Answer:
y = x² +8x -9
Step-by-step explanation:
You want the least-degree polynomial with roots 1 and -9, written in standard form.
FactorsEach root p means there is a factor (x-p). The two roots make the factored form of the polynomial be ...
y = (x -1)(x +9)
Expanding this to standard form, we get ...
y = x² +8x -9
__
Additional comment
A quadratic that has two roots, p and q, will have the standard form ...
y = (x -p)(x -q) = x² -(p+q)x +pq
That is, the linear term coefficient is the opposite of the sum of the roots, and the constant is their product. This means you can write down the equation directly from the roots:
y = x² -(1-9)x +(1)(-9) = x² +8x -9
suppose that 10 green balls and 14 purple balls are placed in an urn. two balls are then drawn in succession. what is the probability that the second ball drawn is a purple ball if the first ball is replaced before the second is drawn? a) 0.1224 b) 0.6250 c) 0.8333 d) 0.4167 e) 0.5833 f) none of the above.
The probability that the second ball drawn is a purple ball is (e) 0.5833
How to determine the probability?From the question, we have the following parameters that can be used in our computation:
Green balls = 10
Purple balls = 14
This means that the total number of balls is
Total = 10 + 14
Evaluate the equation
So, we have
Total = 24
From the question, we understand that the ball is replaced
So, the probability that the second ball is purple ie
P(second purple) = purple/total
This gives
P(second purple) = 14/24
Evaluate
P(second purple) = 0.5833
Hence, the probability is (e) 0.5833
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HELP!!
If a₁ = 3 and an
-
= (an-1)2 + 1 then find the value of a4.
The required value of a₄ is 10,202 to the given recursive formula.
What is an arithmetic sequence?An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.
The given recursive formula in the question as:
aₙ = (aₙ ₋₁ )² + 1 ....(i)
And, a₁ = 3
Substitute the value of a₁ = 3 in equation (i), and solve for n = 2
a₂ = (a₁)² + 1
a₂ = (3)² + 1
a₂ = 9 + 1 = 10
Substitute the value of a₂ = 10 in equation (i), and solve for n = 3
a₃ = (10)² + 1
a₃ = 100 + 1 = 101
Substitute the value of a₃ = 101 in equation (i), and solve for n = 4
a₄ = (101)² + 1
a₄ = 10,201 + 1
a₄ = 10,202
Therefore, the required value of a₄ is 10,202.
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PLEASE I REALLY NEED HELP I DON'T UNDERSTAND PLEASE THANK YOU GUYS FOR THE HELP!! I APPRECIATE IT!!!
The value of KM in triangle ΔKLM is 110.
What is similarity?Similarity of a triangle is the ratio of their corresponding sides or angles which are equal .
In the given triangle ΔHIJ,
HI=13, HJ=25,
And in triangle ΔKLM,
KL=57, KM=?
triangle ΔHIJ is similar to ΔKLM,
By the property of similarity, HI/HJ=KL/KM
Substitute the values here,
13/25=57/KM
KM=25×57/13
KM=109.6
The value of KM=110.
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Please answer part d
Answer:
∆JGF ≅ ∆GJH by the SAA Postulate
Step-by-step explanation:
Given a figure showing two triangles with a common side, and two marked angles not at either end of that side, you want to know the applicable congruence postulate.
SAAThe letters S and A in the congruence postulate references refer to "Side" and "Angle". The sequence of the letters corresponds to the sequence of corresponding parts in the triangles.
In the given figure, two angles in each triangle are marked with a single arc and a double arc. The triangles share a side that has the double-arc angle at one end. Hence, the sequence of corresponding parts can be seen to be (common) Side - (double-arc) Angle - (single-arc) Angle. The SAA congruence postulate applies.
∆JGF ≅ ∆GJH by the SAA Postulate
Find the value of x so that l//m. State the converse used
For the parallel lines (l//m), the value of x is equal to 25 and the converse used is the alternate exterior angle theorem.
What are parallel lines?Parallel lines simply refers to two (2) lines that always have the same or equal distance apart and never meet.
What is the alternate exterior angle theorem?The alternate exterior angle theorem states that when two (2) parallel lines are cut through by a transversal, the alternate exterior angles that are formed are congruent or angles of equal measure and magnitude.
By applying the alternate exterior angle theorem to parallel lines (l//m), we have:
4x - 13 = 2x + 37
4x - 2x = 37 + 13
2x = 50
x = 50/2
x = 25
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Un negocio de celulares tiene 360 celulares, 40% Samsung, 5% iPhone, 10%motorola y el resto Huawei, ¿Qué cantidad de celulares hay de cada marca?
