When triangles are congruent, their corresponding sides and angles are the same. Hence in congruent triangles △DEF and △MNO, side DF is congruent to side MN, thus option B) DE≅MN is the correct answer.
Explanation:In the case of congruent triangles, the corresponding sides and angles are essentially the same. Therefore, we must match up the corresponding sides. A correct statement would be that side DF, from the first triangle, is congruent to side MN, from the second triangle. Hence the correct option is B) DE≅MN.
Additionally, DE would be congruent to MN, and EF would be congruent to NO, completing the congruence between triangles △DEF and △MNO.
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Find dy/dx by implicit differentiation 4x^3 + x^2y − xy^3 = 6
Answer: dy/dx = y^3 - 12x^2 - 2yx / x(x-3y^2)
Step-by-step explanation: Differentiate each term with respect to x, then solve for y.
I hope this helps you out!
A polygon has an area of 144 square inches and one of its sides is 10 inches long. If a second similar polygon has an area of 64 square inches, what is the length of the corresponding side in the second polygon?
17,325 round to the nearest thousand
The ph of water samples from a specific lake is a random variable y with probability density function given by f (y) = $ (3/8)(7 − y) 2 , 5 ≤ y ≤ 7, 0, elsewhere. a find e(y ) and v(y ). b find an interval shorter than (5, 7) in which at least three-fourths of the ph measurements must lie. c would you expect to see a ph measurement below 5.5 very often? why?
I really need help on this question
cory earns 52.50 in 7 hours. find the unit rate
divide them:
52.50 / 7 = 7.50 dollars per hour
Witch set of orderd pairs contains only points that are on the graph of the function y=12-3x
A.(-3,-27),(0,0),(6,54)
B.(-18,10),(-6,6),(18,-2)
C(-5,27),(-1,15),(8,-12)
D(-7,-9),(-4,0)(2,18)
5.5-x=-4.5-x. how do you solve this?
The equation 5.5 - x = -4.5 - x has no solution. After cancelling out the variable x, we are left with 5.5 = -4.5, which is a contradiction.
Explanation:To solve the equation 5.5 - x = -4.5 - x, we first notice that the variable x is present on both sides of the equation. We can simply subtract or add x to both sides to cancel it out. This will give us an equation without variables:
5.5 - x + x = -4.5 - x + x
5.5 = -4.5
This equation suggests that 5.5 is equal to -4.5, which is not true. Therefore, we can conclude that there is no solution to the equation since the two sides of the equation do not balance.
Moreover, this type of equation is an example of a contradiction, meaning that it presents a statement that is inherently false regardless of the value of x. As there is no value of x that can make the equation true, we say that the equation has no solution.
Final answer:
The equation 5.5 - x = -4.5 - x simplifies to 5.5 = -4.5 when the x terms are cancelled out. Since 5.5 does not equal -4.5, the equation has no solutions.
Explanation:
To solve the equation 5.5 - x = -4.5 - x, we can first try to simplify it by adding or subtracting the same value from both sides. This method is based on the principle that whatever you do to one side of the equation, you must do to the other to maintain balance.
In this case, if we add x to both sides of the equation, the x terms will cancel out on both sides, which leaves us with 5.5 = -4.5. Here, we notice that both sides of the equation represent constant values and no longer contain the variable x.
Therefore, since 5.5 and -4.5 are not equal, we can conclude that there is no value of x that can satisfy this equation. This equation is a contradiction, which means there are no solutions.
Please someone help me this is the second time I posted this question....
What is the equation, in point-slope form, for a line that goes through (8, −4) and has a slope of −5/6 ?
A. y−4=−5/6(x−8)
B. y+4=−5/6(x−8)
C. y−4=−5/6(x+8)
D. y+4=−5/6(x+8)
Please provide an explanation on how to do this.
The beads in 7 bracelets if 4 bracelets have 96 bead
The sum of two binomials is 3z-6. If one binomial is z+4, what is the other binomial?
What are the values of the function y = –2x – 4 for x = 0, 1, 2, and 3?
A.0, –6, –8, –10
B.–4, –6, –8, –10
C.-4, –2, 0, 2
D.0, 6, 8, 10
y =-2x-4
x = 0, y = -2(0)-4 = -4
x=1, y = -2(1) -4 =-2-4 = -6
x=2, y = -2(2)-4 = -4-4 =-8
x=3, y = -2(3) - 4 = -6-4 =-10
Answer is B
Answer:
B
Step-by-step explanation:
If point a is located at coordinates (5, 3) and point b is located at coordinates (-3, 9), what is the distance from a to b if the units of the coordinated system are meters?
The distance from a to b if the units of the coordinated system are meters is 10m.
