Answer:yes its 15
Step-by-step explanation:
A triangle has vertices at A(-2, 3), B(2, 1), and C(1, 0). After a transformation, the image of the triangle has vertices at A'(-2, -3), B' (2, -5), and C'(1, -6). Identify the transformation.
The transformation that is applied to the ΔABC to get the ΔA'B'C' is vertical translation by 6 units downwards.
The triangle has the vertices A(-2, 3), B(2, 1), and C(1, 0)
They are transformed such that:
A(-2, 3)→A'(-2,-3)
B(2, 1)→B'(2,-5)
A(-1, 0)→A'(-2,-6)
Now if we carefully observe we can see that the y-coordinate of A' is 6 less than that of A.
Similarly for B and C the coordinates are 6 units less than that of the object, but the x-coordinate remains the same.
This proves that the graph follows a vertical transformation and since the new ordinates are 6 units smaller, so the graph is translated 6 units downwards.
A function, f, that maps to itself is known as a transformation, or f: X→X'. The pre-image X will change into the picture X' following the transformation. This transformation can use any operation, or a combination of operations, including translation, rotation, reflection, and dilation.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The true statements are:
The center of the circle lies on the x-axis
The radius of the circle is 3 units.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The standard equation of a circle is expressed as:
x²+y²+2gx+2fy+C=0
Centre is (-g, -f)
radius = √g²+f²-C
Given a circle whose equation is
x²+y²-2x-8=0
Get the centre of the circle
2gx = -2x
2g = -2
g = -1
Similarly, 2fy = 0
f = 0
Centre = (-(-1), 0) = (1, 0)
This shows that the center of the circle lies on the x-axis
r = radius = √g²+f²-C
radius = √1²+0²-(-8)
radius =√9 = 3 units
The radius of the circle is 3 units.
For the circle x² + y² = 9, the radius is expressed as:
r² = 9
r = 3 units
Hence the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Hence we get the required answers.
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Perform the following operation. Write the answer in scientific notation.
0.008/40,000
(Use the multiplication symbol in the math palette as needed.)
Answer:
8.0 × 10^-3 ÷ 4.0 × 10^4
= 2.0 × 10^-3-4
= 2.0 × 10^-7
or 0.0000002
Solve for X
(9x+1)°
789
(17x - 3)
Type your answer...
The value of x in the given triangle is x = 4
Calculating the value of x in a triangleFrom the question, we are to determine the value of x.
From the given triangle,
We can write that
(9x+ 1)° + 78° + (17x - 3)° = 180° (Sum of angles in a triangle)
Now, we will solve for x
(9x+ 1)° + 78° + (17x - 3)° = 180°
9x° + 1° + 78° + 17x° - 3° = 180°
Collect like terms
9x° + 17x° = 180° - 1° + 3° - 78°
26x° = 104°
x = 104/26
x = 4
Hence, the value of x is 4
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If the 21st and 22nd terms in the expansion of(1+x)⁴⁴ are equal find the value of x
Answer:
21st 22nd are equal so ×=0
If a bar of soap cost 70p and a box of plasters cost 95p how much does buying one of each cost
The cost of buying one of each of the soap and plaster is 165p.
How to calculate the cost?From the information, the bar of soap cost 70p and a box of plasters cost 95p.
It should be noted that in order to find the total cost, we will have to add the. oat of each product.
This will be:
Total cost = Cost of soap + Cost of plaster
= 70p + 95p
= 165 p
The cost is 165p.
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Nicola needs to put up bunting around a whole room
for a party.The room is 4m long and 3m wide.
she has lots of 70 cm lenghts of bunting.Every time she ties two pieces together she needs to use 50mm of each piece of string for the knot. How many pieces
of 70 cm long bunting does she need to go right around the room ?
The pieces of long bunting is 22.
From the question, we have
The room is 4m long and 3m wide.
perimeter of room = 2×(4+3)
=14 m = 1400 cm
she has lots of 70 cm lenghts of bunting.
1400 cm/70 cm = 20
she needs to use 50mm =5 cm of each piece of string for the knot.
