The image of the point (-6, -2) after dilation by a scale factor of 4 centered at the origin is (-24, -8).
What is a scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object,
We have,
To find the image of the point (-6, -2) after dilation by a scale factor of 4 centered at the origin, we can use the following formula:
(x', y') = (kx, ky)
where (x, y) are the coordinates of the original point, (x', y') are the coordinates of the image after dilation, k is the scale factor, and (0, 0) is the center of dilation.
Substituting the values given in the problem, we get:
(x', y') = (4*(-6), 4*(-2))
Simplifying,
(x', y') = (-24, -8)
Therefore,
The image of the point (-6, -2) after dilation by a scale factor of 4 centered at the origin is (-24, -8).
Learn more about scale factors here:
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From the top of a building, 40 feet above the ground, a construction worker locates a rock at a 12° angle of depression. How far is the rock from the building?
Answer:
188 m
Step-by-step explanation:
[tex] \tan(12) = \frac{40}{x} \\ x = \frac{40}{ \tan(12) } \\ x = 188[/tex]
Answer:
I think that the other answer is WRONG
tan(12) = [tex]\frac{x}{40}[/tex]
x = tan(12)*40 = 8.5
Step-by-step explanation:
[tex]\frac{sin\left(78\right)}{40}=\frac{sin\left(12\right)}{x}[/tex] = 8.5
Find the measure of the third angle of a triangle if the measures of the other two angles are given.
118.6 and 42.3
The three inside angles of a triangle equal 180.
Subtract the two known angles from 180.
180 - 118.6 - 42.3 = 19.1
The third angle is 19.1
if A×B ={(-1,1),(-1,2),(2,1),(2,2),(3,1),(3,2)}. find A×A and B×B. i need for exam.
Answer:
hope this will help you more
Step-by-step explanation:
Explanation is in the attachmenthope it is helpful to you
stay safe healthy and happy
what are the lengths of SV and QT? no links.
ok so we see that TR is 17 units, so RV is the same amount
3x+2 so 3x=15 so divide both sides by 3 we get x=5
now we know x=5 4x+1=21 and 9x-4=41
*drops microphone*
Answer:
TR = 12
=> 3x + 2 =17
=> x = 5
We have QT = QV (because QTV is an isosceles triangle)
=> QT = 4x+1=4x5+1=21 units
We have TS = SV (because TSV is an isosceles triangle)
=>SV = 9x-4= 9x5-4=41 units
In the picture shown below, what proportion would NOT give the correct value of x?
Answer: (c)
Step-by-step explanation:
In the given figure, two triangles are similar namely [tex]\triangle ABC[/tex] and [tex]\triangle ADB[/tex]
For similar triangles, the ratio of the corresponding sides are equal.
For option (a), Hypotenuse to Perpendicular ratio is given, that is correct
Similarly for option (b), Perpendicular to hypotenuse ratio is given
Both option (a) and (b) gives the same value of [tex]x[/tex] that is,
[tex]\Rightarrow x=\sqrt{81\times 45}\\\Rightarrow x=60.37[/tex]
Option (c) does not give the correct value of [tex]x[/tex]
Answer:
C
Step-by-step explanation:
In the given figure, two triangles are similar namely and
For similar triangles, the ratio of the corresponding sides are equal.
For option (a), Hypotenuse to Perpendicular ratio is given, that is correct
Similarly for option (b), Perpendicular to hypotenuse ratio is given
Both option (a) and (b) gives the same value of that is,
Option (c) does not give the correct value of
subject
Math, 25.02.2021 09:15 hajuyanadoy
Illustrate the following and determine the number of permutations. 1. Arranging 4 pots with different plants in a row
2. Forming a four-digit ATM pin.
3. Securing a motorcycle with a three-digit combination lock using the numbers 1, 2, 3 and 6
4. Displaying 3 identical small vases, 1 figurine, and a photo frame in a row
5. 3 girls sitting around a circular table
Answer:
1: 16
2: 4940
3: 24
4: 25
5: 9
Step-by-step explanation:
A permutation is a method of calculating the number of possible outcomes. It follows the following general formula;
[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]
There (n) is the number of objects, and (r) is the number of objects selected.
1. Arranging 4 pots with different plants in a row
In order to solve this, one needs two pieces of information, the number of objects, and the number of objects selected. One is given the number of objects; (4), but when the problem states "in a row" it never specifies how many plants are in a row. Thus, let one assume that a "row" can have an infinite amount of space, but in this case, only (4) space will be used. Therefore there are (4) objects with (4) objects selected. However, the drawback is that the combination formula doesn't work when the two parameters (n) and (r) are the same. Hence, to solve this special case, one simply multiplies the two numbers to get the answers:
[tex]n*r\\\\=4*4\\\\=16[/tex]
2. Forming a four-digit ATM pin
One is given that there are (4) digits in the ATM pin, this is the number of objects selected. One is also given that number of objects, there are (10) digits including (0). Set up the permutation and solve;
[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]
[tex]_1_0P_4=\frac{10!}{(10-4)!}\\\\=\frac{10!}{6!}\\\\=\frac{10*9*8*7*6*5*4*3*2*1}{6*5*4*3*2*1}\\\\=10*9*8*7\\\\=4940[/tex]
3. Securing a motorcycle with a three-digit combination lock using the numbers (1), (2), (3), and (6).
There are (4) digits to choose from on the lock. But there are (3) numbers that can be selected.
[tex]_4P_3=\frac{4!}{(4-3)!}\\\\=\frac{4!}{1!}\\\\=\frac{4*3*2*1}{1}\\\\=4*3*2*1\\\\=24[/tex]
4. Displaying 3 identical small vases, 1 figure, and a photo frame in a row.
There are (5) objects, and (5) spaces (read problem (1) for an explanation for the objects being put in a row). Thus, this is a special case; multiply the two numbers to get the result;
[tex]n*r\\=5*5\\=25[/tex]
5. 3 girls sitting around a circular table
There are (3) subjects, and (3) spaces in this problem. Apply the same logic applies to a row in this problem. Therefore, this is another special case; multiply the two numbers to get the result;
[tex]n*r\\=3*3\\=9[/tex]
The velocity of a car over five hours is given by v(t) = 60 ln(t + 1), 0 < t < 5
in kilometers per hour. What is the total distance traveled from t = 0 to t = 5?
Round your answer to the nearest whole number and do not include units.
Answer:
345
Step-by-step explanation:
The velocity of a car over five hours is given by:
[tex]\displaystyle v(t)=60\ln(t+1),\, 0 \leq t \leq 5[/tex]
And we want to find the total distance traveled from t = 0 to t = 5.
Recall that distance is the integral of the absolute value of the velocity function. Since we want to find the total distance traveled from t = 0 to t = 5, our limits of integration are t = 0 and t = 5. Hence:
[tex]\displaystyle D=\int_0^5 |\underbrace{60\ln(t+1)}_{v(t)}|\, dt[/tex]
Since v(t) ≥ 0 for all t in the interval [1, 5], we can remove the absolute value. Use a calculator:
[tex]\displaystyle D=60\left(6\ln(6)-5)=345.0334...\approx 345[/tex]
What number is increased by 40% become 28?
a.5 b. 10 c. 15 d. 20
Answer:
d. 20
Step-by-step explanation:
28 ÷ (100%+40%)
= 28 ÷ 140%
= 28 ÷ 1.4 = 20
Answer:
option d
Step-by-step explanation:
Let the number be x
40% of x = 0.40x
Increased by 40% = 28
That is ,
x + 0.40x = 28
1.40x = 28
[tex]x = \frac{28}{1.40}\\[/tex]
[tex]x = \frac{28 \times 100}{1.40 \times 100 } = \frac{28 \times 100}{140} =\frac{4 \times 100}{20} = 4 \times 5 = 20[/tex]
Therefore, the number is 20
Which segment is adjacent to∠N?
Answer:
SN
Step-by-step explanation:
The line segment that is adjacent to angle ∠N will be NS and NJ. Then the correct options are A and B.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
A line segment in mathematics has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a path that joins two places.
The triangle ΔNSJ is a right angle triangle in which the angle ∠NSJ will be a right angle that is 90°.
The line segment that is adjacent to angle ∠N will be NS and NJ. Then the correct options are A and B.
More about the triangle link is given below.
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What did I do wrong in notes, and why is the answer what it shows on screenshot
Answer:
Hope you find it helpful and usef
In right ΔDEF, DF = 20, m∠ F = 90˚, EF = 17. Which of the following is true? Does option 5 apply
Answer:
Step-by-step explanation:
From the picture attached,
ΔDEF is a right triangle with two sides,
EF = 17 units
DF = 20 units
By applying Pythagoras theorem in the given triangle,
DE² = DF² + EF²
(20)² = DF² + (17)²
DF² = 400 - 289
DF = √111
Trigonometric ratios for the ∠F,
sin(F) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
[tex]\text{sin}F=\frac{\sqrt{111}}{20}[/tex]
[tex]\text{cosF}=\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
[tex]\text{cos}F=\frac{17}{20}[/tex]
[tex]\text{tan}F=\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
[tex]\text{tan}F=\frac{\sqrt{111}}{17}[/tex]
Choose the correct option.
help i’m so confused
Answer:
-27/7
Step-by-step explanation:
put x into the equation
Help me with this....After drawing a histogram....How do u find the class in which the median lies in a histogram....
Answer:
Get all the values of the histogram and put them in order:
For example 2,5,7,1,7,3 becomes 1,2,3,5,7,7 and then you get the middle number, which is in this case (3+5)/2=3.5
Then see which of the readings lie on 3.5.
Step-by-step explanation:
9514 1404 393
Explanation:
The histogram will have a count associated with each class. You may have to read the count from the vertical scale of the graph. If it is a histogram of relative frequencies, each class will have a fraction or percentage instead of a count.
Find the total of all counts. Determine what half that number is. If the total is odd, then round up to the nearest integer. This is the index number of the median value.
Add up the counts in the classes starting at one side of the graph, working toward the other side. (Left-to-right is the usual direction for doing this.) When you find the class that increases the total to a value equal or greater than the index number, this is the class that contains the median.
__
If the histogram is a relative frequency histogram, the class that brings the total to 50% is the one containing the median.
__
There may be cases where the total count is even, and the total of all of the classes up to a point is exactly equal to the index number you're looking for. In that case, the median is between that class and the next. Here's an example:
class 1: count 3
class 2: count 5
class 3: count 4
class 4: count 4
Total count: 3+5+4+4 = 16. Median index = 16/2 = 8
Total of classes 1 and 2 = 3+5 = 8. This means exactly half of the represented values are in class 2 or below, and half are in class 3 or above. If you had access to the actual data values, you would find the median as the average of the 8th and 9th data values (when they are sorted into increasing order). Here, the median might be estimated as the value halfway between the upper bound of class 2 and the lower bound of class 3.
__
2nd example
Consider the same histogram as above, but with a count of 3 in class 4. This brings the total count to 15, and the index of the median is 15/2 = 7.5, rounds to 8. Again, the 8th data value (median) is in class 2. There is no ambiguity in this case.
What is the value of W?
5 units
7 units
14 units
15 units
Answer:
5 units!
Step-by-step explanation:
Because Rectangle Perimeter = 2(a+b)
a=2w-1, b=w
2(2w-1+w)=28
3w-1=14
3w=15
w=5
So the answer is 5! 5! 5! A!A!A!
Fighting!! o(≧o≦)o
Find the measure of the missing angle using the exterior angle sum theorm
Answer:
r = 30°
Step-by-step explanation:
According to the Exterior Angle Sum Theorem, the exterior angle, which is 90°, is equal to the 2 interior angles, which are 60° and r°. We know that the angle next to the exterior angle is 90°, and since all angle sums add up to 180°, r = 30°.
Zachary's art club ordered a giant sub sandwich for a party. It was 6 feet long! When the sandwich arrived, Zachary cut it into 16 equal pieces.
How long was each piece?
Write your answer as a proper fraction or mixed number.
Answer:
3/8 feet long
Step-by-step explanation:
Find how long each piece was by dividing 6 by 16:
6/16
Simplify this by dividing each number by 2:
6/16
= 3/8
So, each piece was 3/8 feet long
which table represents a linear function graph 1. pleasee help also giving brainliest
Answer:
2 i think it is
Step-by-step explanation:
write a equation for y=|x| if the graph is translated right by 3 units and down by 1 unit
Answer:
y=|x -3| -1
Step-by-step explanation:
Evaluate (3n+2) -10 when n=3 !!!!
Hello!
(3n + 2) - 10 =
= (3 × 3 + 2) - 10 =
= (9 + 2) - 10 =
= 11 - 10 =
= 1
Good luck! :)
[tex]\displaystyle\bf (3n+2) -10 \ if \ n=3\Longrightarrow 3\cdot3+2-10=11-10=\boxed{1}[/tex]
Prove: AAB
Step
Statement
Reason
Given
1
ABCD is a parallelogram
ABCD
Select a Reason!!
2
A
B
N
The distance traveled (in meters) by an insect is modeled by the equation d=0.5t where d is the distance traveled in meters and t is the time in minutes. Find the distance traveled in 27.9 minutes.
A. none of these
B. 13.95 meters
C. 55.8 meters
D. 1.395 meters
Answer:
B. 13.95 meters
Step-by-step explanation:
The question is just asking you to talk the amount of time taken, and divide it in half.
d= 0.5(27.9)
Which fraction is the largest? 7/9 3/4 1/2 2/3
Rewrite the fractions as decimals by dividing:
7/8 = 0.7777
3/4 = 0.75
1/2 = 0.5
2/3 = 0.666
0.777 is the largest number so 7/9 is the largest fraction.
Answer: 7/9
Answer:
2/3
Step-by-step explanation:
L.C.M:36
7/9:28/36
3/4:27/36
1/2:1836
2/3:36/36
Which value is 10,000 times larger than 1,300?
Explain.
Which value is 10,000 times larger than 1,300?
answer= 1300×10000
= 13,000,000
helppppppppppppp plzzzzz
the answer is in the picture
The marked price of a palmtop was Rs 10,000. What will be the price of palmtop if 13% VAT was levied, after allowing 15% discount on it ?
Step-by-step explanation:
price after discount and with vat = 9605
Circle W has a radius of 20 in and right central angle, ZVWX. Find the length of vx. Leave your answer in terms of pi.
5
10
15
20
Answer:
The length of the arc is 10 pi
Step-by-step explanation:
Mathematically, the length of an arc is calculated as;
theta/360 * 2 * pi * r
theta represents the central angle subtended by the arc which is a right angle according to the question (a right angle is 90 degrees)
r is the circle radius which is 20 inches
so we have the length of the arc as;
90/360 * 2 * pi * 20 = 40 pi/4 = 10 pi
Find the equation of a quadratic function in general form whose graph has points: (-2, 3) (0, 3) and (-4,-5).
Try your best to show complete work & explain your strategy.
Answer:
-x²-2x+3
Step-by-step explanation:
The first thing I noticed is that the first and second point has the same y intercept despite being only 2 x coordiantes away. This must mean that the vertex's x coordiante is probably (-1,4)
Because the vertex is probably (-1,4) the graph must also be concave down because the point (-4,-5) is below it
writing this in vertex form we get
-a(x+1)²+4
Where a is some constant
solve for a by plugging in (0,3)
3= -a(0+1)²+4
3= -a+4
-1= -a
a=1
therefore the equation looks like
-(x+1)²+4
expanding this so that it's in stantard form...
-(x²+x+x+1)+4
-x²-2x+3
which is the final answer
Identify the ethical issue(s) in each experiment. Beginning in the 1940s, the Department of Medicine at the University of Chicago tested anti-malaria medications on inmates at the Stateville Penitentiary. Inmates readily volunteered, as their parole would be reviewed upon completion of their sentence. Inmates who participated in the study reported that they were informed of the risks involved in participating in the study, including the possibility of death.
In the 1960s, Stanley Milgram studied the willingness of subjects to obey an authority figure, even at the risk of being harmed. The subjects believed they were taking part in a study on learning. They were assigned to the role of teacher and were ordered to administer electrical shocks with increasing voltage to the learner whenever the learner made an error. The learner was an actor who remained unharmed. The subjects were not initially told that it was a study of obedience, as this might affect the outcome, and they were not prepared for possible psychological distress.
In the 1950s and 60s, Saul Krugman infected mentally disabled children enrolled at the Willowbrook State School in New York with hepatitis in order to better understand how the disease spread and how it could be combatted. Parents agreed to enroll their children in the study in exchange for admission to the school.
Full question attached
Answer:
1. Subjects were not aware of the purpose of the experiment.
2. Subjects were not aware of all potential risks.
Subjects were not aware of the purpose of the experiment.
3. Subjects were coerced into participating
Explanation:
Ethics are the moral principles and codes that guide our daily decisions and actions. Ethical issues in conducting experiments or research aim at protecting the dignity of subjects or participants in the research. Major ethical issues in conducting research include: Respect for anonymity and confidentiality, beneficence(should not harm participants), and informed consent(independently volunteers after clear comprehensive information on research).
1. Experiment violates informed consent as participants were not aware of the purpose of research.
2. Experiment violates informed consent and beneficence as participants weren't fully informed and faced the risk of being harmed.
3. Experiment violates beneficence and informed consent as participants faced the risk of being harmed and did not independently volunteer for the research.
Which equation in slope-intercept form represents a line that passes through the point (5,−1) and is parallel to the line y=2x-7?
Answer:
y = 2x - 11
Step-by-step explanation:
y = 2x + b
-1 = 2(5) + b
-1 = 10 + b
-11 = b
What is the nth term rule of the quadratic sequence below?
8,14,22,32 ,44, 58, 74...
Answer:
y=n^2+3n+4
Step-by-step explanation:
Sequence,S: 8,14,22,32 ,44, 58, 74...
First differences of S: 6,8,10,12,14,16,...
Second differences of S: 2,2,2,2,2,2,....
It is indeed a quadratic since the 1st differences that are the same are the second differences.
So the 1st term is 8. If the 0th term was listes it would be 4 since 8-4=4 and 6-4=2.
This means our quadratic it is in the form
y=an^2+bn+c where c=4.
So we have y=an^2+bn+4.
Now we can find a and b using two points from our sequence to form a system of equations to solve.
(1,8) gives us 8=a(1)^2+b(1)+4
Simplifying gives 8=a+b+4
Subtracting 4 on both sides gives: 4=a+b
(2,14) gives us 14=a(2)^2+b(2)+4
Simplifying gives 14=4a+2b+4
Subtracting 4 on both sides gives 10=4a+2b
So we have the following system to solve:
4=a+b
10=4a+2b
I'm going to solve using elimination/linear combination style.
Dividing second equation by 2 gives the system as:
4=a+b
5=2a+b
Subtract the 2nd equation from the first gives:
-1=-1a
This implies a=1 since -1=-1(1) is true.
If a+b=4 and a=1, then b=3. Because 3+1=4.
So the equation is y=1n^2+3n+4 or y=n^2+3n+4.