What is a line segment?A line that has two endpoints and a fixed measurement is called a line segment.
It is given that point a is located at coordinates (5, 3) and point b is located at coordinates (-3, 9)
D = √[(x-p)² + (y-q)²]
Substituting the points we get;
D = √[(-3 - 5)² + (9 - 3)²]
D = √[(-8)² + (6)²]
D = √[(64) + (36)]
D = √100
D = 10
Hence, the distance from a to b if the units of the coordinated system are meters is 10 m.
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Final answer:
The distance between point A (5, 3) and point B (-3, 9) is calculated using the distance formula, resulting in a distance of 10 meters.
Explanation:
The question is asking for the distance between two points in a coordinate system. To find the distance between point A (5, 3) and point B (-3, 9), we can use the distance formula which is derived from Pythagorean theorem. The distance d between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)² + (y2 - y1)²)
For point A and point B, we substitute the coordinates into the formula:
d = √((-3 - 5)² + (9 - 3)²)
= √(64 + 36)
= √100
= 10 meters
Therefore, the distance from A to B is 10 meters.
23,769 rounded to the nearest thousand
Maria wants to find the product of 5 3/20 multiplied by 3 4/25 using decimals instead of fractions how can she rewrite the problem using decimals
Answer:
[tex] 5.15\times 3.16=16.2740[/tex]
Step-by-step explanation:
Maria wants to find the product of [tex]5\frac{3}{20}[/tex] multiplied by[tex]3\frac{4}{25}[/tex]
First we change mixed fraction to fraction and then change into decimal.
#First fraction:
Change mixed to fraction[tex]5\frac{3}{20}\Rightarrow \dfrac{103}{20}[/tex]
Change fraction to decimal[tex]\dfrac{103}{20}\Rightarrow \dfrac{103\times 5}{20\times 5}=5.15[/tex]
#Secondfraction:
Change mixed to fraction[tex]3\frac{4}{25}\Rightarrow \dfrac{79}{25}[/tex]
Change fraction to decimal[tex]\dfrac{79}{25}\Rightarrow \dfrac{79\times 4}{25\times 4}=3.16[/tex]
Now we find the product of both decimal
[tex]\Rightarrow 5.15\times 3.16[/tex]
Using calculator product of 515 and 316 = 162740
Both number has decimal digits two
So, total number of decimal digits is 4
In multiply result write decimal before 4 digits from right.
Therefore,
[tex] 5.15\times 3.16=16.2740[/tex]
the calendar shows the number of days carlota rides her bike each month. each time ahe rides her bike, she travels 10 miles.is it rwasonable to say that carlota will bike more than 500 miles in 6 months?
How do you simplify sqrt of x^20?
Rachel earned 34$, 34 in 4 hours at her job today
Jordan is playing a video game. For every 35 stars she collects, she gets 4,000 points. Her record is 86,000 points. Which of the following proportions could she use to determine x, the number of stars she needs to tie her record?
Analyze the diagram below and complete the instructions that follow.
Find the value of x and the value of y.
A.x = 15, y = 10
B.x = 20, y = 50
C.x = 50, y = 10
D.x = 50, y = 20
Answer is C x=50 y=10
Answer:
C. [tex]x=50[/tex], [tex]y=10[/tex]
Step-by-step explanation:
We have been given an image of two intersecting lines. We are asked to find the value of x and y for our given diagram.
We know that when two line intersect each other, then vertical angles are congruent.
Using vertical angles theorem, we will get a system of equations as sown below:
[tex]3y=x-20...(1)[/tex]
[tex]5x-100=y+140...(2)[/tex]
From equation (1), we will get:
[tex]x=3y+20[/tex]
Upon substituting this value in equation (2), we will get:
[tex]5(3y+20)-100=y+140[/tex]
[tex]5*3y+5*20-100=y+140[/tex]
[tex]15y+100-100=y+140[/tex]
[tex]15y=y+140[/tex]
[tex]15y-y=y-y+140[/tex]
[tex]14y=140[/tex]
[tex]\frac{14y}{14}=\frac{140}{14}[/tex]
[tex]y=10[/tex]
Therefore, the value of y is 10.
To find the value of x, we will substitute [tex]y=10[/tex] in equation (1) as:
[tex]3*10=x-20[/tex]
[tex]30=x-20[/tex]
[tex]30+20=x-20+20[/tex]
[tex]50=x[/tex]
Therefore, the value of x is 50 and option C is the correct choice.
Answer:
Option C) x = 50, y = 10
Step-by-step explanation:
We are given a two pairs of vertically opposite angle in the image.
Vertically opposite angle is formed when two lines intersect anf they are always equal.
