Answers
Let:
The coordinates for the new figure will be given by:
[tex]Do,k(x,y)=(k(x-a)+a,k(y-b)+b)[/tex]Where:
O = Center of dilation at (a,b) = (3,2)
k = Scale factor = 0.1
So:
[tex](1,1)->(0.1(1-3)+3,0.1(1-2)+2)=(2.8,1.9)[/tex][tex]\begin{gathered} (1,2)->(0.1(1-3)+3,0.1(2-2)+2)=(2.8,2) \\ (2,1)->(0.1(2-3)+3,0.1(1-2)+2)=(2.9,1.9) \\ (2,2)->(0.1(2-3)+3,0.1(2-2)+2)=(2.9,2) \end{gathered}[/tex]Since:
(2.8,2), (2.8,1.9), (2.9, 1.9) and (2.9,2) are much closer to the center of dilation we can conclude that the dilated figure is closer to the center of dilation.
Related Questions
Select the two values of x that are roots of this equation.
x2 + 3x – 5 = 0
Answers
The two values for the quadratic equation [tex]x^{2} +3x-5=0[/tex] is [tex]\frac{-3+\sqrt{29} }{2}[/tex] and [tex]\frac{-3-\sqrt{29} }{2}[/tex]
What is quadratic equation?
Quadratic equation is a second-order equation written as ax2 + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0.
The solution of the x = [-b±√(b2-4ac)]/2a
where b= 3 a= 1 and c = -5.
x = -3±[tex]\sqrt{3^{2}-4(1)(-5) } /2[/tex]
x=[tex]\frac{-3-\sqrt{29} }{2}[/tex]
and x = [tex]\frac{-3+\sqrt{29} }{2}[/tex]
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line m and n are parallel when x=
Answers
we have those angles must measure the same so
[tex]\begin{gathered} 4x-6=150 \\ 4x=156 \\ x=\frac{156}{4}=39 \end{gathered}[/tex]so x=39
in ABC, The sum of measures of A and B is 90°. A is 30° less than twice B use this information to find the measure of each angle
Answers
Given:
The sum of measures of A and B is 90°
so, we have the following equation:
[tex]A+B=90\rightarrow(1)[/tex]And, A is 30° less than twice B
so, we have the following equation:
[tex]A=2B-30\rightarrow(2)[/tex]Solving the equations (1) and (2)
Substitute with A from equation (2) into equation (1)
[tex]\begin{gathered} 2B-30+B=90 \\ 3B=120 \\ B=\frac{120}{3}=40 \end{gathered}[/tex]Substitute with B into equation (2) to find A:
[tex]A=2\cdot40-30=50[/tex]So, the answer will be:
The measure of angle A = 50
The measure of angle B = 40
The population of a small town in central Florida has shown a linear decline in the years 1995-2005. In 1995 the population was 24100 people. In 2005 it was 14800 people.
Answers
Part A:
Since the population is showing a linear decline, we can express the function P(t) as
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \end{gathered}[/tex]Given two points
(1995,24100), and (2005,14800)
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{IF }\mleft(x_1,y_1\mright)=\mleft(1995,24100\mright),\text{ and }(x_2,y_2)=\mleft(2005,14800\mright),\text{ THEN} \\ \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{14800-24100}{2005-1995} \\ m=\frac{-9300}{10} \\ m=-930 \end{gathered}[/tex]Now that we have solved for the slope, we can now solve for the y-intercept. We will use the point (2005,14800), but using (1995,24100) will work just as well.
[tex]\begin{gathered} \text{IF }m=-930,\text{ and }(x,y)=\mleft(2005,14800\mright),\text{ THEN} \\ \\ y=mx+b \\ 14800=(-930)(2005)+b \\ 14800=-1864650+b \\ 14800+1864650=+b \\ 1879450=b \\ b=1879450 \end{gathered}[/tex]Convert the function x into a function of time t, then the the function is
[tex]P(t)=-930t+1879450[/tex]Part 2:
What will be the population in 2007.
