A figure has an area of 100 units `2 what will the new area be after dilation with a scale factor of 2\5
Answers
16 u²
1) If a figure has an area and it's been dilated of k= 2/5
2) Then we can sketch that situation, concerning to areas:
So, we can state this dilated figure is going to have an area of 16 u².
Hence, the answer is 16 u²
Related Questions
Given the diagram below, whereAB||CD, find the measure of xand y.
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Notice that there are two triangles between the parallel lines.
Also, notice that the angle 160° and y are same-side interior angles, so they sum 180°.
[tex]160+y=180[/tex]We solve for y.
[tex]\begin{gathered} y=180-160 \\ y=20 \end{gathered}[/tex]On the other hand, angles 30 and x are alternate interior angles, which means they are congruent.
[tex]x=30[/tex]Therefore, x = 30° and y = 20°.what number do you need to add/subtract/multiply/divide each side by in order to solve the problem below?[tex] \frac{5}{6} = - \frac{2}{3} x[/tex]
Answers
The equation is,
[tex]\frac{5}{6}=-\frac{2}{3}\cdot x[/tex]The equation can be solved if on right side there is only variable with any number in multiplication. So equation can be solved as,
[tex]\begin{gathered} \frac{5}{6}\cdot\frac{-3}{2}=-\frac{2}{3}x\cdot\frac{-3}{2} \\ x=-\frac{5}{4} \end{gathered}[/tex]So to eliminate -2/3
The table shows the grading scale for one of your classes. Tell the letter grade that you earn for each score.a. You earn 14 out of a possible 20 points on a quizz.b. You earn 66 out of a possible 80 points on a test.c. You earn 216 out of a possible 250 points for a report.
Answers
a.
[tex]\frac{14}{20}=\frac{7}{10}=0.7[/tex]Therefore, your score would be 70% then you will get a C
b.
[tex]\frac{66}{80}=\frac{33}{40}=0.825[/tex]Your score would be 82.5%, then you will get a B
c.
[tex]\frac{216}{250}=\frac{108}{125}=0.864[/tex]Your score would be 86.4%, then you will get a B
At a New Car Dealership, a particularmodel comes in 4 different trim levels(CX, DX, EX, and Si). The same modelcomes in 5 different colors (Night Black,Pearl White, Evening Blue, Sandy Red,and Forest Green). The model of car alsohas 3 different interior options (GreyCloth, Tan Cloth, Black Leather). Howmany different versions of this model canbe created from these options?
Answers
solution
diferent trim levels = 4
different colors = 5
different interior options = 3
then:
[tex]4\cdot5\cdot3=60[/tex]answer: 60 different versions of this model
Can you help me solve this? And step by step please?
Answers
Given the sequence:
1/2, 3/4, 9/8, 27/16, ..........
We are to find the recursive formular
A recursive geometric formular has a pattern:
An = An - 1 * r
Where r is the common ratio. But before we write the formular, we need to look for the value of r.
This r value has to be the same between each consecutive number in the series.
Sinces it's geometric, r is multiplied in. To get from 1/2 to 3/2 we find the r value in this way:
x/2 = 3/4 where x/2 is the same as 1/2 x.
Cross multiply to get 4x = 6 and x = 3/2.
That means that if r is 3/2, then we can multiply every term in that sequence by 3/2 to get the next term in line.
3/4 times 32 is 9/8. So, r = 3/2 and the formulat is:
An = An - 1 * 3/2
Therefore, the crrect optio is B.
Writing an equation of a probably given the vertex and focus
Answers
The equation of the vertical parabola in vertex form is written as
[tex]y=\frac{1}{4p}(x-h)^2+k[/tex]Where (h, k) are the coordinates of the vertex and p is the focal distance.
The directrix of a parabola is a line which every point of the parabola is equally distant to this line and the focus of the parabola. The vertex is located between the focus and the directrix, therefore, the distance between the y-coordinate of the vertex and the directrix represents the focal distance.
