A = -x² + 20 is a quadratic function in standard form that depicts each area as a function of width.
What makes anything a quadratic function?A quadratic in mathematics is a particular kind of problem that involves squaring, or multiplying a variable by itself. This terminology comes from the fact that a square's area equals the product of its side length and itself. Quadratum, the Greek word meaning square, is where the word "quadratic" originates.
Briefing:Now, give the x and y labels to the two sides.
We are aware that a rectangle's area is;
A = length * width
Thus;
A = xy
Given that she has 40 feet of fencing, the following follows:
y = 0.5(40) - x
y = 20 - x
Consequently, the area in the quadratic function formula is;
A = x(20 - x)
A = 20x - x²
A = -x² + 20
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1) Triangle ABC has vertices A(6,2), B(3,4), and C (2,8). If the triangle is rotated
90° counterclockwise, what are the coordinates of the image A'B'C'?
The coordinates of the image A'B'C are A(-2, 6) B(-3, 4) C(-8, 2)
How do you find the coordinates of a triangle?A specific example of barycentric coordinates for a triangle is referred to as triangular coordinates, and it is also known as a ternary plot or areal coordinates. Triangular coordinates can also refer to any of at least three additional related systems of coordinates in the Euclidean plane.The coordinate geometry formula for the area of a triangle A = (1/2) |x1 1 (y2 2 y3 3) + x2 2 (y3 3 y1 1) + x3 3 (y1 1 y2 2)|, where (x1 1,y1 1), (x2 2,y2 2), and (x3 3,y3 3) are the coordinates of the triangle's vertices, gives the area of a triangle in coordinate geometry.y = mx + c. The points whose coordinates fulfil the equation y = mx + c, on the other hand, always lie on the line with gradient m and y-intercept c.Given data :
Triangle ABC has vertices A(6,2), B(3,4), and C (2,8).
Although I am aware that the coordinates must rotate around the origin, I am unsure of the signs (+ or -).
Consequently, the shape is in the second quadrant of the graph, and the 90-degree angle should be in the fourth quadrant rather than the first (which is 180 degrees anticlockwise) or third (.180 anticlockwise)
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May someone explain this?
m<A = 112.5
m<B = 67.5
m<C = 67.5
m<D = 112.5
Consider the provided information.
The sum of all interior angle of a polygon is: (n-2)*180
Substitute n = 8.
(8-2)*180 = 1080
Thus, the measure of each angle is:
∠B and ∠C are congruent and their sum is 135°
∠B+∠C=135°
∠B=67.5°
Hence, the m angle B and m angle C is 67.5°.
The sum of all angles of a quadrilateral is 360°.
∠A+∠D+∠B+∠C=360°
∠A+∠D=360°-135°
∠A+∠D=225°
∠A and ∠D are congruent and their sum is 225°
∠A+∠D=225°
∠A=∠D=112.5°
Hence, the m angle A and m angle D is 112.5°.
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Name two sets of alternate interior angles
Answer:
1st and 3rd ones.
Step-by-step explanation:
<BAD and <ADE are equal because the transversal connects the two angles on alrenate sides. Also <CBA and <CED are equal, as they are again, alternate and the transversal (the diangonal line) connects them.
question 3 a data analyst is working with the world happiness data in tableau. what tool do they use to select the area on the map representing finland?
Pan tool do the data analyst use to select the area on the map representing Finland.
What is data analyst?
A data analyst is working with the world happiness data in table. To use Pan tool to select the area on the map representing Finland.
A data professional examines data to uncover critical insights about a company's consumers and how the data may be utilized to address problems. They also share this information with corporate executives and other stakeholders.
Pan allows us to shift the map to focus on it or present the areas in the way we wish. Simply pick the Pan Option and move the map around to suit your needs. Alternatively, you may move the map by holding down the Shift key.
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what is 2(x + 4) equivalent to
Answer:
2 x x = 2x
2 x 4 = 4
so 2x + 8 is the answer.
To solve this equation we must expand its terms so that we can then multiply and add.
¿What are the equations?Equations are those mathematical equalities divided between two expressions which are called members and separated by their equal sign, in which known elements and unknown or unknown data appear, related by mathematical operations.
We solve the problem:2 (x + 4)2x + 2 × 42x + 8So, our result of the equation is 2x + 8
¡Hope this helped!
Graph the equation-5y=-6x+15
A.linear
B.quadratic
C.exponential
D.absolute value
The graph of the equation would be linear in nature.
Option (A) is correct.
What is a graph of an equation?
The picture is obtained by plotting all the points of an equation or inequality. If there is only one variable, the graph is on a number line. If there are two variables, the graph is on the coordinate plane. If there are three variables, the graph is in three-dimensional coordinates.
