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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a manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 411 gram setting. based on a 19 bag sample where the mean is 437 grams and the varicance is 441, is there sufficent evidence at the 0.025 level that the bags are underfilled?
Using the Hypothesis testing and statistic Z- test we , find that the bag sample is not underfilled at a significance level of 0.025 i.e., 25% .
In the given question, we shall check the bag is underfilled at given level or not .
We can use the hypothesis testing, The Null and Alternative hypothesis are given as below :
H₀ : u = 411 : the bags are not underfilled
Hₜ : u < 411 : the bags are underfilled
Check it now using statistic Z-test and the test Statistic formula is given by
= ( M – u ) / S.D / √n , where M = mean of sample and S.D = standard deviations n is the number of bags used .
From given data we get, n= 19 ; M = 437 ; S.D = √ variance = √ 441 = 21
Including all of the above variables in formula
Z = (437-411)/21/√19
= 26/21/√19
= 5.395
This is right -tail test in statistic Z -test
P- value = 1 – 0.9999 = 0.111 ( by using Z-table or P-value for Z in Excel )
The sufficient evidence level is 0.025 i.e., alpha (α) = 0.025
P- value >α , this implies that Null hypothesis is not Rejected .
There is sufficient evidence to suggest that bag is not underfilled.
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The value of a new car after 2 years was $11,200. When the car is 6 years old, the value has dropped to $6100.
Find the rate at which the value of the car is depreciating
And
write an equation that models the depreciation of the value of the car
And
How much will the car be worth when it is 8 years old?
The equation of the car can be given as and the price of the car after 8 years is $4445.
What is an exponential function?
A function of the form [tex]a^{x}[/tex] is known as exponential function. In short the function which has an exponent is known as exponential function.
We are given that the value of a new car after 2 years was $11,200. When the car is 6 years old, the value has dropped to $6100.
Let the original price of the car be [tex]P_{0}[/tex]
After two years the price of the car is $11200
Mathematically it can be given as
[tex]11200= P_{0}e^{2x}[/tex]
After 6 years the price of the car is $6100
Mathematically it can be given as
[tex]6100=P_{0}e^{6x}[/tex]
Dividing both equations we get,
[tex]1.83=e^{-4x}[/tex]
Which can also be written as
[tex]e^{4x}=0.54[/tex]
on solving we get,
x=-0.154
Hence the rate at which price of the car is dropping is
[tex]P=P_{0}e^{-0.154t}[/tex]
No we have to find the original price of the car
To do so we substitute t=2 in the equation
we get
11200=[tex]P_0e^{-0.308}[/tex]
On solving we get,
15240=[tex]P_0[/tex]
Now we find the price of the car after 8 years
P=15240·[tex]e^{-1.232}[/tex]
On simplifying we get
P=$4445
Hence the price of the car after 8 years will be $4445
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3. Use your answer from #2 for x, and find the measure of both angles. Select 2 answers.
A
B
116
61°
64°
119⁰
2x-15
3x + 5
None of the available possibilities is an equivalent expression.
Supplemental methods add up to 180 degrees, just like all other options.
An equivalent expression is what?If two expressions function the same way while having different looks, they are said to be comparable. Two identical algebraic expressions have the same value when the same value(s) for the variable are entered (s).
No one in the available possibilities satisfies the requirement of a comparable expression.
2x - 15 + 3x + 15 = 180
2x - 10 + 3x = 180
5x - 10 = 180
5x - 10 + 10 = 180 +10
add the numbers
5x = 190
5x /5 = 190 5
x = 38
As a result, none of the possibilities shown are identical expressions.
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[x-6] +4 =10 solve for X
Answer:
x=12
Step-by-step explanation:
(x-6)=6
x=12
So my grades keep going down
Whats the best way to study
Answer:
Step-by-step explanation:
study
Select all that appear in the DOMAIN {(-8,-12),(4,-8), (2, -10),(-10.-16) -16 -12 -10 -8 -2-4
We know the domain is the set of all x when is represented by ordered pairs: (x, y)
In this case {(-8,-12),(4,-8), (2, -10),(-10.-16) } we can observe that there are four x (the first number of each pair):
Domain = { -8, 4, 2, -10}
Domain = {-10, -8, 2, 4}POSSIBLE POINTS
Write and solve the given inequality: twice the difference of three times a number and five is at most the sum of four times a number and six.
