Segment AB is dilated from the origin to create segment A prime B prime at A' (0, 4) and B' (4, 6). What scale factor was segment AB dilated by?
Answer choices:
A. 1/2
B. 2
C. 3
D.4
Given:
Endpoint of segment AB are A(0,2), B(2,3).
Segment AB is dilated from the origin to create segment A prime B prime at A' (0, 4) and B' (4, 6).
To find:
The scale factor of dilation.
Solution:
If a figure is dilated about the origin with factor k, then
[tex](x,y)\to (kx,ky)[/tex]
Using this rule, we get
[tex]A(0,2)\to A'(k(0),k(2))[/tex]
[tex]A(0,2)\to A'(0,2k)[/tex]
So, the image of A is A'(0,2k).
It is given that image of A is A'(0,4). So,
[tex]A'(0,2k)=A'(0,4)[/tex]
On comparing the y-coordinates from both sides, we get
[tex]2k=4[/tex]
[tex]k=\dfrac{4}{2}[/tex]
[tex]k=2[/tex]
Therefore, the scale factor is 2 and the correct option is B.
Dilation involves changing the size of a line
The scale factor is 2.
From the graph, the coordinates of AB are:
[tex]\mathbf{A = (0,2)}[/tex]
[tex]\mathbf{B = (2,3)}[/tex]
The coordinates of AB are:
[tex]\mathbf{A' = (0,4)}[/tex]
[tex]\mathbf{B' = (4,6)}[/tex]
Divide A' by A or B' by B to calculate the scale ratio (k)
[tex]\mathbf{k = \frac{A'}{A}}[/tex]
So, we have:
[tex]\mathbf{k = \frac{(0,4)}{(0,2)}}[/tex]
Expand
[tex]\mathbf{k = \frac{2(0,2)}{(0,2)}}\\[/tex]
Divide
[tex]\mathbf{k = 2}\\\\\\\\[/tex]
Hence, the scale factor is 2.
Read more about scale factors at:
https://brainly.com/question/16713785
Need help with math who is up points and brainlest for you !!
Answer:
8ft
Step-by-step explanation:
Use similarity and congruence
AB/ED=AC/EF
3/6=4/X
CROSS MULTIPLICATION
3X=6*4
3X=24
X=8ft
The area of square ABCD is 144 square units. The area of square EFGH is 64 square
units. HE AB and GE BC. The blue area is three times the red area. Find the area
of AHBG.
Answer:
80
Step-by-step explanation:
Answer: 24
Step-by-step explanation:
144-24=120
64-24=40
40*3=120 three times smaller
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times the measure of the first angle. The third angle is 10 more than the second.
Answer:
first angle be 30°
second angle be 70°
third angle be 80°
Step-by-step explanation:
first angle be x
second angle be y
third angle be z
x+y+z=180
given, y+z = 5x; z=5x-y
also, z=y+10
5x-y = y+10
5x= 10+y+y = 10+2y
x= (10+2y)/5
x+y+z=180
(10+2y)/5 + y + y+10 = 180
(10+2y)/5 = 180 -2y -10
(10+2y)/5 = 170-2y
multiply both sides by 5
10+2y = 5(170-2y)
10+2y= 850-10y
2y+10y = 850-10
12y= 840
y= 840/12 = 70°
z=y+10 =70+10= 80°
5x= (10+2y) = 10+2(70) = 10+140= 150
x = 150/5 = 30°
Which of the following statements about this function's domain is true?
A.) Domain: 0≤x≤16 and 0
The domain represents all of the values that were measured in this problem.
B.) Domain: 0≤y≤16
The domain represents the set of all possible inputs - the times when depth was measured.
C.) Domain: 0
The domain represents the set of all possible outputs - the various depths of the pool.
D.) Domain: 0≤x≤16
The domain represents the set of all possible inputs - the times when depth was measured.
Answer:
D.) Domain: 0≤x≤16
The domain represents the set of all possible inputs - the times when depth was measured
Step-by-step explanation:
Domain of a function is the possible set of inputs which are usually plotted on the x-axis, while range are corresponding outputs plotted on the y-axis.
In this case, the domain is the set of all possible inputs (x-values), which represents the times the depth was measured.
Domain ranges from 0 to 16. Thus:
Domain: 0 ≤ x ≤ 16
Work out the value of 3 \times(3^2 + 4) - 83×(32+4)−8
Answer:Conversion a mixed number 8 1/
4
to a improper fraction: 8 1/4 = 8 1/
4
= 8 · 4 + 1/
4
= 32 + 1/
4
= 33/
4
To find new numerator:
a) Multiply the whole number 8 by the denominator 4. Whole number 8 equally 8 * 4/
4
= 32/
4
b) Add the answer from previous step 32 to the numerator 1. New numerator is 32 + 1 = 33
c) Write a previous answer (new numerator 33) over the denominator 4.
Eight and one quarter is thirty-three quarters
Conversion a mixed number 3 2/
5
to a improper fraction: 3 2/5 = 3 2/
5
= 3 · 5 + 2/
5
= 15 + 2/
5
= 17/
5
To find new numerator:
a) Multiply the whole number 3 by the denominator 5. Whole number 3 equally 3 * 5/
5
= 15/
5
b) Add the answer from previous step 15 to the numerator 2. New numerator is 15 + 2 = 17
c) Write a previous answer (new numerator 17) over the denominator 5.
Three and two fifths is seventeen fifths
Subtract: 33/
4
- 17/
5
= 33 · 5/
4 · 5
- 17 · 4/
5 · 4
= 165/
20
- 68/
20
= 165 - 68/
20
= 97/
20
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(4, 5) = 20. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 5 = 20. In the next intermediate step the fraction result cannot be further simplified by canceling.
In words - thirty-three quarters minus seventeen fifths = ninety-seven twentieths.
Conversion a mixed number 2 1/
3
to a improper fraction: 2 1/3 = 2 1/
3
= 2 · 3 + 1/
3
= 6 + 1/
3
= 7/
3
To find new numerator:
a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/
3
= 6/
3
b) Add the answer from previous step 6 to the numerator 1. New numerator is 6 + 1 = 7
c) Write a previous answer (new numerator 7) over the denominator 3.
Two and one third is seven thirds
Subtract: 7/
3
- 1/
4
= 7 · 4/
3 · 4
- 1 · 3/
4 · 3
= 28/
12
- 3/
12
= 28 - 3/
12
= 25/
12
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(3, 4) = 12. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the next intermediate step the fraction result cannot be further simplified by canceling.
In words - seven thirds minus one quarter = twenty-five twelfths.
Subtract: the result of step No. 3 - the result of step No. 5 = 97/
20
- 25/
12
= 97 · 3/
20 · 3
- 25 · 5/
12 · 5
= 291/
60
- 125/
60
= 291 - 125/
60
= 166/
60
= 2 · 83/
2 · 30
= 83/
30
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(20, 12) = 60. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 20 × 12 = 240. In the next intermediate step , cancel by a common factor of 2 gives 83/
30
.
In words - ninety-seven twentieths minus twenty-five twelfths = eighty-three thirtieths.
Step-by-step explanation:took a lot of time brainliest plz
The Miller family likes to paddle along the North River.
1. They paddled the same distance each day throughout the course of 3 days, traveling a total of 14 miles. How many miles did they travel each day ?
write the mixed number you got
4 2/3 think of how many time you can put 3 into 14 the section out the rest
Answer:
4 2/3
Step-by-step explanation:
the millers travled 4 2/3
14 ÷ 3/8
I need help plis :(
Answer:
[tex]\frac{112}{3}[/tex]
Step-by-step explanation:
14 ÷ 3/8 = 14 • 8/3
= 112/3
Answer:
37 1/3
Step-by-step explanation:
use Keep Change Flip when dividing with fractions! :) It's helpful
for example: 14 ÷ 3/8
14 (keep as 14)
* (change to multiplication)
8/3 (flip the fraction)
14 times 8/3= 37 1/3
What are the domain restrictions of q^2-3q-4/q^2-7q-8
How do you simplify?
Will give brainliest for CORRECT answer
The person above is correct give them brainliest
Rewrite the following polynomial in standard form
Answer:
-7x³ - ⅑x - 1
Step-by-step explanation:
A polynomial written in standard form would be written in such a way that the term with the highest degree comes first, followed by the second highest and so on, then what comes last is the constant.
Given the polynomial -7x³ - 1 - ⅑x, -7x³ with the highest degree comes first, followed by -⅑x, and then the constant, -1, comes last.
Thus, we would have:
✅-7x³ - ⅑x - 1
cos(2x) + sin^2(x) = 0
cos(2θ) + sin²(θ) = 0
Half-angle identity:
cos(2θ) + (1 - cos(2θ))/2 = 0
Simplify:
2 cos(2θ) + 1 - cos(2θ) = 0
cos(2θ) = -1
Solve for θ :
2θ = arccos(-1) + 2nπ
2θ = π + 2nπ
θ = π/2 + nπ
where n is any integer.
Shape p is translated to shape Q using vector (a b).
Please find A.
Photo attached.
Answer:
-7
Step-by-step explanation:
you basically just move across and because its moving to the left its a negative
Shape P is translated to shape Q using b[tex]\left[\begin{array}{ccc}7\\4\end{array}\right][/tex]..
What is translation of a graph?In mathematics, a translation is the up, down, left, or right movement of a shape. Because the translated shapes appear to be exactly the same size as the original ones, they are congruent with one another.
Given:
The shape P is mentioned on the graph is translated to shape Q.
So, the shape shifted 7 units to left.
and, the shape needs to shift downwards 4 places.
Hence, the required vector is [tex]\left[\begin{array}{ccc}7\\4\end{array}\right][/tex].
Learn more about translation of a graph here: brainly.com/question/14753556
#SPJ2
f(x)=x-7 and g(x)=2x-3
find f(g(4))
Answer:
f(g(4)) = -2
Step-by-step explanation:
First, find g(4) by plugging in 4 as x into the function:
g(x) = 2x - 3
g(4) = 2(4) - 3
g(4) = 8 - 3
g(4) = 5
f(g(4)) can be found by finding f(5), since g(4) = 5
Find f(5) by plugging in 5 into the function:
f(x)= x - 7
f(5) = 5 - 7
f(5) = -2
So, f(g(4)) = -2
You have a map of Southern California. If the distance between
Mrs. Clough's house and Badger Springs middle school on the map
is 3 inches, and the scale is 2 inches represents 12 miles, how far is
the actual distance from Mrs. Clough's house to school.
9514 1404 393
Answer:
18 miles
Step-by-step explanation:
The map distance and ground distance are proportional.
(distance to school)/(3 in) = (12 miles)/(2 in)
Multiplying by 3 in gives ...
distance to school = (12 miles)(3/2) = 18 miles
Plz Help!
This triangle has one side that lies on an extended line segment.
Based on this triangle, what statement about x is true?
x= 33 because 180 – 147 = 33
x = 62 because 147 – 85 = 62 and 85 + 62 = 147
x = 95 because 180 – 85 = 95 and 85 + 95 = 180
x = 118 because
180 147 + 85
33 + 85
=118
Answer:
B. x = 62 because 147 – 85 = 62 and 85 + 62 = 147
Step-by-step explanation:
We are given that
[tex]\angle ABC=85^{\circ}[/tex]
Exterior angle=[tex]147^{\circ}[/tex]
We have to find the value of x.
We know that
Exterior angle=Sum of opposite interior angles of triangle
Using the property
[tex]x+85=147[/tex]
Subtract 85 from both sides we get
[tex]x=147-85[/tex]
[tex]x=62[/tex]
Option B is true.
B. x = 62 because 147 – 85 = 62 and 85 + 62 = 147
A number x is three times the value of number y. A number z is eight times the value of y. The sum of
the three numbers is 528. What are the 3 numbers (HINT: This problem requires 3 equations to solve!!
Step-by-step explanation:
y=a
x= 3a
z=8a
3a+8a+a=524
12a=528
a=44
X=3×44=132
z=8×44= 352
Answer:
y=a
x= 3a
z=8a
3a+8a+a=524
12a=528
a=44
X=3×44=132
z=8×44= 35
2
Step-by-step explanation:
what is 473.2608 rounded to the nearest tenth
Answer:
473.2608 rounded to the nearest tenth Is 473.3
Step-by-step explanation:
Which of the following are mathematical sentences? Check all that apply.
A. 144 +7
B. X-49
c. 4
D. 5g=31
E. 3>2
F. 1+12 = x
can be used to compare changes from one period to another.
a) Decimals
b) Fractions
c) Percentages
d) Digits
Answer:
c) Percentages
Step-by-step explanation:
Percentages can be used to compare changes from one period to another.
In calculating a percentage change, either a percentage increase or percentage decrease, we must have both the new and old measurement of the specific quantity.
For example, let's find percentage increase of the number of students that joined a book club using the parameters below;
Original number of students = 32
New number of students = 36
We will calculate the increase using;
[tex] Increase = original \; number - new \; number [/tex]
Substituting the values, we have;
Increase = 36 - 32 = 4
[tex] Percentage \; increase = \frac{increase}{original \; number} * 100[/tex]
[tex] Percentage \; increase = \frac{4}{32} * 100[/tex]
[tex] Percentage \; increase = 0.125 * 100[/tex]
Percentage increase = 12.5%
Therefore, the number of students in the school club increased by 12.5%.
What is the cos A? ....
Answer:
4/5
Step-by-step explanation:
The polygons are regular. Find the degree measure of y.
Answer:
ajjvtjeiqwchiedgvgfeggyryftyyyug ytugttbghg
When Daria gets to school, the temperature is 5.7°F. The temperature changes by 29.5°F by the time she goes to bed. What is the temperature when Daria goes to bed? Show your work.
Write the following rate in simplest forms.
1. 333 calories burned in 55 minutes.
2. 4 million hits on a website in 16 months.
3. 279 points in 27 games.
4. $49 for 448 photos.
5. 6 pounds of zucchini for 24 servings.
Solve the system of linear equations by substitution.
−5x+y=−7
−3x−2y=−12
Please help I'm having panic attacks about failing this test and failing the class this is my last test and I have a C please help
Answer:
[tex]x = 2 \\ y = 3[/tex]
[tex] - 5x + y = - 7.......(1) \\ - 3x - 2y = - 12......(2) \\ from \: (1) \\ y = - 7 + 5x \\ substitute \: in \: (2) \\ - 3x - 2( - 7 + 5x) = - 12 \\ - 3x + 14 - 10x = - 12 \\ [/tex]
[tex] - 13x = - 26 \\ x = \frac{ 26}{13} \\ x = 2[/tex]
[tex]y = - 7 + 5x \\ = - 7 + 5 \times 2 \\ = - 7 + 10 \\ y= 3[/tex]
How old is Abraham How old is Abraham Lincoln
Answer:
Abraham Lincoln was 56 years old when he died.
Step-by-step explanation:
PLEASE HELP I WILL GIVE BRAINLIEST
9514 1404 393
Answer:
48
Step-by-step explanation:
Evaluate each of the functions by putting the number where x is.
[tex]g(x)=x^2-4\\\\g(-7)=(-7)^2-4=49-4\\\\\boxed{g(-7)=45}\\\\f(x)=x+4\\\\f(-7)=-7+4\\\\\boxed{f(-7)=-3}[/tex]
Then the difference is ...
g(-7) -f(-7) = 45 -(-3) = 45 +3 = 48
Answer:
solution given;
g(x)=x²-4
f(x)=x+4
Now
g(-7)-f(-7)=(-7)²-4-(-7+4)=49-4+3=48
48 is a required answer.
HELP Ross drives 402 miles in 6 hours. If Ross continues to drive at the same rate, how many miles can he drive in 12 hours? A. 804 B. 1,608 C. 335 D. 780
Answer:
804
Step-by-step explanation:
multiply 402 by 2
12÷2=6
6=402miles
402×2=804
#gamer
You start driving north for 24 miles, turn right, and drive east for another 10 miles. At
the end of driving, what is your straight line distance from your starting point?
Answer:
26 miles.
Step-by-step explanation:
To solve this problem, the Pythagorean theorem must be applied, which states that the hypotenuse squared of every right triangle is equal to the sum of its squared legs, that is, A^2 + B^2 = C^2 .
Therefore, applying this formula, to determine the distance in a straight line from the starting point to the driving end point, the following calculation must be performed:
24^2 + 10^2 = X^2
576 + 100 = X^2
√676 = X
26 = X
Thus, the distance between the two points is 26 miles.
The price of an item yesterday was $120. Today, the price rose to $294. Find the percentage increase.
Answer:
145%.
Step-by-step explanation:
Given that the price of an item yesterday was $120, and today, the price rose to $294, in order to find the percentage increase, the following calculation has to be made:
120 = 100
294 = X
((294 x 100) / 120) = X
29,400 / 120 = X
245 = X
245 - 100 = 145
Therefore, the percentage increase of the product was of 145%.