The product of linear factors for p(x) is given as (x-4)(x^2+x-6).
What is the factor theorem?The factor theorem states that;
p(x) is divisible by x-a if and only if p(a)=0p(x) is divisible by x+a if and only if p(-a)=0From the question, given that x-4 is a factor of
p(x) = x^3 − 3x^2 − 10x + 24,
then it is divisible by x-4 and p(4)=0.
Dividing x^3 − 3x^2 − 10x + 24 by x-4 using the long division will result to another factor x^2+x-6 with a remainder of zero.
We can then conclude that (x-4)(x^2+x-6) is the product of linear factors for p(x).
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7. Solve by using extracting square roots 4a²-25= 0
pa answer po rn
w solution po
[tex]4a^{2} -25=0\\(2a-5)(2a+5)=0\\2a-5=0 \\or 2a+5=0\\\\a=\frac{5}{2} \\\\or\\\\a=-\frac{5}{2}[/tex]
IF YOU CHECK CAREFULLY YOU WILL FIND THAT THIS EQAUTION IS MADE OF DIFFERENCE OF SQUARES.
GOODLUCK!!
What is the graph of f(x) = 3x - 4, where x ≥ 1?
Here is the graph for you!!
An archeologist in Turkey discovers a spear head that contains 85% of its original amount of C-14. k = 0.0001 Find the age of the spear head to the nearest year.
The age of the spear head is found to be 1625 years.
What is the age?Let us recall that the age of the sample can be determined by the use of radiometric dating. Let us now define the variables;
The constant of the decay (k) = 0.0001
The amount of the sample originally present (No) = No
The amount of the sample at time t = 0.85No
t = The age of the sample
Given that;
N= Noe^-kt
N/No = e^-kt
0.85No/No = e^-0.0001t
0.85 = e^-0.0001t
ln0.85 = -0.0001t
t = ln0.85/ -0.0001
t = 1625 years
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What is the effect on the graph of f(x) = 1/xwhen it is transformed to
g(x) = 1/x + 17?
OA. The graph of f(x) is shifted 17 units to the left.
OB. The graph of f(x) is shifted 17 units up.
OC. The graph of f(x) is shifted 17 units down.
O D. The graph of f(x) is shifted 17 units to the right.
The correct option is option B that is "The graph of f(x) is shifted 17 units up". It is shifted 17 units up. By adding 17 to the equation, y increases by 17. If y increases by 17, the graph shifts up by 17.
What is graph?In discrete mathematics, a graph is made up of vertices—a collection of points—and edges—the lines connecting those vertices. In addition to connected and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs, there are many other types of graphs.
What is transformation in graph?The process of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation. In particular, the modification of algebraic equations, it is a typical kind of algebraic problem.
It is shifted 17 units up.
By adding 17 to the equation, y increases by 17.
If y increases by 17, the graph shifts up by 17.
Option B, "The graph of f(x) is shifted 17 units up," is the answer. It is moved upward 17 units. Adding 17 to the formula causes y to rise by 17. The graph moves up 17 units if y rises by 17.
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A recent survey showed that 73% of elementary school students have a pet. What is the ratio of students who have a pet to students who do not have a pet?
Answer:
73 : 27
Step-by-step explanation:
You want the ratio of students that have a pet to students that don't have a pet, given that 73% of students have a pet.
No petIf 73% of students have a pet, then the remaining 100% -73% = 27% of students do not have a pet.
RatioThe ratio of students who have a pet to students who don't have a pet is then ...
(have a pet) : (don't have a pet) = 73% : 27% = 73 : 27
According to a recent survey, 73% of elementary school students have a pet, making the ratio of students with pets to those without pets 73:27.
What is ratio?A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
You want the ratio of students that have a pet to students that don't have a pet, given that 73% of students have a pet.
If 73% of students have a pet, then the remaining 100% -73% = 27% of students do not have a pet.
The ratio of students who have a pet to students who don't have a pet is then,(have a pet) : (don't have a pet) = 73% : 27% = 73 : 27
A recent survey found that 73% of elementary school students own a pet, making the proportion of students who own pets to those who don't stand at 73:27.
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Identify the partial quotient in the first step of this problem, as shown:
Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.
-83843/21 is the partial fraction of Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.
4357/21 - 4200
Take LCM as 21.
