Given the vertices of ∆ABC are A (2,5), B (4,6) and C (3,1), find the vertices following each of the
transformations FROM THE ORIGINAL vertices:
a. Rx-axis
b. Ry = 3
c. T<-2,5>
d. T<3,-6>
e. r(90◦, o)
Answers
Part a)
R(x-axis) is the reflection of triangle ABC on the x-axis. The new coordinates is given as A' (2, -5), B' (4, -6), and C' (3, -1)
Part b)
R(y=3) is the reflection of triangle ABC on the line with equation y=3.
The new coordinates are A' (2, 1), B' (4, 0), and C' (3, 5)
Part c)
T(-2, 5) is the translation of triangle ABC two units left and five units up. The new coordinates are A'(0, 10), B' (2, 11), and C'(1, 6)
Part d)
T(3, -6) is the translation of triangle ABC three units right and six units down. The new coordinates are A'(5, -1), B'(7, 0), and C'(6, -5)
Part e)
r(90°, 0) is the rotation of triangle ABC on the origin by 90° clockwise. The new coordinates are A'(5, -2), B'(6, -4) and C'(1 -3)
Related Questions
PLEASE CAN SOMEONE HELP!!!????
Use elimination to solve for x and y:
−2x−y=9
2x−9y=1
My Choices are....
a. (−4,−1)
b. (−1,−4)
c. (5,1)
d. (−1,−7)
Answers
-2x-y=9
2x-9y=1 +
0x-10y=10
-10y=10
divide by -10
y=-1
sub back
-2x-y=9
-2x-(-1)=9
-2x+1=9
-2x=8
divide by -2
x=-4
y=-1
(x,y)
(-4,-1)
A
The values of x and y after solving both the equations by the elimination method are -4 and -1. So option A is correct
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
Two linear equations
−2x − y = 9
2x − 9y = 1
by using elimination method,
−2x − y = 9
2x − 9y = 1
0 - 10y = 10
y = -1
2x − 9× -1 = 1
2x = -8
x = -4
Hence, the values are, -4 and -1
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How much water can be held by a cylindrical tank with a radius of 12 feet and a height of 30 feet?
Answers
what is the slope of a line that passes through (-4,-13) and (19,11)
Answers
m (gradient) = (y1 - y2) / (x1 - x2)
where (x1, y1) is the coordinate of the first point, and (x2, x2) is the coordinate of the second point
in your question:
x1 = -4
x2 = 19
y1 = -13
y2 = 11
m = (-13 -11) / (-4 -19) = -24 / -23 = 24/23 or 1.04 (2d.p.)
hope that helps :)
Answer:
24/23
Step-by-step explanation:
- vs - = + after -24,-23 =
Answer = 24, 23
How do I solve this
Answers
so, hmm which are those? let's check, let's set the denominator to 0, and solve for "x".
[tex]\bf x^2+6x-7=0\implies (x+7)(x-1)=0\implies x= \begin{cases} -7\\ 1 \end{cases} \\\\\\ \textit{let's check, } x=-7\quad \cfrac{(-7)+2}{(-7)^2+6(-7)-7}\implies \cfrac{-5}{49-42-7}\implies \cfrac{-5}{0} \\\\\\ x=1\quad \cfrac{(1)+2}{(1)^2+6(1)-7}\implies \cfrac{3}{1+6-7}\implies \cfrac{-3}{0}[/tex]
Permutations!!
If 9 actors must sit together how many ways are there to seat 13 people around the table?
Answers
To calculate the number of ways to seat 13 people around a table with 9 actors sitting together, we treat the 9 actors as one unit and then arrange the five units around the table, resulting in (4! * 9!) different possible arrangements.
Explanation:The question asks us to calculate the number of ways to seat 13 people around a table if 9 actors must sit together. This can be approached as a permutations problem in combinatorics.
