A polynomial function can be written as (x − 2)(x − 3)(x + 5). What are the x-intercepts of the graph of this function?

15) Evaluating the mathematical expression -10 -144/(-12) shows that 144 is being divided by 12 before subtracting 10, following the application of PEMDAS.

16) The value of the algebraic expression is 2.

The evaluation of an expression is finding its value by substituting variables and applying the PEMDAS rule.

PEMDAS means the order of algebraic operations that applies parentheses, exponents, multiplication, division, addition, and subtraction.

-10 -144/(-12)

-10 + (144/12)

-10 + 12

= 2

Thus, we have evaluated the expression to have a value of 2.

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Answer:

16

Step-by-step explanation:

As the question states, we are counting downwards which means with every interval we are going back -1. Therefore, 17 - 1 = 16

The expression to be added is 9mn +3m² - 12n²

These are expressions having terms, variables, coefficients, factors and constants.

They are also known to be composed of arithmetic operations, such as;

From the information given, we have the expression;

-7 mm + 2m ²+ 3n²

To make it up to 5m² +2mn-9n²., we have

-7mn + 9mn + 2m² + 3m² + 3n² - 12n²

Hence, the expression is 9mn +3m² - 12n²

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Answer:

Step-by-step explanation:

To solve this system of two equations with two variables (x and y), we'll use the substitution method. Here's how:

Solve one of the equations for either x or y, in terms of the other variable. Let's solve the first equation, 2x - 5y = 4, for x:

x = (4 + 5y)/2

Substitute the expression for x from step 1 into the second equation, 4x = 8 + 10y:

4(4 + 5y)/2 = 8 + 10y

Simplify the equation from step 2:

8 + 10y = 8 + 10y

Solve for y by subtracting 8 from both sides:

10y = 10y

Divide both sides by 10 to find the value of y:

y = y

Now that we have the value of y, we can substitute it back into the expression for x from step 1:

x = (4 + 5 *y)/2

So the solution to the system of equations is (x, y) = ((4 + 5 *y)/2, y=y).

The domain of the relation include the following: C. {-5, -2, 0, 1, 4}.

In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left of the graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain:

Domain = {-5, -2, 0, 1, 4}.

In conclusion, the domain of this relation are all the x-values (independent value) that are located on the x-axis of the graph, which include {-5, -2, 0, 1, 4}.

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The proportional relationship used to find the distance that the train will travel after m minutes is given as follows:

d = 0.12m.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

Considering that when the input is of 5, the output is of 0.6, the constant of the relationship in this problem is given as follows:

k = 0.6/5

k = 0.12.

Hence the equation is given as follows:

d = 0.12m.

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Answer: T=Q/p+1

Step-by-step explanation:

Rearrange

The length of the dotted line would be 7.922 ft.

A circle's diameter is measured from the center of the circle outward. It is equivalent to twice the radius, or the distance a circle's radius is measured from its center to any other point on the circle.

The mathematical formula for a circle's diameter is d = 2r if d is the circumference and r is the radius.

When we subtract the circle's thickness from its outer diameter to determine the provided circle's inner diameter, we obtain q = 17.708 - 4.893 - 4.893.

We can solve this for q = 7.922

The dotted line would be 7.922 feet long as a result.

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A situation in which a quadratic equation cannot be solved using the quadratic formula include the following: A. The right-hand side of the equation is 1.

Generally speaking, the standard form of a quadratic function is given by this mathematical expression;

ax² + bx + c = 0

Where:

Mathematically, the quadratic formula is modeled or represented by this mathematical expression:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]

In this context, we can reasonably infer and logically deduce that a quadratic function cannot be solved by using the quadratic formula when the coefficient of the x²-term is equal to zero (0) or when right-hand side of the equation is equal to one (1).

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x = 415.

Check attached image 1.

So at this point, we know the measures of the angles, in terms of "x", which is a variable. We may use the implicit information in the drawing to find more information. Such as the total measure of the sum of angles DBE and CBE. This total measure equals 90°, we know this because there's a square drawn on the base of both angles. Whenever you see a square drawn at the base of an angle, it means the measure of that angle is 90°, a right angle.

Check attached image 2.

