================================================
Explanation:
Part A) Find P(-2)
We'll divide P(x) over (x+2) to get a quotient Q(x) and remainder 8 like so
P(x)/(x+2) = quotient + remainder/(x+2)
P(x)/(x+2) = Q(x) + 8/(x+2)
When multiplying both sides by (x+2), it clears out the fractions and we're left with this
P(x) = (x+2)*Q(x) + 8
From here, plug in x = -2 and simplify
P(x) = (x+2)*Q(x) + 8
P(-2) = (-2+2)*Q(-2) + 8
P(-2) = (0)*Q(-2) + 8
P(-2) = 0 + 8
P(-2) = 8
Luckily we don't need the value of Q(-2) since it cancels out with the zero.
-----------------------------------
Part B) Find P(2)
This time we'll plug in x = 2 and we'll get...
P(x) = (x+2)*Q(x) + 8
P(2) = (2+2)*Q(2) + 8
P(2) = 4*Q(2) + 8
P(2) = 4*5 + 8
P(2) = 20+8
P(2) = 28
"15 fish per fish tank" translated expression
Answer:
15/x
Step-by-step explanation:
x = fish tank
Describe the characteristics of each set of numbers
that make up the set of integers.
Positive and negative numbers are included in the category of integers, which is distinct from decimals and fractions.
What in math is an integer?
A whole number that can be positive, negative, or zero is called an integer. It is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers.There are numerous types of numbers, including integers, whole numbers, rationals , real numbers, and natural numbers. Positive and negative numbers are included in the category of integers, which is distinct from decimals and fractions. It has the following qualities:
Numbers below zero are considered negative numbers.
In the set of integers, zero is included.
There are overlaps between the number categories.
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at 9:30 am andrew left exeter for portsmouth, cycling at 12 mi/h. at 10:00 am stacy left portsmouth for exeter, cycling at 16 mi/h. the distance from exeter to portsmouth is 20mi.find the time they meet
Stacey meets Andrew 1.5 hours after she starts travelling at 11:30 AM and Andrew meets Stacey 2 hours after he starts travelling at 11:30 AM.
How to solve this problem?
Stacey and Andrew in the mentioned problem will meet in a time frame only when the both have travelled equal distances in respect to another.
Given, speed at which Andrew was travelling = 12 mi/h
Speed at which Stacey was travelling = 16 mi/h
Let the time taken by Stacey be = t hours
Therefore, the time taken by Andrew = (t + 0.5) hours
When Stacey overtakes Andrew, they must have covered the same distance, therefore:
16t = 12×(t + 0.5) ⇒ 16t = 12t + 6 ⇒ 4t = 6 ⇒ t = 6/4 ⇒ t = 3/2 ⇒ t = 1.5
Therefore, Stacey meets Andrew 1.5 hours after she starts travelling at 11:30 AM and Andrew meets Stacey 2 hours after he starts travelling at 11:30 AM.
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8 Write an equation of the line passing through the point (-7,-6) with slope m = 4
What are the solutions to the equation?
Finding the value of the given equation's unknown variables is a step in the equation-solving process. The value of the variable satisfies the requirement that the two expressions are equal and is called the solution of that equation.
What Does Solving Equations Mean?Calculating the value of the unknown variable while keeping the equation balanced on both sides is the process of solving equations. When a condition on variable guarantees that two expressions in the variable have the same value, it qualifies as an equation.
The variable's value for which the equation holds true is referred to as the equation's solution If the LHS and RHS are switched, an equation doesn't change. The answer is discovered after isolating the variable for which the value must be determined. Depending on the kind of equation we are working with, we can solve it. There are several types of equations, including linear, quadratic, rational, and radical ones.
When a linear equation has one variable, there is only one solution; when there are two variables, there are two solutions. A quadratic equation's solution yields two roots. To solve an equation, a variety of techniques and steps are used.
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Shaylee is determining if 6 is the solution to the equation.
42 ÷ w = 7 for w = 6
First, Shaylee must substitute
for
.
To simplify, Shaylee must divide
by
.
First Shaylee must substitute 6 for w. To simplify, Shaylee must divide
42 by 6.
What is division?Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.
Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.
In this equation we have
42 ÷ w = 7
The question has already specified the value of w as 6
Hence we would have to remove w and replace it with the value six 6.
