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3 years ago

9

Juan was given a gift card for a coffee shop. Each morning, Juan uses the card to buy one cup of coffee. Each cup of coffee cost

s $2 and the original amount of money on the gift card was $30. Write an equation for A, in terms of x, representing the amount money remaining on the card after buying of coffee.

1 answer:

Black_prince [1.1K]3 years ago

7 0

Answer:

$A=30-2x$

Step-by-step explanation:

Cost of one cup of coffee=$2

The original amount of money on the gift card= $30

Juan's expenses in buying coffee, after $x$ morning are $\$2\times x$ .

The amount of money left, $A$ , on the card $=$ (Original amount) $-$ (Total expenses)

$A=30-2x$

Hence, the equation for, $A$ , the amount of money remaining on the card is

$A=30-2x.$

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5. Find the first, fourth, and tenth terms of the arithmetic

Lubov Fominskaja [6]

The first, fourth and tenth terms of the arithmetic sequence is $-6, -\frac{27}{5}$ and $-\frac{21}{5}$

Explanation:

The given rule for the arithmetic sequence is $A(n)=-6+(n-1)(\frac{1}{5} )$

We need to determine the first, fourth and tenth terms of the sequence.

To find the first, fourth and tenth terms, let us substitute $n=1,4,10$ in the general rule for the arithmetic sequence.

To find the first term, substitute $n=1$ in $A(n)=-6+(n-1)(\frac{1}{5} )$ , we get,

$A(1)=-6+(1-1)(\frac{1}{5} )$

$A(1)=-6+(0)(\frac{1}{5} )$

$A(1)=-6$

Thus, the first term of the arithmetic sequence is -6.

To find the fourth term, substitute $n=4$ in $A(n)=-6+(n-1)(\frac{1}{5} )$ , we get,

$A(2)=-6+(4-1)(\frac{1}{5} )$

$A(2)=-6+(3)(\frac{1}{5} )$

$A(2)=\frac{-30+3}{5}$

$A(2)=\frac{-27}{5}$

Thus, the fourth term of the arithmetic sequence is $-\frac{27}{5}$

To find the tenth term, substitute $n=10$ in $A(n)=-6+(n-1)(\frac{1}{5} )$ , we get,

$A(10)=-6+(10-1)(\frac{1}{5} )$

$A(10)=-6+(9)(\frac{1}{5} )$

$A(10)=-6+\frac{9}{5}$

$A(10)=-\frac{21}{5}$

Thus, the tenth term of the arithmetic sequence is $-\frac{21}{5}$

Hence, the first, fourth and tenth terms of the arithmetic sequence is $-6, -\frac{27}{5}$ and $-\frac{21}{5}$

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4 years ago

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dimaraw [331]

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3 years ago

Solve the inequality and write the solution set using both set-builder notation and interval notation. -3a-15≤-2a+6

sleet_krkn [62]

Answer:

Set builder notation: {a | a ≥ -21}

Interval notation: [-21, ∞)

Step-by-step explanation:

A set represents a collection of things, objects, or numbers. A set builder notation is in the form y = {x | x is an odd number between 8 and 10}, which means y contains all the odd numbers between 8 and 10.

Interval notation is a way to define a set of numbers between a lower limit and an upper limit using end-point values. for example (8, 20) means numbers between 8 and 20.

Given -3a-15≤-2a+6; solving :

-3a - 15 ≤ -2a + 6

-3a + 2a ≤ 6 + 15

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dividing through by -1:

a ≥ -21

The solution is:

Set builder notation: {a | a ≥ -21}

Interval notation: [-21, ∞)

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3 years ago

Pls help, i really need help with. i will mark brainliest with the best/correct answer!!!

Ne4ueva [31]

Answer:

Number 1 is 12.

Step-by-step explanation:

{Solve by cross multiplication}

17 • x = 3 • (80 - x)

{Multiply 3 by distribution,}

17x = 240 - 3x

{Add 3x to both sides of the equation,}

20x = 240

{Divide through out by 20,}

20r/20 = 240/20

x = 12

Thus there were 12 pens :)

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