O [8,00)
O (8,00)
O(-0,8)
O(-0,8]
The inequality is 2(3x - 5) ≤ (4x + 6) and the solution of the inequality is (-0, 8]
Let the number be x,
Twice the difference of three times a number and five = 2(3x - 5)
The sum of four times a number and six is (4x + 6)
2(3x - 5) ≤ (4x + 6)
6x - 10 ≤ 4x + 6
6x - 4x ≤ 6 + 10
2x ≤ 16
x ≤ 8
x can be any positive number less than or equal to 8.
Therefore, the inequality is 2(3x - 5) ≤ (4x + 6) and the solution of the inequality is (-0, 8]
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What is the area of a triangle whose vertices are J(−2, 1), K(0, 3), and L(4, −1)?
Enter your answer in the box.
Based on the vertices of the triangle, the area of the triangle can be found to be 8 cm²
How to find the area of the triangle?First, find the lengths of JK, KL, and JL. When given vertices, you can find the length of a line by the formula:
= √ ( (x₂ - x₁)² + (y₂ - y₁)²)
The length of JK is therefore 2.83 units
The length of KL is therefore 5.66 units
The length of JL is therefore 6.32 units.
Given these units, the area of the triangle can be found by the formula:
= √ s(s - a) ( s - b) ( s - c)
Where:
s = semi perimeter
a, b, and c are the sides of the triangle which are JK, KL, and JL.
The semi-perimeter can be found by the formula:
= ( a + c + c) / 2
= 15.47 / 2
= 7.74
The area of the triangle is therefore:
= √ s(s - a) ( s - b) ( s - c)
= √ 7.74 (7.74 - 2.83) ( 7.74 - 5.66) ( 7.74 - 6.32)
= 8 cm²
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Solve 4(3m + 1) − 2m = −16. m = −0.83 m equals negative 20 over 12 m equals negative 17 over 10 m = −2.
The solution to the equation given as 4(3m + 1) − 2m = −16 is m = -2
How to determine the solution to the equation?The equation is given as
4(3m + 1) − 2m = −16
Open the brackets in the above equation
So, we have
12m + 4 − 2m = −16
Collect the like terms in the above equation
So, we have the following equation
12m − 2m = −16 -4
Evaluate the like terms in the above equation
So, we have the following equation
10m = −20
Divide both sides by 10
m = -2
Hence, the soluton is m = -2
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Nick was thinking of a number. Nick adds 11 then divides by 11 to get an answer of 28. Form an equation with
x
from the information.
Answer:
??
Step-by-step explanation:
help pls it's so hard (that's what she said) but fr
If we draw a vertical line and it crosses the figure more than once, then it is not a function.
So, the only graph that a vertical line will intersect the line once is graph A:
B, C and D are intersected more than 1 time, so they are not functions.
Answer: A
The exponential model A = 64.5 e0.020describes the population, A, of a country in millions, t years after
The exponential model A=64.5e^0.02t describes the population, A of a country in millions, t years after 2003. The population of the country will be 108 million in
we have the expression
A=64.5e^0.02t
For A=108
substitute
108=64.5e^0.02t
108/64.5=e^0.02t
Apply ln both sides
ln(108/64.5)=ln(e^0.02t)
ln(108/64.5)=0.02t(ln(e))
ln(108/64.5)=0.02t
solve for t
t=ln(108/64.5)/0.02
t=26 years
therefore
2003+26=2029
answer is
year 2029Find the equilibrium concentrations of a and b for a=2 and b=2 . assume that the initial concentration of a is 1.0 moll−1 and that no b is present at the beginning of the reaction.
The concentration of A 0.29M and Concentration B 0.755M that the initial concentration of a is 1.0 moll−1 and that no b is present at the beginning of the reaction.
a A (g)⇔ b B (g) k =2.4
when a= 1 and b= 1
A⇔B
initial 1 0
concentration
change -x +x
equilibrium 1-x x
concentration
so, k = [tex]\frac{B}{A}[/tex] = [tex]\frac{x}{1-x}[/tex]= 2.4
x = 2.4 (1-x)
x = [tex]\frac{2.4}{3.4}[/tex] = =0.755
The equilibrium concentration are
concentration of A = 1-x = 1- 0.755 = 0.29M
Concentration B = x = 0.755M
What is initial concentration?The first measured the concentration of the compound in the substance.
