All categories

3 years ago

What’s the equation of a line that passes through (-9,10) and y=3/2x - 3/2

Mathematics

1 answer:

Natalija [7]3 years ago

3 0

Answer:

y = 3x/2 + 23 1/2

y = 3x/2 + 47/2

Step-by-step explanation:

Find the slope

y = 3/2x - 3/2

Equation of a line

y = mx + c

m = 3/2

using a point slope form equation

Substitute the point into the equation

( -9 , 10)

y - y1 = m( x - x1)

x1 = -9

y1 = 10

y - 10 = 3/2( x - (-9)

y - 10 = 3/2( x + 9)

Open the bracket

y - 10 = (3x + 27)/2

y = ( 3x + 27)/2 + 10

LCM = 2

y = ( 3x + 27 + 20)/2

y = ( 3x + 47)/2

Separate to get the value of slope and intercept

y = 3x/2 + 47/2

y = 3x/2 + 23 1/2

The equation of the line is

y = 3x/2 + 23 1/2

You might be interested in

What’s the correct answer

ale4655 [162]

$45x=11\qquad\text{divide both sides by 45}\\\\\boxed{x=\dfrac{11}{45}}=0.2\overline{4}\\\\Answer:\ \boxed{x\approx0.24}$

7 0

3 years ago

Match each circular flower bed on the left to its circumference and its area on the right. Some answer options on the right will

marin [14]

Answer:

Bed A --- Third Option

Bed B --- Fifth Option

Step-by-step explanation:

Flower Bed A)

The formula for circumference is:

$C=2\pi r$

The diameter of A is 10 feet. So, its radius is 5 feet.

Substitute 5 for r. So, the circumference of Bed A is:

$C=2\pi (5)=10\pi\text{ feet}$

The formula for the area of a circle is:

$A=\pi r^2$

Substitute 5 for r:

$A=\pi (5)^2$

Square and simplify:

$A=25\pi \text{ square feet}$

So, the circumference of Bed A is 10π feet and its area is 25π square feet.

Therefore, match Bed A to the third option.

Flower Bed B)

The radius of Bed B is 6 feet. Again, we can use the circumference and area formulas. Substitute 6 for r for circumference:

$C=2\pi (6)$

Multiply:

$C=12\pi\text{ feet}$

Substitute 6 for r for the area formula:

$A=\pi(6)^2$

Square and simplify:

$A=36\pi\text{ square feet}$

So, Bed B has a 12π feet circumference and a 36π square feet area.

Therefore, match Bed B to the fifth option.

And we're done!

8 0

3 years ago

You put $200 into an account earning 6% interest compounded yearly.

VMariaS [17]

Answer:

43.35 years

Step-by-step explanation:

From the above question, we are to find Time t for compound interest

The formula is given as :

t = ln(A/P) / n[ln(1 + r/n)]

A = $2500

P = Principal = $200

R = 6%

n = Compounding frequency = 1

First, convert R as a percent to r as a decimal

r = R/100

r = 6/100

r = 0.06 per year,

Then, solve the equation for t

t = ln(A/P) / n[ln(1 + r/n)]

t = ln(2,500.00/200.00) / ( 1 × [ln(1 + 0.06/1)] )

t = ln(2,500.00/200.00) / ( 1 × [ln(1 + 0.06)] )

t = 43.346 years

Approximately = 43.35 years

7 0

2 years ago

The function g(x) is a translation of f(x) = (x 3)2 – 10. The axis of symmetry of g(x) is 5 units to the right of f(x). Which fu

natali 33 [55]

The axis of symmetry of g(x) is 2 units right side from the origin then the function is $\rm g(x) = (x - 2)^2 + k$ . Then the correct option is A.

<h3>What is a function?</h3>

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

Given

The function f(x) is $(x+3)^2 - 10$ .

The axis of symmetry of f(x) is left side by 3 units.

The axis of symmetry of g(x) is 5 units to the right of f(x).

Then the axis of symmetry of g(x) is 2 units right side from the origin.

Then the g(x) will be

$\rm g(x) = (x - 2)^2 + k$

Thus, the correct option is A.

More about the function link is given below.

brainly.com/question/14674614

5 0

2 years ago

Are the two triangles similar? Explain you reasoning and support your answer?

Anuta_ua [19.1K]

Answer:

yes

Step-by-step explanation:

by the side and letgh

4 0

3 years ago