The given equation is
-5y = -6x + 15
Now arrange it properly, we get
6x - 5y = 15
Now draw the graph, we get
Hence, the degree of the equation is 1. so the graph of the equation would be linear in nature.
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brainliest + ten points to first correct answer! word problem.
A high school soccer team has 18 players. There are 16 years, for juniors, four sophomores, and the rest are freshman. What is the ratio of seniors to freshman?
Incomplete question
What is the domain of this function?
Answer:
C) x >= 3
Step-by-step explanation:
The domain of the function is all the x's for this function/graph/equation.
Since you have a graph, it is all the x's where the graph exists. The graph exists from 3 to the right (forever), so x can be everthing 3 and greater.
x >=3
2) AABC and ADEF are shown below. The
m/A=51°and m/F =39°. Is AABC~ADEF?
Fill in the blanks with words from the
word bank then read it to see if it
sounds correct.
the triangles are
because all angles
and the sides are
Word bank: yes, no, maybe, parallel,
vertical angles, corresponding,
complimentary, congruent, right angles,
similar, proportional.
Answer:
Yes, the triangles are similar, because all angles are congruent and the sides are proportional.
Step-by-step explanation:
In similar triangles the corresponding angles have the same measurement. The sum of the interior angles of a triangle is 180. Both triangles have a 90 angle. 180-90 = 90. The other two answer must add to 90.
90 - 51 = 39. So each triangle has a 90, 51 and 39 degree angle.
The sides are also proportional. The scale factor from the smaller triangle to the larger is 2 and if you go the other way the scale factor is 1/2
PLEASE HELP ASAPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer: yes
Step-by-step explanation: there’s a pattern of 2, as we can see from the first equation. 5+2 is 7, so therefore the answer is yes.
The length of the picture is mixed number six and three fourths inches. There should be a length of fraction one half inch of wood on either side of the picture. What is the total length of wood required? a 7 inches b the mixed number seven and three fourths inches c 8 inches d the mixed number eight and one half inches
Answer:
b) The mixed number seven and three fourths inches.
Step-by-step explanation:
Given:
Length of picture = 6³/₄ inMargin either side of the picture = ¹/₂ inTo find the total length of the wood, sum the length of the picture and two margins:
[tex]\implies \sf Total\;length=6\frac{3}{4}+\dfrac{1}{2}+\dfrac{1}{2}[/tex]
Two halves equal 1:
[tex]\implies \sf Total\;length= 6\frac{3}{4}+1[/tex]
When adding a mixed number to a whole number, simply add the whole numbers together:
[tex]\implies \sf Total\;length= (6+1)\frac{3}{4}[/tex]
[tex]\implies \sf Total\;length= 7\frac{3}{4}[/tex]
Therefore, the total length of the wood required is:
7³/₄ inchesinterval notation: -6.5 < x≤ 3
Answer:
(-6.5,3]
Step-by-step explanation:
DETERMINE WHICH ORDERED PAIRS ARE SOLUTIONS TO THE LINEAR INEQUALITY: 2x - 3y < 15
1: ( 2 , 5 )
2: ( -1 , -7 )
3: ( 3 , -4 )
4: ( 0 , 0 )
The two ordered pairs that are solutions of the inequality are:
( 2 , 5 ) and ( 0 , 0 )
Which ordered pairs are solutions of the inequality?Here we have the linear inequality:
2x - 3y < 15
To check which ordered pairs are solutions, we just need to evaluate these points on the inequality and see if it becomes true or not.
For example, with the first pair (2, 5) we will get:
2*2 - 3*5 < 15
4 - 15 < 15
-11 < 15
This is true, so (2, 5) is a solution.
The other solution is the fourth option (0, 0), so we get:
2*0 - 3*0 < 15
0 < 15
(0, 0) is also a solution.
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Match each of the expressions to the right point.
Match each of the expressions to the right point:
[tex]-\sqrt{18}[/tex] = c
[tex]-\frac{17}{3}[/tex] = b
[tex]-2\pi[/tex] = a
Answer:
Given below in the picture
I hope my answer helps you.
You have $3456 in your account. You just earn interest for this period. You deposited $67 into your account from a yard sale you did. You withdrew some cash to buy a small tv for your kitchen. The Tv was listed for $155 and had a discount of 11% and a sales tax of 6% In the end you have a balance of $3618. What percent interest did you earn this period on your account?
Answer:
$7307
Step-by-step explanation:
you need to add them together okay got.
What is the minimum temperature?
STEM AND LEAF
I will appreciate your help!!
7) The minimum temperature is 31⁰F. So, the answer is option B.
What is stem and leaf plot?The frequency of various types of values can be easily observed using a stem and leaf plot, also known as a stem and leaf diagram. This graph displays numerical data that is arranged in chronological order. There is a stem and a leaf for each piece of data.
