Answer:
The rule of translation (x,y) → (x+6 , y-8)
Step-by-step explanation:
The rest of the question is the coordinates of the ΔABC and ΔA'B'C'
The coordinates of the ΔABC: A(-6,2) , B(-5,5) , C(-1,3)
The coordinates of the ΔA'B'C': A'(0,-6) , B'(1,-3) , C'(5,-5)
It is required the rule of translation.
By Comparing between any of the points and its image
For example between A and A'
Let A(-6,2) = (x,y) and A'(0,-6) = (x+h , y+k)
So, x = -6 and y = 2
And x+h = 0 , y+k = -6
Substitute with x and y to find h and k
So, -6 + h = 0 ⇒ h = 6
And 2 + k = -6 ⇒ k = -8
So, the rule of translation (x,y) → (x+6 , y-8)
The perimeter of an equilateral triangle is directly proportional to the length of one of its sides. The perimeter is 17.7
when the length of a side is 5.29. What is the constant of proportionality
Answer: 3.35 in 3 significant figures.
Step-by-step explanation:
According to question,
Perimeter ∝ length
Here, ∝ means directly proportional.
To remove symbol, introduce a constant. Let the constant be k.
Perimeter ∝ length
Perimeter = k × length
Now, perimeter = 17.7 and length = 5.29
Perimeter = k × length
k = perimeter / length
k = 17.7 / 5.29
k = 3.35 in 3 significant figures.
Answer:
3
Step-by-step explanation:
k=y/x
k=17.75/5.29
k= 3.345
=3
On a coordinate plane, 2 triangles are shown. The first triangle has points M (negative 5, 4), N (negative 2, 3), and L (negative 4, 2). The second triangle has points L prime (negative 4, negative 2), M prime (negative 5, negative 4), and N prime (negative 2, negative 3). What is the rule for the reflection? rx-axis(x, y) → (–x, y) ry-axis(x, y) → (–x, y) rx-axis(x, y) → (x, –y) ry-axis(x, y) → (x, –y)
The reflection transformation of the triangles is C) [tex]( rx-axis(x, y) \rightarrow (x, -y) )[/tex].
The points of the original triangle are:
M (-5, 4) N (-2, 3) L (-4, 2)The points for the reflected triangle are:
L' (-4, -2) M' (-5, -4) N' (-2, -3)Identify the transformation
From the pairs of coordinates, we can observe how each point has changed from the original triangle to the reflected triangle:
M (−5, 4) was reflected to M' (−5, −4). N (−2, 3) was reflected to N' (−2, −3). L (−4, 2) was reflected to L' (−4, −2).Analyze the change in coordinates
We see that for each point, the x-coordinates remain unchanged while the y-coordinates change sign from positive to negative. This indicates that the reflection is across the x-axis.
Reflection rule
The general rule for reflection across the x-axis can be stated as follows:
If a point is given by (x, y), then the reflected point will be (x, -y).
Reflection across the x-axis :
[tex]( rx-axis(x, y) \rightarrow (x, -y) )[/tex]
Complete question
On a coordinate plane, 2 triangles are shown. The first triangle has points M (negative 5, 4), N (negative 2, 3), and L (negative 4, 2). The second triangle has points L prime (negative 4, negative 2), M prime (negative 5, negative 4), and N prime (negative 2, negative 3). What is the rule for the reflection?
a. rx-axis(x, y) → (–x, y)
b. ry-axis(x, y) → (–x, y)
c. rx-axis(x, y) → (x, –y)
d. ry-axis(x, y) → (x, –y)
Which expression is equivalent to 5(2x + 10)?
A. 2x + 15
B. 2x + 50
C. 7x + 15
D. 10x + 10
E. 10x + 50
7-4+6=7 Complete the equation to make it equal
Answer:
7-4+6=7 + 2
Step-by-step explanation:
The original equation 7-4+6=7 is incorrect because it simplifies to 9, not 7. There is no simple way to adjust the equation with the given numbers to make the equation balance correctly. It's crucial to check your work and make sure the equation balances, just like ensuring a chemical equation has equal numbers of atoms on both sides.
