Transformation involves changing the position and size of a shape.
The true statements are:
∠m≅∠m'Δlmn≅Δl'm'n'The coordinates of n" are .N''(3,-1.5)The complete question is as follows:-
The composition do,0.75(x,y) ∘ do,2(x,y) is applied to △lmn to create △l''m''n''. which statements must be true regarding the two triangles? check all that apply. ∠m ≅ ∠m'' △lmn ~ △l''m''n'' △lmn ≅ △l''m''n'' the coordinates of vertex l'' are (-3, 1.5). the coordinates of vertex n'' are (3, -1.5). the coordinates of vertex m'' are (1.5, -1.5).
What is translation?The process of changing the location of the image on the coordinate system will be known as the translation.
The coordinates of the triangle are:
L =(-1,2)
M = (-1,-1)
N = ( 2,-1)
The transformation rule is given as:
do 0.75 (x,y) 2 (x,y)
The transformation rule is a dilation by a factor of 0.75, and then a factor of 2.
Uniform dilation changes the size of a shape, but the angles remain unchanged. This means that:
∠l≅∠l''
∠m≅∠m''
∠n≅∠n''
Δlmn⇒Δl'm'n'
The above highlights mean that:
The angles of both triangles are congruent
The triangles are similar
Next, we apply the rule on the coordinates of the triangle
L'' = 0.75 x 2 x (-1,2)
L'' = ( -1.5,3)
M'' = 0.75 x 2 x (-1,-1)
M'' = ( -1.5 , -1.5)
N'' = 0.75 x 2 x (2,-1)
N'' = (3 , -1.5)
Hence, the true statements are: The coordinates of n" are.
∠m≅∠m'Δlmn≅Δl'm'n'The coordinates of n" are . N''(3,-1.5)Read more about transformations at:
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What are the solutions of the equation (x 2)2 – 2(x 2) – 15 = 0? use u substitution to solve.
The solution of the equation is x=3 or x=-5.
Given that the equation is (x+2)²-2(x-+2)-15=0 and use u substitution method to solve.
Let's assume that the (x+2)=u.
The given equation is rewritten as u²-2u-15=0.
Factorize the quadratic equation by adding or subtracting two number that gives the sum of -2u and product 15u² as
u²-5u+3u-15=0
u(u-5)+3(u-5)=0
Taking out (u-5) as common and get
(u-5)(u+3)=0
Compare each equation with 0 and get
u-5=0 or u+3=0
u=5 or u=-3
Performing back substitution by substituting the values of u in x+2
when u=5 then x is
x+2=5
x=3
And when u=-3 then x is
x+2=-3
x=-5
Hence, the solutions of the (x+2)²-2(x-+2)-15=0 is x=3 and x=-5.
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Answer:X=-5 and X=3
Step-by-step explanation:
a−(−3.75)=6.11
What is a?
Answer:
a = 2.36
Step-by-step explanation:
a-(-3.75)=6.11
The negative 3.75 is being subtracted from the 'a'. A negative number being subtracted from another number makes it positive. So, 3.75 is actually being added to 'a' which is equal to 6.11
I re-wrote the question as:
a + 3.75 = 6.11
Subtract 3.75 from both sides to leave 'a' by itself
a + 3.75 = 6.11
-3.75 -3.75
a = 2.36
Find the surface area of a hexagonal prism if the length of each side of the hexagonal base is 4 cm and the height is 7 cm.
The surface area of a hexagonal prism willl be 251.13844 cm².
What is the surface area?The total land area of all the faces of a three-dimensional object is its surface area. When we wish to wrap something in real life, we employ the notion of surface areas of distinct things.
A=6ah+3√3a²
A=6×4×7+3√3×4²
A≈251.13844
Hence the surface area of a hexagonal prism willl be 251.13844 cm².
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A local pizza shop has a membership program for frequent buyers. The membership costs $20 per month and members get a discounted price of $1.25 per slice of pizza. Chee purchased a membership to this pizza shop. How much would Chee have to pay the pizza shop if she bought 12 slices of pizza this month? What would be the monthly cost for x slices of pizza?
Monthly cost with 12 slices:
Monthly cost with x slices
need answer quickly
The Chee has to pay $35 to the pizza shop if she bought 12 slices of pizza this month and for x slices, the cost would be ($1.25x + 20)
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
The membership costs $20 per month and members get a discounted price of $1.25 per slice of pizza.
Cost for 12 slices = 12×1.25 = $15
Total cost = 20 + 15 = $35 (for this month if she bought 12 slices of pizza)
The monthly cost for x slices of pizza:
= 1.25x + 20
x is the number of slices
Thus, the Chee has to pay $35 to the pizza shop if she bought 12 slices of pizza this month and for x slices, the cost would be ($1.25x + 20)
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Two-Variable Systems of Inequalities
On a piece of paper, graph this system of inequalities. Then determine which
region contains the solution to the system.
ysx-2
y24x-4
O A. Region D
B. Region B
C. Region C
D. Region A
10
6
6
A 4
10 B 84
D
999
B
C
XA¹
10
Inequalities help us to compare two unequal expressions. The correct option is B.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
The solution to two systems of inequalities in the region where the area of the two inequalities overlaps. As it can be observed in this case that the overlap area is B.
Hence, the correct option is B.
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A 210-N mass is suspended from a horizontal beam by two cables that make angles of 29 degrees and 53 degrees with the beam. Find, using vectors, the tension in the cables.
The tension in both cables are calculated as; T₁ = 127.63 N and T₂ = 185.48 N
Resolving forces in the y direction gives us;
T₁ sin 29° + T₂ sin 53° = 210 ------(eq 1)
Resolving forces in the horizontal direction gives;
T₁ cos 29° = T₂ cos 53° ----(eq 2)
T₁ = T₂ cos 53°/cos 29°
Thus;
(T₂ cos 53°/cos 29°)sin 29° + T₂ sin 53° = 210
0.3336T₂ + 0.7986T₂ = 210
T₂ = 210/1.1322
T₂ = 185.48 N
Thus;
T₁ = 185.48 cos 53°/cos 29°
T₁ = 127.63 N
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The angle of depression from the hot-air
balloon to the car is 32°
How high is the hot-air balloon flying?
Give your answer to 2 s.f.
6600 feet
Not drawn accurately
Answer:
3497.47 feet
I think it's the answer because when you look where I've drawn...that's where the angle of depression is and 6600 is the hypotenuse, so you use the sine method where you have opposite over hypotenuse
[tex] \sin(32 = opposite \6600) [/tex]
and you'll get your answer as 3497.47
Si en un autobús hay disponibles solo tres asientos y siete personas están de pie ¿De cuántas maneras distintas podrían ocupar esos asientos?
Usando la fórmula de combinación, se encuentra que hay 35 manerias distintas de ocupar esos asientos.
El orden en que se sientan las personas no es importante, por lo que se utiliza la fórmula de combinación para resolver este problema.
¿Cuál es la fórmula de combinación?[tex]C_{n,x}[/tex] es el número de combinaciones diferentes de x objetos de un conjunto de n elementos, dado por:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
3 personas son selecionadas de un conjunto de 7, por eso, el número de maneras es dado por:
[tex]C_{7,3} = \frac{7!}{3!4!} = 35[/tex]
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Which equation justifies why 93 - ?
=
(0³) 1_9(²+³)_9
93
(³)
93
³_9(²+³)=9
(0³) -
93
93
=9=9
_g(¹-³)_9
=9
=9
The equation that justifies [tex]9^{1/3}=\sqrt[3]{9}[/tex] is [tex](9^{1/3}) ^{3} = 9^{3/3} = 9[/tex]
How to find equation that justifies another?The expression given is [tex]9^{1/3}=\sqrt[3]{9}[/tex].
The equation that justifies [tex]9^{1/3}=\sqrt[3]{9}[/tex] is as follows:
Therefore, using indices law,
[tex]a^{x/y} =\sqrt[y]{a^{x} }[/tex]
Hence,
[tex]9^{1/3}=\sqrt[3]{9}[/tex]
Therefore, the equation that shows it is correct is as follows;
[tex](9^{1/3}) ^{3} = 9^{3/3} = 9[/tex]
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Preform the indicated operation.
(2x+y)(3 x² + y)
Answer:
[tex]6x^3+3x^2y+2xy+y^2[/tex]
Step-by-step explanations:
[tex](2x+y)(3x^2+y)\\2x*3x^2+2xy+3x^2y+y*y - Distribute\\6x^3+3x^2y+2xy+y^2 - Simplify[/tex]
Answer:
6x^3 + 2xy + 3x^ 2y + y^2
Step-by-step explanation:
Apply the distributive property of multiplication. First multiply (3x^2 + y) by 2, obtaining 6x^3 + 2xy, and then multiply (3x^2 + y) by y, obtaining
3x^2y + y^2. Finally, combine like terms (if any) in these two results:
6x^3 + 2xy + 3x^ 2y + y^2
Hello hello :))) please help me with this problem
what are simultaneous equations
Answer:
Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. Each of these equations on their own could have infinite possible solutions.
Peter's father told Peter to buy four-tenths of a pound of chili powder. Each package is marked with its weight. What package should Peter buy?
Peter should buy 0.4 pound weight package
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct," "pct," and occasionally "pc" are also used, the percent sign, " percent ", is frequently used to signify it. A % is a number without dimensions and without a measurement system.
Given Peter's father told Peter to buy four-tenths of a pound of chili powder and Each package is marked with its weight.
We have to find which weight package should Peter buy
The four-tenths of a pound will be 40 % of one pound which is 0.4 pound. So peter should buy 0.4 pound weight package.
Hence Peter should buy 0.4 pound weight package
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a sunflower has increased in height from 72.4cm to 86.2 cm. what is the percentage increase?
Answer:
initial hieght = 72.4 cm
final hieght = 86.2 cm
change in hieght = 9.8 cm
percentage increase = (9.8 ÷ 72.4 ) * 100 = 13.59 %
Anne is visiting a friend who lives 18.5 km away. She travels 10 km by train, 1.5 km by bus, and walks the rest of the way. If she walks at a rate of 3.5 km per hour, for how long will Anne walk
Anne will walk a distance of 7 km, and she takes 2 hours to walk that distance.
For how long will Anne walk?
The total distance is 18.5 km.
She travels 10km by train and 1.5km by bus, for a total of 11.5km.
The distance that she walks is given by:
18.5km - 11.5km = 7km
So she walks for a distance of 7 km, at a speed of 3.5km per hour.
Remember the relation:
distance = time*speed
That can be rewritten to:
time = distance/speed.
Then the time that she walks is given by:
T = (7 km)/(3.5 km/hour) = 2 hours
She walks for 2 hours.
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Draw a graph of y=3x-2. Using a scale of 2cm to 5units on both axes for values from x -2 to +2
What is the x-intercept
What is the y- intercept
Find the value of x when y= 5
Find the value of y when x= 0.5
pls pls ASAP
Function: y = 3x - 2
To find x-intercept, set [y = 0]:
[tex]\rightarrow \sf 3x - 2 = 0[/tex]
[tex]\rightarrow \sf 3x = 2[/tex]
[tex]\rightarrow \sf x = \dfrac{2}{3}[/tex]
The x-intercept: (2/3, 0)
To find y-intercept, set [x = 0]
[tex]\rightarrow \sf y = 3(0) - 2[/tex]
[tex]\rightarrow \sf y = - 2[/tex]
The y-intercept: (0, -2)
When [y = 5], x is:
[tex]\rightarrow \sf 3x - 2 = 5[/tex]
[tex]\rightarrow \sf 3x = 5 + 2[/tex]
[tex]\rightarrow \sf 3x = 7[/tex]
[tex]\rightarrow \sf x = \dfrac{7}{3}[/tex]
[tex]\rightarrow \sf x = 2 \dfrac{1}{3}[/tex]
Value of x is 2.33...
When [x = 0.5], y is
[tex]\rightarrow \sf y =3(0.5) - 2[/tex]
[tex]\rightarrow \sf y =-0.5[/tex]
Value of y is -0.5
Graph shown:
Factorize
ху
+ 3x +3y
+ 18
Answer:
(x+6)(y+3)
Step-by-step explanation:
xy + 3x + 6y + 18x(y + 3) + 6(y+3)(x+6)(y+3)On the day of his 18th birthday, David decided to start saving money regularly.
a) Starting on that day, he could save £ 60 on the same date every month.
How much would he have saved by the day before his 60th birthday?
b) David explored another option.
Starting on his 18th birthday, he could save £ 100 on the same date every year.
If he saved in this way, how old would he be by the time he saved £ 2000?
a) The person will save $15,120 by the day before his 60th birthday. b) David would have had £2000 when he is 37 years old.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
a) Let x be a number of months.
Now, we will find a number of years between 60 and 18 years.
There will be 42 years from 18th birthday to 60th birthday.
Now, we will convert 42 years into months.
42 × 12 = 504
In order to find the total amount saved in 504 months, we will substitute in expression:
30x = 30(504) = 15120
Hence, the person will save $15,120 by the day before his 60th birthday.
b) David starts saving £100 annually from his 18th birthday
We would save £2000 after
(2000/100) years = 20 years
Since his 18th birthday is the first of the 20 years and so he will save £950 for the next 19 years, which is
18 + 19 = 37 years old
Hence, David would have had £2000 when he is 37 years old.
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If a hotel decreases the price of its rooms from $80 to $40. As a result, the total quantity demanded of its service increased from 2000 to 4000. Which type of price elasticity of demand does the hotel room have?
a.
Elastic
b.
Inelastic
c.
Perfectly inelastic
d.
Unitary
Help me O people!
Please!
Answer:
the answer is L
Step-by-step explanation:
that's just how u round
128 (4 + 2) = (128 ÷ 4) + 2
A. True
B. False
Answer:
B. False
Step-by-step explanation:
Just like last time, solve it first to check.
128(4+2)=(128/4)+2
Remember PEMDAS, parenthesis first.
128(6)=(32)+2
Now multiply the left side and add the right side.
128*6=768. The star sign is just another way to write a multiplication sign.
32+2=34
768≠34
This is a false statement. 768 does not equal 34.
Hope this helps!
If not, I am sorry.
make a 2 column proof
please make it simple like JK is parallel to NM(given)
i will also give brainliest
Answer:
Given: L is the midpoint of [tex]\overline{JM}[/tex] (given)
[tex]\overline{JL} =\overline{LM}[/tex] (definition of a midpoint)
Given: [tex]\overline{JK} \parallel \overline{NM}[/tex] (given)
[tex]\angle KJL \cong \angle NML[/tex] (alternate interior angles theorem)
[tex]\angle JKL \cong \angle MNL[/tex] (alternate interior angles theorem)
[tex]\triangle JKL \cong \triangle MNL[/tex] (SAA postulate)
(I have also created it in table form and attached a screenshot)
Which of the following rational functions is graphed below?
Answer:
D
Step-by-step explanation:
I looked at the vertical asymptotes. -1 and 2. from the knowledge I have the answer with x=-1, 2 is D.
Ali had 3 times as many marbles as cho does. After cho gives 4 marbles to Ali, Ali has 18 more marbles than cho does. How many more marbles does cho have in the beginning
a. 5
b. 9
c. 10
d. 15
Answer:
d. 15
Step-by-step explanation:
Let A and C be the initial number of marbles Ali and Cho have, respectively.
We are told that:
A = 3C [Ali had 3 times as many marbles as cho does]
We then discover that
C-4 = A-18 [After cho gives 4 marbles to Ali, Ali has 18 more marbles than cho does]
How many more marbles does cho have in the beginning?
We have 2 equations and 2 unknowns (A and C). That means we can likely rearrange one of the equations and isolate one unknown on the left, and then use that in the second equation.
The first equation already has one of the unknowns isolated (A) so I'll use that in equation 2.
Eq. 1: A = 3C
Eq. 2: C-4 = A-18
Use the definition of A from Eq. 1 (=3C) to replace A in Eq. 2:
Eq. 2: C-4 = A-18
C-4 = (3C)-18 [Replace A with 3C, as promised in E1q. 1]
-2C = -14
C=7
If C = 7, then from Eq. 1, A = 21
In the beginning, Ali has 21 marbles and Cho has 7.
Cho has 15 more marbles than Ali in the beginning.
a. 5
b. 9
c. 10
d. 15
On a coordinate plane, solid circles appear at the following points: (negative 2, negative 5), (negative 1, 3), (1, negative 2), (3, 0), (4, negative 2), (4, 4).
Which explains why the graph is not a function?
Find the value of X in the given
right triangle.
10
x= [?]°
Enter your answer as a decimal rounded to the
nearest tenth.
Expand . ( 3x –2 ) 2 please help me with this.
Answer:
6x-4
Step-by-step explanation:
3x•2= 6x
-2•2=-4
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{9x}^2\textsf{ - 12x + 4}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{(3x - 2)}^2[/tex]
Find: [tex]\textsf{Simplify the expression}[/tex]
Solution: It looks like 2 is at the end of the parenthesis where the power would be instead of distributing the number. If so the following steps would be followed.
Expand
[tex]\textsf{(3x - 2)}^2[/tex][tex]\textsf{(3x - 2)(3x - 2)}[/tex][tex]\textsf{(3x * 3x) + (3x * (-2)) + (3x * (-2)) + (-2 * (-2))}[/tex]Simplify
[tex]\textsf{9x}^2\textsf{ - 6x - 6x + 4}[/tex][tex]\textsf{9x}^2\textsf{ - 12x + 4}[/tex]Therefore, after following the provided information we are able to determine that the expanded form would be 9x^2 - 12x + 4.
Write logb(x/y) as two logs
Answer:
[tex] log_{b}(x) - log_{b}(y) [/tex]
quadrilateral ABCD is similar to quadrilateral EFGH find the measure of side EF round your answer to the nearest tenth if necessary
Answer:
EF = 2.9
Step-by-step explanation:
The geometric figures are similar so we can use the similarity ratio to calculate the length of EF:
GF/ CB = EF/AB
5/29 = EF/17 cross multiply expressions
29EF = 85 divide both sides by 29
EF = 2.9 approximately
Part of the proceeds from a garage sale was $540 worth of $5 and $20 bills If there were 3 more bills $5 bills than $20 bills, find the number of each denomination.
An equation is formed when two equal expressions. There are 21 $20 bills and 24 $5 bills.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the number of $5 bills be x, while the number of $20 bills be y.
Given there were 3 more $5 bills than $20 bills. Therefore, this can be represented as
x = y + 3
Also, The total worth of the dominations is $540. Therefore, we can write,
5x + 20y = 540
Substitute the value of x form the first equation,
5x + 20y = 540
5(y+3) + 20y = 540
5y + 15 + 20y = 540
25y = 525
y = 21
Substitute the value of y in the first equation,
x = 21 + 3
x = 24
Hence, there are 21 $20 bills, and 24 $5 bills.
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