Explanation:
All of the polynomials listed are quadratic polynomials, which have the general form ax^2 + bx + c, where a, b, and c are constants and x is a variable. A polynomial is considered prime if it cannot be factored into the product of two or more polynomials with integer coefficients.It is not possible to determine whether any of the given polynomials are prime without further information, such as the values of the constants a, b, and c. For example, the polynomial x^2 + 7 could be prime, but it could also be factored into the product of two linear polynomials (x + 3)(x + 3), which would make it composite. Similarly, the polynomial x^2 - 25 could be prime, but it could also be factored into the product of two polynomials of the form (x + 5)(x - 5), which would make it composite. Without more information, it is not possible to determine whether any of the given polynomials are prime.
A police officer is estimating the distance from one side of a street to the other. The actual distance is 13.4 m. The police officer’s estimate is 14 m. Find the absolute error and the percent error of the police officer’s estimate.
PLEASE HELP
The absolute error and the percent error of the police officer’s estimate will be 4.29%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
A cop is assessing the separation from one side of a road to the next. The genuine distance is 13.4 m. The cop's gauge is 14 m.
The absolute error and the percent error of the police officer’s estimate are calculated as,
%error = [(14 - 13.4) / 14] x 100
%error = (0.60 / 14) x 100
%error = 4.29%
The outright mistake and the percent blunder of the cop's gauge will be 4.29%.
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There were two candidate A and B conteting for the municipal corporation election in a town. The total number of voter in the town were 80,000. If 90% of the voter had voted and 60% of vote polled were cat in favour of A, find the number of vote received by B
There were two candidate A and B contesting for the municipal corporation election in a town. The total number of voter in the town were 80,000. If 90% of the voter had voted and 60% of vote polled were cat in favour of A, 28,800 the number of vote received by B.
What is municipal corporation election?A state-incorporated city, town, village, or county that has the power to manage local governmental matters, such as creating a police force. A municipal corporation is established by a state's legislature, which also determines its lifespan, privileges, and powers. likewise known as a municipality.
A local governing body, such as cities, counties, towns, townships, charter townships, villages, and boroughs, is referred to legally as a "municipal corporation." Municipally-owned companies can also be referred to as this
Regulation of building construction and land usage. Town planning is included in urban planning. preparing for social and economic progress. water supply for residential, commercial, and industrial uses.
Given that,
Total number voters = 80,000
Total number of votes polled = 90%
Thus,
= (90/100) × 80,000
= 72,000
So, total percent of votes received by B if A gets 60% of polled votes.
= 100% - 60%
= 40%
Hence, total number of votes received by B
= (40/100) × 72,000
= 28,800
Therefore, the number of votes received by B, out of total votes polled is 28,800 votes.
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Tires A mechanic checked the tire pressures on each car that he worked on
for one week. The random variable x represents the number of tires that
were underinflated.
0
P(x) 0.30
1
2
0.25 0.25
3
0.15
4
0.05
The expected value for the given problem is E(x) = 1.4.
What is expected value?
The expected value is a generalization of the weighted average in probability theory. Informally, the expected value is the arithmetic mean of a significant number of outcomes of a random variable that were independently chosen.
A projected average value for an investment at some point in the future is known as the expected value (EV).
Investors use expected value to gauge an investment's merit, frequently in relation to how risky the investment is.
The formula for to find the expected value is given as,
E ( X ) = μ = ∑ x P ( x ) .
E(x) = 0*0.30 + 1*0.25 + 2*0.25 + 3*0.15 + 4*0.05
E(x) = 1.4
Hence, the expected value for the given problem is E(x) = 1.4.
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Here is a graph of y=k/x
-What is the value of k?
The graph of y = k/x has k = 4.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
y = k/x
The coordinates from the graph:
(1, 4) and (2, 2).
This can be considered as,
(1, 4) = (x, y) = (2, 2)
Now,
y = k/x
4 = k/1
k = 4
y = k/x
2 = k/2
k = 4
Thus,
The value of k is 4.
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Please help if possible.
Answer:
$1020.00000$1020.15050$1020.18436$1020.19742$1020.20078Step-by-step explanation:
You want to find the effect of compounding 2% annual interest on $1000 at different intervals for a year. The intervals are ...
1 per year4 per year12 per year52 per year365 per yearCalculatorThe attached calculator display shows the result:
yearly: $1020.00000quarterly: $1020.15050monthly: $1020.18436weekly: $1020.19742daily: $1020.20078Make a frequency distribution and find the relative frequencies for the following number set. Round the relative
frequency to the nearest tenth of a percent.
