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KATRIN_1 [288]
2 years ago
6

Complete the recursive formula of the arithmetic sequence 20, 26, 32, 38, ....

Mathematics
1 answer:
svp [43]2 years ago
6 0

Step-by-step explanation:

a(n) = a +(n-1)d

a=20

d=26-20=6

°.° a(n) = 20 +(n–1)6

a(1) = 20 +(1–1)6=20

hope this helps

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On the last day of school, Mrs. Awesome gave jelly beans to her class. She gave each boy as many jelly beans as there were boys
professor190 [17]

Answer:

28 students

Step-by-step explanation:

Let x be the number of girls in the class. There were two more boys than girls in her class, then the number of boys is x + 2.

Mrs. Awesome gave each boy as many jelly beans as there were boys in the class, so each of x + 2 boys got x + 2 jelly beans, so

Number of boys = x + 2

Number of jelly beans each boy got = x + 2

Total number of jelly beans all boys got = (x + 2)(x + 2)

Mrs. Awesome gave each girl as many jelly beans as there were girls in the class, so each of x girls got x jelly beans, so

Number of girls = x

Number of jelly beans each girl got = x

Total number of jelly beans all girls got = (x)(x)

Hence,

Total number of jelly beans class got = (x + 2)(x + 2) + (x)(x)

Mrs. Awesome brought 400 jelly beans, and when she finished, she had six jelly beans left, so she gave 400 - 6 = 394 jelly beans to the calss.

So,

(x+2)(x+2)+(x)(x)=394\\ \\x^2+2x+2x+4+x^2=394\\ \\2x^2+4x+4-394=0\\ \\2x^2+4x-390=0\\ \\x^2+2x-195=0\\ \\D=2^2-4\cdot (-195)=4+780=784\\ \\\sqrt{D}=28\\ \\x_{1,2}=\dfrac{-2\pm 28}{2\cdot 1}=-15,\ 13

Number of girls cannot be negative, so x = 13, x + 2 = 15 and total number of students is 13 + 15 = 28

3 0
3 years ago
An ice cream store has the pricing shown below. You want to determine the best value. The height of the cone is 4.5 in and the d
nignag [31]

Solution:

Step 1:

We will calculate the volume of ice cream in the single scoop

The volume of the ice cream will be

\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{2}{3}\pi r^3 \\ r=\frac{2in}{2}=1in(cone) \\ h=4.5in \\ r=\frac{3in}{2}=1.5in(radius\text{ of the hemisphere\rparen} \end{gathered}

By substituting the values, we will have

\begin{gathered} V=\frac{1}{3}\pi r^{2}h+\frac{2}{3}\pi r^{3} \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5+\frac{2}{3}\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{99}{14} \\ V=\frac{165}{14} \\ V=11.79in^3 \end{gathered}

Step 2:

We will use the formula below to calculate the volume of the two scoops of ic cream

\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{4}{3}\pi r^3 \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5in+\frac{4}{3}\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{99}{7} \\ V=\frac{132}{7} \\ V=18.86in^3 \end{gathered}

Step 3:

We will use the formula below to calculate the volume of the three scoops of ic cream

\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{6}{3}\pi r^3 \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5+2\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{297}{14} \\ V=\frac{363}{14} \\ V=25.93in^3 \end{gathered}

For the first ice cream with one scoop

\begin{gathered} 1in^3=\frac{3.50}{11.79} \\ 1in^3=\text{ \$}0.30 \end{gathered}

For the second ice cream with two scoops

\begin{gathered} 1in^3=\frac{4.50}{18.86} \\ 1in^3=\text{ \$}0.24 \end{gathered}

For the third ice cream with three scoops

\begin{gathered} 1in^3=\frac{5.50}{25.93} \\ 1in^3=\text{ \$}0.21 \end{gathered}

Hence,

The final answer is

The triple sold at $5.50 has the best value because it has the lowest price of $0.21 per cubic inch of the ice cream

3 0
11 months ago
The range of the function f(x) = x + 5 is {7, 9}. What is the function’s domain?
mina [271]
** x + 5 = 7 x = 2 ** x + 5 = 9 x = 4 {2,4}
4 0
3 years ago
All of the following expressions are equivalent except.___ 2+m m+2 m-(-2) -2-m
Pachacha [2.7K]

Answer:

\Huge \boxed{-2-m}

Step-by-step explanation:

2 + m

Rewrite with variable first.

m + 2

m + 2

Can’t be simplified further.

m - (-2)

Distribute negative sign.

m + 2

-2-m

Rewrite with variable first.

-m - 2

The last expression is not equivalent to m+2.

4 0
2 years ago
The diagram shows an isosceles triangle.
Lapatulllka [165]

Answer:

295°.It is such an easy triangle

4 0
3 years ago
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