Choose the algebraic description that maps ΔABC onto ΔA′B′C′ in the given figure.Question 7 options:A) (x, y) → (x + 4, y + 8)B) (x, y) → (x + 8, y + 4)C) (x, y) → (x – 4, y – 8)D) (x, y) → (x + – 8, y – 4)
Answers
Step 1
Given the triangle, ABC translated to A'B'C'
Required to find the algebraic description that maps triangle ABC and A'B'C'
Step 2
The coordinates of points A, B,C are in the form ( x,y)
Hence
[tex]\begin{gathered} A\text{ has a coordinate of ( -3,-2)} \\ B\text{ has a coordinate of (-6,-5)} \\ C\text{ has a coordinate of (-1,-4)} \end{gathered}[/tex]Step 3
Find the algebraic description that maps triangle ABS TO A'B'C'
[tex]\begin{gathered} A^{\prime}\text{ has a coordinate of (5,2)} \\ B^{\prime}\text{ has a coordinate of ( 2,-1)} \\ C^{\prime}\text{ has a coordinate of ( 7, 0)} \end{gathered}[/tex]The algebraic description is found using the following;
[tex]\begin{gathered} (A^{\prime}-A^{})=(x^{\prime}-x,\text{ y'-y)} \\ OR \\ (B^{\prime}-B)=(x^{\prime}-x,\text{ y'-y)} \\ OR \\ (C^{\prime}-C)=(x^{\prime}-x,\text{ y'-y)} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} =\text{ ( 5-(-3)), (2-(-2))} \\ =(8,4) \\ \text{Hence the algebraic description from triangle ABC to A'B'C' will be } \\ =(x,y)\Rightarrow(x\text{ + 8, y+4)} \end{gathered}[/tex]Hence the answer is option B
Related Questions
you have torn a tendon and is facing surgery to repair it. the surgeon explains the risks to you: infection occurs in 3% of such operations, the repair fails in 17%, and both infection and failure occur together in 2%. what percentage of these operations succeed and are free from infection? give your answer as a whole number.
Answers
Our required probability is 99.82% or a 100%
%, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage.
What is the definition of percentage in statistics?
Percentages. The use of percentages to express statistics is one of the most popular. The word "percent" simply refers to "per hundred," and the sign for percentage is %. By dividing the whole or whole number by 100, one percent (or 1%) is equal to one hundredth of the total or whole.
Given that P(operational infection occurs at a 3% rate)
P(operational repair failures) = 17%
P(infection and failure happen simultaneously) = 2%
The first thing we'll discover is that P(infection or failure) is given by 0.03 + 0.17 - 0.02 = 0.18 = 0.18%.
Therefore, the probability that these procedures will be successful and infection-free is given by 100 - 0.18 = 99.82%.
Consequently, 99.82% of a probability is needed.
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Graph the function. Plot five points on the graph of the function as follows.
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And if you can step by step on how to do it
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The radius of the cylinder is r=3 cm.
The height of the cylinder is h=7 cm.
The expression for the volume of the cylinder is,
[tex]V=\pi r^2h[/tex]Substituting the given values in the above equation,
[tex]\begin{gathered} V=\pi(3\operatorname{cm})^2(7\operatorname{cm}) \\ =\frac{22}{7}\times9cm^2\times7\operatorname{cm} \\ =198cm^3 \end{gathered}[/tex]Thus, option (C) is the correct solution.
I don't understand please explain in simple words the transformation that is happeningwhat is the function notation
Answers
We have the next functions
[tex]f(x)=5^x^{}[/tex][tex]g(x)=2(5)^x+1[/tex]Function notation
[tex]g(x)=2(f(x))+1[/tex]Describe the transformation in words
we have 2 transformations, the 2 that multiplies the function f(x) means that we will have an expansion in the y axis by 2, the one means that we will have a shift up by one unit
find the unit price of a 3 pack of bottle juice for $6.75 fill in the amount per bottle of juice
Answers
EXPLANATION
Let's see the facts:
Unit price = $6.75
Number of packs = 3
The unit price is given by the following relationship:
[tex]\text{Unit price= }\frac{6.75}{3}=2.25\frac{\text{dollars}}{\text{pack}}[/tex]The unit price is 2.25 $/pack
Find the percent increase in volume when 1 foot is added to each dimension of the prism. Round your answer to the nearest tenth of a percent.7 ft10 ft86 ft
Answers
Solution
Step 1
The volume of a triangular prism = Cross-sectional area x Length
Step 2
[tex]\begin{gathered} Cross\text{ sectional area = area of the triangle} \\ Base\text{ = 6ft} \\ Height\text{ = 7ft} \\ Cross\text{ sectional area = }\frac{1}{2}\times\text{ 7 }\times\text{ 6 = 21 ft}^2 \\ Volume\text{ = 21 }\times\text{ 10 = 210 ft}^3 \end{gathered}[/tex]Step 3:
When 1 foot is added to each dimension of the prism.
