Answer:
400.9 m
Step-by-step explanation:
What is the scale factor from AABC to ADEF?
B
48
AA
6
A4 CE
48
6
O A.
C
B. 8
32
D
Answer: 8
Step-by-step explanation:
We are going from a smaller triangle to a larger triangle, so the scale factor is greater than 1.
Eliminate A and D.We know scale factor = (image)/(preimage), so the scale factor is 32/4 = 8
The scale factor of dilation of the triangle is k = 8
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
The result of dilation is that the shapes and boundaries of objects in the input image are expanded or thickened. It is often used in conjunction with other morphological operations such as erosion, opening, and closing to manipulate and enhance images.
Given data ,
Let the first triangle be represented as ΔABC
Let the second triangle be represented as ΔDEF
where the measures of sides of ΔABC are
AB = 6 , BC = 6 and AC = 4
The measure of sides of triangle ΔDEF are
DE = 48 , EF = 48 and DF = 32
The scale factor of dilation k = measure of side DE / measure of side AB
k = 48 / 6
k = 8
Hence , the dilation factor is k =8
To learn more about dilation click :
https://brainly.com/question/13176891
#SPJ5
(3x + 5y = 7
{ 4x - y = 5
Answer:
Step-by-step explanation:
Solution by substitution method
3x+5y=7
and 4x-y=5
Suppose,
3x+5y=7→(1)
and 4x-y=5→(2)
Taking equation (2), we have
4x-y=5
⇒y=4x-5→(3)
Putting y=4x-5 in equation (1), we get
3x+5y=7
⇒3x+5(4x-5)=7
⇒3x+20x-25=7
⇒23x-25=7
⇒23x=7+25
⇒23x=32
⇒x=32/23
→(4)
Now, Putting x=32/23
in equation (3), we get
y=4x-5
⇒y=4(32/23)-5
⇒y=(128-115)/23
⇒y=13/23
∴y=13/23 and x=32/23
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 15, negative 5, 0, 5, 0, negative 5.
Therefore, we can write it as f(x) ≥ 0 over the interval [-1,1].
The given coordinates of the given table are (-3,15), (-2,-5), (-1,0), (0,5), and (1,0).
We need to write a valid prediction about the continuous function f(x).
What is the continuous function?In mathematics, a continuous function is a function such that a continuous variation of the argument induces a continuous variation of the value of the function.
Now, it is clear from the values of f(x) with respect to x, that the function reaches zero at x = -1, then goes up to 5 at x = 0 and then again reaches zero at x = 1.
So, the value of f(x) remains positive within the interval of [-1,1].
Therefore, we can write it as f(x) ≥ 0 over the interval [-1,1].
To learn more about continuous function visit:
https://brainly.com/question/21447009.
#SPJ1
how would you solve 4c + 11 = -25? explain how in complete sentences and list the solution. (yall im so lost in class rn, i need this)
Answer:
c = -9Step-by-step explanation:
4c + 11 = -25
4c = -25 - 11
4c = -36
c = -36 : 4
c = -9
or
4c + 11 + 25 = 0
4c + 36 = 0
c = (-36)/4
c = -9
-------------------
check
4 *(-9) + 11 = -25
-36 + 11 = -25
-25 = -25
the answer is good
Answer:
c= -9
Step-by-step explanation:
1. 4c + 11 = -25
2. Put all like terms together and change the sign. In this case, the +11 will go to the right with the -25 and it will become -11.
Therefore:
4c= -25 -11
4c= -36
3. Make c the subject. Since 4 is being multiplied by c, when it goes to the right, it will divide.
Therefore:
c= -36/4
c= -9
If x is a positive integer, what is the value of x for the equation (x!-(x-3)!)\23=1?
I think the first step is knowing (x!-(x-3)!) equals to 23, but after that i'm stuck, can someone help me?
[tex]\dfrac{x!-(x-3)!}{23}=1\\x!-(x-3)!=23\\(x-3)!((x-2)(x-1)x-1)=23\\(x-3)!((x^3-x^2-2x^2+2x)-1)=23\\(x-3)!((x^3-3x^2+2x)-1)=23[/tex]
23 is a prime number, therefore there are two possibilities:
[tex]\text{I.}\, (x-3)!=1 \wedge x^3-3x^2+2x-1=23[/tex]
or
[tex]\text{II.}\, (x-3)!=23 \wedge x^3-3x^2+2x-1=1[/tex]
[tex]\text{I.}\\(x-3)!=1\\x-3=0 \vee x-3=1\\x=3 \vee x=4[/tex]
Now, we check if any of these solutions is also a solution to the second equation:
[tex]3^3-3\cdot3^2+2\cdot3-1=23\\27-27+6-1-23=0\\ -18=0[/tex]
Therefore, 3 is not a solution.