20×5 = 100
100/70 ≈2
pieces of 70 cm long bunting = 20+2 =22
Divide:
Split is to divide into two or more equal sections, places, groupings, or divisions in its most basic form. To divide something simply means to provide it to a group in equal quantities or to cut it up into equal pieces. Let's imagine a diagonal divides a square into two triangles with equal areas. An integer may or may not be the result of a division operation. Sometimes the result will be expressed as decimal numbers.
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7p5 · 4p3 I have no idea how to do this please help
For triangle XYZ, m∠X = (3g + 19)° and the exterior angle to ∠X measures (6g + 53)°. Find the measure of ∠X and its exterior angle
Check the picture below.
juan thinks the answer is between 5 and 6 melanie says the answer is between 3 and 4 who is correct [tex]\sqrt[3]{28}[/tex]
Answer:
28
Step-by-step explanation:
4,8,12,16,20,24,28. +4 every time
-1.25 + 2 1/5 + (-3.5)
Answer: -2.55
Step-by-step explanation:
Answer:
-2.55
Step-by-step explanation:
-1.25 + 2 1/5 + (-3.5) =
= -1.25 + 2.2 - 3.5
= 0.95 - 3.5
= -2.55
Lamar buys candy that costs $5 per pound. He will buy at most 12 pounds of candy. What are the possible amounts he will spend on candy
Use C for the amount (in dollars) Lamar will spend on candy.
Write your answer as an inequality solved for C.
Answer:
He will spend $60 on candy
Step-by-step explanation:
If the cost for one pound is $5, then just multiply.
12 x $5 = $60
Answer: C=7
Step-by-step explanation: C=12+5
the answer is c=7
Need help with question
Solve each equation below. Show each step and check your work.
a) 56a – 178 = 98 – 248
b) 640 + 70 = 69y + 20
Answer:
A) 0.5
B) 10
Step-by-step explanation:
A) First, you need to Combine Like Terms on the right side of the =
98-248 = -150
Now, you need to Isolate the variable by getting rid of the -178. What you do to one side, you must do the the other.
56a-178(+178) = -150(+178)
56a = 28
Finally, you must remove that 56 on the a. Since it stands for 56 x a, you must do the same you did with the -178 except with Division.
56a/56 = 28/56
a = 0.5
B) Combine Like terms
640+70 = 710
Isolate the variable
710(-20) = 69y+20(=20)
690 = 69y
Remove the 69 with division
690/69 = 69y/69
10 = y
what is 33+900212323
Answer:
900212356
Step-by-step explanation:
x + y is greater than or equal to 4
Answer:
I am going sujshsbeba170
A rock falls from a tower that is 360 feet high. As it is falling, its height is given by the formula ℎ= 200 −162. How many seconds will it take for the rock to hit the ground (h=0)? Round to the nearest tenth of a second.
The time it will takes for the rock to hit the ground (h=0) given the height of 360 feet high is 3.53 seconds.
What is the time of falling?The concept that will be used in the calculation is the concept of height and time .
The formular for the expression is given as ℎ= 200 −16t^2
Then the height of the tower is been given as 360 feet high
ℎ= 200 −16t^2
then
t^2=200/16
t^2=12.5
t=3.53 seconds
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An upcoming business has vowed to increase profits by 2% every year for the next decade. Initially the company started by making $100 million dollars. How much will they be making after 10 years? Keep your answer in millions rounded to a whole number.
The profit that the upcoming business would be making after 10 years is $122 million.
What is the profit in 10 years?The profit of the business in 10 years can be modelled with an exponential equation. This is because the rate of growth of profit each year would be 10% of the last year's profit.
The equation that is used to determine the profit in 10 years is:
FV = P (1 + r)^n
Where:
FV = Future value P = Present value R = interest rate N = number of yearsFV = 100 x (1 + 0.02)^10
FV = $100 million x (1.02^10) = $122 million
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Charles drew a plan for a rectangular piece of
material that he will use for a blanket. Three of the
vertices are (-1.4, -2.7), (-1.4,3.7), and (2.8,3.7).
What are the coordinates of the fourth vertex?
The fourth coordinate of rectangular piece of material is (2.8 , -2.7)
According to the question,
Charles drew a plan for a rectangular piece of material that he will use for a blanket. Three of the vertices are (-1.4, -2.7), (-1.4,3.7), and (2.8,3.7).
