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3 years ago

9

Find a rational number halfway in between 1/2 and 4/9

1 answer:

Valentin [98]3 years ago

7 0

Required number = 1/2 (2/7 + 3/4) = 1/2 ((8 + 21)/28) = {1/2 × 29/28) = 29/56 Hence, 29/56 is a rational number lying halfway between 2/7 and 3/4.

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Line E passes through the points (2, 3) and (4, -3). What is the slope of a line perpendicular to line E?

lilavasa [31]

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ 2 &,& 3~) 
% (c,d)
&&(~ 4 &,& -3~)
\end{array}
\\\\\\
% slope = m
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-3-3}{4-2}\implies \cfrac{-6}{2}\implies \cfrac{-3}{1}$

now, a line perpendicular to that one, will have a "negative reciprocal" slope, thus

$\bf \textit{perpendicular, negative-reciprocal slope for}\quad \cfrac{-3}{1}\\\\
negative\implies +\cfrac{3}{ 1}\qquad reciprocal\implies +\cfrac{ 1}{3}\implies \cfrac{1}{3}$

7 0

3 years ago

Find the solutions of the quadratic equation 14x^2+9x+10=014x

Vesnalui [34]

Answer:

Option B. $x=-\frac{9}{28}(+/-)\frac{\sqrt{479}}{28}i$

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$14x^{2}+9x+10=0$

so

$a=14\\b=9\\c=10$

substitute in the formula

$x=\frac{-9(+/-)\sqrt{9^{2}-4(14)(10)}} {2(14)}$

$x=\frac{-9(+/-)\sqrt{-479}} {28}$

Remember that

$i=\sqrt{-1}$

substitute

$x=\frac{-9(+/-)\sqrt{479}i} {28}$

$x=-\frac{9}{28}(+/-)\frac{\sqrt{479}}{28}i$

5 0

3 years ago

A group of students are asked to evaluate their teacher mid-quarter

Umnica [9.8K]

Answer: perceived lack of anonymity

Step-by-step explanation:

The source of bias that occurs when a group of students are asked to evaluate their teacher mid-quarter is a perceived lack of anonymity.

Perceived lack of anonymity occurs when the responder is afraid that if he or she gives an honest answer, it can end up affecting them negatively.

In this case, the students may be afraid that giving an honest opinion on the teacher will affect them.

7 0

3 years ago

What is the integral of -3x^3

Sati [7]

$\int -3x^3\, dx=-3\int x^3 \, dx=-3\cdot\dfrac{x^4}{4}+C=\dfrac{3x^4}{4}+C$

6 0

4 years ago

In your opinion, which is better. Pancakes, or waffels?

Luda [366]

Buttermilk waffles:)

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3 years ago