Substitute t = 2007.
[tex]\begin{gathered} P(t)=-930t+1879450 \\ P(2007)=-930(2007)+1879450 \\ P(2007)=-1866510+1879450 \\ P(2007)=12940 \end{gathered}[/tex]Therefore, in the year 2007, the population will be 12940.
Determine the average rate of change of f(x) = 4x²+x+3 over the interval [-2, 2].
Answers
Answer: The average rate of change is 1.
Step-by-step explanation:
The average rate of change f(x) on the interval [a,b] is (f(b)−f(a))/(b−a)
a=−2 , b=2, f(x)=4X^2+x+3.
(f(b)-f(a))/(b-a)= (3+(2)+4(2)^2-(3+(-2)+4(-2)^2)) / (2-(-2)) = 1
Finding the absolute maximum and minimum of a function given the graph
Answers
Explanation
An absolute maximum point is a point where the function obtains its greatest possible value.
Similarly, an absolute minimum point is a point where the function obtains its least possible value.
Step 1
check the graph of g:
The y- coordinates (output) at the highest and lowest points are called the absolute maximum and absolute minimum
To locate absolute maxima and minima from a graph, we need to observe the graph to determine where the graph attains it highest and lowest points on the domain of the function
so, for G
[tex]\begin{gathered} \text{maximum}=\text{ None ( the graph continues raising up)} \\ \text{minimum}=-3 \end{gathered}[/tex]Step 2
Now, for h
[tex]\begin{gathered} \text{ Minimum; -5} \\ \text{ ma}\xi mum\colon5 \end{gathered}[/tex]I hope this helps you
the mass of a car is 1990kg rounded to the nearest kilogram. the mass of a person is 58.7kg rounded to one decimal place. write the error interval for the combined mass, m, of the car and the person in the form _______
Answers
The error interval for the combined mass (m) of the car and the person is 2047.7 ≤ m < 2049.7
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments (symbols):
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).The error interval for the mass of car is given by:
Mass of car = 1990 ± 0.5;
Mass of car = 1990 + 0.5 = 1990.5
Mass of car = 1990 - 0.5 = 1989.5
The error interval for the mass of a person is given by:
b = 1990 ± 0.5;
b = 58.7 + 0.5 = 59.2
b = 58.7 - 0.5 = 58.2
For the value of a and b, we have:
a = 1989.5 + 58.2 = 2047.7
b = 1990.5 + 59.2 = 2049.7
Next, we would calculate the combined mass (m):
m = 1990 + 58.7
m = 2048.7
Now, we can write the error interval for the combined mass (m) of the car and the person as follows:
a ≤ m < b
2047.7 ≤ m < 2049.7
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2y + 6 = y — 7. What is the value of y?
Answers
y=-13
Step-by-step explanation:
2y+6=y-7
2y+6-6=y-7-6
2y=y-13
2y-y=y-13-y
y=-13
The value after solving the given expression will be equal to -13.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the given expression in the question is,
2y + 6 = y - 7
Rearrange the equation,
2y - y = -7 - 6
y = -13
Therefore, the obtained value for y will be -13.
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Eric and Nancy both had a successful year selling fish tanks for theirrespective employers, and so they were both given raises.Eric: Eric's base salary is still $1400, but now he makes a commission of$100 for each fish tank that he sells.Nancy: Nancy now gets a base salary of $500 per month, but her commissionhas stayed the same at $250 per fish tank.Eric and Nancy still want to make sure that they contribute the same amountto their total monthly income, and Nancy proposes using algebra to figureout how many fish tanks that they would each need to sell. She tells Ericthat he can calculate his monthly income by using the formula f(x) = 100x +1400. She says that she can calculate her own salary by using the functiong(x)=250x + 500.1 What does the variable x represent in Nancy's formulas?How do you know?
Answers
Answer:
The variable x represents the number of fish tanks he/she sells.
