To prove that (4x - 5)^2 - 5x(3x - 8) is positive for all values of x, we can start by expanding the expression:
(4x - 5)^2 - 5x(3x - 8) = 16x^2 - 40x + 25 - 15x^2 + 40x = -14x^2 + 80x - 25
Now, we can complete the square to find that this expression is always positive:
-14x^2 + 80x - 25 = (-14x^2 + 80x) - 25
= (-14x^2 + 80x + (80/2)^2 - (80/2)^2) - 25
= (-14x + 40)^2 - 25 - 40^2 + 40^2
= 15^2 - 25
= (15 - 5)(15 + 5)
= 10(20)
= 200
Since this expression is equal to 200, which is a positive number, we can conclude that (4x - 5)^2 - 5x(3x - 8) is positive for all values of x.
Triangle ABC was rotated to form triangle A'B'C'. Triangle A'B'C' was reflected across the x-axis to form Triangle A"B"C".
Which of the following statements correctly describes the relationship between Triangle ABC, Triangle A'B'C', and Triangle A"B"C"? Select all that apply.
Group of answer choices
Triangle ABC has greater angle measurements than Triangle A"B"C".
Triangle ABC is congruent to Triangle A"B"C".
Triangle A'B'C' has greater angle measurements than Triangle A"B"C".
Triangle ABC has greater side lengths than Triangle A"B"C".
Triangle A'B'C' is congruent to Triangle A"B"C".
Therefore , the solution of the given problem of triangle comes out to be ΔA"B"C "≅ ΔABC is congruent.
Explain the triangle.The fact that a triangle has sides or vertices qualifies it as a polygon. It is an elementary geometric form. The name given to a triangle with vertices A, B, & C is Triangle ABC. A singular planes and triangle are obtained in Euclidean geometry when the vertices are not collinear. Any triangle that has three sides and three corners is a polygon.
Here,
Triangle A'B'C' is created by reflecting triangle ABC across the y-axis.
Afterward, it was dilated by a ratio of 1/3 to create triangle A "B"C".
Find the right answer for the triangles ABC and A"B"C."
So,
We are aware that reflection undergoes a rigorous transformation, meaning the shape and size of the original object do not change.
As a result, after reflection, figures always match their pictures.
"ABC," "A'B'C," etc (i)
The process of dilation is flexible. Although the size is changed, the shape is still the same.
Figures after dilatation therefore always resemble their photographs.
ΔA'B'C' ≅ ΔA "B"C" ... (ii)
With I and (ii), we obtain
ΔA"B"C "≅ ΔABC
Similar triangles include ABC and ABC.
As a result, choice A is the right one.
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The population of a city is 5876000 in 1980. By 1990 it increased by 10.8%. In the 1990s it increased a further 4.7%. What was the population in the year 2000?
Answer: I think it's 6816606.576
Step-by-step explanation: Hope this helps?
What is log and example?
Logs are a type of mathematical operation used to solve exponential equations.
Logs are written as log boxes, where b is the base. The base is the number that the logarithm is being calculated concerning. The x is the number that the logarithm is calculated. Logarithms allow us to convert multiplication and division problems into addition and subtraction.
For example, log2 (8) can be calculated by taking the logarithm of 2, which is 0.301029996, and then multiplying it by 8, which is 2.408239965. This means that log2 (8) is equal to 2.408239965.
Another example is log10 (100). This can be calculated by taking the logarithm of 10, which is 1 and then multiplying it by 100, which is 100.
This means that log10 (100) is equal to 100. Logs are an important tool in mathematics and are used in a variety of fields, such as chemistry, engineering, and economics.
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Express the following terms in the exponential form: (2a) 4
Answer:
16a^4
Step-by-step explanation:
Answer:
16a^4
Step-by-step explanation:
The expression (2a)^4 can be written in exponential form as 2^4 * a^4. Using the laws of exponents, we can simplify this to:
2^4 = 2 * 2 * 2 * 2 = 16
a^4 = a * a * a * a
So, (2a)^4 = 16a^4
What is the nature of root of equation 2x^2 5x 7 0?
The nature of the roots of the equation x^2 - 5x + 7 = 0 : no real roots
Consider given quadratic equation: x^2 - 5x + 7 = 0
Comparing given quadratic equation with the standard form of quadratic equation i.e., ax^2 + bx + c = 0
a = 1, b = -5, c = 7
First we find the discriminant:
D = b^2 - 4ac
D = (-5)^2 - 4(1)(7)
D = 25 - 4(7)
D = 25 - 28
D = -3
Since, the discriminant D < 0
Therefore, there are no real roots of this equation.
