ABC is dilated by a factor of 5 produce A'B'C.What is A'C, the length of AC after the dilation? What is the measure of angle A?
Answers
We have that the scale factor is 5, then, the dilation is an enlargement.
Then, the new lengths are:
[tex]\begin{gathered} A^{\prime}C^{\prime}=5AC=5\cdot5=25 \\ A^{\prime}B^{\prime}=5AB=5\cdot4=20 \\ B^{\prime}C^{\prime}=5BC=5\cdot3=15 \end{gathered}[/tex]therefore, A'C' =25.
Finally, the dilations don't affect the angles, therefore, angle A remains with the measure of 37°
Related Questions
I have answer for the question it in the image but I don't know if it right and I don't know any other formulas to find the area of a triangle
Answers
Hello there. To solve this question, we'll have to remember which other formulas for area of triangles can be used.
Most specifically, it asks for a formula that works on an obtuse triangle, that is, a triangle that haves an angle that measures more than 90º.
Besides the formula BH/2, that refers to half of the product between the measurements of the base and the height of the triangle, of course, this height must be a projection perpendicular to the base, as in the following drawing:
Another formula that can be used is Heron's formula;
Knowing the measures of all the sides of the triangle (no matter if it is an obtuse, acute or right triangle), say a, b and c, Heron's formula states that the area S of the triangle is given by:
[tex]S=\sqrt{\rho\cdot(\rho-a)\cdot(\rho-b)\cdot(\rho-c)}[/tex]Where
[tex]\rho=\dfrac{a+b+c}{2}[/tex]is the semiperimeter of the triangle.
This is the answer we've been looking for.
Tell whether the sequence is arithmetic. If it is what is the common difference? Explain.
{1, 5, 9, 13, …}
Answers
The sequence is arithmetic because the common difference is 4.
Answer:
the sequence is arithmetic. the cd is 4
Step-by-step explanation:
1 + 4 = 5
5 + 4 = 9
9 + 4 = 13
Which function has an inverse that is also a function?{(-1 -2). (0, 4). (1 3). (5, 14). (7, 4)}{(-1. 2), (0.4), (1.5). (5. 4). (7.2)} {(-1.3), (0.4). (1. 14), (5. 6). (7. 2)} {-1 4), (04). (1.2). (5.3). (7.1)
Answers
Remember that a function is a relation between two sets of numbers where the first set is called domain, and the second set is called range.
The main characteristic that defines a function is that a domain element can be associated with only one element of the range set. In other words, one input value cannot have two different output values.
Therefore, the right answer is the third choice
[tex]\left\lbrace (-1,3\right)(0,4)(1,14)(5,6)(7,2)\}[/tex]Because this represents a function and its inverse also represents a function, that is, it's inverse have the characteristic of a function. The following set represents the inverse
[tex]\left\lbrace (3,-1\right)(4,0)(14,1)(6,5)(2,7)\}[/tex]As you can observe, this inverse set also follows the function definition, because every single input is associated with only one output.
Can someone help me with this please? If the painting is 18 inches high, how wide would it be?
Answers
The ratio of width to height is :
[tex]\frac{w}{h}=\frac{1+\sqrt[]{5}}{2}[/tex]If h = 18 inches, the value of w will be :
[tex]\begin{gathered} \frac{w}{18}=\frac{1+\sqrt[]{5}}{2} \\ \text{Cross multiply :} \\ 2w=18(1+\sqrt[]{5}) \\ w=\frac{18(1+\sqrt[]{5})}{2} \\ w=9(1+\sqrt[]{5}) \\ w=9+9\sqrt[]{5}\quad or\quad 29.12 \end{gathered}[/tex]The answer is w = 29.12 inches
If the rectangle below were to be enlarged by a scale factor of 5, what would the new size be? 2 10 x 15 10 X 6 8 X 15 Od 2 X 3
Answers
To dilate a shape by a determined scale factor, you have to multiply each side of the said shape by the scale factor.
