The product of [tex](x - 8)^2[/tex] is not a polynomial equation because a polynomial equation means a coefficient of x that has a power of two or more powers.
What is a Polynomial Equation?
The equations developed with variables, exponents, and coefficients exists named polynomial equations. It can include various exponents, where the higher one stands named the degree of the equation.
Closure property under multiplication notes that any two rational numbers' outcome will be a rational number, i.e. if a and b exist in any two rational numbers, ab will also be a rational number.
Example: (3/2) × (2/9) = 1/3.
The product of [tex]$(x - 8)^2[/tex]
Simplifying the equation as (x − 8)(x − 8)
Apply Perfect Square Formula, and we get
[tex]$(a-b)^{2}=a^{2}-2 a b+b^{2}$[/tex]
[tex]$&(x-8)^{2}=x^{2}-2 x \cdot 8+8^{2} \\[/tex]
[tex]$&=x^{2}-2 x \cdot 8+8^{2}[/tex]
Simplifying the above equation, we get
[tex]$x^{2}-2 x \cdot 8+8^{2}=x^{2}-16 x+64 \\[/tex]
[tex]$&=x^{2}-16 x+64[/tex]
This is not a polynomial equation because a polynomial equation means a coefficient of x that has a power of two or more powers.
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Instructions: Find the volume of each figure. Round your answers to the nearest tenth, if necessary.
The volume of the cone is 84.9 km³
How to find the volume of a cone?Volume of a cone = 1 / 3 πr²h
where
h = heightr = radiusTherefore,
radius = 3 km
height = √9.5² - 3²
height = √81.25
height = 9.01387818866
height = 9.014 km
Volume of a cone = 1 / 3 × 3.14 × 3² × 9.014
volume of the cone = 254.732197612 / 3
volume of the cone = 84.9107325372
volume of the cone = 84.9 km³
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find the square roots of each of the following number
1: 81
2: 100
Multiply 9 with 9, and we get:
9 × 9 = 81
Multiply 10 with 10, and we get:
10 × 10 = 100
We get the final result as:
9²10²Hope this helps :)
Lucy started the proof of the law of cosines using triangle WXY as shown.
W
Z
X
Given: XZ WY, AWXZand AYXZare right triangles
z; y cos (W) = WZ
Step 1: cos (W) =
Step 2: sin (W) =
Step 3: ZY = x - y cos (W)
Step 4: w²= (z-y cos (W))² + XZ²
Which step contains the first error in calculation?
z; XZ sin (W) = y
OA Step 1- the cosine ratio was applied incorrectly
OB. Step 2 - the sine ratio was applied incorrectly
OC. Step 3- the incorrect value was subtracted
OD. Step 4- the area formula should have been used instead.
4
The step which contains the first error in calculation is: B. Step 2 - the sine ratio was applied incorrectly.
What is the law of sines?The law of sines is also referred to as sine law or sine rule and it can be defined as an equation that relates the side lengths of a triangle to the sines of its angles.
Mathematically, the law of sines is given by this equation:
[tex]\frac{sinA}{a} =\frac{sinB}{b}[/tex]
For any right-angled triangle, the ratio of the length of its opposite sides to the length of its hypotenuse is generally referred to as sine ratio. Thus, sine ratio is given by this formula:
cos(θ) = Opp/Hyp
Where:
Opp is the opposite side of a right-angled triangle.Hyp is the hypotenuse of a right-angled triangle.θ is the angle.In this context, we can infer and logically deduce that the step which contains the first error in calculation is step 2:
sin(W) = y/XZ; XZsin(W) = y.
In conclusion, the correct step should have been written as follows:
sin(W) = XZ/y; ysin(W) = XZ.
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Answer:
step 2 is incorrect
Step-by-step explanation:
B. Step 2 - the sine ratio was applied incorrectly
How would you find the area or perimeter of this shape?
The perimeter of a given shape implies the sum of all its sides. While the area of a given shape is the total value of space it would cover on a 2-dimensional plane.