4357-88200/21
-83843/21
=-3992.5
Hence -83843/21 is the partial fraction of Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.
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How do you distribute 259 or 3.25 pieces of candy into 80 bags
259 pieces of candy can be distributed in 80 bags to give 3 candy per bag and there will be 19 candies remaining
How to distribute 259pieces of candy in 80 bagsThe concept for distributing the required candies is achieved by the mathematical operation called division.
Division is an inverse of multiplication. With division we can share and determine number of candy per bag
The question is solved by
= 259 ÷ 80
= 259 / 80
= 3 19/80
This means that there will be 3 candies per bag and after sharing among the nags there will be 19 candies remaining.
Putting this in decimal gives
= 3.2375 ≅ 3.24
In a situation where we are to count the candies if they are 3.25 pieces per bag the we multiply as follows
= 3.25 * 80
= 260
in this case the total number of candies should be 260
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A triangle has sides with lengths of 30 kilometers, 35 kilometers, and 45 kilometers. Is it a right triangle?
If a triangle has sides with lengths of 30 kilometers, 35 kilometers, and 45 kilometers. No it is not a right triangle.
Determining whether the triangle is a right triangleWe would be making use of converse of Pythagoras' theorem to determine whether the triangle is a right triangle.
In a situation were we have a right triangle the square on longest side will be the same with the sum of square of other sides
Longest side
45² = 2025
Other side
30 ² + 35 ²
900 + 1,225
= 2125
Hence,
2025 ≠ 2125
Based on the above it is not a right triangle because the longest side did not equate the other side.
Therefore it is not a right triangle.
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As 2125 ≠ 2025 therefore it didn't meet the requirements of Pythagoras' theorem, it is not a right-angle triangle.
This type of question makes a right-angled triangle that can be solved by Pythagoras's theorem.
What is Pythagoras's theorem?In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.
Given, A triangle has sides with lengths of 30 kilometers, 35 kilometers, and 45 kilometers.
∴ 30² + 35² = 45².
900 + 1225 = 2025.
2125 ≠ 2025.
It is not a right-angle triangle because it didn't satisfy the property of Pythagoras's theorem.
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What does dilation mean,
Answer: Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller.
Answer: a transformation, which is used to resize the object
Step-by-step explanation:
the shape changes size but not shape
7/12 x 4x3 =? I need help
Cyphon, this is the solution:
We have to multiply the following fractions:
7/12 * 4/3
7 * 4 / 12 * 3
28/36
Simplifying, we have:
7/9 (Dividing by 4 numerator and denominator)
We have to add the following fractions:
- 1/2 + 4/9
Let's find the lowest common denominator between 2 and 9, as follows:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22
9, 18, 27, 36
The lowest common denominator is 18
a fence is to be built to enclose a rectangular area of 280 square feet. the fence along three sides is to be made of material that costs 6 dollars per foot, and the material for the fourth side costs 13 dollars per foot. find the dimensions of the enclosure that is most economical to construct.
Fencing of any rectangular region is basically represent perimeter of that rectangular region.
For most economical fencing, length L = 21.05 feet and width W = 13.301 feet.
How to estimate the length and width of the rectangular region?Area of rectangular region is 280 square feet.
And length is L and width is W.
Area of rectangular region = L × W=280 square feet
W=280 / L
Since, The fence along three sides is to be made of material that costs 6 dollars per foot, and the material for the fourth side costs 14 dollars per foot.
Therefore, Total cost, C = 6(2L + W) + 13W = 12 L + 19 W
Total cost, C = 12 L+ 5,320 / L
To find most economical cost, differentiate above function and equate to zero.
C' = 12 - 5,320 / L²
simplifying the above equation, we get
⇒ 12 - 5,320 / L² = 0
⇒ L² = 5,320 / 12
L = 21.05 feet
Therefore, L = 21.05 feet
Substituting value of L in area equation.
We get, W = 13.301 feet.
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Help me solve question 1 on my algebra homework please
Two lines are parallel if they hay the same slope.
The slope, m, of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]From the graph, line m passes through the points (0, 1) and (3,3), then its slope is:
[tex]m=\frac{3-1}{3-0}=\frac{2}{3}[/tex]Equation of a line in slope-intercept form
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope and (x1, y2) is a point on the line.
