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2 years ago

Solve the equation.

Mathematics

1 answer:

maksim [4K]2 years ago

8 0

Answer:

x=-1

Step-by-step explanation:

3x+12-8x=19+2x (combine liked terms)

-5x+12+19=2x (move variable to the left-hand side and change its sign)

-5x-2x+12=19 (combine liked terms)

-7x=19-12 (divide both sides of the equation by -7)

x=-1

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Usha and Parker should not take another debt to their current situation because their debt to income ratio (DIR) has exceeded the Basic Qualified Mortgage DIR for the common benchmark. The qualified mortgage debt to income ratio is 43% and Usha and Parker debt to income ratio is 47.9%. Debt to income ratio is calculated by dividing total personal debt with net income.

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3 years ago

The equation of the function h is h... PLEASE HELP MATH

Oduvanchick [21]

Answer:

Part A) $h(4) -m(16)=-4$

Part B) The distance between the y-intercepts is equal to 4 units

Part C) The value of h(x) will always be greater than the value of m(x) for any value of x

Step-by-step explanation:

Part A) What is the value of h(4) -m(16)

we have

$h(x)=\frac{1}{2}(x-2)^2$

For x=4

$h(4)=\frac{1}{2}(4-2)^2=2$

Find the equation of the line m(x)

Find the slope

take the points

(8,2) and (12,4)

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{4-2}{12-8}$

$m=\frac{2}{4}$

$m=\frac{1}{2}$

Find the equation of the line in slope intercept form

$y=mx+b$

we have

$m=\frac{1}{2}$

$point\ (8,2)$

substitute

$2=\frac{1}{2}(8)+b$

solve for b

$b=-2$

$y=\frac{1}{2}x-2$

therefore

$m(x)=\frac{1}{2}x-2$

Find m(16)

$m(16)=\frac{1}{2}(16)-2=6$

$h(4) -m(16)=2-6=-4$

Part B) we know that

The y-intercept is the value of y when the value of x is equal to zero

Find the y-intercept of h(x)

For x=0

$h(0)=\frac{1}{2}(0-2)^2=2$

Find the y-intercept of m(x)

For x=0

$m(0)=\frac{1}{2}(0)-2=-2$

therefore

The distance between the y-intercepts is equal to 2-(-2)=4 units

Part C)

Graph both equations

$h(x)=\frac{1}{2}(x-2)^2$

$m(x)=\frac{1}{2}x-2$

using a graphing tool

see the attached figure

The value of h(x) will always be greater than the value of m(x) for any value of x

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3 years ago

What is the equation of the circle with center (0, 0) that passes through the point (–4, –6)?

eimsori [14]

Answer:

Option 4: x^2+y^2 = 52

Step-by-step explanation:

Given

Centre at origin

Point on circle = (-4, -6)

The distance between origin and point on circle will be the radius of the circle

So,

$r = \sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}\\r= \sqrt{(-4-0)^2+(-6-0)^2} \\r = \sqrt{(-4)^2+(-6)^2}\\r = \sqrt{16+36} \\r = \sqrt{52}$

As the center is at origin the standard equation will be:

$x^2+y^2 = r^2\\$

Putting the value of r

$x^2+y^2 = (\sqrt{52})^2\\x^2+y^2 = 52$

Hence, last option i.e. Option 4 is correct ..

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3 years ago

Use function notation to represent each statement:

Mashutka [201]

Answer:

f(1) = 257

Step-by-step explanation:

x-variable: 1 (time is the independent variable)

y-variable: 257 (number of visitors is the dependent variable)

When the time is at 1 (1pm), there are 257 visitors

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2 years ago

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3 years ago