Answers
1) The definition of function F(x) is: B. F(x) = -(x + 2)²(x - 2).
2) The standard definition of the cubic function is: A. F(x) = ax³ + bx² + cx + d.
4) The approximate solution to the system of equations is given as follows: A. (-3.43, 6.30).
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex], is represented by the product of it's linear factors [tex]x - x_1, x - x_2, \cdots x - x_n[/tex], according to the rule the rule presented as follows:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
From the graph, the roots of the function are given as follows:
x = -2, with a multiplicity of 2, as the function just touches the x-axis, not crossing.x = 2, with a multiplicity of 1.Meaning that the cubic function is defined as follows:
F(x) = a(x + 2)²(x - 2).
The y-intercept of the function, numerically, is given as follows:
F(0) = a(2² x (-2))
F(0) = -8a.
The y-intercept is positive, meaning that the leading coefficient is negative, and thus the option B is the correct option.
The general format of a cubic function, with leading coefficient a and constant d positive, is given as follows:
y = ax³ + bx² + cx + d.
Meaning that the correct option for item 2 is given by option A.
How to solve the system of equations?The solution to the system of equations is found through graphing, and is the point of intersection of the two functions.
From the graph given by the image presented at the end of the answer, using rounding, the approximate solution for item 4 is given by option A.
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Related Questions
Find the equation of the linear function represented by the table below in
slope-intercept form.
Answers
Step-by-step explanation:
the slope-intercept form is
y = ax + b
"a" being the slope, "b" being the y-intercept (the y-value when x = 0).
we see that with every increase of x by 1 y increases by 3.
so, the slope "a" is 3.
to get b we use one of the given points, e.g. (1, 5) :
5 = 3×1 + b = 3 + b
b = 2
so, our function is
y = 3x + 2
Consider the following expression. 8y+3x+5 Select all of the true statements below.
Answers
All of the true statements that have to do with the expression 8y+3x+5 are:
5 is a constant3x + 8y + 5 is written as a sum of three terms3x and 5 are like termsWhat is a mathematical expression?An expression in mathematics is made up of a mixture of variables, integers, and functions (such as addition, subtraction, multiplication or division etc.) In some ways, phrases and expressions are comparable.
In the equation 5 is a constant, this is because the value would not have to change because it does not have a variable attached.
The terms of the expression are, 3x, 8 y and 5. This makes it a total of 3 terms in the expression.
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A certain infinite geometric series has first term 7 and sum 4. What is the result when the third term is divided by the second term
Answers
The third term of the geometric series is 7*(1/2)^2 = 3.5 and the second term is 7*(1/2)^1 = 3.5. When the third term is divided by the second term, the result is 1.
A geometric series is a sequence of numbers where each term is obtained by multiplying the previous term by a constant. In this particular series, the first term is 7 and the sum is 4. This means that the constant is 1/2. To find the third term, we multiply the second term by the constant, which gives us 7*(1/2)^2 = 3.5. To find the result when the third term is divided by the second term, we divide 3.5 by 3.5, which gives us 1. This is true for any infinite geometric series with the same first term and sum, because the ratio between every two consecutive terms is always the same.
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What is the greatest possible error for a measurement or 25 miles?
Answers
The greatest possible error for 25 miles is 12.5 miles.
What is the greatest possible error?Half of the unit of measure to which a measurement is rounded is the largest possible error. The maximum error is 2 units when a measurement is taken to the nearest whole unit 4.
Given, A value of 25 miles.
Now, we know the greatest possible error is half of the unit of measure.
Therefore, The greatest possible error for 25 miles is,
= (25/2) miles.
= 12.5 miles.
As 12.5 miles is half the value of 25 miles.
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How many 1/4 are in 3
Answers
Answer:
there are 12 fourths in 3 .
A circle centered at $P$ with radius $10$ and a circle centered at $Q$ with radius $8$ are externally tangent. A common external tangent intersects line $PQ$ at $R.$ Find $QR.$
Answers
If the two circle centered at P and Q with radius 10 and 8 respectively , and if the common external tangent intersects line PQ at R , then the length of QR is 72 .
