Solve one third plus seven ninths equals

Answer

y= 3/2 x  - 2

Step-by-step explanation:

so you have to find the slope which would be

m =  

y2 - y1

x2 - x1

then you find you points that you are using (2, 1) and (0, -2)

when you plug it in it is

m=

-2-1

0-2

you simplify the numbers and get rid of the negatives to get m=3/2 x

then your y intercept is where your line meets the y axis or wherever x=0

so your y intercept is (0, -2) so the b = -2

If the expression be 23 x² + 3x + 8 then the constant exists 8.

The addition, subtraction, multiplication, and division arithmetic operators are used to write a group of numbers together to form a numerical statement in mathematics. The expression of a number can take on various forms, including verbal form and numerical form.

A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms.

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

During the course of a program's execution, a constant's value cannot change. As a result, the value is constant, as implied by its name. During the course of a program's execution, a variable's value can change. As a result, the value might change, as implied by its name.

Let the expression be 23 x² + 3x + 8

then the constant exists 8.

Therefore, the correct answer is option C. 8.

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The term "average" plays a fundamental role in statistics. It refers to a measure of central tendency that summarizes a set of data by representing a typical or representative value.

Calculation for the average of a set of numbers, follow these steps:

Add up all the values in the data set.

Division of the sum by the total number of values.

For example, consider the following data set: 10, 15, 20, 25, 30.

Sum all the values: 10 + 15 + 20 + 25 + 30 = 100.

Divide the sum by the total number of values: 100 / 5 = 20.

In this case, the average of the data set is 20.

The term average provides a concise summary of a data set by representing a typical value. It is calculated by adding up all the values and dividing the sum by the total number of values. The average is a fundamental statistical measure that helps in understanding and analyzing data in various fields such as economics, education, research, and many others.

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Answer:

See the attached worksheet

Step-by-step explanation:

The function is transformed by subtracting 3 from both the x and y values. I'm uncertain how this is expressed in a functional form.

Answer: It represents that 2 will be divided into 3 equal parts.

Step-by-step explanation:

The given fraction : \(\dfrac{2}{3}\)

here, Numerator = 2

Denominator = 3

It represents that 2 will be divided into 3 equal parts.

Answer:

x > -3

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The inequation is,

→ -6 > -4x - 18

Then the value of x will be,

→ -6 > -4x - 18

→ -4x - 18 < -6

→ -4x < -6 + 18

→ -4x < 12

→ x > 12/(-4)

→ x > -12/4

→ [ x > -3 ]

Hence, the answer is x > -3.

9514 1404 393

Answer:

  9 square units

Step-by-step explanation:

Pick's theorem is a useful relationship in circumstances like these. It tells you the area is ...

  A = i + b/2 - 1

where i is the number of interior points (8), and b is the number of points on the border (4).

The area of this figure is ...

  A = 8 + 4/2 -1 = 9

The area of the polygon is 9 square units.

_____

You can also get there by realizing the bounding rectangle is 4 units square. From that, corner triangles are cut. CW from upper left, those triangles have (base, height) dimensions of (3, 2), (1, 3), (3, 1), and (1, 2). So, the total of their areas is (1/2)(6 +3 + 3 +2) = 7 square units. The shaded area is then 16-7 = 9 square units, same as above.

The given sentence "1024 is the smallest four-digit number that is a perfect square" is true because it is the square of 32.

A perfect square is a number that is the product of two equal integers. It's the product of an integer multiplied by itself. A perfect square is a number that can be expressed as the product of a number and itself. For example, 9, 16, 25, and 36 are perfect squares.

It follows that the square root of a perfect square is a whole number because the product of two equal integers is an integer.

Identify the range of four-digit numbers. Four-digit numbers are those that range from 1000 to 9999.

To check if 1024 is the smallest four-digit perfect square, we should examine whether the smallest perfect square between 1000 and 9999 is 1024. If we square 32, we get 1024, which means that 1024 is a perfect square.

As a result, the statement "1024 is the smallest four-digit number that is a perfect square" is true.

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Answer:

29.16

Step-by-step explanation:

8 percent of 27 is 2.16 so you do 27+2.16 and you get 29.16

In 2000 Emily was 9 years old.

Given that in the year 2015 Emily was three times as old as Kaitlin while by the year 2021 Kaitlin will be half as old as Emily will be, to determine how old was Emily on the year 2000 the following calculation must be performed:

Therefore, in 2000 Emily was 9 years old.

