The Quadratic equation modeled is [tex]3x^{2} -4x+1=(3x-1) (3x-1)[/tex].
Quadratic equation as an equation of degree 2, meaning that the highest exponent of this function is 2. The standard form of a quadratic is [tex]y=ax^{2} +bx+c[/tex], where a, b, and c are numbers and a cannot be 0.
the given equation Much easier to understand with the symbol [tex]3x^{2} -4x+1=(3x-1) (3x-1)[/tex]
[tex]3x^{2} -4x+1= 9x^{2} -6x+1\\6x^{2} -2x=0[/tex]
That is how I interpreted the "tile" set up.
Now count up the factors:
These are (4 -x) and ( x +1) factor of Quadratic equation.
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an airplne can cruise at 640 mph how far can it fly in 3/5 of an hour
The plane can fly 384 miles in 3/5 hours.
An airplane can cruise at 570 miles per hour.
We have to find the distance travelled by airplane in 4/3 hours.
Distance = Speed x Time
Distance = 640 x 3/5
Distance = 128 x 3
Distance = 384 miles
Hence, The plane can fly 384 miles in 3/5 hours.
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Figure 2 shows 4 strips of paper formed from cutting ABCD. Figure 1 below shows a piece of rectangular paper ABCD where AB= (3x - 1) cm and BC= The total perimeter of the 4 strips is 170 cm. D C (b) Hence show that ABCD is a square. 2x+5 B 3x-1 Figure 1 (a) Form an algebraic equation in x and solve it. D 2x 326-1 Figure 2 C 2x75 = (2x + 5) cm. B
Order the following numbers from least to greatest. Put the least number on the left. -3 37 7|3 3.
y5+7=17
Responses
y = 50
y = 50
y = 2
y = 2
y = 24
y = 24
y = 120
Answer:
y=2
Step-by-step explanation:
Name the following polynomial by degree and tell the leading coefficient.
−6x3
A
3rd degree; 6
B
1st degree; −6
C
3rd degree; −6
D
1st degree; 6
The leading term, the degree of the polynomial is −6x3 is 3rd degree and coefficient −6.
Option (C) is correct.
What is a polynomial ?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables .It is is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.
Given:
The given expression is
−6x3
We have to find the polynomial by degree and tell the leading coefficient.
According to given question we have
The leading term of a polynomial is the term with the highest degree.
The leading coefficient of a polynomial is the coefficient of the leading term.
The degree of a polynomial is the highest degree of its terms.
Hence, the leading term, the degree of the polynomial is −6x3 is 3rd degree and coefficient −6.
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resent a combinatorial argument for this identity by considering a set of n people and determining, in two ways, the number of possible selections of a committee of any size and a chairperson for the committee.
The committee can be selected by combinatorial argument in
[tex]\sum ^{n}_{k=1} k(^n_k).[/tex] ways.
A counting-based argument is known as a combinatorial argument or combinatorial proof. This line of reasoning has previously been used, for instance in the section on Stirling numbers of the second sort.
By initially selecting k individuals from our group of n, we can then choose one of those k individuals to serve as the committee's chairperson.
A number of methods for completing the first task, k methods for completing the second task, and so on. ways to create a k-member committee with a chairperson.
[tex]\sum ^{n}_{k=1} k(^n_k).[/tex] is the number of methods to construct a committee with a chairman of size less than or equal to n can be found by adding up over 1≤k≤n.
A committee of size less than or equal to n can also be formed with a chairperson by selecting the chairperson first, followed by the members of the committee. The chairperson can be chosen from among n options. The picker has two options for the remaining n-1 individuals: to include them or not. We therefore have n options for the chairperson, 2 options for the following, 2 options for the following, etc. These can be multiplied together to give us [tex]n2^{n-1}[/tex], which is a proof of the identity.
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Reflection over the line y=x of the point (7,2)
Answer:
2,7
Step-by-step explanation:
when y=x similary x= y
Angle R and angle J are a linear pair. If the measure of R = 3x - 5 and the measure of J = 5x + 1 find the measure of J.
The measure of angle J is 116°
What are linear pairs of angle?Linear pair of angles are angles formed when two lines intersect at a single point.
Angles are said to be linear if they are adjacent to each other with the intersection of the two lines.
Note that the sum of angles of a linear pair is equal to 180°.
