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3 years ago

Find the ratio a:b if it is givin that a/3 = b/4

Mathematics

1 answer:

wariber [46]3 years ago

3 0

Answer:

Step-by-step explanation:

Cross multiply the givens

3b = 4a Divide both sides by 4

3b/4 = a Now divide by b

3/4 = a/b

This can be written as

3:4 :: a:b

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Six students collect buttons for a project. The students have 10, 14, 15, 12, 13, and 14 buttons. They divide the buttons evenly

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Lina20 [59]

Option D: Two irrational solutions

Explanation:

The equation is $17+3 x^{2}=6 x$

Subtracting 6x from both sides, we have,

$3x^{2} -6x+17=0$

Solving the equation using quadratic formula,

$x=\frac{6 \pm \sqrt{36-4(3)(17)}}{2(3)}$

Simplifying the expression, we get,

$\begin{aligned}x &=\frac{6 \pm \sqrt{36-204}}{6} \\&=\frac{6 \pm \sqrt{-168}}{6} \\&=\frac{6 \pm 2 i \sqrt{42}}{6}\end{aligned}$

Taking out the common terms and simplifying, we have,

$\begin{aligned}x &=\frac{2(3 \pm i \sqrt{42})}{6} \\&=\frac{(3 \pm i \sqrt{42})}{3}\end{aligned}$

Dividing by 3, we get,

$x=1+i \sqrt{\frac{14}{3}}, x=1-i \sqrt{\frac{14}{3}}$

Hence, the equation has two irrational solutions.

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3 years ago

The triangles below are similar. Find x showing the proportion and all work.

zavuch27 [327]

we are given that

two triangles are similar

so, the ratio of their sides must be same

we get

$\frac{2}{6} =\frac{x}{x+2}$

now, we can solve for x

step-1: Cross multiply both sides

$2(x+2) =6x$

step-2: Simplify left side

$2x +4 =6x$

step-3: Subtract both sides by 2x

$2x +4-2x =6x-2x$

$4 =4x$

step-4: Divide both sides by 4

$x=1$

so,

$x=1$ ............Answer

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4 years ago