Answer:
1) [tex]T_{(a, \, b)}[/tex] = f(x - a) + b
Coordinate change
(x, y) → (x + a, y + b)
2) RFy(x, y) = f(-x)
Coordinate change
(x, y) → (-x, y)
3) RFx(x, y) = -f(x)
Coordinate change
(x, y) → (-y, x)
4) RCCW90(x, y) = f⁻¹(-x)
Coordinate change
(x, y) → (-y, x)
5) RCCW180(x, y) = -(f(-x))
Coordinate change
(x, y) → (-x, -y)
6) A 270 degrees counterclockwise rotation gives;
RCCW270(x, y) = -(f⁻¹(x))
Coordinate change
(x, y) → (y, -x)
Step-by-step explanation:
1) Horizontal translation a units right = f(x - a)
The vertical translation b units up = f(x) + b
Therefore, we get; [tex]T_{(a, \, b)}[/tex] = f(x - a) + b
The coordinate change
(x, y) → (x + a, y + b)
2) A reflection across the y-axis = RFy(x, y) = f(-x)
The coordinate change
(x, y) → (-x, y)
3) A reflection across the x-axis gives RFx(x, y) → (x, -y)
Therefore, in function notation, we get;
RFx(x, y) = -f(x)
4) A 90 degrees rotation counterclockwise, we get RotCCW90(x, y) → (-y, x)
In function notation RotCCW90(x, y) = INVf(-x) = f⁻¹(-x)
5) A 180 degrees counterclockwise rotation about the origin gives;
(x, y) → (-x, -y)
Therefore, we get;
In function notation RotCCW180(x, y) = -(f(-x))
6) A 270 degrees counterclockwise rotation gives RotCCW270(x, y) → (y, -x)
In function notation RotCCW270(x, y) = -(f⁻¹(x))
Work out the height of this triangle with base, b = 8mm and
area, A = 218.8mm?,
Answer:
54.7 mm
Step-by-step explanation:
use the formula area= 1/2 base time height
A=1/2bh
Answer:
54.7mm
Step-by-step explanation:
Area=1/2b×h
218.8=0.5×8×h
218.8=4h
h=218.8÷4
h=54.7
what single transformation maps triangle ABC onto A’B’C?
Answer:
the answer is rotation hope it helps ahhaha
Please help guys I’m really struggling
Answer: y = -4x - 4
Step-by-step explanation:
Point slope form: y - y1 = m(x - x1)
Plug in y1 and x1, and m. M is the slope, x1 and y1 are the values for a coordinate. You don't need to plug anything in for y or x, just y1 and x1.
First, find the slope. To find the slope, use this "formula" : [tex]slope=\frac{rise}{run} =\frac{y1-y2}{x2-x1}[/tex]
Find two coordinate points. Let's use (-2,4) and (0,-4). Based on this, we know that y1 is 4, y2 is -4, x1 is -2, and x2 is 0. Plug these into the formula:
[tex]\frac{4--4}{-2-0} =\frac{4+4}{-2} =\frac{8}{-2}=-4[/tex]
Then, pick any point to plug into the equation. Let's use (0,-4)
Finally, plug everything into the equation:
y - - 4 = -4(x - 0)
y + 4 = -4x
y = -4x - 4
Answer:
[tex]y - 4 = - 4(x + 2)[/tex]
Step-by-step explanation:
Point Slope Form is a algebraic formula when we know a pair of points and it
slope.
It can be represented by
[tex]y - y_{1} = m(x + x _{1})[/tex]
where m is the slope and x 1 and y 1 are the points we know.
The coordinates we know are (-2,4) so we just plug it in.
We also know the slope of the line is rise/run. Look at point (-2,4). The next consecutive point before that is x intercept (-1,0). Let use the slope formula to find the slope
[tex] \frac{0 - 4}{ - 1 - ( - 2)} = \frac{ - 4}{1} = - 4[/tex]
So the slope or m is -4. Plug this in and the coordinates into point slope formula.
[tex]y - 4 = - 4(x - ( - 2)[/tex]
[tex]y - 4 = - 4(x + 2)[/tex]
That the answer.
Una recta pasa por los puntos A(-40) y B(2,-3).calcular su área
Answer:
Supongo que la pregunta completa es:
"Una recta pasa por los puntos A(-4, 0) y B(2, -3)"
Luego dice "calcular su área", pero una recta es un elemento unidimensional (los cuales no tienen área, el área es un concepto bidimensional).
Por lo que el área de esta recta no está definida.
Ignorando esto, podemos encontrar la ecuación que define a nuestra recta.
