Given the function the function f of x equals x to the power of four plus three times x cubed minus fifteen times x squared minus nineteen plus thirty complete each part below using complete sentences.
Part A: Give the x - intercepts and the y - intercept of the graph of the function f(x). Explain how these were found.
Part B: Give the local maximums and local minimums and general intervals of where the function increases and decreases.
Part C: State the general shape of the graph, the end behavior, and if the function is even or odd.

When comparing the means of two groups and their relationships, a t-test is an inferential statistic used to assess whether there is a significant difference.

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The perimeter of the circular figure is P = 36.85 feet

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

Let the perimeter of the figure be represented as P

Now , the perimeter of the figure P = perimeter of circle + perimeter of lengths of sides

The total lengths of sides = ( 3 + 3 + 3 + 3 + 3 + 3 ) feet

The total lengths of sides = 18 feet

And , the circumference of circle = 2πr

The diameter of the circle d = 12 feet - 6 feet

The diameter of the circle d = 6 feet

So , the radius of the circle r = d/2 = 3 feet

And , the circumference of circle = 2 x π x 3

The circumference of circle = 6π

So , perimeter of the figure P = ( 6π + 18 ) feet

Perimeter of the figure P = 36.849 feet

Hence , the perimeter of the figure is 36.85 feet

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Solving this equation, we find that m<1 = 126° and m<2 = 54°.

An equation is an expression that contains one or more mathematical operators, such as addition, subtraction, multiplication, and division, and two or more mathematical variables. Equations are used to solve a variety of problems and can be used to represent various situations in mathematics.

Measure
m<1=126°
m<2=54°
Justification
The sum of the measures of the interior angles of a triangle is 180°. Therefore, if m<1 and m<2 are two of the interior angles of a triangle, then m<1 + m<2 must equal 180°. Solving this equation, we find that m<1 = 126° and m<2 = 54°.

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I would expect the answer to be a lot greater than 24 which is 12000.

Percentage is defined as the part of a whole value per 100 which is represented by the symbol%.

To find the number in which 24 is it's 0.2%, the following is carried out;

The number is represented as = x

That is, 0.2/100 × X = 24

0.2x/100 = 24

0.2x = 100×24

0.2x = 2400

X = 2400/0.2

X= 12000

Therefore, 24 is 0.2% of the number 12000 which can be said that it's alot greater than 24.

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The two factors are 2 and 17.

The numbers that can divide a number exactly are called factors. There is therefore no residual after division. The numbers you multiply together to obtain another number are called factors. A factor is therefore another number's divisor.

Given:

The numbers are 34 and 19.

Now, the factor of 34 = 2, 17

Now, multiply the factor, 17 x 2 = 34

and, the addition = 17 + 2 = 19 which is the second number.

Hence, the number are 2 and 17.

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Answer:

[tex]8 \frac{4}{5} [/tex]

Step-by-step explanation:

convert mixed numbers to fractions

[tex] \frac{11}{4} \times \frac{16}{5} [/tex]

multiply

[tex] \frac{176}{20} [/tex]

simplify

[tex]8 \frac{4}{5} [/tex]

Answer: 53 degrees

Step-by-step explanation:

X = 360 - 307 = 53 degrees

Answer:

53

Step-by-step explanation:

subtract 307 from 360

Answer:

7^3/4

Step-by-step explanation:

use the formula below to solve your problem

Answer:46

Step-by-step explanation: just divide 552 by 12

its 46

Answer: D option is not the correct way to evaluate.

Step-by-step explanation: To find out f(x) which is also known as y.

so, f(x) = 3x^{2} - 2x + 5

f(-5) = 3 × 25 - 2(-5) + 5

= 75 + 10 + 5

= 90

Here we see here that four alternatives are given to find out but the option D is not appropriate.

A. By drawing a graph one can easily find out the value here we will try to find out the graph line and then by drawing it on the graph.

B.  Similar to option A we can find out using option B

C. I had also used the same method to calculate for the value of (-5) above so this option is also correct.

D. When y= -5 then if we find out it for x will not work as here we have to find out f(x) which is function of X i.e. simply Y. so this won't work.

The following option is not a possible way to evaluate that function:

See what x is when y=-5.

The correct option is D.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

Given:

We have a function,

f(x)=3x² -2x+5.

To find the solution:

Step 1:

Graph the equation and look at the table to find the y-value when x=-5

Alternate step :

Graph the equation and find the y-value of the ordered pair when x=-5

Or,

Substitute (-5) wherever there is an x and solve using a calculator.

Therefore, option D is not the right way to find the solution.

