From the graph we can observe that G(x) is obtained by shifting F(x) 3 units to the left and 1 unit upwards.

Thus, both horizontal and vertical translations are involved. Horizontal translation of 3 units to left can be obtained by adding 3 to x in the equation and vertical translation of 1 can be obtained by adding 1 to the entire function.

So,

G(x) = F(x+3) + 1

G(x) = (x+3)² + 1

Thus the correct answer is option C

5 0

3 years ago

Which expression is the factorization of x2 + 10x + 212

Montano1993 [528]

Answer:

The answer is option 1.

Step-by-step explanation:

Firstly, you have to elaborate the expression :

${x}^{2} + 10x + 21$

$= {x}^{2} + 3x + 7x + 21$

Next you have to take out the common factors and factorize it :

${x}^{2} + 3x + 7x + 21$

$= x(x + 3) + 7(x + 3)$

$= (x + 7)(x + 3)$

8 0

3 years ago

Read 2 more answers

Jimmy's costume requires ⅞ + ½ + 1 3/4 yards of fabric. His sister's costume requires 3 x (⅞ + ½ + 1 ⅔) the amount of fabric tha

liq [111]

Answer:

The correct answer is fabric Jimmy's sister needs = $\frac{73}{8}$ × fabric Jimmy needs = $\frac{73}{8}$ × $\frac{25}{8}$ yards of fabric.

Step-by-step explanation:

Jimmy's costume requires ⅞ + ½ + 1 $\frac{3}{4}$ yards of fabric = $\frac{7}{8} +\frac{4}{8} + \frac{14}{8} = \frac{25}{8}$ yards.

His sister's costume requires 3 x (⅞ + ½ + 1 ⅔) the amount of fabric that Jimmy needs = 3× ( $\frac{21}{24} + \frac{12}{24} + \frac{40}{24}$ ) yards of what Jimmy needs = $\frac{73}{8}$ yards of what Jimmy needs.

The relationship between how much fabric Jimmy needs and how much fabric his sister needs is given by

Fabric Jimmy's sister needs = $\frac{73}{8}$ × fabric Jimmy needs = $\frac{73}{8}$ × $\frac{25}{8}$ yards of fabric.

7 0

4 years ago