The expression for f(x) is: [tex]f(x)=(x+4) , (x-2) , (x-9) ,(x+5),(x+5),(x+5)[/tex]
We know that for any polynomial equation with roots:
[tex]a_{1}, a_{2}, a_{3} ,...[/tex]
with multiplicity:
[tex]m_{1}, m_{2}...[/tex]
the equation for the polynomial is given by:
[tex]f(x)=(x-a_{1}) ^{m_{1} }, (x-a_{2}) ^{m_{2} }...[/tex]
If the leading coefficient is negative we may take '-' sign in the starting of the expression.
Here we are given that, f(x) has a leading coefficient of 1, roots -4, 2, and 9 with multiplicity 1, and root -5 with multiplicity 3
Hence, f(x) is given by:
= [tex]f(x)=(x-(-4)) ^{1 }, (x-2) ^{1}, (x-9) ^{1},(x-(-5)) ^{3}[/tex]
= [tex]f(x)=(x+4) , (x-2) , (x-9) ,(x+5),(x+5),(x+5)[/tex]
Hence, the expression for f(x) is: [tex]f(x)=(x+4) , (x-2) , (x-9) ,(x+5),(x+5),(x+5)[/tex]
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Use the power reducing fabulous rewrite the identity in terms of the first power of cosine
The power reducing formula for the fourth power of the cosine function is:
[tex]\cos ^4\theta=\frac{3}{8}+\frac{1}{2}\cos (2\theta)+\frac{1}{8}\cos (4\theta)[/tex]Replace θ=3x to find the expression for cos⁴(3x) in terms of the first power of the cosine function:
[tex]\begin{gathered} \cos ^4(3x)=\frac{3}{8}+\frac{1}{2}\cos (2\cdot3x)+\frac{1}{8}\cos (4\cdot3x) \\ \frac{3}{8}+\frac{1}{2}\cos (6x)+\frac{1}{8}\cos (12x) \end{gathered}[/tex]Therefore, the answer is:
[tex]\cos ^4(3x)=\frac{3}{8}+\frac{1}{2}\cos (6x)+\frac{1}{8}\cos (12x)[/tex]Use the second option to write this expression as input.
pls help me with aswell pls
Outward journey Speed = 20 km/hr , James stopped for 45 Mins ,Average speed homewars 15 km/hr
What is speed, for instance?
A measure of speed is the rate at which something is happening, moving, or moving swiftly. The speed of a car being driven at 45 mph serves as an illustration. A person cleaning a room in 10 minutes is an illustration of speed.From graph Journey Started at 2PM
on 3PM James covered 20 km
Hence Speed = (20 - 0)/(3 -2) = 20 km/hr
outward journey Speed = 20 km/hr
Now outward Distance = 45 km
Time taken = 45/20 = 2 hr 15 min
Hence reached at 4 : 15 PM
Started home at 5 PM
James stopped for 45 Mins (3/4 hrs)
Reached back at 8PM
time taken = 8 - 5 = 3 Hrs
Distance = 45 km
Average speed homeward = 45/3 = 15 km/hr
Average speed homeward = 15 km/hr
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Someone please do this. due soon!! 30 points given as well as marked brainliest!!
All answers based on the Angles Properties.
Given,
From the figure,
Point P is on the bisector of ∠ABC
Fill the table in the given question.
Now, According to the question:
Statement Reason
1. BP is the bisector Given
2. ∠ABP ≅ ∠CBP The definition of angular bisector
3. ∠BXP and ∠BYP are Given
right angles.
4. m ∠BXP ≅ m ∠BYP All right angles are congruent
5. BP ≅ BP Reflexive Property
6. ΔBXP ≅ ΔBYP AAS
7. PX ≅ PY CPCTC
8. Point p is equidistant Definition of equidistant.
from the sides of ∠ABC
Hence, All answers in the table .
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155% as a mixed or whole number
Answer:
[tex]1\frac{11}{20}[/tex]
Step-by-step explanation:
155% = 155 / 100 = 1.55
1.55 =155/1 × 100 / 100 = 155 / 100
155 / 100 = 31 / 20
31 / 20 = 1 11/20
Use the graph to estimate the roots of the equation.
The roots of a function are the points where the graph crosses the x-axis.