[tex]p=1-6=-5[/tex]Using this value for p and (3, 1) as the vertex, we have our equation
[tex]y=-\frac{1}{20}(x-3)^2+1[/tex]Hello, I need some assistance with this homework question, please? This is for my precalculus homework. Q9
Answers
For the given function,
Vertical Asymptote:- x =-3
Horizontal asymptote:- y =20
Oblique asymptote :- No oblique asymptote
Asymptote:
A vertical asymptote is found by letting the denominator equal zero. A horizontal asymptote is found by comparing the leading term in the numerator to the leading term in the denominator. The degree of the numerator is greater than the degree of the denominator, so there is no horizontal asymptote.
Oblique asymptotes occur when the degree of the denominator of a rational function is one less than the degree of the numerator
given,
R(x) = [tex]\frac{20x}{x+3}[/tex]
Vertical Asymptote:-
Equate denominator to zero
x +3 = 0
x = -3
Horizontal asymptote:-
Here degree on x in numerator and denominator is same,
so horizontal asymptote will be,
y= 20/1
y = 20
Oblique asymptote:-
There won't be any slant asymptote, because degree in numerator is equal to the degree in denominator.
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g(0) 10 Cabin Rental Cost ($) У 70 60 50 + (0,57] ) 40 30 10 1 (0.15) 0 1 2 3 4 5 6 7 8 9 10 Number of Days
Answers
f(x) = x +57
g(x) =7x+15
The solution is (7,64). To rent the cabin for 7 days cost $64
1) Let's examine the graph. We can see two linear equations.
Picking two points for f(t) = (7,64) and (0,57) and for g(t) (0,15) and (7,64) let's find out their respectives slopes:
2) For f(t) , let's plug into the slope-intercept formula, plugging one point:
(0,57)
y=mx+b
57=0x +b
57= b
So the rule for the function is, in terms of f(x) = x +57
(0,15)
y=mx +b
15=0x +b
15 =b
So the rule for the function g(t) , in terms of g(x) is g(x) =7x+15
Interpreting the solution:
The solution to this Linear System of Equations is the common point (7,64).
So filling in the blanks we have:
The solution is (7,64). To rent the cabin for 7 days cost $64
Hii I really need help right now I don’t understand.
Answers
The function is given as,
[tex]y=4^x[/tex]For x = -1 , the value of y is calculated as,
[tex]\begin{gathered} y=4^{-1} \\ y\text{ = }\frac{1}{4} \\ y\text{ = 0.25} \end{gathered}[/tex]For x = 0 , the value of y is calculated as,
[tex]\begin{gathered} y=4^0 \\ y\text{ = 1} \end{gathered}[/tex]For x = 1 , the value of y is calculated as,
[tex]\begin{gathered} y=4^1 \\ y\text{ = 4} \end{gathered}[/tex]For x = 2, the value of y is calculated as,
[tex]\begin{gathered} y=4^2 \\ y\text{ = 16} \end{gathered}[/tex]i need to show work pls
Answers
Question #5The table shows four relations.RelationRelation 2Relation 3Rolation 4-2-5-3Y-4-4-2-1- 11312372Which relations represent functions?ARelation 1 and Relation 3BRelation 2 and Relation 4СRelation 3 and Relation 2DRelation 4 and Relation 1
Answers
The RELATION 1 and 3 represent a function
Rationale
There are no x value with several y values.
For a relation to be a function, there should only one y value fot each x
Question 21 (1 point)Find the power function that the graph of f given below resembles, but is shifted tothe left by 3 units.f(x)=(x − 3)³Oy=x³Oy=x-27Oy=x⁹Oy=x-³
Answers
STEP - BY - STEP EXPLANATION
What to find?
The power function that the given graph resembles.
Given:
f(x)=(x − 3)³
First, we need to note that;
If f(x) is shifted left q - units, then the new formula of the function becomes f(x+q).