The radius of the circle that is centered at P is = 10 ;
the radius of circle that is centered at Q is = 8 ;
the common external tangent intersects the line PQ at R ,
Let XYR be external tangent with X on the Circle with center P , and at point Y on circle with center Q .
we extend , the line PQ to point R ,
we get , that triangle XPR is similar to triangle YQR ,
it means that , [tex]\frac{RQ}{RP} =\frac{QY}{PX}[/tex] ;
let the length of RQ be = x , then
length of RP will be = [tex]x+18[/tex] ;
we get ; [tex]\frac{x}{x+18} =\frac{8}{10}[/tex] ;
⇒ [tex]10x=8x+144[/tex] ;
⇒ [tex]2x=144[/tex] ;
⇒ [tex]x=72[/tex] .
Therefore , the length of QR is 72 .
The given question is incomplete , the complete question is
A circle centered at P with radius 10 and a circle centered at Q with radius 8 are externally tangent. A common external tangent intersects line PQ at R. Find QR .
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a cyclist rides at a average speed of 18km/h for 9 minuets. work out the distance traveled by the cyclist in km
Answers
Answer: d=162km
Step-by-step explanation:
the equation of this question is:
speed = distance / time
s=d/t
18=d/9
d=18*9
d=162km
So distance =speed x time
Distance =18 x 0.15
(9 minutes is 0.15 hours)
Distance=2.7km
Complete the equation describing how x
and y are related.
X y
7
9
11_ y = [ ? ]x +
13
15
17
012345
Enter the answer that
belongs in [?].
Enter
Help
Skip
Answers
The complete equation is y =2x+7 after substituting the given values.
What is equation?
An equation is a condition on a variable such that two expressions in the variable should have equal value and Substitution means replacing the variables (letters) in an algebraic expression with their numerical values.
According to the question.
We have a table which shows the relation between x and y.
Let the missing term be a and b.
The the given equation becomes
y = ax+b
For finding the value of a and b.
Substitute x = 0 and y = 7 in equation y = ax + b.
7 = a(0) + b
b= 7
Again, substitute x = 1 and y = 9 in the equation y = ax+ b
9 = a(1)+b
9 = a+7
a=9-7
a=2
substitute the value of a and b in the equation y = ax + b. we get ,
y = 2x+7
Therefore, the complete equation is y = 2x+7
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when canned peaches are delivered to a grocery store, the clerk stocks the new cans in front of the old. if each can sold is accounted for as to its cost, a) lifo (last-in, first-out). b) average. c) random. d) fifo (first-in, first-out).
Answers
According to the given statement If each can sold in accounted for as to its cost Last in first out.
Why do we determine the average?The average is determined by adding together all of the numbers as well as dividing the total by the total number of figures provided. It represents the midpoint of the supplied data set. The numerical number that may display a lot of facts is the average value. We constantly encounter the average computation in our daily lives.
Which 4 averages are there?The four sorts of average that we recognize are mean, mode, median, and range. Although the others are our most popular "measures of central tendency," range is actually a measure of spread or dispersion.
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two cards are selected with replacement from a standard deck of 52 cards. find the probability of selecting a spade and then selecting a heart.
Answers
The probability of selecting a spade and then selecting a heart from a standard deck with replacement is 0.625.
When selecting two cards with replacement from a standard deck of 52 cards, the probability of selecting a specific card on the first draw does not affect the probability of selecting a specific card on the second draw. Therefore, we can simply multiply the probability of selecting one card of a specific suit by the probability of selecting a different card of a specific suit.
The probability of selecting a spade on the first draw is
13/52 = 1/4 = 0.25
since there are 13 spades in a deck of 52 cards.
The probability of selecting a heart on the second draw is also
13/52 = 1/4 = 0.25
since there are 13 hearts in a deck of 52 cards.
Therefore, the probability of selecting a spade and then selecting a heart is:
(0.25) * (0.25) = 0.0625
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Mrs. mccall is renting a truck for one day. the two choices she had are company a and company b. what is the minimum number of miles that mrs.mccall would need to drive in order to make renting from campany b a better deal?