As we know , the opposite sides of rectangle are equal
If we locate these coordinates in our graph and join them
Length of rectangle will be = 2.8+1.4 = 4.2cm
Breadth of rectangle will be = 3.7 + 2.7 = 6.4cm
So, the fourth coordinate should lie 6.4cm far from (2.8,3.7)
Subtracting 6.4 from y-axis,
Fourth coordinate = 3.7 - 6.4
= -2.7
Therefore , The fourth side of rectangle = (2.8 , -2.7)
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A board game uses the deck of 20 cards shown to the right. Two cards are selected at a random from this deck. Calculate the probability that first card selected has a yellow bird and second cared selected has a lion both with and without replacement
The probability that first card selected has a yellow bird and second card selected has a lion both with and without replacement is 1/40 and 1/38. respectively.
What is probability?
Probability is the likelihood of an event or more than one event occurring. It is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.
Probability may also be described as the likelihood of an event occurring divided by the number of expected outcomes of the event. i.e.,
P(A) = f / N
Where:
P(A) = Probability of an event (event A) occurring
f = Number of ways an event can occur (frequency)
N = Total number of outcomes possible
Here deck of 20 cards are given which implies total number of possible outcomes are 20. From these 20 cards 5 cards has lions and 5 cards has birds in which 2 are yellow and 3 are red.
Now two cards are selected randomly.
We have to find the probability that first card selected has a yellow bird and second card selected has a lion both probability that first card selected has a yellow bird and second card selected has a lion both with and without replacement.
Probability with replacement:
Probability that first card selected has a yellow bird = 2/20 ---(1)
Since replacement is allowed so the probability that second card selected has a lion = 5/20---(2)
So, the probability that first card selected has a yellow bird and second card selected has a lion with replacement = (1) * (2) = 2/20 * 5/20 = 1/40.
Probability without replacement:
Probability that first card selected has a yellow bird = 2/20 ---(3)
And since replacement is not allowed, the probability that second card selected has a lion = 5/19---(4)
So, the probability that first card selected has a yellow bird and second card selected has a lion without replacement = (3) * (4) = 2/20 * 5/19 = 1/38.
Therefore, the probability with and without replacement is 1/40 and 1/38. respectively.
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Someone please help step by step how to solve
3(x+2)-5=13
pls
(b) 12 friends travel to the festival.
5 travel by car, 4 travel by bus and 3 travel by train.
Two people are chosen at random from the 12 friends.
Calculate the probability that they travel by different types of transport.
The probability that they two people are chosen and travel by different transport is 47/144
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.
Probability is given as sample space / total outcome
Probability to travel by car p(C)= 5/12
Probability to travel by bus P(B)= 4/12=1/3
Probability to travel by train P(T)= 3/12= 1/4
for two people chosen at random
P(C ×B)= 5/12×1/3= 5/36
P(B×T)= 1/3×1/4= 1/12
P(C×T)= 1/4×5/12= 5/48
Therefore the probability that the two chosen travel by different car is
P(C ×B)+P(B×T)+P(C×T)= 5/36+1/12+5/48
= 141/432
divide through by 3
= 47/144
Hence the get the required answer.
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8. In the following diagram, the diameter of the circle is 15m. What is the distance between the chord and the edge of the circle?
Answer:
7
Step-by-step explanation:
15-8
please help it is urgent
[tex]\frac{6x + 1}{6x - 4} - \frac{47 - 27 {x}^{2} }{5 {x}^{2} - 24} = \frac{5}{6} [/tex]
solve x
Answer:
Soultion\left(x^2+\frac{7}{3}x-\frac{17}{3}\right)=3\left(x^2+\frac{7}{3}x+\frac{49}{36}-\frac{49}{36}-\frac{17}{3}\right)\quad :\quad x=-\frac{7+\sqrt{253}}{6},\:x=\frac{\sqrt{253}-7}{6} steps \left(x^2+\frac{7}{3}x-\frac{17}{3}\right)=3\left(x^2+\frac{7}{3}x+\frac{49}{36}-\frac{49}{36}-\frac{17}{3}\right) simplify -2x^2-\frac{14x}{3}+\frac{34}{3}=0.