From the information given, we have that;
Angle R = 3x - 5Angle J = 5x + 1But we have the expression as;
Angle R + Angle J = 180°
substitute the values into the equation
3x - 5 + 5x + 1 = 180°
collect like terms
8x - 4 = 180°
8x = 180 + 4
8x = 184
To determine the value of x, divide both sides by the 8
8x/8 = 184/8
Divide through
x = 23
But we have that;
Angle J = 5x + 1
Angle J = 5(23) + 1
Angle J = 115 + 1
Angle J = 116°
Thus, the measure of angle J is 116°
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please solve this equation for me its algebra
solve
-4b=48
Answer:-12
Step-by-step explanation: -4b=48 b=48/-4 b=-12
hope it helps
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a tire shop had to fill 3 1/3 tires with.it took a small air compressor 31/4 seconds to fill them up. How long would take to fill 2 tires?
It would take 21 8/ 12 seconds to fill 2 tires
What is proportion?
Proportion can be defined as the comparison between two numbers or elements
It is also an equation with two ratios draw equal to each other.
From the information given,
If 31/ 3 tires (10/ 3 ) tires is filled in 3 1/4 seconds ( 13/ 4)
Then 2 tires = x seconds
cross multiply
x = 13 / 4 × 2 ÷ 10/ 3
x = 26/ 4 × 3/ 10
x = 260/ 12
x = 21 8/ 12 seconds
Thus, it would take 21 8/ 12 seconds to fill
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If 75% of the employees in a company are female and 5% of those female employees are over 6 feet tall what percentage of the company’s employees are both female and over 6 feet tall
The percentage of the company’s employees are both female and over 6 feet tall is 3.75%
Let the total number of employees in the given company be x. So, the number of female employees in the company are : 75% × x
Number of female employees in company = 0.75x
Now, calculating number of female employees that over 6 feet tall = 0.75x × 5%
The number of female employees that over 6 feet tall = 0.0375x
Percentage of the company’s employees are both female and over 6 feet tall = percentage of female and tall employees ÷ total number of employees × 100
Percentage of the company’s employees are both female and over 6 feet tall = (0.0375x÷x)×100
Percentage of the company’s employees are both female and over 6 feet tall = 3.75%
Therefore, the percentage of the company’s employees are both female and over 6 feet tall is 3.75%
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How do I write -2=y into slope intercept form?
Answer:
(0,-2)?
Step-by-step explanation:
What is limit as x approaches zero of f(f(x)) closest to?
a. DNE
b. 1
c. 3
d. 5
note: I thought the answer was does not exist, but it ended up being wrong, please help and explain the answer!
Using limits and numeric value, we have that lim x -> 0 f(f(x)) is closest to:
c. 3.
What is f(f(x))?f(f(x)) is a composite function, hence:
For x = a, first we calculate the numeric value at x = a.Then we calculate the numeric value at x = f(a).What is a limit?A limit is the value that a function f(x) tends as x tends to a value. It there are no undetermined values, we can just verify the numeric value from the graph, but with undetermined values, there are multiple things to look at.
For this function, looking at the graph, we have that:
f(0) = 2, as when x = 0, f(x) = 2.Thus, lim x -> 0 f(f(x)) = lim x - > 2 f(x), because f(0) = 2.Both to the left of x = 2 and to the right of x = 3, from the graph, f(x) approaches 3, hence lim x - > 2 f(x) = 3.This means that option c is the closest approximation for the limit of the function.
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how many liters of acid must be added to a 100-liter solution that is 20 percent acid in order to product a solution that is 25 percent acid?
You can make 106.67 L of 25% v/v acid solution by mixing 6.67 L of pure acid with 100 L of 20% v/v acid solution.
What is an acid?Acids are a type of chemical that can either absorb electrons or give off protons or hydrogen ions. An anion and a cation can form in water when a hydrogen atom that is bonded to an acid releases (dissociates). How acidic a substance is and how acidic its solution pH is depends on how many hydrogen ions it produces.
The word acid stems from the Latin words acidus or acere, which suggest "sour," because one of the characteristics of acids in water is a sour taste (e.g., vinegar or lemon juice).
How thoroughly an acid splits into its ions after being dissolved in water indicates whether it is strong or weak. A strong acid, like hydrochloric acid, completely dissociates into its ions in water.
100 liters * (20/100) = 20 liters acid
Let's assume that the number x represents the amount of pure acid you need to add to your initial solution. The volume of acid will increase by x because you are working with pure acid.
V(acid) = 20 +x
V(solution) = 100+ x
As a result, the percent concentration by volume of the target solution will be equal to
{V(acid)/V(solution)} * 100 = 25%
{(20+x)/(100+x)} * 100 = 25%
(20 +x) 100 = 25(100+x)
2000+100x = 2500 + 25x
75 x = 500
x = 6.67 liters
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a very lucky gambler starts with one dollar and doubles her money on each bet she makes. how much money will she have after five bets?
