If BC= 6x+6 , AB= 8x+9 , and AC=142 find BC

To know if 2/5 and 6/15 are equivalent, we do a multiplication, then,

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{2}{3}=\frac{2\times2}{5\times2}=\frac{4}{10} \ \ \longmapsto \ Not \ the \ result } \end{gathered}$} }[/tex]

Since if we try it with number 1, the result would be the same, then we continue with 2 being closer, then we continue with number 3, successively, until we reach the expected answer.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{2}{3}=\frac{2\times3}{5\times3}=\frac{6}{15} } \end{gathered}$} }[/tex]

the probability that Ron will get in trouble with Professor Snape at least two times in one day is 0.7

We are given

  X    0         1        2         3        4

P(X)    0.15   0.20   0.20   0.30   0.15

we want Ron Weasley to get in trouble at least two time in one day

that mean X 2

P(X 2) = P(X=2) + P(X=3) + P(X=4)

= 0.20+0.30+0.15

= 0.65= 0.7 (rounded to nearest tenth)

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1) Let's sketch this out so that we can better understand it

2) Reminding ourselves of the metric relations of a right triangle we can write out the following:

Note that the radius intersects that chord with a 90º angle so it bisects that chord.

She invested $2,400 in the 2.5% account and $3,600 in the 4% simple interest account

Here, we want to know the amount of money invested in each account

Let the amount invested in the 4% simple interest account be $x ----> (a)

While the amount invested in the 2.5% account be $y -------->(b)

So mathematically;

Both the interests are added to get total interest

x + y = 6,000 ••••••(i)

Let’s now evaluate the interest

for the 4% account , interest = 4/100 * x = 4x/100

For the 2.5% account, interest = 2.5/100 * y= 2.5y/100

The addition of both  interests gives the total simple interest;

4x/100 + 2.5y/100 = 204

Multiply through by 100

4x + 2.5y = 20,400 •••••••(ii)

From i, x = 6,000 - y

Putting this into equation ii

4(6,000-y) + 2.5y = 20,400

24,000 - 4y + 2.5y = 20,400

24,000-20,400 = 4y - 2.5y

1.5y = 3,600

y = 3,600/1.5

y = $2,400

Recalling it again,

x = 6000 - y

x = 6,000 - 2,400

x = $3,600

Therefore, Nina invested $2,400 in the 2.5% account and $3,600 in the 4% simple interest account

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The expression for volume is (28-2x)(22-2x)x and when x=6, the volume is 840 inch^3.

A 3D object's volume is the amount of actual space it occupies. It is a 2D shape's 3D equivalent of area. It is quantified in cubic units like cm3. It means that the amount of space a closed form can occupy in three dimensions depends on its volume. Volume is a gauge of a thing's potential. For instance, a cup is said to have a 100 ml capacity if the brim can hold 100 ml of water. Another way to measure volume is the amount of space a three-dimensional item takes up.

According to question,

Let x be the height of the cubic box

Length = (28-2x)

Breadth = (22-2x)

Volume = x(28-x)(22-x)

When x =6

Volume = 6(28-6×2)(22-6×2)

=6(10)(14)

=840 inch^3

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The enlarged node that the nurse should suspect that the client has a blockage within the right lymphatic duct is the right cervical node

A network of tissues, blood arteries, and organs called the lymphatic system collaborates to transport lymph, a colorless, watery fluid, back into your circulatory system. Every day, your body's arteries, smaller arteriole blood vessels, and capillaries circulate about 20 liters of plasma.

The right lymphatic duct receives drainage from the right cervical node. The thoracic duct receives drainage from the superficial popliteal, superficial inguinal, and lumbar nodes. The sides and back of the neck include the cervical lymph nodes.

Typically, these glands are incredibly tiny. A lymph node, however, is swollen if its diameter is higher than 1 centimeter. Deep inside the neck, the cervical lymph nodes are located.

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Answer:

I believe it stands for Side, Side, Side

Step-by-step explanation:

When two triangles with all three sides are equal they're SSS

Answer:

The biker's pace is 25 miles per hour and the walker's speed is 50/3 miles per hour.

Answer:The speed of the walker is 16.67 miles per hour.

The speed of the cyclist is 25 miles per hour.

How to calculate the value?

Let the speed of a walker = x

Biker's speed = 1.5x

Their relative speed will be:

= 1.5x - x = 0.5x

Distance between them = 12.5 miles

Time taken = 1.5 hours.

It should be noted that distance will be:

= Speed × Time

12.5 = 1.5 × 0.5x

Divide through to get x

12.5 = 0.75x

x = 16.67 miles per hour.

