A chemist mixes 125 milliliters of a solution that is 18% acid with 500 milliliters of pure acid.
Answer the questions below. Do not do any rounding.
(a) How many milliliters of acid are in the resulting mixture?
(b) What percentage of the resulting mixture is acid?

The compound expression (a⁵ · a ÷ a⁻³)⁻¹ is equivalent to the power a⁻⁹.

In this problem we find a compound expression formed by several powers of equal base that must be simplified in a single power with the same base. This can be done by using algebra properties related to powers. First, write the given expression:

(a⁵ · a ÷ a⁻³)⁻¹

Second, multiply the powers of equal base:

(a⁵⁺¹ ÷ a⁻³)⁻¹

(a⁶ ÷ a⁻³)⁻¹

Third, by definition of division and the power of a power:

[a⁶ · (a⁻³)⁻¹]⁻¹

(a⁶ · a³)⁻¹

Fourth, use the multiplication of power of same base:

(a⁶⁺³)⁻¹

(a⁹)⁻¹

Fifth, use the property of a power of a power once again:

a⁻⁹

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What was the question? or was this only meant for your classmates?

1. After constructing the function according to the question, Q(t) = [tex]35e^{\frac{-ln2}{20}t}[/tex].

2. It will take 50 hours for the amount of Diazepam left in the body to reach 7 mg.

What is a function?

Exactly one element of Y is assigned to each element of X in a mathematical function from a set X to a set Y. Both the set X and the set Y are referred to as the function of the domain and codomain, respectively. Examples include f(x) = x/2 ("f of x equals x split by 2") ("f of x equals x divided by 2") Every input "x" has a single output "x/2," which makes it a function: • f(2) = 1.

Solution explained:

According to the question,

Q(t) = [tex]Pe^{rt}[/tex]

The half-life of Diazepam is 20 hours = t

Q(0) = p = 35 { the initial value}

Q(20) = [tex]35e^{20r} = \frac{1}{2} X 35[/tex]

          =  [tex]e^{20r} = \frac{1}{2}[/tex]

          = [tex]20r = -ln2[/tex]

          = [tex]r = \frac{-ln2}{20}[/tex]

Therefore, Q(t) = [tex]35e^{\frac{-ln2}{20}t}[/tex]

Now, Let

Q(t) = 7

[tex]35e^{\frac{-ln2}{20}t}[/tex] = 7

[tex]e^{\frac{-ln2}{20}t} = \frac{1}{5}[/tex]

[tex]{\frac{-ln2}{20}t} = -ln5[/tex]

After calculating,

t = 50 (hours)

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The statement "A system contains two or more linear equations that can be solved or graphed together at once" is true.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

A system contains two or more linear equations that can be solved or graphed together at once.

This statement is true.

For example,

The two linear equations can be:

ax + by = c ____(1)

dx + ey = F _____(2)

We can solve this equation using the substitution method or elimination method.

We can find the point of intersection.

And we can solve and graph together at once.

Thus,

The statement "A system contains two or more linear equations that can be solved or graphed together at once" is true.

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The value of R(x) is - [1-7x]

What is division in algebra?

The four basic arithmetic operations of addition, subtraction, multiplication, and division are used to connect variables and constants in algebraic expressions. The procedure of multiplying and dividing algebraic expressions is the opposite of each other. You can divide algebraic expressions using the long division method, the division of a monomial by another monomial, or the division of a polynomial by another polynomial.

Dividend: The number or value that we divide is known as a dividend.

Divisor: The number that divides the dividend is known as a divisor

Quotient: The result obtained from the division process is known as a quotient

Remainder: The number left over after the division process is known as the remainder.

