The vertices of the image are the points J'(x, y) = (3, - 1), K'(x, y) = (4, - 5) and L'(x, y) = (0, - 3), respectively.
What are the coordinates of the image of a triangle after using a reflection?
Triangles are created by three non-colinear points called vertices and the location of the image of the triangle is found by using a reflection around a line parallel to the x-axis for every point of the figure. This operation is described by the following expression:
P'(x, y) = P(x, y) - 2 · [P(x, y) - (p, k)]
Where:
P(x, y) - Coordinates of the original vertex.p - x-Coordinate of the original vertex.k - y-Coordinate of the equation of the line of reflection.If we know that J(x, y) = (3, - 5), K(x, y) = (4, - 1), L(x, y) = (0, - 3) and k = - 3, then the coordinates of the vertices of the image of the triangle are:
J'(x, y) = (3, - 5) - 2 · [(3, - 5) - (3, - 3)]
J'(x, y) = (3, - 5) - 2 · (0, - 2)
J'(x, y) = (3, - 5) + (0, 4)
J'(x, y) = (3, - 1)
K'(x, y) = (4, - 1) - 2 · [(4, - 1) - (4, - 3)]
K'(x, y) = (4, - 1) - 2 · (0, 2)
K'(x, y) = (4, - 1) + (0, - 4)
K'(x, y) = (4, - 5)
L'(x, y) = (0, - 3) - 2 · [(0, - 3) - (0, - 3)]
L'(x, y) = (0, - 3) - 2 · (0, 0)
L'(x, y) = (0, - 3) + (0, 0)
L'(x, y) = (0, - 3)
The vertices of the image of the triangle are J'(x, y) = (3, - 1), K'(x, y) = (4, - 5) and L'(x, y) = (0, - 3).
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Find the number that makes the ratio equivalent to 1:9.Find the number that makes the ratio equivalent to 1:9. 4:
The number that makes the ratio equivalent to 1:9 include 2 and 18.
The numbers that number that makes the ratio equivalent to 1: 9: 4 include 2, 18, and 8.
How to illustrate the information?It should be noted that ratio is used to show the comparison between the numbers illustrated.
It should be noted that based on the information, 1:9 is equivalent to 2 and 18. This can be illustrated as:
= 2/18 = 1/9.
Also, 1:9:4 equals 2, 18 and 8. In their case, the ratio is multiplied by 2 to get the numbers.
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find the quotient of 4296 and 4
Answer: 1074
Step-by-step explanation:
Since quotient means division, the question would be 4296 divided by 4. So the answer would be 1074.
calcular la altura del sol sobre el horizonte (medida en ángulo) si un edificio de 24 metros de altura proyecta una sobra de 30 metro
Usando propiedades de triangulos rectangulos veremos que el angulo de elevación es 38.65°
¿Como encontrar el angulo de elevacion del sol?
El ángulo de elevación del sol sera el angulo que esta en el vertice derecho del triangulo rectangulo en la imagen.
Sabemos que:
tan(a) = (cateto opuesto)/(cateto adjacente).
En este caso:
cateto opuesto = 24m
cateto adjacente = 30m
Entonces:
tan(a) = 24m/30m = 0.8
Aplicando la funcion inversa, obtenemos:
a = Atan(0.8) = 38.65°
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Find the remainder for the quotient using either substitution or synthetic division.
x - 5 is a factor of the polynomial
f(x) = x^3 - x^2 - 17x - 15)
(The answer must include what the remainder value is and what it indicates.)
(x - 5) is a factor of the polynomial function f(x) = x³ - x² - 17x -15 as there is no remaider.
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given a polynomial function f(x) = x³ - x² - 17x -15.
If (x - 5) is it's factor then f(5) = 0.
∴ f(x) = x³ - x² - 17x -15.
f(5) = 5³ - 5² - 17(5) - 15.
f(5) = 125 - 25 - 85 - 15.
f(5) = 0.
So, the remainder is zero hence (x - 5) is a factor of the polynomial function f(x) = x³ - x² - 17x -15.
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(2x+3)(4x-7) , you get a new expression of the form ax^2+bx+c what is value of a , b , and c
(2x+3)(4x-7)
To convert this quadratic formula on the general expression, we need to multiply both parenthesis as follows:
8x^2 - 14x + 12x - 21 =
8x^2 -2x - 21
where a, b and c correspond to the coefficients of the equation:
a = 8
b = -2
c = -21
I got -3(23q+15) but it says its wrong
Answer:
-72q - 48
Step-by-step explanation:
Use didtributive property to multiply -9 by 5 + 9q-3 - 45 - 72qSubtract 45 from -3 to get -48-48 - 72qThe you have to switch the equation around to because the variable has to be on the left.Answer:
-75q - 45
Step-by-step explanation:
Given expression,
→ -3q - 9(5 + 8q)
Simplifying the expression,
→ -3q - 9(5 + 8q)
→ -3q + (-9 × 5) + (-9 × 8q)
→ -3q - 45 - 72q
→ -75q - 45
Hence, answer is -75q - 45.