To complete the equation 7-4+6=7 to make it equal, we need to perform the operations on the left side of the equation and see if the result is indeed 7, the same as the right side. Let's solve it step by step:
First, subtract 4 from 7, which gives us 3.Next, add 6 to this result, which gives us 3 + 6 = 9.So, the left side of the equation is actually 7-4+6, which calculates to 9.Since 9 does not equal 7, there seems to be an error in the equation as presented.The original equation 7-4+6=7 is incorrect because 7-4+6 equals 9, not 7. To make the equation correct, we would need to change a number or an operation. One possible solution could be adding parentheses: (7-4)+6=7+2, which simplifies to 3+6=9, but again that does not equal 7. Therefore, there is no simple way to correct the equation using basic operations without changing the numbers given.
To make sure the charge and atoms on both sides of an equation balance or to ensure the correctness of a mathematical operation, eliminating terms where possible to simplify the algebra and checking the answer to see if it’s reasonable are important steps.
When balancing equations, whether they are chemical equations or mathematical ones, it's essential to make sure each side is equal to maintain the balance, as seen in the example: 7 carbon atoms, 16 hydrogen atoms, and 22 oxygen atoms on each side of a balanced chemical equation.
area of irregular shapes
Answer:
To find area of irregular shapes you need to divide the irregular shape to get a new shape (for instance: rectangle); then you have to find the area of that particular shape using its formula (for instance: area of square = side*side)
Owen and his friend kayden are going to a carnival that has games and rides . Owen played 5 games and went on 6 rides and spent a total of 28.75 kayden played 4 games and went on 3 rides and spent a total of 16.25. Determine the cost of each game and the cost of each ride
Each game costs 1.25 and each ride costs 3.75
Step-by-step explanation:
Let,
Cost of each game = x
Cost of each ride = y
According to given statement;
5x+6y=28.75 Eqn 1
4x+3y=16.25 Eqn 2
Multiplying Eqn 2 by 2
[tex]2(4x+3y=16.25)\\8x+6y=32.50\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 1 from Eqn 3
[tex](8x+6y)-(5x+6y)=32.50-28.75\\8x+6y-5x-6y=3.75\\3x=3.75[/tex]
Dividing both sides by 3
[tex]\frac{3x}{3}=\frac{3.75}{3}\\x=1.25[/tex]
Putting x=1.25 in Eqn 1
[tex]5(1.25)+6y=28.75\\6.25+6y=28.75\\6y=28.75-6.25\\6y=22.50[/tex]
Dividing both sides by 6
[tex]\frac{6y}{6}=\frac{22.50}{6}\\y=3.75[/tex]
Each game costs 1.25 and each ride costs 3.75
Keywords: linear equation, elimination method
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Final answer:
The cost of one game is 1.25 dollars and the cost of one ride is 3.75 dollars at the carnival. This was determined by setting up and solving a system of equations based on the expenses of Owen and Kayden.
Explanation:
To determine the cost of each game and each ride at the carnival, we can set up a system of equations based on Owen and Kayden's expenses. Let x represent the cost of one game and y represent the cost of one ride.
Owen played 5 games and went on 6 rides for a total cost of 28.75 dollars. This can be represented by the equation:
5x + 6y = 28.75
Kayden played 4 games and went on 3 rides for a total cost of 16.25 dollars. This can be represented by the equation:
4x + 3y = 16.25
We now have a system of linear equations:
5x + 6y = 28.75
4x + 3y = 16.25
To solve the system, we can multiply the second equation by 2 to align the y-terms:
5x + 6y = 28.75
8x + 6y = 32.50
Subtracting the first equation from the multiplied second equation, we get:
3x = 3.75
Dividing both sides by 3, we find that x = 1.25, which is the cost of one game.
To find the cost of one ride, we substitute x = 1.25 into either of the original equations. If we use the second equation 4(1.25) + 3y = 16.25, we get:
3y = 16.25 - 5
3y = 11.25
y = 3.75
Therefore, the cost of one ride is 3.75 dollars.