Firstly, treat the 9 actors as one unit since they must sit together. With this in mind, we effectively have 5 units to arrange: the group of 9 actors and the remaining 4 individuals. As the seating arrangement is around a circular table, we can fix one person's seat and arrange the remaining units. As a result, there are (5-1)! ways to arrange these units since circular permutations eliminate the concept of a distinct 'starting' point that linear permutations have.
Now we need to consider the arrangements of the 9 actors within their group. Since their relative positions to each other matter, they can be permuted in 9! ways.
Therefore, the total number of seating arrangements would be the product of the two permutations: (5-1)! * 9!.
Calculating this gives us (4!) * 9! = (4*3*2*1) * (9*8*7*6*5*4*3*2*1) different possible arrangements.
What is the factored form of the expression k^2 - 9h^2
Answers
a^2 - b^2 = (a+b) (a-b)
So, what we need to do here is apply this equation:
k^2 - 9h^2 =
k * k - (3h)^2 =
(k + 3h) (k - 3h)
A ship travels 10 miles from Point A to Point B, makes a turn of 112, and travels 16 miles to Point C. If the ship travels directly from Point C back to Point A, how many miles will it travel on the last leg of the trip (from Point C to Point A)? Round your answer to the nearest tenth of a mile.
Answers
[tex] 10^{2} + b^{2} = 16^{2} [/tex]
and [tex]100+ b^{2} =256[/tex]
and [tex] b^{2} =256-100[/tex]
so [tex] b^{2} =156[/tex]
Take the square root of both sides to find that b = 12.5
Explain what needs to happen to the inequality sign when dividing or multiplying by a negative number. a. nothing happens c. change the inequality sign to an equals sign b. flip the inequality sign d. the inequality needs to be graphed on a number line
Answers
so the answer is B
Answer:
(B) flip the inequality sign.
Step-by-step explanation:
If we consider an inequality such that [tex]-x\leq7[/tex], then if we multiply the inequality with a negative number such as [tex]-1[/tex], then the inequality becomes [tex]x\geq-7[/tex].
Also, if we divide the above inequality [tex]-x\leq7[/tex], by a negative number that is [tex]-1[/tex], then the inequality becomes [tex]x\geq-7[/tex].
Therefore, if we multiply or divide an inequality by a negative number, then it flips the inequality sign.
Hence, option (B) is correct.
Solve the following system by graphing.
x - y = 4
x + y = 2
What is the solution of the system?
(3, -1)
(3, 1)
(-1, 3)
Answers
the solution is : (3, -1)
put x= 3 and y = -1
you have : 3-(-1) = 4 and 3+(-1) = 2 ..... right
The solution for the system of equation x - y = 4 and x + y = 2 is (3, -1).
What is an equation ?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given pair of equations,
x - y = 4 (1)
And x + y = 2 (2)
To find the solution of the equations,
Add both the equations,
x - y + x + y = 4 + 2
2x = 6
x = 3,
Substitute the value of x = 3 in equation (1),
3 - y = 4
y = -1
The values of x and y are 3 and -1 respectively.
Hence, option (A) is correct.
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A model for a company's revenue is R=-15p^2+300p+12,000, where p is the price in dollars of the company's product. What prize will maximize revenue?
