What is the domain of this relation?

The third term of the sequence is 3/x+5 when the arithmetic sequence is 1/x+3, 2/x+4,....

Given that,

The first two terms of an arithmetic sequence are given that is

1/x+3, 2/x+4,....

We have to find the third term of this sequence.

We know that,

The arithmetic sequence is the set of terms where the common difference between any two succeeding terms is always the same. Recall the definition of a sequence. A group of integers that follow a pattern is referred to as a sequence.

There are two ways of defining an arithmetic sequence. A "sequence where the differences between each pair of succeeding terms are the same" is what it is. Alternatively, "each term in an arithmetic sequence is obtained by adding a fixed number (positive, negative, or zero) to its preceding term."

The sequence has

n/x+(n+2)

Take n=1 is 1/x+3

Take n=2 is 2/x+4

Take n=3 is 3/x+5

Therefore, The third term of the sequence is 3/x+5 when the arithmetic sequence is 1/x+3, 2/x+4,....

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Randall needs 3 quarts of ice cream.

What is the quarts?

An English measurement of volume equal to one-quarter gallon is the quart. There are now three different types of quarts in use: the liquid quart, dry quart, and imperial quart of the British imperial system. One litre is roughly equivalent to each. It is divided into either four cups or two pints.

If Randall needs 24 servings, that means that there would be 24 kids in his class.

If each kid in his class would have 1/8 quart,

you would do 24 x 1/8 which is 3 quarts.

3 quarters

Hence, Randall needs 3 quarts of ice cream.

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Answer:

Step-by-step explanation:

Ok:

If the two books together costs $28.48 and one of them cost $7.44 Subtract to get the other book's price

2. 28.45-7.44=$21.01

3. Answer: The cost of the other one is $21.01

The equation of the line that passes through the points (4, -8) and (7,-8) is 5.33x + y = 13.22.

What is linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given two points,

(x1 = 4 ,y1 = -8) and (x2 = 7, y2 = -8)

The equation's general form will be written first:

y = mx + c

We may compute the slope of the equation (m) as follows:

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m = \frac{-8-8}{7-4}[/tex]

m = -16/3

m = -5.33

equation is y = -5.33x + c.

By entering the values of the x and y coordinates, we can now determine the value of the y-intercept (c):

For the point (4,-8),

-8 = -5.33(4) + c

-8 = -21.32 + c

c = 13.32

So the equation become ;

y = -5.33x + 13.32

or, 5.33x + y = 13.22

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Answer:

C

Step-by-step explanation:

If we use the distributive property for 4 (2x + 1), we see that 4 (2x) = 8x and that 4 (1) = 1. That means 4 (2x + 1) = 8x + 4 which is not equivalent to 2x + 4y. So this limits our answer to either C or D. C is the correct answer because if we use the distributive property again here for 4 (2x + y), we see that 4 (2x) = 8x and 4 (y) = 4y. That means that 4 (2x + y) = 8x + 4y which is the answer we're looking for.

May I please have brainliest for this? Thank you very much!

Answer:

$722.5

Step-by-step explanation:

Since $225 is 30 students we can do 85/30 and multiply 225 by that.

For the proportion, it would be: 255/30=x/85

85/30=2.8 1/3

2.8 1/3*255=722.5

So it would be $722.5 for 85 students

Answer:

$722.5

Step-by-step explanation:

$255/ 30= 8.5

8.5* 85= $722.5

Answer:

11.66

Step-by-step explanation:

10^2 + 6^2 = Z^2

100 + 36 = Z^2

136 = Z^2

sqrt(136) = Z

sqrt 136 = 11.66

Answer: log2-log6=-log3

Step-by-step explanation:

[tex]\displaystyle\\log2-log6=\\\\log\frac{2}{6} =\\\\log\frac{2(1)}{2(3)}=\\\\log\frac{1}{3} =\\\\log3^{-1}=\\\\-log3[/tex]

Answer:

Im not too sure because I haven't done this in a while but, I think the answer is 60cm, don't come at me if its wrong plssss

Step-by-step explanation:

if u divide it along the far left, closer to 12cm, u would have 2 rectangles. they would Both be close and If u added up 12cm and 12cm that would give you 24cm, and if you go to the other rectangle it would be 18 cm plus 18cm that would be 36cm. u do not multiply since it is perimeter and not area. Hope it helped!

Answer:

60 cm

Step-by-step explanation:

18+18+12+12

30+30

60

the 4 unknown sides we know that the 2 lengths equal 18 cm because both of them together are the same length as the base and the 2 widths add up to be 12 cm since it is the same size as the 12 cm width when added together if that makes sense

Hopes this helps

the maximum area of such a rectangle will be 144 unit²

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.

Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

The area of rectangle is A = a*b

A = 2x*(48-x²) = 96x - 2x³

We are asked to maximize the Area as changes so hopefully, we can identify a critical point of

It an associated with a maximum, So we need to find [tex]\frac{dA}{dx}[/tex] = 0

96 - 6x² = 0

x² =96/6 = 16

x = ±6

So the width = 12

Height = 48 - 36 = 12

So the area = 144 unit²

Hence the maximum area of such a rectangle will be 144 unit²

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The 600 chairs capacity of the hall and the arrangement such that an increase in the number of rows by 5 decreases the number of chairs per row by 6 is a word problem that indicates;

(a) There are originally 20 rows of chairs in the hall

(b) The number of empty chairs per row is 6 empty chairs

A word problem is a question in which the information required to find the solution and the description of the situation is provided using sentences, or regular verbal statements rather that symbols, expressions or operators.

(a) The number of chairs the hall can accommodate = 600

Let x represent  the number of rows of chairs, therefore;

The number of chairs per row = 600/x

When the number of rows is increased by and the number of shares per row is decreased by 6, we get;

New number of rows = x + 5

New number of chairs per row = (600/x) -6

The equation for the number of chairs in the hall becomes;

(x + 5) × ((600/x) - 6) = 600

600·x + 6·x² - 570·x - 3000 = 0

6·x² + 30·x - 3000 = 0

x² + 5·x - 500 = 0

(x + 25)·(x - 20) = 0

x = -25 and x = 20

The number of rows is a positive number, therefore;

(b) After re-arrangement, the number of rows, x = 20

The new number of chairs per rows = (600/20) - 6 = 24

The new number of rows = 20 + 5 = 25

Let E represent the number of empty chairs, the number of people in each row becomes 24 - E, which indicates;

25 × (24 - E) = 450

450 ÷ 25 = 18 = 24 - E

E = 24 - 18 = 6

The number of empty chairs per row, E = 6

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Answer:

7.9

Step-by-step explanation:

Using the half-life formula, there will be about [tex]30(0.5)^{11000/5730} \approx 7.9[/tex] grams left.

the probability of the committee consisting of all women is 6.53%.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

number of women = 20

number of men = 13

Total number of persons = 20+ 13 = 33

A committee of 5 people is chosen at random. Total number of ways in which the committee of 5 can be chosen N

N = C(33 5) = 33! / 5!*28!

N = 237336

p(the committee consists of all women) = C (20 3)*C(13 0)/N

p = 15504 / 237336

p = 0.0653

Hence, the probability of the committee consisting of all women is 6.53%

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The value of car after 6 years is £498.53

Define Modeling Exponential Decay

Given that,

Dan buys a car =  £700

Depreciates at a rate of = 5.5% per year

The value after 6 years = 700 (1 - 5.5 / 100) ^6

                                       = 498.527 or 498.53

Therefore, the value of car after 6 years is £498.53

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The expression "(-3 1/4d + 3/5) - (2 7/8d + 7/10) is equivalent to "negative forty nine over 8 times d minus one tenth" or -49/8d - 1/10.

An algebraic expression is a number, variable, or the combination of both and operational symbols.

To determine the equivalent of the expression "quantity negative three and one fourth times d plus three fifths end quantity minus quantity two and seven eighths times d plus seven tenths end quantity" or simply (-3 1/4d + 3/5) - (2 7/8d + 7/10), combine all like terms and perform the necessary operations.

(-3 1/4d + 3/5) - (2 7/8d + 7/10)

⇒ -3 1/4d + 3/5 - 2 7/8d - 7/10

⇒ (-3 1/4 - 2 7/8)d + 3/5 - 7/10

⇒ (-13/4 - 23/8)d + 6/10 - 7/10

⇒ (-26/8 - 23/8)d - 1/10

⇒ -49/8 d - 1/10

Hence, the equivalent expression is "negative forty nine over 8 times d minus one tenth" or -49/8d - 1/10.