$32 money will she have after five bets.
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables." from Wolfram MathWorld .starting amount = $1
she doubles her money on her each bet.
So, when she makes her first bet , her money doubles and keep doubling
on every bet of the previous amount .
Money she makes on her first bet = 2 * 1 = $2
Money she makes on her second bet = 2 * 2 = $4
money on third bet = 2 * 4 = $8
money on fourth bet = 2 * 8 = $16
money on fifth bet = 2 * 16 = $32
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Find the distance between the two points shown on the graph below, located at (1, 2) and (3, 1).
The distance between the two points as depicted on the graph is:
√5.
Given, the points are:
(1,2) = (x₁,y₁) and
(3,1) = (x₂,y₂)
We know that distance between two points is:
d = √(x₂-x₁)²+(y₂-y₁)²
d = √(3-1)²+(1-2)²
d = √(2)²+(-1)²
d = √4+1
d = √5
Hence we get the distance between two given points as √5
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how would you express b⃗ b→b vec using unit vectors? express your answers in terms of the unit vectors x^x^x unit and y^y^y unit . use the button under the menu in the answer box to create unit vectors.
The answer is expressed in terms of unit vectors x^ and y^ as B = B (cos θ x ^ + sin θ y ^)
For expressing the magnetic field B in terms of vectors we need to know the magnitude of the magnetic field and the angle between them.
the angle we have is with respect to the positive side of the x-axis, let's use trigonometry.
cos θ = Bₓ / B
sin θ = / B
Bx = B cosθ
By = B sinθ
hence the resulting vector is
B = Bₓ i ^ + [tex]B_{y}[/tex] j^
The unit vectors are
x ^ = i ^
y ^ = j ^
The answer is expressed in terms of unit vectors x^ and y^ as B = B (cos θ x ^ + sin θ y ^)
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Triangle LMK has vertices L(-6, 0), M(0, -6), and K(-6, -6) and triangle XYW has vertices X(0, 6), Y(8, 6), and W(4, 2). Using the definition of congruence, decide whether the two triangles are congruent. Explain your answer. Give coordinate notation for the transformations you use.
Using the distance between two points formula to calculate the side lengths, it is found that the figures are not congruent.
What are congruent figures?Congruent figures are figures that have the same outer side lengths.
We are given the vertices for this problem, hence we use the distance between two points formula to calculate the lengths.
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, with the hypotenuse being the distance between them.
For Triangle LMK, the side lengths are given as follows:
[tex]LM = \sqrt{(0 - (-6))^2+(-6 - 0)^2} = 6\sqrt{2}[/tex][tex]KM = \sqrt{(-6 - (-6))^2+(-6 - 0)^2} = 6[/tex][tex]LK = \sqrt{(-6 - (-6))^2+(-6 - 0)^2} = 6[/tex]For Triangle XYW, the side lengths are given as follows:
[tex]XY = \sqrt{(8 - 0)^2+(6 - 6)^2} = 8[/tex][tex]WY = \sqrt{(8 - 4)^2+(6 - 2)^2} = 4\sqrt{2}[/tex][tex]XW= \sqrt{(4 - 0)^2+(6 - 2)^2} = 4\sqrt{2}[/tex]Due to different side lengths, the figures are not congruent, and nothing can be stated about the transformations that were used.
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Verify whether x = -1/√3 is a zero of the polynomial 3x²-1.
Answer:
Below.
Step-by-step explanation:
3x² - 1 = 0
3x² = 1
x² = 1/3
x = ±√(1/3)
= -1/√3, 1/√3.
So, -1/√3 is a zero of 3x² - 1 .
Yes, x = -1/√3 is a zero of the polynomial 3x² - 1 because substituting the value results in zero, confirming its solution to the equation.
To verify whether x = -1/√3 is a zero of the polynomial 3x² - 1, we need to substitute this value into the polynomial and check if it results in zero.
Given polynomial: 3x² - 1
Now, substitute x = -1/√3 into the polynomial:
3(-1/√3)² - 1
Now, simplify:
3(1/3) - 1
1 - 1
The result is zero. Since the expression evaluates to zero when x = -1/√3, this means that x = -1/√3 is indeed a zero of the polynomial 3x² - 1.
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Solve: -5(15)
I’m so confused
Answer:
- 75
Step-by-step explanation:
- 5(15) means - 5 × 15 = - 75
What’s the domain and range?
Answer:
Domain: x > -4
Range: y > -1
Step-by-step explanation:
Domain is the points on the x axis that could be vaild for that line.
