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3 years ago

I need help with 9 and 10

Mathematics

1 answer:

Evgen [1.6K]3 years ago

6 0

#9 is
32divided(10-8)divided2-3

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the ages of sari and justin can be represented as two consecutive integers. The product of their age is 72. Justin is older. wri

Lelechka [254]

The age of Sari is 8 years.

The age of Justin is 9 years.

Explanation:

Let x denote the age of Justin.

Let y denote the age of Sari.

Given that the product of their age is 72.

Thus, it can be written in equation as

$xy=72$

Since, the numbers x and y are consecutive integers and Justin is older, then, it can be written as,

$x=y+1$

Therefore, the two equations are $xy=72$ and $x=y+1$

<u>The ages of Sari and Justin:</u>

The ages of Sari and Justin can be determined by solving the two equations.

Let us solve the equations using substitution method.

Substituting $x=y+1$ in the equation $xy=72$ , we have;

$(y+1)y=72$

$y^2+y=72$

$y^2+y-72=0$

Factoring the equation, we get;

$(y-8)(y+9)=0$

$y=8 \ or \ y=-9$

The value of y cannot be negative.

Thus, $y=8$ is the value of y.

Substituting $y=8$ in the equation $x=y+1$ , we have;

$x=8+1$

$x=9$

Thus, the value of x is 9.

Therefore, the age of Sari is 8 years and the age of Justin is 9 years.

5 0

3 years ago

2. 10 caiete costă 20 lei. Câţi lei costă 7 caiete de acelaşi fel?

lutik1710 [3]

Answer:

Tu vorbesti limba romana! Este foarte cool! Nu am întâlnit niciodată pe cineva care să vorbească română

Step-by-step explanation:

4 0

3 years ago

Write an equation (a) in slope intercept form and (b) in standard form for the line passing through (1,9) and perpendicular to 3

maxonik [38]

Answer:

$\large\boxed{a)\ y=\dfrac{5}{3}x+\dfrac{22}{3}}\\\boxed{b)\ 5x-3y=-22}$

Step-by-step explanation:

$\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\m-slope\\b-y-intercept\\\\\text{Let}\ k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\=========================\\\\\text{We have the equation of a line in the standard form.}\\\text{Convert it to the slope-intercept form.}\\\\3x+5y=1\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\5y=-3x+1\qquad\text{divide both sides bvy 5}\\\\y=-\dfrac{3}{5}x+\dfrac{1}{5}\to m_1=-\dfrac{3}{5}$

$a)\\\\y=m_2x+b\\\\m_1=-\dfrac{3}{5}\to m_2=-\dfrac{1}{-\frac{3}{5}}=\dfrac{5}{3}\\\\\text{Put the value of slope and the coordinates of the given point (1, 9)}\\\text{to the equation of a line:}\\\\9=\dfrac{5}{3}(1)+b\\\\9=\dfrac{5}{3}+b\qquad\text{subtract}\ \dfrac{5}{3}\ \text{from both sides}\\\\\dfrac{27}{3}-\dfrac{5}{3}=b\\\\\dfrac{22}{3}=b\\\\\text{Finally:}\\\\y=\dfrac{5}{3}x+\dfrac{22}{3}$

$b)\\\\\text{The standard form of an equation of a line:}\\\\Ax+By=C\\\\\text{Convert the equation}\ y=\dfrac{5}{3}x+\dfrac{22}{3}\ \text{to the standard form:}\\\\y=\dfrac{5}{3}x+\dfrac{22}{3}\qquad\text{multiply both sides by 3}\\\\3y=5x+22\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\-5x+3y=22\qquad\text{change the signs}\\\\5x-3y=-22$