The number of cell phone brands will be:
Samsung = 144
iPhone = 18
Motorola = 36
Huawei = 162
How to calculate the value?From the information, the business has 360 cell phones.
Samsung will be:
= Percentage × Total phone
= 40% × 360
= 0.4 × 360
= 144
iPhone = 5% × 360
= 0.05 × 360
= 18
Motorola = 10% × 360
= 0.1 × 360
= 36
Huawei = 45% × 360
= 0.45 × 360
= 162
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What is the slope of a line perpendicular to the line whose equation is 6x + y = 8.
Fully simplify your answer.
Answer:
1/6
Step-by-step explanation:
y = -6x + 8
Perpendicular line would be the reciprocal of the slope
Como puedo Terminar la sucesion asta el decimo termino 3.8 +2.7
The addition of the decimals given as 3.8 and 2.7 will be 6.5.
What are decimals?Decimals simply means the numbers that are not whole numbers. They consist of whole numbers and fractions. Examples include 3.6, 2.1 eyc.
In this case, we want to find the value of 3.8 and the addition to 2.7. This will be:
= 3.8 + 2.7
= 6.5
Therefore, the value is 6.5.
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Evaluate f(x) = 2|x – 5| for f(–5) and f(0).
Question 20 options:
f(–5) = 10, f(0) = 0
f(–5) = 12, f(0) = 5
f(–5) = –20, f(0) = –2
f(–5) = 20, f(0) = 10
Answer:
D
Step-by-step explanation:
f(-5) = 2|-5-5|
f(-5) = 2|-10|
f(-5) = 2 * 10
f(-5) = 20
f(0) = 2|0-5|
f(0) = 2|-5|
f(0) = 2 * 5
f(0) = 10
a survey has an error in departure (ed) of 0.35 ft, and error in latitude (el) of 0.82 ft. the total distance covered i the survey is 684.5 ft. compute the precision (choose the answer that is closest)
The correct value for the precision is found to be 0.0013 for the survey.
What is called the precision in surveying?Our measurement processes take into account accuracy and precision. How precisely a measurement or observation compares to a predetermined value or benchmark defines its accuracy. Contrarily, precision is the degree to which a measurement is repeatable precisely without reference to any specific significance or standard.The formula for finding the precision is-
Precision = E(closure)/ Perimeter
E(closure) = √(ed)² + (el)²
Where,
error in latitude (el) = 0.82 ft
error in departure (ed) = 0.35 ft.
Perimeter = 684.5 ft.
Find the E(closure)
E(closure) = √(0.82)² + (0.35)²
E(closure) = 0.89
Precision = 0.89/684.5
Precision = 0.0013
Thus, the correct value for the precision is found to be 0.0013 for the survey.
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Simplify.
ab2−−−√+39ab2−−−−√−34ab2−−−−√
Assume all variables are nonnegative.
Answer:In this item, I take it that we are to get the cube root of the given expression, -64x6y9. First, we look into the numerical coefficient, this is the product when -4 is multiplied to itself three times as shown below.
-64 = (-4)(-4)(-4)
Then,
x6 = x2 (x2) (x2)
and,
y9 = (y3)(y3)(y3)
If we take the cube root, we consider only one item per product. Thus, the answer is,
-4x²y³
Step-by-step explanation:
Naomi is cutting patches in the shape of right triangles to make a quilt. Each triangle has a diagonal side of 14.5 inches and a short side of 5.5 inches. What is the length of the third side of each triangular patch?
Find the area of the Polyogon below.
A =
12
14.49
Answer: 695.52
Step-by-step explanation:
The area of each triangle is [tex]\frac{1}{2}(12)(14.49)[/tex].
There are 8 triangles in the figure, so the area is [tex]8(1/2)(12)(14.49)=695.52[/tex].
