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Lubov Fominskaja [6]
1 year ago
7

Use substitution to solve the following system of equations. What is the value of y? {3x+2y=12{5x−y=7 A) y = -3B) y = 3C) y = -2

D) y = 2
Mathematics
1 answer:
Vlad [161]1 year ago
6 0

<em>Answer</em>

B) y = 3

<em>Step-by-step explanation</em>

Given the system of equations:

\begin{gathered} 3x+2y=12\text{ \lparen eq. 1\rparen} \\ 5x-y=7\text{ \lparen eq. 2\rparen} \end{gathered}

Isolating x from equation 1:

\begin{gathered} 3x+2y-2y=12-2y \\ 3x=12-2y \\ \frac{3x}{3}=\frac{12-2y}{3} \\ x=\frac{12}{3}-\frac{2}{3}y \\ x=4-\frac{2}{3}y\text{ \lparen eq. 3\rparen} \end{gathered}

Substituting equation 3 into equation 2 and solving for y:

\begin{gathered} 5(4-\frac{2}{3}y)-y=7 \\ 5\cdot4-5\cdot\frac{2}{3}y-y=7 \\ 20-\frac{10}{3}y-y=7 \\ 20-\frac{13}{3}y=7 \\ 20-\frac{13}{3}y-20=7-20 \\ -\frac{13}{3}y=-13 \\ (-\frac{3}{13})\cdot-\frac{13}{3}y=(-\frac{3}{13})\cdot-13 \\ y=3 \end{gathered}

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Step-by-step explanation:

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= (5x - 1) (x^2 + 4)

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The highway mileage m in miles per gallon for a compact car is approximated by m(s) = -0.025s2 + 2.45s - 30, where s is the spee
kozerog [31]
Highest mileage
m(s) = -0.025s2 + 2.45s - 30
This quadratic equation lokks like a upside down parabolla
So as it is a form of mileage gunction of speed, its maximum value should be K

The "a" in the vertex form "<span>y = a(x – h)2 + k</span>" of the quadratic is the same as the "a" in the common form of the quadratic equation, "<span>y = ax2 + bx + c</span><span>".
</span>

<span>To find the vertex, I look at the coefficients a<span>, </span>b<span>, and </span>c. The formula for the vertex gives me:<span>Y= -0.025s2 + 2.45s - 30
</span><span>h = <span>–b</span>/<span>2a</span> =  -2.45/2× -0.025=49</span><span>Put value of h to get K</span><span>k=-0.025(49)^2+2.45×(49)-30</span><span>k=  -30.025</span><span>k=  -</span>30.0<span>
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3 years ago
Find the exact value of cos a, given that sin a= 8/11 and
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Answer:

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Step-by-step explanation:

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7 0
3 years ago
A building 64 ft high casts a 288-ft shadow. Sarah casts a 18-ft shadow. The triangle formed by the building and its shadow is s
Anastaziya [24]

Answer:

The answer to your question is 4 ft

Step-by-step explanation:

Data

Building's shadow = 288 ft

Building's high = 64 ft

Sarah's shadow = 18 ft

Sarah's height = ?

Process

1.- Use proportions to solve this problem

                               \frac{Sarah's height}{Sarah's shadow} = \frac{building's height's}{building's shadow}

2.- Solve for Sarah's height

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3.- Substitution

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4.- Simplification

  Sarah's height = \frac{1152}{288}

5.- Result

  Sarah's height = 4 ft

5 0
3 years ago
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