Explanation:
Given that Eric's base salary is still $1400, but now he makes a commission of
$100 for each fish tank that he sells and Nancy now gets a base salary of $500 per month, but her commission has stayed the same at $250 per fish tank.
Eric's total income would be;
$1400 plus $100 times the number of fish tanks he sells.
[tex]f(x)=1400+100x[/tex]and Nancy's total income would be;
$500 plus $250 times the number of fish tanks she sells.
[tex]f(x)=500+250x[/tex]Therefore, the variable x represents the number of fish tanks he/she sells.
The number of fish tanks each of them sells will determine the total commission and also determines their total income.
Write the rule for the table, use z for the input.Input-1Output7012co woo WN3.4F(0)
Answers
Lets assume that the input values are x values and the output values are y values.
Then you will have pairs of coordinate values as shown;
(-1,7) , (0,2) , (1,-3) , (2,-8), (3,-13), (4,-18)
Using the coordinates find the slope a;
(-1,7) and (0,2) ---------slope is change in y-values/ change in x-values , (2-7) /(0--1)
= -5/ 1 = -5
Do the same for the next pair of coordinates ,(0,2) and (1,-3) , (-3-2) / (1-0) = -5/1 = -5
If you continue the procedure to the next pair which is (1,-3) and (2,-8) to get the slope as : (-8- -3) / (2-1) = -5/1 = -5
This means that the slope is -5
The relation will be represented by the equation y= mx + c where m is the slope and c is the y-intercept
First plot the points to visualize the graph
From the plot, you notice that when the points are joined, a straight graph is formed sloping to the negative side and intersecting the y-axis at point (0,2).
So to determine the rule, we apply the equation y= mx + c with m= -5 and c =2
This gives y= -5 x + 2
The rule is f(x) = -5x +2 -----------answer
Determine weather the sequence 6,12,24,48 could be an an arithmetic sequence.
Answers
Answer:
The sequence cannot be arithmetic.
Explanation:
Given the sequence: 6,12,24,48
We want to determine if the sequence is arithmetic.
An arithmetic sequence is a sequence made in which the next term is obtained by the addition of a constant term called the common difference.
In the given sequence:
[tex]\begin{gathered} 12-6=6 \\ 24-12=12 \\ 48-24=24 \end{gathered}[/tex]The difference between the terms is not constant.
Therefore, the sequence cannot be arithmetic.
That is just the chart. Disregard question 6. 7. A survey of 381 adult females produced a mean height of 65.2 inches with a standard deviation of 2.8 inches. Construct a confidence interval based on a 95% confidence level.O (64.92, 65.48)© (64.83, 65.57)O (65.19, 65.21)© (64.96, 65.44)
Answers
Step 1
Given;
[tex]\begin{gathered} n=381\text{ adults} \\ Mean\text{ \lparen}\mu)=65.2 \\ \sigma=2.8 \end{gathered}[/tex]Step 2
The confidence interval is given as follows;
[tex]CI=\mu\pm t_{\frac{\alpha}{2}}(\frac{s}{\sqrt{n}})[/tex]The test statistic for a 95% confidence interval with α = 0.05, the degrees of freedom, df= n-1 = 381-1=380
[tex]t_{\frac{\alpha}{2},df}=t_{\frac{0.05}{2},380}[/tex][tex]t_{\frac{\alpha}{2},df}=t_{\frac{0.05}{2},380}=1.97[/tex][tex]\begin{gathered} C.I=65.2\pm1.97(\frac{2.8}{\sqrt{381}})=65.2\pm0.2825932406 \\ C.I=(64.92,65.48) \end{gathered}[/tex]Answer;
[tex]C.I=(64.92,65.48)[/tex]The volume of this rectangular prism is 9.044 cubic feet. What is the value of t?
Answers
The volume of a rectangular prism can be calculated with the following formula:
[tex]V=lwh[/tex]Where "l" is the length, "w" is the width and "h" is the height.
In this case, you can set up that:
[tex]undefined[/tex]Penny is selling candles for $3 each at a fundraiser.