The best way to determine the rate constant k for a first-order half-life is to determine the half-life using experimental data. This is because the first-order half-life is independent of the initial concentration of its initial value. So based on the above relationship, the half-life of a first-order reaction does not depend on the initial concentration.
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A bag contains twelve balls labeled 1 through 12. One ball will be randomly picked.
What is the probability of picking an even number?
Write your answer as a fraction in simplest form
Hello there!
If a bag has 12 balls labelled 1 through 12, that means that the balls inside the bag includes:
1 2 3 4 5 6 7 8 9 10 11 12
When creating a fraction for a probability, the numerator usually consists of a specific probability you are trying to find; the denominator usually consists of the total amount of samples in the bag.
In this example: What is the probability of picking an even number?
Ask yourself: What are we trying to find?
We are trying to find the probability of even numbers.
Then ask yourself: What is the amount of possibilities that we can get an even number from the bag?
The bag consists of: 1 2 3 4 5 6 7 8 9 10 11 12
Even numbers are divisible by 2 and has a remainder of 0 ; which means in this bag, the bolded numbers are even.
Then we can conclude that in this bag, counting all of the bolded numbers, we have 6 possibilities of choosing an even number.
Finally, think about: What is the total amount of samples in this bag?
We know that there are 12 balls, so 12 would be the total amount.
To conclude, we can find 6 even numbers in a bag of 12 balls;
Therefore, the chances you can pick an even number is [tex]\frac{6}{12} ,[/tex] or [tex]\frac{1}{2}[/tex].
10. Eleanor spent 40% of her money on a $130 outfit. How much money
did she have left?
Answer:
$195
Step-by-step explanation:
40% represents £130
40% : $130
100% : total
To find total:
($130 / 40) x 100 = $325 is the total
If $130 spent:
$325 - $130 = $195 is the amount left
Please tell me what is 1,359 divided by 45 is ??
If cos∠E = sin∠F and m∠E = 26°, what is m∠F?
Step 1
Given;
[tex]\begin{gathered} cosE=sinF \\ measure\text{ of angle E=26}^o \end{gathered}[/tex]Required; To find the measure of angle F
Step 2
[tex]\begin{gathered} cos26=sinF \\ \sin\left(90^{\circ\:}-26^{\circ\:}\right)=cos26 \end{gathered}[/tex][tex]\begin{gathered} \sin\lparen F)=\sin\left(90^{\circ\:}-26^{\circ\:}\right) \\ sin(F)=sin(64) \end{gathered}[/tex]Answer;
[tex]m\angle F=64[/tex]6. a) The mass of eight apples is 1 200 g. What is the average mass of one apple in kilograms? b) A5 kg bag of apples costs R65. What is the cost of 500 grams of apples? Approximately how many apples will have a mass of 1 kilogram?
a. The average mass of one apple in kilograms is 150g.
b. The cost of 500 grams of apples is R6.5
How to calculate the values?A. When the mass of eight apples is 1 200g, the average mass of one apple in kilograms will be:
= Total mass / Number of Apple
= 1200g / 8
= 150g
B. A 5 kg bag of apples costs R65. The cost per kg will be:
= Amount / Number of g
= R65 / 5000
= R0.013
The cost for 500 grams will be:
= 500 × R0.013
= R6.50
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6th grade math, Please Help) 2 people pls answer so i can make brainliest! and you will get 20 points :)
Evaluate the Algebraic expression; j+2h= when f=6, g=8, h=12, j=2
OA) 14
OB)18
OC)26
OD)30
Answer:
the answer is 26
Step-by-step explanation:
j+2h
(2) + 2(12)
2 + 24
26
Write the equation of a line given the following information:26) The line has a slope =and passes through (8.-1)27) TH
Answer:
The equation of the line is;
[tex]y=-\frac{3}{4}x+5[/tex]Explanation:
Given that the line has a slope of;
[tex]m=-\frac{3}{4}[/tex]And passes through the point;
[tex](8,-1)[/tex]Applying the point-slope equation of straight line;
[tex]y-y_1=m(x-x_1)[/tex]substituting the given values and solving;
[tex]\begin{gathered} y-(-1)=-\frac{3}{4}(x-8) \\ y+1=-\frac{3}{4}x-\frac{3}{4}(-8) \\ y+1=-\frac{3}{4}x+6 \\ y=-\frac{3}{4}x+6-1 \\ y=-\frac{3}{4}x+5 \end{gathered}[/tex]Therefore, the equation of the line is;
[tex]y=-\frac{3}{4}x+5[/tex]
According to the United States Treasury Department, the U.S. national debt was 1.815 x 10^13 dollars on September 30, 2015. On September 29,
2005, the national debt was 4.974 x 10^12 dollars. Find the amount of increase in the national debt from September of 2005 to September of 2015.