The figure is a rectangle with length l=3 and width w=2, to enlarge it using factor 5, you have to multiply both lengths by 5:
[tex]\begin{gathered} l=3\cdot5 \\ l=15 \end{gathered}[/tex][tex]\begin{gathered} w=2\cdot5 \\ w=10 \end{gathered}[/tex]After dilating the rectangle by scale factor 5, the new size will be 10 x 15
Find the area of each figure. Round to the nearest 10th if necessary.
Answers
1.
First, divide the figure into 3 different figures.
Find the area of each figure, and then add them:
A1 is a rectangle:
Area of a rectangle: Lenght x width
A1 = 8 x 5.3 = 42.4 in2
A2 is also a rectangle:
Lenght = 4
width = 8 - 5.3 = 2.7
A2 = 4 x 2.7 = 10.8 in2
A3 is a triangle:
Area of a triangle = (base x height) / 2
base = 2.7
Height = 8-4 = 4
A3= ( 2.7 x 4 ) / 2 = 5.4 in2
Total area = A1 + A2 + A3 = 42.4 + 10.8 + 5.4 = 58.6 in2
Answer = 58.6 in2
< BackSee SolutionShow ExampleRecord: 1/3 Score: 1 Penalty: 1 offComplete: 11% Grade: 0%Brianna AllenFinding the Slope from PointsJon 03, 7:15:08 PMWhat is the slope of the line that passes through the points (4, -9) and (8, -3)?Write your answer in simplest form.
Answers
To obtain the slope of the line that passes through the two given points, the following steps are recommended:
Step 1: Recall the formula for the slope of a line that passes through any two points (x1, y1) and (x2, y2), as follows:
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]Step 2: Apply the formula to find the slope of the line that passes through the points (4, -9) and (8, -3), as follows:
[tex]\begin{gathered} \text{Given that:} \\ (x_1,y_1_{})=(4,-9) \\ (x_2,y_2)=(8,-3) \\ \text{Thus:} \\ \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow\text{slope}=\frac{-3_{}-(-9)_{}}{8_{}-4_{}}=\frac{-3+9}{4}=\frac{6}{4}=\frac{3}{2} \\ \Rightarrow\text{slope}=\frac{3}{2} \end{gathered}[/tex]Therefore, the slope of the line that passes through the points (4, -9) and (8, -3) is 3/2
? Question
Refer to section 1.3.2, Credit scores, beginning on page 22 of the report.
Arrange the five tiers of credit scores in order, starting with the lowest tier of credit scores.
Answers
The five credit score tiers are listed in ascending order, starting with the lowest tier:
Deep Subprime < Subprime < near prime < prime < superprime
The ability of a consumer to get credit may be significantly influenced by their credit score. These interactive graphs demonstrate how lending behavior has changed for different credit score profiles of borrowers.
We concentrate on the following five commercially available credit score levels:
Subprime's credit scores is between 580 to 619.
Prime's credit score level is between 660 to 719.
The credit score level of deep subprime is below 580.
The credit score level of near prime is 620 - 659.
The credit score level of superprime is 720 or above.
Therefore, the five tires of credit scores from lowest to highest are:
Deep Subprime < Subprime < near prime < prime < superprime
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The measures of the angles of a triangle are shown in the figure below. Solve for x.
(x+9)°
42°
104°
Answers
Answer:
Step-by-step explanation:
first do 104 + 42 it should be 146
second since it is x+9 do 146 - 189, it should be 43.
third check your work by doing 43 + 146
if it equals 189 then do 43 - 9, you should get 34
so x = 34
Answer each part. If necessary, round your answers to the nearest hundredth.х5?(a) At Hoffman's Bike Rentals, it costs $31 to rent a bike for 7 hours.How many dollars does it cost per hour of bike use?Il dollars per hour(b) A color printer prints 10 pages in 3 minutes.How many minutes does it take per page?minutes per pageCheck0 2021 McGraw Hill Education All Rights.