If she starts selling with $4 to help her make change, how many candles, x, will she
have to sell to end up with $19?
Answers
3x + 4 = 19
Subtract 4 from both sides
3x=15
Divided by 3 on both sides
X= 5
She needs to sell 5 candles to end up with $19
Answer: x=5
Step-by-step explanation: Based on the given conditions formulate:: 4+3[tex]x[/tex]x=19
Rearrange variables to the left side of the equation: 3x=19-4
Calculate the sum or difference: 3x=15
Divide both sides of the equation by the coefficient of the variable: x=[tex]15/3[/tex]
Cross out the common factor: x=5
9 is subtracted from the square of a number
Answers
Which is the area of the circle shown? Use 3.14 for π.
1. 18.84 m^2
2. 37.68 m^2
3. 113.04 m^2
4. 354.95 m^2
Answers
Answer:
3: 113.04 m^2
Step-by-step explanation:
pi r^2
3.14 x 36
= 113.04 m^2
:]
The measures of the angles of a triangle are shown in the figure below. Solve for x.
34°
46°
x°
Answers
The measures of the angle x in the triangle is 100 degrees
How to determine the measures of the angle?From the question, we have the following parameters that can be used in our computation:
Angles = 34, 46 and x
The sum of angles in a triangle add up to 180 degrees
This is represented as
Sum of angles = 180
Substitute the known values in the above equation
So, we have
34 + 46 + x = 180
Evaluate the like terms in the above equation
So, we have
80 + x = 180
Evaluate the like terms in the above equation
So, we have
x = 100
Hence, the value of x is 100
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Jonas wants to make a poster of a drawing he made. The original drawing is 8 inches wide, and he wants the poster to be 30 inches wide. What zoom button setting will he have to use on the library copier to create a poster of this size?
Answers
Answer:
He should use a 375% zoom to create a 30-inch wide poster.
Step-by-step explanation:
30/8 = 3.75, and 8*3.75=30. So 375%.
Mark as brainliest please.
A side mirror of a small pick up truck is similar to that of a larger full size pickup truck. If the smaller truck has a rectangular side mirror of width 5.0 in. and height 6.0 in., what is the height in inches of the larger mirror if the width is 10.0 in.?
Answers
If the width of larger full size pickup truck is 10.0 in. then its height is equal to 12inches.
As given in the question,
Side mirror of a small pick up truck is similar to larger full size pick up truck.
Smaller truck has rectangular side mirror
Width = 5.0 in.
Height = 6.0 in.
Larger mirror
Width = 10.0 in.
Let h be the height of the larger mirror
Both the mirrors are similar and rectangular in shape.
Hence, sides are in proportion
5 /6 = 10 /h
⇒h = (6 ×10) / 5
⇒ h = 12 in.
Therefore, if the width of larger full size pickup truck is 10.0 in. then its height is equal to 12inches.
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Jay's family is moving to a new home they packed 22 boxes in 1 5/6 hours what is the average number of boxes they packed per hour Pls asap
Answers
=> 22/(11/6) => 12 boxes per hr
please I just need help with these two questions
Answers
Question 1:
Each of these options can be read as "8 to 15", except for 15:8. This is read as "fifteen to eight". Lets say in 8:15 you have 8 of a and 15 of b. In 15:8, however, you have 15 of a and 8 of b. These are not the same ratio.
Question 2:
The amount of people that can go down the slide in 1 minute is 6, because 18/3 = 6. So:
12/6 = 2
6ppl/1min (multiply both terms by 2)
12ppl/2min
It would take 12 people 2 minutes to go down the slide.
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
80.58
Step-by-step explanation:
do you need an explanation or will this be fine?
what is the quotient of (6.47 x 10^-15) / (3.36 x 10^-29)
Answers
A tailor has 20 yards of shirt fabric. How many shirts can she
complete if each shirt requires 2% yards of fabric?