[tex]4^3-3\cdot4^2+2\cdot4-1=23\\64-48+8-1-23=0\\0=0[/tex]
Therefore, 4 is a solution.
[tex]\text{II.}[/tex]
[tex](x-3)!=23[/tex]
We know that [tex]3!=6[/tex] and [tex]4!=24[/tex], therefore there isn't any [tex]n\in\mathbb{N}[/tex], for which [tex]n!=23[/tex], so there's no solution.
So, the only solution is [tex]x=4[/tex].
If A=P+I make the subject as P
Answer:
[tex]P = A - I[/tex]
Step-by-step explanation:
A = P + I (Given)[tex]\implies P = A - I[/tex]Suppose a bag contains a set of 10 tiled letters: M, T, O, A, T, P, J, A, K, A You draw a tile from the bag, and record the letter and leave it on the table. You shake up the bag, and draw another tile out of the bag. Calculate the probability you will select the letter M on the first draw and the Letter T on the second draw?
Answer:
1/90
Step-by-step explanation:
Comment
To begin with, there are 10 tiles.. You draw one and don't replace it. Then you draw another tile from the 9 that remain. The job is to figure out the probability of that happening.
You have a 1/10 chance of drawing the M.
But now there are only 9 tiles left and you have a 1 in 9 chance of drawing a T
Solution
P(M,T) = 1/10 * 1/9 = 1 / 90
You have a 1 in 90 chance of getting the two tiles in the order you have specified.
A formula for the normal systolic blood pressure for a man age A, measured in mmHg, is given as
P = 0.006A2 − 0.02A + 120. Find the age to the nearest year of a man whose normal blood pressure measures 125 mmHg.
Solving a quadratic equation, the age of the man with a blood pressure of 125 mmHg is of 27 years old.
What is a quadratic function?A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In which:
[tex]\Delta = b^2 - 4ac[/tex]
The pressure is given by:
P = 0.006A² - 0.02A + 120.
When the pressure is of 125 mmHg, we have that:
0.006A² - 0.02A + 120 = 125.
0.006A² - 0.02A - 5 = 0.
Hence the coefficients are a = 0.006, b = -0.02, c = -5, and the solutions, applying the formula are:
A = -30 and A = 27.
Age has to be positive, hence the man is 27 years old.
More can be learned about quadratic functions at https://brainly.com/question/26865936
#SPJ1
The school play sold $550 in tickets one night. The number of $8 adult tickets was 10 less than twice the number of $5 child tickets. How many tickets were sold for the adults vs the child tickets?
Answer:
This is my answer↓:
Step-by-step explanation:
He school play sold $550 in tickets one night.
The number of $8 adult tickets was 10 less than twice the number of
$5 child tickets.
How many of each ticket were sold
Let say child ticket sold = x
Adult tickets was 10 less than twice the number of child tickets.
=> Adult ticket sold = 2x - 10
Child ticket sold = x
$5 child tickets price
=> Revenue = 5x $
Adult ticket sold = 2x - 10
$8 Adult tickets price
=> Revenue = 8(2x - 10) =16x - 80 $
5x + 16x - 80 = 550
=> 21x = 630
=> x = 30
Child ticket sold = 30
Adult ticket sold = 50
Total ticket sold = 80
Mark as brainlist, thanks me, and rate. Hope it helps!!!
Which statements about the system are true? Select two options.
y=-x-4
3y-x = -7
The system has one solution.
The system consists of parallel lines.
Both lines have the same slope.
Both lines have the same y-intercept.
The equations represent the same line.
The slope for both the line is m= 1/3 and they are parallel lines , Option B and C are correct two options
The first equation is
y = (1/3)x-4 and not y = -x-4
(if the equation is not corrected then it will not have two true statements)
What is a System of Equation ?A system of equation is a set of equation which have a common solution
The given system of equation is
y = (1/3)x-4
3y -x = -7
3y = x-7
As it can seen from the standard equation of a line that
y =mx+c
so slope for both the line is m= 1/3
Therefore they are parallel lines
Thus , Option B and C are correct two options
To know more about System of Equation
https://brainly.com/question/12895249
#SPJ1
You are betting on a game with an expected value of -$0.33. What does this mean?
What is the value of this expression when c = -4 and d = 10?
A.
2
B.
9
C.
21
D.
41
The complete question is
"What is the value of this expression when c= -4 and d= 10?
1/4 (c^3+d²)
A.2
B.9
C.21
D.41"
The value of this expression when c = -4 and d = 10 will be option B 9.
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
The given expression is
[tex]1/4 (c^3+d^2)\\\\1/4 ((-4)^3+(10)^2)\\\\1/4 ( -64 + 100)\\\\1/4 (36)\\\\9[/tex]
Hence, the value of this expression when c = -4 and d = 10 will be option B 9.
Learn more about an expression here:
https://brainly.com/question/1249625
#SPJ1
x^2 - 20x= -2x - 80 what is the intermediate step
The short leg of a 90-45-45 triangle is 3 and the long leg is 7. What is the hypotenuse?
The short leg of a 90-45-45 triangle is 3 and the long leg is 7. The hypotenuse would be [tex]c = \sqrt{58}[/tex].
What is the Pythagoras theorem?The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
The short leg of a 90-45-45 triangle is 3 and the long leg is 7.
Since this is a right triangle, we can use the Pythagoras theorem
a^2+b^2 = c^2
where a and b are the legs and c is the hypotenuse
[tex]3^2 + 7^2 = c^2\\\\9 + 49 = c^2\\\\58 = c^2\\\\c = \sqrt{58}[/tex]
Hence, The hypotenuse would be [tex]c = \sqrt{58}[/tex].
Learn more about Pythagoras theorem;
https://brainly.com/question/343682
#SPJ1
If the present value of a growing perpetuity is 214, the required rate of return is 10%, and growth rate is 3%, what is the cash flow in year 1? (Round to the nearest whole number).
The cash flow in year 1 is $15.
What is the cash flow in year 1?A growing perpetuity increases continuously and indefinitely.
Cash flow = present value x (rate of return - growth rate)
214 x (10% - 3%)
214 x 0.07 = $15
To learn more about present value, please check: https://brainly.com/question/17322936
#SPJ1
my dad began paying me an allowance when i was in eighth grade. what is the indirect object?
Answer:
Step-by-step explanation:
The answer would be "me" as the indirect object
Here is the histogram of a data distribution. All class widths are 1.
SO
4
3
2-
2 3
Which of the following numbers is closest to the mean of this distribution?
A. 2
OB. 3
O C. 10
OD. 5
5 6 7 8 9 10
E. 4
The correct answer is option B which is 3
What is mean?
Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.
Given data:-
4,3,2
The mean will be calculated as:-
Mean = (4 + 3 + 2) / 3
Mean = 9 / 3
Mean = 3
Therefore the correct answer is option B which is 3
To know more about mean follow
https://brainly.com/question/968894
#SPJ1
In 2009, there were 12,078 Burger King restaurants; in 2017, there were 16,717 Burger King restaurants. Calculate the average rate of change (slope) for the number of Burger King restaurants over this time period.
The average rate of change (slope) is 579.875 if, in 2009, there were 12,078 Burger King restaurants; in 2017, there were 16,717 Burger King restaurants.
What is the slope?
The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have:
In 2009, there were 12,078 Burger King restaurants; in 2017, there were 16,717 Burger King restaurants.
The slope:
[tex]\rm m =\dfrac{16717-12078}{2017-2009}[/tex]
m = 4639/8
m = 579.875
Thus, the average rate of change (slope) is 579.875 if, in 2009, there were 12,078 Burger King restaurants; in 2017, there were 16,717 Burger King restaurants.
Learn more about the slope here:
brainly.com/question/3605446
#SPJ1
John is 5 years younger than David. Four years later David will be twice as old as John. Find their present age.
David will be 10 and John will be 9
Help me with this please!!!!
Answer:
3
Step-by-step explanation:
Cardinalities are the number of elements in a set.
(A∩B∩C) is the very middle part of the circle, and there are 3 elements there.
1. Which of the following numbers is
rational?
A. 0.78
B. 0.303003000
C. √6
D. 0.3841697
Answer:
A. 0.78
Step-by-step explanation:
A rational number is a number that you can express as [tex]\frac{x}{y}[/tex] where [tex]y\neq 0[/tex].
using Factoring:
Set up an algebraic equation:
An integer is 3 less than 5 times another. If the product of the two integers is 36,
then find the integers.
Answer:
hjjj gogo fgjvsgjgccvvggggggffffffddsddddfffgv
I need help on questions d and e, not sure how to solve!
D.
[tex]m(x) = 0 \\ - 3x = 0 \\ x = 0[/tex]
E.
[tex]m(x) = \frac{ - 3}{25} [/tex]
[tex] \frac{ - 3x}{x {}^{2} + 2x - 24} = \frac{ - 3}{25} [/tex]
[tex] - 3(x {}^{2} + 2x - 24) = - 3(x)(25) \\ divide \: both \: sides \: by - 3[/tex]
[tex]x {}^{2} + 2x - 24 = 25x[/tex]
[tex]x {}^{2} - 23x - 24 = 0[/tex]
[tex](x - 24)(x + 1) = 0 [/tex]
[tex]x = 24 \\ x = - 1[/tex]
Answer:
D
x=0
Step-by-step explanation:
E)
[tex]\frac{-3x}{x^2+2x-24} =\frac{-3}{25} \\x^2+2x-24=25x\\x^2+2x-25x-24=0\\x^2-23 x-24=0\\x^2-24x+x-24=0\\x(x-24)+1(x-24)=0\\(x-24)(x+1)=0\\x=24,-1[/tex]
Which pairs of angles are congruent?
Answer:
b) angles 1 and 4 are congruent.
Hope it helps!
Suppose you are designing a cardboard box that must have a volume of 27 cubic feet. The cost of the cardboard is $0.21 per square foot.
The material in each box will cost $____
Giving out brainliest to whoever answers!
A man has to be at a certain place at a certain time. He finds that he shall be 20 minutes late if he walks at 3 km/h speed and 10 minutes earlier if he walks at a speed of 4 km/h_The distance he has to walk is
Answer:
0.5km or 500m
Step-by-step explanation:
Given Distance = Speed x Time
In this case, we should use the difference in speed and time of the 2 scenarios.
Difference in Time = 20 mins(late) + 10 mins(early)
= 30 mins or 0.5 hour
Difference in Speed = 4km/h - 3km/h = 1km/h
Distance = 1km/h x 0.5 hr = 0.5km or 500m.
Graph A: A horizontal line goes from (1, 0.5) to (2, 0.5). Another horizontal line goes form (2, 0.2) to (7, (0, 2). Graph B: A curve starts at (0, 0), curves up to (1, 1), and then curves down to (2, 0).
Which graph represents a density curve, and why?
graph A only, because the curve is above the horizontal axis, and the area under the curve from 2 to 7 is 1
graph B only, because the curve is above the horizontal axis, and the area under the curve is equal to 1.57
both graph A and graph B, because both curves are above the horizontal axis, and both areas are positive
neither graph A nor graph B, because, even though both curves are above the horizontal axis, neither graph has an area of 1
Pictures posted below
Answer: neither graph A nor graph B, because, even though both curves are above the horizontal axis, neither graph has an area of 1
Step-by-step explanation:
Areas under the graphs:
Graph A
[tex](1)(0.5)+(7-2)(0.2)=1.5\\\\[/tex]
Graph B
[tex]\frac{\pi}{2}(1^{2})=\frac{\pi}{2}[/tex]
As neither of these graphs have an area of 1, neither of them are density curves.
The statement - "neither graph A nor graph B, because, even though both curves are above the horizontal axis, neither graph has an area of 1" is true.
A few fundamental principles apply to density curves:
A density curve's area beneath it represents probability.A density curve's area under it equals one.Base x height in a uniform density curve equals one.The likelihood that x = a will never occur.The likelihood that x < a is the same as that of x ≤ a.Neither curve of Graph A nor of Graph B has the area under the curve summed up as 1, though the curve is above the horizontal axis.
Hence, because neither graph has an area of 1, even if both curves are above the horizontal axis, the statement "neither graph A nor graph B, because, even though both curves are above the horizontal axis, neither graph has an area of 1" is true.
Learn more about density curves here-
brainly.com/question/28001152
#SPJ10
express 2.603603603 . . . as a rational number
Answer:
[tex] \frac{289}{111} [/tex]
Step-by-step explanation:
[tex]2 + \frac{603}{1000 - 1} = 2 \frac{603}{999} = 2 \frac{67}{111} = \frac{289}{111} [/tex]
Given that a is rational and √2 is irrational and a is not equal to 2, show that. √2-1 is irrational
Answer:
Let us assume that √2 is a rational number.
So it can be expressed in the form p/q where p, q are co-prime integers and q≠0
√2 = p/q
Here p and q are coprime numbers and q ≠ 0
Step-by-step explanation:
√2 = p/q
On squaring both the sides we get,
=>2 = (p/q)2
=> 2q2 = p2……………………………..(1)
p2/2 = q2
So 2 divides p and p is a multiple of 2.
⇒ p = 2m
⇒ p² = 4m² ………………………………..(2)
From equations (1) and (2), we get,
2q² = 4m²
⇒ q² = 2m²
⇒ q² is a multiple of 2
⇒ q is a multiple of 2
Hence, p, q have a common factor 2. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number
√2 is an irrational number.
