What is the scale factor if triangle ABC was dilatedto create triangle DEF?2/31/223/2
Answers
Answer
Option B is correct.
Explanation
The scale factor for dilating any figure (reducing or enlarging any figure) is given as
Scale factor = (Length of the image figure)/(Length of original figure)
For this question, we have been told that triangle ABC is the original image and triangle DEF is the new image figure after the dilation occurs.
Note that you need to use corresponding sides in the calculation of scale .factor
Scale factor = (Length of the image figure)/(Length of original figure)
Length of the image figure = 5 ft.
Length of original figure = 10 ft.
OR
Width of the image figure = 3 ft.
Width of the first image figure = 6 ft.
Scale factor = (Length of the image figure)/(Length of original figure)
Scale factor = (5/10) = (3/6) = ½
Hope this Helps!!!
Related Questions
describe the lines of symmetry in the word kid if there is one
Answers
The line of symmetry divides a shape into 2 equal halves. The line of symmetry can be describe as an imaginary line that passes through the center of a figure and create a mirror image of the figure. An example of a line of symmetry is a line dividing a shape into two equal halves .
The imaginary line is the green line and it divide the square into 2 equal halves . Therefore, the word kid has no line of symmetrry
If a figure has been dilated by a scale factor of one third, which transformation could be used to prove the figures are similar using the AA similarity postulate?
Answers
SOLUTION:
If a figure has been dilated by a scale factor of one third, the transformation that could be used to prove the figures are similar using the AA similarity postulate is;
Answer:
A translation because it can map one angle onto another since dilations preserve angle measures of triangles.
Step-by-step explanation:
I believe this is the answer
-/2 Points]DETAILS OSELEMALG1 1.4.328.Translate to an algebraic expression, but do not simplify.the product of -18 and the difference of c and d
Answers
Answer:
[tex]\begin{gathered} -18(c-d) \\ =\text{ 18d-18c} \end{gathered}[/tex]Explanation:
Here, we want to translate the given statement into an algebraic expression
The product of -18 and the difference between c and d
The difference between c and d will be:
[tex]c-d[/tex]Then, we multiply -18 with this. That would give:
[tex]-18(c-d)[/tex]Simplifying the above, we have:
[tex]-18c\text{ + 18d = 18d-18c}[/tex]What is the equation for the line Parallel to x=5 passing through the point (-6,13).
Answers
Given line parallel to x=5 and passes through point (-6,13)
So to find equation of line
Slope of line joining x=5 and the parallel to it will be same m=∞
So the equation of line having m=1/0=∞ and passing through (-6,13) will be
y=m .x+C
[tex]13=\frac{1}{0}\times-6+C[/tex][tex]C=6[/tex]On substituting the value in C we get
[tex]y=\frac{1}{0}x+6[/tex]Hence this is the equation of required line is x=6.
Find the sample variance and standard deviation 5, 57, 10, 51, 34, 24, 29, 28, ,29 , 31
Answers
SOLUTION
Write out the data given, we have
[tex]5,57,10,51,34,24,29,28,29,31[/tex]Write out the formula
[tex]\begin{gathered} \\ s^2=\frac{\sum_{i=1}^n\left(x_i-\bar{x}\right)^2}{n-1} \\ \text{Where } \\ s^2=\text{varaince} \\ n=10,\bar{x}=\operatorname{mean}=29.8 \end{gathered}[/tex]Hence
[tex]\text{sum of squares=}2253.6[/tex]Hence, Sample variance will be
[tex]s^2=\frac{ss}{n-1}=\frac{2253.6}{10-1}=\frac{2252.6}{9}=250.4[/tex]The sample variance is 250. 4
The standard deviation is the square root of the variance
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find x to the nearest 100th if sin x = 7/8
Answers
Answer:
x = 61.04°
Explanation:
Given:
[tex]\sin x=\frac{7}{8}[/tex]Take the arcsin of both sides of the equation.
[tex]\begin{gathered} \arcsin(\sin x)=\arcsin(\frac{7}{8}) \\ \implies x=61.04\degree \end{gathered}[/tex]The value of x is 61.04° to the nearest 100th.
17374474747477484×92929292
Answers
EXPLANATION:
ANSWER:
17374474747477484x 92929292=1.61x10^24
IMPORTANT NOTE ;
To solve long multiplications there are two methods vertically and horizontally, the answers will always be significantly long, so we must know how to round significant figures.
Find the slope of the line that passes through the points (5,3) and (-1, -1). You must reduce your answer.Write your answer as a fraction
Answers
you can calculate the slope of a line if you have two points, the slope formula is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x2,y2) is the rightmost point, for this case (5,3) and (x1,y1) is the other point, So:
[tex]m=\frac{(3)-(-1)}{(5)-(-1)}[/tex][tex]m=\frac{3+1}{5+1}\text{ = }\frac{4}{6}[/tex]We can reduce the answer
[tex]\frac{4}{6}\text{ = }\frac{2}{3}[/tex]Finally, the slope of the line is:
[tex]\frac{2}{3}[/tex]What is -6x+2 if the x is -5
Answers
Answer:
32
Step-by-step explanation:
[tex] - 6x + 2 \\ = - 6 \times - 5 + 2 \\ = 30 + 2 \\ = 32[/tex]
Simplify the rational expression below. When typing your numerator and denominators be sure to but the term with the variable first and do not put spaces between your characters. \frac{\left(12n^2-29n-8\right)}{\left(28n^2-5n-3\right)} The numerator is AnswerThe denominator is Answer
Answers
Given the rational expression below:
[tex]\frac{12n^2-29n-8}{28n^2-5n-3}[/tex]The simplification is as shown below:
[tex]\begin{gathered} \frac{12n^2-29n-8}{28n^2-5n-3}=\frac{12n^2-32n+3n-8}{28n^2-12n+7n-3} \\ \frac{12n^2-32n+3n-8}{28n^2-12n+7n-3}=\frac{4n(3n-8)+1(3n-8)}{4n(7n-3)+1(7n-3)} \\ \frac{4n(3n-8)+1(3n-8)}{4n(7n-3)+1(7n-3)}=\frac{(3n-8)(4n+1)}{(7n-3)(4n+1)} \end{gathered}[/tex]It can be observed from the simplification that (4n+1) is common to both the numerator and denominator. To simplify further we will cross (4n+1) out in the numerator and denominator as shown below:
[tex]\begin{gathered} \frac{(3n-8)(4n+1)}{(7n-3)(4n+1)}=\frac{3n-8}{7n-3} \\ Hence,\frac{12n^2-29n-8}{28n^2-5n-3}=\frac{3n-8}{7n-3} \end{gathered}[/tex]Hence, after the simplification,
the numerator is 3n - 8, and
The denominator is 7n - 3
Replace the question mark with the appropriate value.953 cm2 = ? mm2
Answers
In order to get the required value, we are to use the following converion factor;
1cm^2 = 100mm^2
To convert 953 cm^2 to mm^2, we will say;
1cm^2 = 100mm^2
953cm^2 = x
Then we will calculate x by cross multiplying;
1 * x = 953 * 100
x = 953 * 100
x = 95,300mm^2
Hence the question mark will be replaced by 95,300mm^2
find the domain of g(x)= x/x^2-49.answer in interval notation
Answers
Explanation
Given
[tex]g(x)=\frac{x}{x^2-49}[/tex]The domain of the function is the set of x values that will make the function defined. This is given below.
Using the denominator, we will find the point of singularity.
[tex]\begin{gathered} x^2-49=0 \\ x^2=49 \\ x=7,x=-7 \end{gathered}[/tex]Therefore, the points of singularities are 7 and -7. Hence we will exclude those points from the set of real numbers.
Answer:
[tex](-\infty-7)\cup(-7,7)\cup(7,\infty)[/tex]A particular country has 55 total states. If the areas of 35 states are added and the sum is divided by 35, the result is 191,374 square kilometers. Determine whetherthis result is a statistic or a parameter.Choose the correct answer below.O A. The result is a statistic because it describes some characteristic of a sample.B. The result is a parameter because it describes some characteristic of a sample.OC. The result is a parameter because it describes some characteristic of a population.D. The result is a statistic because it describes some characteristic of a population.
Answers
Lets reminde the differences between parameter and statitics:
A parameter is a number describing a whole population (e.g., population mean), while a statistic is a number describing a sample (e.g., sample mean).
In our case, we took a sample of 35 states and fond the average area of each state, so this number describe our sample of 35 states, so is a "statistic".
Which of the following piecewise functions best describes the graph below ?The answer
Answers
To answer this question, we need to be careful with the domain (x values) and the slope of the lines.
From left to right we have the following functions:
For values less than or equal to -3, we have a line with a positive slope. We have two lines, y = x - 2, and y = x - 3.
If we make:
x = -3, and y = -5, then we have:
1. For y = x - 2
[tex]-5=-3-2\Rightarrow-5=-5[/tex]2. For y = x - 3
[tex]-5=-3-3\Rightarrow-5\ne-6[/tex]Then, we have that the second option is a possible candidate to solve the question.
We can also see that the first option is not an option since the domain is given for x less than -3 (and the graph is for x less or equal to -3 - see the solid circle of the line).
We also have that for the interval from x greater than -3 and less or equal to 5, the value for the function is equal to 8.
We also have that the line has a negative slope for values greater than 6, and the given equation is y = -x + 10.
Therefore, the answer to this question is the second option:
[tex]undefined[/tex]If the xy- plane The graph of the equation (x-6)^2+ (y+5^2)= 16 is a circle. point p is on the circle and has coordinates (10, -5). If PQ is a diameter of the circle, what are the coordinates of Q?
Answers
(x - 6)² + (y + 5)² = 16 is a circle centered at (6, -5) with a radius of 4 units.
The point P(10, -5) has the same y-coordinate as the center of the circle and it is placed 4 units to the right of it.
Then, the point Q must have the same y-coordinate and must be placed 4 units to the left of the center, therefore its x-coordinate is 6 - 4 = 2. In consequence, point Q is placed at (2, -5), as can be seen in the next graph:
Dion features Great Dane 62 cups of draw water Creek has a new bag with 160 cups of dog food beyond will pick up more dog food at the pet store in 2 1/2 weeks will the new bag of food last until then
Answers
The bag contains 160 cups of feed.
If the dog eats 62 cups of feed per week, we can calculate how many weeks of feed does the bag contain by dividing 160 by 62:
[tex]\#\text{weeks}=\frac{160\text{ cups}}{62\text{ cups/week}}\approx2.58\text{ weeks}[/tex]As she will be picking more feed in 2 1/2 = 2.5 weeks, and as 2.58 > 2.5, we know that the bag of feed will last until then.
Answer: Yes, it will last 2.58 weeks, that is greater than 2 1/2 weeks.
I need help with 14 I need answer and a explanation
Answers
Step 1
Like terms in an expression are terms that are exactly alike. Either they are constants(for example 8), variables( for example x ) or a combination of variables and constants ( for example 3x)
Step 2
Draw a conclusion from step 1
The given expression is 3x + 8 + 8x
The like terms here are therefore 3x and 8x because they are alike, consisting of a variable and a coefficient or constant.
the table above gives the annual ales (in billions of dollars) of Pepsico, which operates two major businesses: beverages (including Pepsi) and snack foods. The table shows Pepsico ales in billions of dollars for the 11 years.A) What was the change of annual ales between the first year, 2010, and the 2015 year?B) What is the average rate of change in sales for the 2015 years beginning in 2010?billion dollars per year
Answers
Answer:
A) 5.92 billion dollars
B) 1.184 billion dollars per year
Explanation:
Part A)
The change in annual sales between 2010 and 2015 is calculated as the difference between the sales of 2015 and 2010. So, taking into account the table, we get:
59.42 - 53.5 = 5.92 billions of dollars
Because 59.42 billion are sales in 2015 and 53.5 billion are sales in 2010.
Therefore, the answer is 5.92 billion dollars
Part B)
The average rate of changes in sales from 2010 to 2015 is equal to the change in the annual sales divided by the number of years, so it is calculated as
[tex]\frac{59.42-53.5}{2015-2010}=\frac{5.92}{5}=1.184[/tex]Therefore, the average rate of change is 1.184 billion dollars per year.
The pair of equations 3x + y + 4 = 0 and -3x - 6y + 1 = have * A unique solution*exactly two solutions*infinitely many solutions*no solutions
Answers
Given:
3x + y + 4 = 0
-3x - 6y + 1 = 0
Required:
To calculate which option is correct
Explanation:
The given equations are
3x + y + 4 = 0
3x - 6y + 1 = 0
a1=3; b1=1 ; c1=4
a2=-3;b2=-6 ; c2=1
[tex]\frac{a1}{a2}=\frac{3}{-3}=-1[/tex][tex]\frac{b1}{b2}=\frac{1}{-6}=-\frac{1}{6}[/tex][tex]\frac{c1}{c2}=\frac{4}{1}=4[/tex][tex]\frac{a1}{a2}\ne\frac{b1}{b2}\ne\frac{c1}{c2}[/tex]which means it is A unique solution
Required answer:
Option A
Shawna is creating a banner for a school club. She uses exactly 24 feet of ribbon to create the designshown at left, which is made up of equilateral triangle sides. Find the length, in inches, of eachtriangle's side length.
Answers
the length of the ribbon is 24 ft
in the equilateral triangle all the side has equal values,
let the side is 'a'
then
a + a +a = 24
3a = 24
a = 24/3
a = 8 ft
now we convert feet into inches
we know that 1 ft = 12 inches
so in 8 ft
8 x 12 = 96 inches.
so the side of the triangle is 96 inches.
the measure of angle is 16 what is the measure of a complementary angle
Answers
Two angles are called complementary when their measures add to 90 degrees
Let the two angles are x and y
[tex]x\text{ + y =90}[/tex]one angle is given , x = 16
substitute the value of x=16 and solve for y
[tex]\begin{gathered} x+y=90 \\ 16+y=90_{} \\ y=90-16 \\ y=74 \end{gathered}[/tex]So, the measure of another angle is 74 degree which makes angle 16 to complementary angles
Answer : Measure of complementary angle = 74 degree
Springfield, and Capital City form a right triangle. The distance between Centerville and Springfield is 913 kilometers and the distance between Springfield and Capital City is 976 kilometers. View the map.What is the direct distance between Centerville and Capital City? Round to the nearest kilometer.
Answers
To the nearset kilometer, the distance between Centerville and Capital City is 1,336 km
Here, we want to find the distance between Centerville and Capital city
From what we have in the diagram, we can see a right-angled triangle
Thus, we can use Pythagoras' theorem here
It states that the square of the hypotenuse equals the sum of the squares of the two other sides
The distance between Centerville and Capital city is the hypotenuse as it is the side that faces the right-angle
Let us call the distance h
Thus, according to Pythagoras' theorem, we have it that;
[tex]\begin{gathered} h^2=913^2+976^2 \\ h^2\text{ = 833,569+952,576} \\ h^2=\text{ 1,786,145} \\ h\text{ = }\sqrt[]{1,786,145} \\ h\text{ = 1,336.47 } \end{gathered}[/tex]Help me with this equation can you please help me
Answers
In the function h, the value of a represents the amplitude of the trigonometric function, this amplitude represents half the distance between the maximum point and minimum point of the curve, according to the statement the innertube's height fluctuates between 2 meters and 6 meters, then,
[tex]\begin{gathered} a=\frac{max-min}{2} \\ a=\frac{6-2}{2} \\ \\ a=\frac{4}{2} \\ a=2 \end{gathered}[/tex]then, b can be found through the period of a trigonometric function, the period can be understood as the time or interval in which the function starts at a maximum and gets back to the same point, in the statement the interval is equal to 10, by definition of a trigonometric function can be found by:
[tex]p=\frac{2\pi}{b}[/tex]clear the equation for b,
[tex]b=\frac{2\pi}{p}[/tex]since the period is equal to 10,
[tex]\begin{gathered} b=\frac{2\pi}{10} \\ \\ b=\frac{\pi}{5} \end{gathered}[/tex]the complete function should be,
[tex]h=2sin(\frac{\pi}{5})+4[/tex]Answer:
[tex]a=2;b=\frac{\pi}{5}[/tex]A square red placement has a gold square in the center. The side length of the gold square is (x+2) inches and the width of the red region is 4 inches. What is the area of the red part of the placement?
Answers
A square red placement has a gold square in the center.
The side length of the gold square = (x+2) inches
and the width = 4 inches
Thus the area if the red part of the placement is the product od width and the dimension of square
[tex]\begin{gathered} (x+2)^2-4^2 \\ x^2+4+4x-16 \\ x^2+4x-12 \end{gathered}[/tex]Area of the p;ace is x^2+4x-12
From 1965 to 2000, twice as many people immigrated to the United States from the Philippines as from Vietnam. The total number of immigrants from these two countries was 2,100,000. How many people came to the United States from each country?
Answers
Data:
• Twice as many people immigrated from the Philippines as from Vietnam.
,• People immigrated from Vietnam ( ,V ,)
,• People immigrated from Philipines (, P ,)
Procedure:
0. We have to build two equations based on the information provided:
[tex]P=2V[/tex][tex]V+P=2,100,000[/tex]2. Replacing the first equation in the second, we get the following equation:
[tex]V+2V=2,100,000[/tex][tex]3V=2,100,000[/tex][tex]V=\frac{2,100,000}{3}[/tex][tex]V=700,000[/tex]3. Then, we replace this value in the first equation:
[tex]P=2V[/tex][tex]P=2\cdot700,000[/tex][tex]P=1,400,000[/tex]Answer:
• People immigrated from Vietnam = 700,000
,• People immigrated from Philipines = 1,400,000
Use synthetic division to determine whether the first expression is a factor of the second X-2, 4x^3-3x^2-4x+12(X-2)(__)
Answers
The expression is given as,
[tex]4x^3-3x^2-4x\text{ + 12}[/tex]The given factor is ( x - 2 ) .
Applying the synthetic division method ,
As the remainder is not zero in the last column .
Therefore ( x - 2 ) is not a factor of the given expression .
3) By how many zeros do the following numbers end:a) 7^2 × 2^4 × 5^4 b) 3^5 × 2^7 × 11^2 × 5^6
Answers
SOLUTION
(3). (a) We want to find the number of zeros the number
72 × 24 × 54 end.
To do this, what we have to do is count how many times did 2 and 5 occurred in the question as factor. Number of zeros is equal to the one (2 or 5) which occurred less times.
From7^2 × 2^4 × 5^4, we have
[tex]\begin{gathered} 7^2\text{ there are no 5's or 2's} \\ 2^4,\text{ there are four 2's} \\ 5^4,\text{ there are four 5's } \\ Altogether,\text{ we have four 2's and four 5's} \\ So,\text{ since the number of 2's and 5's are equal, we choose one} \end{gathered}[/tex]Hence the answer is 4 zeros
(b) 3^5 × 2^7 × 11^2 × 5^6
[tex]\begin{gathered} 3^5,\text{ there are no 2's or 5's } \\ 2^7,\text{ there are seven 2's} \\ 11^2,\text{ there are no 2's or 5's} \\ 5^6,\text{ there are six 5's} \\ Making\text{ a total of seven 2's and six 5's. So we go for the lesser} \\ which\text{ is six 5's } \end{gathered}[/tex]Hence the answer is 6 zeros
Find the probability of z occurring in the indicated region of the standard normal distribution.P(0
Answers
To find the probability:
[tex]P(0we need to remember that:[tex]P(0No we need to find each of the probabilities in a standard table, then we have:[tex]\begin{gathered} P(0Therefore:[tex]P(0what's 2 + 2 1 take away 3 divided by 5 * 2
Answers
2+21 = 23
we are ask to take away 3, this implies we are to subtract 3 from 23
That is;
23 - 3 = 20
Then we are to divide by 5 x2
5 x2 = 10
20 ÷ 10 = 2
Hence;
2 + 2 1 take away 3 divided by 5 * 2 =
Categorize each of the following as properties of "Parallel Lines" or "Perpendicular Lines" Never Intersect Perpendicular Lines Answer by dragging items here Intersect at a 90° Angle Have the SAME SLOPE Parallel Lines Answer by dragging items here Have a slope "opposite reciprocal" 1 m = 3 m = - 3 m= 3 → m' = 3
Answers
Two lines are parallel when they never intersect, this means that their slope is equal.
To lines are perpendicular when they intersect at an angle of 90 degrees. This means that their slope are the oposite of the reciprocal.
With this in mind let's choose each option belongs to each kind of line.
Never intersect -> parallel
Intersect at an angle of 90 degrees -> perpendicular
Have the same slope -> parallel
Have a slope oposite reciprocal -> perpendicular
m=3 and m1= -1/3 -> perpendicular
m=3 and m1 = 3 -> parallel