Determining the slopes of each side, we get the slope of [tex]\overline{AB}[/tex] is [tex]2[/tex], the slope of [tex]\overline{BC}[/tex] is -1/2, the slope of [tex]\overline{CD}[/tex] is 2, and the slope of [tex]\overline{AD}[/tex] is -1/2. Since the slopes of sides AB and CD and BC and AD are equal, it follows that [tex]\overline{AB} \parallel \overline{CD}[/tex] and [tex]\overline{BC} \parallel \overline{AD}[/tex]. Thus, ABCD is a parallelogram because it is a quadrilateral with two pairs of opposite congruent sides. However, we can also note that the slope of side AB is the negative reciprocal of that of sides BC, and thus [tex]\overline{AB} \perp \overline{BC}[/tex]. Using the fact that perpendicular lines form right angles, we can conclude that [tex]\angle ABC[/tex] is a right angle, and since ABCD is thus a parallelogram with a right angle, it must also be a rectangle.
Answer:
Answers will vary based on the method used, but the final slope-intercept form of the equation of AB↔ will be the same.Let the equation of AB↔ in slope-intercept form be y=mx+d, where m is the slope and d is the y-intercept.The coordinates of points A and B are (1, 1) and (5, 3), respectively, so the slope of AB↔ is m=yB−yAxB−xA=24=0.5.Substitute the value of m back in the equation:y = 0.5x + d.Substitute the coordinate of point A (1, 1) in the equation above, and solve for d: 1 = 0.5 + dd = 0.5.Therefore, the equation of AB↔ is y = 0.5x + 0.5. To check whether C lies on AB↔ substitute the x-coordinate of C into the right side of the equation: 0.5 (2.6) + 0.5 = 1.8.The result is equal to the y-coordinate of C. Thus, C satisfies the equation of AB↔ which means that C lies on AB↔.
Step-by-step explanation:
I did it
Which of the following graphs represents a linear relationship between x and y?
The third one will represent a linear relationship between x and y.
What is a linear relationship?
A linear relationship is any relationship between two variables that creates a line when graphed in the xy-plane.
Linear equations can be used to represent the relationship between two variables, most commonly x and y. To form the simplest linear relationship, we can make our two variables equal:
y=x
By plugging numbers into the equation, we can find some relative values of
x and y.
0 0
1 1
2 2
3 3
If we plot those points in the xy-plane, we create a line.
Now,
For the given graphs only the third one shows a straight line made from equations.
Hence, It represents the linear relationship between x and y.
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What is the rule for Exponent 1?
The rule for any number raised to the power of 1 is that the number remains unchanged.
Mathematically, this can be written as: a^1 = a where "a" is the base number. The rule for a number raised to the power of 1, is also known as the exponent.
For example, if we take the number 2, and raise it to the power of 1, we would get:
2^1 = 23^1 = 3Key points:
This can be thought of as a shorthand way of writing the number without any changes. It is also the identity property of exponents. It is important to note that this rule applies to any base number, whether it is a whole number, fraction, or even a negative number.In addition to this, we know that any number raised to the power of 0 is 1, this is also known as the identity property for exponents.Learn more about exponents here:
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BRAINLIEST.... PLEASE HELP ASAP *VERY IMPORTANT*
Answer:
[tex]m\angle 1=67^{\circ}[/tex]
Step-by-step explanation:
By the inscribed angle theorem, [tex]m\angle 1=21^{\circ}+46^{\circ}=67^{\circ}[/tex].
Let f(x) = [tex]\sqrt{x^2-2}[/tex] and g(x) = -2f(x+5)
Write a rule for g
g(x)=
The rule for g is g(x) = (-2x - 10)(√(x² - 2)) for the function g(x) = -2f(x+5).
What is function?One way to think of a function is as a rule that assigns or maps each member of a set, x, to the same value, y, known as its image.
x → Function → y
Functions are frequently denoted by a letter, such as f, g, or h. F(x) = x2+ 5 is the formula for the function that squares a number and adds a 3. A function's impact on specific values can be demonstrated using the same idea.
