A man writes 1 on the first line of his paper, then writes 2 and 3 on the second line, then 4, 5, and 6 on the third, and continues so that on any line n he writes the first n integers following the last integer on line n - 1. What is the sum of the first and last integers on line 17

Answer:

[tex]\huge\boxed{\sf The \ expression\ equals \ zero}[/tex]

Step-by-step explanation:

=> 5 + (-5)    [ + (-) = - ]

=> 5 - 5

=> Zero

Answer:

The answer is option A-The expression equals 0.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The shape clearly is reflected across y axis and the x coordinates remain the same. We can see a change in the y coordinates and the shape has shifted 5 units down. Hence (x, y) -> (x, y-5) and then reflection across y axis is the answer

Answer:

B

Step-by-step explanation:

Answer:

c=6.31, a=50.28 degrees, B=75.72 degrees

Step-by-step explanation:

The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. The remaining parts of the triangle can be found as shown.

The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,

[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ B}{\beta} =\dfrac{Sin\ C}{\gamma}[/tex]

where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,

Sin B is the angle and β is the length of the side of the triangle opposite to angle B,

Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.

Given that the length of side a and b is 6 and 7.56, also, the measure of the angle γ is 54°.

Now, Using the law of cosine, we can write,

[tex]c =\sqrt{a^2 + b^2 -2ab\cdot \cos\gamma}[/tex]

[tex]c =\sqrt{(6)^2 + (7.56)^2 -2(6)(7.56)\cdot \cos(54^o)}[/tex]

c = √39.8297

c = 6.311

Now, using the sine law the ratio of the sides and angles can be written as,

[tex]\dfrac{\sin\alpha}{a} =\dfrac{\sin\beta}{b} =\dfrac{\sin\gamma}{c}[/tex]

[tex]\dfrac{\sin\alpha}{6} =\dfrac{\sin\beta}{7.56} =\dfrac{\sin (54^o)}{6.311}[/tex]

[tex]\dfrac{\sin\alpha}{6}=\dfrac{\sin (54^o)}{6.311}[/tex]

α = 50.2775°

[tex]\dfrac{\sin\beta}{7.56} =\dfrac{\sin (54^o)}{6.311}[/tex]

β = 75.726°

Hence, the remaining parts of the triangle can be found as shown.

Learn more about Sine Rule here:

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Greetings from Brasil...

It is said that polygons are similar, so we can use the expression of similarity.

BIG/small = BIG/small

35/14 = 25/X

X = 10

But the scale factor is questioned. Just use one of the expressions. We conclude that the largest is 2.5 times the value of the smallest

35/14 OR 40/16 OR 25/10

-----------------------------------------------------------

BIG/small = BIG/small

25/5 = 40/Y

Y = 8

25/5 OR 25/5 OR 40/8

times the value of the smallest

Answer:

x= 24

Step-by-step explanation:

open the bracket

4×3x =12x + 4 × 2 =8

12×+ 8-6×6

12×+ 12

x= 24

Answer:

12x - 28

Step-by-step explanation:

Because of PEMDAS you start with the parentheses and distribute the 4.

So,

(12x + 8) -6 x 6

Then, solve for the 6's

(12x + 8) -36

Remove the parentheses

12x + 8 - 36

Lastly, you get

12x - 28.

This is as far as you can go because there is no equals sign so you cannot actually solve for x.

Answer:

Felix

Step-by-step explanation:

The graph contains 3 segments,

first one is for the first 4minutes,

second one is for the next 2 minutes (standing still)

third one is for the last 2 minutes.

Only Felix has it right, the other students use absolute time in their statements, in stead of the difference between start and end. (e.g., from 4 to 6 is 2 minutes).

The student that most accurately described Roy's motion is Felix.

There are many tools we can use to find the information of the relation which was used to form the graph.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

We need to find the student that most accurately described Roy's motion.

Here we can see that the graph contains 3 segments, first one is for the first 4 minutes, Second one is for the next 2 minutes (standing still) and the third one is for the last 2 minutes.

Now, Only Felix has it right, the other students use absolute time in their statements, in stead of the difference between start and end.

Therefore, the student that most accurately described Roy's motion is Felix.