The new line has to pass through point P(1, -2). Substituting with this point and m = 2/3 into the general formula:
[tex]\begin{gathered} y-(-2)=\frac{2}{3}(x-1) \\ y+2=\frac{2}{3}(x-1) \end{gathered}[/tex]
Last year the debate club had 25 members. This year there are 37 members in the club. Estimate the percent change in the number of club members.
Answer:
There was a 48% increase from last year.
Step-by-step explanation:
Last year the debate club had 25 members. This year there are 37 members in the club. Estimate the percent change in the number of club members.
= (37 - 25) / 25
= -12 / 25
= 0.48 or 48%
There was a 48% increase from last year.
check:
25 * 1.48 = 37
Just the coordinates is fine :)
To give an entity the desired position, orientation, or shape starting from the current position, orientation, or shape, geometric transformations are required. Scaling, rotation, translation, and shear are the fundamental transformations. Projections and mappings are two additional crucial categories of transformation.
Y =- X is what kind of a transformation?
Y = X's reflection:
The x-coordinate and the y-coordinate switch positions when a point is reflected across the line y = x. Y = -x reflection: The x-coordinate and the y-coordinate switch places when you reflect a point across the line y = -x, and they are negated (the signs are changed).
The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. The cross-sectional reflection of point (x, y)
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40 push-ups in 5 days = push-ups in 6 days
Answer:
48 push ups
Step-by-step explanation:
40 push ups in 5 days can be modelled with the fraction 40/5
you can simplify that to 8/1 after dividing both sides by 5
now set that equal to push ups over 6
but first you must declare a variable for push ups
let x = push ups
8/1 = x/6
multiply both sides by 6
48/1 = x
x = 48
that is your answer
48 push ups
To know how many reflections are made per day, a division is made between the days and the total number of reflections.
40 Flexions ➗ 5 days = 8 flexions a day.
Every day it has 8 flexions, in multiply the 6 days for the 8 flexions of each, then.
8 flexions (1 day) ✖ 6 days = 48 flexions.
Answer: 48 flexions = 6 days ✅.
Shelly was shopping and saw that a 14lb turkey costs $13.86. Calculate the unit price for 1 lb of turkey.
the unit price for 1 lb of turky is $0.99
Explanation:The cost of 14 lb of turkey = $13.86
let the cost of 1 lb of turkey = y
The unit price is the cost for 1lb of turkey:
14 lb = 13.86
1 lb = y
cross multiply:
14(y) = 1(13.86)
14y = 13.86
divide both sides by 14:
14y/14 = 13.86/14
y = 0.99
Hence, the unit price for 1 lb of turky is $0.99
The table shows the inputs and outputs for the function f (x) = -7x-5.Input-10-5O5Output65?-5-40What is the output value of the function when the input is –5?403050
Answer:
30
Explanation:
To know the output value of the function, we need to replace x by -5 and calculated f(x). So:
[tex]\begin{gathered} f(x)=-7x-5 \\ f(-5)=-7(-5)-5 \\ f(-5)=35-5 \\ f(-5)=30 \end{gathered}[/tex]Therefore, if the input x is -5, the output f(x) is 30
So, the answer is 30.
the probability of being satisfied with a product purchased online is 0.555. if you buy 8 products online, what is the probability that you will be satisfied with 3 or more of the purchased products? (round your answer to 3 decimal places if necessary.)
The probability that you will be satisfied with 3 or more of the purchased products is 0.916
Given that,
The chance of being pleased with an internet purchase is 0.555. if you purchase 8 items online
Solution -
let X denote the no of success of
Purchased product online
X ~ B(n,p)
n = 8
P= 0. 555
a = 1 - 0 .555 = 0.445
P ( X = x) = [tex]nc_{x} b^{x} a^{n-x}[/tex]
P ( X = x)= [tex]8c_{x} (0.555^{x} )(0.445)^{8-x[/tex]
P ( X>=3)= [tex]\lim_{3 \to 8} 8c_{x} (0.555^{x} )(0.445)^{8-x[/tex]
P ( X>=3)) = 0.91614
=0.916
Therefore we can conclude the probability that you will be satisfied with 3 or more of the purchased products is 0.916
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in linear regression, the fitted value is the: a. predicted value of the dependent variable b. predicted value of the independent value c. predicted value of the slope d. predicted value of the intercept e. none of these options
predicted value of the slope , A regression model called simple linear regression uses a straight line to calculate the association between one independent variable and one dependent variable.