Given that f(x) = √(x² - 2)
And g(x) = -2f(x+5)
Substitute the function f(x) = √(x² - 2) in g(x) = -2f(x+5)
g(x) = -2(√(x² - 2))(x+5)
g(x) = (-2x - 10)(√(x² - 2))
Thus, the rule for g is g(x) = (-2x - 10)(√(x² - 2)) for the function g(x) = -2f(x+5).
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How do you find the domain and range of a FX graph?
we can find out the domain of a given function by looking at the values of real number where the function f(x) i defined
range can be find out by putting the values of x and find out the values of y and y will be your range of a given function f(x)
let us take an example
suppose f(x)= x+1
here function is defined for all real values
therefore domain is real number
and range is also real number because if we take the value of x whatever we will take we get the value of y
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What kind of polynomial is 3x²?
3x² is a second-degree polynomial, also known as a quadratic equation.
A polynomial is a mathematical expression that consists of constants, variables, and exponents. This polynomial can be represented as an equation in the form of ax^2 + bx + c, where a, b, and c are constants, and x is an unknown. In this case, a = 3, b = 0, and c = 0. In this case, the polynomial is 3x², which contains one constant (3) and one variable (x) with an exponent of 2. To calculate the value of this polynomial, we can substitute a value for x and then solve. For example, if x=2, then 3x² = 3x2 = 3(2)2 = 3(4) = 12.
Therefore, when x=2, 3x² = 12.
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There is an equal chance of the pointer stopping at each
area of the game spinner below.
What is the theoretical probability of spinning the pointer and having it stop on a green area
A. 0.125
B. 0.25
C. 1.00
D. 0.50
Answer:
B. 0.25
Step-by-step explanation:
There are 8 total pieces.
2 of them are green.
that makes it a 2/8 chance it will land on green.
2/8 = 1/4
1/4 = 0.25
Answer:
B. 0.25
Step-by-step explanation:
There are 8 possible landing areas, all with equal size.
There are 2 green area.
p(event) = (number of desired outcomes)/(number of total outcomes)
The desired outcome is landing on green. There are 2 desired outcomes.
The total number of possible outcomes is 8.
p(green) = 2/8 = 1/4 = 0.25
Answer: B. 0.25
pls helppppppppppppppppppp
Answer: look it up
Step-by-step explanation:
Assuming the denominator does not equal zero. Simplify the expression
Consider that the denominator is not zero. The formula that results from simplifying will equal -n-5/2n(1+3n).
The denominator does not equal zero?A fraction is divided by multiplying its reciprocal:
6n²-23n+7/8n3-28n2.
2n²-10n/1-9n²
Factoring the phrase: 6n²-23n+7/4n²(2n-7). 2n(n-5)/1-9n²)
A2-b2=(a+b)(a-b) (3n-1) (2n-7)/4n² can be used to factor the expression (2n-7).
2n(n-5)/(1+3n)(1-3n)
By eliminating the most prevalent element, reduce the proportion to its lowest term. 3n-1/4n²
2n(n-5)/(1+3n)(1-3n)
Purge the expression of all except the lowest word Write 1/2n as a single fraction: -n-5/2n(1+3n)\s-n-5/2n(1+3n).
In general, a fraction with a zero denominator cannot have a single value given to it; therefore, the value is left undefined.
Any definitional attempt results in a contradiction, which is why the outcome of a division by zero is not defined. a=r*b. r*0=a. (1) However, r*0=0 for any r, hence unless a=0, there is no solution to the problem (1).
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·
a right triangle that has a base of 9 and a height of 16
Que knows that the required hypotenuse of the given right triangle is 18.35 units from the Pythagorean theorem.
What is the Pythagorean theorem?To determine the undiscovered side of a right-angled triangle, utilize the Pythagoras theorem.
The hypotenuse (third side) of a right-angled triangle, for instance, can be determined using the formula c2 = a2 + b2, where 'c' stands for the hypotenuse and 'a' and 'b' are the two legs.
So, we have:
Height of 6 and bas of 9 units of the right triangle.
Pythagorean formula:
c=√a²+b²
Now, insert values and calculate as follows:
c = √a²+b²
c = √9²+16²
c = 18.35 units
Therefore, we know that the required hypotenuse of the given right triangle is 18.35 units from the Pythagorean theorem.
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Complete question:
A right triangle has a base of 9 and a height of 16. Calculate hypotenuse.
