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2 years ago

The graph box linear function f passes through the point (1, -9) and has a slope of 3

Mathematics

1 answer:

Marat540 [252]2 years ago

3 0

9514 1404 393

Answer:

C) 4

Step-by-step explanation:

The point-slope equation of the line is ...

y -k = m(x -h) . . . . . line with slope m through point (h, k)

y +9 = 3(x -1) . . . . . line with slope 3 through point (1, -9)

For y=0 (the 0 of the function), we have ...

9 = 3(x -1)

3 = x -1

4 = x

The x-intercept is (4, 0).

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Simplify the expression.

melamori03 [73]

The answer is C. Hope this helps

7 0

3 years ago

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A long jumper lifts off 3 m after starting his run, and lands 6 m later. When he is 8 m from the start line, he is 5 cm above an

slega [8]

Answer:

The equation of the parabola that models the path of the long jumper through the air is $y = -x^{2}+12\cdot x -27$ .

Step-by-step explanation:

Mathematically, we know that parabolas are second-order polynomials and every second-order polynomials, also known as quadratic functions, can be constructed by knowing three different points of the curve. The standard form of the parabola is:

$y = a\cdot x^{2}+b\cdot x + c$

Where:

$x$ - Horizontal distance from the start line, measured in meters.

$y$ - Height of the long jumper, measured in meters.

$a$ , $b$ , $c$ - Polynomial constants, measured in $\frac{1}{m}$ , dimensionless and meters, respectively.

If we know that $(x_{1},y_{1}) = (3\,m, 0\,m)$ , $(x_{2},y_{2}) = (8\,m, 0.05\,m)$ and $(x_{3}, y_{3}) = (9\,m, 0\,m)$ , this system of linear equations is presented below:

$9\cdot a + 3\cdot b + c = 0$ (Eq. 1)

$81\cdot a + 9\cdot b + c = 0$ (Eq. 2)

$64\cdot a + 8\cdot b + c = 0.05$ (Eq. 3)

The coefficients of the polynomial are, respectively:

$a = -\frac{1}{100}$ , $b = \frac{3}{25}$ , $c = -\frac{27}{100}$

The equation of the parabola that models the path of the long jumper through the air is $y' = -\frac{1}{100}\cdot x^{2}+\frac{3}{25}\cdot x -\frac{27}{100}$ .

But we need $y$ measured in centimeters, then, we use the following conversion:

$y = 100\cdot y'$

Then, we get that:

$y = -x^{2}+12\cdot x -27$

Where $x$ and $y$ are measured in meters and centimeters, respectively.

The equation of the parabola that models the path of the long jumper through the air is $y = -x^{2}+12\cdot x -27$ .

4 0

3 years ago

Miss Smith save 5% on her recent Starbucks order because she is a Starbucks Rewards member if the cost of per purchase before th

Dima020 [189]

It would have been $5.48

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3 years ago

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Find two decimals that are equivalent to

mafiozo [28]

Answer:

(4*10)+(7*1/100)=40+7/100=40 7/100

Step-by-step explanation:

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3 years ago

An investor obtains a balloon mortgage with the terms shown below.

Flauer [41]

9514 1404 393

Answer:

a. $3,455.20

Step-by-step explanation:

The monthly payment is given by the amortization formula:

A = P(r/12)/(1 -(1 +r/12)^(-12t))

for loan amount P at annual rate r for t years.

For this mortgage, we use P = $530,000, r = 0.068, t = 30.

A = $530,000(0.068/12)/(1 -(1 +0.068/12)^(-360)) ≈ $3,455.20

The monthly payment is $3,455.20.

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<em>Additional comment</em>

In 7 years, the balloon payment will be $481,559.91.

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2 years ago