Word problem please help thank you

There are four real roots for the quadratic-like equation x⁴ + 9 · x² - 10 = 0: x₁ = + √(- 9 / 2 + 11 / 2), x₂ = + √(- 9 / 2 - 11 / 2), x₃ = - √(- 9 / 2 + 11 / 2) and x₄ = - √(- 9 / 2 - 11 / 2)

In this problem we find a quadratic-like equation of the form a · x²ⁿ + b · xⁿ + c = 0, where a, b, c are real coefficients and whose roots must be found. This can be done by completing the square and clear variable x. First, write the polynomial:

x⁴ + 9 · x² - 10 = 0

Second, use the following substitution: u = x²

u² + 9 · u - 10 = 0

Third, complete the square:

u² + 9 · u + 81 / 4 = 10 + 81 / 4

u² + 9 · u + 81 / 4 = 121 / 4

Fourth, factor the expression and clear variable u:

(u + 9 / 2)² = 121 / 4

u + 9 / 2 = ± 11 / 2

u = - 9 / 2 ± 11 / 2

Fifth, reverse the substitution and clear variable x:

x² = - 9 / 2 ± 11 / 2

x = ±√(- 9 / 2 ± 11 / 2)

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Brian's gross income last month will be $3319.

The percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

From the information, Brian is a salesman for a wholesome computer parts company. He earn straight commission at a rate of 4% last month is total sales were 82,968.

Brian's gross income last month will be:

= 4% × 82968

= $3319

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Answer: Attached

Step-by-step explanation:

The slope of the given line that passes through (3, 14) and (7, 7) is m = - 7/4.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is a straight line that passes through points (3, 14) and (7, 7).

It is given that the line passes through (3, 14) and (7, 7). We can write the slope as -

m = (7 - 14)(7 - 3)

m = - 7/4

Therefore, the slope of the given line that passes through (3, 14) and (7, 7) is m = - 7/4.

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Answer:

Step-by-step explanation: true

Answer:

90

Step-by-step explanation:

a times by b is equal to 3600 and b divided by a is equal to 4/9 which means that a must be a mulitiple of 4 and b must be a multiple of 9. An easy multiple of 4 and a easy mulitple of 9 that times together eqaul 3600 is 90 and 40. So therefore a= 90

The scientific notation of Pill's mass 5 × 10⁻³ g.

And, In milligrams, The pill's mass is 5.0 milligram.

Scientific notation is a way of writing a very large or very small numbers. For example; 230,000,000 can be written in scientific notation as 2.3 x 10⁸.

Given that;

A pain-relieving pill has a mass of 0.005 g.

Now, We can write the mass in scientific notation as;

⇒ 0.005 g

⇒ 5 × 10⁻³ grams

And, We can write the pill's mass in milligram as;

Since, 1 g = 1000 milligram

Hence, We get;

⇒ 0.005 g = 0.005 × 1,000 milligrams

                = 5.0 milligrams.

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13students;it had already said it.

The probability of total of 8 is 0.1389, the probability of at most a total of 5 is 0.2778.

A pair of fair dice is tossed.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur.

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes.

Probability of event to happen

(a)) A total of 8 can be obtained with the following outcomes,

The sample space S contains n(S) = 36 elements when a pair of dice is tossed.

⇒{(2,6),(3,5),(4,4),(5,3),(6,2)} i.e. 5 outcomes.

⇒Required probability = [tex]\frac{5}{36}[/tex] = 0.1389

The probability of a total of 8 is 0.1389.

(b).

At most a total of 5 can be obtained with the following outcomes:

⇒{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(3,1),(3,2),(4,1)} i.e. 10 outcomes.

⇒Required probability =[tex]\frac{10}{36}[/tex] =0.2778

The probability of at most a total of 5 is 0.2778.

Therefore, the probability of total of 8 is 0.1389, the probability of at most a total of 5 is 0.2778.

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In fraction 5 / 6 the number of the groups of 1²/₃ is only 1.

The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction.

A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given that there are two fractions 5/6 and 1²/₃. The group will be calculated as,

Fraction =  1²/₃ = 5 / 3

Fraction = 5 / 6 = ( 5 / 3 ) x ( 1 /2 )

Here in the above fraction of 5 / 6 there is only one 5 / 3 or 1²/₃.