In the given question;

f(x) is dividend and

d(x) is divisor

Q(x) is the quotient

And we have to find the remainder i.e. R(x)

After dividing [tex]\frac{4x^3-8x^2+2x-1}{2x+1}[/tex] we get

Q(x) =[tex]2x^2-5x[/tex]

and R(x) = [tex]-[1-7x][/tex]

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Answer: 9/2

Step-by-step explanation:

Answer:

One number is 16 and the other number is 20

Step-by-step explanation:

Let x = one number

Let y = the other number

x + y = 36

x - y = 4  Or x = 4 + y

Substitue in 4 + y for x in the first equaion

4 + y + y = 36  Combine like terms

4 + 2y  = 36  Subtract 4 from both sides

2y = 32  Divide both sides by 2

y = 16

Substitute 16 for y in either of the orginal equaions

x + y = 36

x + 16 = 36  Subtract 16 from both sides

x = 20

The polynomial function for the given zeros is  x⁷+9x⁶+20x⁵-22x⁴-87x³+37x²+114x-72

Polynomial function:

An expressions that may contain variables of varying degrees, non-zero leading coefficients, positive exponents, and constants is known as polynomial function.

Given,

Here we have the value of zeros as x = -1, 3, 2, 4 and n = 5.

Now, we have to find the polynomial function from it.

Let us consider if a polynomial function f(x) has zeros x = -1, x = 3, x = 2, and x =  4, then it has factors 

=> (x - 1)³ (x + 3)² (x +2) (x + 4)

Here there are four factor, in these polynomial so it can be Quintic Function.

Now, we have to expand this one to get the resulting polynomial,

=> x⁷+9x⁶+20x⁵-22x⁴-87x³+37x²+114x-72

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Answer:

Step-by-step explanation:

8z-6=-2(-4+3)

8z-6=8z-6

on transposing,

8z-8z-6+6=0

Answer:

0

Step-by-step explanation:

The y-coordinates are the same, so the line is horizontal. Therefore, the slope is zero.

The portion of the graph which does not contain (0, 0) is shaded.

What are Linear Inequalities?

When two mathematical statements or two numbers are compared in an unequal way, it is known as an inequality in mathematics. Inequalities can generally be classified as either algebraic or numerical or as a combination of the two. When a polynomial of degree 1 is compared to another algebraic expression of a degree less than or equal to 1, this is an example of a linear inequality, which is an inequality involving at least one linear algebraic expression.

Given the inequalities :

y ≥>2x + 1

y ≤<2x - 2

From y > 2x + 1 ;

Since the inequality sign is ≥, a solid line is used to draw the straight line graph of  y > 2x + 1

From :

y = mx + c

Where, m = slope ; c = intercept

Hence, a straight line graph with ;

Intercept, c = 1 (where the line crosses the y-intercept)

Slope, m = 2

Consider a point, which isn't on the line ;

Take point (0,0) and use it to test the inequality :

0 > 2(0) + 1

0 >0 + 1

0 >1

This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.

From : y < 2x - 2

Since the inequality sign is ≤, a solid line is used to draw the straight line graph of  y < 2x - 2

Graph the line y < 2x - 2, with ;

Intercept, c = - 2

Slope = 2

Consider a point, which isn't on the line ;

Take point (0,0) and use it to test the inequality y < 2x - 2:

0 < 2(0) - 2

0 < 0 - 2

0 < - 2

This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.

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The solution of the function is x = 12

Trigonometric ratios are the ratios of sides of a right-angle triangle. The most common trigonometric ratios are sine, cosine, and tangent.

Consider a right-angle triangle ABC, right-angled at C. In that case, side AB will be the hypotenuse. Also, if we chose AC as the base and BC as the perpendicular. Then, for ∠BAC, value of sinθ = Perpendicular/ hypotenuse = BC/AB

6cos(5x) = 3

divide both sides by 6, we have

cos(5x) = 3/6

cos(5x) = 0.5

taking the anti cosine of both sides

5x = Arc cos 0.5

5x = 60

x = 60/5

x = 12°

In conclusion, the value of x = 12°

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Forming the two telephone charge plans in a slope intercept equation form, like Y=mx + b, is as follows:

The slope intercept equation is an equation of a straight-line with its slope (constant unit rate) combining the x and y intercepts.

Generally, the formula y = mx + b depicts the slope intercept equation with the following values:

y = y coordinate

m = slope

x = x coordinate

b = y intercept

                           Plan A   Plan B

Fixed cost (b)      $25        $50

Variable cost (m)  50          25

x = monthly            12          12

y = the total cost for the period

Thus, Plan A will have a total cost of 50x + 25 and Plan B will have a total cost of 25x + 50.