How is 8 to the power of 0?
Answer:
One
Step-by-step explanation: Anything that has the exponent of 0 will always be 1
help!
is this correct?
Answer: No, the correct answer is 125/100
Step-by-step explanation:
When adding fractions together the denominator must always be the same and stay the same when added together.
Write an exponential function f so that the slope of a line from the point (0, f(0)) to the point (2, f(2)) is equal to 12.
The expression of an exponential function f that has a slope of 12 of a line from the point (0, f(0)) to the point (2, f(2)) is the exponential function;
f(x) = 3·3ˣWhat is an exponential function?An exponential function is a function that includes the argument as an exponent, index or power of a constant.
The points on the function are; (0, f(0)), and (2, f(2))
The required slope between the points x = 0, and x = 2 is 12
Therefore;
(f(2) - f(0))/(2 - 0) = 12
f(2) - f(0) = 12 × (2 - 0) = 24
The
The exponential function can be presented in the form; f(x) = a·bˣ
When x = 0, we get; f(0) = a·b⁰ = a
When x = 2, we get; f(2) = a·b²
f(2) - f(0) = a·b² - a = 24
a·(b² - 1) = 24
Let a = 3, and b = 3, we get;
3 × (3² - 1) = 24
Therefore, possible values of a and b are; a = 3, and b = 3
The exponential function is therefore;
f(x) = 3 × 3ˣThe slope of the line that extends from the point (0, f(0)), to the point (2, f(2), is therefore;
(f(2) - f(0))/(2 - 0) = (3 × 3² - 3 × 3⁰)/(2 - 0) = 12Learn more on exponential functions here: https://brainly.com/question/15662160
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what is 9 + 5 equals to?
Answer: 34
Step-by-step explanation:
Answer: 14
Step-by-step explanation:
What does n² mean in maths?
[tex]\displaystyle n\hat A[/tex] is the number of squares of arrays present.
An arrangement of objects, images, or numbers in rows and columns is called an array. Arrays are a convenient representation of the concept of multiplication. This array has 4 rows and 3 columns. This can also be described as a 4 x 3 array. Arrays are a way of representing multiplication and division using rows and columns. Rows represent the number of groups. The columns represent the number of each group or the size of each group. The number 24 can be represented as a 6-by-4 array (6-by-4) because 6-by-4 = 24. It can also be represented as a 2 by 12 array, since 2 by 12 = 24.
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Find the dimensions of a rectangle whose width is 6 miles less than its length, and whose area is 72 square miles.
Answer:
Dimensions are 12 , 6
Step-by-step explanation:
Forming algebraic equations and solving:Let the length be 'x' miles.
width = (x - 6) miles
Area of a rectangle = length * width
x *(x -6) = 72 square miles
x*x - x *6 = 72
x² - 6x -72 = 0
Sum = -6
Product = -72
Factors = -12 , 6 { -12 * 6 = -72 & -12 + 6 = -6}
x² - 12x + 6x - 72 = 0 {Rewrite the middle term using the factors}
x(x - 12) +6(x - 12)=0
(x -12)(x + 6) =0
x - 12 = 0 ;
x = 12
{x + 6= 0 is ignored, as dimensions will not have negative value}
length = 12 miles
widht = 12 - 6 = 6 miles
Solve the compound inequality
M - 3<6 and m + 2>4
The solution to the inequality is m ∈ (2, 9)
What is the Compound inequality?
A compound inequality is an inequality that contains two or more conditions that must be met simultaneously. It is formed by connecting two or more simple inequalities using the words "and" or "or". The word "and" indicates that all the conditions must be true at the same time, while the word "or" indicates that at least one of the conditions must be true.
The compound inequality "m - 3 < 6 and m + 2 > 4" can be read as "m is less than 6 and 3 less than m and m is greater than 4 and m is 2 more than 4".
To solve the inequality, we can start by isolating the variable on one side of the inequality sign.
m - 3 < 6 => m < 9
m + 2 > 4 => m > 2
The solution is the set of all m that satisfies both inequalities, which is the intersection of the solution sets of each inequality. In this case, it is the set of all real numbers m such that 2 < m < 9.