The new dimensions becomes Base = 7, Height = 8 and length = 11
[tex]\begin{gathered} \text{Cross-sectional area = }\frac{1}{2}\text{ }\times\text{ 7 }\times\text{ 8 = 28 ft}^2 \\ Length\text{ = 11 ft} \\ Volume\text{ = 28 }\times\text{ 11 = 308 ft}^3 \end{gathered}[/tex]Step 4
Find the percent increase in volume
[tex]\begin{gathered} \text{Percent increase in volume = }\frac{308\text{ - 210}}{210}\text{ }\times\text{ 100\%} \\ \text{= }\frac{98}{210}\text{ }\times100 \\ \text{= 46.7} \end{gathered}[/tex]Final answer
46.7
Find the reference angle for the given angles 745 degree.
Answers
Maisa,. let's recall the formula for calculating the reference angle when the angle is > 360 degrees:
Reference angle = Given angle - 360
Reference angle = 745 - 360
Reference angle = 385
It's still higher value than 360, therefore we subtract 360 again.
Reference angle = 385 - 360
Reference angle = 25 degrees
Find the slope of the line in the graph below using: rise m= 0 6 -2)
Answers
Given data:
The given graph of the line.
The slope of the line passing through (4, 0) and (12, 2) is,
[tex]\begin{gathered} m=\frac{2-0}{12-4} \\ =\frac{2}{8} \\ =\frac{1}{4} \end{gathered}[/tex]Thus, the solpe of the line is 1/4.
Step-by-step explanation:
Given data:
The given graph of the line.
The slope of the line passing through (4, 0) and (12, 2) is,
\begin{gathered}\begin{gathered} m=\frac{2-0}{12-4} \\ =\frac{2}{8} \\ =\frac{1}{4} \end{gathered}\end{gathered}
m=
12−4
2−0
=
8
2
=
4
1
Thus, the solpe of the line is 1/4.
Question 5The table below shows the coordinates of a figure that was transformed.Pre-ImageImageA(5,2)B(6, 1)A'(0,0)B'(1, -1)C'(-1,3)C(4,5)Which is a correct description of the transformation?
Answers
You have the following A, B and C points, which are transformed to the points A', B' and C', jus
find the height of the trapezoidA=80 CM2 7Cm9CM
Answers
The area formula for trapezoids is
[tex]A=\frac{(B+b)h}{2}[/tex]Where B = 9 cm, b = 7 cm, and A = 80 cm2. Let's replace these dimensions to find h
[tex]\begin{gathered} 80=\frac{(9+7)\cdot h}{2} \\ 160=16h \\ h=\frac{160}{16} \\ h=10 \end{gathered}[/tex]Hence, the height is 10 cm.Find the perimeter of the rectangle. Write your answer in scientific notation.Area = 5.612 times 10^14 cm squared9.2 times 10^7cm is one side of the perimeter
Answers
Answer: Perimeter = 1.962 x 10^8 cm
Explanation:
The first step is to calculate the width of the rectangle. Recall,
Area = length x width
width = Area /length
From the information given,
Area = 5.612 times 10^14 cm squared
Length = 9.2 times 10^7cm
Thus,
width = 5.612 times 10^14 /9.2 times 10^7
width = 6.1 x 10^6
The formula for calculating the perimeter is
Perimeter = 2(length + width)
Thus,
Perimeter = 2(9.2 x 10^7 + 6.1 x 10^6)
Perimeter = 1.962 x 10^8 cm
which are thrwe ordered pairs that make the equation y=7-x true? A (0,7) (1.8), (3,10) B (0,7) (2,5),(-1,8) C (1,8) (2,5),(3,10)D (2,9),(4,11),(5,12)
Answers
In order to corroborate that the points belong to the equation, we must subtitute the points into the equation.