please show the work
Step-by-step explanation:
15t + 30 = 20t | -15t
30 = 5t
t = 30/5 = 6
20 + 5t = -6t + 86 | + 6t
20 + 11t = 86 | -20
11t = 66
t = 6
18t + 20 = 24t + 50 | -18t
20 = 6t + 50 | -50
-30 = 6t
t = -30/6 = -5
18t - 2 = 10t + 54 | -10t
8t - 2 = 54 | +2
8t = 56
t = 56/8 = 7
7t - 5 = 15t + 91 | -7t
-5 = 8t + 91 | -91
-96 = 8t
t = -96/8 = -12
[tex]x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} \\[/tex]
Answer: [tex]x^{26}[/tex]
Step-by-step explanation:
The [tex]x^2[/tex] appears 13 times. Using the exponent rule [tex]x^a x^b=x^{a+b}[/tex], we get that:
[tex]x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2=x^{2(13)}=x^{26}[/tex]
Describe the sampling distribution of p. Assume the size of the population is 30,000. n 700, p 0.388 Describe the shape of the sampling distribution of p. Choose the correct answer below. O A. The shape of the sampling distribution of p is not normal because n s0.05N and np(1-p)210. O B. The shape of the sampling distribution of p is approximately normal because ns0.05N and np(1-p) <10. C. The shape of the sampling distribution of pis not normal because n s05N and np(1-p)<10 O D. The shape of the samplingdistrbution of p is approximately normal because n s0.05N and np(1 -p)210 Determine the mean of the sampling distribution of p. Round to three decimal places as needed.) Determine the standard deviation of the sampling distribution of p. Round to three decimal places as needed.)
The correct option regarding the sampling distribution of p, considering the Central Limit Theorem, is given as follows:
D. The shape of the sampling distrbution of p is approximately normal because n <= 0.05N and np(1 -p) > 10.
The mean of the sampling distribution of p is of:
0.388.
The standard deviation of the sampling distribution of p is of:
0.0184.
What is defined by the Central Limit Theorem?The Central Limit Theorem defines the distribution of the sampling distribution of sample proportions of a proportion p in a sample of size n, in which:
The mean is [tex]\mu = p[/tex].The standard deviation is [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex]The shape is approximately normal.As long as these two conditions are respected:
[tex]n \leq 0.05N[/tex][tex]np(1 - p) > 10[/tex]The values of the parameters in this context are given as follows:
N = 30000, n = 700, p = 0.388.
Hence the conditions are:
n/N = 700/30000 = 0.0233 < 0.05.np(1 - p) = 700 x 0.388 x 0.612 = 166 > 10.Then the shape is approximately normal and option D is correct.
The mean of the distribution is of:
[tex]\mu = p = 0.388[/tex]
The standard error of the distribution is of:
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.388(0.612)}{700}} = 0.0184[/tex]
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if f represents the number of lots of fliptop pens to produce and t represents the number of lots of tiptop pens to produce, the linear programming model for this problem is:
The linear programming model for this problem is Max 1000F + 1000T
Given that,
If the quantity of flip top pens to be produced is f and the quantity of tiptop pens to be produced is t, then
Number of lots of Flip top pens to produce = F
Number of lots of Tip top pens to produce = T
Therefore, The linear programming formulation is given by:
Max 1000F + 1000T
s.t.
Plastic: 3F + 4T <= 39
Ink Assembly: 5F + 4T <= 45
Molding time: 5F + 2T <= 37
F, P >= 0
Hence, the linear programming model for this problem is Max 1000F + 1000P
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The first container has 3 gallons 3 quarts 1 pint of diesel fuel, the second container has 5 gallons 2 quarts of diesel fuel, and the third container has 6 gallons 1 quart 1 pint of diesel fuel. what is the total quantity of diesel fuel?
The total quantity of diesel fuel is 15.75 gallons.
The total quantity of diesel fuel can be calculated by summing up all the values. But, firstly converting quarts and pint into gallons.
1 quart = 0.25 gallon
For first container, 3 quarts = 0.25 × 3
3 quarts = 0.75 gallon
For second container, 2 quarts = 0.25 × 2
2 quarts = 0.5 gallon
For third container, it has 0.25 gallon
1 pint = 0.125 gallon
For first and third container, it has 0.125 gallon
So, amount of diesel fuel in first container = 3 + 0.75 + 0.125
Amount of diesel fuel in first container = 3.875 gallons
Amount of diesel in second container = 5 + 0.5
Amount of diesel in second container = 5.5 gallons
Amount of diesel in third container = 6 + 0.25 + 0.125
Amount of diesel in third container = 6.375 gallons
So, the total quantity of diesel fuel = 3.875 + 5.5 + 6.375
The total quantity of diesel fuel = 15.75 gallons
Hence, the total quantity is 15.75 gallons.
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Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two
different proportional relationships represented in different ways.
Will give points to first correct answer that follows all the steps right.
Answer:
I Need Help On That Too
Step-by-step explanation:
You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is 0. How confident can you be that your predicted value will be reasonably close to the actual value?
Responses
I can’t be confident at all; this is about as close to a random guess as you can get.