Thus, in the following graph, we can see that the function has 2 roots. These are in:
[tex]\begin{gathered} x=-2 \\ \text{and} \\ x=2 \end{gathered}[/tex]Answer:
x = -2
x = 2
Time Elapsed: HieAttempt due: Jun 20 a40 Minutes, 30 SeGiven: 21 and 23 are supplementaryProve: line m || linenComplete the proof. Number your reasons in the textbox below.Reasons1.2.Statements21 and 23 are supplementary21 + 23 = 18022 = 23Z1 + Z2 = 180°21 and 22 are supplementaryline m || linen3.4.5.6.
Statements and reasons.
1) ∠1 and ∠3 are supplementary
Reason: This is true because it is stated in the question.
2) ∠1 + ∠3 = 180º
Reason: By statement 1, ∠1 and ∠3 are supplementary, and by definition, supplementary angles sum up 180º.
3) ∠2 = ∠3
Reason: From the picture we see that ∠2 and ∠3 are opposite congruent angles, so they are equal.
4) ∠1 + ∠2 = 180º
Reason: from statement 2 we have ∠1 + ∠3 = 180º, and from statement 3 we have ∠2 = ∠3, so we have ∠1 + ∠2 = 180º.
5) ∠1 and ∠2 are supplementary
Reason: from statement 4 we have that ∠1 sum up ∠2, so by definition ∠1 and ∠2 are supplementary.
6) line m || line n
Reason: from the picture we see that ∠1 and ∠2 are internal collateral angles of the lines m and n, and from statement 5 we know that ∠1 and ∠2 are supplementary, so we have that the angle between line m and line n is 180°, and by definition, they are parallel lines.
Summary of the reasons
1) It is stated in the question
2) By statement 1 and by definition of supplementary angles.
3) Because they are opposite congruent angles, so they are equal.
4) By statement 2 and 3.
5) By statement 4, and by definition of supplementary angles.
6) By picture ∠1 and ∠2 are internal collateral angles of the lines m and n, and by statement 5 they are supplementary so they are parallel lines.
f(n) = 3 to the power of n
f(-1) =
The answer to the function as provided that f(n) = 3 to the power of n can thus, solving the linear function as n for -1 we get the answer.
What is a function?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
A statement, rule, or law that establishes a relationship between an independent variable and a dependent variable in mathematics (the dependent variable) is said as a function.
f[n]= [tex]3^n[/tex]
And find f(-1)
So put -1 in place of n
thus f[-1] = [tex]3^{-1[/tex]
=1/3
=0.33
In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
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2x+3x+4x=180 what’s x
[tex](2x + 3x + 4x) = 180 \\ 9x = 18 \\ \frac{9x}{9} = \frac{180}{9} \\ x = 20[/tex]
ATTACHED IS THE SOLUTION with the steps.
Help help help help please Heldon 30 Points
Answer:Rotation then a translation
Step-by-step explanation: rotate 90 degrees clockwise around center J. Then translate 3 to the right, 2 down
Select the correct answer. A mistake was made in the steps shown to simplify the expression. Which step includes the mistake? 1 + 3 2 5 + | - 10 | ÷ 2 Step 1: = 1 + 3 2 5 + 10 ÷ 2 Step 2: = 1 + 9 5 + 10 ÷ 2 Step 3: = 10 5 + 10 ÷ 2 Step 4: = 2 + 10 ÷ 2 Step 5: = 12 ÷ 2 Step 6:
Answer:
step 1 is correct
Step-by-step explanation:
when you find the absolute value of a number i.e | | the result is always positive
eg |-20| = 20
step 1 is correct
WILL GIVE BRAINLIEST! Please help and explain, thank you! All that is needed is to find the unknown side.
Answer: 2
Step-by-step explanation: 12 divided by 3 is 4 so 6 divided by 3 would be 2
⇒I will use the similarity theorem which works by proportion of sides in similar shapes.
⇒The side with magnitude 12 in the bigger triangle is proportional with the side with magnitude 4 in the smaller triangle
⇒The side with magnitude 6 in the bigger triangle is proportional with the side with magnitude x in the smaller triangle. The proportionality theorem allows us to equalize the proportions of the sides
⇒HOW? HERE it is the solution
⇒[tex]\frac{12}{4} =\frac{6}{x} \\[/tex]
⇒[tex]12(x)=4(6)\\12x=24\\\frac{1x}{12} =\frac{24}{12} \\x=2[/tex]
⇒I used cross multiplication
I do not need a whole explanation just make the answer clear, please.
Can anybody help me on this please? Does anyone see my question?