Hence, the solution to the inequality is m ∈ (2, 9)
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Identify the value of y.
Therefore , the solution of the given problem of quadratic equation comes out to be the value of y = 12.
Define quadratic equation.x2+ cx + z = 0 is a quadratic problem with one variable in quadratic algebra. a 0. According to the Underpinning Theorem of Algebra, this quadratic's second order ensures that it has at least one solution. The solutions could be simple or complex. Four variables make up a quadratic equation. This implies that at least one word should be squared. "ax2 + bx + c = 0" is one of the basic formulae for solving quadratic equations, where the numbers or integers a, b, and c stand in for the undefined variable "X".
Here,
Given : A right angled triangle with dimension of y, y+3 and 9
To find the value of y :
We use pythagoras theorem :
So,
=> (y+3)² = y²+9²
=> y² + 9 + 6y = y²+ 81
=> y² - y² + 6y = 81-9
=> 6y =72
=>y =72/6
=>y=12
Therefore , the solution of the given problem of quadratic equation comes out to be the value of y = 12.
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PLEASEEE HELPP Are the expressions below sometimes, always, or never equivalent? Explain how you know. 12(8y - 16k) and 16(2y - 4k)
No, These both expressions are not equal to each other.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expressions are,
⇒ 12(8y - 16k) and 16(2y - 4k)
Now, We can check both expressions as;
⇒ 12 (8y - 16k)
⇒ 12 × 8 (y - 2k)
⇒ 96 (y - 2k)
⇒ 16 (2y - 4k)
⇒ 16 × 2 (y - 2k)
⇒ 32 (y - 2k)
Thus, We get;
⇒ 96 (y - 2k) ≠ 32 (y - 2k)
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Help me please (geometry)
Answer:
x = 3
y = 4
Step-by-step explanation:
The opposite sides of a parallelogram are always equal.
From the above statement, we get two equations-
[tex]4x+6 = 7x-3[/tex] and [tex]4y-3=3y+1[/tex]
Solving for x:
[tex]4x+6=7x-3\\6=3x-3\\9=3x\\3=x[/tex]
Solving for y:
[tex]4y-3=3y+1\\y-3=1\\y=4[/tex]
Create math problems with the words : increased, sum, found, collected, earned, and spent (for addition)
Insert parentheses to make the equation true 5-3-1+6^2=50
The equation is true when putting parentheses. The equation becomes:
(5 - 3)(-1 + 6)² = 50.
What is an equation?
In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
The given equation is 5 - 3 - 1 + 6² = 50.
Here we need two parentheses.
Since 50 can be written as 50 = 25 × 2 = 5² × 2
Now 2 can be written as (5-3) and 5 can be written as (-1+6).
Now put the parentheses:
(5 - 3)(- 1 + 6)²
= 50
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#6: Emma takes care of dogs while their owners are on vacation. She charges $35 for each of the first 3 days she takes care of a dog and $25 for each day thereafter. Which equation can be used to find the total cost (y), in dollars, to have Emma take care of a dog for x days, where x is a whole number greater than 3? A.y = 75 + 35(x - 3) B.y = 105 + 25(x - 3) C.y = 25 + 35x D.y = 35 + 25x +
The requried equation used to find the total cost of care of dogs is given as, 1. y = 35x for 0 ≤ x ≤3 2. y = 35 + 25x for 3 < x. None of the op[tions are correct.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Emma takes care of dogs while their owners are on vacation. She charges $35 for each of the first 3 days she takes care of a dog and $25 for each day thereafter.
Two equations will be formed,
1. y = 35x for 0 ≤ x ≤3
2. y = 35 + 25x for 3 < x
Thus, the requried equation used to find the total cost of care of dogs is given as, 1. y = 35x for 0 ≤ x ≤3 2. y = 35 + 25x for 3 < x. None of the op[tions are correct.
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What is the absolute value of a complex number called?
The absolute value (Modulus) of a number is the distance of the number from zero.
Absolute value is always acting for in the modulus(|z|) and its value is always positive.
So, the absolute value of the complex number is Z = a + ib is |z| = √ (a2 + b2).