We know that the sum of angles DBE and CBE equal 90°. Hence:

[tex]DBE+CBE=90[/tex]

In terms of variable "x", this is:

[tex](0.1x-22)+(0.3x-54)=90[/tex]

[tex]0.1x-22+0.3x-54=90[/tex]

[tex]0.1x+0.3x-54-22=90\\ \\0.4x-76=90[/tex]

[tex]0.4x-76+76=90+76\\ \\0.4x=166[/tex]

[tex]\frac{0.4x}{0.4} =\frac{166}{0.4} \\ \\x=415[/tex]

To see if "x = 415" is the correct answer, take the original equation, substitute "x" by "415" and, if the same number appears on both sides of the equal (=) sign, then we've found our answer!

[tex](0.1x-22)+(0.3x-54)=90\\ \\(41.5-22)+(124.5-54)=90\\ \\(19.5)+(70.5)=90\\ \\90=90[/tex]

x = 415.

The equation of the rational function with the given features is given as follows:

F(x) = [4(x² + 5x + 4)]/(x² - x - 6).

A rational function is a fraction, in which both the numerator and the denominator contain instances of the variable x.

Considering the x-intercepts, the numerator of the function is defined as follows:

y = a(x + 4)(x + 1)

y = a(x² + 5x + 4).

Considering the y-intercept at (0,4), the leading coefficient a is given as follows:

a = 4.

The vertical asymptotes determine the zeros of the denominator, which is given as follows:

(x + 2)(x - 3) = x² - x - 6.

Hence the function is defined as follows:

F(x) = [4(x² + 5x + 4)]/(x² - x - 6).

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The probability that the sample proportion is less than 0.33 is approximately 0.7422.

The sample proportion of first-time customers can be modeled by a normal distribution with mean p, the true proportion of first-time customers, and standard deviation [tex]\sqrt{\frac{p(1-p)}{n}}[/tex], where n is the sample size.

In this case, p = 0.32, n = 80, and we want to find [tex]P(\hat{p} < 0.33)[/tex].

The standardized version of [tex]\hat{p}[/tex] is given by:

[tex]z = \frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

Substituting the values, we get:

[tex]z = \frac{0.33-0.32}{\sqrt{\frac{0.32(1-0.32)}{80}}} \approx 0.6579[/tex]

Using a standard normal distribution table (or a calculator or statistical software), we find that the probability of z being less than 0.6579 is approximately 0.7422.

Therefore, the probability that the sample proportion is less than 0.33 is approximately 0.7422.

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Answer:

Step-by-step explanation:

inequality form

d≤ 1

Interval Notation:

(−∞,1]

The measures of the center or variability that are greater than 5 degrees are :

The mean of the data on temperature this week and the last is :

= ( 4 + 10 + 6 + 9 + 6 ) / 5

= 7 degrees Fahrenheit 4+ 10+ 6+9+ 6

The mean of the data on temperature last week and the last is :

= ( 13 + 9 + 5 + 8 + 5 ) / 5

= 8 degrees Fahrenheit

The range of this week's temperature is :

= 10 - 4

= 6 degrees Fahrenheit

All these measures of center are above 6 degrees.

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The full question is:

Temperatures for 5 Days This Week and Last Week

Low Temperatures This Week (Degrees Fahrenheit) 4 10 6 9 6 Low Temperatures Last Week (Degrees Fahrenheit) 13 9 5 8 5 Which measures of center or variability are greater than 5 degrees? Select three choices.

a) the mean of this week’s temperatures

b) the mean of last week’s temperatures

c) the range of this week’s temperatures

d)the mean absolute deviation of this week’s temperatures

e) the mean absolute deviation of last week’s temperatures

Tom sold 27 raffle tickets and Steve sold 98 raffle tickets.

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Given:

Together, Steve and Tom sold 125 raffle tickets for their school.

Steve sold 17 more than three times as many raffle tickets as Tom.

Let s be the number of raffle tickets sold by Steve and t be the raffle tickets sold by Tom.

So,

3t + 17 + t = 125

4t = 108

t = 27

And s = 98

Therefore, Steve sold 98 and Tom sold 27 tickets.

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The steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.