The perimeter of the shape is 104 cm.
The area of the shape is 640 [tex]cm^{2}[/tex].
The perimeter of a given shape implies the sum of all its length of sides., such that the value of each individual side is summed to a total value.
The area of a given shape is the total value of space it would cover on a 2-dimensional plane. The area of shapes depends on the type of shape.
In the given question, the given shape has 12 sides. Some of these sides can sum up to a given length as shown in the diagram.
So that;
perimeter = 2 + 32 + 10 + 10 + 2 + 32 + 8 + 8
= 104 cm
Thus, the perimeter of the shape is 104 cm
ii. The area of the shape = length x width
= 32 x 20
= 640 [tex]cm^{2}[/tex]
Therefore, the area of the given shape is 640 [tex]cm^{2}[/tex].
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Find the area of this parallelogram. D(-3,4) c(3,4) a(-6,-4) b(0,-4)
If the vertices of parallelogram ABCD is A(-6,-4),B(0,-4),C(3,4),D(-3,4) ,then the area of parallelogram ABCD will be 48 square units.
Given that the vertices of parallelogram ABCD is A(-6,-4),B(0,-4)
,C(3,4),D(-3,4).
We are required to find the area of parallelogram ABCD.
Let the point of intersection of height of parallelogram from point A is point E.
When we see the graph on which the parallelogram then we will be able to know that point E has coordinates of (-3,-4).
Area of parallelogram=Base*Height
=AB*DE
DE=[tex]\sqrt{(-4-4)^{2} +(-3+3)^{2} }[/tex]
=[tex]\sqrt{64}[/tex]
=8 units
AB=[tex]\sqrt{(-4+4)^{2} +(0+6)^{2} }[/tex]
=[tex]\sqrt{36}[/tex]
=6 units
Area=6*8
=48 square units.
Hence if the vertices of parallelogram ABCD is A(-6,-4),B(0,-4),C(3,4),D(-3,4) ,then the area of parallelogram ABCD will be 48 square units.
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prove that if all the altitude lengths are different in a triangle, then the triangle is scalene. (use indirect proof or contrapositive)
The term "altitude" is the same as "height of a triangle". It is perpendicular to the base. Since we can rotate the triangle to have any side be horizontal, there are effectively 3 possible bases. Hence, there are 3 heights. It all depends how you look at it.
Let h1, h2, and h3 be the three altitudes or heights.
Without loss of generality, we'll focus on the first two heights h1 and h2. Their respective bases are b1 and b2.
If we use b1 as the base, then the area is...
area = 0.5*base*height = 0.5*b1*h1
Similarly, the other base gives the area of:
area = 0.5*b2*h2
------------------------
Since both formulas refer to the same area (because we're working with the same triangle), we can set the expressions equal to one another
0.5*b1*h1 = 0.5*b2*h2
b1*h1 = b2*h2
Let's see what happens when b1 = b2, so,
b1*h1 = b2*h2
b1*h1 = b1*h2
b1h1 - b1h2 = 0
b1(h1 - h2) = 0
b1 = 0 or h1 - h2 = 0
b1 = 0 or h1 = h2
If the bases b1 and b2 were equal, then either those bases must be 0 which isn't possible, or the altitudes must be equal. However, the initial premise is that the heights must be different from one another.
Therefore, the bases b1 and b2 can't be the same length.
We could follow the same steps and logic to conclude that if the altitudes h1 and h3 were different, then the bases b1 and b3 can't be the same. Similarly, we would conclude that b2 and b3 can't be the same. This is where the "without loss of generality" kicks in.
In other words, we only need to focus on one subcase to extend the logic to the other cases, without having to actually do every single step. That would be a bit tedious busywork.
In conclusion, we've shown that if the heights are different, then their respective bases must be different. This leads to wrapping up the proof that we have a scalene triangle.
Side note: I used an indirect proof or proof by contradiction. I assumed that a non-scalene triangle was possible and it led to a contradiction of h1 = h2.