What is y equal to ?
y=10, hope that helps.
if s is a linearly dependent set, then each vector is a linear combination of the other vectors in s.
a. True
b. False
The statement "if s is a linearly dependent set, then each vector is a linear combination of the other vectors in s" is false.
What is the linearly dependent set?A vector set's linear independence is an important attribute. If no vector in a set can be written as a linear combination of the other vectors in the set, the set is said to be linearly independent. The set is said to be linearly dependent if any of the vectors can be represented as a linear combination of the others.
If S is a linearly dependent set, then each vector in S is a linear combination of the others.
This is false.
For example, v₁ = (1,0), v₂ = (2,0), and v₃ = (1,1). Then v₂ = 2v₁ but v₃ is not a linear combination of v₁ and v₂, since it is not a multiple of v₁. But 2v₁ - 1v₂ + 0 v₃ = 0.
If an indexed set of vector S is linear dependent, then it is only necessary that one of the vectors is in the set.
Hence, the correct answer would be option (B).
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Samson uses 6 gallons of water on 20 plants in his garden.
At that rate, how much water will it take to water 30 plants
Which inequality represents all values of × for which the quotient below is lefined?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given expression
[tex]\sqrt{28(x-1)}\div\sqrt{8x^2}[/tex]STEP 2: Simplify the expression
For the quotient to be defined, the numerator and the denominator must be greater than zero, this means that:
[tex]\begin{gathered} \sqrt{8x^2}>0 \\ \mathrm{Square\:both\:sides} \\ \left(\sqrt{8x^2}\right)^2>0^2 \\ 8x^2>0 \\ x<0\quad \mathrm{or}\quad \:x>0 \end{gathered}[/tex]For the numerator,
[tex]\begin{gathered} \mathrm{Square\:both\:sides} \\ \left(\sqrt{28\left(x-1\right)}\right)^2>0^2 \\ \mathrm{Simplify} \\ 28x-28>0 \\ x>1 \\ \mathrm{Combine\:the\:intervals} \\ x>1\quad \mathrm{and}\quad \:x\ge \:1 \\ x>1 \end{gathered}[/tex]Merging both interval, we have:
[tex]\begin{gathered} x<0,x>0,x>1 \\ x>1 \end{gathered}[/tex]Hence, the answer is given as:
[tex]x>1[/tex]A sea Lion is at sea level it dove at a rate of 7.3 feet per minute. what is the elevation of the sea lion after half an hour?
A small cube has sides that are 1/2 cm. How many small cubes would fit
inside a rectangular prism that has a length of 10, a width of 5, and a height
of 2?
min
2 cm
5 cm
in
10 cm
67 cubes of area 1.5 cm² can be fitted in the rectangular prism of volume 100 cm³.
What exactly is a rectangular prism?A rectangular prism can also be referred to as a "cuboid."Though it appears to be a cube, it is not.The only difference between it and a cube is that it has rectangle-shaped faces as opposed to a cube's square faces.A cuboid is a six-sided solid in geometry known as a hexahedron.Its faces are quadrilaterals.In the sense that a cuboid can be transformed into a cube by changing the length of its edges or the angles between its faces, the word "cuboid" means "like a cube."So, first, we need to find the volume of the rectangular prism as follows:
The formula for the volume of the rectangular prism: V= whl
Substitute values as follows:
V = whlV = 5 × 2 × 10V = 100The volume of a rectangular prism is 100 cm³.
Now, the area of the cube:
The formula for the area of the cube: is 6a²
The area of the cube is 1.5 cm².
A number of cubes that can be fitted in the rectangular prism:
100/1.5 = 66.667Rounding off: 67Therefore, 67 cubes of area 1.5 cm² can be fitted in the rectangular prism of volume 100 cm³.
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The correct question is given below:
A small cube has sides that are 1/2 cm. How many small cubes would fit inside a rectangular prism that has a length of 10, a width of 5, and a height of 2?