Solution to the quadratic equation

The solution to the quadratic equation is determined as follows;

2x² + 12x - 3 = 0

2x² + 12x = 3

divide through by 2

x² + 6x = ³/₂

take half of coefficient of x, square it and add it both sides of the equation

(x + 3)² = ³/₂ + 3²

x² + 6x + 9 = 9 + ³/₂

2(x² + 6x + 9) = 18 + 3

Thus, the steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.

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We cannot make any definitive inferences about the entire school population, however, so the answer is E. None of the above.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The total number of students are 10+11+23+6=50

Based on the survey of 50 students about their preference for an additional sports team, we can observe that lacrosse is the most popular sport among the surveyed students, with 23 supporters.

It is likely that there would be enough interest to form an ice hockey team, as there were 11 supporters.

We cannot make any definitive inferences about the entire school population, however, so the answer is E. None of the above.

Hence, We cannot make any definitive inferences about the entire school population, so the answer is E. None of the above.

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The table shown below represents the results from a sample group of 50 students

surveyed about a preference for an additional sports team.

Sports Team    Number

Gymnastics       10

Ice hockey         11

Lacrosse             23

Swimming           6

If the school has 500 students, what can be inferred from the survey?

A. There would not be enough students to form a 20-person ice hockey

team.

B. About half of the students prefer lacrosse to the other sports.

C. Fewer than ten students in the school prefer swimming to the other

sports.

D. About 10% of the students prefer gymnastics.

E. None of these

The probability of drawing an orange marble and then a green marble without replacement  is (a) 1/15 .

The probability of drawing an orange marble on the first draw = 2/10 because there are 2 orange marbles out of total of 10 marbles .

After 1 orange marble is drawn, there are 9 marbles left in the box, of which 3 are green.

So, the probability of drawing a green marble on the second draw, given that an orange marble was drawn on the first draw, is 3/9.

⇒ P(orange, green) = P(orange) × P(green | orange was drawn)

⇒ P(orange, green) = (2/10) × (3/9) = 6/90 = 1/15  ;

Therefore , the value of P(Orange , Green) is = 1/15 .

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The given question is incomplete , the complete question is

A box contains 5 purple marbles, 3 green marbles and 2 orange marbles. Draws are made without replacement. P(orange ,green)

(a) 1/15

(b) 2/15

(c) 3/31

(d) 1/5

The theoretical probability that a sum greater than 10 is obtained is given as follows:

p = 1/12.

Out of 108 trials, the expected number of trials with a sum greater than 10 is given as follows:

9.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The 36 total outcomes for the pair of dices is given as follows:

Out of these outcomes, three of them, (5,6), (6,5) and (6,6) have a sum greater than 10, hence the probability is given as follows:

p = 3/36

p = 1/12.

Then the expected number is given as follows:

E(X) = 108 x 1/12

E(X) = 9.

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Answer:

9

Step-by-step explanation:

experiment, Kim rolled a fair die twice. The theoretical probability of both rolls equaling a sum greater than 10 is Predict how many times.

Therefore the experement is 9

Answer:1/2 head and 1/2 tails

Step-by-step explanation: no.of experiments for heads = 5

total no of experiments=10

probability=5/10=1/2

no.of experiments for  = 5

total no of experiments=10

probability=5/10=1/2

The exact values of the six trigonometric functions of θ are:

sin(θ) = 0

cos(θ) = -√2/2

tan(θ) = 0

csc(θ) = undefined

sec(θ) = -√2

cot(θ) = undefined

The given point (-14,0) lies on the x-axis in the negative x-axis direction. Drawing a line from the origin to this point creates a right triangle with the hypotenuse being the line from the origin to (-14,0), the opposite side being the y-coordinate of (-14,0), and the adjacent side being the x-coordinate of (-14,0). The length of the hypotenuse can be found using the Pythagorean theorem:

h^2 = (-14)^2 + 0^2

h^2 = 196

h = 14√2

Using the definitions of the six trigonometric functions in terms of the opposite, adjacent, and hypotenuse sides of a right triangle, we can find the exact values of these functions for θ:

sin(θ) = opposite/hypotenuse = 0/14√2 = 0

cos(θ) = adjacent/hypotenuse = -14/14√2 = -√2/2

tan(θ) = opposite/adjacent = 0/-14 = 0

csc(θ) = 1/sin(θ) = undefined (since sin(θ) = 0)

sec(θ) = 1/cos(θ) = -√2

cot(θ) = 1/tan(θ) = undefined (since tan(θ) = 0)