This is
42 ÷ 6
Next we have to find the value or the answer when we do this division. This can be easily done with a calculator
42 ÷ 6 = 7
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4. A triangle has two sides measuring 8 cm and 15 cm. Write an inequality to represent the possible lengths of the third side.
Answer:
7 < x < 23
Step-by-step explanation:
given 2 sides of a triangle then the third side x is in the interval
difference of 2 sides < x < sum of 2 sides , that is
15 - 8 < x < 15 + 8
7 < x < 23
you want to know the opinions of american school teachers about establishing a national test for high school graduation. you obtain a list of the members of the national education association (the largest teachers' union) and mail a questionnaire to 2500 teachers chosen at random from this list. by the deadline, 1347 teachers return the questionnaire. the population is
The list of the members of the national education association is the Population.
Given, that a list of the members of the national education association is obtained and the questionnaire is mailed to 2500 teachers chosen at random from the list.
1347 teachers from those 2500 teachers return the questionnaire.
So, as we know that
A population is the group that you want to draw conclusions about.
Here, we want to know the opinions of American school teachers about establishing a national test.
So, The list of the members of the national education association is the Population.
Also, 1347 responses which we got is the sample.
Hence, The list of the members of the national education association is the Population.
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Please help
At the beginning of spring, London planted a small sunflower in her backyard. The sunflower's height in inches,
h
h, after
w
w weeks, is given by the equation
h
=
4
w
+
15
h=4w+15. What could the number 4 represent in the equation
The change in the sunflower's height for every one additional week.
The sunflower's height after one week.
The sunflower's final height
The sunflower's height after 0 weeks.
if we want to create a 95% confidence interval for a population proportion with a margin of error (m) of 0.099, what sample size is necessary? use the simplified formula (n
For the specified requirements, 97 sample size are required.
Given that,
Confidence Interval = 95
Margin of error (m) =0.099
We know , to find Sample size for estimating a population proportion
n = (Z*/m)² P(1-P)
where , m is margin of error
P is estimated proportional value.
If we have no preconceived of the value of the population proportion
, then we use P= 0.50 because it is most conservative and it will give use the largest sample size calculation.
for a 95% confidence interval ,
Z* = 1.960 , m=0.099
Using equation we get
n = (1.96/0.099)²(0.5)( 1 - 0.5 )
By solving,
n = 97.02≅ 97
The necessary sample size is 97
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The range of f(x) = |x| is y ≥ 0. If a < 0 and b ≠ 0 for g(x) = a|x| + b, what is the range of function g?
The range of the function g, given the premises for f(x) = |x| and a < 0 while b ≠ 0 is; the set of all real numbers.
Range of a functionIt follows from the task content that the range of the function g(x) = a|x| + b is to be determined given the parameters as in the task content.
Since the function f(x) = |x| has a range of y ≥ 0, and a is a negative number ( < 0), it therefore means that the a|x| is always a number less than 0 (<0).
However, the possible values of constant, b include all real numbers except 0.
On this note, the function g(x) = a|x| + b has a range which is the set of all real numbers. This is so because, g(x) > 0 when a|x| < b and g(x) < 0 when a|x| > b.
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Which of the following best describes the ordered pairs listed below? (-2, -1), (1, -4), (5, -8), (9, -12) A. function only B. both a relation and a function C. relation only D. neither a relation nor a function
Since each input is mapped to only one output, the best description of the ordered pairs is given by:
B. both a relation and a function.
When does a relation represents a function?
A relation represents a function if each value of the input is mapped to only one value of the output.
For a point in the format (x, y), we have that:
=> x is the input.
=> y is the output.
=> The meaning is that the input x is mapped to the output y.
For this problem, the points are given as follows:
(-2, -1), (1, -4), (5, -8), (9, -12)
Each input is mapped to only one input, that is, there are no repeated values of x, hence the best description of the ordered pairs is given by:
B. both a relation and a function.
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simplify
2-5-(6/2+1)
Answer:
-7
Step-by-step explanation:
6/2=3
3+1= 4
2-5= -3
-3-4= -7
6/2+1= 4
2-5-4= -7
*Do what is in the parenthesis first!!*
Find the equation to represent the volume of
a cylinder with diameter 10 and height of 2x.
The volume of a cylinder is 50πx
We know that
The volume (V) of a cylinder is,
V = πr²h
where
r is the radius of the cylinder
h is the height of the cylinder
From the question, we have
a cylinder with diameter 10 and height of 2x.
r = 10/2 =5
V = πr²h
V = π*5²*2x
V = 50πx
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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What is the ratio of 1 1/2 hours to 50 minutes
Answer:
50 mins: 1 and a 1/2 hours
Answer:
9:5
Step-by-step explanation:
1.5 hours is equivalent to 90 minutes (60 x 1.5)
so it's a ratio of 90:50
this can be simplified to a ratio of 9:5 by dividing both sides by their shared factor of 10
on the grid,draw the graph of y=2x-3 for values of x from -3 to 5
The graph of the equation y = 2x - 3 at the interval of -3 to 5 is attached below.
Graph:
Graph means the diagram that shows the variation of a variable in comparison with that of one or more other variables.
Given,
Here we have the equation y = 2x - 3
Now, we need to plot the graph of the given equation at the interval of -3 to 5..
To plot the graph for the given function,
The given interval is taken as the value of x and we have to calculate the value of y from it,
Now, we have to take the given interval -3, -2, -1, 0, 1, 2, 3, 4, 5 are the samples value for x.
So, we have to apply the values on the equation,
Then we get the value of the function as,
x = -3 => y = 2(-3) - 3 = -6 - 3 = 9
x = -2 => y = 2(-2) - 3 = -4 - 3 = -7
x = -1 => y = 2(-1) - 3 = -2 - 3 = -5
x = 0 => y = 2(0) - 3 = 0 - 3 = -3
x = 1 => y = 2(1) - 3 = 2 - 3 = -1
x = 2 => y = 2(2) - 3 = 4 - 3 = 1
x = 3 => y = 2(3) - 3 = 6 - 3 = 3
x = 4 => y = 2(4) - 3 = 8 - 3 = 5
x = 5 => y = 2(5) - 3 = 10 - 3 = 7
The completed table is attached below.
Now, we have to plot the graph through the derived table, then we get the graph like the following.
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what fraction multiplied by 31/27 equals 1
Answer: 27/31 is the answer
Step-by-step explanation:
31/27 x 27/31 = 1 because 27/31 is the recprical
Answer:x = 31/27 = 1.148
Step-by-step explanation:
Each bag of grass seed covers 55 square
yards. How many bags of grass seed will
Sasha need to purchase to cover her
backyard?
38 yd
28 yd
The area of Sasha's backyard is 1064 yard square. So the number of bags required would be 20.
What is area?
The measurement that expresses the size of a region on a plane or curved surface is called area. It's S.I. unit is m².
Main Body:
The area of Sasha's backyard = 38*28
= 1064 yd square
Now 1 bag covers 55 yd square
so, bag required for 1064 yd = 1064/55
= 19.3 approximately
Therefore the amount of required bags are 20.
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What is 5.2E11 in standard form
The standard form of 5.2E11 using the set scientific notation and rules is 311345.5369.
What is a standard form in mathematics?The standards for putting mathematical elements in standard form make it easier for anyone to read, write, and interact with them. The standard form is the most popular approach to representing a mathematical element.
In mathematics, the standard form is the most prevalent way of describing a specific element. Every element in arithmetic is represented in a standard form, from enormous numbers to little integers, or equations to lines.
A standard form is a method of writing a particular mathematical notion, such as an equation, or expression, in a way that adheres to specified criteria. The standard form is used to portray very big or very small numbers in a succinct manner.
The standard form of 5.2E11 using the set scientific notation and rules is:
311345.5369.
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PLSS HELP EXTRMELY URGENT WILL GIVE BRAINLIEST!
2 parents and their 7 children are taking family photos. Seats are arranged in two rows
so that the first row has 4 chairs and the back row has 5 chairs. If exactly two children
must be sitting in the first row, how many ways can the seating be arranged?