The slope of the line is represented by the word m which is obtained as 0.5.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
To determine a line's inclination or steepness, use the slope formula. Calculating the ratio of the change in the y-axis to the change in the x-axis may be used to calculate the slope of any line.
From the graph, the data is observed as,
(x₁,y₁)=(0,1)
(x₂,y₂) = (-2,0)
The slope of the line is found as,
[tex]\rm m =\dfrac{0-1}{-2-0} \\\\ m = 0.5[/tex]
Thus, the slope of the line is represented by the word m which is obtained as 0.5.
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Please help 20 points
I don't understand how I'm supposed to solve this I divided both sides and then multiplied but it says my answer is wrong
My teacher said to put 1 under 12
Answer: 16
Step-by-step explanation: Solve for x
by simplifying both sides of the equation, then isolating the variable.
Answer:
x= 1/3
Step-by-step explanation:
1. Combine multiplied terms into a single fraction
2. Multiply all terms by the same value to eliminate fraction denominators
3. Cancel multiplied terms that are in the denominator
4. Divide both sides by the same factor
5. Simplify
A baker uses 20 cups of flour to make bread. She uses 2 1/2 cups of flour to make each loaf. The baker sells 3/4 of the loaves of bread that she makes. How many loaves of bread does the baker sell?
Determine which integer will make the inequality 5x + 12 > 2x + 6 false.
S:{−3}
S:{3}
S:{−1}
S:{1}
The integer is x>-2
5 x+12>2 x+6
Subtract 12 from both sides
5 x+12-12>2 x+6-12
Simplify
5 x>2 x-6
Subtract 2x from both sides
5 x-2 x>2 x-6-2 x
Simplify
3 x>-6
Divide both sides by 3
[tex]\frac{3 x}{3} > \frac{-6}{3}$$[/tex]
Simplify
x>-2
Positive, negative, and zero are all examples of integers. The Latin word "integer" signifies "whole" or "intact." As a result, fractions and decimals are not included in integers.
An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero. A few examples of integers are: -5, 0, 1, 5, 8, 97, and 3,043.
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Complete the tables of values for x+2y =7
Which scatterplot would have a trend line with a negative slope?
On a graph, points are scattered all over the graph.
On a graph, points are grouped together and decrease.
On a graph, points are grouped together and increase.
Answer: B, the middle graph - "On a graph, points are grouped together and decrease."
Step-by-step explanation:
A negative slope means the x-value is going down as the y-value increases. The only option that consistently meets this criteria is B, "On a graph, points are grouped together and decrease."
Answer:
The 2nd Graph aka B
Step-by-step explanation:
got it right on edge
Question 3 options:
Premises:
If you have a cat, then it will chase mice.
You have a cat.
Conclusion:
Your cat will chase mice.
The Law of
The law of mathematical logic that was used to derive the given conclusion is; Law of Syllogism
What is the Law of Syllogism?The law of syllogism is defined as a type of logical argument using deductive reasoning.
Now, In mathematical logic, the Law of Syllogism states that if the following two statements are true:
(1) If d , then e .
(2) If e , then f .
Then we can derive a third true statement:
(3) If d , then f .
Now, applying that law to our question, we see that;
1) If you have a cat, then it will chase mice.
2) You have a cat.
Then we can derive a third true statement:
3) Your cat will chase mice.
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I need help! Anyone who takes time out of there day to help me thank you so much!
Answer:
Step-by-step explanation:
Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options. 18 x minus 15 = 72 50 x minus 25 = 72 18 x minus 9 = 72 3 (6 x minus 3) = 72 x = 4.5
The equations with same value of x as (3/5)(30x - 15) = 72 is 18x - 9 = 72, 3(6x - 3) = 72 and x = 4.5
How to solve an equation?An equation shows the relationship between two or more numbers and variables.
Given the equation:
(3/5)(30x - 15) = 72
Opening the parenthesis:
18x - 9 = 72
Factorizing the equation:
3(6x - 3) = 72
Dividing through by 3:
6x - 3 = 24
6x = 27
Dividing through by 6:
x = 4.5
The solution to the equation (3/5)(30x - 15) = 72 yields x = 4.5
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please help me with this homework question!!!
Answer:
51.06 degree
Step-by-step explanation:
x=sin^(-1)(7/9)
= 51.06 degree
I need to know what is the missing reason for line 7 in this proof
Similarity Theorems
Triangles ABG and DCB are similar by the AA similarity postulate
"If two angles in one triangle are congruent to two angles in another triangle, then the two triangles are similar"
The steps previous to statement 7 prove angles C and B are congruent because they are formed by two parallel lines that intersect a common line.