Simplify (12x + 5) + (3x + 7)
Answer:
Your final answer is 15x+12
Step-by-step explanation:
Remove parathenes ( ) group like terms add similar elements add the numbers 5 + 7 = 12
At bright minds learning , 75% of employees work as instructors . If there are 300 employees at bright mind Learning , how many of them work as instructors
Answer:
Number of instructors are 225.
Step-by-step explanation:
Given:
Total number of employees at bright mind learning = 300
Number of instructors = 75%
We have to convert this percentage and find the number.
So,
[tex]75\%[/tex] can be written as [tex]\frac{75}{100}=0.75[/tex]
Now 75% of 300 employees are the instructors at Bright mind learning.
Can be written as [tex]0.75*300=225[/tex]
Number of instructors at Bright mind learning =225
a college graduates by a factor of 1.045 every year since 1999. in 1999 924 student graduated approximately how many students will graduate in 2014
Answer:
1788
Step-by-step explanation:
The number of students who graduates from college is multiplied by a factor of 1.045 every year since 1999.
So, the number of students graduated every year can be modeled as
[tex]G(x) = 924(1.045)^{x}[/tex] where x is the number of the year since 1999.
Now, in 2014, the x value is (14 + 1) = 15 years.
So, the number of students who will graduate in 2014 is given by
[tex]G(15) = 924(1.045)^{15} = 1788.2[/tex] ≈ 1788. (Answer)
Is the expression 3(x+ 1 1/2)-3 equivalent to 3x+ 1 1/2?
Answer:
No, because 3x+9/2 isn't equivalent to 3x+3/2.
Step-by-step explanation:
1 1/2=3/2
3(x+3/2)=3x+9/2
please help!
Simplify 5 + 2{x - 4[3x + 7(2 - x)]}.
A -34x - 107
B 34x - 107
C 34x + 107
Answer:
Should be B
Step-by-step explanation:
5 + 2 ( x-4[3x+7(2-x)]
5+2 (x-4[ 4x + 14])
5+2 (17x - 56)
5 + 34x - 112
34x - 107
HELPPPPPP!!!
Rule: y=x-1/4
Step-by-step explanation:
if x=1/4 then y=1/4-1/4=0
if x=13/4 then y=13/4-1/4=12/4=3
if x=2 then y=2-1/4=8/4-1/4=7/4=1 3/4
The running back for the Bulldogs football team carried the ball 5 times for a total loss of 11 1/4 yards. Find the average change in field position on each run. Enter the average change as a simplified mixed number.
Answer:
[tex]\displaystyle 2\ \frac{1}{4}[/tex]
Step-by-step explanation:
Fractions
They can be expressed as proper fractions, improper fractions or mixed numbers. Proper fractions are such that the numerator is less than the denominator, like 2/5, 7/11, -9/10. Improper fractions are those whose numerators are greater than the denominator, such as 5/3, 10/9, -21/8.
Mixed numbers are expressions made of whole numbers and a proper fraction, like 4 3/5, 1 1/2, -5 4/9. Mixed numbers can be transformed to improper fractions and vice-versa.
The question requires us to find the average change in field position on each run of the running back for the Bulldogs football team which carried the ball 5 times for a total loss of 11 1/4 yards.
The number 11 1/4 is mixed, to express it as an improper fraction, we add the numbers like
[tex]\displaystyle 11+\frac{1}{4}=\frac{45}{4}[/tex]
This improper fraction will now be divided by 5 to find the average of 5 runs:
[tex]\displaystyle \frac{\frac{45}{4}}{5}=\frac{9}{4}[/tex]
We now need to separate the improper fraction to a mixed number, let's just divide 9 by 4 to get 2 as the quotient and 1 for the remainder, thus
[tex]\boxed{\displaystyle \frac{9}{4}=2\ \frac{1}{4}}[/tex]
What symbols can make 8 2 6 3 equal to 14
Answer:
The closest you would get is (8*2)-6+3=13
Step-by-step explanation:
Kayla takes 3 quizzes each week. How many weeks of school will Kayla have to attend his quarter before she will have taken a total of 9 quizzes
Answer:3 weeks
Step-by-step explanation:The reason for that is because if Kayla is taking 3 tests each week then 3 times 3 is 9 so three weeks.