Answers
[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{lccclll} R = &{{ -15}}p^2&{{ +300}}p&{{ +12,000}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)[/tex]
so the Revenue will be the highest at [tex]\bf {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}[/tex] and that will happen at the price of [tex]\bf -\cfrac{{{ b}}}{2{{ a}}}[/tex]
[tex]R(p)=-15 p^{2}+300p+12,000[/tex]
Move the 12,000 over to the other side and set the equation equal to 0:
[tex]-15 p^{2}+300p=-12,000[/tex]
In order to complete the square, the leading coefficient on the squared term has to be a 1 and it's a -15, so we have to factor that out:
[tex]-15( p^{2}-20p)=-12,000 [/tex]
Now it's ready to complete the square on it. Do this by taking half the linear term, squaring it, and then adding it in. Our linear term is 20p. Half of 20 is 10 and 10 squared is 100, so we will add in 100 on the left. Let's do this next step in two parts:
[tex]-15( p^{2}-20p+100)=-12,000 [/tex]
That's not quite complete yet because if we add in 100 inside the parethesis on the left we have to add in that same amount on the right. But on the left, we didn't just add in 100, we added in -15 TIMES 100 cuz we can't just forget about the -15 we factored out. That looks like this then:
[tex]-15( p^{2}-20p+100)=-12,000-1,500 [/tex]
The whole reason for doing this is to create a perfect square binomial on the left which is what we have done. The perfect square binomial is this (and we are going to do the subtraction on the right at the same time):
[tex]-15(p-10)^{2}=-13,500[/tex]
If we move the right side over to the left we get this:
[tex]-15(p-10) ^{2}+13,500=0 [/tex]
which gives us a vertex of (10, 13,500). That means that at a price of $10, the max revenue will be $13,500. See how beautifully that works out!??
Which expression is equivalent to (cos x)(tan(–x))?
A. -sin x
B. sin x
C. -csc x
D. csc x
Answers
[tex][cos(x)][tan(-x)][/tex] is the same as [tex][cos(x)][ -\frac{sin(x)}{cos(x)}] [/tex]
We can now cancel out the cos(x), which leaves us only with -sin(x) remaining. So your answer is A.
Find the volume of revolution bounded by the curves y = 4 – x2 , y = x, and x = 0, and is revolved about the vertical axis.
Answers
The rest of solution in the attachment.
There's a mistake in the picture
It shoud be
[tex]V=\pi\left(\dfrac{289\sqrt{17}-521}{60}\right)\approx35[/tex]
It costs $35$35 per hour to rent a boat at the lake. You also need to pay a $25$25 fee for safety equipment. You have $200$200. For how long can you rent the boat?
Answers
Need help with this please
Answers
A. Move the graph of y=[x] UP 3 units
B. Move the graph UP 1 unit
C. Move the graph DOWN 1 unit
D. Move the graph DOWN 3 units
The graph you're given on the problem screen is not a very good one, I think. Would it help to draw y = [x] on a piece of graph paper where one square = 1 unit? The graph you're shown has one square = 2 units, which could lead to some confusion.
So, draw the graph of y = [x], then figure out which way the graph was moved -- and how far -- to get the graph in the problem.
Here is a link to a YouTube video that might help a lot.
https://youtu.be/UQ3a2QH_-GU
Find all complex solutions of 3x^2+3x+4=0.
(If there is more than one solution, separate them with commas.)
Answers
Now we can compare it with general form of quadratic equation ([tex]ax^2 + bx + c = 0[/tex])
a = 3 , b = 3 and c = 4
Now we can apply quadratic formula which is given as
[tex]x =\frac{ -b+/- \sqrt{b^2-4ac} }{2a}[/tex]
Now we can plugin value of a , b or c
[tex]x = \frac{-3+/- \sqrt{(3)^2 - 4*3*4} }{2*3} [/tex]
[tex]= \frac{-3+/- \sqrt{9 - 48} }{6} = \frac{-3+/- \sqrt{-39} }{6} [/tex]
In general we know [tex] \sqrt{-1} = i [/tex]
So we can write [tex] \sqrt{-39 } = \sqrt{-1} * \sqrt{39} = i \sqrt{39} [/tex]
So
[tex]x = \frac{-3+/-i \sqrt{39} }{6} [/tex]
So [tex]x = \frac{-3+i \sqrt{39} }{6} [/tex] or [tex]x = \frac{-3- \sqrt{39} }{6} [/tex]
The complex solutions to the equation[tex]3x^2+3x+4=0 are x = (-3 + i\sqrt{39})/6 and x = (-3 - i\sqrt{39})/6.[/tex]
Explanation:To find all complex solutions of the quadratic equation [tex]3x^2+3x+4=0[/tex]e the quadratic formula:
[tex]x = \((-b \pm \sqrt{b^2-4ac})/(2a)\).[/tex]
Here, a = 3, b = 3, and c = 4. Plugging these values into the formula, we get:
[tex]x = \((-3 \pm \sqrt{3^2-4 \cdot 3 \cdot 4})/(2 \cdot 3)\).[/tex]
This simplifies to:
[tex]x = \((-3 \pm \sqrt{-39})/6\).[/tex]
Since the discriminant (under the square root sign) is negative, we know that the solutions will be complex. Using i to represent the square root of -1, we can write the solutions as:
[tex]x = \((-3 \pm i\sqrt{39})/6\).[/tex]
So, the complex solutions are [tex]x = (-3 + i\sqrt{39})/6 and x = (-3 - i\sqrt{39})/6.[/tex]
5⁄6 · n = 10 (solve for n)
Answers
When you divide 5/6 and 10 you get 12.
