A tank has an intake valve and a release valve. The rate of follow through each valve is inversely proportional to the area of its cross-section. The cross-section area of the input can be described by the equation, f(x)= x^2+2x+1; The cross-section area of the release can be described by the equation, f(x)= x^2+4x+3. If the proportion constant is equal for the input and output, find x such that the volume of material in the tank remains constant.

The predicted height for someone with a femur length of 55 cm is of:

175 cm.

The linear function in this problem is obtained using the point-slope format, which is given as follows:

y - y' = m(x - x').

In which:

From the image given at the end of the answer, two points on the line are given as follows:

(35, 139) and (40, 151).

Given two points the slope is calculated as the change in y divided by the change in x, hence:

m = (151 - 139)/(40 - 35) = 2.4.

Considering the first point, the definition of the line is given as follows:

y - 139 = 2.4(x - 40).

The predicted height for someone with a femur length of 55 cm is y when x = 55, hence:

y - 139 = 2.4(x - 40).

y - 139 = 2.4(55 - 40)

y = 175 cm.

The graph of the linear function is given by the image shown at the end of the answer.

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The equation (i), (ii), and (v) are the equivalent.

What is the equivalent expression?

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.

We have,

2 + x = 5

x + 1 = 4

9 + x = 6

x + (-4) = 7

-5 + x = -2

If we take x =3,

the sums would be true.

for the equation (i) take x = 3,

2 + x = 5

2 + 3 = 5

LHS = RHS = 5

for equation (ii) take x = 3,

x + 1 = 4

3 + 1 = 4

LHS = RHS = 4

for equation (iii) take x = 3,

9 + x = 6

9 + 3 = 6

12 ≠ 6

LHS ≠ RHS

for the equation (iv) take x = 3,

x + (-4) = 7

3 + (-4) = 7

-1 ≠ 7

LHS ≠ RHS

for the equation (v) take x = 3,

-5 + x = -2

-5 + 3 = -2

-2 = -2

LHS = RHS = -2

Hence, if If we take x =3, the sums would be true. the equation (i), (ii), and (v) are the equivalent.

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The prove can be shown on the picture attached. And here the describe that support the picture:

Then we can know the 2 triangles are identical or congruent.

The median drawn from the vertex bisects the angle whose two adjacent sides are equal in isosceles and equilateral triangles. In the case of equilateral and isosceles triangles, the median not only bisects the side opposite the vertex, but it also bisects the angle of the vertex.

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The correct option is angles are complementary if their sum is 90º.

When the sum of two angles is 90°, then they are complements of each other and hence called complementary angles.

Given is a statement, If the sum of two angles is 90º, then the angles are complementary.

Rewriting the sentence to check the hypothesis, in it.

It should be this:

The two angles are complementary if the sum of the two angles are 90 degrees.

A.) There are two angles.

While this is a true statement, it's a little too vague to understand. We can eliminate this answer choice.

B.) The sum of two angles is 90 degrees.

This is also a true statement, but it doesn't describe what type of angles sum to 90 degrees, so we can eliminate this as well.

C.) The angles are complementary.

This is similar to answer choice A. It's a little too vague for specific understanding. We can eliminate this answer choice.

D.) Angles are complementary if their sum is 90 degrees.

This is an accurate statement, and provides details to support its claim, also rewriting the original sentences into one properly.

Hence, the correct option is option D.

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The starting salary of $31,000 and the annual raise of $3,100 indicates that the series is an arithmetic series and the total salary over a ten-year period is $467,500

An arithmetic series consists of the addition of the terms of an arithmetic progression.

The starting salary offered by the company = $31,000

The amount by which the company raises the salary every year = $3,500

The total salary over a ten year period can be found by expressing the situation using an arithmetic progression formula as follows;

The sum of n terms of an arithmetic progression can be found using the formula;

Sₙ = (n/2)·(2·a + (n - 1)·d)

Where;

Sₙ = The sum of n terms of the series

n = The number of terms in terms in the series

a = The first term of the series

d = The common difference between the terms of the series

The details from the question indicates;

n = 10

a = $31,000

d = $3,500

Therefore; S₁₀ = (10/2) × (2 × 31,000 + (10 - 1) × 3,500) = 467,500

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Answer:

14 gallons

Step-by-step explanation:

456 - 28.5g = 5

28.5g =399

G=14

[tex]\int\limits\frac{4}{x^2+2} \, dx[/tex] =  [tex]2^{\frac{3}{2} }tan^{-1}(\frac{x}{\sqrt{2} })[/tex] + C where C is the integrating constant.