Sabemos que una recta se escribe como:
y = a*x + b
donde a es la pendiente y b es la ordenada al origen.
Sabemos que para una recta que pasa por los puntos (x₁, y₁) y (x₂, y₂), la pendiente será:
a = (y₂ - y₁)/(x₂ - x₁)
Entonces, para nuestra recta que pasa por los puntos (-4, 0) y (2, - 3) la pendiente será:
a = (-3 - 0)/(2 - (-4) )
a = -3/6 = -1/2
Entonces nuestra línea es algo como:
y = (-1/2)*x + b
para encontrar el valor de b, usamos el hecho de que esta línea pasa por el punto (2, -3)
esto significa que cuando x = 2, tenemos que tener y = -3
reemplazando esos dos valores obtenemos
-3 = (-1/2)*2 + b
-3 = -1 + b
-3 + 1 = b
-2 = b
La ecuación que define a esta recta es:
y = -(1/2)*x - 2
Nuevamente, el área de esta recta no está definida, por lo que no podemos calcular el área de esta recta.
SOMEONE PLEASE HELP ME WITH THIS PROBLEM!!!!
9514 1404 393
Answer:
20.0 square units
Step-by-step explanation:
There are many ways the area can be computed here. Perhaps the intended one is to find the length of the third side, then use the usual triangle area formula.
b = √(c² -a²) = √(9² -7²) = √32 ≈ 5.7
Then the area is ...
A = 1/2bh = 1/2(5.7)(7) ≈ 20.0
The area is approximately 20.0 square units.
_____
Additional comment
It is highly unusual to make use of rounded intermediate results. That is a guarantee that the final answer will have more error than necessary. Ordinarily, you would never do that.
An alternate solution might be ...
angle = arccos(7/9) ≈ 38.9°
area = 1/2(7)(9)sin(38.9°) ≈ 19.8 . . . . square units (assuming the sine value is not rounded to 0.6)
Find the measures of angles x,y and z in the figure. Show your work!!
WILL GIVE BRAINLIEST!!!
Answer:
x = 106°
y = 106°
z = 106°
Step-by-step explanation:
Find x:
Angle on straight line = 180°
[tex]74+x=180[/tex]
[tex]x=180-74[/tex]
x = 106°
Find y:
Angle y and x are corresponding angle which means x and y will be same
y = 106°
Find z:
Angle y and z are equal because, opposite angles are always equal.
z = 106°
hope this helps......
Answer:
x = 106°
y = 106°
z = 106°
Step-by-step explanation:
What is Write down the equation of the perpendicular line to y=3x+3?
Answer:
[tex]gradient = - \frac{1}{3} \\ { \tt{equation \: is \: y = - \frac{1}{3}x + 3 }}[/tex]
Answer:
The equation of a perpendicular line to
y =( -1/3 )x+b (b is a normal number)
Step-by-step explanation:
1.Use the slope-intercept form to find the slope.
Tap for more steps...
m = 3
2. the perpendicular line to y=3x+3
must have a slope that is the negative reciprocal of the original slope.
thus,
m perpendicular = −1/3
A certain polygon has its vertices at the following points: (1, 1), (1, 8), (8, 1), and (8, 8)
Answer:
Can u explain more pls?
Step-by-step explanation:
Answer:
Square
Step-by-step explanation:
14. Phyllis wants to hire a clown to entertain at her daughter's birthday party.
• The clown charges a $25 travel fee.
• The clown also charges $5.50 per hour to entertain.
Which equation describes the relationship between the cost, C, Phyllis must pay and the number of hours, n, the clown provides
entertainment?
Answer:
C=25+5.50n
Step-by-step explanation:
C=25+5.50n where c is the total cost and n is the number of hours the clown entertains.
If A and B are independent events, P(A and B) =
Answer:
If A and B are independent events, then the events A and B' are also independent. Proof: The events A and B are independent, so, P(A ∩ B) = P(A) P(B). From the Venn diagram, we see that the events A ∩ B and A ∩ B' are mutually exclusive and together they form the event A.
Answer:
Step-by-step explanation:
Given A and B are independent events, P(A and B) = P(A)*P(B)
Which statement is not always true for a parallelogram?
A. Consecutive angles are supplementary.
B. Diagonals are congruent.
C. Opposite sides are congruent.
D. Opposite angles are congruent.
Explanation:
If the diagonals are congruent, then we'd have a rectangle. Any rectangle is a parallelogram, but not the other way around.
If we had a non-rectangular parallelogram, with none of the angles 90 degrees, then the diagonals will not be the same length.
Choices A, C and D are true for any parallelogram (rectangle or not).
Amy earned $25 after babysitting for 3 hours if amy always charges the same rate,how much will she make after babysitting for 7 hours
Paul's company rents cars to people who are at least 25 years old. Which graph best represents the possible ages of people who can rent cars from Paul's company?
A number line with an open circle on 25, with shading to the right.
A number line with a closed circle on 25, with shading to the right.
A number line with an open circle on 25, with shading to the left.
A number line with a closed circle on 25, with shading to the left.
Answer:
A number line with a closed circle on 25, with shading to the right.
Explanation:
A closed circle means "greater than or equal to" or "less than or equal to".
A open circle means "less than" or "greater than"
Therefore, since the question says: "who are at least 25 years old", a closed circle is the correct answer.
And says it says "at least 25 years old" it means that it shaded to the right, and that the circle is on the number 25.
Answer:
A number line with a closed circle on 25, with shading to the right.
Step-by-step explanation:
...
Sandra y José son dos amigos que se encuentran en diferentes partes de la ciudad de Lima (Observa el plano), la distancia que los separa en el plano es de 7 cm ellos quisieran saber ¿Cuál es la distancia real en metros que los separa? Sabiendo que el plano ha sido dibujado a escala 1: 20 000.
Respuesta:
1,4 kilometros
Explicación paso a paso:
Dado que :
Distancia que separa a Sandra y José en el mapa = 7cm
Dibujo a escala = 1: 20.000; Esto se puede interpretar en el sentido de que 1 cm en el mapa equivale a 20.000 cm en el suelo.
Por tanto, una distancia de 7 cm en el mapa será:
20.000 * 7 = 140.000 cm en el suelo = distancia real
Por lo tanto, la distancia real = 140.000 cm.
Recordar :
1 cm = 10 ^ -5 km
140000 cm = 1.4 kilometros
Por lo tanto, la distancia real entre Sandra y José es de 1,4 km.
Which product is negative?
(-3/8)(-5/7)(1/4)
(3/8)(-5/7)(-1/4)
(3/8)(5/7)(1/4)
(-3/8)(-5/7)(-1/4)
Answer:
[tex]( - \frac{ 3}{8} )( - \frac{5}{7} )( - \frac{1}{4} )[/tex]Step-by-step explanation:
[tex]( - \frac{ 3}{8} )( - \frac{5}{7} )( - \frac{1}{4} )[/tex][tex] \frac{3}{8} \times \frac{5}{7} \times (- \frac{1}{4} )[/tex][tex] \frac{3 \times 5}{8 \times 7} ( - \frac{1}{4} )[/tex][tex] - \frac{15}{56 \times 4} [/tex][tex] - \frac{15}{224} [/tex]Hope it is helpful.....Which is a simplified form of the expression 3a + 7 – a – 7?
A. 2a
B. 4a
C. 2a + 14
D. 4a - 14
Answer:
A. 2a
Step-by-step explanation:
imagine an imaginary 1 in front of the a
3a + 7 – 1a – 7
subtract numbers without variables
3a + 7 – a – 7
3a-1a
subtract 1a from 3a
2a
Answer:
A. 2a
Step-by-step explanation:
3a + 7 - a + 7
= 3a - a + 7 - 7
= 2a + 0
= 2a
A basketball-player scores a free-throw with probability 0.9. What is the probability that her first miss occurs on the 6th shot
Answer:
[tex]Pr = 0.059049[/tex]
Step-by-step explanation:
Given
[tex]p = 0.9[/tex] --- probability of scoring
Required
Probability that his first miss is his 6th shot
Let q represent the event that he did not score.
Using complement rule:
[tex]q = 1 - p = 1 - 0.9 = 0.1[/tex]
The event that his first miss is his 6th is represented as:
p p p p p q ---- That he scoress the first 5 attempts
So, the probability is:
[tex]Pr = p^5 * q[/tex]
[tex]Pr = 0.9^5 * 0.1[/tex]
[tex]Pr = 0.059049[/tex]
A regular six sided die and an eight equal segment spinner, numbered 1 to 8, are rolled/spun simultaneously. What are the odds in favor of spinning a prime number on the spinner and rolling a number less or equal to 4 on the die?
Answer:
1/3
Step-by-step explanation:
In statistics, the probability of both an event A and an event B happening is equal to the probability of A happening multiplied by the probability of event B happening.
Let's say spinning a prime number is event A and rolling a number ≤ 4 is event B.
There are 8 possibilities on an eight equal segment spinner, and there are 4 prime numbers between 1 and 8 (including 8), which are 2, 3, 5, and 7. This means that the probability of spinning a prime number is 4/8, or 1/2
There are 6 possibilities on a die, and there are 4 possibilities of rolling a 4 or less (1, 2, 3, 4). Therefore, the probability of rolling 4 or less on a die is 4/6, or 2/3
The probability of both of these happening can be calculated by multiplying these together, so 1/2 * 2/3 = 2/6 = 1/3
100 people study one language at a college. Some people study French, some study Spanish. The rest of the people study German. 54 of the people in Year 10 and the rest in Year 11. 20 of 29 people who study Spanish in Year 11. 31 people study German, 15 year 11 students study French. Work out the number of Year 10's who study German.
Hello,
[tex]Data:\\\\\begin{array}{|c|c|c|c|c|}Year&French&Spanish&German&Total\\----&----&----&----&---\\Y10&-&-&-&54\\Y11&15&20&-&-\\----&----&----&----&---\\&-&29&31&100\\\end{array}\\\\Calculus:\\\\\begin{array}{|c|c|c|c|c|}Year&French&Spanish&German&Total\\----&----&----&----&---\\Y10&25&9&20&54\\Y11&15&20&11&46\\----&----&----&----&---\\&40&29&31&100\\\end{array}\\\\[/tex]
20 Year10's students learn German.
========================================================
Explanation:
Make a table that has "Year 10", "Year 11", and "Total" as the three rows.
Then you'll have the columns "French", "Spanish", "German", "Total".
In the bottom right corner is the value 100. This is the grand total of everyone surveyed.
We're told that 54 people are in Year 10, which leaves 100-54 = 46 people in Year 11.
Along the "total" column on the far right side, we'll have 54, 46, and 100 in that order from top to bottom.
--------------------------
The info that "20 of the 29 people who study Spanish in Year 11" tells we have 20 people in year 11 who study Spanish, out of 29 people who study Spanish. That leaves 29-20 = 9 people in Year 10 who study Spanish. In the "Spanish" column, we have the values 9,20,29 in that exact order from top to bottom.
Next, we'll write 31 at the bottom of the "German" column to indicate 31 people study German.
The last bit of info is that "15 Year 11 students study French". So we'll write 15 in the "year 11" row and "french" column.
--------------------------
After all that info is sorted out and entered into the table, you should end up with what is shown in figure 1 (see attached image below). Ignore figure 2 for now as we'll work our way to getting there eventually.
The variables a,b,c,d are placeholders for positive whole numbers.
There are probably a few approaches to take, but possibly the quickest is to notice that in the second row, we can say
15+20+c = 46
c+35 = 46
c = 46-35
c = 11
We have 11 students who study German in Year 11.
Once you determine c, it helps us find b. Focus on the German column to see that
b+11 = 31
b = 31-11
b = 20
There are 20 students in Year 10 who study German. You could stop here if you want.
--------------------------
Just two more variables to go.
Along the top row, we see that
a+9+20 = 54
a+29 = 54
a = 54-29
a = 25
and along the bottom row we see that
d+29+31 = 100
d+60 = 100
d = 100-60
d = 40
Or you could note along this first column to say
a+15 = d
d = a+15
d = 25+15
d = 40
So there are a few alternative paths to take.
--------------------------
All of the sections mentioned so far only involve filling out the table that is shown below in figure 2.
To answer the question your teacher wants to ask, which is how many Year 10 students study German, well that's simply 20 students. Refer to the conclusion of the previous two sections earlier.
By this point, we just simply copy the value from the completed table. This value being of course in the "Year 10" row and "German" column.
Given: ABCD is a parallelogram.
Prove: ∠A and ∠D are supplementary.
Parallelogram A B C D is shown.
By the definition of a parallelogram, AB∥DC. AD is a transversal between these sides, so ∠A and ∠D are
angles. Because AB and DC are
, the same-side interior angles must be
by the same-side interior angles theorem. Therefore, ∠A and ∠D are supplementary.
Answer:
By the definition of a parallelogram, AB∥DC. AD is a transversal between these sides, so ∠A and ∠D are
✔ same-side interior
angles. Because AB and DC are
✔ parallel
, the same-side interior angles must be
✔ supplementary
by the same-side interior angles theorem. Therefore, ∠A and ∠D are supplementary.
Step-by-step explanation:
Answer:
The answer above is correct!
The correct options are:
First box: option D. same-side interior
Second box: option C. parallel
Third box: option D. supplementary
Step-by-step explanation:
Hope this helped - just got it right on edge!
Brainliest would be greatly appreciated :)
Find the measure of the missing angle using the exterior angle sum theorm.
Answer:
85°
Step-by-step explanation:
The exterior angle of a triangle is=sum of the opposite interior angles
So
? °=45°+40°
These tables of values represent continuous functions. In which table do the values represent an exponential function?
Answer:
c
Step-by-step explanation:
An exponential function is a function where the number is raised to a constant power
exponential function is usually in the form : f(x) = [tex]a^{x}[/tex]
a is positive and not equal to 1
x is a real number
to determine which option is an exponential function, determine which of the options have a common ratio
Option A :
28/7 = 4
49 / 28 = 1.75
option C
12 / 4 = 3
36 /12 = 3
the correct answer is C
Weiling took part in a Mathematics quiz which consist of 60 questions. For every correct answer, 3 marks would be awarded. For every wrong answer, 2 marks would be deducted. Weiling answered all the questions and scored a totał of 140 marks for the quiz. How many questions did she answer correctiy?
Answer:
Right answer = 52
Wrong answers = 8
Step-by-step explanation:
Every correct answer = + 3
Every wrong answer = - 2
Number of correct answers = x
Number of wrong answers = y
x + y = 60 - - - (1)
3x - 2y = 140 - - - (2)
From (1) :
x = 60 - y
Put x = 60 - y into (2)
3(60 - y) - 2y = 140
180 - 3y - 2y = 140
180 - 5y = 140
-5y = 140 - 180
-5y = - 40
y = 8
x = 60 - y
x = 60 - 8
x = 52
Right answer = 52
Wrong answers = 8
Select the correct answer. Help
what is the explicit formula for this sequence
Answer:
A
Step-by-step explanation:
Start with the 3.
You know that there is a difference of 4 between (say) 2 and 5. The 3 is a sign that the sequence is increasing. The members of the sequence are going up.
n - 1 means that the nth terms is calculated as an and uses the number of terms to be n-1. That means that the first term is a1 which is the starting point of the sequence.
The answer is an = a1 + (n-1)*d
d = 3
a1 = - 7
So let's try the formula out.
a4 = -7 + (4 - 1)*3
a4 = -7 + 3 * 3
a4 = -7 + 9
a4 = 2
Is 2 the 4th term in the series? Yes it is!
The cost of 5 gallons of ice cream has a variance of 64 with a mean of 34 dollars during the summer. What is the probability that the sample mean would differ from the true mean by more than 1.1 dollars if a sample of 38 5-gallon pails is randomly selected? Round your answer to four decimal places.
Answer:
Probability[(X - μ) < 1.1] = 0.6046
Step-by-step explanation:
Given:
σ² = 64
Mean μ = 34
Find:
Probability[(X - μ) < 1.1]
Computation:
Standard deviation σ = √σ²
Standard deviation σ = √64
Standard deviation σ = 8
Probability[(X - μ) < 1.1] = Probability[-1.1 < (X - μ) < 1.1]
Probability[(X - μ) < 1.1] = Probability[-1.1/(8/√38) < (X - μ) < 1.1/(8/√38)]
Using z table
Probability[(X - μ) < 1.1] = 0.6046
make b the subject of the formula
A=1/2bh
Answer:
[tex] \blue{b = \dfrac{2A}{h}} [/tex]
Step-by-step explanation:
[tex] A = \dfrac{1}{2}bh [/tex]
Step 1. Switch sides.
[tex] \dfrac{1}{2}bh = A [/tex]
Step 2. Since the fraction 1/2 multiplies b, multiply both sides by the reciprocal of 1/2 which is 2.
[tex] 2 \times \dfrac{1}{2}bh = 2 \times A [/tex]
[tex] bh = 2A [/tex]
Step 3. Since h is multiplying b, and you want b alone, divide both sides by h.
[tex] \dfrac{bh}{h} = \dfrac{2A}{h} [/tex]
Answer:
[tex] b = \dfrac{2A}{h} [/tex]
A swimmer can swim 50.2 meters in 1 minute. How far can he swim in half an hour? *
Answer:
1506meters
Step-by-step explanation:
1hour-60minutes
which means half an hour is 30minutes,so it's more like they are asking you to find how far the swimmer can swim in 30minutes
50.2-1min
x -30min
x=50.2×30
x=1506meters
Change 18° into sexagesimal seconds.
Answer:
She's, "HOT"!
Step-by-step explanation:
Which equation is the inverse of 2(x – 2)2 = 8(7 + y)?
Answer:
y = (4x - 71)/8
Step-by-step explanation:
2(x - 2)2 = 8(7 + y) solve for y instead of x for the inverse equation
4x - 8 = 63 + 8y
4x - 8 - 63 = 8y
4x - 71 = 8y
y = (4x - 71)/8
Answer:
A
Step-by-step explanation:
