Answer:
Horizontal translation of the parent graph
Step-by-step explanation:
<h2><u>Definitions</u>:</h2>
In the <u>vertex form</u> of a quadratic function, f(x) = a(x - h)² + k, where:
- (h, k) = vertex of the graph
- <em>a</em> = determines the width and direction of the graph's opening.
A <u>horizonal translation</u> to the parent graph is given by, y = f(x - h), where:
- <em>h</em> > 0 ⇒ Horizontal translation of <em>h</em> units to the right
- <em>h</em> < 0 ⇒ Horizontal translation of |<em>h </em>| units to the left
In the graph of g(x) = (x + 12)², the <u>vertex</u> occurs at point (-12, 0).
While the <u>vertex</u> of the parent graph, f(x) = x² occurs at point, (0, 0).
<h2><u>Answers</u>:</h2>
Since the vertex of g(x) occurs at point, (-12, 0), substituting the value of (<em>h</em>, <em>k </em>) into the vertex form will result into:
g(x) = a(x - h)² + k
g(x) = [x - (-12)]² + 0
g(x) = (x + 12)² + 0
g(x) = (x + 12)²
Therefore, the graph of g(x) = (x + 12)² represents the horizontal translation of the parent graph, f(x) = x², where the graph of g(x) is <em>horizontally</em> translated 12 units to the left.
En Español
En la class de ciencias hay muchos estudiantes. A Irene siempre le gusta estudiar y haver la tarea. En todos los exámenes saca cien. Pablo nunca estudia y no le gusta tomar aptunes. En los exámenes saca cuarenta, cincuenta y trienta. Muchas veces, a Sandra le gusta hacer la tarea. En los exámenes saca noventa, cuarenta y cien. A Eduardo a veces le gusta estudiar y hacer la tarea. En los exámenes saca noventa, noventa y noventa. A Javier nunca le gusta leer libros. En los exámenes saca cuarenta, cincuenta y cuarenta. Todos los estudiantes son differentes y me gusta enseñar ciencias a todos.
In english
In science class there are many students. Irene always likes to study and do her homework. In all the exams he gets a hundred. Pablo never studies and does not like to take aptunes. In the exams he gets forty, fifty and thirty. Many times Sandra likes to do her homework. In the exams he gets ninety, forty and one hundred. Eduardo sometimes likes to study and do homework. In the exams he gets ninety, ninety and ninety. Javier never likes to read books. On the exams he gets forty, fifty and forty. All students are different and I like to teach science to everyone.
Hope this helps!
Answer: V = 706.5 cubic millimeters
Step-by-step explanation:
V = (3.14)(r^2)(h)
V = (3.14)(5^2)(9)
V = (3.14)(25)(9)
V = 706.5
Answer:
Victor gives 28 tools to IIya.
Step-by-step explanation:
Consider the provided information
The ratio of the number of Victor’s tools to the number of Ilya’s tools is 5:2
Let V represents the Victor and I represent llya
Therefore,
It is given that Victor has 42 more tools than Ilya.
Solve the above equation.
Thus, IIya has 28 tools.
Victor has 42 more tools than Ilya. Therefore 42 + 28 = 70.
Victor has 70 tools.
We want to find the number of tools victor needs to give to IIya so that the ratio of the number of Victor's tools to the number of Ilya’s tools will be 3:4
Let Victor gives x tools to IIya. Thus,
Hence, Victor gives 28 tools to IIya.
#1) A
#2) B
#3) C
#5) A
#7) D
#10) D
#11) D
#14) A
#15) D
#16) A
#19) D
Explanation
#1) If the data set is linear, the slope will be constant throughout the entire data set. For data set A, the slope between the first two points is:
m = (y₂-y₁)/(x₂-x₁) = (1--2)/(3-1) = 3/2
Between the second two points,
m=(4-1)/(5-3) = 3/2
Between the third pairs of points,
m=(7-4)/(7-5) = 3/2
The slope is constant throughout the entire set. The set is also increasing; as x increases, y increases as well.
#2) Substituting 4 for y and 1 for x,
y = (x+1)²
4 = (1+1)² = 2²
9 = (1+2)² = 3²
16 = (1+3)² = 4²
This works for each point, so this is the solution.
#3) Since he runs 10 laps per hour t, this is 10t. Adding the first lap to this, we get y=10t+1.
#5) If a sequence is arithmetic, each term is found by adding a constant (called the common difference) to the previous term. If the common difference is 2, this means that 2 was added each time. This only works for choice A.
#7) For x to vary directly as y, this means that y/x = k; in other words, the quotient of y and x is constant for every point.
#10) The formula for slope is:
m=(y₂-y₁)/(x₂-x₁)
Using the information we're given, we have
3=(d-5)/(4-2)
3=(d-5)/2
Multiply both sides by 2:
3*2 = ((d-5)/2)*2
6 = d-5
Add 5 to both sides:
6+5 = d-5+5
11 = d
#11) Using point slope form,
y-y₁ = m(x-x₁)
y-1 = 3(x--2)
y-1 = 3(x+2)
Using the distributive property,
y-1 = 3*x + 3*2
y-1 = 3x + 6
Add 1 to both sides:
y-1+1 = 3x+6+1
y=3x+7
#14) If two lines are parallel, they have the same slope. The slope of the given equation is 4; the only one with a slope of 4 is A.
#15) If two lines are perpendicular, they have slopes that are negative reciprocals (opposite signs and flipped). The slope of the given equation is 2; this means the slope of the perpendicular line would be -1/2. The only one with this slope is D.
#16) The two equations are not the same, so there are not infinitely many solutions. The variables do not both cancel, so there is at least one solution. This only leaves one solution as the answer.
#19) Using 1 for 7 and 4 for x, we check each equation. The only one that comes out correct is D.