Let q=3
[tex]f(x)=(x-3)^3[/tex][tex]f(x)=(x-3+3)^3[/tex][tex]f(x)=x^3[/tex]ANSWER
y=x³
What is the equation of the horizontal asymptote of the graph of y = 1/x+5 – 4?
Answers
We can find the horizontal asymptote of this kind of functions using the limit:
[tex]\begin{gathered} \lim _{x\to\infty}\frac{1}{x+5}-4=\frac{1}{\infty}-4=-4 \\ \lim _{x\to\infty}\frac{1}{x+5}-4=\frac{1}{-\infty}-4=-4 \end{gathered}[/tex]Therefore the equation of the horizontal asymptote is:
[tex]y=-4[/tex]The local newspaper charges $34.80 for an 8-week subscription. Paige buys an 8-week subscription. How much does it cost her each week?
Answers
Answer:
$4.35
Step-by-step explanation:
8 weeks = $34.80
1 week = x
Cross-multiply
$34.80/8
=$4.35
So, for each week, Paige will pay $4.35
$(4.35 × 8 = 34.8)
the center of the circle is at O. determine the measure of angle ABC
Answers
If the center of the circle is at O.then the measure of angle ABC is 28 degree
The measure of angle ABC can be calculated by using central angle theorem
What is central angle theorem
The Central Angle Theorem states that the central angle from two chosen points A and B on the circle is always twice the inscribed angle from those two points ie if the angle inscribes at the circumference is x, then the angle at the center is 2x.
The angle ABC = 1/2 angle AOC
the angle ABC = 1/2 x 56
the angle ABC is 28
Therefore, if the center of the circle is at O.then the measure of angle ABC is 28 degree
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Please help I only have the first given answer.
Answers
By the property of congruency of triangles, the following conclusions are taken from the figure
[tex]\angle EAB = \angle ECD[/tex] [Alternate angle]
[tex]\angle EBA = \angle EDC[/tex] [Alternate angle]
AB = CD [Given]
What is congruency of triangles?
Two triangles are said to be congruent if their corrosponding sides and corrosponding angles are same.
There are five axioms of congruency
They are SSS axiom, ASA axiom, AAS axiom, SAS axiom, RHS axiom
Here,
In[tex]\Delta AEB[/tex] and [tex]\Delta DEC[/tex]
[tex]\angle EAB = \angle ECD[/tex] [Alternate angle]
[tex]\angle EBA = \angle EDC[/tex] [Alternate angle]
AB = CD [Given]
So,
[tex]\Delta AEB \cong \Delta DEC[/tex] [ASA axiom]
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what is the mean? 66, 594, 69, or 74what is the median? 74, 66, 69, or 75what is the mode? 74, 90, 21, or 66what is the range? 69, 66, 74, or 594
Answers
We have the distribution;
74, 90, 21, 68, 62, 84, 34, 87,74.
Let's arrange this from ascending to descending order, we obtain;
[tex]21,34,62,68,74,74,84,87,90[/tex]i. The mean or average of this distribution is
[tex]\begin{gathered} \frac{21+34+62+68+74+74+84+87+90}{9}=\frac{594}{9} \\ \operatorname{mean}=66 \end{gathered}[/tex]ii. The median is the central value, in this distribution, there are 9 values, so the median value is the 5th value.
[tex]\operatorname{median}=74[/tex]iii. The mode is the value with the highest frequency, this is the most occurring value, in this distribution;
[tex]\text{mode}=74[/tex]iv. The range is the difference between the highest and lowest values, this is;
[tex]\begin{gathered} 90-21=69 \\ \text{Range}=69 \end{gathered}[/tex]
Which of the numbers 12, 13, or 14 is the solution of 106 = 118 - x?
Answers
The given expression is
[tex]106=118-x[/tex]First, we add x on each side
[tex]\begin{gathered} 106+x=118-x+x \\ 106+x=118 \end{gathered}[/tex]Then, we subtract 106 from each side
[tex]\begin{gathered} 106-106+x=118-106 \\ x=12 \end{gathered}[/tex]Trapezoid ABCD is shown on the coordinate plane.Trapezoid formed by ordered pairs A at negative 4 comma 1, B at negative 3 comma 2, C at negative 1 comma 2, D at 0 comma 1.If trapezoid ABCD is reflected over the x-axis and then reflected over the y-axis, which final step would carry the trapezoid onto itself?Group of answer choicesRotate 180°Rotate 90° clockwiseReflect over the x-axisReflect over the y-axis
Answers
Given: The coordinates of a trapezoid as below
[tex]\begin{gathered} A(-4,1) \\ B(-3,2) \\ C(-1,2) \\ D(0,1) \end{gathered}[/tex]To Determine: The final step on the trapezoid after it is reflected over the x-axis and then reflected over the axis
Solution
Please note that a reflection over the x-axis and reflection over the y-axis is different from the last step, which is a reflection over the y-axis
The reflection over the y-axis could either be a rotation of 90^0 clockwise or anticlockwise.
So get the trapezid onto itself after a reflection over the y-axis from a reflection over teh x-axis requires two steps
We have step 1: Reflection over the x-axis, then
Step 2: Reflection over the y-axis
Hence, the final step is reflection over the y-axis
5)For positive values of x, which expression isequivalent toSquare root 16x2*x2/3+square root 8x^5/3
Answers
The answer is option B
Given:
/16x^2 + x^2/3 + 3/8x^5
You need to simplfiy the expression given which will give you
6 3/x^5 or the second option
[tex]6\sqrt[3]{x^5}[/tex]Use the given information to determine the lateral and surface areas of thesolid. Round your answer to the nearest unit.
Answers
Here, we want to use the given information to calculate the lateral and the total surface area
To find the lateral area, we have to calculate the perimeter of the base and multiply this by the height of the triangular prism
Now, we will make the shape lie on its side
This mean the triangles will represent the base
Mathematically, the perimeter of a triangle is the sum of its side
We need the last side of the triangle
We can get this by the use of Pythagoras' theorem
As we can see, the side measure 5 is the hypotenuse as it faces the right angle
The square of the hypotenuse equals the sum of the squares of the two other sides
3,4 and 5 are a Pythagorean triple
This means that, the measure 3 is the last side of the triangle
So the perimeter is;
[tex]3+4+5\text{ = 12 in}[/tex]The height is the measure 8 inches
Thus, the lateral area is;
[tex]12\text{ }\times8=96in^2[/tex]Now, we want the total surface area, but firstly, we need the area of the base
The area of the base is the area of the triangle
[tex]\begin{gathered} B\text{ = }\frac{1}{2}\times b\times h \\ \\ B\text{ = }\frac{1}{2}\times4\times3=6in^2 \end{gathered}[/tex]two times this is 12 in^2
The total suface area is thus;
[tex]96in^2+12in^2=108in^2[/tex]im gonna send a photo of the problem
Answers
You have the following interval:
(-∞,-2]
the previous interval can be written as follow:
x ≤ -2 as an inequality
and on the number line you have:
Amount of Water (ml) 5 8 8.5 8 8.ŏ 8 8 8 10 I → 0 1 2 3 4 5 6 7 8 9 Days What information does the intercept provide A The amount of water in the beaker decreased by 40 ml. B. The water was gone by the eighth day.
Answers
First, we need to identify the y-intercept that is the value of the coordinate y when the coordinate is 0 in this case our y-intercept is in 40
The y-intercept provide the start amount of water therefore the correct choice is D. the water level started at 40 mL
A small yoga studio offers two plans for sessions.•Plan A: Pay a $320 yearly fee and then $5 per session. • Plan B: Pay no yearly fee and $15 per session. Complete each statement. Both plans will cost the same for __?__ sessions. To attend one session each week for a year, plan _?__ will be cheaper.
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1) Firstly, let's express each plan by using linear equations.
Plan A:
5x+320
Note that the $320 payment is done once, then 5 per session.
Plan B
15x
2) To get to know when opting for plan A or Plan B is not relevant, we need to equate both equations and solve it for x (x stands for the number of sessions)
[tex]\begin{gathered} 5x+320=15x \\ 5x-15x=-320 \\ -10x=-320 \\ 10x=320 \\ \frac{10x}{10}=\frac{320}{10} \\ x=32 \end{gathered}[/tex]So if you attend 32 sessions then, doesn't really matter which plan is it.
3) Now, let's figure out which plan is more interesting to take:
[tex]\begin{gathered} C_A(x)=5x_{}+320 \\ C(1)=5(1)+320 \\ C(1)=325 \\ --- \\ C_B(x)=15x \\ C_B(1)=15(1) \\ C_B(1)=15 \end{gathered}[/tex]So the plan B is cheaper to attend 1 session
a local business club has 7 exclusive board members and 31 General members and how many committees of five members can be chosen so that only general managers are included
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We need to choose 5 members from the general only
The number of general members = 31
As the arrangement is not required
So, the number of committees will be:
[tex]31C5=\frac{31!}{(31-5)!\cdot5!}=169,911[/tex]so, the answer will be 169,911 committees
F (x) +5 x-2 Someone pls help me I’m crying
Answers
Given the function:
[tex]f(x)=2x^2+5\sqrt[]{x-2}[/tex]to find f(3), we have to make x = 3 and substitute on the function, to get the following:
[tex]\begin{gathered} f(3)=2(3)^2+5\sqrt[]{3-2}=2(9)+5\sqrt[]{1}=18+5=23 \\ \end{gathered}[/tex]therefore, f(3)=23
I need help with my math
Answers
Given data:
The given points are (-2,-1) and (3, -1).
The slope of the line passing through the given points is,
[tex]\begin{gathered} m=\frac{-1-(-1)}{3-(-2)} \\ =\frac{0}{5} \\ =0 \end{gathered}[/tex]Thus, the slope of the line passing through the given points is 0.
Britta is preparing a budget. What does this task MOST likely involve?A. She is looking at her credit card bills to predict her credit score.B. She is not allowing herself to spend any money for 30 days.C. She is allotting a set amount of money for her expenses.D. She is determining which investments are the best fit for her goals.
Answers
From the question we are to determine Britta most likely task in preparing a budget.
First let's know what a budget is.
A budget is an estimation of revenue and expenses over a specified future period of time and is utilized by governments, businesses, and individuals. A budget is basically a financial plan for a defined period, normally a year that is known to greatly enhance the success of any financial undertaking.
So with the above explanation of what a budget is, Britta most likely task is to allot a set amount of money for her expenses.
Therefore the correct option is C, which is She is allotting a set amount of money for her expenses.
What is the value of this expression?
5 (912−14 )+ 0.5
Enter your answer, in simplest form, in the box.
Answers
Answer:
4490.5
Step-by-step explanation:
5(898)+0.5
=4490.5
Kevin recorded the distances he ran last week. The total number of miles he ran on Monday through Wednesday is the same as the total number of miles he ran on Thursday and Friday. How many miles did Kevin run on Wednesday?
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Kevin recorded the distances he ran last week. The total number of miles he ran on Monday through Wednesday is the same as the total number of miles he ran on Thursday and Friday. How many miles did Kevin run on Wednesday?
_______________________
The total number of miles he ran on Monday through Wednesday is the same as the total number of miles he ran on Thursday and Friday.
x + (x + 9) + (x + 4) = 2x + (4x - 2)
_____________________
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__________________
x + (x + 9) + (x + 4) = 2x + (4x - 2)
3x + 13 = 6x -2
6x - 3x = 13 + 2
3 x = 15
x = 15/3 miles
x = 5 miles
___________________________
5 + ( 5 + 9) + ( 5 + 4) = 2x + (4x - 2)
28 = 28
________________________
on Wednesday
x=5
x+ 4 = 9
_________________
Answer
On Wednesday he ran 9 miles
_________________
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Do you have any questions regarding the solution?