Therefore, the exact values of the six trigonometric functions of θ are:

sin(θ) = 0

cos(θ) = -√2/2

tan(θ) = 0

csc(θ) = undefined

sec(θ) = -√2

cot(θ) = undefined

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The specified radical expressions in the questions are evaluated and presented in the simplest form as follows;

(2) [tex]\sqrt[3]{x^2\cdot y^2} \cdot \sqrt[4]{x^5\cdot y^3} = \sqrt[12]{x^{23}\cdot y^{17}}[/tex]

(3) f(g(x)) = √(6·x + 1) - 5

(4) x = (15 ± √(33))/2

(5) x = 126

A radical is a mathematical expression which contains the radical expression, '√', which represent a fractional indices of the form 1/n.

(2) The specified radical expression is presented as follows;

∛(x²·y²) × [tex]\sqrt[4]{x^5 \cdot y^3}[/tex]

Expressing the above radical expression in index form, we get;

∛(x²·y²) × [tex]\sqrt[4]{x^5 \cdot y^3}[/tex] = [tex]x^{\frac{2}{3} }\times y^{\frac{2}{3} } \times x^{\frac{5}{4} } \times y^{\frac{3}{4}}[/tex]

Adding the index of like variable terms, we get;

[tex]x^{\frac{2}{3} }\times y^{\frac{2}{3} } \times x^{\frac{5}{4} } \times y^{\frac{3}{4}} = x^{\frac{2}{3} + \frac{5}{4} } \times y^{\frac{2}{3} + \frac{3}{4} }[/tex]

(2/3) + (5/4) = (2×4 + 5×3)/12 = 23/12 = 1 11/12

Therefore; [tex]x^{\frac{2}{3} + \frac{5}{4} } = x^{\frac{23}{12} }[/tex]

2/3 + 3/4 = (2 × 4 + 3 × 3)/(12) = 17/12 = 1 5/12

Therefore; [tex]y^{\frac{2}{3} + \frac{3}{4} } = y^{\frac{17}{12} }[/tex]

Which indicates that we get; [tex]x^{\frac{2}{3} + \frac{5}{4} } \times y^{\frac{2}{3} + \frac{3}{4} } = x^{\frac{23}{12} } \times y^{\frac{17}{12} }[/tex]

Therefore; ∛(x²·y²) × [tex]\sqrt[4]{x^5 \cdot y^3}[/tex] = [tex]x^{\frac{23}{12} } \times y^{\frac{17}{12} }[/tex]

(3) The functions, f(x) = √(3·x + 4) - 5, g(x) = (2·x - 1)

The composite function, f(g(x)) can be found as follows;

f(g(x)) = √(3·g(x) + 4) - 5 = √(3·(2·x - 1) + 4) - 5

f(g(x)) = √(3·(2·x - 1) + 4) - 5 = √((6·x - 3) + 4) - 5 = √(6·x + 1) - 5

(4) (√(x - 1)) = x - 7

Squaring both sides, we get;

(√(x - 1))² = (x - 7)²

Therefore;

(√(x - 1))² = x - 1 = (x - 7)² = x² - 14·x + 49

x - 1 = x² - 14·x + 49

x² - 14·x + 49 - (x - 1) = 0

x² - 15·x + 48 = 0

The quadratic formula can be used to solve the above equation to get;

x = (-(-15) ± √((-15)² - 4×1×48))/(2 × 1) = (15 ± √(33))/2

(5) 2·∛(x - 1) + 6 = 16

2·∛(x - 1) + 6 = 16

Subtracting 6 from both sides, we get;

2·∛(x - 1) + 6 - 6 = 16 - 6 = 10

2·∛(x - 1) = 10

∛(x - 1) = 10/2 = 5

∛(x - 1) = 5

∛(x - 1)^3 = 5^3

∛(x - 1)^3 = x - 1

5^3 = 125

∛(x - 1)^3 = x - 1 = 125

x = 125 + 1 = 126

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The function table.

table

x f(x)

-4 4(-4)+3 = -16+3 = -13

0 4(0)+3 = 0+3 = 3

2 4(2)+3 = 8+3 = 11

4 4(4)+3 = 16+3 = 19

5 4(5)+3 = 20+3 = 23

What is Function?