What do you mean by integration?

The summing of discrete data is indicated by the integration. To determine the functions that will characterise the area, displacement, and volume that result from a collection of little data that cannot be measured separately, the integral is calculated.

The idea of integration has evolved to address the following issues:

once the derivatives of the problem function have been determined.

to determine the region enclosed by a function's graph under specific restrictions.

Given function f(x) = [tex]\frac{4}{x^2+2}[/tex]

[tex]\int\limits\frac{4}{x^2+2} \, dx[/tex]

Substitute u = [tex]\frac{x}{\sqrt{2} }[/tex]

⇒ [tex]\frac{du}{dx} =\frac{1}{\sqrt{2} }[/tex]

⇒ dx = [tex]\sqrt{2}[/tex] du

= [tex]\frac{2^{\frac{5}{2}} }{2u^2+2}du[/tex]

On simplifying

= [tex]2^{\frac{3}{2} }[/tex][tex]\int\limits\frac{1}{u^2+1} \, du[/tex] .........(1)

Now  [tex]\int\limits\frac{1}{u^2+1} \, du[/tex] = [tex]tan^{-1} (u)[/tex]

Substitute this value in equation (1)

= [tex]2^{\frac{3}{2} }tan^{-1}(u)[/tex]

Substitute the value of u here

= [tex]2^{\frac{3}{2} }tan^{-1}(\frac{x}{\sqrt{2} })[/tex]

Therefore, [tex]\int\limits\frac{4}{x^2+2} \, dx[/tex] =  [tex]2^{\frac{3}{2} }tan^{-1}(\frac{x}{\sqrt{2} })[/tex] + C where C is the integrating constant.

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Answer:4

Step-by-step explanation:

The statement B is as x approaches positive infinity f(x) approaches positive infinity is true.

What is the definition of the limit?

A point or level beyond which something does not or may not extend or pass.

We have to check for continuity by evaluating 2ˣ and -x² - 4x + 1

at the breakpoint x = 0

2⁰ is 1 and -x² - 4x + 1 is also 1,

So these two functions approach the same value as x approaches 0.

Now do the same thing with

-x² - 4x + 1  and (1/2)x + 3 at x = 2;

The first comes out to -11 and the second to 4.  

Thus, this function is not continuous at x = 2.  

We must reject statement A.

for D we have as x increases without bound,

(1/2)x  + 3

also increases without bound.  

Therefore the statement D is true statement.

Statement C is  False,

because the quadratic has a maximum -x² - 4x + 1 has a maximum at

x = -b/[2a],

x = -(-4) / [-2],

x = -2

There are no limitations on the values of the input, x.

A is also a false negative number are in real numbers.

Therefore, the statement B is as x approaches positive infinity f(x) approaches positive infinity is true.

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Answer:

The Answer is B for Edmentum users

Step-by-step explanation:

The solution is

A) The vertical asymptote of the function f ( x ) is = -3

B) The holes in the graph of f ( x ) = ( 0 , 6 )

C) The horizontal asymptote of the function f ( x ) is = 6

What are Asymptotes?

