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Bingel [31]
3 years ago
6

Solve this system of equations: 5x + y = 7 20x + 2 = y

Mathematics
1 answer:
xz_007 [3.2K]3 years ago
7 0

Answer:

x = 1/5, y = 6

Step-by-step explanation:

5x + y = 7

y = 7 - 5x

Set equations equal to each other to eliminate y

7 - 5x = 20x + 2

7 = 25x + 2

5 = 25x

x = 1/5

y = 7 - 5(1/5)

y = 7 - 1

y = 6

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r = £6.00

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£35 = 4(£6.00) + x(£2.15)
£35 = £24 + £2.15x
£11 = £2.15x
x = 5.12

Since she can buy 5.12 packets of pencils, it is equal to 5 packets of pencils.
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2 years ago
The sides of this rectangle are
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The longer side is at first 7cm and the shorter is 2cm.

So since 7cm(the longer side)×5=35cm then the shorter side(2cm) multiplied by 5 should give you the right answer.
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3 years ago
The graph shows the volume (y) of a cup of water (in ml). The cup has a small leak and the volume of water is decreasing at a co
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Answer:

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Step-by-step explanation:

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5 0
3 years ago
Find the equation of the line using the point-slope formula. Write the final equation using slope-intercept form. Perpendicular
polet [3.4K]

Answer:

<u>Slope-intercept form</u>: y = -5x - 8

<u>Point-slope form</u>:  y - 2 = -5(x + 2)

Step-by-step explanation:

Given the equation, 5y = x - 4, which passes through point (-2, 2):

Transform the given equation into its <u>slope-intercept form</u>, y = mx + b.

In order to do so, divide both sides by 5 to isolate y:

5y = x - 4

\displaystyle\mathsf{\frac{5y}{5}\:=\:\frac{1x\:-\:4}{5}}

\displaystyle\mathsf{y\:=\:\frac{1}{5}x\:-\:\frac{4}{5}}  ⇒  This is the slope-intercept form of 5y = x - 4.

Next, we must determine the equation of the line that is perpendicular to \displaystyle\mathsf{y\:=\:\frac{1}{5}x\:-\:\frac{4}{5}}.    

<h2>Definition of Perpendicular Lines:</h2>

<u>Perpendicular lines</u> have <em>negative reciprocal</em> slopes.  This means that if we multiply the slopes of two lines, their product will equal to -1.  

In other words, if the slope of the given equation is m₁, and the slope of the other line perpendicular to the given linear equation is m₂, then:  m₁ × m₂ = -1.

  • Slope of the given equation: m₁ = ⅕
  • \displaystyle\mathsf{Slope\:of\:other\:line\:(m_2 )\:=\:-5\:or\:-\frac{5}{1}}

If we multiply these two slopes:

  • m₁ × m₂ = -1
  • \displaystyle\mathsf{m_1\:\times\\\:m_2\:=\:\frac{1}{5}\times\\-\frac{5}{1}\:=\:-1}

Now that we have identified the slope of the other line that is perpendicular to  5y = x - 4, we must determine the y-intercept of the <u>other line</u>.  

  • The <u>y-intercept</u> is the point on the graph where it crosses the y-axis, for which it is the value of "y" when its corresponding x-coordinate equals to zero (0).
  • Thus, the standard coordinates of the y-intercept is (0, <em>b</em>), for which its y-coordinate is the value of "<em>b</em>" in the slope-intercept form, y = mx + b.

Using the <u>slope</u> of the other line, m₂ = -5, and the given point, (-2, 2), substitute these values into the slope-intercept form to find the value of the y-intercept, <em>b</em>:

y = mx + b

2 = -5(-2) + b

2 = 10 + b

Subtract 10 from both sides to isolate b:

2 - 10 = 10 - 10 + b

-8 = b

The equation of the other line that is perpendicular to 5y = x - 4 is:

Linear Equation that is perpendicular to 5y = x - 4 in slope-intercept form:  

<h3>⇒   y = -5x - 8 </h3>

<h2>Rewrite the Equation in Point-slope Form:</h2>

The <u>point-slope form</u> is: y - y₁ = m(x - x₁)

In order to rewrite y = -5x - 8 in its point-slope form, we must substitute the value of the given point, (-2, 2) into the point-slope form:

y - y₁ = m(x - x₁)

y - 2 = -5[x - (-2)]

y - 2 = -5(x + 2) ⇒  This is the <u>point-slope form</u> of the line that is perpendicular to 5y = x - 4.

6 0
2 years ago
The volume of a rectangular prism is (x3 – 3x2 5x – 3), and the area of its base is (x2 – 2). If the volume of a rectangular pri
34kurt

To solve the problem we will put the values given to us in the formula of volume of a prism.

<h2>Prism</h2>

A prism is a 3d shape whose two sides are the base sides which are polygon, with the other faces as parallelograms.

The height of the prism is \dfrac{(x^3-3x^2+5x-3)}{(x^2-2)}.

<h2>Explanation</h2>

Given to us

  • volume of a rectangular prism = (x3 – 3x2 5x – 3),
  • area of its base = (x2 – 2)
  • the volume of a rectangular prism is the product of its base area and height,

As given  to us,

\rm{ Volume\ of\ prism = Area\ of\ base \times Height

\rm{ Height=\dfrac{Volume\ of\ prism}{Area\ of\ base}

Substituting the values we get,

\rm{ Height=\dfrac{(x^3-3x^2+5x-3)}{(x^2-2)}

Hence, the height of the prism is \dfrac{(x^3-3x^2+5x-3)}{(x^2-2)}.

Learn more about Volume of Prism:

brainly.com/question/1578538

5 0
2 years ago
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