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Tammy has a rectangular rug with an area of 21 square feet. The rug is 4 feet longer than it is wide. Which equation can be
used to determine the length and the width of the rug?
A 21 - -W² - 4W
B. 21 = 42
C. 21 - W2 + 4w
D. 21 - W2 + 4
The equation to determine the length and the width of the rug is
21 = W² - 4W.
What is a rectangle ?A rectangle is a quadrilateral with four right angles in the Euclidean plane. It may alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.
A quadrilateral is a rectangle.
A rectangle's opposing sides are equal and parallel to one another.
Each vertex of a rectangle has a 90° internal angle.
360° is the total of all interior angles.
The diagonals cut each other in half.
The diagonals are all the same length.
The Pythagorean theorem may be used to determine the length of the diagonals.
A rectangle is also referred to as a parallelogram since its sides are parallel.
While all parallelograms are rectangles, not all rectangles are parallelograms.
The length of the rug is l ft
Then the width of the rug will be l-4 ft
So the are will be l*(l-4) = [tex]l\x^{2} - 4l[/tex]
We know area is 21
so the equation is 21 = [tex]l\x^{2} - 4l[/tex] (Option a)
And after solving the equation the lenght is7m and breadth is 3 m.
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If we remove 11 books from my shelf and multiply the remaining number of books by 12, we will get the same result as of we remove 10 books from the shelf and multiply the remaining number of books by 11. How many books are on my shelf before any are removed?
Answer:
22
Step-by-step explanation:
I timesed 11 by 12 which is 132 and then timesed 10 with 11 which then gave me 110. I then subtracted 132 with 110 which gave me the answer 22. if we remove 11 from the 22 books we then end up with 11. then times it by 12 = 132. then if you subtract 10 of the 22 books then we end up with 12. then times it by 11 which is 132 as well.
What is a midpoint for zero?
The midpoint for zero is (0,0).
The midpoint can be zero. This is dependent on the value of the two points. For two points on a number line on points with values -4, and 4, the midpoint is 0. And for two points such as (-2, 5), and (2, -5), the midpoint is equal to (0, 0).
The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.
A compass and straightedge setup can be used to locate the midpoint of the line segment they determine given two points of interest. By initially building a lens out of circular arcs with equal radii centered at the two endpoints and joining the cusps of the lens, one can determine the midpoint of a line segment immersed in a plane. The midpoint of the segment is then the place where the line joining the cusps intersects the segment.
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A rectangle measures 1 3/4
inches by 3 3/4
inches. What is its area?
please help!
Answer:
6 and 9/16
Step-by-step explanation:
The area of a rectangle can be calculated by multiplying the width and length. So 1 3/4*3 3/4=7/4*15/4=105/16 or 6 and 9/16
Please hurry its timed
By algebra properties and trigonometric formulas, the roots x₁ = 30° + n · 360° and x₂ = 210° + n · 360° are solutions of trigonometric function tan x - √(1 - 2 · tan² x) = 0. (Correct choice: B)
How to determine the solutions of a trigonometric equation
In this problem we find a given trigonometric function, whose solution must be found by combining algebra properties and trigonometric formulas. First, write the entire expression:
tan x - √(1 - 2 · tan² x) = 0
Second, use algebra and root properties:
tan x = √(1 - 2 · tan² x)
tan² x = 1 - 2 · tan² x
3 · tan² x = 1
Third, clear x by algebra properties and inverse trigonometric properties:
tan² x = 1 / 3
tan x = √(1 / 3)
tan x = 1 / √3
tan x = √3 / 3
x = tan⁻¹ (√3 / 3)
x = 30° or x = 210°
Since tangent function has a period of 2π (360°), then the solutions of the trigonometric function is:
x₁ = 30° + n · 360°, x₂ = 210° + n · 360°.
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How many dimes are in 4.72
Answer: 47
Step-by-step explanation:
4.72 / .1= 47
47
Classify each statement about the function f(x)=2x^3+8 as true or false.
The domain of the function is all real numbers.
The domain of the function is all real numbers.
The range of the function is (0, [infinity]).
The y-intercept is (0, 0).
The center of symmetry is (0, 8)
Statement A,B is true rest all statement are false about the given function.
Given the function: [tex]2x^3+8[/tex]
Statement A:
The domain of a function is the set of all possible input values (x-values) for which the function produces a valid output (y-value).
