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goldfiish [28.3K]

3 years ago

9

Jada has some pennies and dimes. The ratio of Jada's pennies to dimes is 2 to 3. From the information given, can you determine h

ow many coins Jada has? If Jada has 55 coins, how many of each kind of coin does she have?

1 answer:

Anuta_ua [19.1K]3 years ago

4 0

Answer:

No, we can't determine how many coins Jada has.

She will have 22 pennies and 33 dimes.

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Find the formula for an exponential function that passes through the two points give.

Ksenya-84 [330]

Answer:

$y=3(2)^{x}$

Step-by-step explanation:

Given.

Two points are given.

$(x, y)=(-1,\frac{3}{2})$ and $(x, y)=(3,24)$

An exponential function is in the general form.

$y=a(b)^{x}$ -------(1)

We know the points $(-1,\frac{3}{2})$ and $(3,24)$

put the first point value in equation 1

$\frac{3}{2}=a(b)^{-1}$

$\frac{3}{2}=\frac{a}{b}$

$a=\frac{3}{2}\times b$ --------(2)

put the second point value in equation 1

$24=a(b)^{3}$ ----------(3)

Put the a value from equation 2 to equation 3

$24=\frac{3}{2}\times b(b)^{3}$

$b^{3+1}=\frac{24\times 2}{3}$

$b^{4} = 16\\b=\sqrt[4]{16} \\b=2$

Put the b value in equation 2

$a=\frac{3}{2}\times 2$

$a=3$

Put the a and b value in equation 1

$y=3(2)^{x}$

So, the exponential function that passes through the points $(-1,\frac{3}{2})$ and $(3,24))$ are $y=3(2)^{x}$ .

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3 years ago

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Answer:

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Step-by-step explanation:

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Rounded to the nearest hundredth, what is the positive solution to the quadratic equation 0 = 2x2 + 3x – 8? Quadratic formula: x

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ANSWER

$x=1.39$ to the nearest hundredth.

EXPLANATION

We have the equation,

$0=2x^2+3x-8$

Which can be rewritten as

$2x^2+3x-8=0$

The question demands the use of the quadratic formula.

Comparing this to the general quadratic equation;

$ax^2+bx+c=0$

$a=2,b=3,c=-8$

The quadratic formula is given by;

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

We now substitute all the values in to the formula;

$x=\frac{-3\pm\sqrt{(3)^2-4(2)(-8)}}{2(2)}$

We simplify to obtain;

$x=\frac{-3\pm\sqrt{9+64}}{4}$

$x=\frac{-3\pm\sqrt{73}}{4}$

We now split the plus or minus sign to obtain;

$x=\frac{-3-\sqrt{73}}{4}$

This implies that;

$x=-2.89$

Or

$x=\frac{-3+\sqrt{73}}{4}$

This will evaluate to;

$x=1.39$

Hence, the positive solution rounded to the nearest hundredth is

$x \approx 1.39$

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