]

It will reach $450 after t years, for which A(t) = 450, hence:

[tex]A(t) =300(1.15)^t\\450= 300(1.15)^t\\1.15^t=\frac{450}{300}\\\\1.15^t =1.5\\log(1.15)^t=log1.5\\t log 1.15 = log 1.5\\t = \frac{log1.5}{log1.15}\\\\ t =2.9[/tex]

It will take about 2.9 years for Emma's balance to reach $450

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