Quick algebra 1 question for 50 points!
Only answer if you know the answer, Tysm!
Answer:
x=1
Step-by-step explanation:
2/3(9x-6) = 1/4(12-4x)
We want to solve for x
Distribute
6x-4=3-x
Add x to each side
6x-4+x = 3-x+x
7x-4 = 3
Add 4 to each side
7x-4+4 = 3+4
7x=7
Divide by 7
7x/7 = 7/7
x=1
Answer:
x = 1
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] (9x - 6) = [tex]\frac{1}{4}[/tex] (12 - 4x) ← distribute parenthesis on both sides
6x - 4 = 3 - x ( add x to both sides )
7x - 4 = 3 ( add 4 to both sides )
7x = 7 ( divide both sides by 7 )
x = 1
NEED HELP ASAP
let h(x)=-1/3x+2. Find -4h(9)
Answer:
4
Step-by-step explanation:
h(x) = -1/3x+2 where we need to find -4h(9)
h(9): x = 9
h(x) = -1/3(9) + 2
h(x) = -3 + 2
h(x) = -1
-4h(9) is -4h(x):
-4(-1) = 4
The sky wheel has 42 glass enclosed gondolas. What is the measure of each central angle between gondola cars, to the nearest hundredth degree?
A sky wheel is a mechanical device that has a shape of a circle divided into a given number of equal sectors. Thus, the measure of each central angle required in the question is [tex]8.6^{o}[/tex].
A sky wheel is a mechanical device that has a shape of a circle divided into a given number of equal sectors. Thus each sector has an equal central angle. Since the sum of the internal angles of a circle is [tex]360^{o}[/tex].
From the given question, it has been stated that the sky wheel has 42 glass-enclosed gondolas. This implies that the sky wheel has been divided into 42 equal sectors.
Therefore,
the measure of each central angle = [tex]\frac{360^{o} }{n}[/tex]
where n represents the number of gondolas (42).
Thus,
the measure of each central angle between gondolas cars= [tex]\frac{360}{42}[/tex]
= 8.5714
The measure of each central angle between gondolas cars is approximate [tex]8.6^{o}[/tex].
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I need help with this
Example 1 Find 6 – 9. 6 – 9 = 6 + ( – 9) To subtract 9, add – 9. = – 3 Simplify
Answer:
Step-by-step explanation: This example is saying that adding a negative number is the same as subtracting a positive number. For example 2-3 = 2 + (-3).
What is the quotient of the given values to the correct level of precision? 16.017 in. ÷ 0.370 in. 43 43.289 43.29 43.3
Answer:43.289
Step-by-step explana
State the converses of the following statements. In each case, also decide whether the converse is true or false.
(1) If n is an even integer, then 2n + 1 is an odd integer.
(2) If a transversal intersects two parallel lines, then each pair of corresponding angles is equal.
(3) If each pair of opposite sides of a quadrilateral is equal, then the quadrilateral is a parallelogram.
(4) If the decimal expansion of a real number is terminating, then the number is rational.
Help!
Answer:
See below.
Step-by-step explanation:
Converse
The converse of a statement is formed by switching the hypothesis and the conclusion.
Hypothesis: The part after the "if".Conclusion: The part after the "then".Question 1Given statement: If n is an even integer, then 2n + 1 is an odd integer.
Hypothesis: "n is an even integer"Conclusion: "2n + 1 is an odd integer"Converse: If 2n + 1 is an odd integer, then n is an even integer.
Question 2Given statement: If a transversal intersects two parallel lines, then each pair of corresponding angles is equal.
Hypothesis: "a transversal intersects two parallel lines"Conclusion: "each pair of corresponding angles is equal"Converse: If a transversal intersects two lines such that each pair of corresponding angles is equal, then the two lines are parallel to each other.
Question 3Given statement: If each pair of opposite sides of a quadrilateral is equal, then the quadrilateral is a parallelogram.