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The hours that it would take Nisha to make the gungharoos is 301.5 hours

The equation of the line in the scatter plot is given as

y= 4.75x - 2.5

Where x is the number of ghungaroos that Nisha would make

We have to put in the value of x as 64 because the question tells us that She made a total of 64 gungharoos

Hence we would have:

y = 4.75 * 64 - 2.5

y = 304 - 2.5

y =301.5

The hours that it would take Nisha to make the gungharoos is 301.5 hours

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The length of the isosceles trapezoid height CE is 14 meters.

To find the length of the height CE of the isosceles trapezoid, we can use the Pythagorean theorem.

The isosceles trapezoid CE is the hypotenuse of the right triangle formed by height CE and distance AC. CE is also the height of the trapezoid. Let the length of CE be 'x'

The Pythagorean theorem states that the square of the length of the hypotenuse of a right triangle (CE) is equal to the sum of the squares of the lengths of the other two sides (AC and CE).

x² = AC² + CE²

We know that AC = 14 meters and CE = x.

So x² = 14² + x²

x² = 196 + x²

x² = x² + 196

0 = 196

x = √196 = 14

Therefore, the length of height CE is 14 meters.

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Answer: To differentiate a function using the first principle, we first need to know the function and it's original value. Given that the function is f(x) = 5√x .

The first principle of differentiation states that the derivative of a function f(x) at a point x is approximately equal to the change in f(x) for an infinitesimal change in x. We can use this principle to find the derivative of a function f(x) at a point x by calculating the limit of the ratio (f(x+dx)-f(x))/dx as dx approaches zero.

To differentiate f(x) = 5√x with respect to x using the first principle, we take the following steps:

Find the change in f(x) as x changes by dx, which is f(x + dx) - f(x)

Divide that change by dx to find the slope of the function at that point

Take the limit of that slope as dx approaches zero

So:

f(x + dx) = 5√(x + dx)

f(x) = 5√x

change in f(x) = f(x + dx) - f(x) = 5√(x + dx) - 5√x

slope = change in f(x) / dx

= (5√(x + dx) - 5√x) / dx

The limit as dx approaches zero is the derivative of the function,

lim (dx->0) [(5√(x + dx) - 5√x) / dx]

= lim (dx->0) [(5(x+dx)^1/2 - 5x^1/2) / dx]

= 5 * lim (dx->0) [(x+dx)^1/2 - x^1/2] / dx

= 5 * (1/2)x^(-1/2)

So the derivative of the function f(x) = 5√x is (5/2)x^(-1/2)

This is the slope of the function at a point x, which is the rate of change of the function at that point x.

Step-by-step explanation:

The equation of line is y = -2/3x - 4, option C is correct.

A line's slope is defined as the ratio of the change in y coordinate to the change in x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

Given coordinates

(-6, 0) and (0, -4)

equation of line is y = mx + c

m = (y₂ - y₁)/(x₂ - x₁)

m = (-4 - 0)/(0 + 6)

m = -2/3

and c is y-intercept  = -4

equation is y = mx + c

y = -2/3x - 4

Hence option C is correct.

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Answer:

The equation of line is y = -2/3x - 4, option C is correct.

Step-by-step explanation:

Answer:

a)  See below.

b)  Arithmetic sequence

[tex]\textsf{c)} \quad a_n=10n-7[/tex]

Step-by-step explanation:

From inspection of the given table, t(n) increases by 10 each time n increases by 1.

Therefore:

[tex]\implies a_7=53+10=63[/tex]

[tex]\implies a_8=63+10=73[/tex]

Completed table:

[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} n&t(n) \\\cline{1-2} \vphantom{\dfrac12} 4& 33\\\cline{1-2} \vphantom{\dfrac12} 5& 43\\\cline{1-2} \vphantom{\dfrac12} 6&53 \\\cline{1-2} \vphantom{\dfrac12} 7&63\\\cline{1-2} \vphantom{\dfrac12} 8& 73\\\cline{1-2} \end{array}[/tex]

As the given sequence has a constant difference of 10, it is an arithmetic sequence.