Answers
EXPLANATION
If it cost $31/7 hours, we can apply the unitary method to get the unit cost:
[tex]\text{unit price=}\frac{31\text{ dollars}}{7\text{ hours}}=4.42\text{ dollars/hours}[/tex]It will cost 4.42 dollars/hours
We can apply the same reasoning to the printer.
If m ll n, which statement is true? 3 1 5 2. 4 6 O A.
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∠1 and ∠2 have equal measures because they are corresponding angles
3 hours 6 minutes 45 seconds Plus 8 hours 55 minutes 20 seconds
Answers
12h 2 minutes and 5 seconds
1) Adding 3 hours 6 minutes and 45 seconds to 8 hours 55 minutes and 20 seconds we can write like this:
2) Every time we hit 60'' (seconds) we add to its neighbor then we can find the following sum.
1h ----60'
1 minute ----60''
3) Then the sum of those is equal to 12h 2 minutes and 5 seconds
Suppose that at age 25, you decide to save for retirement by depositing $95 at the end of every month in an IRA that pays 6.25% compounded monthly. How much will you have from the IRA when you retire at age 65? Find the interest.
Answers
1. At age 65 when you retire, you have (future value) $202,531.69 from the IRA.
2. The total interest earned on the monthly investment of $95 at 6.25% for 40 years is $156,931.69.
How is the future value determined?The future value, which represents the compounded value of the monthly investments, can be computed using the FV formula or an online finance calculator as follows:
Number of years = 40 (65 - 25)
N (# of periods) = 480 months (40 x 12)
I/Y (Interest per year) = 6.25%
PV (Present Value) = $0
PMT (Periodic Payment) = $95
Results:
Future Value (FV) = $202,531.69
Sum of all periodic payments = $45,600 ($95 x 480 months)
Total Interest = $156,931.69
Thus, the future value of the monthly investment is $202,531.69 with an interest of $156,931.69.
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3. Trigonometric Function a. Describe two real-world situations that could be modelled by a trigonometric function. Cannot be Ferris Wheel ride, tides, hours of daylight. Cite any Internet source you may have used for reference. b. Clearly define all variables in the relationship. c. Clearly justify why this model fits the real applications with specific reference to key features of the function. d. Your justification should also include reference to the graphical and algebraic models. e. Accurately describe what changes to the base function y = sin x would be necessary to fit both real applications.
Answers
For this problem, we need to describe a real-life situation where trigonometric functions can be used to model the problem.
Let's assume that a certain vehicle's position is controlled by the speeds of the wheels on each side of the car. Whenever the speeds on the left wheels and right wheels are equal, then the car moves forward, if the speed on the left side is greater than the one on the right side the car goes right, and if the speed on the right side is greater, then the vehicle goes to the left side. This type of car is called a differential drive car, and it's very common on remote-controlled (RC) vehicles.
If we want to model the speed of the car in a two dimensional grid, such as below:
We need to assume that the vehicle will have two components of velocity, one that is parallel to the x-axis and one that is parallel to the y-axis. These will form the linear velocity for the vehicle. We also need an angular velocity, which is the rate at which the angle of the vehicle changes.
If we assume that the wheels of the vehicles are at a distance of "L" apart from each other, then we can model the angular velocity of the vehicle as:
[tex]\omega=\frac{v_r-v_l}{L}[/tex]Where "vr" is the speed on the right wheel, and "vl" is the speed on the left wheel. The movement will happen with the center of the car as the center of the movement, with this we can assume that the velocity of the vehicle on the two axes should be:
[tex]\begin{gathered} v_x=\frac{1}{2}(v_r+v_l)\cdot cos(\theta)\\ \\ v_y=\frac{1}{2}(v_r+v_l)\cdot sin(\theta) \end{gathered}[/tex]Therefore we can describe the vehicle speed with the following equations:
[tex]\begin{gathered} \omega=\frac{v_{r}-v_{l}}{L}\\ \\ v_x=\frac{1}{2}(v_r+v_l)cos(\theta)\\ \\ v_y=\frac{1}{2}(v_r+v_l)s\imaginaryI n(\theta) \end{gathered}[/tex]The input variables are "vr" and "vl" which are the speeds of each wheel and the angle of the vehicle "theta", the output is the speed at the x coordinate and the speed at the y coordinate, and the angular speed.