Thus, we can write:
[tex]3y = x -20\\\Rightarrow x - 3y = 20\\5x-100 = y +140\\\Rightarrow 5x - y =240[/tex]
Solving the two equations in two variable, we get:
[tex]x - 3y = 20\\5x - y =240\\\text{Multiplying first equation by 5}\\5x - 15y = 100\\\text{Subtracting the equations}\\5x - 15y-(5x-y) = 100-240\\-14y = -140\\y = 10\\ x - 3(10) = 20\\x = 20 + 30\\x =50[/tex]
The value of x is 50 and y is 10.
—
Is 1.0227 a rational number?
write a trinomial expression equivalent to (2x+5)(3x-2)
The required trinomial expression that is equivalent to (2x+5)(3x-2) is 6x² + 11x - 10.
According to the question, we have to determine the trinomial expression that is equivalent to the (2x+5)(3x-2).
A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the quadratic equation, cubic equation, etc. ax+b is a polynomial.
Here,
Given expression in the question,
= (2x+5)(3x-2)
Following the distributive property
= 2x (3x - 2) + 5 (3x - 2)
= 6x² - 4x + 15x - 10
= 6x² - 11x - 10
Thus, the required trinomial expression that is equivalent to (2x+5)(3x-2) is 6x² + 11x - 10.
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Final answer:
The trinomial expression equivalent to (2x+5)(3x-2) is calculated using the FOIL method, resulting in 6x² + 11x - 10.
Explanation:
To write a trinomial expression equivalent to the product of two binomials, (2x+5)(3x-2), we perform the multiplication by using the distributive property (also known as the FOIL method).
Multiply the first terms: 2x × 3x = 6x²
Multiply the outside terms: 2x × (-2) = -4x
Multiply the inside terms: 5 × 3x = 15x
Multiply the last terms: 5 × (-2) = -10
Combine like terms:
6x² + (15x - 4x) - 10 = 6x² + 11x - 10
The trinomial expression equivalent to (2x+5)(3x-2) is 6x² + 11x - 10.
The product of 2, and a number increased by 6, is -24
The mathematical expression is,
⇒ 2x + 6 = - 24
And, The value of number = - 15
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.
Given that;
The algebraic expression is,
''The product of 2, and a number increased by 6, is -24''
Now,
Since, The algebraic expression is,
''The product of 2, and a number increased by 6, is -24''
Let a number = x
Hence, We can formulate;
⇒ 2x + 6 = - 24
Solve for x as;
⇒ 2x = - 24 - 6
⇒ 2x = - 30
⇒ x = - 15
Thus, The value of number = - 15
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Steven bagged 52 pounds of potatoes. About what is that measure in kilograms? Round to the nearest hundredth
During a certain period of time, a car can cover the distance of 120 miles, going at an average speed of 55 mph. What distance over the same period of time would cover a truck, going at an average speed of 44 mph
A town's population has been growing linearly. In 2003, the population was 60000, and the population has been growing by 2700 people each year.
Write an equation for the population x years after 2003.
What the answer to this
Solve for y: 10y + 3.8 = 38.8
The solution for ( y ) is ( y = 3.5 ).
To solve for y in the equation [tex]\( 10y + 3.8 = 38.8 \)[/tex], follow these steps:
Start with the given equation:
[tex]\[ 10y + 3.8 = 38.8 \][/tex]
Subtract 3.8 from both sides to isolate the term with y:
[tex]\[ 10y + 3.8 - 3.8 = 38.8 - 3.8 \][/tex]
[tex]\[ 10y = 35 \][/tex]
Divide both sides by 10 to solve for y :
[tex]\[ \frac{10y}{10} = \frac{35}{10} \][/tex]
y = 3.5
So, the solution for ( y ) is ( y = 3.5 ).
Planes flies 2951 miles in 6.5 hours what is the speed of the airplane miles per hour
What is the solution to the following system of equations? 3x-2y=12 and 6x-4y=24
Answer:
A. It has infinitely many solutions
Step-by-step explanation:
I took the Solving Linear Systems By Substitution Quiz on Edge
The given system of equations 3x-2y=12 and 6x-4y=24 has no solution.
As per the question, we have to determine the solution to the following system of equations, 3x-2y=12 and 6x-4y=24
What is the equation?The equation is the relationship between variables and is represented as y =ax +b is an example of a polynomial equation.
Here,
Given a system of the equation,
3x-2y = 12
x = 12 + 2y / 3 - - - - -(1)
6x - 4y =24 - - - - -(2)
Put the value of equation 1 in the equation
6 (12 + 2y / 3) - 4y = 24
2 (12 + 2y) - 4y = 24
24 +4y - 4y = 24
24 = 24
Thus, the given system of equations 3x-2y=12 and 6x-4y=24 has no solution.
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