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Answer:

Step-by-step explanation:

x = -9/5 = -1.800 or

x = 0

Answer:

D. The sixth root of three

Step-by-step explanation:

Translate from words to math symbols:

three to the one third power all over three to the one sixth power

[tex]\frac{3^{\frac{1}{3} } }{3^{\frac{1}{6} } } \\[/tex]

Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents:

[tex]\frac{\sqrt[3]{3} }{\sqrt[6]{3} }[/tex]

Simplify:

[tex]\frac{\sqrt[3]{3} }{\sqrt[6]{3} } = \frac{\sqrt[3]{3} }{\sqrt[6]{3} } * \frac{\sqrt[6]{3^{5} } }{\sqrt[6]{3^{5} } } = \frac{\sqrt[3]{3} *\sqrt[6]{3^{5} } }{\sqrt[6]{3^{6} } } = \frac{3^{\frac{1}{3} }*3^{\frac{5}{6} } }{3^{\frac{6}{6} } } = \frac{3^{(\frac{1}{3} +\frac{5}{6} )} }{3} = \frac{3^{(\frac{2}{6} +\frac{5}{6} )} }{3} = \frac{3^{\frac{7}{6} } }{3} = \frac{3^{\frac{1}{6} } *3}{3} = \\\\3^{\frac{1}{6} } = \sqrt[6]{3}[/tex]

Answer:

[tex]\sqrt[6]{3}[/tex]

D. the sixth root of three

Answer:

3! = 3*2*1 = 6

Step-by-step explanation:

! is factorial meaning that you multiply that number by all of the number below it

9! = 9*8*7*6*5*4*3*2*1

1011 = 1011*1010*1009*1008...3*2*1

The temperature decrease for every meter that the mountain climber's altitude increases is given by:

-100 ºF.

The function that models this situation is a linear function, which has the format defined as follows:

y = mx + b.

In which the coefficients are given as follows:

In the context of this problem, the function is defined as follows:

f(a) = -100a + 75.

Hence the slope of the function is of:

-100.

Representing the temperature decrease for each meter of altitude increase of the climber.

The function is defined as:

f(a) = -100a + 75.

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The value of z = 0 + 0i

What is complex numbers ?

A complex number can be represented in the form a + bi, where a and b are real numbers. A complex number is a part of a number system that extends the real numbers by adding an element designated by the symbol I sometimes known as the imaginary unit, and meeting the equation displaystyle i2=-1.

( x + iy ) - 4i ( x - iy ) = 0

x + iy - 4ix + 4i²y = 0

x + i (-4x + y ) + 4y = 0

x + 4y + ( - 4x + y )i = 0

Now two complex numbers are equal if both the real and imaginary parts are equal, which gives you the system of equation

x + 4y = 0 ⇒(1)

-4x + y = 0 ⇒ (2)

Multiplying equation (1) with 4

4x + 16y = 0

Solving the equations

4x + 16 y = 0

-4x + y = 0

      17 y = 0

          y = 0

Putting the value of y in (1)

x + 4(0) = 0

x = 0

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The owner of a landscaping company can determine how much time, on average, his employees spend mowing one lawn by taking hours per lawn.

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Answer:

x= -7

Step-by-step explanation:

The sum of the angles in a triangle is 180°. This can be abbreviated to ∠ sum of ∆.

Adding the angles in the triangle,

84° +(x +59)° +(x +51)°= 180° (∠ sum of ∆)

2x= 180 -84 -59 -51

2x= -14

Divide both sides by 2:

x= -14 ÷2

x= -7

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The additional information that could be used to prove that ΔXYZ ≅ ΔFEG by ASA or AAS are:

∠Z ≅ ∠G and XZ ≅ FG

∠Z ≅ ∠G and XY ≅ FE .

The AAS is a theorem that states that we can prove that two triangles are congruent if they have two pairs of congruent angles and a pair of non-included sides.

The SAS is also another theorem that states that we can prove that two triangles are congruent if they have two pairs of congruent sides and a pair of included congruent angles.

From the image attached below, we are only given one pair of congruent angles, which is ∠X ≅ ∠F.

Therefore, for both triangles to be congruent by AAS or SAS, the additional information needed are:

∠Z ≅ ∠G and XZ ≅ FG or ∠Z ≅ ∠G and XY ≅ FE .

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Tracy need 5 weeks to save enough money to buy a new guitar.

Given that,

Tracy is saving to buy a new guitar. Which having costs $253.77(including tax).

Tracy has already saved $136. 27.

Now she needs = 253. 77- 136. 27

                          = $117.50

she can save each week = $23. 50

Tracy will take weeks to save enough money

     = [tex]\frac{117.50}{23.50}[/tex]

     = 5 weeks.

Therefore, Tracy need 5 weeks to save enough money to buy a new guitar.

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Answer:

Step-by-step explanation:

i think its 1

The time derivative dp(t)/dt of the x component of the system's total momentum is m₁a₁(t)+m₂a₂(t).

A moving body's motion is measured by its momentum, which is the product of its mass and velocity. The formula for momentum is p=mv. Here, p is momentum, m is mass (in kg), and v is the velocity (m/s).