Range is the points on the y axis that could be valid for that line.
place the following complex number in a two dimensional complex plane and find their absolute value "1+i)
The point (1,1) represents 1+i in the two dimensional complex plane. Absolute value of 1+i = [tex]\sqrt{2}[/tex].
Given the complex number, z = 1+i
The general form of a complex plane is x+iy, where x and y are real numbers.
We can place any complex number into a two-dimensional complex plane with two axes - X and Y.
For z = 1+i, x = 1 and y = 1. So the point (1,1) will represent z = 1+i in the two dimensional complex plane.
The absolute value of a complex number z = x+iy is given by ,
|z| = [tex]\sqrt{x^2+y^2}[/tex]
So for z = 1+i, |z| = [tex]\sqrt{1^2+1^2}=\sqrt{2}[/tex]
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The cost for decorations and the disc jockey for the homecoming dance was $1,800. The class members sold 279 tickets and made a profit of $3,450. If x represents the price of each ticket sold, which equation could be used to find x?.
solving equations: please help:)
-(x+7)-5= -3x-12+2x
Answer:
x = 3
Step-by-step explanation:
Hello!
Solve for x by isolating the variable
Solve for x- (x + 7) - 5 = -3x - 12 + 2x [tex]\rightarrow[/tex] Distribute-x - 7 - 5 = -3x -12 + 2x [tex]\rightarrow[/tex] Simplify-x - 12 = -3x + 2x [tex]\rightarrow[/tex] Add 3x to both sides2x - 12 = 2x [tex]\rightarrow[/tex] Add 2x4x - 12 = 0 [tex]\rightarrow[/tex] Subtract 124x = 12 [tex]\rightarrow[/tex] Divide by 3x = 3The value of x is 3.
For which domain would f(x) = x be discrete?
Select one:
a.
D = {1, 2, 3, ...}
b.
D={x|0
c.
D = {x|x≥2}
d.
D={all real numbers}
c
in an arithmetic expression
melissa drew a scale drawing of a city. a neighborhood park is 36 inches wide in the drawing. the actual park is 60 yards wide. what is the scale of the drawing?
The scale of the drawing by using proportion is 3 : 5.
According to the given question.
Melissa drew a scale drawing of a city.
The width of the park in the drawing is 36 inches.
And the actual width of the park is 60 yards.
As we know that, a proportion is a fraction of a total amount, and the measures are related using a rule of three.
Therefore, the scale of the drawing by using proportion
= 36iches/ 60 yards
= 3/5
= 3 : 5
Hence, the scale of the drawing by using proportion is 3 : 5.
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find an equation of the line that satisfies the given conditions. through (4, 6), parallel to the x-axis
The equation of line passing through the point (4, 6) and parallel to x axis is y = 6.
According to the given question.
A line which is passes through the point (4, 6).
And also parallel to x-axis.
As we know that, the equation of line parallel to the x-axis, cuts the y-axis at the point (0, b) is y = b.
Since, the line is passing through the point (4, 6) and parallel to x-axis, cuts the y-axis at the point (0, 6).
As per the formula, the equation of line passing through the point (4, 6) and parallel to x axis is y = 6.
Hence, the equation of line passing through the point (4, 6) and parallel to x axis is y = 6.
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`y=2x^{2}+12x+20` find the vertex
Answer: (-3,2)
Step-by-step explanation:
Answer:
(-3, 2)
Step-by-step explanation:
There are two methods on finding the vertex. The one I will be using is the faster version.
y=2x^{2}+12x+20
a=2 b=12 c=20
First use the formula -b/2a.
-(12)/2(2)=
=-12/4=-3
-3 is the x-coordinate.
Plug in -3 into the equation for x.
y=2(-3)^{2}+12(-3)+20
y=2(9)+12(-3)+20
y=18-36+20
y=2
The y-coordinate is 2
Use (x, y) for the vertex.
x=-3
y=2
The vertex is (-3, 2)
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A triangle on a coordinate plane is translated according to the rule T–8, 4(x, y). Which is another way to write this rule?
(x, y) → (x + 4, y – 8)
(x, y) → (x – 4, y – 8)
(x, y) → (x – 8, y + 4)
(x, y) → (x + 8, y – 4)
Another way to write this rule is (x, y) = (x - 8, y + 4)
Which is another way to write this rule?The translation rule is given as:
T–8, 4(x, y).
The above means that
x = x - 8
y = y + 4
Express as a transformation rule
So, we have
(x - 8, y + 4)
Rewrite as:
(x, y) = (x - 8, y + 4)
Hence, another way to write this rule is (x, y) = (x - 8, y + 4)
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