Answers
On solving the provide question, we can say that by unitary method McCall would need to drive 126 miles in order to make renting from Company B a better deal
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
so, we have -
Company A charges = $35 per day
plus = $0.45 per mile.
Company B charges = $60 per day
plus = $0.25 per mile.
McCall would need to drive 126 miles in order to make renting from Company B a better deal
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Directions: Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.
Answers
Answer to Problem 13 is 34.5
Answer to Problem 15 is 22.9
==================================================
Work Shown for Problem 13
sin(x)/17 = sin(91)/30
sin(x) = 17*sin(91)/30
sin(x) = 0.56658036
x = arcsin(0.56658036) or x = 180-arcsin(0.56658036)
x = 34.51210645 or x = 180-34.51210645
x = 34.51210645 or x = 145.48789355
x = 34.5 or x = 145.5
If x = 34.5, then the missing unmarked angle is 180-x-91 = 180-34.5-91 = 54.5 which is a valid angle (since it's between 0 and 180).
If x = 145.5, then the missing unmarked angle is 180-x-91 = 180-145.5-91 = -56.5; but this is NOT valid because the angle needs to be between 0 and 180 (i.e. negative angles aren't allowed)
In short, x = 34.5 is valid while x = 145.5 is not valid.
Therefore, the only possible answer is 34.5
---------------------------------------------
Work Shown for Problem 15
sin(x)/20 = sin(119)/45
sin(x) = 20*sin(119)/45
sin(x) = 0.38871987
x = arcsin(0.38871987) or x = 180-arcsin(0.38871987)
x = 22.87486940 or x = 180-22.87486940
x = 22.87486940 or x = 157.1251306
x = 22.9 or x = 157.1
If x = 22.9, then the missing unmarked angle is 180-x-119=180-22.9-119 = 38.1 which is valid since it's between 0 and 180.
If x = 157.1, then 180-x-119=180-157.1-119 = -96.1 which is NOT a valid angle since it's not between 0 and 180. This allows us to rule out the case that x = 157.1
The only possible answer is therefore 22.9
---------------------------------------------
Side notes:
Make sure your calculator is in degree mode. Unfortunately some calculators like to default to radian mode. A quick check is to see if sin(30) produces the result 0.5Arcsine is the same as inverse sine, which is denoted as [tex]\sin^{-1}[/tex] on many calculators.An instructor wants to write a quiz with 9 questions where each question is worth 3, 4, or 5 points based on difficulty. he wants the number of 3-point questions to be 1 more than the number of 5-point questions, and he wants the quiz to be worth a total of 35 points. determine the number of 3-point, 4-point, and 5-point questions.
Answers
The quiz should have 5 3-point number of questions, 3 4-point questions, and 4 5-point questions, for a total of 35 points.
3-point questions: 5
4-point questions: 3
5-point questions: 4
1. The total number of questions is 9.
2. The total number of points for the quiz is 35.
3. There should be 1 more 3-point question than 5-point questions.
4. So, 5 of the questions should be worth 3 points each, for a total of 15 points.
5. That leaves 4 points remaining.
6. 4 points can be achieved by having 3 4-point questions (12 points) and 4 5-point questions (20 points).
7. Therefore, the number of 3-point, 4-point, and 5-point questions should be 5, 3, and 4 respectively.
The quiz should have 5 3-point questions, 3 4-point questions, and 4 5-point questions, for a total of 35 points.
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H(x) = 1/8 x^3 -x2 what is the average rate of change of h over the Interval-2 < x< 2
Answers
The average rate of change of a function over an interval is the total change in the function's output (or y-value) divided by the total change in the function's input (or x-value) over that interval.