To check your answer multiply 5/6 and 12 and you will get 10.
N=12
in a certain county, the number of charter schools is 4 less than twice the number of alternative schools. We know that there are 48 charter schools in the county. How many alternative schools are in the county?
Answers
Answer:
There are [tex]26[/tex] alternative schools in the country
Step-by-step explanation:
Let
x------> the number of charter schools
y-----> the number of alternative schools
we know that
[tex]x=48[/tex]
[tex]x=2y-4[/tex] -----> equation A
substitute the value of x in the equation A and solve for y
[tex]48=2y-4[/tex]
[tex]2y=48+4[/tex]
[tex]2y=52[/tex]
[tex]y=26[/tex]
A comic-strip writer churns out a different number of comic strips each day. For 16 days, the writer logged the number of comic strips written each day (sorted low to high): {1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 7}. What type of skew can be observed in this distribution?
positive skew
negative skew
zero skew
skew cannot be observed
Answers
We have the data set already in ascending order, so finding the quartiles is quite straight forward.
We have Q₁ = 2, Q₂ = 3, Q₃ = 5 (refer to the first picture below)
The box plot is given in the second picture and from this plot, we can see that the data tail slightly on the right, and this shows a positive skew.
What is the prime factorization of -96? tell me how do u get the answer
Answers
the prime factorization of -96 is : - 3×2^5
Answer: -1 x 2^5 x 3
Step-by-step explanation: To find the prime factorization of -96, we need to first factor out -1, which gives us 1 x (-1) x 2 x 2 x 2 x 2 x 2 x 3. Then, we can rewrite -1 as -1^1, and combine the 2's to get 2^5. So the prime factorization of -96 is -1^1 x 2^5 x 3.
Remember, negative numbers can also have prime factorizations.
What kind of transformation is illustrated in this figure ?
Answers
How many three digit numbers can be made from the digits 1,\ldots,9 if repetitions of digits are not allowed?
Answers
9*8*7 = 504
Look at a simpler example, with 1, 2, 3:
123
132
213
231
312
321
6 numbers
3*2*1 = 6
There are 84 three digit numbers can be made from the digits 1, ..., 9
What is Combination?
A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Given that;
The numbers are,
⇒ 1, 2, ..., 9
Now,
All the three digit numbers can be made from the digits 1, ..., 9 are;
⇒ [tex]^{9} C_{3}[/tex]
⇒ 9! / 3! 6!
⇒ 9 × 8 × 7 / 6
⇒ 84
Thus, There are 84 three digit numbers can be made from the digits
1, ..., 9.
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Accuracy is a measure of how close an answer is to the actual or expected value
Answers
:)
During one year about 163 million adults over 18 years old in the United States spent a total of about 93 billion hours online at home. On average, how many hours per day did each adult spent online at home?
