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2 years ago

14

At a school cafeteria a cold lunch costs $1.80, and a hot lunch costs $3.00. During one school year a teacher spent a total of $

288.60 on cold lunches and hot lunches. The number of cold lunches the teacher bought was 1 fewer than swice the number of hot lunches the teacher bought.
Which system of equations can be used to find c, the number of cold lunches, and h, the number of hot lunches, the teacher bought during the school year?

1 answer:

Fudgin [204]2 years ago

6 0

Answer:

H=44

C=87

Step-by-step explanation:

1.8 (C) + 3.00 (H) = 288.6

C= 2H-1

1.8 (2H-1) + 3 (H) = 288.6

3.6 H -1.8 + 3 H = 288.6

6.6 H = 290.4

H= 290.4/6.6 = 44

C=87

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Find an equation of the line through (1,8) and parallel to y = 4x +3. Write the equation using function notation.

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Answer:

f(x) = 4x + 4

Step-by-step explanation:

When a line is parallel to another line, the slopes are always equal. Therefore, the coefficient for x has to be four. If you multiply the y-coordinate by 4, you get 4. To get 8, you have to add four, so the equation is simply f(x) = 4x+4.

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2 years ago

Read 2 more answers

Justin is 2 years older than one third Marcella’s age. Aimee is 5 years younger than 2 times Justin’s age. Define a variable and

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Answer:

Step-by-step explanation:

J = (1/3)M + 2 <=== ur expression would be : (1/3)M + 2

A = 2J - 5

if marcella is 63....

J = (1/3 * 63) + 2 A = 2J - 5

J = 63/3 + 2 A = 2(23) - 5

J = 21 + 2 A = 46 - 5

J = 23 <== justin's age A = 41 <=== Aimee's age

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3 years ago

If the polygon is translated 4 units down and 5 units right, what will the coordinates of the new image be? Use prime notation i

steposvetlana [31]

Using prime notation, the new coordinates after translation are;

<em>New coordinates;</em>

A': (-1, 1)

B': (-1, -2)

C': (3, -2)

D': (3, 2)

From the attached image, we can see that the coordinates are;

A(-6, 5)

B(-6, 2)

C(-2, 2)

D(-2, 6)

Translating the polygon down by x units means the value of the y-coordinates will reduce by 4.

In a similar fashion, translation 5 units to the right means that the x-coordinates would increase by 5.

Applying these translation numbers to our coordinates, we will now have;

A(-6 + 5, 5 - 4)

B(-6 + 5, 2 - 4)

C(-2 + 5, 2 - 4)

D(-2 + 5, 6 - 4)

Simplifying each of them gives us the new coordinates as;

A: (-1, 1)

B: (-1, -2)

C: (3, -2)

D: (3, 2)

Read more at; brainly.com/question/4726090

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1 year ago

Learning Task 3

ASHA 777 [7]

Answer:

1. The sides are: 38.5, 39.5, 40.5 and 41.5

2. Presently, Inzo is 15 years old and Miz is 10 years old

3. $Distance = 3682km$

4. Possible pairs are: (12, 14), (16, 18) and (20, 24)

5. $L < 38m$

Step-by-step explanation:

The question has lots of missing details. See the comment section for complete question

Solving (a):

Given

Shape: Quadrilateral

Sides: Consecutive

$Perimeter = 160$

Let one of the sides be x. The other sides will be x + 1, x + 2 and x + 3.

So, the perimeter is:

$Perimeter = x + x + 1 + x + 2 + x + 3$

This gives:

$160 = x + x + 1 + x + 2 + x + 3$

Collect Like Terms

$160 -1-2-3= x+x+x+x$

$154= 4x$

Divide both sides by 4

$38.5 = x$

$x =38.5$

<em>So, the sides are: 38.5, 39.5, 40.5 and 41.5</em>

<em></em>

Solving (b):

Given

Presently: $Inzo = 10 + Miz$

Five years ago: $Miz - 5= \frac{1}{3} * (Inzo-5)$ --- (Missing from the question)

Required: Determine their present ages

Substitute $10 + Miz$ for Inzo in the second equation

$Miz - 5 = \frac{1}{3} * (10 + Miz - 5)$

$Miz - 5 = \frac{1}{3} * (Miz + 5)$

Multiply both sides by 3

$3Miz - 15 = Miz + 5$

Collect Like Terms

$3Miz -Miz = 15 + 5$

$2Miz= 20$

Divide both sides by 2

$Miz = 10$

Substitute 10 for Miz in $Inzo = 10 + Miz$

$Inzo = 10 + 5$

$Inzo = 15$

<em>So presently, Inzo is 15 years old and Miz is 10 years old</em>

Solving (3):

Given

Express Train:

$Speed = 100kph$

$Time = t$

Local Train:

$Speed = 45kph$

$Time = t + 45$

Required: Determine the distance between A and B

Distance is calculated as:

$Distance = Speed * Time$

For the express train:

$Distance = 100 * t$

For the local train

$Distance = 45 * (45 + t)$

Distance between both stations are equal; So,

$100 * t = 45 * (45 + t)$

$100 t = 2025 + 45t$

Collect Like Terms

$100 t -45t= 2025$

$55t= 2025$

Divide by 55

$t = 36.82$

Substitute 36.82 for t in $Distance = 100 * t$

$Distance = 100 * 36.82$

$Distance = 3682km$

Solving (4):

Let the even numbers be: n and n + 2.

Sum greater than 24: $n + n + 2 > 24$

Sum less than 60: $n + n + 2 < 60$

So, we have:

$n + n + 2 > 24$

$2n + 2 > 24$

Collect Like Terms

$2n > 24-2$

$2n > 22$

$n > 11$

$n + n + 2 < 60$

$2n + 2< 60$

Collect Like Terms

$2n < 60-2$

$2n < 58$

Divide by 2

$n$

So, we have:

$n > 11$ and $n < 29$

So, possible pairs are: (12, 14), (16, 18) and (20, 24)

Solving (5):

Given

$Perimeter < 152m$

Required: Find the possible lengths

Let the length be L.

Perimeter is calculated as:

$Perimeter =4 * L$

$Perimeter =4 L$

So, we have:

$4L < 152m$

Divide through by 4

$L < 38m$

Hence, length is less than 38m (e.g. 37m)

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2 years ago

Answer this and your a legend

ivanzaharov [21]

Answer:

1 = 1 liter

2 = 1 kiloleter

3 = 1 quart

4 = 1 pint

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Step-by-step explanation:

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2 years ago