What is linear regression?
When modeling the relationship between a scalar answer and one or more explanatory variables in statistics, linear regression is a linear method. Simple linear regression is used when there is only one explanatory variable, and multiple linear regression is used when there are numerous variables.
A regression model called simple linear regression uses a straight line to calculate the association between one independent variable and one dependent variable. Both variables ought to have numerical values.
When the parameters are linear, a regression equation (or function) is said to be linear in statistics. Although the predictor variables can be transformed in ways that result in curvature, the equation must be linear in the parameters.
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in linear regression, the fitted value is the: predicted value of the dependent variable
When you enter the values of the predictors, factor levels, and other inputs into a statistical model, the predicted mean response value is known as the fitted value.
What is the predicted variable called?The independent variable, commonly referred to as the predictor variable, is used to forecast dependent variables. In data science and the scientific method, predictor variables are used rather frequently.Regression models that fit data well produce predicted values that closely match the values of the actual data. If there were no useful predictor variables, the mean model, which utilizes the mean for every predicted value, would typically be employed.Researchers can anticipate or explain variation in one variable based on another variable using regression. Defined terms: The response variable is the one that scientists are attempting to predict or explain. Because it is reliant on another variable, it is also sometimes referred to as the dependent variable.To learn more about predicted variable refer to:
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Have no clue how to do this if you could help or give best guess that would be awesome.
We are asked to find an equivalent amount to 100 USD in french francs. Acording to the table, on tuesday, a dollar costs 4.3450 french francs, then we can find how many francs we got by multiplying 100 USD and 4.345, then we get:
Francs = 100×4.3450 = 434.50
Then, the answer is 434.5 french francs
Please help quickly!! (30 POINTS)
Given f(x)=3x^2 −5x−2.
What is the value of f(−2/3)?
The value of the function f(−2/3) will give the value 8/3.
What is the answer for f(-2/3)?A function is important to show the expression that's given.
Given: f(x) = 3x^2 −5x−2.
To find f(-2/3), we substitute x = -2/3 into the equation:
f(-2/3) = 3 x (-2/3)^2 - 5(-2/3) - 2
= 3 x 4/9 + 10/3 -2
= 12/9 + 10/3 - 2
= (12 + 30 - 18) / 9
= 24 /9
= 8/3
Therefore, f(-2/3) evaluates to 8/3.
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Answer:1700
Step-by-step explanation:
What’s the answer plss
Answer: 8.4cm
Step-by-step explanation:
sin cos tan
SOH CAH TOA
It is cos because CAH does not have opposite (o) in it and we want to find the opposite.
O is opposite (opposite angle)
A is adjacent (next to angle)
H is hypotenuse (opposite right angle)
This is how I remember it
Cos(61)*17.4=8.435
8.4cm
Checks: 32.96,121.03 and 24.70;cash:22 one dollar bills, 5 ten dollar bills, and 15.21 in coins; less $20 cash recieved
The balance of the checks and cash (receipts and payments) is -$245.90.
How is the balance determined?The balance is the difference between receipts of cash and payments of checks and cash.
Using addition and subtraction operations, the balance is determined as follows:
Check Payments:32.96
121.03
24.70
Total checks = $178.69
Cash Payments:22 one dollar bills = $22.00 (22 x $1)
5 ten dollar bills $50.00 (5 x $10)
15.21 in coins $15.21
Total cash payments = $87.21
Cash Receipts:$20 cash received
Total cash = $67.21
Balance = -$245.90 [$20 - ($87.21 + $178.69)]
Thus, the balance of the checks and cash totals -$245.90, showing that payments outstripped receipts.
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Question Completion:How much is the balance between receipts and payments?
How many more pounds of milk chocolate were sold than white chocolate at the candy store last week?
Responses
A 18
B 18 2/3
C 19
D 19 2/3
Answer:
the answer for your question is option A
Answer:b
Step-by-step explanation:
the population of elk in a national forest was measured to be 12,000 in 2003, and was measured again to be 12,700 in 2004. if the population continues to grow linearly at this rate, what will the elk population be in 2014?
The elk population in 2014 will be 19,700 ,A population is an identified grouping of objects with the purpose of analysis and data collection.
