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3 years ago

Find domain of gg(x)=x+5/2x^2-x-3

1 answer:

3 0

$g(x)=\frac{x+5}{2x^2-x-3}\\\\D_g:\\2x^2-x-3\neq0\\\\2x^2+2x-3x-3\neq0\\\\2x(x+1)-3(x+1)\neq0\\\\(x+1)(2x-3)\neq0\iff x+1\neq0\ \wedge\ 2x-3\neq0\\\\x\neq-1\ \wedge\ x\neq1.5\\\\D_g:x\in\mathbb{R}\ \backslash\ \{-1;\ 1.5\}$

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in math class,26 students passed the quiz and 8 did not pass. what is the ratio of students who passed the test total students.

erastovalidia [21]

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3 years ago

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Vedmedyk [2.9K]

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Step-by-step explanation:

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3 years ago

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Two ships set sail in different directions from the same place. Tyler's ship sail 35 miles while Noah's ship sails for 42 miles.

earnstyle [38]

Answer:

The angle between their paths when they started is 93°.

Step-by-step explanation:

The Law of Cosines

It relates the length of the sides of a triangle with one of its internal angles.

Let a,b, and c be the length of the sides of a given triangle, and x the included angle between sides a and b, then the following relation applies:

$c^2=a^2+b^2-2ab\cos x$

When the two ships travel in different directions from the same point in the plane, they form an angle we called x in the image below.

Tyler's ship sails a=35 miles and Noah's ship sails for b=42 miles. At some time they are c=56 miles apart.

Since we know the values of all three side lengths, we solve the equation for x:

$\displaystyle \cos x=\frac{a^2+b^2-c^2}{2ab}$

Substituting values:

$\displaystyle \cos x=\frac{35^2+42^2-56^2}{2(35)(42)}$

Calculating:

$\displaystyle \cos x=-\frac{147}{2940}=-\frac{1}{20}$

Computing the inverse cosine:

$x = \arccos(-0.05)$

$x \approx 93^\circ$

The angle between their paths when they started is 93°.

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3 years ago

The percentage of pepperoni in a pizza is 35.67%. What is 35.67% rounded to the nearest whole percent?

Inessa05 [86]

36% because 65 is nearer to the whole number

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4 years ago

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Julio is training for a swimming race. The first part of his training schedule is shown. Session 1 2 3 456 Swimming distance (mi

Volgvan

An arithmetic sequence is a sequence in which the difference between each consecutive term remains same (constant).

The explicit formula for an arithmetic sequence is $A_n=a+(n-1)d$ , where a is first term of sequence, d is the common difference between consecutive terms.

A) We can see from Julio's swimming distance that it is in arithmetic sequence as after every successive training session Julio's swimming distance increased by 0.30 miles.

$0.55-0.25=0.30$

$0.85-0.55=0.30$

$1.75-1.45=0.30$

Therefore, we can see that Julio's training schedule is an arithmetic sequence.

B) Let us find Julio will take how many days to swim 2.95 miles by using explicit formula.

$A_n=a+(n-1)d$

Let us substitute our given information in above formula.

$2.95=0.25+(n-1)0.30$

$2.95=+0.25+0.30n-0.30$

$2.95=0.30n-0.05$

$2.95+0.05=0.30n$

$3.00=0.30n$

$n=\frac{3.00}{0.30}=10$

We are told that Julio swims every two days, this implies that he would swim on alternate days. So he will swim 2.95 miles on 10*2 =20th day.

Let us find 20th day will be which day. As Julio started his training schedule on Tuesday, 20th day will be a Sunday. Therefore, Julio will swim for 2.95 miles on a Sunday.

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3 years ago