[tex]\boxed{\begin{minipage}{8 cm}\underline{General form of an arithmetic sequence}\\\\$a_n=a+(n-1)d$\\\\where:\\\phantom{ww}$\bullet$ $a_n$ is the nth term. \\ \phantom{ww}$\bullet$ $a$ is the first term.\\\phantom{ww}$\bullet$ $d$ is the common difference between terms.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

The common difference is 10. Therefore:

To find the first term, a, substitute the value of d and one of the terms into the formula:

[tex]\begin{aligned}\implies a_4=a+(4-1)(10)&=33\\a+3(10)&=33\\a+30&=33\\&a=3\end{aligned}[/tex]

Therefore, to write an equation for the given arithmetic sequence, substitute the found values of a and d into the formula:

[tex]\implies a_n=3+(n-1)(10)[/tex]

[tex]\implies a_n=3+10n-10[/tex]

[tex]\implies a_n=10n-7[/tex]

Answer:

6/8

Step-by-step explanation:

1/8+1/4+3/8

1/8+2/8+3/8

The probability that a random U.S. citizen you meet is not planning to start a new degree program or continue their education in the next year is; 0.8649

Probability of selection defines the probability that a population unit is included in a sample generated by probability sampling.

It simply means that the probability of selection.

For example,  at a school board meeting there are 9 parents and 5 teachers. Two teachers and 5 parents are female. If a person at the school board meeting is selected at random, we can use the concept of probability selection to find the probability that the person is a parent or a female.

Now, we are told that a recent survey of 37 million citizens in the United States, 5 million were planning to start a new degree program or continue their education in the next year. Thus, we can say that;

Total number of people in survey = 37 million

Number of people planning to start a new degree program or continue their education in the next year = 5 million

Thus;

P(People starting new program) = 5 million/37 million

= 5/37

Thus;

P(People NOT starting new program) = 37/37 - 5/37

= 32/37 = 0.8649

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The combined expression for the given expression will be ( 5y -11 ) / ( y² - 9 ).

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is ( 4 / y² - 9 ) + ( 5 / y + 3 ).

The expression will be solved as below,

E = ( 4 / y² - 9 ) + ( 5 / y + 3 ).

E = 4 / ( y +3 ) ( y - 3 ) + 5 / ( y + 3 )

E = 1 / ( y + 3 ) [ ( 4 / ( y- 3 ) + 5 ]

E = 1 / ( y +3 ) [ ( 4 + 5y - 15 ) / ( y - 3 ) ]

E = ( 5y - 11 ) / ( y² - 9 )

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x=8.

[tex]2log(x)=log(64)[/tex]

[tex]\frac{2log(x)}{2} =\frac{log(64)}{2}\\ \\log(x)=\frac{log(64)}{2}[/tex]

When a logarithm doesn't have it's base expressed (base is tipically written as a subscript) we can assume it'sbase is 10. Therefore, to solve this equation, take the following step:

[tex]10^{log(x)} =10^{\frac{log(64)}{2}} \\ \\x=10^{\frac{log(64)}{2}}\\ \\x=8[/tex]

If the result is correct, then the equation should return the same value of both sides of the equal symbol (=) when we substitute the variable "x" by it's calculated value, 8.

[tex]2log(8)=log(64)\\ \\1.806179974=1.806179974[/tex]

As you can tell, the same number appears on both sides of the equal symbol, this means that the result is correct!

Answer:

x = 8

Step-by-step explanation:

Given expression:

[tex]2\log x=\log 64[/tex]

[tex]\textsf{Apply the log power law}: \quad n\log x=\log x^n[/tex]

[tex]\implies \log x^2=\log 64[/tex]

Rewrite 64 as 8²:

[tex]\implies \log x^2=\log 8^2[/tex]

[tex]\textsf{Apply the log equality law}: \quad \textsf{If\;\;$\log x=\log y$\;\;then\;\;$x=y$}[/tex]

[tex]\implies x^2=8^2[/tex]

Square root both sides:

[tex]\implies x=8[/tex]

Answer:

-1

Step-by-step explanation:

Step-by-step explanation:

8 + (-9) is an expression that represents the mathematical operation of adding 8 and -9.

