The dashed-line triangle is a dilation image of the solid-lined triangle.
A graph is shown with x and y axes that extend from negative 8 to positive 8 in increments of 2.
A triangle formed by solid black line segments is shown with vertices at negative 9 comma 4, negative 9 comma negative 8, and 7 comma negative 8.
A second smaller triangle formed by dashed line segments is shown with vertices at negative 5 comma 6, negative 5 comma 2, and 0 comma 2.
Is the dilation an enlargement or a reduction? What is the scale factor of the dilation? (1 point)
reduction; one-third
enlargement; one-third
reduction; 3
enlargement; 3
Answers
Triangles ABC and A'B'C' are similar because of AAA.
Also,
[tex] \frac{AB}{A'B'}= \frac{15}{5}=3 \\\\ \frac{AC}{A'C'}= \frac{12}{4}=3 [/tex]
Therefore
ΔA'B'C' is 1/3 the size of ΔABC.
This means that the scale factor from ΔABC to ΔA'B'C' is a 3-factor reduction.
Answer: reduction; one-third.
The dilation is a reduction.
The scale factor of the dilation is one-third.
Related Questions
Which angle pairs are supplementary ?
Answers
Answer:
4,5
Step-by-step explanation:
construct a recursive rule to describe the sequence: 2, 4, 6, 8,...
Answers
Answer:
a[1] = 2; a[n] = a[n-1] + 2
Step-by-step explanation:
The first term of the sequence is 2, so the first part of the definition is ...
a[1] = 2
Each term is 2 more than the previous one, so the rest of the definition is ...
a[n] = a[n-1] + 2
_____
Comment on recursive rules
A recursive rule has two parts. The first part tells what the initial value of the sequence is. The second part relates the next term to the previous term or terms.
For arithmetic and geometric sequences, each term is related to the previous term by a constant. For an arithmetic sequence, each term is the last term plus the common difference. For a geometric sequence, each term is the last term multiplied by the common ratio.
For the arithmetic sequence 2, 4, 6, 8,.., the recursive rule can be written as: the first term a_1 is 2, and for all subsequent terms (n > 1), a_n equals the previous term a_(n-1) plus 2.
Explanation:The sequence given is an arithmetic sequence, where each term increases by 2. A recursive sequence is a sequence in which each term is defined based on its preceding terms. For the sequence 2, 4, 6, 8,... the recursive rule can be constructed as follows:
a_1 = 2
a_(n) = a_(n-1) + 2 for n > 1
In these rules, a_1 is the first term in the sequence, and a_(n) is the nth term of the sequence. a_(n-1) represents the term before the nth term in the sequence. This rule states that each term in the sequence is 2 more than the previous term.
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A cube an edge length is 18in. What is it's volume?
Answers
Good luck ^-^
on vacation, your family decides to rent a car. The total cost involves the one time rental fee of $56.34 and $0.49 per mile
Which expression represents the total rental cost in terms of the rental fee and the cost per mile
A. 56.34 +.49x
B.56.34 - .49x
C. -56.34 - .49x
D. 56.34x + .49
Answers
Use logarithmic differentiation to find the derivative with respect to x of the function y= (sin x)^lnx
Answers
y = (sinx)^lnx
ln(y) = ln((sinx)^lnx)
power rule logarithm
ln(y) = ln(x) ln(sinx)
Take derivative
y'/y = ln(sinx)(1/x) + ln(x) cosx/sinx
multiply both sides by y
y' = y( ln(sinx)/x + ln(x)cotx )
remember y = (sinx)^lnx
sub this in for y
y' = (ln(sinx)/x + ln(x)cotx)(sinx)^lnx
The product of two consecutive even integers is 288 find the integers.
Answers
n and n+2 are the integers
n*(n+2)=288
n^2+2n=288
n^2+2n-288=0
288=2*2*2*2*2*3*3=(2*2*2*2)*(2*3*3)=16*18 and 18-16=2
factor(n+18)(n-16)=0
n+18=0
n=-18
n+2=-16
this is one solution
n-16=0
n=16
n+2=18
this is another solution
as you can see, it's just a matter of factoring 288using arithmetic...√288=16.97≈1716 and 18 are the integers (as well as -16 and -18)
If possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible. Statement 1: If x = 7, then 7x – 2 = 47. Statement 2: x = 7
Answers
Answer:
x=7
Step-by-step explanation:
The Law of Detachment can be used to conclude that 7x - 2 = 47.
Explanation:The Law of Detachment states that if a conditional statement is true and its hypothesis is true, then its conclusion must also be true. In this case, Statement 1 is a conditional statement: 'If x = 7, then 7x - 2 = 47.' Statement 2 tells us that x = 7. Since the hypothesis of Statement 1 is true (x = 7), we can apply the Law of Detachment to conclude that its conclusion must also be true. Therefore, we can validate Statement 1: '7x - 2 = 47.'
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how to write this number 2,015,473 in expanded form
Answers
Congruent angles have the same...
A. Ending
B. Origin
C. Measure
Answers
Answer: Congruent angles have the same measure
Step-by-step explanation:
Kelsey is asked to find the probability of rolling a composite number on a die. She states that this is a simple event. True or false
Answers
a rectangle has perimeter 182 inches and length 52 inches what is the width
Answers
Width= 39 inches
Someone please help me
Answers
the first one,
Scientific notation has to have a number to the left of the decimal point
Suppose a1={1,{2}}a1={1,{2}} and a2={∅,{1,2}}a2={∅,{1,2}} and a3={∅,{1},2}a3={∅,{1},2}. enter "t" for each true, and "f" for each false statements. f equation editorequation editor 1. |p(a2)|=4|p(a2)|=4 t equation editorequation editor 2. a1⊆a3a1⊆a3 f equation editorequation editor 3. {∅}⊆p(a1){∅}⊆p(a1) f equation editorequation editor 4. |p(a2)|=8|p(a2)|=8 f equation editorequation editor 5. {1,2}∈p(a3){1,2}∈p(a3) f equation editorequation editor 6. (∅,2)∈p(a1)(∅,2)∈p(a1) f equation editorequation editor 7. {1}∈p(a1){1}∈p(a1) f equation editorequation editor 8. {∅}∈p(a2){∅}∈p(a2) f equation editorequation editor 9. {{1}}∈p(a3){{1}}∈p(a3) f equation editorequation editor 10. {1}∈p(a3){1}∈p(a3) f equation editorequation editor 11. {{1,2}}⊆p(a2)
Answers
A submarine was situated 800 feet below sea level. If it's ascends 250 feet, what is its new position?
Answers
The distance between P and T on the coordinate grid is ___ units. (Input whole numbers only.) Image of a coordinate grid with point P located at negative 10, 15 and point T located at 15, 15.
Answers
That made no sense.
Answer:
The distance between P and T on the coordinate grid is 25 units.
Step-by-step explanation:
Coordinate of P = (-10,15)
Coordinate of T = (15,15)
By distance formula we have distance between ( a,b) and (c,d) is
[tex]\sqrt{(c-a)^2)+(d-b)^2}[/tex]
Here (a,b) = Coordinate of P = (-10,15) and (c,d) = Coordinate of T = (15,15)
Substituting
[tex]\texttt{Distance =}\sqrt{(c-a)^2)+(d-b)^2}=\sqrt{(15-(-10)^2)+(15-15)^2}=\sqrt{25^2}=25units[/tex]
The distance between P and T on the coordinate grid is 25 units.
Assume that f is a one-to-one function. (a) if f(1) = 12, what is f −1(12)
Answers
The domain of f(x) = range of f(-1)x and vice-versa.
So f-1(12) = 1.
Which numbers are a distance of 3 units from 12 on a number line?
Answers
Answer:
Probably 15 and 9
Edgar anderosn earns $300 a week plus a 15% commission only on sales he makes after his first $1000 sales if Mr.Anderson's sales for one week are $2500 what is his gross pay for that week
A. $525
B. $775
C. $675
D. $450
Answers
He earns $300 a week
The sales for one week are $2500
Percentage of commission on sale above $1000= 15%
[2500-1000]*(15/100)
=1500*(15/100)
=15*15 dollars
=$225
Then Gross pay of Edgar Anderson for the week = (300+225)dollars
=$525
A family swimming pool membership costs $55 per month plus a one-time registration fee of $25. If a family has paid a total of $465, how many months have they been members?
Answers
total without registration fee = 465 - 25
= 440
55 = 1 month
440 = 1 ÷ 55 x 440
= 8 months
They have been members for 8 months.
The family has been members of the swimming pool for 8 months. This was calculated by setting up an equation with the formula for the total cost, C = 55m + 25, and solving for the number of months (m), with C set to the amount paid of $465.
To determine how many months a family has been members of a swimming pool with a membership cost of $55 per month plus a one-time registration fee of $25 and a total payment of $465, we need to set up an equation and solve for the number of months.
Let's denote the number of months as m. The total cost of the membership for m months is the monthly rate times the number of months plus the registration fee.
The equation representing the total cost (C) is:
C = 55m + 25
We know that the total cost is $465, so we substitute this value into the equation:
465 = 55m + 25
To solve for m, we first subtract 25 from both sides:
440 = 55m
Then, we divide both sides by 55 to find the number of months:
m = 440 / 55
m = 8
So, the family has been members for 8 months.
In a normal distribution, what percentage of scores fall between –1 and +1 standard deviation units of the mean?
Answers
Hope I helped :)
Which normal distribution has a wider spread: the one with mean 3 and standard deviation 4 or the one with mean 4 and standard deviation 3 ? the normal distribution with mean 4 and standard deviation 3 has the wider spread?
Answers
Answer:
The correct option is 1. The normal distribution with mean 3 and standard deviation 4 has a wider spread.
Step-by-step explanation:
Normal distribution is defined by two variables, mean and standard deviation.
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
The spread of a normal distribution is not dependent on mean, it is completely dependent of standard deviation. Larger standard deviation means wider spread.
It is given that first normal distribution has
[tex]\mu_1=3[/tex]
[tex]\sigma_1=4[/tex]
Second normal distribution has
[tex]\mu_2=4[/tex]
[tex]\sigma_2=3[/tex]
Since [tex]\sigma_1>\sigma_2[/tex], therefore the normal distribution with mean 3 and standard deviation 4 has a wider spread.
Hence the correct option is 1.
Final answer:
The normal distribution with a mean of 3 and a standard deviation of 4 has a wider spread than a normal distribution with a mean of 4 and a standard deviation of 3, as the spread is determined by the standard deviation.
Explanation:
The question is asking which of the two normal distributions has a wider spread. The spread of a normal distribution is determined by its standard deviation. A normal distribution with a higher standard deviation will have a wider spread. In this case, the normal distribution with a mean of 3 and a standard deviation of 4 will have a wider spread compared to the normal distribution with a mean of 4 and a standard deviation of 3. Thus, the statement 'the normal distribution with mean 4 and standard deviation 3 has the wider spread' is incorrect.
In a normal distribution, as the standard deviation increases, the distribution curves become wider and shorter, reflecting a greater spread in the data. Because both distributions are normally distributed, we can compare the standard deviations directly to determine the spread: a standard deviation of 4 indicates a wider spread than a standard deviation of 3.
What is the difference between a buffalo and a birthday cake?
Answers
Answer:
The buffalo is an animal and the birthday cake is a food.
Step-by-step explanation:
Hi, Buffaloes are heavily built oxen, with sparsely haired skin, large ears, long, tufted tails, broad muzzles and massive angulated horns. In having only 13 pairs of ribs they resemble the typical oxen. African buffaloes all have the hair of the back directed backwards.
A birthday cake is like a normal cake but made for the special celebration of birthdays.
a container holds 2 gallons of juice. how much is this in pints
Answers
If the equation of a line has a slope of zero and passes through the point (3,3) which form would be used to write the question of the line
Answers
an equation is : y - 3 = 0(x-3)
y-3=0
the form would be used to write the question of the line is : y = 3
A store is having a sale on almonds and jelly beans. For 8 pounds of almonds and 3 pounds of jelly beans, the total cost is $18 . For 2 pounds of almonds and 5 pounds of jelly beans, the total cost is $13 . Find the cost for each pound of almonds and each pound of jelly beans.
Answers
2a + 5j = 13....multiply by -4
--------------
8a + 3j = 18
-8a - 20j = - 52 (result of multiplying by -4)
-------------add
-17j = - 34
j = -34/-17
j = 2 <=== jelly beans cost $ 2.00 per lb
8a + 3j = 18
8a + 3(2) = 18
8a + 6 = 18
8a = 18 - 6
8a = 12
a = 12/8
a = 1.50 <=== almonds cost $ 1.50 per lb
By setting up a system of equations and solving them, we find that the cost per pound of almonds is $1.50, and the cost per pound of jelly beans is $2.00.
To find the cost for each pound of almonds and each pound of jelly beans, we can set up two equations to solve the problem algebraically. Let's denote the cost per pound of almonds as a and the cost per pound of jelly beans as b. We have two scenarios provided:
8 pounds of almonds and 3 pounds of jelly beans cost a total of $18.
2 pounds of almonds and 5 pounds of jelly beans cost a total of $13.
We can translate these scenarios into two algebraic equations:
8a + 3b = 18
2a + 5b = 13
Now, we will solve this system of equations to find the values of a and b.
Step 1: Multiply Equation (2) by 4
8a + 20b = 52 (We multiplied all terms by 4 to match the coefficient of a in Equation (1))
Step 2: Subtract Equation (1) from the new equation
8a + 20b - (8a + 3b) = 52 - 18
17b = 34
Step 3: Solve for b
b = 34 / 17
b = 2
Now we know each pound of jelly beans costs $2.
Step 4: Substitute b back into Equation (1) to solve for a
8a + 3(2) = 18
8a + 6 = 18
8a = 12
a = 12 / 8
a = 1.5
So, each pound of almonds costs $1.50.
Therefore, the cost per pound of almonds is $1.50, and the cost per pound of jelly beans is $2.00.
Once again, I find myself stuck in the abyss of Polynomials.
This one was more confusing being that I need to multiply the first term to the trinomial,
then the second term to the trinomial...continuing on till your brains fries...then you combine terms. May I get some help please?
Answers
Basically we are going to have 2x times all of (x^2+3x-2)
And then we add on 2 times all of (x^2+3x-2)
Let's distribute through each piece
For the first part...
2x*(x^2+3x-2) = 2x*(x^2)+2x*(3x)+2x*(-2)
2x*(x^2+3x-2) = 2x^3+6x^2-4x
And then the second part..
2*(x^2+3x-2) = 2*(x^2)+2*(3x)+2*(-2)
2*(x^2+3x-2) = 2x^2+6x-4
-----------------------------------------
Putting this all together, we can say
(2x+2)*(x^2+3x-2) = 2x*(x^2+3x-2)+2*(x^2+3x-2)
(2x+2)*(x^2+3x-2) = 2x^3+6x^2-4x+2x^2+6x-4
(2x+2)*(x^2+3x-2) = 2x^3+8x^2+2x-4
-----------------------------------------
The final answer is 2x^3+8x^2+2x-4
Daniel got a life insurance check of $5875 after the death of a close relative. He deposited it into a savings account at 1.7 percent interest for five years. What was the total amount of money in the account after five years?
A. $6462.50
B. $6433.13
C. $6374.38
D. $6315.63
Answers
A=p (1+rt)
A future value?
P present value 5875
R interest rate 0.017
T time 5years
A=5,875×(1+0.017×5)
A=6,374.38
So the answer is c
Hope it helps!
Sv02 change before you start slowing the draw time on your mixed venous sample 4%
Answers
The value of -4^2 is _____.
16
-16
8
18
Answers
Hank delivers packages in his office building on Tuesday he delivers four more packages then on Monday and on Wednesday he delivered six more packages then on Monday if he delivers 28 packages all together how many did he deliver on Monday??
A)6
B)10
C)18
D)22
Answers
Work shown:
M- 6 packages delivered
T- 6+4=10
W- 6+6=12
Now add packages delivered each day
6+10+12=28
Please vote my answer brainliest. thanks!
6 i hope this helps you