This works very well because if the vehicle is moving parallel to the x-axis, the angle will be 0, the cosine of 0 is 1, therefore the speed on the y axis will be 0 and the speed on the x-axis will be given by 0.5(vr+vl). The opposite happens when the vehicle is moving parallel to the y-axis.
Set up the equation for the following word problem and solve the equation. Let y be the unknown number.18 times a number minus 97 is equal to 9 less than the number.Step 1 of 2: Write out the equation.
Answers
Hello there. To solve this question, we'll have to remember some properties about set up an equation and solving them.
"Let y be an unknown number. 18 times a number minus 97 is equal to 9 less than the number."
We need to find this number.
Starting with the equation:
[tex]18y-97=y-9[/tex]On the left hand side, we have 18y as 18 times the number, then subtracted 97 for the minus 97 part. On the right hand side, 9 less than the number is represented as the number minus 9.
So, subtract y - 97 on both sides of the equation
[tex]\begin{gathered} 18y-97-(y-97)=y-9-(y-97) \\ 18y-97-y+97=y-9-y+97 \\ 17y=88 \end{gathered}[/tex]Divide both sides of the equation by a factor of 17
[tex]\begin{gathered} \frac{17y}{17}=\frac{88}{17} \\ \\ y=\frac{88}{17} \end{gathered}[/tex]This is the number we've been looking for.
The domain of a function is all whole numbers between 2.5 and 7.5. Can you represent the domain using set-builder notation in more that one way? Explain
Answers
The set builder notation of "The domain of a function is all whole numbers between 2.5 and 7.5" is Domain = {x: x∈W , 2.5<x<7.5 }.
In the Set Builder form , a statement or expression is used to represent all the elements of the set .
In the question ;
it is given that
the domain of the function is all whole numbers between 2.5 and 7.5 .
the set of whole numbers is represented by W.
Since the numbers between 2.5 and 7.5 are included , so "<" will be used .
The Set Builder notation is Domain = {x: x∈W , 2.5<x<7.5 } .
Therefore , the set builder notation of "The domain of a function is all whole numbers between 2.5 and 7.5" is Domain = {x: x∈W , 2.5<x<7.5 }.
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Log^5(1/25)=-2 in exponential form
Answers
We'll use the follwowing property, which comes from the definition of a logarithm:
[tex]\log _ab=c\Leftrightarrow a^c=b[/tex]i.e, The logarithm with base a of b is c if, and only if a to the c power equals b.
Using this to translate
[tex]\log _5(\frac{1}{25})=-2[/tex]Into exponential form, will yield:
[tex]5^{-2}[/tex]Because:
[tex]5^{-2}=\frac{1}{25}[/tex]ANSWER:
[tex]5^{-2}[/tex]You have $73.50. You earn additional money by mowing lawns. Then you purchase a new pair of shoes for $99.99 and have $23.51 leftmuch money do you earn mowing lawns?
Answers
The question provides the following information;
Money at hand = 73.50
Money earned = x
Purchases made = 99.99
Money left over = 23.51
These sets of numbers can be put into an equation as shown below;
(73.5 + x) - 99.99 = 23.51
This equation means what you had at the beginning plus what earned from mowing lawns is a total of 73.5 + x. Subtract the cost of shoes purchased from this total and you'll now have a balance of 23.51
We can now solve for the money earned from mowing lawns as follows;
(73.5 + x) - 99.99 = 23.51
Add 99.99 to both sides of the equation (in order to isolate the 73.5 + x on the left side of the equation). You now have;
73.5 + x = 123.5
Next you subtract 73.5 from both sides of the equation (in order to isolate the x on the left hand side)
x = 50
This means the money earned from mowing lawns is $50
Between what two consecutive integers must solution 2^x=7 lie?
Answers
Answer:
2 and 3
Explanation:
Given the equation:
[tex]2^x=7[/tex]Now, observe the following:
[tex]\begin{gathered} 2^2=4 \\ 2^3=8 \\ 4<7<8 \\ \implies2^2<2^x<2^3 \end{gathered}[/tex]Taking the indices:
[tex]2Therefore, the solution of 2^x=7 lies between the consecutive integers 2 and 3.Probability knowledge check (this is math not chemistry I am looking at the tab correctly)
Answers
Given: The odds in favor of receiving a gift are 4/19.
Required: To determine the probability of receiving a gift.
Explanation: The probability of an event A that has an odd of happening as A/B can be calculated as
[tex]P(A)=\frac{A}{A+B}[/tex]Here A=4 and B=19. Putting the values, we get,
[tex]\begin{gathered} P(A)=\frac{4}{4+19} \\ =\frac{4}{23} \\ \end{gathered}[/tex]Final Answer: The probability of Brian receiving a gift is 4/23.
At a local market, 3 apples and 2 pears cost $2.70. Three apples cost the same as 4 pears. Type a system of equations to find the cost for one apple and the cost for one pear.
Answers
Data:
Apple: A
Pears: P
3A+2P=$2.70
3A=4P
to find the cost for one apple:
A union voted on whether to go on strike 120 people vote the ratio of yes and no votes is 2:3 how many people vote no
Answers
Answer:
80
Step-by-step explanation:
This is a ratio and we can set it up as follows and solve for x:
[tex]\frac{2}{3} = \frac{x}{120}[/tex]
Multiply both sides by 120
80 = x
Divide 120 / 5 = 24
Then multiply the individual digits of ratio (2:3) by 24
2 x 24 = 48
3 x 24 = 72
Put these numbers together in a ratio, 48:72
Therefore 72 people voted no.
Hope this helps
Which set of equations can be solved using the matrix equation:this is an online homework assignment I need help on for pre calculus
Answers
The given matrix equation is:
[tex]\begin{pmatrix}4 & -1 \\ -2 & -1\end{pmatrix}\begin{pmatrix}x \\ y\end{pmatrix}=\begin{pmatrix}-5 \\ -3\end{pmatrix}[/tex]To get the required equations, we will have to carry out the matrix multiplication, thus we have:
[tex]\begin{gathered} (4\times x)+(-1\times y)=-5 \\ (-2\times x)+(-1\times y)=-3 \end{gathered}[/tex][tex]\begin{gathered} 4x-y=-5 \\ -2x-y=-3 \end{gathered}[/tex]Hence, the correct option is option D
A cell phone regularly sells for $210 is on sale for 30% off. With this discount, find the sale price. Round to the nearest cent if necessary
Answers
To know the price to
if a triangle has side lengths of 4x + 6, 6, and 5x; what is the perimeter
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9 + 4 + (-1) +(-1) +...+ (-546) = 0X X80Σ (-3 + 10) = 0E=1
Answers
Answer
The sum of the sequence = -30072
Explanation
We are given a sequence of numbers and asked to find the sum of the terms up until the last term given. The sequence given is
9, 4, -1,.............., -546
On careful observation of this sequence, we can see that it is an arithmetic progression with a common difference of -5 between consecutive terms.
Common difference = (n + 1)th term - nth term
= 4 - 9 Or -1 - 4
= -5
For an arithmetic progression, the formula for the last term is given as
Last term = a + (n - 1)d
where
L = last term = -546
a = first term = 9
n = number of terms in the sequence = ?
d = common difference = -5
So, we can solve for the number of terms
-546 = 9 + (n - 1)(-5)
-546 = 9 - 5n + 5
-546 = 14 - 5n
14 - 5n = -546
-5n = -546 - 14
-5n = -560
Divide both sides by -5
(-5n/-5) = (-560/-5)
n = 112
We can now use the formula for the sum of an arithmetic progression to find the sum of this sequence.
[tex]\text{Sum of an A.P. = }\frac{n}{2}\lbrack2a+(n-1)d\rbrack[/tex]We know all of these parameters now
Sum of this AP = (112/2) [(2 × 9) + (112 - 1)(-5)]
= 56 [18 + (111 × -5)]
= 56 [18 - 555]
= 56 [ -537]
= -30072
Hope this Helps!!!
Can you guys help me simplify this?
-2x^5y^3/6x^7y^2
Answers
Answer is in photo
determine the sample space of all the possible outcomes of choosing a card number 1 2 3 or 4 and a blue green or yellow marble how many outcomes involves choosing a Blue Marble
Answers
There are a total of 4 outcomes that involve choosing a blue marble
Here, we want to write a sample space for the selection
For us to have the sample space, we will have to write out the possible outcomes
We shall be representing the blue marble by b, the green by g and the yellow by y
We have the sample space as follows;
{1B,1G,1Y,2B,2G,2Y,3B,3G,3Y,4B,4G,4Y}
From the sample space, we can see that there are actually 12 possible results
Now, to get the outcomes involving blue marbles, we simply select the members of the sample space having B at the back
We have these as 1B, 2B, 3B and 4B
This is a total of 4 outcomes
The figure shows the measures of various angles of a roof and it supports. Find the measure of angle 1, the angle between an eave and a horizontal support beam.
Answers
Answer:
35 degrees.
Explanation:
The figure shown is an isosceles triangle. An isosceles triangle has two of its sides and base angles to be equal.
Since the sum of the angles in a triangle is 180 degrees, hence:
110 + (base angles) = 180
110 + (<1 + <1) = 180 (since base angles are the same)
110 + 2<1 = 180
2<1 = 180-110
2<1 = 70
Divide both sides by 2
2<1/2 = 70/2
<1 = 35 degrees
Hence the angle between an eave and the horizontal support beam is 35 degrees.
Need help asap thank you!
Answers
All potential solutions are covered by theoretical domains and ranges. The solution sets are constrained by actual domains and ranges to fit inside predetermined constraints. Make a function equation out of a word problem that specifies the domain and range of application. All potential solutions are covered by theoretical domains and ranges.
Domain and range: what are they?C = 9 + 7.34
One room costs = $7.34.
Charges of n room = Charges of one room × Number of Rooms
Charges of n room = 7.34 n
Reservation Room = $ 9
Total Cost (c) = Reservation Room + Charges of n room
C = 9 + 7.34
They only clean a maximum of 15 rooms.
Domain = { 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}
When n = 1 , C = 9 + 7.34 ×1 = 16.34
When n = 2 , C = 9 + 7.34 ×2 =23.68
When n = 3 , C = 9 + 7.34 ×3 =31.02
When n = 4, C = 9 + 7.34 ×4 =38.36
When n = 5 , C = 9 + 7.34 ×5 = 45.7
When n = 6, C = 9 + 7.34 × 6 = 53.04
When n = 7 , C = 9 + 7.34 ×7 = 60.38
When n = 8 , C = 9 + 7.34 ×8 =67.72
When n = 9 , C = 9 + 7.34 × 9 =75.06
When n = 10, C = 9 + 7.34 ×10 = 82.4
When n = 1 1, C = 9 + 7.34 ×1 1 = 89.74
When n = 12 , C = 9 + 7.34 ×1 2 = 97.08
When n = 13 , C = 9 + 7.34 ×1 3 = 104.42
When n = 1 4, C = 9 + 7.34 ×14 = 111.76
When n = 1 5, C = 9 + 7.34 ×15 = 119.1
C = 9 + 7.34
Domain = { 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}
Range = { 16.34,23.68,31.02,38.36,45.7, 53.04,60.38,67.72,75.06,82.4,89.74,97.08,104.42,111.76,119.1}
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