Speed of cyclist = 16.67 × 1.5 = 25 miles per hour.

As per the terms from the two sequences given in tables as attachment hereby along with the question statement, the following statements from the provided options are true.

(i) [(a₁) > (g₂)]

(iv) Initially (aₙ) is greater than (gₙ), and as "n" gets larger, (gₙ) is greater than (aₙ).

As per the question statement and the reference tables attached thereby along with the question, we are provided with terms from the two sequences in table format, and five statements based on the sequences.

We are required to determine which statements among the five, are true.

To solve this question, we will use the trial-and-error method, where we will consider individual statement and assess it's honesty.

First statement is [(a₁) > (g₂)], which is true. As we can see from the table, that, [(a₁) = 10] and [(g₂) = 4], i.e., (10 > 4), or, [(a₁) > (g₂)].

Second statement is that, "The constant difference for (aₙ) is 10" which is False. We can clearly see from the table that, (a₁ = 10), (a₂ = 15), (a₃ = 20), (a₄ = 25) and so on, and [(25 - 20) = (20 - 15) = (15 - 10) = 5], i.e.,

[(a₄ - a₃) = (a₃ - a₂) = (a₂ - a₁) = 5]. Hence, the common difference for (aₙ) is 5, and not 10.

Third statement is that, "(aₙ) can be modelled by a linear function, and (gₙ) can be modelled by an exponential function" which is true for the first part, but false for the second, making the complete statement false as whole.
From the left hand side table, we can see that, (a₂ = 15) and (a₁ = 10),

Or, [a₂ = (10 + 5)]

Or, [a₂ = (a₁ + 5)]

Similarly, (a₃ = 20),

Or, [a₃ = (15 + 5)]

Or, [a₃ = (a₂ + 5)]

That is, we can generalise (aₙ) as

[aₙ = {(aₙ₋₁) + 5}] where, (n = 2, 3, 4, 5...) and (a₁ = 10).

Hence, (aₙ) can be modelled by a linear function.

But from the right hand side table, we can see that, (g₂ = 4) and (g₁ = 2),

Or, [g₂ = (2 * 2)]

Or, [g₂ = 2g₁]

Similarly, (g₃ = 8),

Or, [g3 = (2 * 4)]

Or, [g₃ = 2g₂], it goes on for (gₙ).

Therefore, we can generalise (gₙ) as

[gₙ = 2*(gₙ₋₁)] where, (n = 2, 3, 4, 5...) and (g₁ = 2).

Here, (gₙ) can also modelled as a linear function and not as a exponential function (which goes in the form of "xⁿ").

Coming to the fourth statement, "Initially (aₙ) is greater than (gₙ), and as "n" gets larger, (gₙ) is greater than (aₙ)" is true, as from both the tables,

For (n = 5), [aₙ = a₅ = (a₄ + 5) = (25 + 5) = 30],

And [gₙ = g₅ = (2 * g₄) = (2 * 16) = 32], which is greater than 30,

Or, [(g₅) > (a₅)].

Similarly, for (n = 6), (a₆ = 35) while (g₆ = 64), i.e., [(g₆) > (a₆)], and it continues for greater values of "n".

Coming to the last statement, that [a₁₀ > g₆], is false. As we can observe from the both the tables and their sequence,

For (n = 5), (aₙ = 50), for (n = 6), (aₙ = 35), for (n = 7), (aₙ = 40), for (n = 8), (aₙ = 45), for (n = 9), (aₙ = 50) and for (n = 10), (aₙ = 55),

While on the other hand, for (n = 5), (gₙ = 32) and for (n = 6), (gₙ = 64).

Since (64 > 55), therefore, [(g₆) > (a₁₀)].

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Answer:

explain  15/256

Answer: x= 11

Step-by-step explanation:

Answer:

x=11

Step-by-step explanation:

im assuming u r trying to find x

you need to solve the bracket first (2×x =2x , 7×2= 14)

After that move numbers with x to ur left, to make life easier

3x-2x= x

14-3 = 11

x=11

The angles ∠4 and ∠6  are found to be supplement angles.

For the given question;

∠5 ≅ ∠6 ( both are congruent means equal)

As, ∠4 and ∠5 are forming on the straight line. Thus,

∠4 + ∠5 = 180 (linear pair)

But, ∠5 ≅ ∠6 , replacing ∠5 with ∠6 .

∠4 + ∠6 = 180 supplement angles.

Thus, ∠4 and ∠6 are found to be supplement angles.