Kwesi is putting on sunscreen. He uses 3\text{ ml}3 ml3, start text, space, m, l, end text to cover 45 \text{ cm}^245 cm
2
45, start text, space, c, m, end text, squared of his skin. He wants to know how many milliliters of sunscreen (g)(g)left parenthesis, g, right parenthesis he needs to cover 240\text{ cm}^2240 cm
2
240, start text, space, c, m, end text, squared of his skin. He assumes the relationship between milliliters of sunscreen and area is proportional.
How many milliliters of sunscreen does Kwesi need to cover 240 \text{ cm}^2240 cm
2
240, start text, space, c, m, end text, squared of his skin?
Answer:
16 mL
Step-by-step explanation:
The ratio of areas is (245 cm²)/(45 cm²) = 16/3, so Kwesi expects the ratio of volumes to be the same:
(needed volume)/(3 mL) = 16/3
needed volume = (16/3)×(3 mL) = 16 mL
Kwesi expects to need 16 mL of sunscreen to cover 240 cm² of skin.
Which term names FDR‘s plan for ending the Great Depression
Answer:
New Deal
Explanation:
In order to bring an end to the Great Depression, Franklin Delano Roosevelt (the 32nd President of the United States) proposed the "New Deal."
The "New Deal" was a set of programs which allowed the government to have a direct role in making the American lives easier. This mainly supported the poor people, especially the farmers and those who lost their jobs or who were unemployed.
The programs started with the First New Deal, followed by the Second New Deal. The First New Deal focused on reformation while the second one was directed towards protecting the people.
Thus, this explains the answer.
consider the functions given below
f(x) + -3x-5
g(x) + f(x)+9
what is the y intercept of g
The y-intercept of the function g(x), defined as g(x) = f(x) + 9 where f(x) = -3x - 5, is 4. This is determined by evaluating g(0), resulting in a y-intercept at the point (0, 4).
Explanation:The question asks about finding the y-intercept of the function g(x), which is defined in terms of another function f(x). Given that f(x) is equal to -3x - 5 and g(x) equals f(x) + 9, to find the y-intercept of g(x), we substitute x with 0 in the function f(x) and then add 9. The y-intercept is the point where the function crosses the y-axis, which is when x = 0.
First, we find the value of f(0):
f(0) = -3(0) - 5 = -5Next, we determine g(0) by adding 9 to the value of f(0):
g(0) = f(0) + 9 = -5 + 9 = 4Therefore, the y-intercept of g(x) is 4, which means the line representing g(x) crosses the y-axis at the point (0, 4).
Kendra’s work is shown in the table. Where, if anywhere, did Kendra first make a mistake? Steps Kendra’s Work Step 1 Negative 3 x + 7 y = negative 15. Negative 2 x minus 7 y = 5. Negative 5 x = negative 10. Step 2 Negative 5 x = negative 10. x = 2. Step 3 Negative 3 (2) + 7 y = negative 15. Negative 6 + 7 y = negative 15. 7 y = negative 9. y = Negative StartFraction 9 Over 7 EndFraction = negative 1 and StartFraction 2 Over 7 EndFraction
Answer:
Step 3 because when dividing 7y=-9, you divide by 7, not 9. Kendra divided the whole thing by 9, which is incorrect. You want to get the Y by itself(as in y, not a fraction of y) to solve the rest of the problem.
Step-by-step explanation:
Step 1.
-3x+7y=-15
-2x-7y=5
-5x=10 and x=2
Step 2.
-5x =-10. x = 2.
Step 3.
-3 (2) + 7 y = - 15. - 6 + 7 y = - 15. 7 y = - 9. y = -9/7 = - 1 2/7
What are the angle measurements of 6x + 1° = 3x + 11°
Answer:
[tex]x=3\frac{1}{3}^\°[/tex]
Step-by-step explanation:
Given equation:
[tex]6x+1\°=3x+11\°[/tex]
To find the angle measure of [tex]x[/tex]
Solution:
In order to find the angle measure [tex]x[/tex] , we will isolate [tex]x[/tex] on left side by carrying out math operations on both sides.
