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3 years ago

A first number plus twice a second number is 4. Twice the first number plus the second totals 20. Find the numbers

Mathematics

1 answer:

pychu [463]3 years ago

4 0

Answer:

The first number is 6

The second number is -1

6+(-2)=4

6*2=12 12+(-1)=11

Step-by-step explanation:

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282.74

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4 years ago

Write an equation for the perpendicular bisector of the line segment joining the two points.

Leona [35]

Points (1, 7) and (-3, 2)

Slope for a line between (x₁, y₁) and (x₂, y₂) , m = (y₂ -y₁) / (x₂- x₁)

The slope for the line joining the two points = (2 - 7) / (-3 - 1) = -5/-4

Slope = 5/4

Hence the perpendicular bisector would have a slope of -1/(5/4) = -4/5

By condition of perpendicularity

For points (1, 7) and (-3, 2),

Formula for midpoints for (x₁, y₁) and (x₂, y₂) is ((x₁ +x₂)/2 , (y₁+ y₂)/2)

Midpoint for (1, 7) and (-3, 2) = ((1+ -3)/2 , (7+2)/2) = (-2/2, 9/2)

= (-1, 9/2)

Since the slope of perpendicular bisector is -4/5 and passes through the midpoint (-1, 9/2)

Equation y - y₁ = m (x - x₁)

y - 9/2 = (-4/5) (x - -1)

y - 9/2 = (-4/5)(x + 1)

   5(y - 9/2) = -4(x + 1)

   5y - 45/2 = -4x - 4

   5y = -4x - 4 + 45/2

5y + 4x = 45/2 - 4

5y + 4x = 22 1/2 - 4 = 18 1/2

5y + 4x = 37/2

10y + 8x = 37

The equation of the line to perpendicular bisector is 10y + 8x = 37

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4 years ago

George drew a line on a coordinate system by starting at (0,-5), then moved 2 units to the right and 1 unit up to locate each ne

faltersainse [42]

Answer:

y = 1/2x - 5

Step-by-step explanation:

I'm going to use slope-intercept form. Your y-intercept is already shown when x is zero, which is (0,-5). Your slope is defined as rise over run, so 1/2 in this case. This gives you an equation of f(x) = 1/2x-5

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3 years ago

Find the equation of the exponential function, in y=a(b)^x form that passes through the points (-2,3) and (6,35). Round both a a

Lesechka [4]

I supose your function is: $y(x)=a \cdot b^x$

Step 1. Replace the coordinates of the first point in your equation:
x=-2, y=3

$3=a \cdot b^{-2}$

Solve the equation for "a":
$a=3 \cdot b^2$

Step 2. Replace the coordinates of the second point in your equation:
x=6, y=35

$35 = a \cdot b^6$

Replace the value of "a" from Step 1.
$35 = 3 \cdot b^2 \cdot b^6$
Calculate "b":
$b= \sqrt[8]{\frac{35}{3}} = 1.359466$

Step 3. Replace "b" in first equation and calculate "a":
$a=3 \cdot b^2=5.5444434$

The equation is:
$y(x)=5.54 \cdot 1.36^x$

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4 years ago