Select all of the TRUE statements
A.
Dilations of a triangle are congruent to the original triangle.
B.
Dilations always increase the length of line segments.
C.
Dilations of a triangle are similar to the original triangle.
D.
Dilations of perpendicular lines remain perpendicular lines.
E.
Dilations increase the measure of angles.
F.
Dilations of an angle are congruent to the original angle.
Answers
The statements which are true include the following:
C. Dilations of a triangle are similar to the original triangle.
D. Dilations of perpendicular lines remain perpendicular lines.
F. Dilations of an angle are congruent to the original angle.
The types of transformation.In Geometry, there are different types of transformation and these include the following:
ReflectionRotationTranslationDilationWhat is dilation?Dilation simply refers to a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
In this context, we can reasonably infer and logically deduce that a dilation of perpendicular lines would always remain perpendicular lines because it takes each of the line to another perpendicular line.
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Related Questions
Enter values to write the function that matches the graph shown.
Answers
Answer:
\(k(x) = (x + 1) (4x + 16)\\\)
Step-by-step explanation:
The equation of a parabola given roots \(x_1\) and \(x_2\) is
\(y = a( x - x_1)(x - x_2)\)
where a is a constant
The x-intercepts of a parabola will be the roots of the quadratic equation to the parabola since k(x) = 0 at these points
The x-intercepts are (-1, 0) and (-4, 0)
Therefore the equation of the parabola is of the form
\(k(x) = a ( x - (-1) ) ( x - (-4) )\)
\(= a( x+ 1) (x + 4)\)
To find a, find a point (x, y) through which the parabola passes and plug this value into the above equation to solve for a
We see that the parabola passes through (-5, 16) and (0, 16). The latter point is also the y-intercept of the parabola
This means k(x) = 16 at x = 0
Plugging (0, 16) into the equation gives
\(k(x) = a(x + 1) ( x + 4)\)
\(a(x + 1) ( x+ 4) = k(x)\)
\(a(0 + 1) (0 + 4) = 16\)
\(a \cdot 1 \cdot 4 = 16\)
\(4a = 16\)
\(a = 16/4 = 4\)
Equation of the parabola is
\(k(x) = 4 (x + 1) (x + 4)\)
which can be rewritten as
Help, Help, Please
\( \sf find \: the \: value \: of \: \theta \: when \: \theta \: is \: acute\: angle\)
\( \sf \cos^{2}(\theta) - \sin^{2}(\theta) =2-5 \cos(\theta) \)
\(\text{note:explanation is a must}\)
Answers
Answer:
θ = \(\frac{\pi }{3}\) (60° )
Step-by-step explanation:
Using the identity
sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x
Given
cos²θ - sin²θ = 2 - 5cosθ
cos²θ - (1 - cos²θ) = 2 - 5cosθ
cos²θ - 1 + cos²θ = 2 - 5cosθ
2cos²θ - 1 = 2 - 5cosθ ( subtract 2 - 5cosθ from both sides )
2cos²θ + 5cosθ - 3 = 0 ← in standard form
(cosθ + 3)(2cosθ - 1) = 0 ← in factored form
Equate each factor to zero and solve for θ
cosθ + 3 = 0
cosθ = - 3 ← not possible as - 1 ≤ cosθ ≤ 1
2cosθ - 1 = 0
cosθ = \(\frac{1}{2}\) , so
θ = \(cos^{-1}\) (\(\frac{1}{2}\) ) = \(\frac{\pi }{3}\) ( or 60° )
Answer:
\( \huge \boxed{ \boxed{\blue{ { \theta = 60}^{ \circ} }}}\)
Step-by-step explanation:
to understand thisyou need to know about:trigonometryPEMDASlet's solve:\( \sf \: rewrite \: \sin ^{2} ( \theta) \: as \: 1 - \cos ^{2} ( \theta) : \\ \sf \implies \: \cos ^{2} ( \theta) - (1 - \cos ^{2} ( \theta)) = 2 - 5 \cos( \theta) \)\( \sf \: remove \: parentheses \: and \: change \: its \: sign : \\ \sf \implies \: \cos ^{2} ( \theta) - 1 + \cos ^{2} ( \theta)) = 2 - 5 \cos( \theta) \)\( \sf \: add : \\ \sf \implies \: 2\cos ^{2} ( \theta) - 1 = 2 - 5 \cos( \theta) \)\( \sf \: move \: left \: hand \: sides \: expression \: to \: right \: hand \: sides \: : \\ \sf \implies \: 2\cos ^{2} ( \theta) + 5 \cos( \theta) - 1 -2 = 0\)\( \sf \: rewrite \: 5\cos( \theta) \: as \: 6 \cos( \theta) - \cos( \theta) : \\ \sf \implies \: 2\cos ^{2} ( \theta) + 6 \cos( \theta) - \cos( \theta) - 3 = 0\)\( \sf \:factor \: out \: 2 \cos( \theta) \: and \: - 1 : \\ \sf \implies \: 2\cos ( \theta)( \cos( \theta) + 3 ) -1( \cos( \theta) + 3) = 0\)\( \sf \: group: \\ \sf \implies \: (2\cos( \theta) - 1) ( \cos( \theta) + 3 ) = 0\)\( \sf \: rewrite \: as \: two \: seperate \: equation: \\ \sf \implies \: \begin{cases}2\cos( \theta) - 1 = 0\\ \cos( \theta) + 3 = 0 \end{cases} \)\(\sf add \: 1 \: to \: the\: first \: equation \: and \: substract \: 3 \: from \: the \: second \: equation: \\ \sf \implies \: \begin{cases}2\cos( \theta) = 1\\ \cos( \theta) = - 3 \end{cases} \)\( \sf the \: second \: eqution \: is \: false \: \\ \sf because \: - 1 \leqslant \cos( \theta) \leqslant 1 \: \\ \sf but \: we \: can \: still \: work \: with \: the \: second \: equation\)
\( \sf substract \: both \: sides \: by \: 2 : \\ \implies\frac{ 2\cos( \theta) }{2} = \frac{1}{2} \\ \implies\cos( \theta) = \frac{1}{2} \\ \therefore \: \theta \: = {60}^{ \circ} \)in how many ways can 10 identical math books and 2 different english books be arranged on a shelf such that the english books are not next to each toher
Answers
In total, there are 660 ways to arrange the 10 identical math books and 2 different English books on the shelf such that the English books are not placed next to each other.
To calculate the total number of arrangements, we can consider the English books as distinct entities and treat them separately from the math books.
We have 12 books in total, including 10 identical math books and 2 different English books. Let's denote the English books as E1 and E2.
If the English books are placed together, we can treat them as a single entity. This reduces the problem to arranging 11 entities: the combined English books (E1E2) and the 10 math books. There are 11! (factorial) ways to arrange these entities.
However, within the combined English books (E1E2), there are 2! ways to arrange the individual English books. Therefore, we need to multiply the total number of arrangements by 2!.
Since the total number of arrangements with the English books together is 11! × 2!, we need to subtract the number of arrangements where the English books are placed next to each other from this total.
If the English books are next to each other, we can treat them as a single entity. This reduces the problem to arranging 11 entities: the combined English books (E1E2) and the 10 math books. There are 11! ways to arrange these entities.
Hence, the number of arrangements where the English books are next to each other is 11!.
Finally, we subtract the number of arrangements where the English books are next to each other from the total number of arrangements:
Total arrangements = 11! × 2! - 11!
Simplifying this expression, we get:
Total arrangements = 11! × (2 - 1) = 11! = 39,916,800
Therefore, there are 39,916,800 ways to arrange the books on the shelf such that the English books are not placed next to each other.
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Naomi bought stock in a company two years ago that was worth
x
x dollars. During the first year that she owned the stock, it increased by 23%. During the second year the value of the stock increased by 26%. Write an expression in terms of
x
x that represents the value of the stock after the two years have passed.
Answers
The expression that represents the value of the stock after two years have passed is 1.5498x
What is the expression that reperesnts the value of the stock after two years?
Percentage is the fraction of an amount expressed as a number out of hundred. The sign used to represent percentages is %.
The value of the stock after year 1 = worth of the stock when it was bought x (1 + percentage increase in year one)
1.23x
The value of the stock after year 2 = worth of the stock in year 1 x (1 + percentage increase in year two)
1.26 x 1.23x = 1.5498x
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Pleaseee help asap 20 points!!! : Which of the following is the expanded form of a number? Select all correct answers.
(A) 7·1000+8·100+3· 1/100
(B) 4·100+9·100+3· 1/10 +4· 1/10
(C) 71·10+4·1+6· 1/100 +5· 1/1000
(D) 5·1000+5·100+5·1+5·1/100
(E) 3·1000+8·1000+9·1/1000
(F) 9·1000+3·101+5· 1/10
Answers
(A) 7·1000+8·100+3· 1/100 is in expanded form.
(B) 4·100+9·100+3· 1/10 +4· 1/10 is in expanded form.
(C) 71·10+4·1+6· 1/100 +5· 1/1000 is in expanded form.
(D) 5·1000+5·100+5·1+5·1/100 is in expanded form.
(E) 3·1000+8·1000+9·1/1000 is in expanded form.
(F) 9·1000+3·101+5· 1/10 is not in expanded form because 3·101 is not a specific place value.
Therefore, the expanded form of a number is given by options A, B, C, D, and E.
What is the f/x function called?
Answers
The domain and scope of the identity function are the same. Equation for the identity function is f(x) = x, or y = x.
What is function?An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable). A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.
identity function are the same.
Equation for the identity function is
f(x) = x, or y = x.
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Question 16 of 40
Which equation shows x2 + 6x - 6 = 0 rewritten by completing the square?
A. (x+3)2 = 15
B. (x + 3)2 = 9
C. (x+3)2 = 6
O D. (X+3)2 = 54
SUBMIT
Answers
Answer: a (x+3)^2=15
I need help I totally forgot this.
Answers
Answer:
you did not show the full question mate
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Calculate the distance d using the distance formula
d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)
with (x₁, y₁ ) = (- 2, - 4) and (x₂, y₂ ) = (6, 11)
d = \(\sqrt{(6+2)^2+(11+4)^2}\)
= \(\sqrt{8^2+15^2}\)
= \(\sqrt{64+225}\)
= \(\sqrt{289}\)
= 17 → A
PLS THIS IS TIMED! I WILL GIVE BRAINLIEST!!!!
Answers
Answer:
the answer is y= 5(0.25)^x or C
Step-by-step explanation:
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
f(x) = 4/x
g(x) = 4/x
Answers
Answer:
Hello,
Step-by-step explanation:
\(f(x)=\dfrac{4}{x} \\\\g(x)=\dfrac{4}{x} \\\\\\(gof)(x)=f(g(x))=f(\dfrac{4}{x} )=\dfrac{4}{\dfrac{4}{x} } =\dfrac{4*x}{4} =x\\\\\\(fog)(x)=g(f(x))=g(\dfrac{4}{x} )=\dfrac{4}{\dfrac{4}{x} } =\dfrac{4*x}{4} =x\\\)
At a sandwich shop, they charge $2.75 for the basic sandwich and then $0.45 per ounce for the toppings. If
Willa paid for her sandwich with a $5 bill, how many ounces of toppings could she have ordered?
Answers
The reasoning is you first do 5-2.75 because you must subtract the basic sandwich from the total cost. Then, you must divided 2.25/0.45 because that is the cost of the remaining toppings.
Answer: 3 toppings
Step-by-step explanation: If 2 topping equals $1 then its would come out to $3.75.$0 .75+$0.45= $1.20 the.n $3.75+ $1.20 = $4.95. That comes up to 3 toppings
Simplify: –3(y 2)2 – 5 6y What is the simplified product in standard form? y2 y.
Answers
Answer:
Simplify: –3(y + 2)2 – 5 + 6y
What is the simplified product in standard form?
-3
y2 +
-6
y +
-17
Step-by-step explanation:
The simplification of the given expression will be -17.
What is simplification?
The process of reducing the complex mathematical expressions into the simplest form is called simplification.
Given expression will be simplified as:-
= -3 ( y + 2 ) 2 - 5 + 6y
= ( -3y - 6 ) 2 - 5 + 6y
= ( -6y - 12 -5 + 6y )
= ( -17 )
Hence the simplification of the given expression will be -17.
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I've tried geometric, alternating, and lagrange error bound i need help thank you
Answers
The Lagrange error bound is a method for estimating the error in approximating a function using a polynomial
Let's say you have a function f(x) and you want to approximate it using a polynomial of degree n, denoted by Pn(x). The Lagrange error bound states that the absolute error between f(x) and Pn(x) is bounded by:
|f(x) - Pn(x)| ≤ M/[(n+1)!] |x - c|^(n+1)
where M is a bound on the (n+1)th derivative of f(x) on an interval containing x and c is some constant value in that interval (typically the midpoint of the interval). Note that the bound depends on the choice of x and c.
In practice, the Lagrange error bound can be used to estimate the error in polynomial approximations. You can choose a value of x and a degree n for the polynomial, then use the bound to find an upper bound on the absolute error. If the error is too large, you may need to increase the degree of the polynomial or choose a different value of x.
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The given question is complete, the complete question is:
What is Lagrange error bound ?
Rewrite the equation in Ax+BY =C form please and thank you
Answers
Answer:
3x - y = 20
a = 3, b = -1, and c = 20
Step-by-step explanation:
y + 2 = 3(x - 6) => y + 2 = 3x - 18 => 3x - y = 20
Expand the following:
c) 4(2x +1)
Answers
Answer:
= 4(2x +1)
= 4× 2x + 4×1
= 8x +4
Answer:
4*(2*x+1)
Step-by-step explanation:
Simplified we would write it as,
8x + 4, but we want to expand, so we would write out each operation being performed.
HELP!
Stephen put two angles together to make a complementary angle. Angle A was 52.4°. What is the measure of Angle B?
Answers
Answer:
the answer is 48
Step-by-step explanation:
a complementary angle is when their angles add up to 90 degrees
can i get the crown?
a) 10 - 3(2a + 3) + 4(a - 6)
Simplify
Answers
Answer:
-2a - 23
Step-by-step explanation:
10 - 3(2a+3) + 4(a-6)
10-6a-9 + 4(a-6)
10-6a-9 + 4a - 24
-23-6a+4a
-23-2a
Therefore, -2a - 23 is the answer
Help pl, I really need the anwer
Complete the recurive formula of the geometric equence 56, -28, 14, -7,. D(1) = ______
d(n) = d(n - 1) * ________
Answers
The recursive formula for the sequence is aₙ = (-1/2) * aₙ₋₁
A geometric series is a set of numbers where each term increases or decreases by a predetermined ratio.
The common formula for geometric series is
Tₙ = a₁ rⁿ⁻¹
The nth term of the sequence can be found using the explicit formula shown above.
When the (n-1) th term is given, the nth term is found using the recursive formula.
The pattern in geometry is,
56, -28, 14, -7,.................
The sequence's initial term is 56.
By comparing the second term to the first term, the common ratio may be calculated.
r = -28/56 = -1/2
The recursive formula looks like this:
aₙ = r * aₙ₋₁
aₙ = (-1/2) * aₙ₋₁
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Whats the distance between (-1,-2) and (3,4)
Answers
Answer:
the answer is 7,21
Step-by-step explanation:
Distance formula is d=√(x1-x2)²+(y1-y2)²√(-1-3)²+(-2-4)²√(-4)²+(-6)²√16+36√527.21The answer is 7,21
Find the common ratio of the geometric sequence
17, -34, -68, ...
Answers
The common ratio of the geometric sequence will be negative 2.
Given that:
Geometric sequence: 17, -34, -68, .....
A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.
Let a₁ be the first term and r be the common ratio. Then the nth term of the geometric sequence is given as,
aₙ = a₁ · (r)ⁿ⁻¹
The common ratio of the geometric sequence is calculated as,
r = (-34) / (17)
r = - 2
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Brigid is picking strawberries at the Pick-Your-Own Farm. Her goal is to pick 5 bushels of strawberries. She has already picked 1
1
2
bushels, and she picks at a rate of
5
8
bushel per hour. The scenario is represented as
5
8
h + 1
1
2
= 5, where h is the number of hours she picks. How many more hours will it take Brigid to fill 5 bushels of strawberries?
2 and StartFraction 3 Over 16 EndFraction hours
2 and StartFraction 3 Over 16 EndFraction hours
5 and three-fifths hours
10 and two-fifths hours
Answers
Answer:
We can start by isolating the variable "h".
5 8 h + 1 1 2 = 5
Subtracting 11/2 from both sides:
5 8 h = 5 - 1 1 2
Simplifying:
5 8 h = 8 1 2
Dividing both sides by 5/8:
h = 8 1 2 ÷ 5 8
Converting the mixed number to an improper fraction:
h = (8 x 8 + 1) ÷ 5 8
h = 65/8
Now, we can convert this fraction to a mixed number:
h = 8 1/8
Brigid has already picked for 8 1/8 hours, so the amount of time needed to pick the remaining strawberries is:
5 - (1 1/2 + 5/8 x 8) = 5 - (3 5/8) = 1 3/8
Therefore, Brigid still needs to pick for 1 3/8 hours to fill 5 bushels of strawberries. The answer is 1 and 3/8 hours or 2 and 3/16 hours (if simplified).
Step-by-step explanation:
one of the numbers in the diagram is chosen at random find the probability that the number is in set A' giving your answer as a decimal
Answers
Answer:
Step-by-step explanation:
3.2
If this is wrong, Im very very sorry
you play a game 5 times. the results of the plays are probabilistically independent, and on each play, your probability of winning, p(w), is 0.4, and your probability of losing, p(l), is 0.6. what is the probability of the sequence w, w, l, l, w?
Answers
The probability of the sequence W, W, L, L, W is (0.4)³ + (0.6)².
Given data;
Five games are played. Each play has a probability of winning, P(W), of 0.4, and a probability of losing, P(L), of 0.6. The results of the plays are probabilistically independent.
To get the probability of the sequence W, W, L, L, W.
Now,
As the results are probabilistically independent,
The probability of the sequence is;
→ [(P(W)]³ + [(P(L)]²
→ (0.4)³ + (0.6)²
Hence, the probability of the sequence W, W, L, L, W is (0.4)³ + (0.6)².
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Finding the surface area
Answers
Answer: so you do length times width times height and then you divide by two
Step-by-step explanation:
What is this answer please
Answers
Answer:
A. The quotient of 2 and a number
Step-by-step explanation:
2n would be 2 multiplied by n
It can also be written as twice a number or double a number or the product of two and a number.
The quotient of 2 and a number would be 2/n therefore the answer is the quotient of 2 and a number
Answer:
A. The quotient of 2 and a number
Step-by-step explanation:
2n would be multiplied not divided.
The zoo charges an entry fee of $12.50 plus $5.00 per animal show ticket. Let t represent the number of animal show tickets purchased and c represent the total cost of the entry fee and animal show tickets. Write an equation to calculate the total cost for a person who pays the entry fee and purchases t tickets.
Answers
Answer:
c=5t+12.50, it cost 17.50 for one person
Step-by-step explanation:
5$ per person
and 12.50 added
c= total cost
Question 5 of 100. Marty (62), single, has 2022 taxable income of $510,000. What is Marty's marginal tax rate?
35%
37%
38.5%
39.6%
Answers
Marty's taxable income of $510,000 falls within the last tax bracket, his marginal tax rate would be 37%.
To determine Marty's marginal tax rate, we need to refer to the tax brackets for the given year. However, as my knowledge is based on information up until September 2021, I can provide you with the tax brackets for that year. Please note that tax laws may change, so it is always best to consult the current tax regulations or a tax professional for accurate information.
For the 2021 tax year, the marginal tax rates for individuals are as follows:
10% on taxable income up to $9,950
12% on taxable income between $9,951 and $40,525
22% on taxable income between $40,526 and $86,375
24% on taxable income between $86,376 and $164,925
32% on taxable income between $164,926 and $209,425
35% on taxable income between $209,426 and $523,600
37% on taxable income over $523,600
Since Marty's taxable income of $510,000 falls within the last tax bracket, his marginal tax rate would be 37%. However, please note that tax rates can vary based on changes in tax laws and regulations, so it's essential to consult the current tax laws or a tax professional for the most accurate information.
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HELP ASAPP!!!! :((
A. 225
B.275
Answers
harry has $2.25 in nickels, dimes, and quarters. if he had twice as many nickels, half as many dimes, and the same number of quarters, he would have $2.50. if he has 27 coins altogether, then how many of each does he have?
Answers
Answer:
Step-by-step explanation:
Then you will subtract:
The answer is $25:00
11 dividend by 100,100