Learn more about finding the graphed function here:

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Surface area of small sphere = 1441cm^2

Surface area of bigger sphere = 2567cm^2

Surface area of largest sphere = 1441 + 2567

= 4008cm²

Must click thanks and mark brainliest

Answer:  y = (-4/3)*sqrt(2/3)

This is the same as writing [tex]y = -\frac{4}{3}\sqrt{\frac{2}{3}}[/tex]

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

Explanation:

The phrasing "where the absolute value of the slope is minimized" is an interesting way of saying "the tangent slope is 0". This is because absolute values are never negative, so the smallest it can get is 0.

Your teacher has given you

y = x^3 - 2x

which differentiates into

dy/dx = 3x^2 - 2

after using the power rule

The derivative function lets us determine the slope of the tangent. The slope is the dy/dx value. Since we want a slope of 0, we'll set 3x^2-2 equal to zero and solve for x. So you have the correct idea, but you won't involve the second derivative.

dy/dx = 0

3x^2 - 2 = 0

3x^2 = 2

x^2 = 2/3

x = sqrt(2/3)

Notice how I'm ignoring the negative version of this root. This is due to the fact that [tex]x \ge 0[/tex]

-------------------------

Now plug this x value back into the original equation to find its corresponding y coordinate.

y = x^3 - 2x

y = x(x^2 - 2)

y = sqrt(2/3)*( 2/3 - 2 )

y = sqrt(2/3)*( -4/3 )

y = (-4/3)*sqrt(2/3)

Note that x = sqrt(2/3) leads to x^2 = 2/3 after squaring both sides.

-------------------------

Therefore, the equation of this tangent line is y = (-4/3)*sqrt(2/3)

All horizontal lines are of the form y = k, for some constant k. This constant value is basically what number you want the horizontal line to go through on the y axis. That number would be (-4/3)*sqrt(2/3).

Answer:

(2m + 1 + y) (2m + 1 - y)

Step-by-step explanation:

steps are done in the above photo and i have also written the identifies

Answer:

both angles are the same, so you can use it interchangeably in proving.

But i suggest you to mantain only one, because it's easier to understand and it looks better.

Answer:

a² + b² = 20

Step-by-step explanation:

Given

(a - b) = 4 ← square both sides

(a - b)² = 4²

a² - 2ab + b² = 16 ← substitute ab = 2

a² - 2(2) + b² = 16

a² - 4 + b² = 16 ( add 4 to both sides )

a² + b² = 20

Answer:

A = 2, B = 3 and C = 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

2x + 3y = 2 ( subtract 2x from both sides )

3y = - 2x + 2 ( divide all terms by 3 )

y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{2}{3}[/tex] ← in slope- intercept form

with slope m = - [tex]\frac{2}{3}[/tex]

Parallel lines have equal slopes, thus

y = - [tex]\frac{2}{3}[/tex] x + c ← is the partial equation

To find c substitute (2, 0) into the partial equation

0 = - [tex]\frac{4}{3}[/tex] + c ⇒ c = [tex]\frac{4}{3}[/tex]

y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{4}{3}[/tex] ← in slope- intercept form

Multiply through by 3

3y = - 2x + 4 ( add 2x to both sides )

2x + 3y = 4 ← in standard form

with A = 2, B = 3 and C = 4

Answer:

Option C is correct.

Step-by-step explanation:

Answer:

Step-by-step explanation:

82 hope this helps

Answer:

Least common denominator = (x - 1)²(x - 2)

Step-by-step explanation:

Least common denominator of two rational expressions = LCM of the denominator of the expressions.

[tex]\frac{x^3}{x^2-2x+1}[/tex] and [tex]\frac{-3}{x^{2}-3x+2}[/tex]

Factorize the denominators of these rational expressions,

Since, [tex]x^{2}-2x+1[/tex] = x² - 2x + 1

                             = (x - 1)²

And x² - 3x + 2 = x² - 2x - x + 2

                         = x(x - 2) -1(x - 2)

                         = (x - 1)(x - 2)

Now LCM of the denominators = (x - 1)²(x - 2)

Therefore, Least common denominator will be (x - 1)²(x - 2).