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Answer:

x = [tex](\frac{z-y}{5}) ^{2}[/tex]

Step-by-step explanation:

5[tex]\sqrt{x}[/tex] + y = z ( subtract y from both sides )

5[tex]\sqrt{x}[/tex] = z - y ( divide both sides by 5 )

[tex]\sqrt{x}[/tex] = [tex]\frac{z-y}{5}[/tex] ( square both sides to clear the radical )

([tex]\sqrt{x}[/tex] )² = [tex](\frac{z-y}{5}) ^{2}[/tex]

x = [tex](\frac{z-y}{5}) ^{2}[/tex]

The day with greater actual attendance is Thursday with 98 students

A percentage is defined as the ratio that can be expressed as a fraction of 100

Given:

Expected numbers: Wednesday= 70 students andThursday= 112 students

20% of Wednesday = 20/100 x 70 = 14 students. That is 14 students are absent on Wednesday but attended on Thursday instead. This means 56 (70 -14) students scheduled for Wednesday attended.

25% of the students who planned to attend on Thursday attended on Wednesday instead:

25% of Thursday = 25/100 x 112 = 28 students.  This means 84 students scheduled for Thursday attended

Actual Wednesday attendance = 56 + 28 = 84 students

Actual Thursday attendance = 14 + 84 = 98 students

Therefore, Thursday had a greater actual attendance with 98 students

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Answer:

30 = 6

45 = x

cross multiply

30x = 45*6

30x = 270

divide both sides by

30x/30 = 270/30

X = 9

9-6 = 3 days

Factoring -4 out of -8+20 factored expression is -4(2 + 5).

Factor expressions, also known as factoring, refer to the process of rewriting an expression as the product of factors. 3x + 12y, for example, can be factored into a simple expression of 3 (x + 4y). Calculations become easier in this manner. The terms 3 and (x + 4y) are referred to as factors.

To factor a given expression goes thus:

Each term should be written as the prime factorization.

Determine the factors that all of the terms share.

Multiply those common variables.

In this case, factoring 4 out of -8+20 factored expression is -4(2 + 5).

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Answer: p(t) = 100×1.0153^(12t)

1.53% per month

In general, the function will be written ...

 p(t) = (initial value)×(growth factor)^t

where t is in units comparable to those applicable to the growth factor. The growth factor is found from ...

 growth factor = 1 + growth rate

Here, the growth rate is given as 20% per year, so the growth factor per year is ...

 1 +20% = 1.20

The initial value is given as 100, so we can write the exponential function as ...

 p(t) = 100×1.20^t

__

The time period units for t are supposed to be years, but we want to find the growth rate for a month. We can do that by recognizing there are 12 months in a year. In the above equation, we can use (1/12)(12t) in place of t, then figure the growth factor (and growth rate) per month.

 p(t) = 100×(1.20^(1/12))^( 12t)

 p(t) = 100×1.0153^(12t) . . . . population exponential function

This shows the monthly growth factor is 1.0153, so the monthly rate of change (growth rate) is ...

 1.0153 -1 = 0.0153 = 1.53% . . . . monthly rate of change

Step-by-step explanation:

Answer: 20 [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

First of all, 5 [tex]\frac{4}{10}[/tex] = 5.4

Remember, 1/10 = 0.1, 2/10 = 0.2, and so on.

This means we can change the equation to 25.92 - 5.4, which gives us 20.52.

This is close to 20.50, which is equivalent to 20 [tex]\frac{5}{10}[/tex], which is equivalent to 20 [tex]\frac{1}{2}[/tex].

Value of the expression (a²- 8a - 26) ÷ (a + 2) using synthetic division is given by quotient is a - 10 and remainder is -6.

As given in the question,

Given expression is equal to,

(a²- 8a - 26) ÷ (a + 2)

Simplify the given expression using synthetic division is shown in the attached file,

Another way of division,

(a²- 8a - 26)

= a² -10a + 2a -20 -6

= a (a -10) + 2( a - 10) -6

= ( a + 2 )( a - 10 ) - 6

Quotient of the given division is equal to ( a - 10 )

Remainder of the given division is equal to -6

Therefore, value of the expression (a²- 8a - 26) ÷ (a + 2) using synthetic division is given by quotient is a - 10 and remainder is -6.