Write a sentence describing the increase in the national debt from 2005 to 2015 using scientific notation and using standard form.
The increase in the national debt from 2005 to 2015 using scientific notation is 1.3176 × 10^13.
What is scientific notation?Scientific notation simply means a way of expressing numbers that are either too large or too small.
The U.S. national debt was 1.815 x 10^13 dollars on September 30, 2015 and in September 29,
2005, the national debt was 4.974 x 10^12 dollars.
The increase will be the difference between the two notations. This will be:
= 1.815 x 10^13 - 4.974 x 10^12
= 1.3176 × 10^13
The increase is 1.3176 × 10^13.
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The required respective increase in the national debt of America for the period 2005 to 2015 is 1.3176 × 10¹³.
As of the given condition,
According to the United States Treasury Department, the U.S. national debt was 1.815 x 10^13 dollars on September 30, 2015. On September 29, 2005, the national debt was 4.974 x 10^12 dollars.
Here,
The required increase in the debt is evaluated as the arithmetic difference of the debt in the years 2015 and 2005.
So.
Increase in debt = 1.815 × 10¹³ - 0.4974 × 10¹³ = 1.3176 × 10¹³
Thus, the required respective increase in the national debt of America for the period 2005 to 2015 is 1.3176 × 10¹³.
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Given the points:
(5,2) and (3,-4)
Select the THREE equations that represent the line that passes
through them.
The equations of the line according to the given points will be:
3x - y - 13 = 06x - 2y - 26 = 012x - 4y - 52 = 0We know that,
The equation of a line passing through two points is:
( y -y 1) / ( x - x1 ) = ( y2 - y1 ) / ( x2 - x1 )
(y - 2) / (x - 5) = (-4 - 2) / (3 - 5)
=> (y - 2) / (x - 5) = -6 / -2
=> y - 2 = 3 (x - 5)
=> 3x - 15 - y + 2 = 0
=> 3x - y - 13 = 0
Some more equations of the same line can be calculated just by multiplying the coefficients of x and y so that they remain proportional to the previous equation.
For Example,
6x - 2y - 26 = 012x - 4y - 52 = 0Here we can see that the coefficients of x and y and also the constant term are proportional to every equation compared with each other.
These lines are also called coincident lines.
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I need this answered please
If they meet in 2 hr the rate of the slower car is 86.
What is rate?
rate is the ratio between two of related quantities in the different units. If the denominator of the ratio is expressed as of a single unit of one of those quantities.
Sol- as per the given question
{d =380
{t=2
Substitute {d=380 formula
{t=2
d=v×t
380=2v
=2(18+2x)=380
Apply the distributive property
36+4x=380
Rearrange variables to the left side of the equation
4x=380-36
4x=344
Divided both side of the equation by the coefficient of variable
X=344/4
By cross out the common factor we get
X=86
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X - 2 = 3.5 A: 1.5 B: 5.5 C: 5 1/2 D: 5 3/6
To solve this expression we have to add 2 to both sides of the equation:
[tex]x-2+2=3.5+2[/tex][tex]x=5.5[/tex]So, the correct option is: B: 5.5
Please help me anwser this
Answer:
(x + 3)² + (y - 6)² = 9
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
here (h, k ) = (- 3, 6 ) and r = 3 , then
(x - (- 3 )² + (y - 6)² = 3² , that is
(x + 3)² + (y - 6)² = 9
I need help with this geometry question !! Pls help
The values of variable x are x₁ = 16, x₂ = - 4.
The measure of angle R is 60°.