What is population?A population is an identified grouping of objects with the purpose of analysis and data collection. Examples include people and animals. It comprises of a related collection of species that live in a specific area and have the ability to interbreed.
The population increased by 12,700-12,000 = 700 between the two measures, however, it did so over a period of 1 year, from 2004 to 2003. Divide 700 elk by 1
The elk population in 2014 will be 19,700We must first establish the method
2014=700 should add 10 times then we will get the 2014th year population.
so the population of 2014th will 19700
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Alexis has two job offers. Job #1 pays $12 an hour and will allow her to work 40 hours a week. Job #2 pays $8 an hour and also requires a 40-hour week. However, Job #2 also pays bonuses based on sales. The other salespersons told Alexis they average about $100 a week in bonuses. Which job will likely pay the most money per week?
Answer:
$8 an hour and also requires a 40-hour week
Step-by-step explanation:
In one year, a school uses 13,480 pieces of white paper, 7,880 fewer pieces of blue paper thanwhite paper, and 1,500 fewer pieces of yellow paper than blue paper. How many pieces of paperdoes the school use in all?
Answer:
23,180 pieces
Explanation:
The number of white paper used = 13,480 pieces
Since they used 7,880 fewer pieces of blue paper than white paper
The number of blue paper used = 13,480 - 7880 =5,600 pieces
They also used 1,500 fewer pieces of yellow paper than blue paper.
The number of yellow paper used = 5,600-1500 =4100 pieces
Therefore. the total number of pieces of paper
=13,480 + 5,600 + 4100
=23,180 pieces
Kadeem and Quinn both drive 25 miles. Kadeem drives at a constant speed of 50 miles and hour. Quinn drives at a constant of 75 miles an hour. Who takes longer to drive 25 miles? How much longer?
Kadeem takes 0.5 hours to travel 25 miles, and Quinn 0.33 hours, so Kadeem takes longer.
Who takes longer to drive 25 miles?
Remember the relation:
Speed*time = distance.
Notice that if the distance is fixed, then for a longer speed the time needed will be smaller.
Here we know that:
Kadeem drives at a constant speed of 50mi/h
Quinn drives at a constant speed of 75 mi/h.
Replacing that in the equation:
Kadeem's case:
(50 mi/h)*t = 25mi
t = (25 mi)/(50 mi/h) = 0.5 hours.
Quinn's case:
t = (25mi)/(75 mi/h) = 0.33 hours.
So Kadeem takes longer.
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Select all the equations that have no solution. (Select all that apply.)
a. 2t+1=1+ 2t
b. 2t+1 = 2t
c. 2(t+1) = 2t + 1
d. 2t+t=2t+1
e. 2t = 1
The equations that have No solution are2t + 1 = 1 + 2t , 2t + 1 = 2t and 2(t+1) = 2t + 1 , the correct options are (a) , (b) and (c) .
In the question ,
equations are given ,
we have to find which equation have NO Solution .
So,
(a) First equation is given as
2t + 1 = 1 + 2t
On rewriting the terms , we get
2t - 2t = 1 - 1
0 = 1-1 ,
we cannot find the solution of x .
hence this equation has No solution .
(b) equation is
2t + 1 = 2t
On rewriting the terms , we get
2t -2t = -1
0 = -1
hence ,this equation have No Solution .
(c) equation is 2(t+1) = 2t + 1
2t + 2 = 2t + 1
2t - 2t = 1 - 2
0 = -1
hence , this equation have No Solution .
(d) equation is 2t+t=2t+1
3t = 2t + 1
3t - 2t = 1
t = 1
hence , this equation have Unique Solution .
(e) equation is 2t = 1
So, t = 1/2
hence , this equation have Unique Solution .
Therefore , The equations that have No solution are 2t + 1 = 2t and 2(t+1) = 2t + 1 , the correct options are (a) , (b) and (c) .
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an= a(n-1) +15; a1=8
Answer:
an=7/2
Step-by-step explanation:
an=a(n-1)+15
given a1=8
multiply; a(n-1)
a(n-1)=an-a1
enter an-a1 in the equation
an=an-8+15
an=an+7
collect like terms;
an-an=(-7)
divide by negative both side
an-an/(-)=(-(-7)
2an=7
divide by 2 both side
2an/2=7/2
therefore the answer is an=7/2