An asymptote is a line that a curve approaches but never touches. A line where the graph of a function converges is known as an asymptote. When graphing functions, asymptotes are typically not required

There are 3 types of asymptotes

Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k. Horizontal Asymptote is when the function f(x) is tending to zero

Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k. Vertical asymptotes are defined when the denominator of a rational function tends to zero

Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b

Given data ,

Let the function be f ( x ) = ( 6x² + 6x - 36 ) / ( x² + 3x )

A)

Now , to find the vertical asymptote

To find the vertical asymptote of a rational function, we simplify it first to lowest terms, set its denominator equal to zero, and then solve for x values

So , when x² + 3x = 0

x ( x + 3 ) = 0

So , x + 3 = 0

x = 0 is a hole in the graph

x = -3 is the vertical asymptote

B) The hole in the graph is ( 0 , 6 )

C)

Now , to find the horizontal asymptote

If both the polynomials have the same degree, divide the coefficients of the leading terms

So , 6x² and x² are the polynomials having the same degree

So , the coefficients are 6 and 1

y = (leading coefficient of numerator) / (leading coefficient of denominator)

y = 6 is the horizontal asymptote

Hence ,

A) The vertical asymptote of the function f ( x ) is = -3

B) The holes in the graph of f ( x ) = ( 0 , 6 )

C) The horizontal asymptote of the function f ( x ) is = 6

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The equations of the perpendicular lines are matched as follows:

y = 1/3x + 4 → y = -3x - 4.

y = 2/5x - 7 → y = -5/2x + 7.

y = -5/2x + 8 → y = 2/5x - 6.

y = -2x + 6 → y = 1/2x + 3.

y = 7/5x - 9 → y = -5/7x - 11.

If the equations of lines are written in slope-intercept form as y = mx + b, where the slope is the value of m, then the slope of lines that are perpendicular to each other will be negative reciprocal of each other.

For example, if the equation of a line is y = 1/2x + 5, the equation of a line that is perpendicular to it would have a slope of -2.

y = 1/3x + 4 has a slope of 1/3. The negative reciprocal of 1/3 is -3. Therefore, the line that is perpendicular to it would be, y = -3x - 4.

y = 2/5x - 7 has a slope of 2/5. The negative reciprocal of 2/5 is -5/2. Therefore, the line that is perpendicular to it would be, y = -5/2x + 7.

y = -5/2x + 8 has a slope of -5/2. The negative reciprocal of -5/2 is 2/5. Therefore, the line that is perpendicular to it would be, y = 2/5x - 6.

y = -2x + 6 has a slope of -2. The negative reciprocal of -2 is 1/2. Therefore, the line that is perpendicular to it would be, y = 1/2x + 3.

y = 7/5x - 9 has a slope of 7/5. The negative reciprocal of 7/5 is -5/7. Therefore, the line that is perpendicular to it would be, y = -5/7x - 11.

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Answer:

Step-by-step explanation:

ok this is hella easy what kind of geometry is this

ok on to the answers

statement 1: angle 1 is a right angle, angle 2 is a right angle

reason 1: given

statement 2: angle 1 is congruent to angle 2

reason 2: all right angles are congruent theorem

second problem

statement 1: angle 1 and angle 2 are vertical angles

reason 1: either say given or shown in diagram (id do both if ur teacher is picky)

statement 2: angle 1 is congruent to angle 2

reason 2: vertical angles are congruent theorem

Here is the two column proof:

    Statement                                        Reason                                              

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

    Statement                                        Reason                                              

We know that Martin will need 16.5 gallons of gasoline using mathematical operations.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations.

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).

So, each day Martin travels:

12 * 2 / 24 miles from home to work and back home.

As she works for 22 days: 24*22 = 528 miles

So, the equation can be:

32x = 528

x = 528/32

x = 16.5

Therefore, we know that Martin will need 16.5 gallons of gasoline using mathematical operations.

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1) The annual decay rate of the exponential function is given as follows: 12.94%.

2) The number of people who started the rumor is of 10.

3) The number of people who will have heard the rumor after 3 days is given as follows: 96 people.

For item 1, the format of the exponential function is given as follows:

A(t) = A(0)(1 - r)^t.

In which r represents the annual decay rate.

The half-life of Radium-228 is 5.75 years, hence:

A(5.75) = 0.5A(0).

Thus the annual decay rate of the exponential function is given as follows:

0.5A(0) = A(0)(1 - r)^5.

(1 - r)^5 = 0.5

Applying the fifth root to both sides:

1 - r = (0.5)^(1/5)

1 - r = 0.8706

r = 1 - 0.8706

r = 0.1294 = 12.94%.