The lengths of side RS are RS₁ = 256 and RS₂ = 16.
The lengths of side RT are RT₁ = 256 and RT₂ = 16.
How to find the variables associated to a given triangle
In this problem we need to find the values of four variables related to a triangle, which is seen in the picture, indicating an equilateral triangle. The solution of this question must be done by using definitions and theorems from Euclidean geometry:
Value of variable x
According to Euclidean geometry, the measures of the three sides in an equilateral triangle are the same. Then, the variable x can be found by solving the following equation:
RT = RS
x² = 12 · x + 64
x² - 12 · x - 64 = 0
(x - 16) · (x + 4) = 0
There are two possible solutions:
x₁ = 16, x₂ = - 4
Measure of the angle R
Equilateral triangles have three internal angles of 60°. Therefore, m ∠ R = 60°.
Length of side RS
There are two options:
RS₁ = 16²
RS₁ = 256
RS₂ = (- 4)²
RS₂ = 16
Length of side RT
There are two options:
RT₁ = 12 · 16 + 64
RT₁ = 256
RT₂ = 12 · (- 4) + 64
RT₂ = 16
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What is the area of the rectangle with verticals at A(-4,0), B(-3,1) C(0,-2) and D(-1,-3)? Use the distance formula to find the length of segment AB (the base), and Segment BC (the height) Hint A=bh
The area of the rectangle would be 4.90 units which is shown in the given graph.
What is the area of rectangle?The area of a rectangle is defined as the product of the length and width.
The rectangle is given which has:
verticals at A(-4,0), B(-3,1) C(0,-2) and D(-1,-3)
The length of segment AB = √ (-3 - (-4))² + (1 - 0)² = √ (1 + 1) = √2
The length of segment BC = √ (-3 - 0)² + (1 - (-2))² = √ (9 + 3) = √12
The area of the rectangle = length of segment AB x length of segment BC
The area of the rectangle = √2 x √12
The area of the rectangle = √24
The area of the rectangle = 4.90 units
Thus, the area of the rectangle would be 4.90 units
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Alexa buys an oil painting online for $941.20. If shipping and handling are an additional 20% of the price, how much shipping and handling will Alexa pay?
Express the equation y=x^2+8x+25 in the form y=a(x-h)^2+ka. y=a(x-h)^2+kb. y=(x+4)^2+9c. y=(x-4)^2-9d.y=(x-4)^2+9
ANSWER :
The answer is B. y = (x + 4)^2 + 9
EXPLANATION :
From the problem, we have :
[tex]y=x^2+8x+25[/tex]Group the terms in which the constant term and the terms with variables are separated.
[tex]y=(x^2+8x)+(25)[/tex]add and subtract a variable m to the parenthesis to maintain equivalency.
[tex]y=(x^2+8x+m)+(25-m)[/tex]Calculate the value of m using b^2/4a^2 with a = 1 and b = 8
[tex]m=\frac{b^2}{4a^2}=\frac{8^2}{4(1^2)}=16[/tex]Then :
[tex]\begin{gathered} y=(x^2+8x+16)+(25-16) \\ y=(x^2+8x+16)+(9) \end{gathered}[/tex]The first parenthesis will be a perfect square trinomial.
Factor and simplify :
[tex]\begin{gathered} y=(x^2+8x+16)+9 \\ y=(x+4)^2+9 \end{gathered}[/tex]Inequalities in Two Triangles.
[?] < x < [ ]
I will mark the answer as brainliest, thanks!
The inequality of the two triangle are 32° < x < 68° and the range of the value x is defined as x ≥ 4.
Inequality:
Inequality means the relationship between two values that are not equal is defined by inequalities which means they are not equal.
Given,
Here we have the two triangles with some angle values.
Now, we need to find the inequality of these triangle.
To find the inequality of the triangle first we have to write down the values provided, they are,
77, 11x - 33, 68°, 32°
Through this we have identified that, the value of x is lies in between 68° and 32°.
So, it ca be written as,
32° < x < 68°
The next this is to use the triangle inequality theorem, that is,
"The sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c."
Therefore, based on the given equation we have written it as,
11x - 33 ≥ 77
Subtract 33 on both sides then we get,
11x ≥ 44
Therefore, x ≥ 4.
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