For the function 2x^3 + 8, the domain is all real numbers, which is represented as (-infinity, +infinity).
It is because the expression inside the function, 2x^3, is defined for all real numbers.
so above statement is true.
Statement B:
statement A and B are same so it's also true.
Statement C:
The range of a function is the set of all possible output values (y-values) that the function can produce.
For the function 2x^3 + 8, the range is also all real numbers (-infinity, +infinity)
It is because the function is a polynomial of odd degree (3) and it does not have any restriction on the output value. Since the function does not have any restriction, it can take any real number as an output value and thus the range is all real numbers.
so this statement is false.
Statement D:
The y-intercept of the function 2x^3 + 8 is 8. It is the point at which the graph of the function crosses the y-axis, which occurs when x = 0. So when x = 0, y = 2(0)^3 + 8 = 8.
so this statement if false.
Statement E:
A function has a center of symmetry if it is unchanged (i.e. is symmetric) when reflected across a line or point. The line or point across which the function is symmetric is called the axis of symmetry or center of symmetry.
The function 2x^3 + 8 does not have a center of symmetry. It is because the function is a polynomial of odd degree and it does not have any symmetry. The polynomials of odd degree are not symmetric about any point or line.
So this statement is also false.
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In the figure shown, what is the value of x?
Answer:
Step-by-step explanation:
SHOW HIGH CLARITY IMAGE, BUT USE CONGRUENCE OF TRINALGES AND FIND X BY EQUATING THE GIVEN SIDE I GUESS
IF YES MARK ME BRAINLIEST
What is the angle between the lines 2x 3y =- Z and 6x =- Y =- 4z?
90° is the angle between the lines 2x = 3y = -z and 6x = -y = -2z and explained with directions of ratios as below
Direction ratios of line 2x = 3y = -z which can be mentioned as [tex]\frac{x}{1/2} = \frac{y}{1/3} = \frac{z}{-1}[/tex] hence [tex](\frac{1}{2} , \frac{1}{3} ,-1 )[/tex]
Direction ratios of line 6x = -y = -2z which can be mentioned as
[tex]\frac{x}{1/6} = \frac{y}{-1} =\frac{z}{-1/4}[/tex] hence [tex](\frac{1}{6} , -1 , \frac{-1}{4} )[/tex]
hence the dot product of the direction ratio of two line is
[tex]\frac{1}{2} .\frac{1}{6} + \frac{1}{3} . (-1) + (-1) . \frac{-1}{4}[/tex]
= [tex]\frac{1}{12} -\frac{1}{3} + \frac{1}{4}[/tex]
= 0
hence this shows that angle between the given equations is 90°
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find the measure indicated in each parallelogram
Answer:
Step-by-step explanation:
WX≅VY
VY = 7
CD≅BE
BE = 13
A high school student working part time as a shelf stocker had a gross income of $6675 last year. If his federal tax rate was %10 and his state tax was 3% what was the amount withheld from his Pat last year in federal tax, state tax, and FICA combined?
A. 867. 75
B. 667. 50
C. 200. 25
D. 1378. 39
The total amount withheld from the student's pay last year in federal tax, state tax, and FICA is $667.50 + $201.25 = $868.75
What is percentage?Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the symbol "%" (percent sign). Percentages are used to express how much of something there is in relation to the whole. For example, if a student answers 80% of the questions correctly on a test, it means they answered 80 out of 100 questions correctly.
What is tax?A tax is a financial charge imposed by a government on individuals, businesses, or other entities to raise revenue for government spending. Taxes are typically based on a percentage of income or sales, and can be levied on various forms of income, including wages, salaries, and profits. The purpose of taxation is to fund government programs and services, such as roads, schools, and national defense. Taxes can also be used to redistribute wealth and influence economic behavior.
The amount withheld from the student's pay last year in federal tax is $6675 x 0.1 = $667.50
The amount withheld from the student's pay last year in state tax is $6675 x 0.03 = $201.25
The total amount withheld from the student's pay last year in federal tax, state tax, and FICA is $667.50 + $201.25 = $868.75
So the answer is A. 867.75
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I need serious help !!
================================================
Explanation:
The x and y are placeholders for numbers.
Think of them as boxes so to speak, and we fill each box with a number.
In this case we will plug in x = 6 and y = 2.
The steps are shown below.