We have:
[tex]6x+1\°=3x+11\°[/tex]
Subtracting both sides by [tex]3x[/tex]
[tex]6x-3x+1\°=3x-3x+11\°[/tex]
[tex]3x+1\°=11\°[/tex]
Subtracting both sides by 1°.
[tex]3x+1\°-1\°=11\°-1\°[/tex]
[tex]3x=10\°[/tex]
Dividing both sides by 3.
[tex]\frac{3x}{3}=\frac{10\°}{3}[/tex]
[tex]x=\frac{10}3}^\°[/tex]
Converting fraction to mixed number by dividing and writing the quotient as whole number and the remainder as numerator.
∴ [tex]x=3\frac{1}{3}^\°[/tex] (Answer)
Mr. Walker, the contest sponsor, bought toy Wheels in a package of six dozen for $81. what was the unit cost of each wheel?
Answer:
1.125
Step-by-step explanation:
the unit cost is how much it cost per wheel
dozen is 12
so 12 times 6 is 72
so then you do 81/72 to get your answer
and you are probably wondering how i got the divison from was because i'm supposed to divide to find a unit cost.
the 81 was the total for the 72 packages of toy wheels
Answer:
first find how much a dozen of 6 is, so 6*12=72
next to get the cost of one divide 81/72=$1.125
$1.13
Step-by-step explanation:
5x + 2y = 29 and 8x - 8y = 80
Answer:
both of The answers are equal to Zero
Solve this 8x-6(3-2x)
Answer:
20x−18
Step-by-step explanation:
Apply the distributive property.
8x−6⋅3−6(−2x)8x-6⋅3-6(-2x)
Multiply −6-6 by 33.
8x−18−6(−2x)8x-18-6(-2x)
Multiply −2-2 by −6-6.
8x−18+12x
Add 8x8x and 12x12x.
20x−18
The given expression 8x - 6(3 - 2x) simplifies to 20x - 18.
The expression is given as follows:
8x - 6(3 - 2x)
As we know that algebraic expressions are mathematical statements that comprise at least two variables or integers.
Start by distributing the -6 to the terms inside the parentheses:
⇒ 8x - 6 × 3 + 6 × 2x
Simplify the above expression to get:
⇒ 8x - 18 + 12x
Combine like terms in the above expression to get:
⇒ 20x - 18
Therefore, the given expression 8x - 6(3 - 2x) simplifies to 20x - 18.
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A rectangular painting is 24 inches wide and 20 inches tall without the frame. With the frame, it is 28 inches wide and 24 inches tall. What is the area of the frame not covered by the painting? Show your work.
The area of the frame not covered by the painting is 192 square inches
Solution:
Given that, A rectangular painting is 24 inches wide and 20 inches tall without the frame
The area of rectangle is given as:
[tex]Area = length \times width[/tex]
Find the area of painting without frame:
Length = 20 inches
Width = 24 inches
[tex]Area\ Without\ Frame = 20 \times 24 = 480[/tex]
Thus area of painting without frame is 480 square inches
With the frame, it is 28 inches wide and 24 inches tall
Find the area of painting with frame:
Length = 24 inches
Width = 28 inches
[tex]Area\ with\ frame = 24 \times 28 = 672[/tex]
Thus area of painting with frame is 672 square inches
What is the area of the frame not covered by the painting
Area of the frame not covered by the painting = Area with farme - Area without frame
Area of the frame not covered by the painting = 672 - 480 = 192
Thus the area of the frame not covered by the painting is 192 square inches
use an identity to find the value of expression. sin 40° csc 40°
Answer:
Step-by-step explanation:
1. sin37xcsc37
For this use the recipricol identity. csc37 = 1/sin37
sin37x(1/sin37) = (sin37)/(sin37) = 1
2. sec^2(23) - tan^2(23)
For this one use the pythagorean identity
sec^2(23) = 1+tan^2(23)
1+tan^2(23) - tan^2(23) = 1
Match Each Equation to the situation it represents.
the first situation goes with the first equation
the second situation goes with the third equation
the third situation goes with the third equation
The equation for Statement 1 is 4+5x=16, the equation for Statement 2 is (5-4)x=16 and the equation for Statement 3 is 16-4x=5.
