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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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 :)
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]
A farmer sells 8. 5 kilograms of apples and pears at the farmer's market. 3/4 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market? Express your answer in fraction and decimal form. Solve on paper. Then check your work on Zearn. The farmer sold kg or kg of pears
In fraction form, this is 6.375/8.5, or 3/4.In decimal form, this is 0.75.
What is fraction?Fraction is a mathematical expression which represents a part of a whole. It consists of a numerator and a denominator which are separated by a fraction bar. The numerator is the number of parts and the denominator is the total number of parts in the whole. Fractions can be used to represent parts of a whole number or parts of a physical object. Fractions can also be used to express ratios or rates.
To solve on paper, we can use the following equation:
Pears = 8.5 kg - (3/4 x 8.5 kg)
Pears = 8.5 kg - (6.375 kg)
Pears = 2.125 kg
Therefore, the farmer sold 2.125 kg of pears at the farmer's market in fraction form, and 0.75 in decimal form.
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HELPPPPPP PLEASEeeeeeeeeeeeeee
Answer:
-1, 0, 4
Step-by-step explanation:
2f - 8 ≤ 6f + 4
-4f ≤ 12
f ≥ 12/-4 **flip the inequality when you divide by a negative number
f≥ -3
Check all the answers that are ≥ -3
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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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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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
Put 38200 in standard Form
Answer: Thirty-eight thousand two hundred.
Step-by-step explanation: You'd get Thirty-eight thousand two hundred because the standard form is writing out the number using letters. So, we should break this down:
38,000 + 200 is a good strategy to divide big numbers.
So, 38,000 = Thirty-eight thousand
And 200 = two hundred
So, combine it and you get Thirty-eight thousand two hundred or Thirty-eight thousand and two hundred. (it's the same thing)
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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Solve x=[tex]\sqrt{x} b^2-4ac\frac{x}{y} 2a[/tex]
The solutions to the quadratic function y = x² + 4x + 3, using the quadratic formula, are given as follows:
x = -1 and x = -3.
How to solve a quadratic function?The standard definition of a quadratic function is given as follows:
y = ax² + bx + c.
In which the leading coefficient a must assume a value different of zero.
The solutions to the quadratic function ax² + bx + c = 0 are obtained using the quadratic formula, as follows:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
The quadratic function for this problem is defined as follows:
x² + 4x + 3 = 0.
Hence the coefficients are:
a = 1, b = 4, c = 3.
The first solution is:
[tex]x = \frac{-4 - \sqrt{4^2 - 4(1)(3)}}{2} = -3[/tex]
The second solution is:
[tex]x = \frac{-4 + \sqrt{4^2 - 4(1)(3)}}{2} = -1[/tex]
Missing InformationThis problem was incomplete, hence the quadratic formula is used to solve y = x² + 4x + 3, as an example.
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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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when journalizing an accounts payable account what account is debited
a. accounts payable
b. it depends on the transaction
c. cash
d. accounts receivable
How many dimes are in 4.72
Answer: 47
Step-by-step explanation:
4.72 / .1= 47
47
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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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
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.
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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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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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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y=-2x + 11 and y= 4x + 2
(Answer for 100 brainlist!!)
Just solve the x value for the frist equation and the y value for the secound equation
x=-1.5
y=8
the answer is in the picture below
Jane had 27 stickers two weeks ago. Then she bought stickers every day for two weeks. She bought 3 stickers two weeks ago, and on each day after that, Jane bought two more stickers than she had bought on the previous day. How many stickers does Jane have now
Answer:
Jane has 251
Step-by-step explanation:
Stickers Initially = 27 Jane bought stickers on 1st day = 3 Remaining days = 13 Each next day she bought 2 more stickers than the previous day, so: Stickers bought in the last 2 weeks (14 days) = n+(n+2)+(n+2+2)+(n+2+2+2)+.............+(n+2(13))here n =3 So:Stickers bought in the last 2 weeks (14 days) = 3+5+7+9+11+13+15+17+19+21+23+25+27+29Stickers bought in the last 2 weeks (14 days) = 224 At Present Jane has Total Stickers = Stickers Initially+ Stickers bought in the last 2 weeks (14 days)At Present Jane has Total Stickers = 27+224
What are the 3 triangles called?
The types of 3 triangles are called-
equilateral,isosceles, andscalene.Explain the classification of the 3 triangles?Scalene triangle:
The scalene triangle has sides that are all measured differently.In such a triangle, no side will be the same length as any other side.Every interior angle in a scalene triangle is also unique.Isosceles triangle:
The lengths for two of the sides in such an isosceles triangle are equal.The angles that are opposite their equal sides are therefore equal.An isosceles triangle, in other words, has two equal sides with two equal angles.Equilateral triangle:
Each side of an equilateral triangle has an equal length.Each internal angle in this scenario will be 60 degrees in length.An equilateral triangle is often referred as an equiangular triangle since its angles are equal.To know more about the classification of the 3 triangles, here
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Solve the equation −14 - 1 4 (x – 26) = –200 for x.
Hello there!
Answer:
x = 39 2/7
Step-by-step explanation:
-14 - 14(x - 26) = -200
- 14 + 14 - 14(x - 26) = -200 + 14
-14(x - 26) = -186
-14(x - 26)/(-14) = -186/(-14)
x - 26 = 93/7
x - 26 + 26 = 93/7 + 26
x = 275/7
x = 39 2/7
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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Find the measure of angle A.
110°
O 80°
O 105°
O 30°
O100°
14 + 6x
A
3x-3
Answer:
[tex]80^{\circ}[/tex]
Step-by-step explanation:
The interior angles of the triangle are [tex]70^{\circ}, (14+6x)^{\circ}[/tex], and [tex](3x-3)^{\circ}[/tex].
Angles in a triangle add to [tex]180^{\circ}[/tex].
[tex]70+14+6x+3x-3=180 \\ \\ 81+9x=180 \\ \\ 9x=99 \\ \\ x=11[/tex]
So, [tex]m\angle A=14+6(11)=80^{\circ}[/tex].
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
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 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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