Each first or second digit of the data value is divided into a stem, and the last digit is represented by a leaf, in a stem and leaf plot, which is represented by a particular table. The stem and leaf plot key is the "|" symbol that is used to indicate the values of the stem and the leaf. In the case of 46, the stem is 4 and the leaf is 6.
7) The minimum value in the stem is 3
And the minimum value in the leaf is 1
So, according to the given key 4|3=43°F
Here | denotes the key symbol.
So, in this solution the minimum value of stem is 3 and the minimum value of leaf is 1
Therefore, it must be 3|1
Hence, from the given key
This can be written as 31⁰F
Therefore, the answer is option B.
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What is the area of AUVW?
-10 -8
-6
W
-4
V
2
104
B
56
2
0
2 $
-6
-8
-10
U
A
6
6
8
00
10
The area of ΔUVW is 21 units.
What is the area of the triangle?
The total area bounded by a triangle's three sides is referred to as the triangle's area. In essence, it is equal to 1/2 of the base times the height, or A = 1/2 b x h. As a result, we need to know the triangular polygon's base (b) and height (h) in order to calculate its area.
From given figure we can see that WV is the height of the triangle and WU is the base.
W = (-3, 6), V = (-3, -8) and U = (0, 6).
To find the distance WV and WU by using the distance formula.
[tex]d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
So,
[tex]WV = \sqrt{(-3+3)^2 +(-8-6)^2} = \sqrt{(-14)^2} = 14\\ WU = \sqrt{((0+3)^2+(6-6)^2} = \sqrt{3^2} = 3[/tex]
Hence, the height is 14 units and the base is 3 units.
⇒
Area of triangle = 1/2 x base x height
= 1/2 x 3 x 14
Area of triangle = 21 units
Hence, the area of ΔUVW is 21 units.
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Fred is playing tennis. For every 2 of his serves that land in, 3 serves land out. If he hit 22 serves in, how many serves landed out?
pls solve with solution(s)^^
1.) 2.25 divided by 2.5 =
2.) 35 divided by 0.05 =
3.) 45 divided by 0.15 =
4.) 630.21 divided by 0.07 =
5.) 0.29 divided by 9.28 =
The solutions for the given division are explained below:
What is meant by division?One of the four fundamental operations of arithmetic, or how to mix numbers to create new ones, is division. Addition, subtraction, and multiplication are the other operations.
In its most basic form, the division of two natural numbers involves counting the instances in which one number is contained inside another, among other possible applications. It is not required that this number be an integer. When two natural numbers are divided with a remainder, or in the Euclidean method, the result is an integer quotient, or the number of times the second number is entirely included in the first, and a remainder, or the portion of the first number.
1) 2.25/2.5=0.9
2) 35/0.05=700
3) 45/0.15=300
4) 630.21/0.07=9003
5) 0.29/9.28=0.03125
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cos theta = 3/5 and sin theta < 0. Identify the quadrant of the terminal side of theta and
find sin theta
The angle is in 4th quadrant and the value of [tex]sin\theta[/tex] is -(4/5).
What is Trigonometry ?One of the most significant areas of mathematics, trigonometry has a wide range of applications. The study of the connection between the sides and angles of the right-angle triangle is essentially the focus of the field of mathematics known as "trigonometry." Therefore, employing trigonometric formulae, functions, or trigonometric identities can be helpful in determining the missing or unknown angles or sides of a right triangle. Angles in trigonometry can be expressed as either degrees or radians.
There are two other sub-branch classifications for trigonometry. The two varieties of trigonometry are as follows:
Plane TrigonometrySpherical TrigonometryEverything is normal in Quadrant I, and Sine, Cosine, and Tangent are all positive.
However, the x direction is negative and the cosine and tangent become negative in Quadrant II.
Sine and cosine have negative values in Quadrant III.
Sine and tangent are negative in Quadrant IV.
since,
[tex]cos\theta = 3/5 (+ve)\\\ sin\theta\ is\ ( -ve)[/tex].
So the angle is in 4th Quadrant.
we know,
[tex]sin^{2}\theta + cos^{2}\theta = 1[/tex]
⇒ [tex]sin^{2}\theta = 1 - (\frac{3}{5}) ^{2}[/tex]
⇒[tex]sin^{2}\theta = 1 - \frac{9}{25} = \frac{16}{25}[/tex]
⇒ [tex]sin\theta = -\frac{4}{5}[/tex] (since The angle is in 4th Quadrant)
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The sum of three consecutive integers is 42. Which of the equations could represent this relationship? Select the two correct answers. x + (x + 1) + (x + 2) = 42 x + (x + 2) + (x + 4) = 42 (x minus 1) + x + (x + 1) = 42 (x minus 2) + x + (x + 2) = 42 x + 2 x + 3 x = 42
There are two ways to represent this equation: "x + (x + 1) + (x + 2) = 42" and "(x minus 1) + x + (x + 1) = 42".