An equivalent expression for 8 + (-9) is 8-9 which is the same as 8 + (-9)

Both expressions are equivalent and have the same value, which is -1.

So, 8 + (-9) and 8-9 are equivalent expressions.

The value of the combined function f(g(x)) will be -16x^2+88x-120.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

Now,

Given functions are f(x)=1-x^2 and

g(x)=11-4x

Therefore,

the combined function will be f(g(x))=1-(11-4x)^2

=1-121-16x^2+88x

Hence,

           The value of the combined function f(g(x)) will be -16x^2+88x-120.

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Right question would be :-

Consider functions f and g. f ⁡ ( x ) = 1 − x 2 g ⁡ ( x ) = 11 − 4 ⁢ x Evaluate f(g(x))?

Answer:

Step-by-step explanation:

when 2 and 4 are factors of a number then 8 will also be factor of that number. Example: let's take the number 8 here 2,4 and 8 are factors of the number.

Answer: not sure if this is what you want but a number is divisible by 2 if it ends in 2, 4, 6, 8 or 0  a number is divisible by 5 if it ends in 5 or 0  a  number is divisible by 10 if it ends in a 0

Step-by-step explanation:

Answer: We need to add 1 7/8 to 5 5/8 to make 7 as an improper fraction. ✅

PLEASEEEE GIVE BRANLIEST

Step-by-step explanation: To add 5 5/8 to a number to make 7 as an improper fraction, we need to convert 5 5/8 to an improper fraction.

To convert a mixed number to an improper fraction, we take the whole number, multiply it by the denominator of the fraction, and add the numerator. So, 5 5/8 becomes (5 x 8) + 5 / 8 = 40 + 5 / 8 = 45/8.

Now, we can add 45/8 and the number that we need to add to make 7 as an improper fraction.

45/8 + x = 7

To find x, we can subtract 45/8 from both sides of the equation:

x = 7 - 45/8

x = 1 7/8

So, we need to add 1 7/8 to 5 5/8 to make 7 as an improper fraction. ✅

The equation of the slant asymptote of the function is y=2x³+5x²+1.

A slant asymptote, also known as an oblique asymptote, occurs when the degree of the numerator polynomial is greater than the degree of the denominator polynomial. The slant asymptote gives the linear function which is neither parallel to x-axis nor parallel to the y-axis.

The given function is f(x)=2x³+5x²+(x-5)/x² +1

Find the oblique asymptote using long polynomial division.

Vertical Asymptotes: x=0

No Horizontal Asymptotes

Oblique Asymptotes: y=2x³+5x²+1

Therefore, the equation of the slant asymptote of the function is y=2x³+5x²+1.

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The solution to the equation 120 + 18 1/4x = 180 –13/4x is x = 120/43

From the question, we have the following parameters that can be used in our computation:

120 + 18 1/4x = 180 –134x

Express the equation properly

This gives

120 + 18 1/4x = 180 –13/4x

Collect the like terms in the above equation

So, we have the following representation

18 1/4x + 13/4x = 180 - 120

Evaluate the like terms in the above equation

So, we have the following representation

21 1/2 x = 60

Express as decimal

21.5x = 60

Divide both sides by 21.5

x = 60/21.5

Simplify the fraction

x = 120/43

Hence. the solution is x = 120/43

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Answer:

To calculate the marginal tax rate on the investment, you'll need to figure out the additional tax on the new income. In this example, $500 will be taxed at 15% and $500 at 25%. This produces tax of $200, which on income of $1,000 makes the marginal tax from making that investment equal to $200 / $1,000 or 20%.

By the property of parallelograms that diagonals are equal in length and they bisect each other we have determined the values of x and y.

A basic quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.

The area of a parallelogram is base multiples by height as two triangles form a parallelogram.

We know the diagonals of a parallelogram are equal and they bisect each other, From this property, we can write,

OA = OC.

x + 23 = 31.

x = 31 - 23.

x = 8 units.

XZ = 2(OX).

26 = 2(- 44 + x).

26 = - 88 + 2x.

2x = 114.

x = 57 units.

OL = OJ

8x - 56 = 24.

8x = 80.

x = 10.

OM = OK.

36 = 4y + 20.

4y = 16.

y = 4.

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