10 20 40 50 60 80
10 20 40 60 60 80
20 30 50 60 70 90
20 30 50 60 80 90
Number Frequency Relative Frequency
The relative frequencies for the following number set is 10 30 40 50 60 70 10 30 40 60 60 80 20 30 50 60 70 90 20 30 50 60 70 90
How do you find the relative frequency in a frequency distribution?
Divide the frequency by the total number of data values to obtain the relative frequency. Add all of the earlier relative frequencies to the relative frequency for the current row to obtain the cumulative relative frequency. Divide the total number of occurrences of the result you're interested in by the total number of occurrences if your data are observational. This may be expressed mathematically as relative frequency = frequency of the desired result / all occurrences.
There are 24 items.
Relative Frequency:
10 - (2) - 8.33%
20 - (1) - 4.17%
30 - (4) - 16.67%
40 - (2) - 8.33%
50 - (3) - 12.5%
60 - (5) - 20.83%
70 - (3) - 12.5%
80 - (1) - 4.17%
90 - (2) - 8.33%
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What is the distance between points m and n? meters
Answer: 9.8
Step-by-step explanation:
Graph the inequality on the axes below.
3x + y ≤ -3
Answer:
y ≤ -3x - 3
Step-by-step explanation:
The graph crosses the y axis at -3. The slope is -3. (0, -3) . From that point do down vertical 3 spaces and horizontally 1 space. You will be at the point (1,-6) Draw a line to join those 2 points. The inequality is ≤ that means the solutions are the points on the line and below the line. This is shown in the pink shading.
y ≤ -3x - 3
Step-by-step explanation:
The graph crosses the y-axis at -3. The slope is -3. (0, -3) . From that point do down vertical 3 spaces and horizontally 1 space. You will be at the point (1,-6) Draw a line to join those 2 points.
The inequality is ≤ which means the solutions are the points on the line and below the line. This is shown in the pink shading.
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A school is arranging a field trip to the zoo. The school spends 546.53 dollars on passes for 40 students and 3 teachers. The school also spends 351.60 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
There are $21.5 money was spent on a pass and lunch for each student.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that:
The amount spent by school on pass of 40 students and 3 teachers = $546.53
And, the amount spent for the lunch only for students = $351.60
Now,
The money spent for pass of 43 person = $546.53
Then, The amount of pass for each person = 546.53/43
= $12.71
Since, there are 40 student then amount of lunch for each students = ⇒ 351.60/40
⇒ $8.79
Therefore, amount of pass and lunch for each student = 12.71 + 8.79
= $21.5
Thus, $21.5 is the required answer.
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f(x) = x²+x-6
g(x) = 4x +9
Find: g(f(x))
The value of the function g(f(x))=4x²+4x-15 if f(x) = x²+x-6
g(x) = 4x +9.
What is meant by a function?An exact one of each element of Y is assigned to each element of X via a mathematical function from a set X to a set Y. The sets X and Y are denoted by the terms "domain" and "codomain," respectively.
The fundamental concept of functions was the connection between fluctuating quantities and other variables. One illustration of this is the impact of time on a planet's position. Beginning at the end of the 17th century and continuing until the 19th century, the concept was developed using the infinitesimal calculus.
Given,
f(x) = x²+x-6
g(x) = 4x +9
f(g(x))=f(4x+9)
g(f(x))=4(x²+x-6)+9
g(f(x))=4x²+4x-24+9
g(f(x))=4x²+4x-15
Therefore, the value of the function g(f(x))=4x²+4x-15 if f(x) = x²+x-6
g(x) = 4x +9.
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What percentage of trains were late in this particular week? 27.6% 38.2% 40.0% 72.4%
Answer:
27.6•\• is the answer from me
Determine the perimeter of the right triangle shown. Round your final answer to the nearest whole number, if necessary.
Answers: 7 units
14 units
25 units
26 units
answer : 26
steps
get hypotenuse
a² + b² = c²
7² + 8² = c²
49 + 64 = c²
113 = c²
square root of c is √113 which 10.63
7 + 8 + 10.63 = 25.63
Please hurry and help!
Graph the following linear equation using the intercepts.
\displaystyle -10 x-12 y=-60−10x−12y=−60
The x−intercept is 6 and the y-intercept is 5.
What is an equation of a line?
In high school algebra, "the equation of a line" is a crucial concept. This refers to an equation in the (x,y) plane with a line as its solution set. The "slope-intercept" form is the most widely used form in algebra. y = mx + b. In essence, x is used as a parameter in this formula, and y is written as a function of x: y = f(x) = mx+b.