[tex]\frac{3\text{x}+4}{\text{y}}\\\\\frac{3*6+4}{2}\\\\\frac{18+4}{2}\\\\\frac{22}{2}\\\\11\\\\[/tex]
The final answer is choice B
-----------
This means,
[tex]\frac{3\text{x}+4}{\text{y}} = 11 \ \text{when} \ \text{x} = 6 \ \text{and y} = 2 \\\\[/tex]
Put another way
[tex](\text{x},\text{y}) = (6,2) \ \text{ is a solution to } \frac{3\text{x}+4}{\text{y}} = 11[/tex]
In a visual sense, the point (6,2) is on the equation of [tex]\frac{3\text{x}+4}{\text{y}} = 11[/tex]
What is the axis of symmetry of the function f x =-( x 9 )( x 21?
The axis of symmetry of the function f(x) = -( x 9 )( x 21) is x = 15.
The axis of symmetry of a parabola is a line that divides the parabola into two exact mirror images. In this case, the parabola is defined by the quadratic function f(x) = -(x-9)(x-21). To find the axis of symmetry, we can take the average of the x-coordinates of the two solutions, which are 9 and 21. The average of 9 and 21 is 15, so the axis of symmetry is x = 15. This means that the parabola is symmetrical about the line x = 15, and the vertex of the parabola is located at the point (15,0).
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Question 1 : (2.3 × 10^4) × (1.5 × 10^-2)
Question 2: (3.6 × 10^-5) ÷ (1.8 × 10²)
The value of the expressions (2.3 × 10⁴) × (1.5 × 10⁻²) and (3.6 × 10⁻⁵) ÷ (1.8 × 10²) will be 345 and 2 × 10⁻⁷, respectively.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expressions are given below.
(2.3 × 10⁴) × (1.5 × 10⁻²) and (3.6 × 10⁻⁵) ÷ (1.8 × 10²)
Simplify the expression (2.3 × 10⁴) × (1.5 × 10⁻²), then the value of the expression will be given as,
⇒ (2.3 × 10⁴) × (1.5 × 10⁻²)
⇒ 345
Simplify the expression (3.6 × 10⁻⁵) ÷ (1.8 × 10²), then the value of the expression will be given as,
⇒ (3.6 × 10⁻⁵) ÷ (1.8 × 10²)
⇒ 2 × 10⁻⁷
The value of the expressions (2.3 × 10⁴) × (1.5 × 10⁻²) and (3.6 × 10⁻⁵) ÷ (1.8 × 10²) will be 345 and 2 × 10⁻⁷, respectively.
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A diagonal of a polyhedron is a line segment connecting two non-adjacent vertices. How many diagonals does a pentagonal prism have
A pentagonal prism have 35 diagonals.
We know tha in a polygon or polyhedron the formula for finding the number of diagonals is: n(n-3)/2,
where n= the number of sides
We find the number of diagonals of a pentagonal prism.
As we know a pentagonal prism has two pentagonal bases like top and bottom and five rectangular sides.
For a pentagonal prism n = 10
So, using above formula the total number of diagonals would be,
d = [10 × (10 - 3)] / 2
d = (10 × 7) / 2
d = 70/2
d = 35
Therefore, the total number of diagonals would be = 35
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On a coordinate plane, a line is drawn from point C to point D. Point C is at (negative 1, 4) and point D is at (2, 0).
Point C has the coordinates (–1, 4) and point D has the coordinates (2, 0). What is the distance between points C and D?
d = StartRoot (x 2 minus x 1) squared + (v 2 minus v 1) squared EndRoot
units
The length of the line is 5 units.
What is distance?The distance between two points is the length of the line joining the two points.
Formula: distance= √(x_2-x_1)²+(y_2-y_1)²
Given that, endpoints are (-1,4) and (2,0) of the line segment.
The length= √(2+1)²+(0-4)²
=5units
Hence, The length of the line is 5 units.
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Work out the area of this shape. Give your answer
in cm².
4 cm
4 cm
10 cm
Answer:
48cm^2
Step-by-step explanation:
Rectangle=LxW
Triangle=bh/2
Rectangle: 10x4=40cm^2
Triangle: 4x4=16/2=8cm^2
40+8=48cm^2
Hope this helps :)
How do you verify inverse?
To verify the inverse we can use Horizontal Line Test.
Suppose F is a function.
F does not have an inverse if any horizontal line crosses the graph of f more than once. If no horizontal line crosses the graph of F more than once, then F does have an inverse. In mathematics, having an inverse is a very significant quality, and it has a name.