This equation with respect to time is written as dp(t)/dt. Then, momentum for block 1 is written as,

[tex]\begin{aligned}\frac{dp_1(t)}{dt}&=\frac{d(m_1v_1(t))}{dt}\\&=m_1\frac{dv_1(t)}{dt}\\&=m_1a_1(t)\end{aligned}[/tex]

The momentum for block 2 is written as,

[tex]\begin{aligned}\frac{dp_2(t)}{dt}&=\frac{d(m_2v_2(t))}{dt}\\&=m_2\frac{dv_2(t)}{dt}\\&=m_2a_2(t)\end{aligned}[/tex]

In both equations, the value dv/dt=a with respect to time.

Then, the total momentum is,

[tex]\begin{aligned}\frac{dp(t)}{dt}&=\frac{dp_1(t)}{dt}+\frac{dp_2(t)}{dt}\\&=m_1a_1(t)+m_2a_2(t)\end{aligned}[/tex]

Therefore, the value is m₁a₁(t)+m₂a₂(t).

The complete question is -

In this problem, you will analyze a system composed of two blocks, 1 and 2, of respective masses m1 and m2. To simplify the analysis, we will make several assumptions:

At time t, the x components of the velocity and the acceleration of block 1 are denoted by v1(t) and a1(t). Similarly, the x components of the velocity and acceleration of block 2 are denoted by v2(t)and a2(t). In this problem, you will show that the total momentum of the system is not changed by the presence of internal forces.

Part B

Find the time derivative dp(t)/dt of the x component of the system's total momentum.

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Answer: 50% of her average running speed is her average walking speed

Step-by-step explanation:

60 ÷ 4 = 15
60 ÷ 8 = 7.5
7.5 is half of 15, making it 50% of her running speed.

Answer:

37

Step-by-step explanation:

4b+10-b = 3b + 10 = 3(9) + 10 = 27 + 10 = 37

Answer:

A, B, D, E

Step-by-step explanation:

Given expression:

When multiplying decimals, multiply as if there are no decimal points:

[tex]\implies 6 \times 154 = 924[/tex]

Count the number of digits after the decimal in each factor:

Therefore, there is a total of 5 digits.

Put the same number of total digits after the decimal point in the product:

[tex]\implies (0.06) \cdot (0.154)=0.00924[/tex]

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

Answer option A

[tex]\boxed{6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}}[/tex]

When dividing by multiples of 10 (e.g. 10, 100, 1000 etc.), move the decimal point to the left the same number of places as the number of zeros.

Therefore:

[tex]\implies 6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}=(0.06) \cdot (0.154)[/tex]

Therefore, this is a valid answer option.

Answer option B

[tex]\boxed{6 \cdot 154 \cdot \dfrac{1}{100000}}[/tex]

Multiply the numbers 6 and 154:

[tex]\implies 6 \times 154 = 924[/tex]

Divide by 100,000 by moving the decimal point to the left 5 places (since 100,000 has 5 zeros).

[tex]\implies 6 \cdot 154 \cdot \dfrac{1}{100000}=0.00924[/tex]

Therefore, this is a valid answer option.

Answer option C

[tex]\boxed{6 \cdot (0.1) \cdot 154 \cdot (0.01)}[/tex]

Again, employ the technique of multiplying decimals by first multiplying the numbers 6 and 154:

[tex]\implies 6 \cdot 154 = 924[/tex]

Count the number of digits after the decimal in each factor:

Therefore, there is a total of 3 digits.

Put the same number of digits after the decimal point in the product:

[tex]\implies 0.924[/tex]

Therefore, as (0.06) · (0.154) = 0.00924, this answer option does not equal the given expression.

Answer option D

[tex]\boxed{6 \cdot 154 \cdot (0.00001)}[/tex]

Again, employing the technique of multiplying decimals.

As there are a total of 5 digits after the decimals:

[tex]\implies 6 \cdot 154 \cdot (0.00001)=0.00924[/tex]

Therefore, this is a valid answer option.

Answer option E

[tex]\boxed{0.00924}[/tex]

As we have already calculated, (0.06) · (0.154) = 0.00924.

Therefore, this is a valid answer option.

When the denominator is bigger than the numerator, a fraction is expressed as one with a numerator and a denominator. 55 cups of jam divided equally into 4 containers yields 13.75 cups per container. 13.75 cups of jam are contained in each container.

We have,

55 cups of blueberry jam were produced by Jada, who then evenly distributed the jam across 4 containers.

jam content of each container.

= 55 cups / 4 container

= 13.75 cups / 1 container

This indicates that there are 13.75 cups of jam in each container.

55 cups of jam are divided into 4 equal containers in this manner.

13.75 cups / 1 container

The amount of jam in each container is 13.75 cups of jams.

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