Answers
A graph of triangle ABC is shown below.
A graph of triangle A'B'C, the image of ΔABC after a translation right 1, down 3 is shown below.
A graph of triangle A"B"C", the image of ΔABC after a dilation of 2 is shown below.
ΔA"B"C" does not represent a rigid motion because the pre-image and the image are not congruent.
How to perform the sequence of transformations?By translating the pre-image triangle ABC vertically down 3 units and horizontally right 1 unit, the coordinates of the image of triangle A'B'C'D' include the following:
(x, y) → (x + 1, y - 3)
Coordinate A = (2, 3) → Coordinate A' = (2 + 1, 3 - 3) = (3, 0)
Coordinate B = (4, 0) → Coordinate B' = (4 + 1, 0 - 3) = (5, -3)
Coordinate C = (5, 4) → Coordinate C' = (5 + 1, 4 - 3) = (6, 1)
By applying a dilation with a scale factor of 2 centered at the origin, we have:
Coordinate A = (2, 3) → Coordinate A" = (4, 6)
Coordinate B = (4, 0) → Coordinate B" = (8, 0)
Coordinate C = (5, 4) → Coordinate C" = (10, 8)
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Related Questions
Please help me PLEASE ANYEONE?!!!?!!
Answers
Step-by-step explanation:
1/3 ÷ 3
= 1/3 ÷ 3/1
= 1/3 X 1/3 = 1/9
Similarly
1/4 ÷ 5 = 1/4 X 1/5 = 1/20
Answer: 1/9
Picture a pie and and having 1 slice out of the total 3 pieces, which would be 1/3 of the pie. Now, we want to divide the the pie into 3 more equal-piece groups. This means every original piece of the pie would now have 3 slices in each piece, so the pie would have a total of 9 pieces now. We want to keep our original 1 slice of pie, but now we have taken 1/9 of the pie, a much smaller slice.
What we have done is simply multiplied the denominator (bottom number of the fraction) by 3. In other words, the number of total pieces of pie is tripled from 3 to 9, meaning more slices would have to be cut, but the amount of pie stays the same. We are just taking a smaller slice. This is why the rule for dividing fractions is Keep Change Flip, because we really just want to the denominator to multiply.
Question 10: 1/4÷5
Answer: 1/20
The same logic applies.
the salaries of engineers at a computer company are normally distributed with mean $83,422 and standard deviation $8,278
Answers
The probability of observing an income between $70,000 and $90,000 for engineers at this computer company is 0.6217, or about 62.17%.
To solve this problem, we need to standardize the given income range using the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can do this by using the formula:
z = (x - μ) / σ
where x is the income, μ is the mean income, and σ is the standard deviation.
For the lower bound of $70,000, we have:
z₁ = (70,000 - 83,422) / 8,278 = -1.62
For the upper bound of $90,000, we have:
z₂ = (90,000 - 83,422) / 8,278 = 0.79
We can now find the probability of observing an income between $70,000 and $90,000 by calculating the area under the standard normal curve between z₁ and z₂.
We can use a standard normal distribution table or a calculator to find this probability, which turns out to be approximately 0.6217. This means that about 62.17% of engineers at this company earn an income within this range.
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Complete question is:
The salaries of engineers at a computer company are normally distributed with mean $83,422 and standard deviation $8,278. What is the probability of observing an income between $70,000 and $90,000?
Determine the measures of the arcs and angles:
*It may help to find all central angle measures before answering the hotspots.
If you do any calculating, you can type that into the hotspot with your final answer.
m HE
m HD
m DG
m EG
m < DEG
m < HGE
Answers
The values of the arc length and angles are:
HE = 62
HD = 118
DG = 62
EG = 118
∠DEG + ∠HGE = 62
We have,
The central angle is equal to the intercepted arc length.
So,
62° = HE
And,
∠A = HD
∠A + 62 = 180
∠A = 180 - 62
∠A = 118
HD = 118
And,
DG = ∠M (say)
∠A + 118 = 180
∠M = 180 - 118
∠M = 62
DG = 62
And,
∠A is opposite to ∠N (say)
So,
∠A = ∠N = 118
∠A = EG
EG = 118
And,
From the definition of the exterior angle.
∠DEG + ∠HGE = 62 ______(1)
Also,
The sum of the three angles in AEG = 180
∠EAG + ∠DEG + ∠HGE = 180
∠EAG = 180 - 62 = 118
So,
∠DEG + ∠HGE = 180 - 118
∠DEG + ∠HGE = 62 _______(2)
Thus,
HE = 62
HD = 118
DG = 62
EG = 118
∠DEG + ∠HGE = 62
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Plot the coordinates on the number line provided and then find the coordinate of the indicated point
on a number line that partitions the segment into the given ratio.
A is at 1, and B is at 10. Find the point, T, so that T is two-thirds of the distance from A to B.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3
4 5 6 7 89
+
10
Answers
Answer:
t = 6.8
Explanation:
We know that A is at 1, B is at 10, so that is where we place those two.
First, we need to know what 2/3 of 10 is because the distance between A and B is 10.
Solving 2/3 of 10:
_____________________
- Divide 10 by the denominator, 3
10 ÷ 3 = 3.3333......
- Multiply 3.3333..... by 2
3.3333..... x 2 = 6.6666666666667
or about 6.8 if we round up, which is prefered in these scenarios
Now that we know what 2/3 of 10 is, we can use that number as where to put it on the number line.
So t = 6.8
Hope this helps :)
Circle A has a circumference of 8π/x+2 units and Circle B has a circumference of 4π/x+2 units. What is a simplified expression for the difference in the areas of Circle A and B
Answers
The simplified expression for the difference in the area of circle A and B is 12π/(x+2)²
What is area of a circle?A circle is simply a round shape that has no corners or line segments. The area of a circle is expressed as;
A = πr²
The circumference of a circle = 2πr
for circle A;
8π/x+2 = 2πr
r = 8π/x+2 × 1/2π
r = 4/x+2
area = πr² = (4/x+2)²π
for circle B
4π/x+2 = 2πr
r = 4π/x+2 × 1/2π
r = 2/2x+2
area =( 2/2x+2)²π
difference = (4/x+2)²π - ( 2/x+2)²π
= π/(x+2)²( 4²-2²)
= π/(x+2)²(16-4)
= 12π/(x+2)²
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Find the total cost for the month in dollars. The federal tax is 3%. Use the figure below.
Monthly phone service plan is $52.00. Four lines and 3,487 minutes are used.
Answers
Answer:
The total cost per month is $190.76 to the nearest cent.
Step-by-step explanation:
From the given table, the monthly service plan costing $52.00 is:
Monthly Service Plan = $52.00Number of included minutes per month = 2,000 minutesCost per additional line per month = $21.99Overage per minute rate = $0.06The base calling plan includes two lines.
Therefore, for 4 lines, we will need to pay for 2 additional lines per month:
⇒ $21.99 × 2 = $43.98 per month
If 3,487 minutes are used per month, then the overage of minutes is:
⇒ 3487 - 2000 = 1487 minutes per month
As the overage rate is $0.06 per minute, then the cost of the additional minutes is:
⇒ 1487 × $0.06 = $89.22 per month
Therefore, the total cost per month before tax is:
⇒ $52.00 + $43.98 + $89.22 = $185.20
To apply the federal tax of 3%, multiply the total cost by 1.03:
⇒ $185.20 × 1.03 = $190.756 = $190.76 (nearest cent)
Therefore, the total cost per month is $190.76 to the nearest cent.
An online television company is sending out surveys to rank 10 TV-show genres watched. What is the probability that you guess the top 3 genres correctly and in the correct order?
Write your answer as an exact fraction which is reduced as much as possible.
Answers
Answer:
The probability of guessing the first genre correctly is 1/10. After guessing the first genre, the probability of guessing the second genre correctly is 1/9. Similarly, the probability of guessing the third genre correctly is 1/8. Therefore, the probability of guessing the top 3 genres correctly and in the correct order is:
1/10 * 1/9 * 1/8 = 1/720
So the exact probability is 1/720, which is already reduced to its simplest form.
If the price of a particular chocolate bar is increased by 20%, and it used to be $2, what is the new price after the increase?
Answers
To find this, you can multiply the original price ($2) by 1.20, which represents the 20% increase.
$2 x 1.20 = $2.40
So the chocolate bar now costs $2.40 after the 20% increase.
Asap need help quick
Answers
The function rule for the graph is -2 ≤ x ≤ 1 , where x is the domain
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is plotted on the graph
The values of the output represents the range of the function and the domain of the function is the input
So , the x values ranges from [ -2 , 1 ]
Hence , the function rule is domain ranges from -2 ≤ x ≤ 1
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a parallelogram has a base of 6 centimeters and a height of 10 centimeters. this parallelogram has the same area as a triangle with a height of 5 centimeters. what is the measure, in centi,of the base of the triangle?
Answers
The area of the parallelogram can be found using the formula A = base × height:
A = 6 cm × 10 cm
A = 60 cm²
The area of a triangle is given by the formula A = 1/2 × base × height. We know the height is 5 cm and the area is also 60 cm² (since it is equal to the parallelogram). So, we can solve for the base:
60 cm² = 1/2 × base × 5 cm
Dividing both sides by 1/2 × 5 cm gives:
base = 24 cm
Therefore, the base of the triangle is 24 centimeters.
Answer:
24cm
Step-by-step explanation:
binge drinking and auto accidents
44% engaged binge drinking
37% drank moderately
9% abstain
17% accident/binge
9% accident/non-binge
what’s p(accident/abstain)
Answers
Answer:
We can solve this problem using the following steps:
1. **Calculate the probability of being in each group.**
The probability of being in the binge drinking group is 44%.
The probability of being in the moderate drinking group is 37%.
The probability of being in the abstain group is 9%.
2. **Calculate the probability of being in the accident group.**
The probability of being in the accident group is 17% + 9% = 26%.
3. **Calculate the probability of being in the abstain group and having an accident.**
The probability of being in the abstain group and having an accident is the probability of being in the abstain group multiplied by the probability of having an accident, given that you are in the abstain group.
The probability of being in the abstain group is 9%.
The probability of having an accident, given that you are in the abstain group, is the probability of being in the accident group and being in the abstain group, divided by the probability of being in the abstain group.
The probability of being in the accident group and being in the abstain group is 9%.
The probability of being in the abstain group is 9%.
Therefore, the probability of having an accident, given that you are in the abstain group, is 9% / 9% = 1.
4. **Calculate the probability of having an accident and being in the abstain group.**
The probability of having an accident and being in the abstain group is the probability of being in the abstain group and having an accident.
The probability of being in the abstain group is 9%.
The probability of having an accident, given that you are in the abstain group, is 1.
Therefore, the probability of having an accident and being in the abstain group is 9% * 1 = 9%.
**Answer:**
The probability of having an accident and being in the abstain group is 9%.
Kendra is doing her math homework. For each problem, she uses 12
1
2
of a sheet of paper. How many sheets of paper will she need to complete 10 problems?
Answers
There are 5 sheets of paper will she need to complete 10 problems.
We have to given that;'
Kendra is doing her math homework. For each problem, she uses 1/2 of a sheet of paper.
Hence, For complete 10 problems, number of sheets are,
⇒ 1/2 of 10
⇒ 1/2 x 10
⇒ 5
Thus, There are 5 sheets of paper will she need to complete 10 problems.
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dillon has a bank account that pays 3.2% simple interest. his balance is $1,766. how long will it take for the amount in the account to grow to $2,000? round to the nearest year.
Answers
It will take approximately 4 years for the amount in Dillon's bank account to grow to $2,000.
We use the formula for simple interest to solve this problem;
I = P × r × t
where;
I = the interest earned
P = the initial principal (balance) = $1,766
r = the interest rate (as a decimal) = 3.2% = 0.032
t = the time (in years) we need to find
We know that the interest earned is the difference between the final amount (balance + interest) and the initial principal (balance), so we can write;
Interest = Final Amount - Initial Principal
Plugging in the values, we get;
I = $2,000 - $1,766
I = $234
Now we can substitute the values of I, P, and r into the simple interest formula and solve for t;
234 = 1766 × 0.032 × t
Dividing both sides of the equation by (1766 * 0.032) to isolate t:
t = 234 / (1766 × 0.032)
t ≈ 4.19
So, it will take approximately 4.19 years for the amount in Dillon's bank account to grow to $2,000. Since time cannot be in decimal years, we round to the nearest whole year:
t ≈ 4
Therefore, it will take 4 years for the amount in Dillon's bank account to grow to $2,000.
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please help me i relly need help
Answers
Answer:
h(x) = 3·2^x
Step-by-step explanation:
You want the equation of the exponential curve h(x) = a·b^x when it goes through the points (0, 3) and (1, 6).
PointsWhen x=0, the equation is ...
h(0) = a·b^0 = a
We know that h(0) = 3, so a = 3.
When x=1, the equation is ...
h(1) = 3·b^1 = 3b
We know that h(1) = 6, so 3b = 6, or b = 2.
The equation is h(x) = 3·2^x.
<95141404393>
The constraints of a problem are listed below. What are the vertices of the feasible region?
[tex]x+y\leq 7\\x-2y\leq -2\\x\geq 0\\y\geq 0[/tex]
Answers
The vertices of the feasible region is (4, 3)
What are the vertices of the feasible region?From the question, we have the following parameters that can be used in our computation:
x + y ≤ 7
x - 2y ≤ -2
x ≥ 0
y ≥ 0
Express as equations
So, we have
x + y = 7
x - 2y = -2
Subtract the equations
3y = 9
So, we have
y = 3
Next, we have
x + 3 = 7
This gives
x = 4
Hence, the vertex of the feasible region is (4, 3)
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=
Let v be the vector from initial point P₁ to terminal point P2. Write v in terms of i and j.
P₁ =(-6,5), P2 = (5,5)
V=
(Type your answer in terms of i and j.)
Answers
The Vector form is v = 11i + 0j.
We have,
P₁ =(-6,5), P2 = (5,5)
If we have the point p1 and p2 then the vector form p1 -> p2 is
v = p2 - p1
v = [ p(2x) - p(1x)) i + [ p (2y) - p(1y)] j
v = (5 - (-6)) i + (5 - 5)j
v = 11i + 0j
v = 11 i
Thus, the vector form is v = 11i + 0j.
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I need help on the things in the image
Answers
The match of the given words as per the definition of the terms related to data set is as follow.
1 → g
2 →c
3 → b
4 → d
5 → f
6 → a
7 → e
The description of the each word as per the definition is ,
Mean represents the average of the data.
1→g
Spread represents the similarity or variability of the set of observed values of the data.
2→c
Center represents the middle value of the data set.
3→ b
Shape represents the values of the data set when plotted on the graph.
4 → d.
Median represents the middle value of the data set after arranging in ascending or descending order.
5 →f
Distribution represents measure of all the values of the data set spread.
6→a
variability represents the set of such values which satisfies the statistical question or relation.
7 → e.
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F(x) = 2^x
Elija todas las siguientes afirmaciones que describen el gráfico.
A. Cuando x tiende a infinito negativo, f(x) tiende a 0.
B. Cuando x tiende a infinito negativo, f(x) tiende a infinito.
OC. Cuando x tiende a infinito, f(x) tiende a 0.
OD. Cuando x tiende a infinito, f(x) tiende a infinito.
Answers
By analyzing the end behavior of the function we can see that the correct options are A and D.
Which statements are true for the given function?Here we have the exponential function:
[tex]F(x) = 2^x[/tex]
This is an exponential growth, this means that as x increases also does the function, then the end behavior of the function is:
as x → ∞, f(x) → ∞
And when x is a really large negative number, the function tends to zero, then we have:
as x →-∞, f(x) → 0
Then the correct options are A and D.
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An object is dropped from a height of 400 feet. The amount of time, in seconds, the object takes to hit the ground can be found by solving the equation - 16r2 + 400 = 0. How many seconds will it take to hit the ground?
05
O 5 or-5
O 12
O 25
Answers
It will take 5 seconds for the object to hit the ground
How many seconds will it take to hit the ground?From the question, we have the following equation that can be used in our computation:
-16r^2 + 400 = 0
So, we have
- 16r^2 = -400
Divide by -16
This gives
r^2 = 25
Take the square root of both sides
r = 5
Hence, the number of seconds is 5
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In a normal distribution, what percentage of the data falls within 2 standard
deviations of the mean?
A. 99.7%
B. 68%
C. 34%
D. 95%
Answers
The percentage of the data that falls within 2 standard deviations of the mean is B. 68%
Calculating the percentage of dataFrom the question, we have the following parameters that can be used in our computation:
Percentage = 2 standard deviations
As a general rule:
The percentage of the data that falls within 2 standard deviations of the mean is 68%
This means that the correct option is (b) 68%
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Which choices are equivalent to the expression below? Check all that apply.
4√3
A. 48
B. 12.4
C. √24√2
D. 3 16
E. 4.3
F. 48
Answers
The choices that are equivalent to the expression 4√3 will be ✓48 and ✓24.✓2.
How to explain the expressionIt is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
4✓3 will be:
= ✓4² × ✓3
= ✓48
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PLEASE HELP (WILL GIVE BRAINLIEST
Answers
Answer:
second option
Step-by-step explanation:
the volume of a cone is calculated as
[tex]\frac{1}{3}[/tex] πr²h
the volume of a sphere is calculated as
[tex]\frac{4}{3}[/tex] πr³
then the volume of a hemisphere is
[tex]\frac{1}{2}[/tex] × [tex]\frac{4}{3}[/tex] πr³ = [tex]\frac{2}{3}[/tex] πr³
then the volume (V) of the composite solid is
V = [tex]\frac{1}{3}[/tex] πr²h + [tex]\frac{2}{3}[/tex] πr³
Circle the students error in the problem below and rewrite what correct step should be
Answers
The students error is in step 3 and the correct solution is g(x) = 2x² + 4x - 4
Circling the students errorFrom the question, we have the following parameters that can be used in our computation:
The steps to solve the expression
From step 2 to step 3, we have
g(x) = 2(x + 1)(x + 1) - 6
g(x) = 2(x² + 1x + 1) - 6
The step 3 is incorrect
Because when the expression is expanded, we have
g(x) = 2(x² + 2x + 1) - 6
This gives a solution of
g(x) = 2x² + 4x - 4
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answer quick i need done
Answers
The new vertices of the triangle after moving the triangle 5 units down, are A(1,-7), B(9,-7), and C(5,-3). So, correct option is B.
To determine the coordinates of the triangle after it is translated 5 units down, we need to subtract 5 from the y-coordinates of each vertex.
Let's start with vertex A(1,-2). If we subtract 5 from -2, we get -7. Therefore, the new coordinates of vertex A are (1,-7).
Next, let's look at vertex B(9,-2). Again, if we subtract 5 from -2, we get -7. So the new coordinates of vertex B are (9,-7).
Finally, let's consider vertex C(5,2). If we subtract 5 from 2, we get -3. So the new coordinates of vertex C are (5,-3).
In this case, we are moving the triangle 5 units down, which means that we are subtracting 5 from the y-coordinates of each vertex. This is a common transformation in geometry, and it's important to be familiar with it when working with shapes and figures in the Cartesian plane.
So, correct option is B.
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What is the initial value of Y=2x+3
Answers
Answer:3
Step-by-step explanation: Initial value = y-intercept
Simplify.
^m√a^2m
help asap please
Answers
Answer:
Step-by-step explanation:
m
2
−2m−8
Factor the expression by grouping. First, the expression needs to be rewritten as m
2
+am+bm−8. To find a and b, set up a system to be solved.
a+b=−2
ab=1(−8)=−8
Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product −8.
1,−8
2,−4
Calculate the sum for each pair.
1−8=−7
2−4=−2
The solution is the pair that gives sum −2.
a=−4
b=2
Rewrite m
2
−2m−8 as (m
2
−4m)+(2m−8).
(m
2
−4m)+(2m−8)
Factor out m in the first and 2 in the second group.
m(m−4)+2(m−4)
Factor out common term m−4 by using distributive property.
(m−4)(m+2)
I need help
Given the function f(t) = 2t + 1 and its domain is described by the set (1, 2, 3, 5) what is the range? (Enter the values of the range from least to greatest
Answers
The range of the given linear function; f(t) = 2t + 1 given its domain (1, 2, 3, 5) is; (3, 5, 7, 11).
What is the range of the given function?It follows from the task content that the range of the given function is to be determined given its domain as defined by the set; (1, 2, 3, 5).
Therefore;
At t = 1; f(1) = 2(1) + 1 = 3.
At t = 2; f(2) = 2(2) + 1 = 5.
At t = 2; f(3) = 2(3) + 1 = 7.
At t = 5; f(5) = 2(5) + 1 = 11.
Ultimately, the range of the given function as required is given by the set; (3, 5, 7, 11).
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how much cardboard is needed to make the single slice pizza box shown
Answers
that would be 5 pieces of cardboard needed
Help time limit
State the domain and range for each graph and then tell if the graph is a function (yes or no)
Answers
Answer:yes, it’s a function, domain is all real # range all real #
Step-by-step explanation:
The change in water level of a pond is shown in the table.
Week
1
2
3
4
5
Water level (inches)
-1 1/4
1 3/8
2 1/2
-1 5/8
-1 3/4
Between which two weeks did the water level change the most? Calculate the change.
Answers
Between Weeks 3 and 4, the water level varied the greatest.
To determine which two weeks had the greatest change in water level, we need to find the difference between each pair of consecutive weeks and identify the largest difference.
Here are the differences between consecutive weeks:
Week 1 to Week 2: (1 3/8) - (-1 1/4) = 2 5/8
Week 2 to Week 3: 2 1/2 - 1 3/8 = 1 1/8
Week 3 to Week 4: (-1 5/8) - 2 1/2 = -4 1/8
Week 4 to Week 5: (-1 3/4) - (-1 5/8) = -1/8
The largest difference is between Week 3 and Week 4, with a difference of 4 1/8 inches.
Therefore, the water level changed the most between Week 3 and Week 4.
Note that the differences are calculated by subtracting the water level of the earlier week from the water level of the later week.
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