1. How do you write each number in scientific notation?
2 How do you convert the units to hours per day.
Answers
[tex]\bf 163,000,000\implies 163\times 10^6 \\\\\\ 93,000,000,000\implies 93\times 10^9\\\\ \cfrac{93\times 10^9}{163\times 10^6}\impliedby \textit{hours per year for one adult} \\\\\\ \cfrac{93\times 10^9\times 10^{-6}}{163}\implie
s \cfrac{93\times 10^{9-6}}{163}\implies \cfrac{93\times 10^3}{163}[/tex]
that's how many hours each adult spent a year... now, how many hours is that per day? well, there are 365 days a year, so, we simply divide it by 365
[tex]\bf \cfrac{\frac{93\times 10^3}{163}}{365}\implies \cfrac{\frac{93\times 10^3}{163}}{\frac{365}{1}}\implies \cfrac{93\times 10^3}{163}\cdot \cfrac{1}{365}\implies \cfrac{93\times 10^3}{163\cdot 365}\quad \cfrac{hours}{day}[/tex]
Final answer:
To write each number in scientific notation, express it as a product between 1 and 10 and a power of 10. Each adult spent an average of 570.55 hours per day online at home.
Explanation:
To write each number in scientific notation, we need to express it as a product of a number between 1 and 10 and a power of 10.
163 million can be written as 1.63 x 10⁸
93 billion can be written as 9.3 x 10¹⁰
To convert the units to hours per day, we need to divide the total number of hours by the number of adults.
So, each adult spent an average of (93 x 10¹⁰) / (163 x 10⁸) = 570.55 hours per day online at home. Scientific notation simplifies large numbers, facilitating computations and providing a concise representation of quantities in mathematical contexts.
Toby gets 78 votes, which is 52% of the total votes cast. How many students voted in Toby’s grade?
Answers
52% = 0.52
78/0.52 =150
150 students voted
Jake has proved that a function, f(x), is a geometric sequence. How did he prove that?
A He showed that an explicit formula could be created.
B He showed that a recursive formula could be created.
C He showed that f(n) ÷ f(n − 1) was a constant ratio.
D He showed that f(n) − f(n − 1) was a constant difference.
Answers
C. He showed that f(n)/(f(n-1) was a constant ratio.
Write 5000 = 12 as an order pair
Answers
If XYZ measures 75, what is the measure of XWZ ? A. 285 B. 210 C. 75 D. 150
(Its a circle, and its saying that the arc is 775 and wants to know what the rest of the circle is)
Answers
The measure of XWZ is 285
what is arc?The arc of a circle is defined as the part or segment of the circumference of a circle.
Given:
<XYZ = 75
As, we know central angle of 360
So, arc(XWZ) + <XYZ = 360
arc (XWZ) = 360 - 75
arc(XWZ) = 285
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Find the area of a square with apothem 9 in. Round to the nearest whole number.
281 in2
305 in2
458 in2
324 in2
Answers
So, if the apothem is 9in, the length of the side is 2 * 9in = 18 in.
And, the area of the square is (length of the side)^2 = (18 in)^2 = 324 in^2
Answer: 324 n^2
Answer:
The area of the square is 324 square inches.
Step-by-step explanation:
The apothem of the square is 9 inches.
The side of the square is twice the length of the apothem.
Hence, the side of the square is given by
[tex]a=2\times 9=18\text{ in}[/tex]
The area of a square is the given by
[tex]A=a^2\\A=18^2\\A=324\text{ in}^2[/tex]
Therefore, the area of the square is 324 square inches.
Find the probability of at least 2 girls in births. Assume that male and female births are equally likely and that the births are independent events. Round to three decimal places.
Answers
Male and FemaleMale and Male Female and Male Female and Female
All four variants are equally likely.Probability of each one is 1/4 = 0.25.So, Result "Female and Female"
are probability = 0.250 --- if round to three decimal places.
Factor completely 36x2− 121.
Answers
Factorising (a² - b²) gives (a+b)(a-b)
Factorising 36x² - 121 gives (6x+11)(6x-11)