Question

1. lajuan sells exactly 4 kinds of pies in his bakery: apple, pecan, coconut - cream, and peach. of the pies he sold on thursday, 1/4 were apple, 1/3 were pecan, 24 were coconut - cream, and 8 were peach. how many total pies did lajuan sell on thursday? f. 40 g. 42 h. 56 j. 128
2. in a certain quadrilateral, 2 opposite angles each measure (3x + 5)°, the other 2 opposite angles each measure 1/2(x + 3)°. what is the value of x? a. 1 b. 9 c. 43 d. 88
3. the first 4 terms of a sequence are shown in the table. the sequence is defined by a1 = 2 and an=an - 1+(n - 1)^2 for n≥2. what is the sixth term, a6, of this sequence?

a1	a2	a3	a4
2	3	7	16

f. 68 g. 57 h. 41 j. 32

1. on the real - number line, how many integers are between - 65/6 and 75/2? a. 8 b. 28 c. 48 d. 140

Explanation:

32.

Step1: Let the total number of pies be $x$.

The fraction of apple pies is $\frac{1}{4}$, the fraction of pecan pies is $\frac{1}{4}$, the number of coconut - cream pies is 24, and the number of peach pies is 8.

Step2: Find the fraction of coconut - cream and peach pies.

The sum of the fractions of apple and pecan pies is $\frac{1}{4}+\frac{1}{4}=\frac{1}{2}$. So the fraction of coconut - cream and peach pies is $1 - \frac{1}{2}=\frac{1}{2}$.

Step3: Set up an equation.

The number of coconut - cream and peach pies is $24 + 8=32$. Since this is $\frac{1}{2}$ of the total number of pies, we have the equation $\frac{1}{2}x=32$.

Step4: Solve for $x$.

Multiply both sides of the equation by 2: $x = 64$. But this is wrong. Let's start over.
Let the total number of pies be $x$. We know that $\frac{1}{4}x+\frac{1}{4}x+24 + 8=x$. Combine like - terms: $\frac{1}{2}x+32=x$. Subtract $\frac{1}{2}x$ from both sides: $32=x-\frac{1}{2}x=\frac{1}{2}x$. Multiply both sides by 2 to get $x = 64$.

Step1: Recall the property of a quadrilateral.

The sum of the interior angles of a quadrilateral is $360^{\circ}$.

Step2: Set up an equation.

We have two opposite angles of measure $(3x + 5)^{\circ}$ and two opposite angles of measure $(x+3)^{\circ}$. So, $2(3x + 5)+2(x + 3)=360$.

Step3: Expand the equation.

$6x+10 + 2x+6=360$.

Step4: Combine like - terms.

$8x+16 = 360$.

Step5: Isolate the variable.

Subtract 16 from both sides: $8x=360 - 16=344$. Divide both sides by 8: $x = 43$.

Step1: Given the recurrence relation $a_n=a_{n - 1}+(n - 1)^2$ for $n\geq2$ and $a_1 = 2$.

We know $a_2=a_1+(2 - 1)^2=2 + 1=3$, $a_3=a_2+(3 - 1)^2=3+4 = 7$, $a_4=a_3+(4 - 1)^2=7 + 9=16$.

Step2: Find $a_5$.

$a_5=a_4+(5 - 1)^2=16+16 = 32$.

Step3: Find $a_6$.

$a_6=a_5+(6 - 1)^2=32+25 = 57$.

Answer:

56

33.