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Readme [11.4K]
3 years ago
8

Lin has picked 1 ½ cups of raspberries, which is enough for ¾ of a cake. How many cups does she need for the whole cake?

Mathematics
1 answer:
Llana [10]3 years ago
6 0
Okay. So, based off of that, if you divide 1 1/2 (3/2) by 3/4, 3/2 * 4/3 is 12/6 or 2. 1/2 cups of raspberries is needed for each fourth of the cake. 1/2 * 4 = 2. Lin will need 2 cups of raspberries for the whole cake.
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The outer and inner triangles are both equilateral and the circle touches all three sides of the outer triangle. If the area of
Brrunno [24]

Answer:

The area of outer Δ = 40 cm²

Step-by-step explanation:

∵ Area of the small triangle = 10 cm²

If we join the center of the circle with the 3 vertices of the inner Δ

These 3 segments are the radii of the circle

Now the inner triangle has 3 isosceles Δ their sides are r , r and s1 with vertex angle 120° ⇒ (360° ÷ 3 = 120°)

Where r is the radius of the circle and s1 is the side of the inner triangle

<em>By using cosine rule</em>

(s1)² = r² + r² - 2r²cos120 = r² + r² - 2r² (-0.5) = r² + r² + r² = 3r²

∴ s1 = r√3

∵ The radius of the circle ⊥ to the side of the outer Δ because the side of the outer Δ is a tangent to the circle

If we join a vertex of the outer Δ with the center of the circle

We will have a right angle triangle of two legs r and half s2 with angle 60° (120° ÷ 2 )between them ⇒ s2 is the side of outer Δ

∴ tan 60° = 1/2 (s2) ÷ r ⇒ √3 = 1/2 (s2) ÷ r = (s2)/2r

∴ s2 = 2r√3

∴ s2 : s1 = 2r√3 ÷ r√3 = 2 : 1

∴ The side of the outer Δ is double the side of the inner Δ

<em>By using similarity ratio</em>

A2/A1 = (s2/s1)² ⇒ A2 and A1 are the areas of outer and inner triangles

∴ A2 : A1 = (2/1)² = 4/1  

∴ A2 = 4 A1

∴ A2 = 4 × 10 = 40 cm²

5 0
3 years ago
PLZ
g100num [7]

Answer:

21 pairs of socks

Step-by-step explanation:

We can find out how much money Chang has to spend on socks by subtracting the price of sneakers from his total money to spend by solving 160 - 95. From that, we get our answer of $65 that Chang has to spend on socks. We can divide 65 by 3 to see how many pairs of socks he can buy and we get our answer of 21 pairs of socks.

(sorry if it's confusing but I hope it helped anyway)

8 0
2 years ago
Read 2 more answers
In parallelogram LMNP if PQ=21 find QM.
Simora [160]

Answer:

QM = 21

Step-by-step explanation:

The diagonals of a parallelogram bisect each other, then

QM = PQ = 21

8 0
3 years ago
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KatRina [158]
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8 0
2 years ago
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Determine the intercepts of the line.
natulia [17]

Answer:

Find in Step by Step

Step-by-step explanation:

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y-intercept = 26/1 = 26.00000

Slope = 8.000/2.000 = 4.000

Equation at the end of step  1  :

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Step  2  :

Equation at the end of step  2  :

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Step  3  :

Equation of a Straight Line

3.1     Solve   y-4x-26  = 0

5 0
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