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3 years ago

Solve for a 15=3(a+7)

Mathematics

2 answers:

saveliy_v [14]3 years ago

7 0

A=-2 is the correct answer

astraxan [27]3 years ago

5 0

Answer:

a = -2

Step-by-step explanation:

15 = 3(a+7)

15 = 3a + 21

-6 = 3a

a = -2

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What is the equation of the line that passes through (-2,3) and is parallel to 2x+3y=6?

Vsevolod [243]

Answer:

Step-by-step explanation:

$\bold{METHOD\ 1:}$

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

Let $k:y=m_1x+b_1,\ l:y=m_2x+b_2$

then

$l\ \parallel\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}$

We have the equation of a line:

$2x+3y=6$

Convert to the slope-intercept form:

$2x+3y=6$ subtract 2x from both sides

$3y=-2x+6$ divide both sides by 3

$y=-\dfrac{2}{3}x+2\to m_1=-\dfrac{2}{3}$

therefore the slope is $m_2=-\dfrac{2}{3}$

Put the value of the slope and the coordinates of the point (-2, 3) to the equation of a line:

$3=-\dfrac{2}{3}(-2)+b$

$3=\dfrac{4}{3}+b$ subtract 4/3 from both sides

$\dfrac{9}{3}-\dfrac{4}{3}=b\to b=\dfrac{5}{3}$

Finally:

$y=-\dfrac{2}{3}x+\dfrac{5}{3}$

Convert to the standard form (Ax + By = C):

$y=-\dfrac{2}{3}x+\dfrac{5}{3}$ multiply both sides by 3

$3y=-2x+5$ add 2x to both sides

$2x+3y=5$

$\bold{METHOD\ 2:}$

Let $k:A_1x+B_1y=C_1,\ l:A_2x+B_2y=C_2$ .

Lines k and l are parallel iff

$A_1=A_2\ \wedge\ B_1=B_2\to\dfrac{A_2}{A_1}=\dfrac{B_2}{B_1}$

We have the equation:

$2x+3y=6\to A_1=2,\ B_1=3$

then the equation of a line parallel to given lines has the equation:

$2x+3y=C$

Put the coordinates of the point (-2, 3) to the equation:

$C=2(-2)+3(3)\\\\C=-4+9\\\\C=5$

Finally:

$2x+3y=5$

4 0

3 years ago

The bowling team scores – 45

Sliva [168]

Answer:

7.5

Step-by-step explanation:

7 0

4 years ago

Solve the equation 4 sin (x +30°) = 2 for 0 < x < 365

tatuchka [14]

$4 \sin(x + 30) = 2 \\ \sin(x + 30 ) = \frac{2}{4} \\ \sin(x + 30) = \frac{1}{2} \\ \sin(x + 30) = \sin(30) \\ x + 30 = 30 \\ x = 30 - 30 \\ x = 0$

Hence, x = 0°, 180° and 360° Ans

3 0

3 years ago

Size Cost 4R = $0.25 per photo 5R = $0.50 Per photo 6R = $0.80 per photo A school ordered 308 photos of size 4R and some photos

lbvjy [14]

Answer:

0.25×308=$77

185-77=$108

108/0.50×1

=216photos

Total photos=216+308

=524photos

Step-by-step explanation:

3 0

3 years ago

Evaluate each expression

qwelly [4]

Step-by-step explanation:

a = 2
b = 3
c = 5

$\longrightarrow \rm{{\Bigg ( \dfrac{a}{b} \Bigg )}^c} \\ \\ \longrightarrow \rm{{\Bigg ( \dfrac{2}{3} \Bigg )}^5} \\ \\ \qquad \qquad \bigstar \: \boxed{ \bf{ \Bigg ({\frac{x}{y} \Bigg )}^{m} = \frac{ {x}^{m} }{ {y}^{m}} }} \\ \\ \longrightarrow \rm{ \frac{ {(2)}^{5} }{ {(3)}^{5} } } \\ \\ \longrightarrow \bf{ \frac{ 32 }{ 243} }$

Therefore, 32/243 is the answer.

3 0

3 years ago