How many triangles exist with the given side lengths?

12 in, 15 in, 18 in
A.
No triangle exists with the given side lengths.

B.
More than one unique triangle exists with the given side lengths.

C.
Exactly one unique triangle exists with the given side lengths.

Given is the Rate of each hamburger = 2.10 dollars each.

The number of hamburgers that we sell = 3 hamburgers.

Charges for all 3 hamburgers = 3 x 2.10 = 6.30 dollars.

Tax charged on these 3 hamburgers = 0.38 dollars.

Total Bill = Charges for 3 hamburgers + Tax

Total Bill = 6.30 + 0.38 = 6.68 dollars.

Customer paid = 10 dollars.

The amount to be returned to customer = Bill paid by customer - Total Bill charged = 10 - 6.68 = 3.32 dollars.

Hence, the customer would get a change of 3.32 dollars.

To solve the equation, we first distribute the 2 on the left, then collect like terms and finally isolate x. The solution to the equation 2(x + 3) = x + 10 is x = 4.

To solve the equation 2(x + 3) = x + 10, we will first distribute the 2 on the left-hand side of the equation to get 2x + 6. Therefore, the equation becomes: 2x + 6 = x + 10.

The next step is to collect like terms. To do this, we subtract x from both sides, which gives us: x + 6 = 10.

Finally, to solve for x, we subtract 6 from both sides of the equation: x = 4. Hence, the solution to the equation 2(x + 3) = x + 10 is x = 4.

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Final answer:

x = 4

Explanation:

To solve the equation 2(x + 3) = x + 10, we first expand the left side of the equation:

2 × x + 2 × 3 = x + 10

2x + 6 = x + 10

Now subtract x from both sides to move all x terms to one side:

2x - x + 6 = 10

1x + 6 = 10

Subtract 6 from both sides to solve for x:

x = 10 - 6

x = 4

Thus, the solution to the equation is x = 4. Checking the solution, we substitute x back into the original equation:

2(4 + 3) = 4 + 10

2(7) = 14

14 = 14

Final answer:

Using the Pythagorean theorem, it is determined that the ladder reaches 12 feet up the side of the house when the base is placed 5 feet away.

Explanation:

To solve for the height at which the ladder reaches the house, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle.

In this scenario, the ladder represents the hypotenuse (c), the distance from the base of the ladder to the house gives one leg of the triangle (a), and the height the ladder reaches up the side of the house is the other leg (b).

According to the Pythagorean theorem, a² + b² = c². Plugging in our known values allows us to solve for b²:

Therefore, the top of the ladder will be 12 feet above the ground.

The mass of the fruit is 74 grams and the mass of the yoghurt is 111 grams.

Given :

Solution :

Now to form a linear equation first let x be the mass in gram. Than total mass of the desert is given by:

[tex]3x+2x=185[/tex]

[tex]5x = 185[/tex]

[tex]x = \dfrac{185}{5}[/tex]

x = 37 grams

Therefore the mass of the fruit = [tex]2 \times 37[/tex] = 74 grams and the mass of the yoghurt = [tex]3\times 37[/tex] = 111 grams.

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Answer:

64

Step-by-step explanation:

took the test

It says that the recipe for 9 servings would require 3/4 cup milk.

He wants to prepare recipe for 6 servings. Let's assume it requires X cups milk.

Now we can use concept of proportions to solve this problem.

The proportion of X cups for 6 servings would be same as 3/4 cup milk for 9 servings. Mathematically, we can write it as follows :-

[tex] \frac{X \;cups \;milk}{6 \;servings} = \frac{\frac{3}{4} \;cups \;milk}{9 \;servings} \\\\
Or\; \frac{X \;cups \;milk}{\frac{3}{4} \;cups \;milk} = \frac{6 \;servings}{9 \;servings} \\\\
\frac{X }{\frac{3}{4} } = \frac{6 }{9 } \\\\
X = \frac{6}{9}*\frac{3}{4} \\\\
X = \frac{6*3}{9*4} \\\\
X = \frac{18}{36} \\\\
X = \frac{1}{2} \;cup \;milk [/tex]

Hence, we require [tex] \frac{1}{2} [/tex] cup milk for 6 servings.

Final answer:

Chantelle will cover 1.25 miles each hour of her hike.

Explanation:

To find out how many miles Chantelle will cover each hour of her trip, we need to divide the total distance of 82.5 miles by the total time of 8.25 hours per day for 8 days.

First, we calculate the total time of the trip by multiplying the hours per day (8.25) by the number of days (8): 8.25 hours/day x 8 days = 66 hours.

Next, we divide the total distance by the total time: 82.5 miles / 66 hours = 1.25 miles/hour.

Therefore, Chantelle will cover 1.25 miles each hour of her hike.

The correct answer is £166, £581.

To share £747 in the ratio of 2:7 between Tom and Ben.

Let's define the total parts: 2 + 7 = 9

Tom's share: [tex]\frac{2}{9} \times 747 = \frac{1494}{9} = £166[/tex]

Ben's share: [tex]\frac{7}{9} \times 747 = \frac{5229}{9} = £581[/tex]

Therefore, the calculation to share £747 in the ratio of 2:7 between Tom and Ben is:

[tex]\text{Tom's share} &= \frac{2}{9} \times 747 = \frac{1494}{9} = £166[/tex]..

[tex]\text{Ben's share} &= \frac{7}{9} \times 747 = \frac{5229}{9} = £581\end{aligned}[/tex]

Where Tom receives £166, and Ben receives £581.

If Joe walked 4/9 of a mile in 4/5 of an hour then the unit rate is  5/9 miles/hour.

A division is a process of splitting a specific amount into equal parts.

The distance walked by Joe is 4/9 of a mile.

The time taken by Joe to walk 4/9 of a mile is 4/5 of an hour.

We need to find the unit rate in miles per hour.

To find this we just need to divide 4/9 by 4/5.

Rate = Distance/Time

Distance = 4/9 miles

Time = 4/5 hour

Rate  = 4/9 ÷ 4/5

Rate = 4/9 × 5/4

Rate = 5/9 miles/hour.

Hence, if Joe walked 4/9 of a mile in 4/5 of an hour then the unit rate is  5/9 miles/hour.

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