Now, the absolute value of the complex number is the positive square root of the sum of the square of the real part and the square of the unreal part, i.e.,
The complex number is defined as the number in the form a+ib, where a is the real part while ib is the unreal part of the complex number in which i is known as iota and b is a real number.
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Write a linear function containing the following parts: (0,-8) and (2,0)
y = 4x - 8 is linear equation .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Linear equations with two variables, and so forth, are what the equation is known as if it has two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and x + y = 2. Another example is 3x - y + z = 3.
(0,-8) and (2,0)
m = 0 - (-8)/2 - 0
= 8/2 = 4
y - (-8) = 4 ( x - 0)
y + 8 = 4x
y = 4x - 8
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If it takes 1 4 cup of flour to make 1 6 of a cake, how many cups of flour are needed to make a whole cake?
Answer:
1 1/2 cups of flour.
Step-by-step explanation:
You can work this as a proportion:
1/4 cup → 1/6 of a cake
x cups → 1 cake
Cross-multiply.
(1/4 cup)(1 cake) = (x cups)(1/6 cake)
Solve for x.
x = 6(1/4) = 1 1/2 cups
Maya wants to be able to take a series of four triangles and place them in a mobile design where all four triangles are attached at one point and are balanced so that they stay horizontal. Which statement best describes where she should attach each triangle?
A) Where the medians intersect
B) where the altitudes intersect
C) where perpendicular bisectors intersect
D) at any vortex
PLS I WILL GIVE BRAINLIEST
The statement best describes where she should attach each triangle is perpendicular bisectors intersect.
What is triangle?When perpendicular bisectors overlap, the sentence best indicates where she should join each triangle. A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees.
Here,
When perpendicular bisectors overlap, the sentence best indicates where she should join each triangle.
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What are prime multiples of 3?
Prime multiples of number 3 is number 3 itself as other multiples of three are representing composite numbers.
As given in the question,
Given number is equal to :
3
Multiples are those numbers which we get when we multiply the given number by any other integer.
Multiples of three are equal to :
3 × 1 = 3
3 × 2 = 6
3 × 3 = 9
3 × 4 = 12
3 × 5 = 15
............... so on.
When we multiple 'n' by three we get 3n.
All other multiples have more than two factors that is one , three , and at least number itself.
So other multiples of three are composite numbers.
Prime multiples has only two factors one and number itself.
3 represents the prime multiple.
Therefore, three is the only number which is the prime multiple of 3.
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What should be subtracted from x2 y2 2xy to get x2 y2 algebraic expressions?
To get the simplified form of the algebraic expression x²+ y², we need to subtract -2xy from the expression x² +y²-2xy.
To subtract 2xy from the expression x² + y² - 2xy and get x² + y², you can simply remove the -2xy term. This is because subtracting 2xy is the same as adding -2xy, which is the same as negating 2xy and keeping it in the same position.
The reason for this is that subtracting a number is the same as adding its opposite. In this case, -2xy is the opposite of 2xy, so when you subtract 2xy, you are effectively adding -2xy.
Therefore, x² + y² - 2xy and x² + y² are equivalent expressions, since they both represent the same mathematical value.
In mathematical terms:
x² +y²-2xy = x²+ y² +2xy
In other words, the subtraction of 2xy is a commutative operation and the order of the terms does not matter. If you add or subtract the same value, it does not change the final result.
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What should be subtracted from x² +y²-2xy to get x²+ y² algebraic expressions?
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Miriam is calculating the budget for her upcoming vacation. She plans to distribute the budget into three categories: lodging, food/dining, and sightseeing. Miriam wants to follow the guidelines below when calculating the budget:
● 2/7 (in fraction) of the budget will be spent on lodging
● The amount spent on sightseeing will be twice as much as the amount spent on lodging.
What fraction of Miriam’s budget would be left for food/dining if Miriam follows these guidelines?
The fraction of Miriam’s budget would be left for food/dining if Miriam follows these guidelines is 1/7.
How to compute the fraction?The fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.
From the information, 2/7 of the budget will be spent on lodging.
The amount spent on sightseeing will be twice as much as the amount spent on lodging. This will be:
= 2 × 2/7
= 4/7
The fraction of Miriam’s budget would be left for food/dining if Miriam follows these guidelines will be:
= 1 - (2/7 + 4/7)
= 1/7
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