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Answer:

0.7667

Step-by-step explanation:

The required measure of angle m∠3 = 60° for the given figure.

An interior angle is defined as an angle produced on the inside of a polygon by extending the sides of the polygon.

As per the interior angle property, we have

40° + 85° + m∠1 = 180°

m∠1 = 180° - 40° - 85°

m∠1 = 55°

Since m∠1 = m∠2 (opposite angles)

m∠2 + m∠3 + 55° = 180°

55° + m∠3 + 55° = 180°

m∠3 = 180° - 55° - 55°

m∠3 = 60°

Thus, the required measure of angle m∠3 = 60°

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Answer:

  d.  m = 9/4

Step-by-step explanation:

You want the solution to ...

  1/√8 = 4^(m -3)

It will be convenient to rewrite this equation in terms of powers of 2.

  [tex]\dfrac{1}{\sqrt{8}}=4^{(m-3)}\qquad\text{given}\\\\\dfrac{1}{2^{\frac{3}{2}}}=(2^2)^{(m-3)}\qquad\text{using powers of 2}\\\\-\dfrac{3}{2}=2(m-3)\qquad\text{equate the exponents of 2}\\\\-\dfrac{3}{4}=m-3\qquad\text{divide by 2}\\\\\boxed{m=\dfrac{9}{4}}\qquad\text{add 3}[/tex]

The original cost of the item, given the cost to the store and the markup, can be found to be $ 200

Given that the cost to the store is $ 160 and they would charge a  25 % markup on this cost, the original cost can be denoted as x and the formula would be:

x = Cost to store x ( 1 + markup percentage )

The original cost to the customer would then be:

= 160 x ( 1 + 25 %)

= 160 x 1 .25

= $ 200

The original cost charged by the store to the customer is $ 200.

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The question is:

Find the original cost that the store will charge to the customer. cost to store=$160 markup= 25%

One possible solution we have is 10 bags of popcorn and 7 bags of pretzels.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Let, 'x' represents the number of bags of popcorn and 'y' represent the number of pretzels.

Therefore, The two inequalities representing the context are,

x + y ≥ 13 and 7x + 5y ≤ 85.

Solving these two inequalities graphically, A possible solution

we have, (10, 3).

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The probability of not landing on the number 8 is 9/10.

Given is a the board game life has a spinner with 10 equal spaces.

Probability of getting a 8 -

P{E} = 1/10

Probability of not getting a 8 -

P'{E} = 1 - P{E} = 1 - 1/10 = 9/10

P'{E} = 9/10

Therefore, the probability of not landing on the number 8 is 9/10.

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A quadrilateral is a four-sided polygon, and it can come in various shapes and forms such as square, rectangle, rhombus, parallelogram, etc.

To find the value of x (the measure of an interior angle in a quadrilateral) using the formula (n-2) * 180 / n, you need to know that a quadrilateral has 4 sides (n = 4).

Given that the interior angle is 69, we can substitute n = 4 into the formula:

x = (4-2) * 180 / 4

This simplifies to:

x = (2) * 180 / 4

x = 90

Therefore, the measure of an interior angle in a quadrilateral is 90 degrees. Since you have given one of the angle as 69 degree, we can say that the quadrilateral is not a convex quadrilateral.

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Answer:

see explanation

Step-by-step explanation:

(a)

the radius r of a circle is half the diameter , so

r = 10 ÷ 2 = 5

(b)

the equation of a circle in standard form is

(x - h )² + (y - k )² = r²

where (h, k ) are the coordinates of the centre and r the radius

here (h, k ) = (3, - 8 ) and r = 5 , then

(x - 3)² + (y - (- 8) )² = 5² , that is

(x - 3)² + (y + 8)² = 25 ← equation of circle

The value of x and y in the equation will be 15.2 and -1.84 respectively.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

Based on the information given, the equation is given as:

6x - 3y = 66

x + 3y = -10

Subtract equation i from ii

5x = 76

Divide

x = 76 / 5

x = 15.2

The value of y will be:

= x + 3y = 10

15.52 + 3y = 10

3y = -5.52

y = -5.52 / 3

y = -1.84

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Answer: The probability is 1/20, or in decimal form 0.05 (probability of 5%)

Step-by-step explanation:

This is because there are 20 people in the class, including Shania. Since they are all equally likely and Shania is 1 out of the 20 students in the class, she has a 1 in 20 chance (which when simplified equals 0.05). When the symbol is added, you move the decimal 2 points to the right to get your probability, because a value of 1 is a 100% probability (as shown by the method took to find probability previously in the explanation, Shania/the number of people in the class: 1/20).

