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3 years ago

The function f is defined by f(x)=3x+k, where k is a constant. Find k, if the graph of f passes through the point (−1,8).

Mathematics

1 answer:

Gelneren [198K]3 years ago

8 0

Answer:

k = 11

Step-by-step explanation:

f(x)=3x+k,

We know the input is -1 so replace x with -1 and the output is 8 so replace f(x) with 9

8 = 3(-1) +k

8 = -3+k

Add 3 to each side

8+3 = -3+3+k

11= k

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Principle = $15,500 Interest Rate = 8.75% Time = ? Years Simple Interest = $5425.00

amid [387]

We must find time by using the simple interest formula:

I = P x i x t

I is the interest
P is the total principal
i is the rate of interest per year
t is the total time in years

In this example, when we plug our known values in, our formula looks like this:

t = $\frac{I}{i*p}$

t = $\frac{5425}{0.0875 * 15500}$

t = 4

So time (in years) would be 4 years.

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3 years ago

Find the equation of the line <br> Use exact numbers <br><br> Thank you in advance!

Taya2010 [7]

Answer:

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3 years ago

X^2+4x+y^2-10y+20=30 find the center of the circle by completing the square

swat32

Answer:

a). Center of the circle = (-2, 5)

b). Equation of the line ⇒ y = $-\frac{4}{5}x+\frac{58}{5}$

Step-by-step explanation:

Equation of the circle is,

x² + 4x + y²- 10y + 20 = 30

a). [x² + 2(2)x + 4 - 4] + [y²- 2(5)y + 25] - 25 + 20 = 30

[x² + 2(2)x + 4] - 4 + [y² - 2(5)y + 25] - 25 + 20 = 30

(x + 2)² + (y - 5)²- 29 + 20 = 30

(x + 2)² + (y - 5)²- 9 = 30

(x + 2)² + (y - 5)² = 39

By comparing this equation with the standard equation of a circle,

Center of the circle is (-2, 5).

b). A point (2, 10) lies on this circle.

Slope of the line joining this point to the center (-2, 5),

$m_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

= $\frac{10-5}{2+2}$

= $\frac{5}{4}$

Let the slope of the tangent which is perpendicular to this line is ' $m_{2}$ '

Then by the property of perpendicular lines,

$m_{1}\times m_{2}=-1$

$\frac{5}{4}\times m_{2}=-1$

$m_{2}=-\frac{4}{5}$

Now the equation of the line passing though (2, 10) having slope $m_{2}=-\frac{4}{5}$

y - y' = $m_{2}(x-x')$

y - 10 = $-\frac{4}{5}(x-2)$

y - 10 = $-\frac{4}{5}x+\frac{8}{5}$

y = $-\frac{4}{5}x+\frac{8}{5}+10$

y = $-\frac{4}{5}x+\frac{58}{5}$

Therefore, equation of the line will be, y = $-\frac{4}{5}x+\frac{58}{5}$

7 0

3 years ago

To the nearest tenth, which is the BEST estimate for the volume of the given pyramid?

mixer [17]

Answer:

4.2 cubic inches

Step-by-step explanation:

Find the diagram attached

Volume of the rectangular pyramid = BH/3

B is the base area

H is the height of the pyramid

Given

Base area = 3.2in * 1.4in

Base area = 4.48sq. in

Height = 2.8in

Volume of the rectangular pyramid = 4.48*2.8/3

Volume of the rectangular pyramid = 12.544/3

Volume of the rectangular pyramid = 4.2 cubic inches

5 0

3 years ago

Is 15 kilometers equivalent to 1,500,000 centimeters

Ann [662]

Hi
Yes 15 kilometers is 1500000 cm

This is because in metric conversion, you multiply by ten each time you convert to the next unit.

Heres a useful way to remember

K ing (kilo)
H enry (hecto)
D oesn't (deca)
U sually (unit) <-metre, litre ect.
D rink ( deci)
C hocolate (centi)
M ilk (milli)

6 0

4 years ago