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Answer:

25 and 11

Step-by-step explanation:

because subtract 14 from 36 it will give u 11 so 11 is your smaller number and 25 is your bigger

Hope this helps :)

Answer:

The numbers are 11 and 25.

Step-by-step explanation:

Assign x to the the numbers.

One of the numbers is 14 more than the other.

x + (x+14) = 36

Smaller number = x

Bigger number = x +14

2x + 14 = 36

2x = 22

x = 11 = smaller number

x = 11 + 14 = 25 = bigger number

Answer:

$600

Step-by-step explanation:

1,200 · 0.05 = 60

60 · 10 = 600

The equation of the tangent line to the parabola at the point (1,5) is y = 4x + 1.

To find the slope of the tangent line to the parabola at the point (1,5), we need to find the derivative of the equation y = 6x - x² and evaluate it at x = 1.

Taking the derivative of y with respect to x:

dy/dx = d(6x - x²)/dx

= 6 - 2x

Now, we can substitute x = 1 into the derivative to find the slope at that point:

slope = 6 - 2(1)

= 6 - 2

= 4

So, the slope of the tangent line to the parabola at the point (1,5) is 4.

To find the equation of the tangent line, we need to use the point-slope form of a line.

The equation is given by:

y - y₁ = m(x - x₁)

Substituting the values we have:

y - 5 = 4(x - 1)

Expanding and simplifying:

y - 5 = 4x - 4

Moving the constant term to the other side:

y = 4x + 1

Therefore, the equation of the tangent line to the parabola at the point (1,5) is y = 4x + 1.

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Complete question =

Find the slope of the tangent line to the parabola at the point (1,5). y = 6x-x². find an equation of the tangent line.

The situation that represents the expression, 3/5 divided by 1/4 is Option B

The interquartile range is described as  the range of values that resides in the middle of the scores.

It is abbreviated as (IQR)

From the information given, we have the expression in a fraction form as;

3/5 divided by 1/4

Now, we can see that the value of 3/5 is divided by 4, since

3/5 ÷ 1/4

Take the inverse of the divisor, we get;

3/5 × 4/1

Multiply the values, we have;

12/5

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Answer:

approximately 17.3 years

Step-by-step explanation:

Compound interest is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P \((1 + r/n)^{nt}\)

The formula used to find continuously compounded is:

t = log (A/P) / r

The time it will take to double her money is 17.329 years.

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P \((1 + r/n)^{nt}\)

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

P = $5,000

r = 4%

Amount = 2 x 5000 = $10,000

n = infinite number of times.

Now,

Solve the equation for t

The formula used to find for continuously compounded is:

t = log (A/P) / r

t = log (10,000.00/5,000.00) / 0.04

t = 17.329 years

Thus,

The time it will take to double her money is 17.329 years.

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The maximum temperature in the rod at any particular time is 2.

To find the maximum temperature in the rod at any particular time, we can analyze the initial temperature distribution and how it evolves over time.

The given equation ut = u_xx represents a heat conduction equation, where ut is the rate of change of temperature with respect to time t, and u_xx represents the second derivative of temperature with respect to position x.

The boundary conditions u(0,t) = 0 and u(1,t) = 0 indicate that the ends of the rod are kept at a constant temperature of zero. This means that heat is being dissipated at the boundaries, preventing any temperature buildup at the ends of the rod.

The initial temperature distribution u(x,0) = 2sin(4πx) describes a sine wave with an amplitude of 2 and a period of 1/2, oscillating between -2 and 2. This initial distribution represents the initial state of the rod at time t=0.

As time progresses, the heat conduction equation causes the temperature distribution to evolve. The maximum temperature at any particular time will occur at the peak of the temperature distribution.

Intuitively, since the initial distribution is a sine wave, we can expect the maximum temperature to occur at the peaks of this wave. The amplitude of the sine wave is 2, so the maximum temperature at any time t would be 2.

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Based on the evaluation of the conditions, the output "x < 0 and z > 0" will be printed. Therefore, the correct answer is B. x < 0 and z > 0.

The correct indentation of the statement would be as follows:

if (x > 0)

if (y > 0)

System.out.println("x > 0 and y > 0");

else if (z > 0)

System.out.println("x < 0 and z > 0");

Given that x = 1, y = -1, and z = 1, let's evaluate the conditions:

The first if statement checks if x > 0, which is true since x = 1.