Here, we have
The given equation of a line is:
−10x − 12y = −60
10x + 12y = 60
x/6 = y/5 = 1
Hence, the x−intercept is 6 and the y-intercept is 5.
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a random sample of size 36 is taken from a population with mean 17 and standard deviation 6. the probability that the sample mean is greater than 18 is?
The probability that the sample mean is greater than 18 as calculated is 0.8413.
Given data,
n = 36, sample size
μ = 17, population mean
σ = 6, population standard deviation
when x = 18
z = (18 - 17)/1 = 1
P(x <18) = 0.8413
Therefore , the probability = 0.8413
A population's standard deviation serves as a gauge for how widely distributed its individual data points are. It's a way to express how dispersed from the mean the data is.
While a large standard deviation indicates that the data is more spread, a small standard deviation indicates that the data points are often close to the mean.
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Does 0.010110111011110... represent a
rational number or an irrational number?
Explain your reasoning.
Answer:
This is an irrational number.
Step-by-step explanation:
If you see the decimal, it has the values of 1 and 0, but are not constant.
If it were to be 0.010101010... it would be rational.
But this decimal does not look like that, so its irrational.
Hope this helps.
Given the side measures, which of the following could form a right triangle?
A. 61 m, 60 m, 11 m
B. 24 in, 34 in, 28 in
C. 55 ft, 45 ft, 35 ft
D. 48 cm, 46 cm, 15 cm
The side measures that could form a right triangle are B (24 in, 34 in, 28 in) and C (55 ft, 45 ft, 35 ft).
What is the right triangle is triangle?
A right triangle is a triangle in which one angle measures 90 degrees. The sides of a right triangle can be used to determine if a triangle is a right triangle using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Using this information, we can determine which of the given sets of side measures could form a right triangle:
A. 61 m, 60 m, 11 m: We can use the Pythagorean theorem to see if these sides could form a right triangle. We'll let the hypotenuse be the side with a length of 61 m, and the other two sides are the ones with lengths of 60 m and 11 m. Plugging these values into the Pythagorean theorem, we get:
(61 m)² = (60 m)² + (11 m)²
61² = 60² + 11²
61² ≠ 60² + 11²
Since the left side does not equal the right side, these sides cannot form a right triangle.
B. 24 in, 34 in, 28 in: Using the Pythagorean theorem, we can see that these sides could form a right triangle:
(34 in)² = (24 in)² + (28 in)²
34² = 24² + 28²
34² = 24² + 28²
The left side equals the right side, so these sides could form a right triangle.
C. 55 ft, 45 ft, 35 ft: Using the Pythagorean theorem, we can see that these sides could form a right triangle:
(55 ft)² = (45 ft)² + (35 ft)²
55² = 45² + 35²
55² = 45² + 35²
The left side equals the right side, so these sides could form a right triangle.
D. 48 cm, 46 cm, 15 cm: Using the Pythagorean theorem, we can see that these sides could not form a right triangle:
(48 cm)² ≠ (46 cm)² + (15 cm)²
48² ≠ 46² + 15²
Since the left side does not equal the right side, these sides cannot form a right triangle.
Hence, The side measures that could form a right triangle are B (24 in, 34 in, 28 in) and C (55 ft, 45 ft, 35 ft).
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Which of the following statements is correct for a triangle?
A. triangle can have two obtuse angles
B.The difference of two sides of a triangle is greater than any other side of the same triangle.
C.A triangle can have an obtuse angle and a right angle.
D.None of these
Which equation is equivalent to the quadratic equation x^2− 8x +19 = 0 where k represents the absolute value of the maximum value of the function? options:A (x-4)^2+k=0 B:(x-4)^2-k=0 C:(x+4)^2+k=0 D:(x+4)^2-k=0
The equation that is equivalent to quadratic equation x^ 2-8x+19=0 is
(x-4)^ 2+k = 0 using quadratic equation properties .
What is quadratic equation ?
A quadratic equation is a second order equation written as ax2 + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0.
Properties of graph of quadratic equation :
1. The shape of curve y = f(x) is a parabola.
2. If a>0, the parabola opens upwards.
3. If a<0, the parabola opens downwards.
4.The coordinates of vertex of parabola in all these cases is
(-b/2a , -D/4a).
The given equation is x^ 2-8x+19=0
a = 1,
b = -8,
c = 19.
As a>0, 2nd property is correct i.e. no maximum value , only minimum value can be find that will be at vertex.
So, the vertex = (4,3)
The minimum value = 3 at 4.