For the given statements we need to match the given equations.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Statement 1: An adults and 5 children rent skates. It costs $4 per adult for stakes and a total of $16.
Let the cost of 5 children rent skates be 5x.
Now, 4+5x=16
Statement 2: It costs Mikael $4 to make a bike bag, and he sells each for $5. He has made a profit of $16 so far.
Profit=Selling Price-Cost Price
⇒Profit=5-4
⇒(5-4)x=16
Statement 3: It was 16° C. It began falling 4° C per hour until it reached 5° C.
It began falling 4° C per hour, which can be written as 4x.
Now, 16-4x=5
Therefore, the equation for Statement 1 is 4+5x=16, the equation for Statement 2 is (5-4)x=16 and the equation for Statement 3 is 16-4x=5.
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Help trigonometry ( angles of evaluation and depression)
Answer:
y ≈ 242.4 ft
Step-by-step explanation:
The lower angle in the triangle is 29° ( alternate angles )
Using the sine ratio in the right triangle
sin29° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{500}[/tex]
Multiply both sides by 500
500 × sin29° = y, thus
y ≈ 242.4 ft ( to the nearest tenth )
what is the answer to x over 7 = 89
Answer: x = 623
Step-by-step explanation: In this problem, notice that x is being divided by 7 so to get x by itself,
we need to multiply both sides of the equation by 7.
Notice that on the left side, the 7 and 7 cancel each other out so we're just left with x. On the right side we have
89 x 7 which is 623 so x = 623.
Finally, we can check our answer by plugging a 623 back into the original equation. So we have [tex]\frac{(623)}{7} = 89[/tex] or 89 = 89. Since this is true, our answer checks.
Determined if the sequence is geometric if it is find the common ratio : -1,1,4,8
The given sequence is not geometric because they don't have a common ratio.
What is geometeric sequence?
A geometric sequence is set of numbers which have a common ratio. The next number in a geometirc sequence is the multiple of the previous number.
Ratios of the numbers in the sequence-1/1 = -1
4/1 = 4
8/4 = 2
The numbers don't have a common ratio.
Thus, we can conclude that the given sequence is not geometric because they don't have a common ratio.
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The common ratio is not the same for all pairs of consecutive terms, so the sequence is not geometric.
To determine if a sequence is geometric, we need to check if there is a common ratio between consecutive terms.
In a geometric sequence, each term is obtained by multiplying the previous term by a constant value called the common ratio.
Let's check the given sequence: -1, 1, 4, 8.
To find out if it is geometric, we need to check if the ratio of consecutive terms is constant:
Common Ratio (r) = (Second Term) / (First Term)
= 1 / (-1)
= -1
Now, let's check if the common ratio is the same for the other pairs:
1st and 2nd terms: 1 / (-1) = -1
2nd and 3rd terms: 4 / 1 = 4
3rd and 4th terms: 8 / 4 = 2
The common ratio is not the same for all pairs of consecutive terms. Since the common ratio is not constant, the given sequence (-1, 1, 4, 8) is not a geometric sequence.
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Write a recursive rule for the sequence.
243, 81, 27, 9, 3, ..
Final answer:
A recursive rule for the sequence 243, 81, 27, 9, 3, ... is to multiply each term by one-third (⅓) of the previous term. The first term is 243, and the rule can be expressed as an = ⅓ × an-1 for n >= 2.
Explanation:
To write a recursive rule for the sequence 243, 81, 27, 9, 3, ... we must first identify the pattern. Observing the sequence, we see that each term is one-third of the previous term. Therefore, to get from one term to the next, we multiply by ⅓ (which is the same as dividing by 3).
The recursive formula for this sequence can be written as follows:
Let the first term a1 = 243. Then for each n >= 2, an = ⅓ × an-1, where an represents the nth term of the sequence.
This recursive rule clearly indicates that every term is a fraction of the preceding term, which is consistent with the pattern of division by three observed in the original sequence.