Given the function h(x) = 1/8 x^3 - x^2, the average rate of change over the interval -2 < x < 2 is:
(h(2) - h(-2)) / (2 - (-2))
First, we have to find h(2) and h(-2) by substituting these values in the function:
h(2) = 1/8 (2)^3 - (2)^2 = 1/8 * 8 - 4 = 0.5
h(-2) = 1/8 (-2)^3 - (-2)^2 = 1/8 * -8 - 4 = -4.5
So, the average rate of change is:
(0.5 - (-4.5)) / (2 - (-2)) = 5 / 4 = 1.25
Therefore, the average rate of change of h over the interval -2 < x < 2 is 1.25
A car rolls forward 5 ft. The car wheel has a 16 in radius. Through what angle (to the nearest tenth of a degree) does the wheel turn?
Answers
Answer:
214.9°
Step-by-step explanation:
You want to know the angle of rotation that moves a point on a circle of 16 inch radius a distance of 5 feet.
Arc lengthThe relation between the length of an arc and the central angle in radians is ...
s = rθ
The distance of 5 ft is equal to 60 inches, so we have ...
60 = 16θ
AngleSolving for θ gives ...
θ = 60/16 = 15/4 . . . . radians
The angle in radians can be converted to an angle in degrees by multiplying it by 180°/π:
15/4 radians = (15/4)·(180°/π) ≈ 214.9°
The wheel turned through an angle of about 214.9°.
How do you solve absolute value Grade 7?
Answers
In grade 7, one common method to solve absolute value equations is by isolating the absolute value on one side of the equation and then solving for the two possible solutions.
Here is a step-by-step process to solve an absolute value equation:
Isolate the absolute value on one side of the equation by adding or subtracting the same value to both sides of the equation.
For example, |x| = 3 can be rewritten as x = 3 or x = -3
Split the equation into two separate cases, one for when the value inside the absolute value sign is positive, and one for when it is negative.
Solve each case separately.
Check your solutions by plugging them back into the original equation and making sure they are valid solutions.
Write your answer in interval notation if the solutions are continuous or list them as individual values if they are not.
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Select the correct description for the quadratic expression below
Answers
the product of x and a factor not depending on x
What is quadratic equation
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.
The equation given 3x(m-6n)²
This expression contains two factors:
1 factor: 3x
2 factor: (m-6n)²
Hence the product of x and a factor not depending on x.
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which expression evaluates to true if and only if the units digit of an integer variable x is less than 6
Answers
The units digit of an integer every square of an integer ends with (=has a units digit) 0, 1, 4, 5, 6, or 9.
This question can be answered in a variety of ways. Finding squares with the unit digits 0, 4, 5, and 6 is one way to demonstrate by means of elimination that the answer must be 2. The reason this method works is that you're presuming one of the answers to this specific multiple-choice question is true, but it's not actually that fulfilling.
A more effective method is to note that any number has the form (10m+i) such that 0i9. By squaring, you may determine exactly which numbers are feasible units digits in a square by getting 100m2+20mi+i2, etc. in turn.
Every square of an integer should have the units digit (0, 1, 4, 5, 6, or 9) as its final value.
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Which represents the polynomial written in standard form?
8x2y2 – 3x3y + 4x4 – 7xy3
4x4 – 3x3y + 8x2y2 – 7xy3
4x4 – 7xy3 – 3x3y + 8x2y2
4x4 + 8x2y2 – 3x3y – 7xy3
–7xy3 – 3x3y + 8x2y2 + 4x4
Answers
Answer: [tex]4x^4 -3x^3 y+8x^2 y^2 -7xy^3[/tex]
Step-by-step explanation:
In standard form, the terms are arranged in order from highest to lowest exponent of the variable that comes first alphabetically.
over a period of one year, two points on opposite sides of a mid-ocean ridge moved a distance of 4 centimeters farther apart. what is this distance, in meters? (1 meter
Answers
As per the given points, the distance is 0.08 meter.
The term distance in math is known as the length of the line joining the two points.
Here we have given that over a period of one year and the two points on opposite sides of a mid-ocean ridge moved a distance of 4 centimeters farther apart.
Here we have to calculate the distance between the two point in meter.
Let us consider that x be the distance between the two points.
As we know that in each side there is 4 centimeter distance.
Then the total distance between the two points,
=> 4 x 2 = 8 centimeter.