Answer:

its 5/4! haha i used to be good at this when i was in 6th grade:)

Answer:

Required force (F) = 500 N

Step-by-step explanation:

Given:

Mass of carriage (m) = 1,000 kg

Acceleration (a) = 0.5 m/s²

Find:

Required force (F)

Computation:

Required force (F) = Mass × Acceleration

Required force (F) = 1,000 kg × 0.5 m/s²

Required force (F) = 500 kg-m/s²

Required force (F) = 500 N

Answer:

Answer:

Required force (F) = 500 N

Step-by-step explanation:

Given:

Mass of carriage (m) = 1,000 kg

Acceleration (a) = 0.5 m/s²

Find:

Required force (F)

Computation:

Required force (F) = Mass × Acceleration

Required force (F) = 1,000 kg × 0.5 m/s²

Required force (F) = 500 kg-m/s²

Required force (F) = 500 N

THANKS

1

3.0

(2 votes)

Step-by-step explanation:

Given:

Mass of carriage (m) = 1,000 kg

Required force (F) = 500 kg-m/s²

Required force (F) = 500 N

Answer:

-5pi/9

Step-by-step explanation:

The conversion factor is pi/180

-100 degrees * pi/180 = -100/180 *pi =-10pi/18 = -5pi/9

If a ★ b = 0.5ab, then

0.1 ★ b = 0.5 (0.1) b = 0.05b = 10

==>   b = 10/0.05 = 200

Denote the number by 10a + b, where both a and b are integers picked from {1, 2, 3, …, 9}.

"the difference of whose digits is 3"   ==>   |a - b| = 3

"4 times the number is equal to 7 times the number obtained by reversing the digits"   ==>   4 (10a + b) = 7 (10b + a)

Simplifying the second equation, you get

40a + 4b = 70b + 7a

33a - 66b = 0

a - 2b = 0

Assume a > b, in which case we would have |a - b| = a - b, so

a - b = 3

Eliminate a to solve for b, then for a :

(a - b) - (a - 2b) = 3 - 0

b = 3   ==>   a = 6

Then the original number is 63.

If instead we had assumed a < b, we would have had |a - b| = b - a = 3. Then

2 (b - a) + (a - 2b) = 2×3 + 0

-a = 6

But neither a nor b can be negative, so this case is moot.

Answer:

She bought 2 videos and 8 CDs.

Answer:

Step-by-step explanation:

To find the perpendicular distance between them that's the height we use the formula

[tex]Area \: \: of \: \: a \: \: trapezium = \frac{1}{2} (a + b) \times h[/tex]

where

a and b are the parallel sides of the trapezium

h is the perpendicular distance

From the question

Area = 31.5cm²

a = 7.5 cm

b = 5.3 cm

Substituting the values into the above formula we have

[tex]31 .5 = \frac{1}{2} (7.5 + 5.3) \times h[/tex]

[tex]31.5 = \frac{1}{2} \times 12.8h[/tex]

[tex]31.5 = 6.4h[/tex]

Divide both sides by 6.4

[tex]h = \frac{31.5}{6.4} [/tex]

h = 4.921875

We have the final answer

Hope this helps you

Answer:

30

Step-by-step explanation:

[tex]c^{2} = b^{2} + a^{2} \\[/tex] =  formula

a = 24

b = 18

576+324 = 900

do [tex]\sqrt{900} \\[/tex]

= 30

Answer:

False

Step-by-step explanation:

Required

State if the product of rational numbers and integer is an integer

The statement is false and the proof is as follows

Literally, rational numbers are decimal numbers that can be represented as a fraction of two integers;

Take for instance: 0.2, 0.5, 2.25, etc.

When any of these numbers is multiplied by an integer, the resulting number can take any of two forms;

1. It can result to an integer:

For instance;

[tex]0.2 * 5 = 1[/tex]

[tex]0.5 * 4 = 2[/tex]

[tex]2.25 * 8 = 18[/tex]

2. It can result in a decimal number

For instance;

[tex]0.2 * 3 = 0.6[/tex]

[tex]0.5 * 5 = 2.5[/tex]

[tex]2.25 * 7 = 15.75[/tex]

From (1) above, we understand that the product can result in an integer.

Hence, the statement is false

Answer:

I'm pretty sure is

Positive b

Answer:

salt: pepper

4 :   3

Step-by-step explanation:

salt: pepper

2/3  : 1/2

Multiply each by 6

2/3 *6 : 1/2 *6

4 :   3

Answer:

a = -8

Step-by-step explanation:

-5/2 a + 5 = 25

Subtract 5 from each side

-5/2 a + 5-5 = 25-5

-5/2 a = 20

Multiply each side by -2/5

-2/5 *-5/2 a = 20*-2/5

a = -8