Since the condition in the first if statement is true, we move to the inner if statement, which checks if y > 0. However, y = -1, so this condition is false.

The inner if statement is followed by an else if statement that checks if z > 0. Since z = 1, this condition is true.

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Answer:

20/3

Step-by-step explanation:

To figure this out, you would multiply 5 by the reciprocal of the fraction. The reciprocal is the fraction flipped around. 3/4 flipped around would be 4/3.

5*4/3=20/3

Hope this helps!! Have a nice day c:

Answer:

10 envelopes

Step-by-step explanation:

What we know:

- There are 3 drawings for each envelope

- There are 28 drawings in total

To find out the number of envelopes Declan would need, we divide 28 by 3 (check the picture attached).

28÷3=9 R1

28 divided by 3 gives us 9 with a remainder of 1, which means if Declan had 9 envelopes, he would be able to fit 3 drawings in each with 1 drawing left over. He would need a 10th envelope to use for the last drawing.

Therefore, Declan would need 10 envelopes to mail all the drawings to his grandma.

I hope this helps! Happy holidays :)

The fluid force on the sheet metal's top side when submerged horizontally in 7 feet of water is 12441.6 lb.

Given,

The area of the top side of a piece of sheet metal = 4 square feet

The sheet metal is submerged horizontally in 7 feet of water.

Fluid Force on the top side can be found as follows,

Formula used:

Fluid Force = weight-density × volume × depth of fluid

Fluid Force = 62.4 × volume × 7

As the sheet metal is completely submerged, the volume is equal to the area of the sheet metal.

Volume = Area × Depth

= 4 × 7

= 28

Fluid Force = 62.4 × 28 × 7

                   = 12441.6 lb

Thus, the fluid force on the sheet metal's top side when submerged horizontally in 7 feet of water is 12441.6 lb.

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Therefore, the fluid force on the top side is 55838.08 lb.

Given, the area of the top side of a piece of sheet metal is 4 square feet and it is submerged horizontally in 7 feet of water.

The weight-density of water is 62.4 pounds per cubic foot.To find: the fluid force on the top side.Solution:Fluid force formula is given by,

F = ρ * g * V

Where, ρ is the density of the fluidg is the acceleration due to gravityV is the volume of the fluid displaced.Furthermore, the volume of fluid displaced is equal to the volume of the metal sheet submerged in the water.

Therefore,Volume of fluid displaced = Volume of metal sheet submerged in the water = area of metal sheet * depth submerged

Volume of metal sheet submerged in the water = 4 square feet * 7 feet

= 28 cubic feet

Now, calculate the fluid force on the top side of the metal sheet by using the fluid force formula.

F = ρ * g * V

Here, the density of water,

ρ = 62.4 pounds per cubic foot

g = 32.2 ft/s² (the acceleration due to gravity)

V = 28 cubic feet∴

F = 62.4 * 32.2 * 28 lb

= 55838.08 lb

Therefore, the fluid force on the top side is 55838.08 lb.

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For any positive integer n, 1 × 1! + 2 × 2! + . . . + n × n! = (n + 1)! - 1

We use mathematical indution technique to prove  1 × 1! + 2 × 2! + . . . + n × n! = (n+1)! - 1, for  a positive integer n.

Let T(n) be the given expression  1 × 1! + 2 × 2! + . . . + n × n! = (n+1)! - 1

For n = 1,

1 × 1! = 1

and (1 + 1)! - 1 = 1

This means T(1) is true.

Assume that T(k) is true.

So, 1 × 1! + 2 × 2! + . . . + k × k! = (k + 1)! - 1

We need to prove T(k + 1) is also true.

i.e., to prove: 1 × 1! + 2 × 2! + . . . + (k + 1) × (k + 1)! = ((k + 1) + 1)! - 1

Consider,

1 × 1! + 2 × 2! + . . . + (k + 1) × (k + 1)!

= 1 × 1! + 2 × 2! + . . . + k × k! + (k + 1) × (k + 1)!

= (k + 1 )! - 1 + (k + 1) × (k + 1)!

= (1 + k + 1)(k + 1)! - 1

= (k + 2)(k + 1)! - 1

= (k + 2)! - 1

= ((k + 1) + 1)! - 1

This means, T(k+1) is also true.

So, ​T(n) is true for all positive integers n .

Hence proved.

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Answer:

19+4i

Step-by-step explanation:

Multiply using the FOIL method, then combine the real and imaginary parts of the expression.

