Write the quadratic function in the form f (x) = a (x

Anne, Barry, and Cathy enter a coffee shop. Anne orders two coffees, one juice, and two doughnuts and pays $7.50. Barry orders o

Evgesh-ka [11]

Answer:

Coffee = $2.00

Juice = $1.50

Doughnut = $1.00

Step-by-step explanation:

Given

Let:

$c = coffee\\ j= juice\\ d = doughnut$

So, we have:

Anna

$2c + j + 2d = 7.50$

Barry

$c + 3d = 5.00$

Cathy

$3c + j + 4d = 11.50$

Required

The price of each

We have:

$2c + j + 2d = 7.50$

$c + 3d = 5.00$

$3c + j + 4d = 11.50$

Make c the subject in: $c + 3d = 5.00$

$c = 5.00 - 3d$

Substitute $c = 5.00 - 3d$ in $2c + j + 2d = 7.50$ and $3c + j + 4d = 11.50$

$2c + j + 2d = 7.50$

$2[5.00 - 3d] + j + 2d = 7.50$

$10.00 - 6d+ j + 2d = 7.50$

Make j the subject

$j = 7.50 - 10.0 +6d - 2d$

$j = -2.50 +4d$

$3c + j + 4d = 11.50$

$3[5.00 - 3d] + j + 4d = 11.50$

$15.00 - 9d + j + 4d = 11.50$

Make j the subject

$j = 11.50 - 15.00 + 9d -4d$

$j = -3.50 + 5d$

So, we have:

$j = -3.50 + 5d$ and $j = -2.50 +4d$

Equate both values of j

$-3.50 + 5d = -2.50 + 4d$

Collect like terms

$5d - 4d = 3.50 -2.50$

$d = 1.00$

Substitute $d = 1.00$ in $j = -3.50 + 5d$

$j = -3.50 + 5d$

$j = -3.50 + 5 * 1.00$

$j = -3.50 + 5.00$

$j = 1.50$

To solve for c, we substitute $d = 1.00$ in $c + 3d = 5.00$

$c + 3 * 1.00 =5.00$

$c + 3.00 =5.00$

Solve for c

$c =- 3.00 +5.00$

$c =2.00$

7 0

2 years ago

Write the equation for the area of a triangle with a height that is 5 more than twice its base using one variable. Please help m

zysi [14]

Answer:

$A=b(b+\frac{5}{2} )$

Step-by-step explanation:

hey there!!!

we know already that the area of a triangle is given as

$A=\frac{1}{2}b *h$

where b= base

and h= heigth

Given that the height is 5 times more than twice it base

let h= 2b+5

Now we substitute h=2b+5 in the area of the triangle

$A=\frac{1}{2}b * (2b+5)$

$A= \frac{2b^2}{2} +\frac{5b}{2}$

$A= b^2+\frac{5b}{2}\\\\A=b(b+\frac{5}{2} )$

7 0

3 years ago

1.Dakota bought 1.7 pounds of ham, 3.15 pounds of onions, and 6 cans of soup. What was the total cost before sales tax? Round

MrRa [10]

Answer: 15.73

Step-by-step explanation:

4 0

3 years ago

A cookie recipe calls for 5/6

RUDIKE [14]

Answer:

9.9 cups

Step-by-step explanation:

5/6 times 12 equals 9.9

3 0

3 years ago

Please help me i have a hw

aalyn [17]

Answer:

1.B 2.H 3. A

Step-by-step explanation:

1. First, find out the percentage of people who voted for Mathematika in survey one.

The total amount of people who voted is 14+17+19, which equals 50. 17/50 people voted for Mathematika, 17/50 = 0.34.

To find out how many people out of 300 will vote for Mathematika, multiply the 0.34 by 300. 300 x 0.34 = 102, so 102 people will vote for Mathetika.

2. You use the same logic for number 2. 14+17+19+20+19+11 = 100, so 100 people voted in total. 34 people voted for Infinitus. 34/100 = 0.34. Multiply 0.34 by 750 to get 255 people will vote for Infinitus.

3. The mean = the average. To find the average, add up all of the numbers, then divide that number by the amount of numbers added together.

7+9+11+13+15 = 55

5 numbers were added together so you divide 55 by 5

55/5 = 11. The mean is 11

9+10+11+12+13 = 55

There were 5 numbers added together

55/5 = 11. Both the means were the same

4 0

3 years ago

Write the quadratic function in the form f (x) = a (x - h)2 +k.