Hypothesis: "each pair of opposite sides of a quadrilateral is equal"Conclusion: "the quadrilateral is a parallelogram"Converse: If a quadrilateral is a parallelogram, then each pair of opposite sides of the quadrilateral is equal.
Question 4Given statement: If the decimal expansion of a real number is terminating, then the number is rational.
Hypothesis: "the decimal expansion of a real number is terminating"Conclusion: "the number is rational"Converse: If a real number is rational, then the decimal expansion of the number is terminating.
The graph below shows the speed of a car that is driven through a town and then on a major highway. During which of the following time intervals was the car stopped at a traffic light?
Considering the graph of the velocity of the car, it is found that the interval in which it was stopped at a traffic light was:
Between 3 and 4 minutes.
When is a car stopped at a traffic light?When a car is stopped at a traffic light, the car is not moving, that is, it's velocity is of zero.
In this problem, the graph gives the velocity as a function of time, and it is at zero between 3 and 4 minutes, hence the interval in which it was stopped at a traffic light was:
Between 3 and 4 minutes.
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2 Question is down below.
The height of the flagpole is 12.4 meters and the altitude of the balloon is 29.1 meters
How tall is the flagpole?See attachment for the diagram, when redrawn
Start by calculating the length AB using the following tangent function
tan(22) = BC/AB
This gives
tan(22) = 9/AB
Make AB the subject
AB = 9/tan(22)
Evaluate the quotient
AB = 22.3
The length DB is then calculated using:
tan(9) = DB/AB
This gives
tan(9) = DB/22.3
Make DB the subject
DB = 22.3 * tan(9)
Evaluate
DB = 3.35
The height of the flagpole is then calculated as:
Height = DB + BC
This gives
Height = 3.35 + 9
Evaluate
Height = 12.35
Approximate
Height = 12.4
Hence, the height of the flagpole is 12.4 meters
How to determine the altitude of the balloon?The diagram that illustrates the scenario is added as an attachment
Calculate the value of y using the following tangent functions
tan(57) = x/y and tan(72) = (15 + x)/y
Make y the subject in tan(57) = x/y and tan(72) = (15 + x)/y
y = x/tan(57) and y = (15 + x)/tan(72)
Substitute y = x/tan(57) in y = (15 + x)/tan(72)
x/tan(57) = (15 + x)/tan(72)
Evaluate the tangent ratios
x/1.5 = (15 + x)/3.1
Cross multiply
3.1x = 22.5 + 1.5x
Evaluate the like terms
1.6x = 22.5
Divide by 1.6
x = 14.1
The altitude of the balloon is then calculated as:
Altitude = 14.1 + 15
Altitude = 29.1
Hence, the altitude of the balloon is 29.1 meters
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4√2/9+√2+√1/18. 1/√3-1-1/√3+1
Answer:
Exact form: 78√2 - 17√3 / 54
Decimal form: 1.49747766
Step-by-step explanation:
Rationalize and simplify the expression.
Evacuate the following using suitable identities (102)^3
The value of [tex](102)^3[/tex] exists 1061208.
How to estimate the value of [tex](102)^3[/tex]?Let us rewrite [tex](102)^3[/tex] as [tex](100+2)^3[/tex]
Now utilizing the identity [tex](a+b)^3=a^3+b^3+3ab(a+b)[/tex], we get
a = 100 and b = 2 then substitute the values of a and b then
[tex](100+2)^3=100^3+2^3+[(3\times100\times2)(100+2)][/tex]
= 1000000 + 8 + (600 × 102)
= 1000000 + 8 + 61200
= 1061208
Hence, [tex](102)^3=1061208[/tex]
Therefore, the value of [tex](102)^3[/tex] exists 1061208.
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Determine the slope of the line.
Answer:
2
Step-by-step explanation:
→ Find 2 points from the line
( 0 , 6 ) and ( - 3 , 0 )
→ Find the change in y coordinates
0 - 6 = -6
→ Find the change in x coordinates
-3 - 0 = -3
→ Divide the 2 results
-6 ÷ -3 = 2
Use the recursive formula to find the first five terms in the arithmetic sequence.