Then the meter equivalent is calculated as,
=> 8/100 = 0.08
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The manager at Apex Gym wants to know when the new pricing model (higher per-class fee but lower membership fee) will be better than the old pricing model used last year. He uses a table to calculate the members’ costs for different numbers of classes.
Answers
The completed table to show the member cost for different numbers of classes is :
No. of classes Cost under old model Cost under new model
2 170 110
4 200 170
5 215 200
6 230 230
7 245 260
How to find the member costs ?Assuming that the number of classes is x, then the formula to find the cost with a certain number of classes with the old model is:
= 15 x + 140 membership fee
4 classes :
= 15 x 4 + 140
= $ 200
5 classes :
= 15 x 5 + 140
= $ 215
6 classes :
= 15 x 6 + 140
= $ 230
7 classes :
= 15 x 7 + 140
= $ 245
Cost under new model would take the formula:
= 30 x + 50 membership fee
4 classes :
= 30 x 4 + 50
= $ 170
5 classes :
= 30 x 5 + 50
= $ 200
6 classes :
= 30 x 6 + 50
= $ 230
7 classes :
= 30 x 7 + 50
= $ 260
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In 1997, a city had a population of 220,000 people. Each year since, the population has grown by 6.2%.
Let t be the number of years since 1997. Let y be the city’s population.
Write an exponential function showing the relationship between y and t.
Answers
The exponential function that shows the relationship between y and t is y = 220,000(1.062^t).
What is the exponential function?An exponential equation can be described as an equation with exponents. The exponent is usually a variable.
The general form of exponential equation is f(x) = e^x
Where:
x = the variable e = constantThe form of the exponential equation that can be used to determine the population after 1997 is:
FV = P (1 + r)^n
Where:
FV = future population P = present population R = growth rateN = number of yearsy=220,000 x ( 1+ 0.062)^t
y = 220,000(1.062^t).
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the random variable x is exponentially distributed, where x represents the waiting time to see a shooting star during a meteor shower. if x has an average value of 53 seconds, what are the parameters of the exponential distribution?
Answers
The random variable x is exponentially distributed, where x represents the waiting time to see a shooting star during a meteor shower. if x has an average value of 53 seconds, what are the parameters of the exponential distribution:
X ~ Exp( μ = 53)
Random Variable:
A random variable is a variable that can take many values. This is because random events can have multiple outcomes. So don't confuse random variables with algebraic variables. Algebraic variables represent the values of unknown quantities in computable algebraic equations. A random variable, on the other hand, can have a range of values that could be the result of a random experiment.
Suppose two dice are rolled and a random variable X is used to represent the sum of the numbers. The minimum value of X is 2 (1 + 1) and the maximum value is 12 (6 + 6). Therefore, X can have any value between 2 and 12 (inclusive). If probabilities are assigned to each outcome, we can determine the probability distribution of X.
According to the Question:
We know that the random variable X who represents the waiting time to see a shooting star during a meteor shower follows an exponential distribution and for this case we can write this as:
X ~ Exp( μ = 53)
But, also we can define the variable in terms of like this:
X ~ Exp (λ =1/λ =1/53)
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Given that 2 cos x = √3, where 0° < x < 90°,
find the value of x.
Answers
Answer:
30 degrees.
Step-by-step explanation:
2 cos x = √3
cos x = √3/2
x = 30.
Helpppppppppppppp meeeeeeeee plssssssssss
Answers
By algebra properties, the rational equation 1 / [1 / (x + 2) + 1 / (x + 3)] is equivalent to the rational expression (x² + 5 · x + 6) / (2 · x + 5). (Correct choice: B)
How to determine the simplified form of a rational equation
In this problem we find a rational equation, whose simplified form has to be found by means of algebra properties. First, write the entire expression:
1 / [1 / (x + 2) + 1 / (x + 3)]
Second, expand the denominator by addition of fractions with distinct denominator:
1 / [[(x + 3) + (x + 2)] / [(x + 2) · (x + 3)]]
Third, use division of fractions:
[(x + 2) · (x + 3)] / [(x + 3) + (x + 2)]
Fourth, simplify both numerator and denominator:
(x² + 5 · x + 6) / (2 · x + 5)
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hope runs a pizza restaurant. she must pay $70 to keep the restaurant open each day even if she does not sell any pizza. additionally, each slice of pizza that she makes and sells costs her $0.6. write a formula for the function c ( x ) that expresses hope's total daily costs as a function of the number of slices x that she makes/sells.