Answers
Answer:
2%/100% ×20=
Step-by-step explanation:
from this one of the zeros from the hundred would cancel the zero from 20 which will give you 2/10×2 and mind you percentage cancel percentage. from this 2 will cancel 10 leaving the answer 2 over 5
Kelly downloaded 195 pictures from her cell phone to her computer. These pictures took up 585 megabytes of space on her computer. Each picture took up the same amount of space. How many megabytes do 39 of these pictures take?
Answers
The amount of space taken by 39 of these pictures is 117 megabytes.
What is the unitary method?The unitary approach is a problem-solving process that begins by identifying the value of a single unit and then multiplying that value by the needed value.
Given:
Number of pictures downloaded by Kelly from her cell phone to her computer = 195
Amount of space taken by the pictures = 585 megabytes
Now, an equal amount of space is taken by each picture.
To determine, the megabytes taken by 39 of these pictures.
By the unitary method,
195 pictures = 585 megabytes
39 pictures = ? megabytes
Divide 585 megabytes by the number of pictures 195 and then multiply it by 39.
= (585/195) × 39
= 117 megabytes
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Here is the imagine of the triangle ABC and it’s dilations using center D and scale factor 2
Answers
(3) The question state that we should explain the relationship between angle ACB and A'C'B' in the given diagram.
From the the diagram in the question, we can see that wa have two different triangle which are ABC and A'B'C'.
The relationship between angle ACB and angle A'C'B' is that they are corresponding angles. because they are on the same side of the line.
Corresponding angles are any pair of angles each of which is on the same side of one of two lines cut by a trasnsversal and on the same side of the transversal.
Therefore, the relationship between angle ACB and angle A'C'B' is that they are corresponding angles.
Can someone please answer this question for me:
Answers
Answer:
16c²+ 32 cd +16d²
Step-by-step explanation:
area of rectangle is side²
(4c+4d)²
16c²+ 16cd+16cd+16d²
16c²+32cr+16d²
2. Perform the indicated operation. Express your answer in simplest form. Show any necessary work. Then answer the question. (a) -2.48/12.4 (b) -12.5/-0.025 (c) Imagine your friend uses long division to determine the quotients, and is confused by how quickly you were able to determine the correct answer without performing long division. Explain how you were able to determine the quotients without performing long division.
Answers
Part a
we have the expression
[tex]\frac{-2.48}{12.4}[/tex]Multiply the fraction by 100/100 to remove decimal numbers
[tex]\frac{-2.48}{12.4}\cdot\frac{100}{100}=-\frac{248}{1,240}[/tex]Simplify the fraction
[tex]-\frac{248}{1,240}=-\frac{1}{5}[/tex]Part b
we have the expression
[tex]\frac{-12.5}{-0.025}[/tex]Multiply the expression by 1,000/1,000 to remove decimal numbers
so
[tex]\frac{-12.5}{-0.025}\cdot\frac{1000}{1000}=\frac{12,500}{25}[/tex]Simplify
[tex]\frac{12,500}{25}=\frac{500}{1}=500[/tex]Part c
to determine the quotients without performing long division
step 1
Convert the decimal numbers of the quotient to integer numbers, multiplying the numerator and denominator by a fraction of the form 10/10, 100/100,1000/1000, etc
step 2
Simplify the fraction in the simplest form
solve for x.
0.4x-2.8/4=1.5
x=
Answers
Answer:
5.5
Step-by-step explanation:
0.4x = 2.2
x = 5.5
Please help withstandard deviation with measurements
Answers
Answer: Standard Deviation, σ: 0.23979157616564
Count, N: 8
Sum, Σx: 33.6
Mean, μ: 4.2
Variance, σ2: 0.0575
Steps
σ2 =
Σ(xi - μ)2
N
=
(4.5 - 4.2)2 + ... + (4.1 - 4.2)2
8
=
0.46
8
= 0.0575
σ = √0.0575
= 0.23979157616564
Step-by-step explanation: but here
it isnt letting me do the fraction or the other things so yeah it will look wrong but its write for the entire graph