On the other side, angles DBC and AGB are congruent also because they are both right angles.
With two corresponding congruent angles, the AA similarity postulate is satisfied and the triangles are similar.
Rewrite the following numbers as rational numbers in the form of p/q (where P and Q are integers and Q≠O) in there lowest terms:
a). 0.75
b). 0.12
c). 0.80
d).1.25
The numbers in the rational form ( in there lowest form) of p/q are
(a) 0.75 = 3/4
(b) 0.12 = 3/25
(c) 0.80 = 4/5
(d) 1.25 = 5/4
In the question ,
number in the decimal form are given , and we have to express them in the rational form that is p/q .
So ,the expressions in rational form and lowest form are
(a) 0.75 [tex]=[/tex] 75/100 = 3/4
(b) 0.12 [tex]=[/tex] 12/100 = 6/50 = 3/25
(c) 0.80 [tex]=[/tex] 80/100 = 8/10 = 4/5
(d) 1.25 [tex]=[/tex] 125/100 = 5/4
Therefore , The numbers in the form of p/q are (a) 0.75 = 3/4 , (b) 0.12 = 3/25 , (c) 0.80 = 4/5 , (d) 1.25 = 5/4 .
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Write an expression that is equivalent to 3/4a + 2/3 - 1/2a - 1/3 + 1/2a
there is a linear relationship between the distance that a car drives and the amount of gas left in the tank of the car. the value of r2 for this linear relationship is 98.01%. what is the value of r?
A linear relationship between the distance that a car drives and the amount of gas left in the tank of the car is negative, and the value of r is -0.99
A linear relationship between the distance that a car drives and the amount of gas left in the tank of the car are negative because when a car travels a distance, it consumes fuel, and so fuel decrease with distance
Calculating the value of r
Given, r^2=98.01%
r^2=0.9801
r=±√0.9801
r=±0.99
Since r should be negative, so we pick the negative value and reject the positive value
r=-0.99
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8% of us adults have blood type b-positive. suppose we take a random sample of 38 us adults. let x represent the number of adults (out of the sample of 38) with blood type b- positive. this situation can be modeled with a binomial random variable x. 4. calculate the mean of x. show all work and round your answer to two decimal places.
Mean of the number of adults (out of the sample of 38) with blood type b- positive (x) is 3.04
Let x be the number of adults out of 38 with blood type b-positive
Probability, p of adults with blood type b-positive=8%=0.08
Sample size, n=38
Using binomial random variable x binomial(n=38, p=0.08)
p(X=x)=[tex]\left \ ({{n} \atop {x}}) \right. p^{x} q^{n-x}[/tex], where x=0,1,2,3,.....n
Mean of x:
Mean of x=(probability of adults with blood type b-positive*sample size)
So, mean of x=p*n, where n=38, p=0.08
=0.08*38
=3.04
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Can someone please help me with this 20 points!
4/x-2 + 3/x-3 = 5
X=
X=
Note: the answers have to be either integers or decimals
Answer:
x = 4 , x = 2.4
Step-by-step explanation:
[tex]\frac{4}{x-2}[/tex] + [tex]\frac{3}{x-3}[/tex] = 5
multiply through by (x - 2)(x - 3)
4(x - 3) + 3(x - 2) = 5(x - 2)(x - 3)
4x - 12 + 3x - 6 = 5(x² - 5x + 6)
7x - 18 = 5x² - 25x + 30 ( subtract 7x - 18 from both sides )
0 = 5x² - 32x + 48
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 5 × 48 = 240 and sum = - 32
the factors are - 20 and - 12
use these factors to split the x- term
0 = 5x² - 20x - 12x + 48 ( factor the first/second and third/fourth terms )
0 = 5x(x - 4) - 12(x - 4) ← factor out (x - 4) from each term
0 = (x - 4)(5x - 12)
equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
5x - 12 = 0 ⇒ 5x = 12 ⇒ x = 2.4
Can you help me help my sister we are both confused.
Answer:
A: Common multiple of 4 and 6 is 24
B: They would both be common multiples but they are two different multiples of 4 and 6.
C: 3/4= 18/24 1/6= 4/24
Step-by-step explanation:
A common multiple is a number that two numbers can be multiplied to. Something that both 4 and 6 can be multiplied to is 24, but there are many other multiples of 4 and 6 as well.