If we substitute the points from option A, we get
[tex]\begin{gathered} 7=7-0 \\ 7=7 \end{gathered}[/tex]for (1,8), we have
[tex]\begin{gathered} 8=7-1 \\ 8=6\text{ !!!} \end{gathered}[/tex]then, option A is false.
Now, if we substitute the points in option B, for point (2,5), we have
[tex]\begin{gathered} 5=7-2 \\ 5=5 \end{gathered}[/tex]which is correct. Now, for point (-1.8) we obtain
[tex]\begin{gathered} 8=7-(-1) \\ 8=8 \end{gathered}[/tex]Since all the points fulfil the equation, then option B is an answer.
Lets continue with option C and D.
If we substitute point (1,8) from option C, we have
[tex]\begin{gathered} 8=7-1 \\ 8=6\text{ !!!} \end{gathered}[/tex]then, option C is false.
If we substite point (4,11) from option D, we get
[tex]\begin{gathered} 11=7-4 \\ 11=2\text{ !!!} \end{gathered}[/tex]then, option D is false.
Therefore, the answer is option B.
A building worth $829,000 is depreciated for tax purposes by its owner using the straight-line depreciation method.
The value of the building, y, after x months of use, is given by y=829,000-2700x dollars. After how many years will
the value of the building be $699,400?
Answers
The value of the building would be $699,400 in 4 years.
What will be the value of the building?Depreciation is the when the value of an asset reduces as a result of wear and tear. Straight line depreciation is a method used in depreciating the value of an asset linearly with the passage of time.
The equation that can be used to determine the value of the building with a straight line depreciation is:
Value of the asset = initial value of the asset - (number of months x deprecation rate)
y = 829,000 - 2700x
The first step is to determine the number of months it would take for the building to have a value of $699,400.
$699,400 = 829,000 - 2700x
829,000 - 699,400 = 2,700x
129,600 = 2,700x
x = 129,600 / 2,700
x = 48 months
Now convert, months to years
1 year = 12 months
48 / 12 = 4 years
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Multiply. (−5 2/5)⋅3 7/10. −19 49/50. −15 7/25. −9 1/10. -1 7/10
Answers
To perform this multiplication, first, we have to transform the mixed numbers into fractions as follows:
[tex]-5\frac{2}{5}=-\frac{5\cdot5+2}{5}=-\frac{27}{5}[/tex][tex]3\frac{7}{10}=\frac{3\cdot10+7}{10}=\frac{37}{10}[/tex]Substituting these values into the multiplication, we get:
[tex]\begin{gathered} (-5\frac{2}{5})\cdot3\frac{7}{10}= \\ =(-\frac{27}{5})\cdot\frac{37}{10}= \\ =-\frac{27\cdot37}{5\cdot10}= \\ =-\frac{999}{50} \end{gathered}[/tex]This result can be expressed as a mixed number as follows:
[tex]-\frac{999}{50}=-\frac{950+49}{50}=-(\frac{950}{50}+\frac{49}{50})=-(19+\frac{49}{50})=-19\frac{49}{50}[/tex]
The price of Stock A at 9 A.M. was $15.21. Since then, the price has been increasing at the rate of $0.07 each hour. At noon the price of Stock B was $15.96. It begins to decrease at the rate of $0.15 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
Answers
The price of the two stocks will be same in 1 hours .
in the question ,
it is given that
the price of the stock A at 9 A.M is $15.21
price increases at the rate of 0.07 each hour .
so the price of the stock A at 12 P.M. is 15.21 + 0.21 = $15.42
and the price of the stock A after x hours from 12 P.M. is given by the equation
stock A = 15.42 + 0.07(x)
the price of stock B at 12 P.M. is $15.96
price decreases at the rate of 0.15 each hour .
the price of the stock B after x hours from 12 P.M. is given by the equation
stock B = 15.96 - 0.15(x)
since the price of the two stocks is same , we equate both the equations .
15.42 + 0.07(x) = 15.96 - 0.15(x)
15.42 + 0.07x = 15.96 - 0.15x
0.15x + 0.07x = 15.42 - 15.21
0.22x = 0.21
x = 0.9545
x ≈ 1
Therefore , The price of the two stocks will be same in 1 hours .
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I need answer for this word problems you have to shown that you can make several lattes then you add milk and begin to stirring. you use a total of 30 ounces of liquid. write an equation that represents the situation and explain what the variable represents.
Answers
hello
the question here is a word problem and we can either use alphabhets to represent the variables.
let lattes be represented by x and milk be represented by y
[tex]x+y=30[/tex]since the total ounce of liquid is equals to 30, we equate the whole sentence to 30.