The complete question is :

Evaluate the given expression using synthetic division :

(a²- 8a - 26) ÷ (a + 2)

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The value of 3 less than the quotient of a number y and 4 when y is 20 is 2.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

The expression less than the quotient of a number y and 4 will be:

y/4 - 3

When y is 20, the value will be:

y/4 - 3

20/4 - 3

5 - 3

= 2

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The probability of choosing a blue marble is 0.59.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

The jar contains 7 red marbles and 10 blue marbles.

The probability of choosing a blue marble will be:

= Number of blue marbles / Total marbles

= 10/17

= 0.59

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Answer:

nu tg hi yum

Step-by-step explanation:

The true statements about the circle are the radius of the circle is 3 units, the center of the circle lies on the x-axis and the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9

Given: the equation is x²+y²–2x–8 = 0

In order to determine true statements about the circle, we have to rewrite the given equation and compare it with the standard form of the equation of a circle.

The standard form of the equation of a circle is

(x-a)² + (y-b)² = r²

where (a, b) is the center and r is the radius

using the completing square method on the given equation:

x²+y²–2x–8 = 0

x²-2x + (-1)² + y² + (0)²= 8 + (-1)²

(x-1)² + (y-0)² = 9

(x-1)² + (y-0)²  = 3²

Thus, the center is (0, 1) and the radius is 3

Therefore, the options are the radius of the circle is 3 units, the center of the circle lies on the x-axis and the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9

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The slope of the straight line passing through the two given points is undefined which means the line is parallel to the y-axis.

Let us consider the two points A(x₁,y₁) and B(x₂,y₂) be the two points (7,-6) and (6,-6) on the cartesian coordinates.

Let the slope of the line joining A (7,-6)  and B(6,-6)  be m.

We know that the slope of a line is given by:

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

Slope of the line

= (6-7) / (-6+6)

= -1 / 0

= undefined

Since the slope is undefined we can say that the straight line is parallel to the y axis.

we know that tan 90° = ∞

So any line parallel to this line will have the same slope as the y axis.

Hence the slope of the given line is undefined or infinity.

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The linear equation with the given slope in the slope-point form is:

y = (1/2)*(x + 1) + 4

We know that for a line with a slope m and a point (a, b), the point-slope form of the line is written as:

y = m*(x - a) + b

In this case, we know that our line has a slope of 1/2 and it passes through the point (-1, 4), so we can replace this on the above formula to get:

y = (1/2)*(x + 1) + 4

This is the linear equation in the point-slope form.

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The equivalent expression for 11(9a+3b) is 33(3a+b)

How should an equivalent be written?

The numerator and denominator must be multiplied or divided by the same number when writing equivalent fractions. This explains why these fractions have the same value when they are simplified.

How does math equivalent work?

We need to multiply the denominator of 7 by a number that will give us 21 in order to obtain equivalent fractions, which requires multiplying both the numerator and the denominator by the same number. We may find an equal fraction by multiplying the numerator and denominator by 3, so 3 times 7 gives us 21.

Given expression: 11(9a+3b)

Take 3 outside from the expression, we get,

= 33(3a+b), which is called the equivalent expression

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To solve we must expand the terms and then simplify and finally multiply.

The expressions are two algebraic expressions which are equivalent when they both take the same numerical value, for any value of the domain of each of the variables.

So the Result of the Expression is 99a + 33b

¡Hope this helped!

Slope = m = 2

y = mx + b

y = 2x + b

Plug in (-2, 1) to find b

1 = 2(-2) + b

b = 5

y = 2x + 5

Answer: Substituting x = 2y + 4 into the equation 6x + 8y = 7.

Step-by-step explanation:

       Since they solved for x, their next step will likely being solving by substitution, where you substitute for one variable to solve the other one.

       There are a few different ways to solve systems of equations, so this might not be her next step.

Answer:

D and E

Step-by-step explanation:

Dilations shrink or enlarge, but do not change angle measurements.