Help me with my calculus plsssss
A printer takes 5 seconds to print 3 pages.How many pages can it print in 125 seconds
360 whole -5/6 in fracton
The value of 360 whole -5/6 in fraction upon calculation is found to be 2156/6 or 359.33
360 - 5/6 solving in fraction
This can be written as
360/1 - 5/6
taking the LCM of 1 and 6, the LCM is 6
Multiplying 6 with the numerator and denomenator of the term having 1 as its denominator and multiplying 1 with the numerator and denomenator of the term having 6 as its denominator,
360 x 6)/ 1 x 6 - (5 x 1)/ 6 x 1
= [tex]\frac{360*6}{1*6} - \frac{5*1}{6*1}[/tex]
=[tex]\frac{2160 - 5}{6}[/tex]
= 2156/6
= 359.333
Therefore the value of 360 whole -5/6 in fraction upon calculation is found to be 2156/6 or 359.33
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14=12<2x
Please answer fast
Answer:
x=-1
Step-by-step explanation:
−2x+12=14
−2x=14−12
−2x=2
x=
−2
2
Triangle A has a single transformation performed on it to create Triangle B. Michelle says the single transformation must have been a translation 8 units to the right.
what is the transformation that could have been performed on Triangle A to create Triangle B to prove Michelle's statement is false.
Answer:The single transformation that maps triangle A onto triangle B is the reflection about the x-axis
Step-by-step explanation:
A recent survey on movies found that 1 out of 6 students likes comedy films. Graph the relationship between the total number of students and the students who like comedy films for different number of students given in the table below.
Total Number of Students 90 180 270 360
Probability of people liking comedy movies = 1/6
Hence,
If total number of people are 90, then the number of people liking comedy movies = 90/6 = 15
If total number of people are 180, then the number of people liking comedy movies = 180/6 = 30
If total number of people are 270, then the number of people liking comedy movies = 270/6 = 45
If total number of people are 360, then the number of people liking comedy movies = 360/6 = 60
Let the x-axis represent the total number of people and,
The y-axis represent the number of people liking comedy films.
The function will be :-
f(x) = x/6 , where x is the total number of people.
The graph is attached.
-8(2m + 5) = 8 helpppp
Answer:
m = -3
Step-by-step explanation:
Distribute 8 to both sides
Add 40 to both sides
Add the numbers
Which you'll get 48
-16 divided by 48 = -3
Write and solve an equation to find the value of x.
The angles are supplementary.
Jo
x 50°
equation: x + 50 =
solution: x=
The value of x can be determined as 130 as is found out by solving the linear equation this formed from the provided data in the question.
What is a linear equation?An equation is said to be linear if the maximum power of the variable is consistently 1. It is also known to be as the one-degree equation.
There are numerous ways to express linear equations, but they often contain constants (such as "2" or "c") and call for straightforward variables (like "x" or "y").
The coefficients present in a linear equation, can be any expressions as long as they don't contain any of the variables, can be thought of as the equation's parameters.
Most of the times, a linear equation is written to represent a straight line.
Here it is provided that the equation is
x + 50 = 180
⇒ x = 130
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A line passes through the point (-3, -2) and has a slope of
1.
What is the equation of the line?
y=x+1
y=-x-1
3
y=-x-1
4|3
Answer:
y=x+1
Step-by-step explanation:
first use the equation in point - slope form:
y+2=1(x+3)
then rearrange them to make it in slope intercept form - y=mx+b
y= 1x + 1 or y=x+1
solve each compound inequality and graph the solution!!! I need answers and step by step equations for 20,22, and 24 please!!!!!!
The answer for 20 is ( ∞ , 4) .
The answer for 22 is ( ∞ , 3) .
The answer for 24 is ( -∞ , -24/11) .
What is compound inequality?An inequality that consists of two or more parts is called a compound inequality. Either "or" or "and" may be used in these components. A number between 5 and 10 could be used as x in an inequality, for instance, if it states that "x is larger than 5 and less than 10". Any time one of the two inequalities is true when the two inequalities are united by the word or, the compound inequality is solved. The two separate solutions have been combined to form the final answer. Inequalities that are separated by "and" or "or" form a compound inequality. The intersection of the inequality graphs is shown by the graph of a compound inequality with a "and."(20) 2x - 5 > 3
x > 8/2
x > 4
Hence , ( ∞ , 4)
(22) -x + 1 > -2
x > 3
Hence , ( ∞ , 3)
(20) -5/8x + 2 + 3/4x > -1
11x > -24
x > -24/11
Hence , ( ∞ , -24/11)
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How many square feet of sod are needed to cover a football field? A football field measures 360ft by 160ft
Answer:
57,600 square feet
57600 square feet of sod are needed to cover a football field.
What is Area of Rectangle?
The area of Rectangle is length times of width.
Given,
A football field measures 360ft by 160ft
We need to find square feet of sod are needed to cover a football field
Which means we need to find the area of football field
let the length of football field is 360 ft
Three hundred sixty feet
Width of football field is One hundred sixty feet 160ft.
Area=Length×Width
=360×160
=57600 square feet
Hence, 57600 square feet of sod are needed to cover a football field.
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A triangular prism has a cross-sectional area of 15 cm squared and a volume of 225 cm squared.
What is the length of the prism?
The length of the triangular prism that has a volume of 225 cm³ and cross-sectional area of 15 cm² is calculated as: 15 cm.