Step-by-step explanation:
I got you my boy.
CAN SOMEONE HELP WITH THIS QUESTION?✨
Answer:
24.359
Step-by-step explanation:
The height is opposite of the 77 so we are using sin. The length of the ladder is the hypotenuse.
sin(77°)=height/25 Set up equation sin=height/hypotenuse
25*sin(77°)=height Multiply both sides by 25
25*.96437=height
height=24.359
se the distributive property to find an expression that is equivalent to 42x + 12 .
The equivalent expression using the distributive property is 6(7x + 2)
How to determine the equivalent of the expressions?From the question, we have the following expression
42x + 12
Rewrite the given expression as follows
This is represented using
(42x + 12)
Factor out 2 from the expression
So, we have the following representation
42x + 12 = 2(21x + 6)
Factor out 3 from the expression
So, we have the following representation
42x + 12 = 2 * 3(7x + 2)
Evaluate the products
42x + 12 = 6(7x + 2)
The above represents the equivalent expression
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7/15 - 6 2/5 = need the answers
The fraction solve 7/15 - 6 2/5 , we get the answer -89/15.
Given,
In the question:
The Fraction is given as:
7/15 - [tex]6\frac{2}{5}[/tex]
To solve the above fraction.
Now, According to the question;
Let's know
What is fraction in math?
A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator.
Come to the question:
7/15 - [tex]6\frac{2}{5}[/tex]
7/15 - 32/5
Take the L.C.M
= [tex]\frac{7-96}{15}[/tex]
= -89/15
Hence, The fraction solve 7/15 - 6 2/5 , we get the answer -89/15.
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Please help an 8th grader in needdddddddddddddddddddddddddddddddddddddddddddd
Answer:
The two points used to find the slope:
[tex]x_1,y_1[/tex]: 2,30
[tex]y_1,y_2:[/tex] 4,10
Final equation: y = -10x + 50
Step-by-step explanation:
From a fellow 8th grader <3
First, let's review the slope of a line: y = mx + b
Where m is the slope, and b the y-intercept
Let's find the slope. To do this I will select 2 points from this graph, and using the slope formula I will calculate it
Slope formula: [tex]\frac{rise}{run} =\frac{change- in- y}{change-in-x} =\frac{y^2-y^1}{x^2-x^1}[/tex]
To get the most accurate answer, I will be using the 2 points given that are directly on the line:
1 = (2, 30)
2 = (4, 10)
Slope: [tex]\frac{10-30}{4-2} =\frac{-20}{2} =-10[/tex]
m = -10
It makes sense that it is a negative, since the graph continues downwards.
Let's update our equation: y = -10x + b
We can see that the line intersects the y-axis at y = 50
Plug this into our b-value:
y = -10x + 50
Now, I would recommend using a graphing calculator (like a TI-83) or an online one (like desmos) to double check this. I have attached a screenshot of this line on desmos. From there we can see if this line matches up with the one seen on your graph.
Our answer is:
The two points used to find the slope:
[tex]x_1,y_1[/tex]: 2,30
[tex]y_1,y_2:[/tex] 4,10
Final equation: y = -10x + 50
Please let me know if this helped you, and if this was the correct answer! If it is incorrect I will do my best to revise my answer.
Answer: y intercept is (0,50) and Slope is -10.
Final equation is y= -10x+50
Step-by-step explanation:
Y-intercept is at what point the line intercepts the y-axis. It intersects at (0,50) coordinate point as you can see.
Slope is change in y divided by the change in x. When you change x by 1, y changes by -10. So it is -10/1 = -10. Slope is -10.
Since we know y intercept and slope equation is y=-10x+50
Where does 1/6 land on a number line
Answer:
On a number line, 1/6 would land in the exact middle between 0 and 2/6
Step-by-step explanation:
Not too sure what your question meant, but I hope my answer helped!
If it wasn't what you were looking for, please let me know and elaborate on your question and I'll be happy to help out! :)
a) What are the coordinates of A?
b) What are the coordinates of B?
Answer:
coordinates of A are (-4.5, 2)
coordinates of B are (0, -3.5)