If and only if a function f has an inverse, then it is one-to-one. The following definition, which is also the one that is most frequently used, is equivalent. If f(a) = f(b) implies a = b for all a and b in its domain, then a function f is one-to-one.
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Angie puts 1/3 of a gallon of gas in her lawn mower. She can mow the lawn 4 times before
she needs to refill it How many gallons of gas does it take to mow the lawn once? How
many times can she mow the lawn with one gallon of gas?
( please explain how u got your answer )
Answer:
1/12 gallon per mowing12 mowings per gallonStep-by-step explanation:
Given that Angie can mow her lawn 4 times using 1/3 gallon of gas, you want to know how much gas is required for each mowing, and how many times Angie can mow on one gallon of gas.
Gallons per mowingTo find the number of gallons required for each mowing of the lawn, divide the number of gallons by the number of mowings:
(1/3 gal)/(4 mowings) = 1/(3·4) gal/mowing = 1/12 gal/mowing
It takes 1/12 gallon to mow the lawn once.
Mowings per gallonThe reciprocal of this value has the reciprocal units.
1/(1/12 gal/mowing) = 12 mowings/gal
Angie can mow the lawn 12 times with one gallon of gas.
__
Additional comment
It often proves useful to keep the units with the numbers when working rate problems. This can eliminate a lot of mistakes. The units are treated as you would treat a variable.
slope of a line parallel to the line whose equation is x - 2y = -8
Answer:
Step-by-step explanation:
slope is the coefficient of x when the coeficient of y is 1.
we need change the form.
2y=x+8
y=[tex]\frac{1}{2}[/tex]x+4
so, the slope of a line parallel to the line is 1/2
What is the opposite reciprocal of 0/6
Answer: The reciprocal of a number is defined as 1 divided by that number. The opposite of a number is the number with the opposite sign. Therefore, the opposite reciprocal of a number is equal to the reciprocal of the opposite of that number.
In this case, the opposite reciprocal of 0/6 is the reciprocal of the opposite of 0/6. The opposite of 0/6 is 0/-6, which is equal to -0/6. The reciprocal of -0/6 is 1/(-0/6) = -6/0.
However, division by 0 is not defined, so it is not possible to find the reciprocal of -0/6. Therefore, the opposite reciprocal of 0/6 is undefined.
Step-by-step explanation:
Answer:
there is no reciprocal for 0/6
Step-by-step explanation:
Which statement about the offer are true ? Check all that apply
Answer: The first and third options are correct.
Step-by-step explanation:
The length, breadth and height of a cuboidal tank is 4m, 2m and 0.75 m respectively. What is the capacity of the tank
The cuboidal tank has a volume of [tex]6m^3[/tex] with dimensions of 4 m in length, 2 m in width, and 0.75 m in height.
How can I determine a cuboidal tank's capacity?The total amount of room or volume that a cuboidal tank can hold is known as its capacity. By multiplying the tank's length, width, and height collectively, it is determined.
The tank in this instance measures 4 metres long, 2 metres wide, and 0.75 metres high. We must multiply these three parameters collectively to determine the tank's capacity:
[tex]4m * 2m * 0.75m = 6m^3[/tex]
The tank can therefore hold [tex]6m^3[/tex] of liquid.
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Describe a real-life situation involving markup, markdown, or discount that the equation y=x+0.4x could represent.
the retail price y in dollars for an item with the original cost and a markup of 40%
O the discount price y in dollars for an item with the original cost and a discount of 40%
O the sale price y in dollars of an item with the original cost and a markdown of 40%
O the discount amount y in dollars for an item with the original cost and a discount of 40%
The equation y = x + 0.4x is the retail price y in dollars for an item with the original cost and a markup of 40% .
What is equation ?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.
y = x + 0.4x {markup ↑}y = x - 0.4x {markdown , discount ↓}y = 0.4xSo, we choose the first equation.
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Which figure could be the result of dilating the trapezoid with a scale factor between 0 and 1?
10
9-
8
7
6
5
4
$
0
7
6
5
4
3
1 2 3 4 5 6 7 8 9
O
x
घ
A trapezoid will appear smaller than the original trapezoid if it is dilated with a scale factor between 0 and 1.
What shape is a trapezoid?An open, flat shape with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium. A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel.
What are a trapezoid's three characteristics?What three characteristics do trapezoids have? An isosceles trapezoid has equal base angles and diagonals. The midpoints of the two opposing sides are parallel to the point where the diagonals intersect. An isosceles trapezoid has opposite sides that are congruent to one another or have the same length.
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