As a result, their student film's overall budget was $1200, with $192 spent on props and 68% of the budget allocated to equipment.

A number or ratio that is expressed as a fraction of 100 is known as a percentage in mathematics. There are also sporadic uses of the acronyms "pct.," "pct," and "pc." However, the percent sign "%" is widely used to signify it. There are no dimensions to the percentage amount. Percentages are essentially fractions because they have a numerator of 100. Put the percent sign (%) next to a number to indicate that it is a percentage. For instance, you would score a 75% if you answered 75 out of 100 questions on a test correctly (75/100). Divide the money by the total to get percentages, then multiply the result by 100. The formula (value/total) x 100% is used to determine the percentage.

given

On a student movie, some pals were engaged.

On props and equipment, they used the entire budget.

A total of $24% of the budget was spent on equipment, or $912, on props.

Let's write down the movie's overall budget as x.

$870 was spent on the equipment.

The props budget is equal to 24% of x.

Equipment costs plus prop costs equal the total budget.

x = 912 + 24% of x

x = 912 + 0.24x

x - 0.24x = 912

0.76x = 912

x= 912/0.76

x = $1200

As a result, their student film's overall budget was $1200, with $192 spent on props and 68% of the budget allocated to equipment.

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For the functions f(x) = -x²- 8 and g(x) = 3x + 5 the value for f(g(-4)) = -57.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The given functions are -

f(x) = -x²- 8

g(x) = 3x + 5

The evaluation is for f(g(-4)).

Substitute value of x = -4 in function g(x) -

g(x) = 3x + 5

= 3(-4) + 5

= -12 + 5

= -7

Now, substitute the value of x = -7 in function f(x) -

f(x) = -x²- 8

= - (-7)² - 8

= - 49 - 8

= -57

Therefore, the value is obtained as -57.

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Answer: When simplified, (-3x2 + 2x − 4) − (-2x2 − x + 4) is:

-x2 + 3x − 8.

To simplify the expression you can start by combining like terms:

-3x^2 - (-2x^2) = -3x^2 + 2x^2 = -x^2

then,

-x^2 + 2x -4 - (-x -4) = -x^2 + 2x -4 + x +4 = -x^2 + 3x

And finally,

-x^2 + 3x − 8.

Step-by-step explanation:

There are 67 more baseballs than basketballs.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, a coach buys 125 more soccer balls than basketballs He buys 58 fewer baseballs than soccer balls.

Let the number of soccer balls be x, and that of basketballs and baseballs be y and z respectively.

Therefore, according questions,

x-y = 125

x = 125 + y...(i)

x-z = 58

x = 58 + z...(ii)

Now, since, LHS of both equations are equal,

125 + y = 58 + z

z - y = 67

Since, y is being subtracted by z and result is positive, therefore, number of baseball is greater than number of basket balls,

Hence, there are 67 more baseballs than basketballs.

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The highest grade point is 93 and the lowe

Here we use the Linear Equation concept to calculate the unknown highest and lowest grades. Since we don't know both grade points we represent them with two different variables and will form mathematical expressions as given in the problem.

Solve the equation for the value of variables to get the number of points in given grades.    

Here we have

The highest grade was 14 points higher than the lowest grade.  

Let 'x' be the highest grade and 'y' be the lowest grade

From the given data,

=> x = y + 14 ---- (1)  

Given the sum of the two grade points is 172  

=> x + y = 172 --- (2)

Substitute x = y + 14

=> y + 14 + y = 172

=> 2y + 14 = 172

=> 2y = 158

=> y = 79

Substitute y = 79 in (1)

=>  x = 79 + 14

=>  x = 93

Therefore,

The highest grade point is 93 and the lowest grade point is 79.  

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The equation 12x + 6y = -20 and -3x + y = 5 will have infinitely many solutions when the coefficient of y in 12x + 6y = -20 is -4

When the lines are coincident and they share the same y-intercept, and slope the system of equations has an infinite number of solutions.

If the slope and y-intercept of two lines match, they are in fact the exact same line.

In the problem, the equations are 12x + 6y = -20 and -3x + y = 5

when the ratio of each parameter are equal then the lines have infinite many solutions

x: 12 / -3 = -4

constant: -20 / 5 = -4

let the coefficient be k

y:  k / 1 = -4, k = -4

hence the coefficient should be -4

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We can write that -

An irrational number is a number that cannot be expressed as a fraction p/q for any integers {p} and {q}.

Given are the numbers to be verified as rational or irrational.

Therefore, we can write that -

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