So, the value of k = 3,
Given equation can be written as x^ 2-8x+16+3 = 0.
= (x-4)^ 2 +3 = 0.
The option A is correct.
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For which situation does one quantity change at a constant rate per unit interval relative to another quantity?
Responses
For every day that passes, a person drives 54 miles.
.
For every month that passes, a savings account earns interest at a rate of 1.5%
For every week that passes, a vine doubles in length 2 times a week.
.
For every year that passes, a population of insects increases by 6%
Answer:
(a) For every day that passes, a person drives 54 miles
Step-by-step explanation:
You want to know the situation in which one quantity changes relative to another at a constant rate.
DrivingThe rate of change is described as 54 miles for each day. This is a constant rate of change. Miles relative to days are described by a linear function.
SavingsWe assume the description means that the balance in the savings account increases by 1.5% with each passing month. While this interest rate is a constant, the amount by which the balance changes each month is not constant. The balance relative to time is described by an exponential function.
VineIf the vine doubles in length twice a week, its length increases by 300% each week. As with savings, this growth rate is constant, but the amount of growth each week is not. The length of the vine is described by an exponential function.
PopulationAs with savings, this growth rate is constant, but the amount of increase each year is not. The population is described by an exponential function.
The situation with a constant rate of change is ...
For every day that passes, a person drives 54 miles.
__
Additional comment
When the quantity is graphed, the "rate of change" refers to the slope of the curve on the graph. The graph of an exponential growth function does not have a constant slope, but has a slope that increases exponentially.
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r(x) = x^2 + 5x + 4 write r(x) in factored form. I would like an explanation as to how you get the answer please!
Answer: (x+1)(x+4)
Step-by-step explanation:
Step 1: Use the sum-product pattern
x^2 + 5x + 4
x^2 + 4x + x + 4
Step 2: Common factor from the two pairs
x(x+4) + x+4
Step 3: Rewrite in factored form
(x+1)(x+4)
Tell whether the point (13, 17) is a solution to the system of linear equations?
y = -x + 30
y = x + 6
yes
no
Answer:
No
Step-by-step explanation:
When the 2 equations are graphed the point (13, 17) is not
a solution to the system of linear equations.
So the answer is no.
If you want to look for the solution**- the solution to the equation is (12, 18)
A quadratic function has roots at 2 and 4 and a vertex at (3, −2). What is the equation of the function in vertex form?
Answer:
Step-by-step explanation:
(Offering Lots of Points) Please help me with this question!
Answer:
Linear function: y = x + 7.75
Step-by-step explanation:
A store sells packages of comic books with a poster. We are told that:
A poster and 4 comics books cost $11 75.A poster and 11 comics books cost $18.75.Let p be the cost of one poster.
Let c be the cost of one comic book.
Write a system of equations using the given information and the defined variables:
[tex]\begin{cases}p + 4c = 11.75\\p + 11c = 18.75\end{cases}[/tex]
Subtract the first equation from the second equation to eliminate p:
[tex]\begin{array}{crcrcl}&p&+&11c&=&18.75\\-&(p&+&4c&=&11.75)\\\cline{2-6}&&&7c&=&\;\;7.00\\\cline{2-6}\end{array}[/tex]
Solve for c:
[tex]7c=7.00[/tex]
[tex]c=1.00[/tex]
Therefore, the cost of one comic book is $1.00.
Substitute the found value of c into one of the equations and solve for p:
[tex]\begin{aligned}p+4(1.00)&=11.75\\p+4.00&=11.75\\p&=7.75\end{aligned}[/tex]
Therefore, the cost of one poster is $7.75.
Now we know the cost of one poster and one comic, we can write a linear function that models the cost y of a package containing x number of comic books:
[tex]y = 1.00x + 7.75[/tex]
[tex]y =x + 7.75[/tex]
We are told that another store sells a similar package modeled by a linear function rule with initial value $6.99. The initial value is the y-intercept of each function, i.e. the cost of the package when zero comics are sold. So the linear function for this package is:
[tex]y = x + 6.99[/tex]
To determine which store has the better deal, we need to compare the y-intercepts (the initial values). The store with the lower initial value provides a better deal because it charges less for the basic package (when the number of comic books is zero).
Since 6.99 is less than 7.75, the other store offers a better deal, as it has a lower initial cost for the basic package.