The first five terms of the sequence are 1/5, 2/5, 3/5,4/5, 1
Recursive functionsRecursive functions are functions that is used to determine the next term of a given sequence giving the common difference.
Given the recursive function shown below;
f(1) = 1/5
f(n) = f(n-1) + 1/5
For the second term;
f(2) = f(1) + 1/5
f(2) = 1/5 + 1/5
f(2) = 2/5
For the third term;
f(3) = f(2) + 1/5
f(3) = 2/5 + 1/5
f(3) = 3/5
For the fourth term;
f(4) = f(3) + 1/5
f(4) = 3/5 + 1/5
f(4) = 4/5
For the fifth term;
f(5) = f(4) + 1/5
f(5) = 4/5 + 1/5
f(5) = 5/5 = 1
Hence the first five terms of the sequence are 1/5, 2/5, 3/5,4/5, 1
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what is the decimal representation of 3/40
Answer:
0.075
Step-by-step explanation:
to convert a fraction to a decimal fraction
divide the numerator by the denominator, that is
[tex]\frac{3}{40}[/tex] = 3 ÷ 40 = 0.075
Which value is a solution for the equation tan/2=-1
The value of the solution is 3π/2.
What is a trigonometric equation?
An equation involving one or more trigonometric ratios of unknown angles is called a trigonometric equation.
tan x/2 = -1
tanx/2 = tan(-π/4)
tanx=tanФ
⇒ The general equation of tanx=tanФ is
⇒ x=nπ+Ф
x/2=nπ+(-π/4)
at n=0
x/2=-π/4
x=-π/2
at n=1
x/2=π-π/4
x/2=3π/4
x=3π/2
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Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Questions: Which value is a solution for the equation tan x/2 = -1?
A. 5pi/4
B. 7pi/4
C. 3pi/4
D. 3pi/2
Based on the graph which congruence theorems or postulates are reasons why these graphs are equal?
Triangles DEF and JKL can be proven to be congruent triangles based on:
C. ASA
E. AAS
F. LA
What is the ASA Congruence Theorem?The ASA congruence theorem states that if two triangles that are have two pairs of corresponding congruent angles and a pair of corresponding included congruent sides, then both triangles are congruent to each other.
What is the LA Congruence Theorem?The LA congruence theorem states that two right triangles are congruent if they have a pair of congruent legs and a pair of congruent angles that are corresponding to each other.
What is the AAS Congruence Theorem?The AAS congruence theorem states that two triangles with two pairs of congruent angles and a pair of congruent non-included sides are congruent.
From the image given, triangles DEF and JKL can be proven to be congruent triangles using the LA, AAS, and ASA congruence theorems.
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I don't understand this question... Can anyone explain this to me please?
Answer:
First answer lol
Step-by-step explanation:
is the domain by any chance x ≥-2?
need some help, please
Answer:
c = 15
Step-by-step explanation:
expand the left side and compare with like terms on the right side
2x(4x + 5) + 3(4x + 5) ← distribute parenthesis
= 8x² + 10x + 12x + 15 ← collect like terms
= 8x² + 22x + 15
compare to ax² + bx + c
then c = 15
please help if u can! greatly appreciated
don't answer if u dont know PLEASE
a. log₈8 = 1
b. log₇6/5
c. log₉3¹
The solution to the problem are1. log₈ 2 * 4 would produce an integer
= log₈8 = 1
The output is an integer
2. log₇6/5 would give us an irrational number
= log₇1.2
This would give us an irrational number
3. log₉3¹ would give us a rational number
= log₉9^[tex]^\frac{1}{2}[/tex] = 1/2 log⁹9
= 1/2
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The answer to question 5 is “x(x-2y)(3x-2y)” and the answer to question 6 is “(x-y)(2-x+y)”. I know these answer cause I have the answer book but I don’t know how to get the answer . Can some one solve questions 5 and 6 with the steps to get these answers cause I have to show my work but I don’t understand how to get the answers . Also use the substitution method like I did in question 4.(urgent !!)