I can be a little confident; it might be close, or it might be way off.
I can be very confident; it will be close, but it probably won’t be exact.
The correct option regarding the correlation coefficient is that A. I can’t be confident at all; this is about as close to a random guess as you can get.
What is a correlation coefficient?The correlation coefficient is a statistical measure of the strength of a two-variable linear relationship. Its values can range between -1 and 1. A correlation coefficient of -1 denotes a perfect negative, or inverse, correlation, in which values in one series rise while those in the other fall, and vice versa.
A coefficient of one indicates that there is a perfect positive correlation, or a direct relationship. A correlation coefficient of 0 indicates that no linear relationship exists. In science and finance, correlation coefficients are used to assess the degree of association between two variables, factors, or data sets.
In this case, the fat that the person gets 0 implies that it's probably a random guess. In conclusion, the correct option is A.
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In a city school, 60% of students have blue eyes, 55% have dark hair and 20% have neither blue eyes nor dark hair. determine the probability that a randomly selected student will have blue eyes and dark hair
The probability of of a random student having blue eyes and dark hair
is 35% .
let consider the total students in the school be (U) = 100%
out of them ,
students having blue eyes (A) = 60%
students having dark hair (B) = 55%
students with neither blue eyes nor dark hair (A∪B)' = 20%
let the students with blue eyes and dark hair be (A∩B) = x %
Then according to the set theorem
U = n(A∪B) + n(A∪B)'
U = n(A) + n(B) - n(A∩B) + n(A∪B)'
100 = 60 + 55 - x +20
∴ x = 60 + 55 +20 - 100
x = 35 %
So the probability of random student having blue eyes and dark hair is 35% .
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a hospital director is told that 54% of the treated patients are insured. the director wants to test the claim that the percentage of insured patients is below the expected percentage. a sample of 200 patients found that 100 were insured. find the value of the test statistic. round your answer to two decimal places.
The value of test statistic is -1.14
Define Standard error.
The standard error (SE)of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation. If the statistic is the sample mean, it is called the standard error of the mean (SEM).
Null Hypothesis
P = 0.54
Alternate Hypothesis
P < 0.54
For 0.05 level , the value of Z = 1.645
Decision rule ,
reject null Hypothesis if test statistic Z < -1.645
sample size (n) = 200
sample success (x) = 100
Standard error SE = √(p * (1 - p) / n
= √0.54 * (1 - 0.54) / 200
Standard error SE= 0.0352
Sample proportion (р) = x/n
= 100 / 200 ⇒ 0.5
test statistic Z = (р - P) / SE
= (0.5 - 0.54) / 0.0352
test statistic Z = -1.136 or -1.14
Therefore, the value of test statistic is -1.14
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What is the degree of the following
polynomial:
3x^5 + 4x^3 + 8x^2 - 14x +9
Answer:
Step-by-step explanation:
Here is an example:
Use this step by step explanation in your equation to help you find the answer.
For polynomial 2x2 - 3x5 + 5x6.
We observe that the above polynomial has three terms. Here the first term is 2x2, the second term is -3x5 and the third term is 5x6.
Now we will determine the exponent of each term.
(i) the exponent of the first term 2x2 = 2
(ii) the exponent of the second term 3x5 = 5
(iii) the exponent of the third term 5x6 = 6
Since, the greatest exponent is 6, the degree of 2x2 - 3x5 + 5x6 is also 6.
Therefore, the degree of the polynomial 2x2 - 3x5 + 5x6 = 6.
thanks to anyone who answers!
The sum of three consecutive numbers is 84. What is the largest of these numbers?
a 26
b 27
c 28
d 29
How do you solve this equation to find x?
Answer: x=10
Step-by-step explanation:
Images below
Help this helps
What is 7) 952 divided?
Complete the table and answer the questions that follow. (If a root occurs twice, count it twice; if
thrice, count it three times, and so on. The first one is done
Polynomial Equation
1. (x+1)² (x-5) = 0
2. X-9 0
3. (x+8) (x-8)= 0
4. x² + 3x +2=0
(x+1)(x+2) = 0
5. (x² - 4x + 4)(x-3)²
(x-2)(x-2)(x-3)(x-3) = 0
6. 2
7. (x-3)(x + 1)(x - 1) = 0
8. (x²-4)(x-3)³ = 0
(x+2)(x-2)(x-3)(x-3)(x-3)=0
9. x(x-4)(x + 5)(x - 1) = 0
10. (x + 1)5 (x - 1)² =0
Degree
3
Real Roots of the
Equation
-1 (2times); and 5
Number of Real Roots
3
An equation of the form P=0 is referred to as a polynomial equation. P is a polynomial with coefficients in some field, typically the field of the rational numbers. A polynomial equation, on the other hand, can include a number of variables. The phrase polynomial equation is typically preferred over algebraic equation when discussing situations with multiple variables.