Solve for x. 8x-2x+7>21+10
Answers
Answer: [tex]x > 4[/tex]
Step-by-step explanation:
[tex]8x-2x+7 > 21+10\\\\6x+7 > 31\\\\6x > 24\\\\x > 4[/tex]
A storm is moving at 30km/hr .it is 60 km away. What time will it arrive
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From the information provided, the storm is travelling at a speed of 30km/hr. In other words, its travelling 30 kilometers every hour. If the storm is 60 kilometers away, then we have the following ratio;
[tex]undefined[/tex]a rectangular prisim has a volume of 80cm cubed it has a length of 2cm and a width of 5cm. What is the prisms height?
Answers
rectangular prism volume is ,
[tex]\begin{gathered} V=l\times b\times h \\ 80=2\times5\times h \\ h=\frac{80}{10} \\ h=8\text{ cm } \end{gathered}[/tex]The transformation T-2,3 maps the point (7,2) onto the point whose coordinates are
Answers
we know that
the rule of the translation in this problem is 2 units at left and 3 units up
so
(x,y) ------> (x-2,y+3)
Apply the rule
(7,2) ------> (7-2,2+3)
(5,5)1. The equations y = x2 + 6x + 8 and y = (x + 2)(x+4) both define thesame quadratic function.Without graphing, identify the x-intercepts and y-intercept of the graph.Explain how you know
Answers
Given the quadratic equation
[tex]y=x^2\text{ +6x + 8}[/tex](1) x-intercepts are -2 and -4 is the points that pass through the x-axis
when y = 0
[tex]\begin{gathered} y\text{ = 0 } \\ x^2\text{ + 6x + 8 = 0} \\ x^2+2x\text{ +4x +8 = 0} \\ (x\text{ + 2)(x +4)=0} \\ x\text{ +2 = 0 or x +4 =0} \\ x\text{ = -2 or x = -4} \end{gathered}[/tex](11) y-intercepts = 8 is the points that pass through the y axis when x = 0
[tex]\begin{gathered} y=x^2\text{ +6x +8} \\ \text{when x = 0} \\ y=0^2\text{ +6(0) +8} \\ \text{y = 8} \end{gathered}[/tex]
A 43-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first
piece, and the third piece is three inches more than five times the length of the first piece. Find the
lengths of the pieces.
What is the length of the first piece?
Answers
The length of the first piece is 5 inches when a 43-inch piece of steel is cut into three pieces.
According to the question,
We have the following information:
A 43-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is three inches more than five times the length of the first piece.
Now, let's take the length of the first piece to be x inches (as shown in the figure).
Length of second piece = 2x inches
Length of third piece = (3+5x) inches
Now, we have the following expression for addition:
x + 2x + 3 + 5x = 43
8x+3 = 43
8x = 43-3
8x = 40
x = 40/8
x = 5 inches
Hence, the length of the first piece is 5 inches.
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I need some help with this (and no this is not a test)
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You have the following expression:
[tex]a_n=3+2(a_{n-1})^{2}[/tex]consider a1 = 6.
In order to determine the value of a2, consider that if an = a2, then an-1 = a1. Replace these values into the previous sequence formula:
[tex]\begin{gathered} a_2=3+2(a_1)^{2}= \\ 3+2\mleft(6\mright)^2= \\ 3+2(36)= \\ 3+72= \\ 75 \end{gathered}[/tex]Hence, a2 is equal to 75
A) 14x + 7y > 21 B) 14x + 7y < 21 C) 14x + 7y 5 21 D) 14x + 7y 221match with graph
Answers
As all the options are the same equation
so, we need to know the type of the sign of the inequality
As shown in the graph
The line is shaded so, the sign is < or >
The shaded area which is the solution of the inequaity is below the line
So, the sign is <
So, the answer is option B) 14x + 7y < 21
Maura and her brother are at a store shopping for a beanbag chair for their school's library. The store sells beanbag chairs with different fabrics and types of filling. Velvet Suede Foam 2 7 Beads 2 7 What is the probability that a randomly selected beanbag chair is filled with beads and is made from velvet? Simplify any fractions.
Answers
The store sells a total of 18 types of chairs (this is the sum of all the types of chairs in the two way frequency table). From this table we notice that only two of them are filled with beads and made from velvet. Then the probability of choosing this is:
[tex]P=\frac{2}{18}=\frac{1}{9}[/tex]Therefore the probability is 1/9
Jx+Ky< assume J<0
The equivalent inequality with x isolated in the left side is
Answers
The equivalent inequality with x isolated in the left side is x<(L-Ky)/J
What is equivalent inequality?A positive number divided by both sides of an inequality results in an equal inequality. And if the inequality symbol is reversed, division on both sides of an inequality with a negative value results in an analogous inequality.
Following step by step process-
Jx+Ky<L (Given)
Subtracting Ky on both the side
Jx<L-Ky
Now dividing by J both side
x<(L-Ky)/J
Therefore, equivalent inequality with x isolated in the left side is x<(L-Ky)/J.
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The complete question is:
"Jx+Ky<L assume J<0
The equivalent inequality with x isolated in the left side is"
Score: U OQuestion Help3.3.29CeringritdA train travels 140 km in the same time that a plane covers 630 km. If the speed of the plane is 30 km per hr less than 5 times the speed ofTrain140the train, find both speeds.Planey 630The train's speed is km per hr
Answers
Notice that the time for both trips is the SAME but not known (let's use the letter T to address this unknown).
We also assign St to the speed of the train, and Sp to the speed of the plane.
Then, the relationship between the speeds according to the information they provide, is given by the equation:
Sp = 5 * St - 30
we also know that the train covers 140 km in the time T, Then according to the formula for speed (distance divided by time) we can say:
St = 140 km / T, therefore T = 140 km / St
We do something similar with the information on the distance covered by the plane:
Sp = 630 km / T which solving for T gives:
T = 630 km / Sp
Now we equal the expressions for T (since that time is the SAME as we noticed before, and get:
630 km / Sp = 140 / St
we corss-multiply to get the speeds in the numerator:
630 St = 140 Sp
ANd we use the very first equation we wrote (Sp = 5 * St - 30)
to replace Sp in terms of St:
630 St = 140 (5 St - 30)
Now use distributive property on the right to eliminate the parenthesis:
630 St = 700 St - 4200
add 4200 to both sides, and subtract 630 St from both sides :
4200 = 700 St - 630 St
4200 = 70 St
divide both sides by 70 to isolate St completely:
St = 4200 / 70
St = 60 km/h (this is the speed of the train)
Now we can find the value of the speed of the plane, using the first equation again:
Sp = 5 * St - 30 = 5 (60) - 30 = 300 - 30 = 270 km/h
Then the speed of the plane is: 270 km/h
Applying the product rule to expression \left(3^3\div 3^4\right)^5gives us Answer raised to the power of Answerdivided by Answer raised to the power of AnswerSimplify that into a reduced fraction.The numerator is AnswerThe denominator is Answer
Answers
Given the expression
[tex](3^3\div3^4)^5[/tex]Using product rule
[tex]\begin{gathered} (3^3\div3^4)^5=(\frac{3^3}{3^4})^5 \\ =(3^{3-4})^5=(3^{-1})^5 \\ =3^{-1\times5}=3^{-5} \end{gathered}[/tex]Where
[tex]3^{-5}=\frac{1}{3^5}=\frac{1}{243}[/tex]Hence, answer is 1/243
[tex](3^3\div3^4)^5=\frac{1}{243}[/tex]The numerator is 1
The denominator is 243
Cai says you can divide both quantities in a ratio by the same non-zero number to find an equivalent ratio. Explain why cai is correct.
Answers
In this case, Cai is right.
Basically, Cai is right because a ratio is a fraction. So, if you divide the numerator and denomirator by the same number, the fraction won't be changed, in that case you would get an equivalent fraction.
For example, if we have 4/6, and we divide both numbers by 2, we get 2/3, these operations are valid because you are dividing both numbers by the same (2).
Which statements are true about the result of simplifying this polynomial?
Answers
To answer the question, we must simplify the following expression:
[tex]t^3(8+9t)-(t^2+4)(t^2-3t)[/tex]We expand the terms in the polynomial using the distributive property for the multiplication:
[tex]8t^3+9t^4-(t^4-3t^3+4t^2-12t)[/tex]Simplifying the last expression we have:
[tex]^{}^{}8t^4+11t^3-4t^2+12t[/tex]We see that the simplified expression:
• is quartic,
,• doesn't have a constant term,
,• has four terms,
,• is a polynomial,
,• it is not a trinomial.
Answer
The correct answers are:
• The simplified expression has four terms.
,• The simplified expression is a polynomial.
