The concession stand at the local high school sells pretzels and lemonade. The total cost of two pretzels and a lemonade is $5.75. The total cost of two lemonades is $0.25 more than the cost of a pretzel. What is the cost of a pretzel?

Answers

Answer 1

Answer: $2.35

Working
Let p represent the cost of pretzels and L the cost of a lemonade.
From the second paragraph,
2p+ L= 5.75

From the equation above, the cost of a pretzel p can be expressed as:
2p= 5.75 - L
p= 5.75/2 - l/2
The cost of two lemonades exceeds that of a pretzel by 0.25:
2 L= 5.75/2 -L/2+0.25

Solving this gives:
L=1.05

Then replace the value of L in p= 5.75/2 - L/2
This gives the value of a pretzel.

Answer 2

Answer:

Final answer:

By using a system of equations, we can find that the cost of a pretzel is approximately $1.83.

Explanation:

This question can be solved using a system of linear equations. Let's define P as the cost of a pretzel and L as the cost of lemonade. So from the problem, we have 2 equations: 2P + L=$5.75 and L= P + $0.25.

Now, we can substitute the equation for L into the first equation to get: 2P + (P + $0.25) = $5.75, which simplifies to 3P + $0.25 = $5.75. Subtracting $0.25 from both sides gives 3P = $5.50. Dividing by 3 will then give the cost of a pretzel, so P = $5.50/3 = $1.83.

Learn more about System of Equations here:

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What is the perimeter of polygon ABCD?

Answers

Answer:

The perimeter is the sum of the length of the sides of a certain shape. In this case, the perimeter of the polygon would be the sum of the lengths of sides AB, BC, CD, and DA.

Step-by-step explanation:

Lets start computing the length of each side of the polygon. Using points A and B as a first example, we find that the distance between them will be:

$d_(AB)=√((x_A - x_B) ^2+(y_A - y_B) ^2 )$

Where $(x_A , y_A )$ and $(x_B , y_B )$ are the coordinates of points A and B respectively.

From the graph we can see that point A has coordinates (5, 12), B has coordinates (9, 9), C has coordinates (12, 5), and D has coordinates (0, 0). Puting values and computing the lengths we find that:

Lenght AB:

$d_(AB)=√((x_A - x_B) ^2+(y_A - y_B) ^2)=√((5 - 9) ^2+(12 - 9) ^2)$

$d_(AB)=√((-4) ^2+(3) ^2 ) =√(16 + 9 )=√(25)$

$d_(AB)=5$

Lenght BC:

$d_(BC)= √((x_B - x_C) ^2 + (y_B - y_C) ^2 ) = √((9 - 12) ^2 + (9 - 5) ^2 )$

$d_(BC)=√((-3) ^2 + (4) ^2 )=√(9 + 16 ) =√(25)$

$d_(BC)=5$

Lenght CD:

$d_(CD)= √((x_C - x_D) ^2 + (y_C - y_D) ^2 ) = √((12 - 0) ^2 + (5 - 0) ^2 )$

$d_(CD)=√((12) ^2 + (5) ^2 ) = √(144 + 25 ) = √(169)$

$d_(CD)=13$

Lenght DA:

$d_(DA)= √((x_D - x_A) ^2 + (y_D - y_A) ^2 ) = √((0 - 5) ^2 + (0 - 12) ^2 )$

$d_(DA)=√((-4) ^2 + (-12) ^2 ) = √(25 + 144 ) = √(169)$

$d_(DA)=13$

Therefor the result will be:

$Perimeter = d_(AB) + d_(BC) +d_(CD) +d_(DA)= 5 + 5 + 13 + 13 = 36$

Answer: 36 lol

Step-by-step explanation:

What is 30% as a fraction

Answers

= 30%

= 0.3

= 3/10

Hope this helps.

$\boxed{30\% = (3\not0)/(10\not0)= (3)/(10)=0.3 }$

Determine the exact value of k so that the quadratic function f(x) = x2 - kx + 5 has only one zero.

Answers

$f(x)=ax^2+bx+c\n\n\Delta=b^2-4ac\n\nif\ \Delta < 0-no\ zeros\nif\ \Delta=0-one\ zero\nif\ \Delta > 0-two\ zeros$

$f(x)=x^2-kx+5=0\n\na=1;\ b=-k;\ c=5\n\n\Delta=(-k)^2-4\cdot1\cdot5=k^2-20\n\none\ zero\ if\ \Delta=0\n\ntherefore\nk^2-20=0\ \ \ \ |add\ 20\ to\ both\ sides\n\nk^2=20\n\nk=\pm√(20)\n\nk=\pm√(4\cdot5)\n\n\boxed{k=-2\sqrt5\ or\ k=2\sqrt5}$

I like this question. When we factorise this question the brackets have to be identical.
5 has to be square rooted to become √5. From, FOIL we know that the last digit is times by the other last digit to find the 5, as our brackets are identical this number is the same. The square root of 5.
This number is doubled in identical brackets to find the middle number. so it is 2√5. As there is a minus number there the brackets are: (x-√5)(x-√5). Multiplying this out gives us: x²-2√5 x+5. k=2√5 (or -2√5, depending on if the minus is counted or not)

Question 71 pts
Bobby ran 1 lap around the track in 52.36 seconds. Jessie ran a lap in 49.4 seconds. How many
seconds faster was Jessie's lap?
O 29.6 seconds
O 0.296 seconds
4.742 seconds
O 2.96 seconds

Answers

Answer:

0.296

Step-by-step explanation:

I’ll mark brainliest! Pls helpp

Answers

Answer:

60 yds

Step-by-step explanation:

10 + 15 + 4 + (10 - 4) + 20 + (20 - 15) = 60

Answer: 60 Yards

In this model, we have all sides except for two. In order to find the perimeter of this, you would need all sides.

To find the missing sides you can see that the lenght of the side on the left is 10 yards. And the entire right side is equal to that left side. So, to find the missing side x you would need to solve: x+10-4. So, x is 6.

Do the same for the top and bottom to get the other missing side that is perpendicular to the side that is 4 yards is 5 yards.

Now that you have the lengths of all of the sides, you can solve for the perimeter. You would do,

$15+4+6+20+10+5=60$

Please mark brainliest if correct :)

A line includes the points (2, 10) and (1, 0). What is its equation in slope-intercept form?

Answers

Answer:

y=10x-10

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