FOIL

A technique for distributing two binomials. The letters FOIL stand for First, Outer, Inner, Last. First means multiply the terms which occur first in each binomial, Outer means multiply the outermost terms in the product, Inner means multiply the innermost terms, and Last means multiply the terms which occur last in each binomial.

Result of multiplication of complex numbers will be 19 + 4i

Given,

(3 + 2i)(5 – 2i)

Here,

Complex numbers standard form : x ± iy

Here,

x = real part

y = complex part.

i = iota = \(\sqrt{-1}\)

So,

Multiplication :  (3 + 2i)(5 – 2i)

⇒15 -6i + 10i -4i²

Here,

i = √-1

i² = -1

So,

15 -6i + 10i -4i²

15 -6i + 10i - 4(-1)

⇒19 + 4i

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The probability of drawing a white ball on the second draw, without replacing the first ball, is 8/13.

To solve this problem, we need to use conditional probability.

The probability of drawing a white ball on the first draw is 8/13 (since there are 8 white balls and 13 total balls in the urn).

If a white ball is drawn on the first draw, then there will be 7 white balls and 5 black balls left in the urn. So the probability of drawing a white ball on the second draw, given that a white ball was drawn on the first draw, is 7/12.

If a black ball is drawn on the first draw, then there will be 8 white balls and 4 black balls left in the urn. So the probability of drawing a white ball on the second draw, given that a black ball was drawn on the first draw, is 8/12.

Now we can use the law of total probability to find the overall probability of drawing a white ball on the second draw:

P(white on second draw) = P(white on first draw) * P(white on second draw | white on first draw) + P(black on first draw) * P(white on second draw | black on first draw)
= (8/13) * (7/12) + (5/13) * (8/12)
= 56/156 + 40/156
= 96/156
= 8/13

Therefore, the probability of drawing a white ball on the second draw, without replacing the first ball, is 8/13.

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Answer:

well the volume of a sphere is V = 4/3 x pie x r3 so the radius is half of the diameter so that would be 8 not going to show work but the answer is 2144.66

The measure of angle ABC is given as follows:

m < ABC = 145º.

Two angles are defined as supplementary angles when the sum of their measures is of 180º.

In a parallelogram, we have that the opposite angles are supplementary.

The opposite angles for this problem are given as follows:

Hence the measure of angle ABC is given as follows:

m < ABC + 35º = 180º.

m < ABC = 145º.

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The standard form of the quadratic inequality represented by the description is; y <  -2x² + 160x - 2400

An inequality with a quadratic expression is referred to as a quadratic inequality.

It is of the form y = ax² + bx + c (or substitute <,≥ or ≤ for > ) represents a region of the plane that a parabola encircles.

Let's assume that the equation is y = a(x - h)² + k

Where (h, k) is the coordinate of the vertex. Thus;

y = a(x - 40)² + 800

Put the point (60, 0) in the equation

0 = a(60 - 40)² + 800

0 = a(20)² + 800

-800 = 400a

a = -800/400

a = -2

Thus, the equation is;

y = -2(x - 40)² + 800

The inequality is a dashed line and shaded below the parabola and is;

y <  -2(x - 40)² + 800

= y <  -2(x² - 80x + 1600) + 800

y <  -2x² + 160x - 3200 + 800

y <  -2x² + 160x - 2400

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Answer:

51 1/4 is the answer

Hope this helps!

Answer:

51 1/4

Step-by-step explanation:

Area of a parallelogram= base × height

A= BH

= 41/5 × 25/4

= 205/4 or 51 1/4

Answer:

2/3 is your answer

Step-by-step explanation:

Hope this helps

P.S.(from k12)

The slope of the line is 2/3.

Here,

Graph of a line on coordinate plane. Axes are labeled x and y.

Three points are with ordered pairs (2, 3), (5, 5), and (8, 7) and the line passes through these three points.

We have to find the slope of the line.

What is the slope of the line?

Let two points (x₁, y₁) and (x₂, y₂) are on the line, then slope of the line is calculated as;

\(m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

Now,

Three points are passes through the line are (2, 3), (5, 5), and (8, 7).

To find the slope, Let any two point from three given points.

Let (2, 3) and (5, 5) on the line.

Hence, Slope is calculated as,

⇒ \(m = \frac{5-3}{5-2} = \frac{2}{3}\)

Therefore, The slope of the line is 2/3.

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Answer:-900

Step-by-step explanation: