Every coordinate point of the original triangle has its scale factor doubled by one-half if the scale factor is one. multiply by half after dilation with a scale factor of two.
How do you dilate by scale factor?We locate the dilation's center point and measure the distances between it and other points on the preimage and the image in order to get the scale factor for the dilation. As correctly stated by Math Bits Notebook, the scale factor is determined by the ratio of these distances.Keep in mind that each coordinate must be multiplied by the scale factor in order to enlarge an object in the coordinate plane. The mapping will be (x, y) (1.5 x, 1.5 y) with this dilation. The original is represented by the blue quadrilateral in the graph above, while the dilatation is shown by the red picture. Connect the image's vertices to the centre of dilation by drawing straight lines.To learn more about multiply refer to:
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Every coordinate point of the original triangle has its scale factor doubled by one-half if the scale factor is one. multiply by half after dilation with a scale factor of two.
How do you dilate by scale factor?We locate the dilation's center point and measure the distances between it and other points on the preimage and the image in order to get the scale factor for the dilation. As correctly stated by Math Bits Notebook, the scale factor is determined by the ratio of these distances.
Keep in mind that each coordinate must be multiplied by the scale factor in order to enlarge an object in the coordinate plane. The mapping will be (x, y) (1.5 x, 1.5 y) with this dilation. The original is represented by the blue quadrilateral in the graph above, while the dilatation is shown by the red picture. Connect the image's vertices to the center of dilation by drawing straight lines.
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Rotate the rectangle 90° clockwise about the origin.
The coordinates of the new rectangle formed after transformation are; A'(3, -1); B'(6, -1); C'(6, 4); D'(3, 4)
How to carry out rotational transformation?We are told that the original rectangle which I labelled ABCD in the attached image is rotated 90° clockwise about the origin.
Now, from the translation of Rectangle ABCD into A'B'C'D' using the transformation rule in the question, the new coordinates are;
A'(3, -1)
B'(6, -1)
C'(6, 4)
D'(3, 4)
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Find the mean for the given set of data.
-4,-3,-1,-1, 0, 1
-1 1/3
-1
-3/4
The mean for the given set of data exists at -1 1/3.
What is mean?Mean exists an arithmetic average of the data set and it can be estimated by dividing a totality of all the data points by the digit of data points in the data set. It exists a point in a data set that exists as the average of all the data points we keep in a set.
Mean = (Sum of terms) / (Number of elements)
To find the mean, we must add all of the numbers and then divide them by the number of values you were given.
-4 + -3 + -1 + -1 + 0 + 1 = -8
There exist a total 6 number of elements in the set of data.
Mean = (Sum of terms) / (Number of elements)
Mean = (-4 + -3 + -1 + -1 + 0 + 1) / 6
-4 + -3 + -1 + -1 + 0 + 1 = -8
Mean = -8 / 6
= -4/3 = -1 1/3
The mean for the given set of data exists at -1 1/3.
Therefore, the correct answer is option a) -1 1/3.
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If point U is reflected across the x = -3, what are the coordinates of its reflection image?
The coordinates of U after the reflection are: (-5, -3)
How to get the coordinates after the reflection?
By looking at the graph, we can see that the coordinates of point U are:
U = (-1, -3)
And we want to reflect it across the line x = -3.
Notice that because this is a vertical line, the y-component does not change by the reflection. Only changes the x-component, such that the distance between the original coordinates and the final coordinates to the line don't change.
The original x-component is x = -1, the distance to the line is:
d = |-3 - (-1)| = 2 units.
Then the new x-component will also be at 2 units of the line, but in the other direction:
new x-component: x = -3 - 2 = -5
The coordinates of U after the reflection are:
(-5, -3)
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How to determine instantaneous rate of change with pi
The instantaneous rate of change of the function is 5/π
How to determine the instantaneous rate of change?The function is given as
[tex]f(x) =\cos(x - \pi) + 4[/tex]
Where
[tex]x = \pi[/tex]
Calculate f(π) as follows
[tex]f(\pi) =\cos(\pi - \pi) + 4[/tex]
This gives
[tex]f(\pi) =\cos(0) + 4[/tex]
Evaluate the expression
[tex]f(\pi) =5[/tex]
The instantaneous rate of change is then calculated as;
[tex]f'(x) = \frac{f(\pi)}{\pi}[/tex]
This gives
[tex]f'(x) = \frac{5}{\pi}[/tex]
Hence, the instantaneous rate of change of the function is 5/π
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help me I need the good answers!!!?
1) Q.1 Find the equation of a line that passes through (1, 2) and (5, 4).
equation of a line is y=mx+ c
where m is that gradient and c is y intercept
so first we find the gradient (m)
M= change in y intercept ÷change in x
M=4-2÷5-1
M=2÷4=1/2(as a fraction)(you can also use o.5)
there 1/2is the gradient
then to find the equation of the line
y= 1/2x +c (from coordinates 1,2 we substitute)
2=1/2(1)+c
2-1/2=c
c=1.5
or
from the coordinates 5,4
4=1/2(5) +c
4=5/2+ c
c=4-5/2
c=1.5
equation of the line=y=0.5x + 1.5
or y=1/2x +1.5
hope it helps you^_^
A compound inequality is shown below.
x ≤ 3 and x ≥ 0
Which graph represents the solution of the inequality?
Answer:
b
Step-by-step explanation:
edge
For the pair of points, find the slope of the line that passes through both points. (1,1) and (5,7)
Answer: 3/2
Step-by-step explanation:
[tex]\frac{7-1}{5-1}=\frac{6}{4}=\frac{3}{2}[/tex]
please help me, i want now
The value of angle C in the triangle is 50°.
How to calculate the triangle?From the information given, the angle A = 60° while B is given as 70° and we are told to calculate the value of C.
It should be noted that the sum of angles on a triangle is 180°. Therefore, the value of C will be:
= 180° - (60° + 70°)
= 180° - 130°
= 50°
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The circle below is centered at (3, 1) and has a radius of 2. What is its
equation?
Answer:
( x-3) ^2 + ( y-1) ^2 = 4
Step-by-step explanation:
The equation for a circle is given by
( x-h)^2 + ( y-k) ^2 = r^2 where (h,k) is the center and r is the radius
( x-3) ^2 + ( y-1) ^2 = 2^2
( x-3) ^2 + ( y-1) ^2 = 4
A Delivery service charges $25 per pound for making a delivery. If there is an additional 8% sales tax, what is the cost of delivering an item that weighs 4/5 of a pound?
The cost of delivering an item that weighs 4/5 of a pound?$21.60.
How to find the delivery cost?Let x = the number of pounds
Thus, we can say that;
Cost = 25x * 1.08
Since we want to find the cost of delivering an item that weighs 4/5 of a pound, the we will put 4/5 for x to get;
Cost = (25 * 4/5) * 1.08
Cost = 20 * 1.08
Cost = 21.6
The delivery cost would be $21.60.
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Which expression is equivalent to startfraction 10 x superscript 6 baseline y superscript 12 baseline over negative 5 x superscript negative 2 baseline y superscript negative 6 baseline endfraction? assume x not-equals 0, y not-equals 0.
[tex]3/ 5x^6*y^6[/tex] is the solution f the expression [tex](-9x^-1*y^-9) / (-15x^5*y^-3)[/tex]
Given expression:
(-9x^-1*y^-9) / (-15x^5*y^-3)
As we know, any number with negative power can be written in inverse form with positive power.
[tex]x^-a = 1/x^a[/tex]
Two number having same base their powers are added:
[tex]x^a + x^b = x^a+b[/tex]
[tex]= > (-9x^-1*y^-9) / (-15x^5*y^-3)= (-3x^-1*y^-9) / (-5x^5*y^-3)\\=3/(5x^6 y^6)[/tex]
Hence the solution would be [tex]3 (5x^6 y^6)[/tex].
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Answer:
b
Step-by-step explanation:
Sauna spent 4/5 of her allowance on food and shopping what fraction of her allowance had she left
Answer: 1/5
Step-by-step explanation: You just subtract 4/5 from 1, or 5/5. And BOOM! you get 1/5.
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The choice which best describes how to measure the center of these data is; both centers are best described by the median.
MedianThis is a measure of central tendency which helps determine the middle value in a data by rearranging the data either in an ascending order or a descending order.
Mean on the other hand, is used to find the best average of a data set.
Therefore, the mean cannot be used to find the center of the data.
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A survey of 400 nurses yielded the following information: 279 were health club members, 215 were smokers, and 160 of the health club members were smokers. how many of the 400 surveyed nurses were health club members or were smokers?
Health club members or were smokers is [tex]334[/tex] from a A survey of [tex]400[/tex] nurses yielded.
How can we find the health club members or were smokers ?
Events of health club members is [tex]P(M)=279[/tex]
Events of smokers is [tex]P(S)=215[/tex]
Probability of health club members and smokers is [tex]p(M and S)=160[/tex]
Probability of health club members or were smokers is =?
So we use the formula
[tex]p(M or S)=p(M)+p(S)-p(M and S)\\ = 279+215-160\\ = 334[/tex]
Probability of health club members or were smokers is [tex]334[/tex]
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A dog takes 3 steps to walk the same distance for which a cat takes 4 steps. Suppose 1 step of the dog covers 1 foot. How many feet would the car cover in taking 12 steps
Answer:
the cat would take 13 steps
We want the following inequality to be
true:
|x| < 9
Which of the following are possible
values for x?
Choose all answers that apply:
A
B
x = -10
x = 7
x = 13
Answer:
x = 7
Step-by-step explanation:
The integer values of x that satisfy |x| < 9 are ...
{-8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7. 8}
Of these values, the only one listed as an answer choice is ...
x = 7
__
Additional comment
The expression |x| means "the absolute value of x". It is the value of x with the sign made positive. That is |-10| = 10, a number greater than 9. Of course, |13| = 13, also a number greater than 9.
An angle of measure 120 degrees intersects the unit circle at point (-1/2,√3/2) What is the exact value of cos(120)
The exact value of cos120 if the measure 120 degrees intersects the unit circle at point (-1/2,√3/2) is 0.5
Solving trigonometry identityIf an angle of measure 120 degrees intersects the unit circle at point (-1/2,√3/2), the measure of cos(120) can be expressed as;
Cos120 = cos(90 + 30)
Using the cosine rule of addition
cos(90 + 30) = cos90cos30 - sin90sin30
cos(90 + 30) = 0(√3/2) - 1(0.5)
cos(90 + 30) = 0 - 0.5
cos(90 + 30) = 0.5
Hence the exact value of cos120 if the measure 120 degrees intersects the unit circle at point (-1/2,√3/2) is 0.5
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Answer:
It's -0.5
Explanation:
Answered it
Quick algebra 1 question 25 points!
Only answer if you know the answer, quick shout-out to subtomex0, tysm for the help!
Answer:
1. Translate 5 units up (Fixed after a comment from subtomex0 - Thanks again!)
2. Vertical Compression by a scale factor of 3/8
3. Reflect across the y-axis, and shift 2 units to the left
4. Vertical stretch by a scale factor of 6, and shifting 1 unit up
5. Shifting 11 units to the left
6. Vertical stretch by a scale factor of 8
7. Vertical compression by a scale factor of 1/2, and reflection across the y-axis.
Find the difference. express the answer in scientific notation. (8.64 times 10 superscript 20 baseline) minus (7.83 times 10 superscript 20 baseline) 8.1 times 10 superscript 19 0.81 times 10 superscript 20 8.1 times 10 superscript 21 0.81 times 10 superscript 40
Answer:
Its A or B
Step-by-step explanation:
Using the net below, find the surface area
of the triangular prism.
7 cm
5 cm
15 cm
4 cm
Surface Area
5 cm
7 cm
[?] cm²
Enter
Answer:
118
Step-by-step explanation:
The total area is the area of the large rectangle in the middle plus the areas of the two triangles.
The length of the entire rectangle is 5 cm + 5 cm + 4 cm = 14 cm.
The width of the rectangle is 7 cm.
Each triangle has a base of 4 cm and a height of 5 cm.
A = LW + 2 × (1/2)bh
A = (14 cm)(7 cm) + (4 cm)(5 cm)
A = 98 cm² + 20 cm²
A = 118 cm²
How many different teams of 4 can be chosen from a group of 15 adults and 16 children if each team must have at least one child on it?
The Number of teams is mathematically given as
N= 30100
What is the Number of teams?Generally, the equation for Number of teams is mathematically given as
X items are selected from n items by [tex]^nC_x[/tex] ways
[tex]^nC_x = \frac{n!}{ [ (n-x)! * x! ]}[/tex]
Number of teams
N= n(1 child and 3 adults) + n(2 child and 2 adults) + n(3 child and 1 adults) + n(4 child)
N= 16C1 * 15C3 + 16C2 * 15C2 + 16C3 * 15C1 + 16C4 * 15C0
N= 16 * 455 + 120 * 105 + 560 * 15 + 1820
N= 30100
In conclusion, the Number of teams
N= 30100
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Joni and Lori began running from the same point. Joni ran 5 miles west while Lori ran 7 miles north. How far apart were they when they finished
The distance they finishes is 8.6 miles
Given that miles run by Joni is 5 miles and the miles ran by Lori is 7 miles
We need to find the distance they finished
To calculate the total distance along the diagonal line, the Distance Formula first squares the differences between the two x coordinates and the two y coordinates, then adds those squares, and finally calculates their square root.
We know that
According to the Distance formula
= [tex]\sqrt{(5)2+(7)^2}[/tex]
= [tex]\sqrt{25+49}[/tex]
= [tex]\sqrt{74}[/tex]
= 8.6 miles
Therefore the distance finished is 8.6 miles
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someone please help- just look at the picture
Answer:
30
Step-by-step explanation:
18/60 =.3 x 100 = 30
HELP HELP HELP
HELP HELP HELP
HELP HELP HELP
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
As per the given information ~
The given triangles are similar, so their corresponding sides should be in same ratio :
[tex]\qquad \sf \dashrightarrow \: \dfrac{2x}{4} = \cfrac{5}{x - 3} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{x}{2} = \cfrac{5}{x - 3} [/tex]
[tex]\qquad \sf \dashrightarrow \: x(x - 3) = 10[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} - 3x = 10 [/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} - 3x - 10 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} - 5x + 2x - 10 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: x(x - 5) + 2(x - 5) = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: (x + 2)(x - 5) = 0[/tex]
so, x = 5 or -2
but since side length can't be negative, we will take x = 5 neglecting the negative value (-2)
So, side lengths of unknown sides are :
[tex] \qquad \sf \dashrightarrow \: {2x = 2 × 5 = 10 units} [/tex]
and
[tex]\qquad \sf \dashrightarrow \: x - 3 = 5 - 3 = 2 \: \: units[/tex]
What is the value of tan D₂ 12 5 O O O O | | 13 5 12
Answer:
12/5
Step-by-step explanation:
to find tan D you need the opposite and the adjacent sides.
12 is opposite D and 5 is adjacent to D
so using the equation tan=Opposite/adjacent
tanD=12/5
Figure ABCD is a parallelogram.
A
5x + 3
C
B
38
What is the value of x?
6
07
08
09
Answer:
7
Step-by-step explanation:
5x+3=38 subtract the 3 from the 38 leaving you with 35/5 getting you 7
The value of x in the given parallelogram is 7.
What is Quadrilateral?A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles
A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
So 5x+3=38
We need to find the value of x
Subtract 3 from both sides
5x=38-3
5x=35
Five times of x equal to thirty five
Divide both sides by 5
x=7
Hence, the value of x in the given parallelogram is 7.
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Quick algebra 1 question for some points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
[tex]8 \: cars = 120 \: dollars \\ 1 \: car = \frac{120}{8} = 15 \: dollars[/tex]
[tex]m(c) = 15c[/tex]
option dAnswer:
d: m=15c
Step-by-step explanation:
Usually (not always), variable y depends on variable x.
Since in this question, the amount of money Paul can earn changes based on the number of cars he washes, y is the amount of money, and x is the number of cars he washes.
This can be represented as: 120 = 8 times ___
___ is the amount of money Paul earns by cleaning 1 car.
___ is 120 divided by 8, which is 15.
--> Paul earns $15 by cleaning each car.
The new equation will be m = 15c
If you rolled two dice, what is the probability
that you would roll a sum of 9?
Give your answer as a simplified fraction. Enter
the number that belongs in the green box.
second
first
1 2 3 4 5 6
1 1,1 1,2 1,3 1,4 1,5 1,6
2 2,1 2,2 2,3 2,4 2,5 2,6
3 3,1 3,2 3,3 3,4 3,5 3,6
4 4,1 4,2 4,3 4,4 4,5 4,6
5 5,1 5,2 5,3
5,4 5,5 5,6
6 6,1 6,2 6,3 6,4 6,5 6,6
The probability you will roll a sum of 9 is 1/4.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is one and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.
The probability you will roll a sum of 9 = total times a sum of 9 is derived / total sample spaces
total times a sum of 9 is derived = (3 + 6) , (6 + 3) , (4 + 5) , (5 + 4) Total sample spaces = 36The probability you will roll a sum of 9 = 4/36 = 1/9
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Measures of the two triangles DEF and PQR
are shown in the figure. Check if the
triangles are congruent. If congruent, which
of the following statements is true?Justify.
∆DEF ≅ ∆PQR ;
∆ DEF ≅ ∆ QPR ;
∆DEF ≅ ∆RPQ
Triangles ABC and triangle PQR are congruent triangles based on angle-side-angle congruency theorem.
What are congruent triangles?Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent to each other. Also, their corresponding angles are congruent to each other.
Triangles ABC and triangle PQR are congruent triangles based on angle-side-angle congruency theorem.
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