What is the Volume of a Triangular Prism?A triangular prism looks like the shape shown in the image that is attached below. The shaded part is the cross-sectional area of the triangular prism.
The volume of a triangular prism = area of cross-section × length of the prism
The volume of a triangular prism = (1/2 × b × h) × l
Given the following:
Cross-sectional area of the triangular prism = 15 cm²
Length of the triangular prism = l
Volume of the triangular prism = 225 cm³
Substitute the values into the given formula for the volume of the prism:
225 = 15 × l
225 = 15l
Divide both sides by 15
225/15 = 15l/15
15 = l
l = 15 cm
Length of the prism is therefore 15 cm.
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Alan makes a fruit salad using strawberries and blueberries. He uses 5
cups of strawberries for every 3 cups of blueberries. Which measure
represents the amount of strawberries Alan uses for every 1 cup of fruit
salad?
3/8 cup
3/5 cup
5/8 cup
5/3 cup
Answer:
5/8
Total = 5 cup of strawberry + 3 cup of blueberries
=8
1 cup of fruits=8 cup of mix fruits(5 cup of strawberry + 3 cup of blueberries)
=8-3
=5/8
a girl is standing at one corner of a snowy rectangular field that measures 100 ft by 100 ft, as drawn. she wishes to reach a warm cabin located at the diagonally-opposite corner of the field. suppose she trudges through the snow at 3 ft/sec to reach a point p at the other side of the field, then walks the remaining distance along a plowed road at 5 ft/sec to reach the cabin. in order to reach the cabin as quickly as possible, how far is point p from the cabin?
For Sally to reach the cabin fastest the distance from point P to the distance cabin at point C must be 25 ft
Let Sally be at point S and the cabin diagonal-opposite to her at point C. We need to find the distance between P and C such that Sally reaches the cabin the quickest. We know SX = 100ft
By Pythagoras' theorem
SX² + XP² = SP²
⇒100² + x² = SP²
⇒SP = √(100²+x²) (1)
speed = distance/ time
⇒ time = distance / speed
We need to minimize the time taken by sally
time taken to reach cabin t = (SP/3) + (PC/5)
⇒t = (SP/3) +(PC/5)
⇒t = (√(100²+x²) /3) + (PC/5)
⇒t = (√(100²+x²) /3) + (100-x/5)
⇒dt/dx = x/ (3*√(100²+x²)) -(1/5) = 0 (to minimize)
⇒5x = 3√(100²+x²)
⇒25x² = 9(100² + x²)
⇒16x² = 90000
⇒x²= 5625
⇒x = √5625
⇒x= 75 ft
Thus the distance from point P to cabin C = PC = 100 - x = 100-75=25 ft
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hurry need answer asap
Answer:
x = 4
Step-by-step explanation:
Make is filling grocery bags at a foot pantry. Each bag's contents will be identical, and there will be no food left over. Mike has 27 boxes of oatmeal and 18 boxes of raisins.
3. what is the greatest number of bags can she fill?
4. how many boxes of each food will go in each bag?
__ boxes of oatmeal __ boxes of raisins
please help asap thank u so much
The greatest number of bags that she can fill is 9.
The number of boxes of oatmeal that will be in each bag is 3
The number of boxes of raisins that will be in each bag is 2
What is the greatest number of bags she can fill?In order to determine the greatest number of bags that she can fill, we needed to determine the highest common factor of 18 and 27. The highest common factor of a number is the greatest number that perfectly divides two or more numbers.
Factors of 18 = 1, 2, 3, 6, 9, 18
Factors of 27 = 1, 3, 9, 27
Highest common factor = 9
The greatest number of bags that she can fill is 9.
Number of boxes of oatmeal that will be in each bag: 27 / 9 = 3
Number of boxes of raisins that will be in each bag: 18 / 9 = 2
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What is value of x in the equation below? 33 ≥ -6x + 9
Answer:
x ≥ -4
or [-4, ∞)
Step-by-step explanation:
What is value of x in the equation below?
33 ≥ -6x + 9
subtract 9 from both sides:
33 - 9 ≥ -6x + 9 - 9
24 ≥ -6x
divide both sides by -6 and remember to flip sign direction:
24/-6 ≥ -6x/-6
-4 ≤ x
or: x ≥ -4
in set builder notation: [-4, ∞)
Answer:
Below in bold
Step-by-step explanation:
33 ≥ -6x + 9
-6x ≤ 33 - 9
-6x ≤ 24
x ≥ -4
- note that the inequality is flipped as we are dividing by a negative.
PLEASE HELP: answer following questions, will make brainliest!
For each question give the output of each expression with the given input.
A.
F(x) =x +3
F(4)=
B.
F(x)=2x-9
F(5)=
C.
F(x)= -6x+2
F(-3)=
