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maxonik [38]
3 years ago
8

What is the slope of the equation y - 3 = -4(x - 5)?

Mathematics
2 answers:
Reil [10]3 years ago
6 0

Answer:

Step-by-step explanation:

A

MissTica3 years ago
3 0

Answer:

A - 4

Step-by-step explanation:

Given equation of line is:

y - 3 = -4(x - 5) \\ equating \: it \: with \\ y-y_1 =m(x-x_1)  \\ \purple{ \bold{ slope \: (m) =  - 4}}

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Which equation represents a circle that contains the point (-5, 3) and has a center at (-2, 1)? Distance formula: vaa -02 (x - 1
natali 33 [55]

Given:

The center of the circle = (-2,1).

Circle passes through the point (-5,3).

To find:

The equation of the circle.

Solution:

Radius is the distance between the center of the circle and any point on the circle. So, radius of the circle is the distance between the points (-2,1) and (-5,3).

Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

r=\sqrt{(-5-(-2))^2+(3-1)^2}

r=\sqrt{(-5+2)^2+(2)^2}

r=\sqrt{(-3)^2+(2)^2}

On further simplification, we get

r=\sqrt{9+4}

r=\sqrt{13}

The standard form of a circle is:

(x-h)^2+(y-k)^2=r^2

Where, (h,k) is the center of the circle and r is the radius of the circle.

Substitute h=-2, k=1 and r=\sqrt{13}.

(x-(-2))^2+(y-1)^2=(\sqrt{13})^2

(x+2)^2+(y-1)^2=13

Therefore, the equation of the circle is (x+2)^2+(y-1)^2=13.

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Find the simply interest earned on an investment of $15,000 at a rate of 5.25% for two years.
uysha [10]
Ill show you step by step.

This is what the equation should look like 

Y=Initial value(1+/- Increasing or Decreasing value)^2 Which stands for time

So Y=15,000(1+.0525)^2

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So now you need to do 15,000(1.10775625)
------------------------------------------------------------------------------------
Which equals <span>16616 rounding to the nearest Ones

16616.3 rounding to the nearest tenth</span>
3 0
3 years ago
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Which of the following pairs of functions are inverses of each other?
natta225 [31]

Answer:

The pair which are inverse of each other are:

Option: C

f(x)=11x-4\ and\ g(x)=\dfrac{x+4}{11}

Step-by-step explanation:

Two functions f(x) and g(x) are said to be inverse of each other if:

fog(x)=gof(x)=x

i.e. the composition of two functions give identity no matter what the order is.

A)

f(x)=\dfrac{x}{12}+15 and g(x)=12x-15

Now we calculate fog(x):

fog(x)=f(g(x))\\\\fog(x)=f(12x-15)\\\\fog(x)=\dfrac{12x-15}{12}+15\\\\fog(x)=x-\dfrac{15}{12}+15\\\\fog(x)=x-\dfrac{55}{4}\neq x

Hence, option: A is incorrect.

B)

f(x)=\dfrac{3}{x}-10\ and\ g(x)=\dfrac{x+10}{2}

Now we calculate fog(x):

fog(x)=f(g(x))\\\\fog(x)=f(\dfrac{x+10}{3})\\\\fog(x)=\dfrac{3}{\dfrac{x+10}{3}}-10\\\\fog(x)=\dfrac{9}{x+10}-10\neq x

Hence, option: B is incorrect.

D)

f(x)=9+\sqrt[3]{x}\ and\ g(x)=9-x^3

Now we calculate fog(x):

fog(x)=f(g(x))\\\\fog(x)=f(9-x^3)

fog(x)=9+\sqrt[3]{9-x^3}\neq x

Hence, option: D is incorrect.

C)

f(x)=11x-4\ and\ g(x)=\dfrac{x+4}{11}

Now we calculate fog(x):

fog(x)=f(g(x))\\\\fog(x)=f(\dfrac{x+4}{11})

fog(x)=11\times (\dfrac{x+4}{11})-4\\\\fog(x)=x+4-4\\\\fog(x)=x

Similarly,

gof(x)=g(f(x))\\\\gof(x)=g(11x-4)\\\\gof(x)=\dfrac{11x-4+4}{11}\\\\gof(x)=\dfrac{11x}{11}\\\\gof(x)=x

Hence, option: C is the correct option.

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3 years ago
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