Answer:
[tex]\Huge \boxed{ \texttt{\bf{y = x + 7.75} }}[/tex]
Step-by-step explanation:
To find the linear function rule that models the cost [tex]\texttt{y}[/tex] of a package containing any number [tex]\texttt{x}[/tex] of comic books, we can use the given information:
A poster and 4 comics cost $11.75A poster and 11 comics cost $18.75Let's denote the cost of a poster as [tex]\texttt{P}[/tex] and the cost of a comic book as [tex]\texttt{C}[/tex]. Then, we can write two equations:
[tex]\texttt{ P + 4C = 11.75}[/tex] (Equation 1) [tex]\texttt{P + 11C = 18.75}[/tex] (Equation 2)To solve these equations, we can use the method of elimination. Let's use this method to eliminate [tex]$$P$$[/tex]:
[tex]\texttt{(P + 11C) - (P + 4C) = 18.75 - 11.75}[/tex][tex]\texttt{7C = 7}[/tex][tex]\texttt{C = 1}[/tex]Now, substituting the value of [tex]\texttt{C}[/tex] back into equation 1:
[tex]\texttt{P + 4(1) = 11.75}[/tex][tex]\texttt{P = 11.75 - 4}[/tex][tex]\texttt{P = 7.75}[/tex]Now that we have the cost of a poster (P) and a comic book (C), we can write the linear function rule as:
[tex]\Large \boxed{\texttt{y = x + 7.75}}[/tex]
[tex]\texttt{y}[/tex] is the total cost of a package [tex]\texttt{x}[/tex] is the number of comic books in the package.Now, suppose another store sells a similar package modelled by a linear function rule with an initial value of $6.99. This means that the cost of a poster at the other store is $6.99. Since the cost of a comic book is the same at both stores ($1), the linear function rule for the other store is:
[tex]\Large \boxed{ \texttt{y = x + 6.99}}[/tex]
Comparing the two linear function rules, we can see that the second store has a better deal because the initial cost of a poster is lower ($6.99) compared to the first store ($7.75).
________________________________________________________
(-20, 12)
(17, 2)
(-11, 8)
(17, 8)
(11, 2)
Is this relation a function?
Answer:
No because x-coordinate 17 appears twice.
Step-by-step explanation:
In a function, no two ordered pairs can have the same x-coordinate.
Here, points (17, 2) and (17, 8) have 17 as the x-coordinate. Since the same x-coordinate, 17, is used more than once, this relation is not a function.
a) what is the cube root of 729
b) describe how to construct a cube root of 729
Answer:
9
Step-by-step explanation:
a.) cube root of 729
³√729
= 9
b.) look for a number that you will multiply thrice to get 729
which is 9 or u will use your calculator
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The median, or middle value, is 42 48 52 54 59 61 61 64 65 67 68 70 72 75 80
The median or the middle value of 42 48 52 54 59 61 61 64 65 67 68 70 72 75 80 is 64.
What is a median?It is the middle value of the given set of numbers after arranging the given set of numbers in order.
We have,
42 48 52 54 59 61 61 64 65 67 68 70 72 75 80
The given set of numbers is in ascending order.
There are 15 numbers.
The middle number will be the 8th number.
8th number = 64
Thus,
The median is 64.
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In a box of chocolates, of the chocolates are white chocolate, are milk
chocolate, and the rest are dark chocolate.
What fraction of the chocolates are dark chocolate?
......................................................................
Rufus has collected 100 pounds of aluminum cans to recycle. He plans to collect an additional 25 pounds each week. In how many weeks will Rufus have a total of 400 pounds of cans?
Answer: 12
Step-by-step explanation:
7. Use the Division Property of Equality to write an equation that is
equivalent to 5x = 14.
Answer: x = 14/5 or x = 2.8
Step-by-step explanation:
Step 1: Divide both sides of the equation by five: a common nonzero real number.
(5x)/5= 14/5
Step 2: Simplify
x = 14/5
Sonny has 2x + 3 dollars. Allan has 6x + 4 dollars. How much money did Sonny have if they both had $407 all together?
Answer:
$103
Step-by-step explanation:
In order to determine how much money Sonny has, we need to write a mathematical equation to solve for x. We know how much money Sonny and Allan each have in terms of x, and we can add the two expressions together to equal a total amount of $407. This will be represented and simplified as follows:
2x + 3 + 6x + 4 = 4078x + 7 = 407Now we can solve the equation for x.
8x = 400x = 50We know that x is equal to 50, so we can plug it back into Sonny's expression to find out how much money she has.
2(50) + 3 = 100 + 3 = 103Sonny has $103.We can check our work by solving for the amount of money Allan has and then adding up the two amounts to make sure the total is $407.
6(50) + 4 = 300 + 4 = 304CHECK: $103 + $304 = $407