A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.

We can complete the function table by substituting the given values of x into the rule for f(x) and simplifying in the following table.

Therefore, the completed function table is as follows.

so final table is

x f(x)

-4  -13

0  3

2 11

4  19

5  23

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Answer:

2nd answer : it is equivalent but not completely factored

Step-by-step explanation:

the "pulling out" of 3 as factor was completely correct.

but

3(x² - 4) can be further factored.

remember :

(a + b)(a - b) = (a² - b²)

therefore,

(x² - 4) = (x + 2)(x - 2)

and then

3(x + 2)(x - 2)

would be a complete factorization.

Answer: B) The expression is equivalent, but is not completely factored

Step-by-step explanation:

Velocity of rock when it hits the ground is -22.9955152 ft/s

Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time

Its position function is s(t) = –25t² + 1.86t

When it reaches back ground s(t) = 25 m/s

Substituting

               s(t) = –25t² + 1.86t = 25

Using the quadratic formula (-b±√b²-4ac)/2a

(-1.86 ±√1.86-4*25*-25)2*25

(-1.86 ±√1.7298+625)50

(-1.86 ±√626.7298)/50

(-1.86÷25)50

(-1.86+25)50 or( -1.86 -25)50

48.14/50 = 0.9628

This figure is taken because its positive

Time = 0.9628 seconds

Now we need to find velocity when it reaches ground, that is velocity after 0.9628 seconds.

Differentiating s(t) equation

   Substituting t = 0.9628 seconds

               v(t) = –25(0.9628)² + 1.86(0.9628)

v(t) = -23.174596 + 0.1790808

Velocity of rock when it hits the ground is -22.9955152 ft/s

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A graph of the solution to this inequality 2.45 < x ≥ 4.6 is shown in the image attached below.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

Next, we would translate the word problem into an algebraic equation as follows;

2.45 < x ≥ 4.6

By splitting, we have the following compound inequality:

x > 2.45

x ≥ 4.6

In this scenario, we would use an online graphing calculator to plot the inequality as shown in the graph attached below. Additionally, the graph contains a dashed line because of the greater than (>) symbol.

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Step-by-step explanation:

You would find a the same way as finding B, just backwards

[tex]( {x}^{2} - 1)( {x}^{2} + 5)[/tex]

Distributing we get

[tex] {x}^{4} + 5 {x}^{2} - {x}^{2} - 5[/tex]

Simplifying it...

[tex] {x}^{4} + 4 {x}^{2} - 5[/tex]

find derivative of e^(e^x)

use chain rule to find d/dx of e^x is e^x.

so chain rule finds the value e^(e^x) d/dx = e^(e^x) x e^x

simplify to e^[(e^x)+x]

The length of the segment QV is  9.2 units

What is a square?

Regular quadrilaterals, such as a square, have four equal sides and four equal angles (right angles, 90-degree angles, or angles of /2 radian). It is also known as a rectangle with two neighbouring sides of identical length. It is the only regular polygon whose internal angle, central angle, external angle, and diagonal length are all equal (90°).

diagonal length, d=a√2 , where,  d--> diagonal length ,  a= side length

So, d= 13* 1.4142 = 18.3847 units

Diagonals bisect each other

QV = d/2 = 18.3847/2  = 9.1923

Rounding to 1 decimal place

QV = 9.2 units

The length of the segment QV is  9.2 units

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The approximate length of the guy wire supporting the radio tower, as determined using trigonometry with the given information of a 45 degree angle and a height of 145 feet up the tower, is 145 feet.

We can use trigonometry to solve this problem. Let's call the length of the guy wire "x". The opposite side of the right triangle formed by the guy wire and the ground is 145 feet (the height of the tower where the guy wire is attached), and the angle opposite the guy wire is 45 degrees.

Using the trigonometric function tangent, we can set up the following equation:

[tex]tan(45)[/tex] = opposite / adjacent

where "opposite" is 145 feet and "adjacent" is the length of the guy wire, x. Simplifying this equation, we get:

1 = 145 / x

Multiplying both sides by x, we get:

x = 145

Therefore, the length of the guy wire is approximately 145 feet to the nearest tenth.

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