Answer: .................................................
how many ways can the seating be arranged?
answer = 128 ways
correct or what???
help meeeeeeeeeeeeeeeeee please
Answer:
try using the Pythagorean theorem
Step-by-step explanation:
hypotenuse ² = Opposite ² +Adjacent ²
where hypotenuse is the side facing the right angle sign;(x+3)
The bottom of a 5.5-meter ladder is 3.3 meters from the base of a wall, and it just reaches the bottom of a window in the wall. If the window is 1 meter high, what is the distance from the top of the window to the base of the wall?
The distance from the top of the window to the base of the wall is 5.4 m.
According to the question,
We have the following information:
The bottom of a 5.5-meter ladder is 3.3 meters from the base of a wall, and it just reaches the bottom of a window in the wall. And the window is 1 meter high.
Now, we know that the ladder, wall and base will make a right-angled triangle. We can use Pythagoras theorem to find height of the wall.
(Pythagoras theorem: square of hypotenuse = sum of squares of base and height)
Let's take height of the wall to be h meters.
[tex]h^{2}[/tex] = [tex](5.5)^{2} -(3.3)^{2}[/tex]
[tex]h^{2}[/tex] = 30.25-10.89
19.36
h = √19.36
h = 4.4 m
Now, the distance from the top of the wall window to the base of the wall is:
4.4 + height of the window
4.4+1
5.4 m
Hence, the distance from the top of the window to the base of the wall is 5.4 m.
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Please solve the equation
[tex]5 {}^{2x + 1} - 26(5 {}^{x} ) \: + 5 = 0[/tex]
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
[ log 5 = 0.69 ]
[ log 26 = 1.41 ]
The formula for log [tex]x^n[/tex] = n log x
The value of x is 0.043
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
[tex]5^{2x + 1} - 26(5^x) + 5 = 0[/tex]
[tex]5^{2x + 1} + 5 = 26(5^x)[/tex]
The formula for log [tex]x^n[/tex] = n log x
Taking logs on both sides.
log [tex](5^{2x + 1} + 5)[/tex] = log [tex]26(5^x)[/tex]
log [tex]5^{2x + 1}[/tex] + log 5 = log 26 + log [tex]5^{x}[/tex]
(2x + 1) log 5 + log 5 = 1.41 + x log 5
[ log 5 = 0.69 ]
[ log 26 = 1.41 ]
(2x + 1) x 0.69 + 0.69 = 1.41 + 0.69x
1.39x + 0.69 + 0.69 = 1.41 + 0.69x
0.70x = 1.41 - 1.38
x = 0.03 / 0.70
x = 0.043
Thus,
The value of x is 0.043
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Mila bought stock in a company
two years ago that was worth z
dollars. During the first year that she owned the stock, it decreased by
35%. During the second year the value of the stock decreased
by 32%.
Write an expression in terms of z that represents the value of the stoc
after the two years have passed.
The expression is 2z+0.67
From the question, we have
During the first year that she owned the stock, it decreased by 35%. During the second year the value of the stock decreased by 32%.
z-35%+z-32%
=z-7/20+z-8/25
=2z+0.67
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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A suit is on sale for $296.40, which is 62% less than the regular price.
What is the regular price?
Answer: The total price is $478.06
Step-by-step explanation:
For this we use regular price of the suit as x
x is 100% of the price therefore 62% of x=296.4
Now we cross multiply
62 × x = 100 × 296.40
62x = 29,640
Now that we got rid of those complicated percentages we simply divide both sides by 62 to isolate x
29,640/62 = 478.064516129
Since we are working with dollars and cents that do not get smaller than .01 we can shave off all the extra decimals near the end
478.06
The regular price is $478.06
Now we just check our work to prevent any awkward and simple mistakes
478.06 x .62 = 296.3972 or 478.06 x .62 = 296.39
Keep in mind the one cent difference is because we shaved off the extra decimals at the end
Hope this helps!
A bowling alley charges $15 per game. Customers are also charged an additional $3 to rent bowling shoes.
Which statement is true, based on the given description?
The description shows a linear relationship, but not a proportional relationship.
The description shows a linear relationship and a proportional relationship.
The description does not show a linear relationship or a proportional relationship.
The description shows a proportional relationship, but not a linear relationship.
The statement that is true on the bowling alley charges and the additional cost for renting bowling shoes is The description shows a linear relationship, but not a proportional relationship.
