Mathematics, 07.01.2020 07:31, ginocousins06

It takes 1/2 cups of sugar to make 3/8 gallons of sweet tea. if the recipe is for 1 gallon of sweat tea, how much sugar is needed to make triple the recipe?
a) 2 cups of sugar
b) 3 cups of sugar
c) 4 cups of sugar
d) 6 cups of sugar

Answers: 1

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answered: Mangolinux7173

Option C

4 cups of sugar is needed

Solution:

Given that It takes 1/2 cups of sugar to make 3/8 gallons of sweet tea

cups of sugar = $\frac{1}{2}$

gallons of sweet tea = $\frac{3}{8}$

If the recipe is for 1 gallon of sweat tea, then the cups of sugar needed is given as:

$\frac{3}{8} \text{ gallons of sweet tea } = \frac{1}{2} \text{ cups of sugar }$

$1 \text{ gallon of tea } = x \text{ cups of sugar }$

On cross-multiplying we get,

$1 \times \frac{1}{2} = x \times \frac{3}{8}\\\\x = \frac{1}{2} \times \frac{8}{3}\\\\x = \frac{4}{3}$

So to make triple the receipe, quantity of sugar needed is:

so the receipe is for 3 gallon of sweet tea, then sugar needed is:

$\rightarrow \frac{4}{3} \times 3 = 4$

Thus 4 cups of sugar is needed

answered: Guest

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

answered: Guest

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

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It takes 1/2 cups of sugar to make 3/8 gallons of sweet tea. if the recipe is for 1 gallon of sweat...