Then for items 2 and 3 we just obtain the numeric values.

The number of people who started the rumor is N(0), hence:

N(0) = 600/(1 + 59e^(-0.7 x 0)) = 600/60 = 10 people.

The number of people who heart the rumor after three days is N(3), hence:

N(3) = 700/(1 + 69e^(-0.8 x 3)) = 96 people.

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Equivalent expression to the given expression [ ( 5/7)² ( 1/3)⁻³]⁻¹ is equal to

Option d. ( 7 /5)² ( 1/3)³.

As given in the question,

Given expression is equal to :

[ ( 5/7)² ( 1/3)⁻³]⁻¹

Apply law of exponent power to power we get,

( mᵃ nᵇ )ˣ =  (m)ᵃˣ × (n )ᵇˣ

( x /y)⁻ᵃ = ( y /x)ᵃ

Here m = 5/ 7, n = 1/3 , a = 2 , b = -3 and x = -1

Equivalent expression of the given expression is:

[ ( 5/7)² ( 1/3)⁻³]⁻¹

= ( 5 / 7 )^(2 × -1) ( 1 / 3)^(-3 × -1)

= ( 5 / 7 )⁻² ( 1 / 3)³

= ( 7 / 5 )²× ( 1 / 3)³

Therefore , equivalent expression of [ ( 5/7)² ( 1/3)⁻³]⁻¹  is equal to the

option d.( 7 /5)² ( 1/3)³.

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Answer:

The inequality which represents the graph shown is -6-y >= x^2 - 7x.

Answer: i think it's 942,480

Step-by-step explanation:

i just multiplied all of the numbers but i'm probably wrong srry

Answer:

7986m^2

Step-by-step explanation:

140-102=38

area of triangle:

(38*66)/2=1254m^2

area of rectangle:

66*102=6732m^2

total area:

1254+6732=7986m^2

For the given expression -21 is not a irrational number.

What is irrational number?

In mathematics, all real numbers that are not rational are referred to as irrational numbers. Irrational numbers can't be expressed as the ratio of two integers, in other words.

Any real number that cannot be expressed as the ratio of two integers—that is, as p/q, where p and q are both integers—is an irrational number. For instance, there is no integer or fraction that equals the square root of 2.

Consider the given expression,

(-14) + (-7)

Solving this, we get

(-14) + (-7) = -14 - 7 = -21

Here 21 can be written in the form p/q.

⇒ -21 = -21/1

So, -21 is a rational number.

Hence, -21 is not a irrational number.

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Y Intercept is the point where a line or curve crosses the y-axis of a graph or in other words where x=0.

Knowledge of the y-intercept can be used when graphing lines or when writing an equation in slope-intercept form.

Formula to calculate y-intercept.

We get the y-intercept by using the equation of a straight line which is;

y = mx + b

Where;

m is the gradient of the slope

b is the y-intercept.

We can use the following formula to calculate the y-intercept.

y – a = m ( x – b )

a and b being a point on a line.

Example:

Suppose you have a straight line whose gradient is 3 and a point 2,1, calculate its y-intercept.

Since the y-intercept is when x=0, therefore;

y – 2 = 3 ( x – 1 )

y – 2 = 3x – 1

y = 3x – 1

Therefore, the number that has replaced b is -1, which means that -1 is the y-intercept.

Answer:

b=12

Step-by-step explanation:

The total price for the car is $26000.

The monthly payment is $500.

From the information illustrated, Bank AAA is charging 4% in total fees to borrow money for a car loan and the person want to buy a car that costs $25,000.

The total amount that will be paid will be:

= Amount of car + Interest

= $25000 + ($25000 × 4%)

= $26000

The amount on a 5 year loan will be:

Interest = PRT

= ($25000 × 4% × 5)

= $5000

Total amount to be paid = $25000 + $5000

= $30000

Monthly payment = Total amount / Number of months

= $30000 / 60

= $500

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Answer:

8

Step-by-step explanation:

72 ÷ 9 = 8

Answer:

8

Step-by-step explanation:

72 divided by 9 is 8

Answer:

slope=3/2 y- intercept=9

Answer:

Slope: 3/2

y-intercept: 9

Step-by-step explanation:

Slope-Intercept Form is given in the form: [tex]y = mx+b[/tex], where [tex]m = \text{slope and }b=\text{y-intercept}[/tex].