What is a linear relationship?In a linear relationship, the values of the two variables can be drawn on a graph such that they form a line. There would often be a y-intercept and then a slope or a constant rate of change. In this case the constant rate of change is the $15 per game and the additional cost to rent bowling shoes is the y-intercept. This is therefore a linear relationship.
A proportional relationship would have a constant rate of change but there would be no y - intercept. As there is a y - intercept in this scenario, this is not proportional.
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Answer: A: The description shows a linear relationship, but not a proportional relationship.
probability works not by compensating for imbalances but by overwhelming them. suppose that the first 1010 tosses of a coin give 1010 tails and that tosses after that are exactly half heads and half tails. (exact balance is unlikely, but the example illustrates how the first 1010 outcomes are swamped by later outcomes.) (use decimal notation. give your answers as exact numbers.) what is the proportion of heads after the first 10 tosses?
The proportion of heads after the first 10 tosses of a coin is zero i.e 0/10 = 0
A probability is a number that reflects the likelihood or probability that a particular event will occur. Probabilities can be expressed as percentages ranging from 0 to 1, and can also be expressed as percentages ranging from 0% to 100%. A probability of 0 indicates that the particular event is unlikely to occur, and a probability of 1 indicates that the event will definitely occur.
Probability is calculated by dividing the number of ways the event can occur by the total number of outcomes.
We have given the following points ,
A coin is tossed 10 times and it comes with tail in each time of first 10 tosses.
When a coin is toosed , there two possibilities either it comes with head or tail. Both can't be come at once.
As we see first ten tosses of a coin gives tails as a result . Then, there is no chance of occurrence head in first 10 tosses.
So, there in no heads in first 10 tosses. The probability or proportion of heads after the first 10 tosses is 0/10 = 0..
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#Complete Question:
Probability works not by compensating for imbalances but by overwhelming them. Suppose that the first 10 tosses of a coin give 10 tails and that tosses after that are exactly half heads and half tails. (Exact balance is unlikely, but the example illustrates how the first 10 outcomes are swamped by later outcomes.) (Use decimal notation. Give your answers as exact numbers.) What is the proportion of heads after the first 10 tosses?
I need to paint a straight face consisting of six panels he has a green red and magenta paint and each panel should be painted with only one color how many ways are there to paint the fence
There are 20 ways to paint the fence consisting of six panels each with one color out of green, red, and magenta.
There is a total of 6 panels and 3 paint colors and each panel has to be painted with only 1 color.
∴ Total number of panels = 6
Total number of colors = 3 (green, red, and magenta)
To calculate the number of ways to paint 6 panels with one of the 3 colors, the formula of combination is used. Combinations are ways of selecting objects from a group or collections, in a way that the order of the objects does not matter.
The number of ways or the combinations of 6 panels taken with each color out of 3 at a time is given by [tex]^6C_3[/tex]
[tex]^6C_3[/tex] = 6! / [3! (6-3)!]
[tex]^6C_3[/tex] = (6*5*4*3*2*1) / [3*2*1 (3)!]
[tex]^6C_3[/tex] = 720 / (6*6)
[tex]^6C_3[/tex] = 720 / 36
[tex]^6C_3[/tex] = 20
Therefore, 20 combinations are possible to paint 6 panels each with only one color out of green, red, and magenta.
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Hong made $153 for 9 hours of work.
At the same rate, how many hours would he have to work to make $187?
hours
X
Answer:
11 hours
Step-by-step explanation:
153 divided by 9 (which is 17) 17$ per hour so add 17 and 17 together which would be 34 and add it to 153 which would be 187$ he worked 2 more hours so in total he worked 11 hours.
and i know that was a bad explanation but its whatever hope this helped.
the wheels on Kiran's bike are 64 inches in circumference. How many times doo the wheels rotate if Kiran rides 300 yards ?
Answer:
169 times
Step-by-step explanation:
We know that the circumference of Kiran's bike wheel is 64 inKiran rides total distance of 300 yardsTo find number of rotations made by wheel...
Know that 1 yard = 36 in
300 yards = 36 x 300 = 10800 in
Number of rotation = Total distance covered by wheel ÷ Circumference of wheel
Number of rotations = 10800 ÷ 64 = 168.75 ≅ 169
Therefor, the wheel rotates = 169 times
Hope this helps! :)