What is Polynomial Equation ?One or more variables, coefficients, and non-negative integer exponents of variables make up a polynomial, which is an expression. A mathematical statement that has a "equal to" symbol between two algebraic expressions with equal values is called an equation.
Sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials.
4x² + 6x + 21=0 where 4x²+6x+21 is considered as a polynomial expression which is written on the left side and has been fixed to make the polynomial expression equal to zero to form a complete polynomial equation.
1 Already answered
2 Degree:1 Real Roots of an equation:8 Number of Real Roots:1
3 Degree:2 Real Roots of an equation:2,-2 Number of Real Roots:2
4 Degree:5 Real Roots of an equation:-1,1-3,-3,-3 Number of Real Roots:5
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A swimming pool is draining at a constant rate.
The table shows the proportional relationship between
the change in the water level and the number of hours
the pool has drained. Complete the table to show the change
in water level at 9 and 23 hours?
The level of water in the swimming pool after a specified duration of the water draining at a constant rate is found as follows;
10. a. The water level is changing (reducing) at a rate of 1.75 inches per hour.
b. After 9 hours, the change in the water ls 15.75 inches
c. The change in the water level after 23 hours is 40.25 inches
What is a constant rate?A constant rate is a rate that is fixed or steady and does not vary following a change of the other variables?
The table of values for the draining swimming pool obtained from a similar question on the internet is as follows;
Hours Draining [tex]{}[/tex] Change in Water Level (inches)
2 [tex]{}[/tex] -35
9 [tex]{}[/tex] ?
17 [tex]{}[/tex] -29.75
23 [tex]{}[/tex] ?
The relationship between the hours the swimming pool drains and the water level is a proportional relationship., such that the ratio of each coordinate pair in the table is a constant.
Let H represent the hours draining and let C represent the change in water level, we have;
C ∝ H
C = k·H
[tex]k = \dfrac{C}{H}[/tex]
Where;
k = The constant of proportionality, which is the rate at which the water level is changing per hour
a. The rate at which the water level changes per hour can be found from the first pair of points on the table as follows;
The first pair of points = (2, -3.5)
[tex]k = \dfrac{-3.5}{2} = -1.75[/tex]
The rate at which the water level is changing per hour is -1.75 inches per hour
The water level is decreasing at 1.75 inches per hour
b. The change in water level after 9 hours is found by using the formula;
C = k × H
Where, H = 9, we have;
Change in water level, C = -1.75 × 9 = -15.75
The change in water level after 9 hours is 15.75 inches
c. The change in water level after 23 hours is found by plugging in H = 23 as follows;
C = -1.75 × 23 = -40.25
The change in water level after 23 hours is -40.25 inches
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Can anyone state the vertex of the graph?
The graph has no vertex
The transformations from the parent function are
Vertical shift down 2Horizontal shift left 4How to determine the vertex?To determine the vertex of a graph, we look for the location of the maximum or the minimum point of the graph
Because the graph is a cubic function, the graph has no maximum or minimum (by definition)
This means that there is absence of a vertex in the graph
The transformation from the parent functionIn (a), we have
We can see that the graph is a cubic function
This function is represented as
y = ∛x
In this graph, we can see that the graph is 4 units to the left i.e. y = ∛(x - 4)
And 2 units below the origin i.e. y = ∛(x - 4) + 2
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help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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250 bicycles must be manufactured to minimize the cost.
The cost C in dollar of manufacturing x bicycles at a production plant is given by:
C(x) = 3x² - 1500x + 198,500
a. To find number of bicycle that can minimize the cost
differentiate C(x) with respect to x
C'(x) = 6x - 1500
equating C'(x) = 0
6x - 1500 = 0
x = 1500/6
x = 250 , is our stationary point
Differentiate C'(x) = 6x - 1500 again and put x = 250,
C''(x) = 6 (positive)
At x = 250 , cost is minimum
Therefore , 250 bicycles must be manufactured to minimize the cost.
b. C(x) = 3x² - 1500x + 198,500
putting x = 250,
C(x) = 3(250)² - 1500(250) + 198,500
= 187,500 - 375 ,000 + 198,500
= $11,000 is the minimum cost
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