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 phrase with two equal sides and an equal sign is called an equation. An example of an equation is 4 + 6 = 10.
Here,
There are 2 ways,
x+(x+1)+(x+2)=42
(x-1)+x+(x+1)=42
This equation can be written as "x + (x + 1) + (x + 2) = 42" or "(x minus 1) + x + (x + 1) = 42," respectively.
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Graph the linear equation y = 2x + 1.
Can someone help with this and teach me how?
432x486
209952 is the value of 432x486
What is Multiplication?Multiplication is a method of finding the product of two or more numbers
We need to multiply 432 and 486
Steps to follow to find this
1. Line up both your numbers with one on top of the other.
2.Make sure that the places match up for the ones, tens, and hundreds
3. Multiply the top number by the last digit of the second number – the 'ones' unit.
432
×486
___________
2592
3456+
1728++
_____________
209952
Hence, 209952 is the value of 432x486
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Pythagorean Theorem On Coordinate Systems-Independent Worksheet
Find the distance between all the points listed below
Help me people please
Answer: The distance between the points (3, 4) and (0, 0) is 5.
Step-by-step explanation: The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem can be used to find the distance between two points in a coordinate system.
To find the distance between two points in a coordinate system, you can use the following steps:
Identify the coordinates of the two points.
Calculate the difference between the x-coordinates and the y-coordinates of the two points.
Use the Pythagorean Theorem to find the distance between the two points.
For example, to find the distance between the points (3, 4) and (0, 0), you would do the following:
Identify the coordinates of the two points: (3, 4) and (0, 0).
Calculate the difference between the x-coordinates and the y-coordinates of the two points: 3 - 0 = 3 for the x-coordinates and 4 - 0 = 4 for the y-coordinates.
Use the Pythagorean Theorem to find the distance between the two points: the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides, so the distance between the points is equal to the square root of 3^2 + 4^2 = 9 + 16 = 25 = 5.
Therefore, the distance between the points (3, 4) and (0, 0) is 5.
Simplify the expression: 5x + 8 – 13y – 4x – 18 + 16y A. x + 3y – 10 B. x – 3y + 10 C. 3y + 10 D. x – 3y
Answer:
(A) x + 3y - 10
Step-by-step explanation:
Algebraic ExpressionsThis Questions tests on the concept of solving algebraic expressions.
Eg. 7x + 4y + 3y + 9x = 16x + 7y
(Note that BODMAS rule applies to algebraic expressions as well.)
SolutionGiven from the question:
5x + 8 - 13y - 4x - 18 + 16y
= 5x - 4x - 13y + 16y + 8 - 18 (Regroup the terms)
= x + 3y - 10 (A)
below.
Enter your answer in the box below.
5432
2 3 4 5
Answer: 1/-4
Step-by-step explanation:
Find your initial y and x points (-2y and 0x) and then find another point that is equivalent (-1y and -4x) and use m=rise/run = y2-y1/x2/x1 to get your answer of 1/-4
EXERCISE 12.1 There are 20 girls and 15 boys in a class. (a) What is the ratio of number of girls to the number of boys? (b) What is the ratio of number of girls to the total number of students in the class?
Answer:
(a) 4 : 3
(b) 4 : 7
Step-by-step explanation:
a)
20:15
divide both by the HCF which is 5
4:3
b) 20 + 15 = 35
20 : 35
divide both by HCF which is 5
4:7
PLEASE HELPPPP brainiest answer will be marked.
35/12 is the value of tanZ
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Tanz is also given by ratio of sinz and cosz
The tangent formula for a right-angled triangle can be defined as the ratio of the opposite side of a triangle to the adjacent side.
tanz=opposite side/adjacent side
tanz=xy/yz
=35/12
Hence, 35/12 is the value of tanZ
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What’s the value of r in the equation -4/3(r+3)= -2
Answer:
-4 = -6(r+3)
r+3 = 2/3
r = -1/2/3
What is the equation of the line that passes through the point (-1,-5) and has a slope of 1?
Answer:
y=x-4
Step-by-step explanation:
if the slope is 1, the y intercept is -4
What is the equation of the line that passes through the point (-1,-5) and has a slope of 1?
The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.
Since the line passes through the point (-1,-5) and has a slope of 1, we can substitute these values into the equation to solve for the y-intercept. We get:
y = 1x + b
(-5) = 1(-1) + b
-5 = -1 + b
-4 = b
Therefore, the equation of the line that passes through the point (-1,-5) and has a slope of 1 is y = 1x - 4.