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3 years ago

Using synthetic divison, what is the quotient of this expression? 2x^2+5x-7 over x-2

Mathematics

1 answer:

a_sh-v [17]3 years ago

7 0

Answer:

A. 2x + 9 + 11 over x - 2

Step-by-step explanation:

2x^2+5x-7 over x-2

divide - 2x^2 + 5x - 7 over x - 2 = 2x + 9x - 7 over x - 2

= 2x + 9x - 7 over x - 2

divide - 9x - 7 over x - 2 = 9 + 11 over x - 2

= 2x + 9 + 11 over x - 2

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Solve for x. 2/x =2/6

olganol [36]

The answer is x = 6.

Here are the steps.

1. Simplify 2/6 to 1/3 ( 2/x = 1/3 ).

2. Multiply both sides by x ( 2 = 1/3x ).

3. Simplify 1/3x to x/3 ( 2 = x/3 ).

4. Multiply both sides by 3 ( 2 * 3 = x ).

5. Simplify 2 * 3 to 6 ( 6 = x ).

Now finally switch it up and the answer is x = 6.

7 0

3 years ago

What are the domain and range of the algebraic function you found by graphing the equation y = 36 – 3x? Please hurry I'm being t

pychu [463]

Answer:

Domain $=(-\infty,\ \infty)$

Range $=(-\infty,\ \infty)$

Step-by-step explanation:

Domain : Domain of a function $f(x)$ is the set of all possible values of $x$ for which $f(x)$ exists.

Range : range of a function $f(x)$ is the set of all possible values of $f(x)$ .

Here $f(x)=36-3x$

$x$ can be any value from $-\infty$ to $\infty$ .

$\forall\ x=a\ there\ exists\ f(x)\ such\ that\ f(a)=36-3a$

hence possible value of $x$ can be any value between $-\infty$ and $\infty$

$domain =(-\infty,\ \infty)$

let $y=-f(x)$

$y=36-3x\\3x=36-y\\\\\\x=\frac{36-y}{3}\\$

so $\forall\ f(x)=y\ there\ exist\ x\ \in(-\infty,\ \infty)$ .

hence $f(x)$ can have any value between $-\infty\ to\ \infty.$ .

Range $=(-\infty,\ \infty)$

4 0

3 years ago

A survey was conducted to determine the average age at which college seniors hope to retire in a simple random sample of 101 sen

tatyana61 [14]

Answer:

96% confidence interval for desired retirement age of all college students is [54.30 , 55.70].

Step-by-step explanation:

We are given that a survey was conducted to determine the average age at which college seniors hope to retire in a simple random sample of 101 seniors, 55 was the average desired retirement age, with a standard deviation of 3.4 years.

Firstly, the Pivotal quantity for 96% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample average desired retirement age = 55 years

$\sigma$ = sample standard deviation = 3.4 years

n = sample of seniors = 101

$\mu$ = true mean retirement age of all college students

<em>Here for constructing 96% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.</em>

<u>So, 96% confidence interval for the population mean, </u> $\mu$ <u> is ;</u>

P(-2.114 < $t_1_0_0$ < 2.114) = 0.96 {As the critical value of t at 100 degree

of freedom are -2.114 & 2.114 with P = 2%}

P(-2.114 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.114) = 0.96

P( $-2.114 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.114 \times {\frac{s}{\sqrt{n} } }$ ) = 0.96

P( $\bar X-2.114 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.114 \times {\frac{s}{\sqrt{n} } }$ ) = 0.96

<u>96% confidence interval for</u> $\mu$ = [ $\bar X-2.114 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.114 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $55-2.114 \times {\frac{3.4}{\sqrt{101} } }$ , $55+2.114 \times {\frac{3.4}{\sqrt{101} } }$ ]

= [54.30 , 55.70]

Therefore, 96% confidence interval for desired retirement age of all college students is [54.30 , 55.70].

7 0

3 years ago

Find the <br> x-intercept and <br> y-intercept of the line.

vova2212 [387]

<h3><u>The x intercept is at (-7, 0).</u></h3><h3><u>The y intercept is at (0, 1).</u></h3>

To find both the x and the y intercept, we need to solve one at a time.

For the x intercept, we need to make the value of y equal to 0, and solve for x.

-x + 7y = 7

-x + 7(0) = 7

-x = 7

Multiply both sides by -1.

x = -7

The x intercept is -7.

Now for the y intercept.

-(0) + 7y = 7

7y = 7

Divide both sides by 1.

y = 1

The y intercept is at 0, 1.

5 0

3 years ago

Which congruence statements are true? Choose all answers that are correct?<br><br> A: B: C: D:

tester [92]

Answer:

Correct choices are A and C

Step-by-step explanation:

Inscribed angles property: The inscribed angles subtended by the same arc are equal.

1. Angles EFH and EGH are both inscribed angles subtended by the arc EH. Therefore, these angles are congruent (option A is true).

2. Angles GHF and GEF are both inscribed angles subtended by the arc GF. Therefore, these angles are congruent (option C is true).

3. Angles EGH and FHG are interior angles of the triangle KGH and can be congruent (if triangle is isosceles) or can be not congruent (in general). Thus, option B is false.

4. Angles EFH and FHG in general are not congruent. They can be congruent only when arcs EH and FG have the same measure. In general, option D is false.

4 0

3 years ago

Using synthetic divison, what is the quotient of this expression? 2x^2+5x-7 over x-2​

Using synthetic divison, what is the quotient of this expression? 2x^2+5x-7 over x-2