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===============================================

Work Shown:

1 foot = 12 inches

3*1 foot = 3*12 inches

3 feet = 36 inches

I multiplied both sides by 3 so that the "12" turns into "36".

Answer:3 feet

36/12=3

3x12=36

so 36 inches= 3 feet

hope it helps

The statement that The cube root of zero is zero is true .

The number that results in the original number after being multiplied three times is known as the cube root of a number.[tex]\sqrt[3]{}[/tex] The sign is used to represent a number's cube root in radical form.

The cube root of 0 will be calculated and explained here. First, observe that the mathematical symbol for the cube root of O is as follows:

[tex]\sqrt[3]{0}[/tex]

The number (n), which you can multiply twice by itself to get the number zero, is the cube root of zero. Alternatively, n×n×n should equal 0. Consequently, the following equation can be used to address the issue:

[tex]n^{3}[/tex] = 0

The answer to the cube root of 0 is as follows when the aforementioned equation is solved:

[tex]\sqrt[3]{0}[/tex]= 0

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Answer: 2080

Step-by-step explanation:

62² −42²

3844−42²

3844−1764

2080

Answer:

y = 6m - 13

Step-by-step explanation:

Parallel lines have the same slope.  The slope in the equation y = 6x -2 is 6.

To write an equation in the slope intercept form, we need a slope and a y-intercept.  We have the slope, we need to find the y-intercept.

To find the y intercept, we need a slope, and x on the line and a y on the line.  The point (3,5) gives us the x and the y.

slope = 6

x = 3

y = 5

y = mx + b  plug in what we know and solve for b

5 = 6(3) + b

5 = 18 + b  Subtract 18 from both sides of the equation

-13 = b

y = mx  + b

y = 6m - 13

Answer: 8.75

Step-by-step explanation:

3 1/8 into a decimal is 3.125

3 1/2 into a decimal in 3.5 or 3.50

4/5 into a decimal is 0.8 or .8

Then just multiply 3.125 and 3.5 and you get 10.9375

Next, multiply 10.9375 by 0.8 and you get 8.75

Therefore your answer is 8.75

The exponents are solved below\

What are exponents?

Exponentiation is a mathematical process denoted by the symbol bn that involves two integers, the base b and the exponent or power n, and is spoken as "b (raised) to the (power of) n." Exponentiation corresponds to repeated multiplication of the base when n is a positive integer: bn is the product of multiplying n bases. Typically, the exponent is displayed as a superscript to the right of the base. In such scenario, bn is referred to as "b raised to the nth power," "b (raised) to the power of n," "the nth power of b," "b to the nth power," or, more succinctly, "b to nth." In other words, when a base raised to one exponent is multiplied by the same base raised to another exponent, the exponents accumulate.

The exponents are solved as follows

(10⁻²)⁹ = 10⁻¹⁸ = 1/10¹⁸

10⁻³ - 10⁻⁸ = 1/10³ - 1/10⁸ = (10⁵ - 10⁸)/10⁸ = 9.9999x10⁻⁴

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The probability of all XY in a group of four siblings is 1/16 (6.5%), and also the probability of all XX offspring is 1/16 (6.5%).

Let us first know how do chromosomes work?

Long DNA molecules called chromosomes contain all or a portion of an organism's genetic code. Males receive one X and one Y chromosome from each parent, whereas females receive two X chromosomes from each parent.

For females, the likelihood or probability of inheriting two X chromosomes is 1/2 (50%) while for men, the probaility of receiving one X chromosome and one Y chromosome is similarly 1/2.

Therefore, the probability that all XY siblings are present in a group of 4 siblings is:

[tex]1/2 * 1/2 * 1/2 * 1/2 = 1/16[/tex]

Also the probability that a family of four siblings or offspring includes all XX is

[tex]1/2 * 1/2 * 1/2 * 1/2 = 1/16[/tex]

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The probability of all XY in a group of four siblings is 1/16 (6.5%), and also the probability of all XX offspring is 1/16 (6.5%).

For females, the likelihood or probability of inheriting two X chromosomes is 1/2 (50%) while for men, the probability of receiving one X chromosome and one Y chromosome is similarly 1/2.

Therefore, the probability that all XY siblings are present in a group of 4 siblings is:

1/2*1/2*1/2*1/2=1/16

Also the probability that a family of four siblings or offspring includes all XX is

1/2*1/2*1/2*1/2=1/16

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Answer:

13 sec

Step-by-step explanation:

Prius' acceleration

  60 mi/hr = 88 ft s

accel = change  in v / change in time =  88 f/s  / 10.3 s = 8.54 ft / s^2

F = ma     =    2903 * 8.54 = 24802  lb ft/s^2

Now increase the mass to 4903 by adding a 2000 lb trailer  (which, by the way is way past the towing capacity of an anemic Prius !)

    F = ma

   24802 = 4903 a    shows a = 5.06 ft/s^2

  45 mi/hr = 66 ft/s

      a = change in v / change in time

      5.06 = 66 / 5.06 = 13 sec

Answer:

x² + 4x - 12

Step-by-step explanation:

Roots: -6 and 2

Leading coefficient: x²

(x + 6)(x - 2)

x(x - 2) + 6(x - 2)

x² - 2x + 6x - 12

x² + 4x - 12

I hope this helps!

Mark has 35 unique combinations to choose from, so can he co go 5 weeks with this set of clothes

Number of pants in Mark's closet = 5

Number of shirts in Mark's closet = 7

Combinations are ways to choose elements from a collection in mathematics where the order of the selection is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.

He can choose amongst the pants in 5 ways, similarly, he can choose among the shirts in 7 ways

Total number of combinations = 5*7 = 35 unique combinations

So, if he wears one combination each day he can last 35 days or 5 weeks, without buying new clothes

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Answer: no equation can pass through those points

Step-by-step explanation:

the x value -4 has two y values, 5 and -2. a function needs at most 1 y value to be considered a function.

These work out to 60,466,176 case insensitive combinations of letters.

There are 10 digits 0–9.

The are 26 letters in the modern alphabets.

However, you didn’t specify whether capital and lowercase letters count as the same letter or separate. In the former case, there are 26 letters, in the latter, there are 52.

There is also such a thing as lowercase numbers, but since they aren’t in common standard usage, I won’t count those.

You also didn’t specify that characters couldn’t be repeated, so I am going to assume that the same character can appear multiple times in a 5 character combination.

Also, since the combinations are an alphanumeric string of characters rather than a number, I will assume that leading zeroes are allowed.

So, there are either 36 (10 digits and 26 letters).

To find the number of combinations you multiply the number of possibilities for each character;

36 x 36 x 36 x 36 x 36

These work out to 60,466,176 case insensitive combinations of letters.

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Answer:  The answer is 5 shirts

Step-by-step explanation:

8x + 6 = 50

subtract 6 from each side:

8x +6 (-6) = 50 (-6)

8x=44

divide by 8:

8x/8=44/8

x=5.5

round to single shirts:

x=5 shirts

Answer:

Step-by-step explanation: you have to divide 50 by 8 then get your answer of 6.25, but you also have to consider two things; the extra $6.00 flat fee, and you cant buy 6.25 shirts, so what we do is multiply 8 times 6 to get 48, but we have to consider the extra $6.00, so you take away 8 which gives you 5 shirts, plus the shipping fee so in all he can buy 5 shirts.

Given: Pair of parallel lines and a transversal with angles x and y.

Required: To determine which type of angles are formed by x and y.

Explanation: Consider the following figure below showing a pair of parallel lines and a transversal

In the figure, line l is parallel to line m, and line n is the transversal.

Further alternate angles are the pair:

The angles lying inside the parallel lines are alternate interior, while the angles lying outside the parallel lines are the alternate exterior.

While the corresponding angles are the pair:

Finally, the consecutive interior angles are the pair of non-adjacent angles that lie on the same side of the transversal. In the figure above, the consecutive interior angles are:

Hence the given pair of angles x and y are consecutive interior angles.

Final Answer: Option D is correct.

Factors of 50 are the numbers which on dividing 50 leave no remainder. 50 is a composite number, therefore, it has more than 2 factors.

We can get the factors of 50 by Prime Factorization. We can draw a factor tree to get the prime factors of 50 as shown below:

Therefore, the prime factors are:

Hence, the other factors are:

Therefore, the factors of 50, including 1 and 50, are:

The question asks to sum all the factors between 1 and 50. This means that 1 and 50 are not included in the sum.

Therefore, the sum will be:

The correct option is OPTION A.

Answer:

x = -1, y = -1

Step-by-step explanation:

[tex]4x + 3 = - 8x - 9[/tex]

[tex]12x + 3 = - 9[/tex]

[tex]12x = - 12[/tex]

[tex]x = - 1[/tex]

[tex]y = 4( - 1) + 3 = - 4 + 3 = - 1[/tex]

Given the points A(3,4) and B(-1,10), we can find the distance between them using the following function:

then, we have the following: