Math  /  Algebra

Question7 Si f(x)=x2f(x)=x^{2}, ¿qué función es el resultado de desplazar f(x)3f(x) 3 unidades hacia la izquierda y 2 unidades hacia abajo? (1) g(x)=(x+2)23g(x)=(x+2)^{2}-3 (3) j(x)=(x+3)22j(x)=(x+3)^{2}-2 (2) h(x)=(x2)2+3h(x)=(x-2)^{2}+3 (4) k(x)=(x3)2+2k(x)=(x-3)^{2}+2
8 La ecuación utilizada para calcular la velocidad de un objeto es la siguiente: v2=u2+2asv^{2}=u^{2}+2 a s, donde uu es la velocidad inicial, vv es la velocidad final, aa es la aceleración del objeto y ss es la distancia recorrida. Cuando se resuelve esta ecuación para aa, el resultado es (1) a=v2u22sa=\frac{v^{2} u^{2}}{2 s} (3) a=v2u22sa=v^{2}-u^{2}-2 s (2) a=v2u22sa=\frac{v^{2}-u^{2}}{2 s} (4) a=2s(v2u2)a=2 s\left(v^{2}-u^{2}\right)
9 La clase de Matemáticas de la Sra. Smith hizo una encuestó a los estudiantes para determinar sus sabores favoritos de helado. Los resultados se muestran en la siguiente tabla. \begin{tabular}{|c|c|c|c|} \cline { 2 - 4 } \multicolumn{1}{c|}{} & Chocolate & Vainilla & Combinado \\ \hline 11. ^{\circ} grado & 42 & 27 & 45 \\ \hline 12. ^{\circ} grado & 67 & 42 & 21 \\ \hline \end{tabular}
De los estudiantes que prefieren chocolate, Aproximadamente, ¿qué porcentaje era de 12.12 .^{\circ} grado? (1) 27.5 (3) 51.5 (2) 44.7 (4) 61.5

Studdy Solution

STEP 1

1. The original function is f(x)=x2 f(x) = x^2 .
2. We need to apply transformations to this function.

STEP 2

1. Determine the transformation for shifting the function 3 units to the left.
2. Determine the transformation for shifting the function 2 units down.
3. Combine the transformations to find the resulting function.
4. 1. Isolate the term containing a a .
2. Solve for a a .

STEP_1: High_Level_Step: 1 Subtract u2 u^2 from both sides to isolate the term with a a :
v2=u2+2as v^2 = u^2 + 2as v2u2=2as v^2 - u^2 = 2as
High_Level_Step_Completed: TRUE
STEP_2: High_Level_Step: 2 Divide both sides by 2s 2s to solve for a a :
a=v2u22s a = \frac{v^2 - u^2}{2s}
High_Level_Step_Completed: TRUE
The correct answer is option (2) a=v2u22s a = \frac{v^2 - u^2}{2s} .
**Problem 9:**
_ASSUMPTIONS_:
1. We need to find the percentage of 12th-grade students who prefer chocolate.

_HIGH_LEVEL_APPROACH_:
1. Determine the total number of students who prefer chocolate.
2. Determine the number of 12th-grade students who prefer chocolate.
3. Calculate the percentage.

STEP_1: High_Level_Step: 1 Determine the total number of students who prefer chocolate:
Total chocolate=42+67=109 \text{Total chocolate} = 42 + 67 = 109
High_Level_Step_Completed: TRUE
STEP_2: High_Level_Step: 2 Determine the number of 12th-grade students who prefer chocolate:
12th-grade chocolate=67 \text{12th-grade chocolate} = 67
High_Level_Step_Completed: TRUE
STEP_3: High_Level_Step: 3 Calculate the percentage of 12th-grade students who prefer chocolate:
Percentage=(67109)×10061.5% \text{Percentage} = \left(\frac{67}{109}\right) \times 100 \approx 61.5\%
High_Level_Step_Completed: TRUE
The correct answer is option (4) 61.5%.

STEP 3

To shift the function 3 units to the left, replace x x with x+3 x + 3 :
f(x)=x2f(x+3)=(x+3)2 f(x) = x^2 \rightarrow f(x + 3) = (x + 3)^2

STEP 4

To shift the function 2 units down, subtract 2 from the function:
f(x+3)=(x+3)2(x+3)22 f(x + 3) = (x + 3)^2 \rightarrow (x + 3)^2 - 2

STEP 5

Combine the transformations to find the resulting function:
The resulting function is j(x)=(x+3)22 j(x) = (x + 3)^2 - 2 .
The correct answer is option (3) j(x)=(x+3)22 j(x) = (x + 3)^2 - 2 .
**Problem 8:**
_ASSUMPTIONS_:
1. The given equation is v2=u2+2as v^2 = u^2 + 2as .
2. We need to solve for a a .

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