So it's very convenient to have a linear equation in this form to identify the slope and y-intercept. To get into this form, we simply need to isolate the y-value.

We start with the initial equation:

[tex]-3x+2y=18[/tex]

The first step to isolating "y" is to move any terms on the same side as the "y" variable to the other side. So let's move the 3x term to the other side, by adding 3x to both sides.

[tex](-3x+3x)+2y=18+3x\implies 2y=18+3x[/tex]

From here, the only thing that is with the "y" variable is the coefficient. The [tex]2y[/tex] is the same thing as: [tex]2\ *\ y[/tex]. We want to get rid of the 2, which we do by dividing by 2, to cancel out the multiplication by 2.

[tex]\frac{2y}{2} = \frac{18 + 3x}{2} \implies y = \frac{18 + 3x}{2}[/tex]

Now from here we want to distribute the division by 2 as such:

[tex]y = \frac{18 + 3x}{2} \implies y = \frac{3}{2}x + \frac{18}{2} \implies y= \frac{3}{2}x + 9[/tex]

So now we have the equation:

[tex]y= \frac{3}{2}x + 9[/tex]

this is in the slope-intercept form:

[tex]y=mx+b[/tex]

in this form the coefficient of x is the slope, so 3/2 is the slope. The constant is the y-intercept, so 9 is the y-intercept.

Answer:

B. H0 : p = 5.8% H1 : p > 5.8%

The null hypothesis, denoted H0, is a statement that asserts that there is no significant difference between a sample statistic and a population parameter. In this case, the null hypothesis would be that the true percentage of the population that suffers from long-term COVID symptoms is equal to 5.8 percent. This is represented symbolically as H0 : p = 5.8%.

The alternative hypothesis, denoted H1, is a statement that contradicts or negates the null hypothesis. In this case, the alternative hypothesis would be that the true percentage of the population that suffers from long-term COVID symptoms is greater than 5.8 percent. This is represented symbolically as H1 : p > 5.8%.

Answer:

[tex]7x+10[/tex]

Step-by-step explanation:

[tex]\frac{1}{3}(9x+12)+4x+6 \\ \\ =3x+4+4x+6 \\ \\ =7x+10[/tex]

Answer:

x= -3

Step-by-step explanation:

5x + 15 =0

5x= -15

x= -3

Answer:

x= -3

5x= -15

x = -15/3

x= -3

The required quotient is given as [tex]3x^2-7x+10[/tex] and the remainder term is [tex]-\frac{1}{x+4}[/tex]

In the question, it is asked to determine the quotient of the expression, [tex]\frac{\left[3x^3+5x^2-18x+39\right]}{x+4}[/tex].

It is a method for performing the division of polynomials, with little writing and lesser calculations than complex division.

Here,

As performing synthetic division of polynomials, the terms in the product remaining as fractions will be the remainder of the division while the polynomial is said to be the quotient of the division.
[tex]= \frac{\left[3x^3+5x^2-18x+39\right]}{x+4}\\=3x^2-7x+10-\frac{1}{x+4}[/tex]

Thus, the required quotient is given as [tex]3x^2-7x+10[/tex] and the remainder term is [tex]-\frac{1}{x+4}[/tex]

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Answer:

the answer is 163.375 lbs

Step-by-step explanation:

Rational numbers are numbers that can be expressed in the form of a ratio of two integers, where the denominator is not equal to zero. Examples of rational numbers include fractions such as 1/2, -3/4, 0.5 and -2.5.  The mathematical formula for a rational number is a/b, where a and b are both integers and b ≠ 0.

Solution:

85.4-28.4-215 +972-30.25

=85.4-28.4-21.625+97.75-30.25

=163.375

The quantity of food left at the end of the month is equal to the amount provided by the management at the beginning of the month plus the amount given in the middle of the month less the amount taken in previous weeks.

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