What is an algebraic expression?
An expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, etc.
What is the substitution method?
The substitution method is generally used to solve the system of equations. In this method, first, solve the equation for one variable, and substitute the value of the variable in the other equation
5th question :
⇒ x(2y-x)²+2x²(x-2y)
let (x-2y) = A
⇒we can also write (2y-x)² as (x-2y)² as both have the same value
x(x-2y)²+2x²(x-2y)
x(A)²+2x²(A)
By taking xA common
⇒ xA(A+2x)
On putting the value of A=(x-2y)
⇒ x(x-2y) (x-2y+2x)
⇒x(x-2y) (3x-2y)
6th question :
2(x-y)-(y-x)²
let (x-y) = B
⇒we can also write (y-x)² as (x-y)² as both have the same value
2(x-y)-(x-y)²
2B-(B)²
By taking B common
⇒ B(2-B)
On putting the value of B=(x-y)
⇒(x-y) (2-{x-y})
⇒(x-y) (2-x+y)
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PLEASE HELP, I REALLY NEED IT!!!
The number which is express in each of the models as given in the image attached to the task content are as follows;
a). 1.37
b). 1.37
c). 1.37.
What numbers are expressed according to the given models in the task content?It follows from the task content that the models describe that One flat represents 1 whole, One rod represents 1 tenth and one unit represents 1 hundredth.
It therefore follows from the task content that in each of the models, the algebraic sum of flat(s), rods and units as the case may be results in the value; 1.37 as the utmost number represented by the models.
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1.) You go skiing on one route with an equation = 2 + 4 and then
immediately go to a route with an equation = 4 + 1. Which of the
following responses best describes your routes?
A: Your second route was steeper than your first, and the second route was higher up
the mountain.
B: Your first route was positive (uphill), but your second route was negative (downhill).
C: Your first route was steeper than your second, and both were positive (uphill).
D: Your first route was flatter than your second, and your first route began at a higher
point than your second
The best information that describes your routes is the second route was steeper than your first, and the second route was higher up the mountain.
What is the slope of a linear equation?The slope of a linear equation is the change in the rise over the run. So, the slope of a linear equation shows that the larger the slope, the steeper the line becomes.
From the given information:
y = 2x + 4 --- (1)
y = 4x + 1 --- (2)
Using the slope-intercept formula:
y = mx + b
m = slopeb = y-interceptFrom the first equation, the slope is 2 and in the second equation, the slope is 4.
Therefore, we can conclude that the second route was steeper than your first, and the second route was higher up the mountain.
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How many lbs of peanuts must mike add to 9 lbs of mixed nuts containing 40% peanuts to make a mixture with 73% peanuts
The new mixture exists 56.5% peanuts.
How to estimate the total number of peanuts required for the mixture?The first batch of 9 lb of mixed nuts possesses 40% peanuts.
This means the quantity of peanuts exists:
9 [tex]*[/tex] 40/100 = 3.6 lb
The second batch of 9 lb of mixed nuts possesses 73% peanuts.
This means the quantity of peanuts exists:
9 [tex]*[/tex] 73/100 = 6.57 lb
The total quantity of peanuts in the mix exists
3.6 lb + 6.57 lb = 10.17 lb
There exist 9 lb + 9 lb = 18 lb of mix.
Therefore, the percent of peanuts in the mix exists:
10.17 / 18 [tex]*[/tex] 100 = 56.5%
The new mixture exists 56.5% peanuts.
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HELP!!!!QUICK!!!!!!!!!!!
Answer:
= – 5 – 7
Step-by-step explanation:
3 – 8 = – 5 + 4 – 5 = – 1 –1 – 6 = –7= –5 – 7
Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction if needed.
Answer:
9/41
Step-by-step explanation:
Cosine represents adjacent / hypotenuse.
When A is the reference angle, AB is the adjacent side (9) and AC is the hypotenuse (41).
9/41 is already simplified.