Answers
Sorry if wrong
Suppose that A and B are two independent events for which P(A) = 0.31 and P(B) = 0.76. What is the probability of (A|B), (B|A), (A and B), and (A or B)?
Answers
The probability of (A and B) is 0.2356, the conditional probability of (A|B) is 0.31, the conditional probability of (B|A) is 0.76, and the probability of (A or B) is 0.8144.
Probability is a measure of the likelihood of a particular event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain to occur.
When events A and B are independent, the probability of them occurring together is the product of their individual probabilities.
P(A and B) = P(A) * P(B) = 0.31 * 0.76 = 0.2356
P(A|B) = P(A and B) / P(B) = 0.2356 / 0.76 = 0.31 (It is same as P(A) because events A and B are independent)
P(B|A) = P(A and B) / P(A) = 0.2356 / 0.31 = 0.76 (It is same as P(B) because events A and B are independent)
P(A or B) = P(A) + P(B) - P(A and B) = 0.31 + 0.76 - 0.2356 = 0.8144
Therefore, the probability of (A and B) is 0.2356, the conditional probability of (A|B) is 0.31, the conditional probability of (B|A) is 0.76, and the probability of (A or B) is 0.8144.
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What is the solution of the system?
4g + h = -4
12g + 2h = -4
Enter the coordinate pair in the blanks in alphabetical order (g, h) (_, _)
Answers
The coordinate pair of the given solution of the system would be= (g, h) (1,-8).
What is the substitution equation?Substitution equation is defined as the equation that can be solved when a value is being solved and substituted for the other missing value to be gotten.
4g + h = -4 ---->. eq 1
12g + 2h = -4 ----> eq 2
Make h the subject of formula;
h = -4 - 4g -----> eq 3
Substitute equation 3 into equation 2;
12g + 2( -4 - 4g) = -4
12g - 8 -8g = -4
4g -8 = -4
4g = -4 +8
4g = 4
g = 4/4= 1
Solve for g = 1 in equation 1;
4(1) + h = -4
4 + h = -4
h = -4-4
h = -8
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If y varies directly as x, and y is 20 when x is 4, what is the constant of variation for this relation?1/54/5516
Answers
The constant of variation for this relation will be option (C.) 5
Constant of variationThe ratio between two variables in a direct variation or the product of two variables in an inverse variation.
We solve the problem as follows.
Given that y is directly proportional x
y = kx, where k = proportionality constant
Constant of proportionality is the constant value of the ratio between two proportional quantities. Two varying quantities are said to be in a relation of proportionality when, either their ratio or their product yields a constant. The value of the constant of proportionality depends on the type of proportion between the two given quantities: Direct Variation and Inverse Variation.
According to the provided data,
y = 20
x = 4.
So,
20 = 4k
k = 20/4 = 5
Therefore constant of variation will be 5
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What is the value of x?
Answers
The value of x is 15 units.
What are Corresponding Angles ?
When two parallel lines are intersected by another line, comparable angles are the angles that are created in matching corners or corresponding corners with the transversal (i.e. the transversal).
For instance, angle p and angle w are the comparable angles in the image below.
Step-by-step explanation:
In the given triangle RSQ and ΔRST it is given that
∠RTS ≅ ∠SRQ ≅ 90°
∠RSQ is common in two triangles Δ RSQ and Δ RST.
Therefore two angles are equal so both the triangles are common.
From this property we opposite sides of the corresponding angles will be in the same ratio.
SR/SQ = ST/SR
x/(9 + 16) = 9/x
By cross multiplication on each side of the equation
x² = 25×9 = 225
x = √225 = 15
Therefore measurement of x is 15 units.
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