Using the slope formula, find the slope of the line through the given points <br> 8,5 and 6,1

find the ordered pairs for the x- and y-intercepts of the equation 5x − 6y = 30 and select the appropriate option below. a. the

Hoochie [10]

$5x-6y=30\ \ \ \ |subtract\ 5x\ from\ both\ sides\\\\-6y=-5x+30\ \ \ \ |divide\ both\ sides\ by\ (-6)\\\\y=\frac{5}{6}x-5\\\\x-intercept\ if\ y=0\\subtitute\\\\\frac{5}{6}x-5=0\ \ \ |add\ 5\ to\ both\ sides\\\\\frac{5}{6}x=5\ \ \ \ |\cdot\ \frac{6}{5}\\\\\fbox{x=6}\\\\y-intercept\\subtitute\\\\y=\frac{5}{6}\cdot0-5\\\\\fbox{y=-5} \\\\Answer:\boxed{x-intercept\ (6;\ 0);\ y-intercept\ (0; -5)}\to\fbox{A.}$

8 0

2 years ago

What is the rate of decay for the function f(x) =2(0.95)^x ( x is on top of the parentheses)

SIZIF [17.4K]

Answer:

The decay rate is 5%.

Step-by-step explanation:

Let a substance is decaying at the rate of r% per hour from the initial value of P for t hours, then the final value of the substance is given by the function

$f(t) = P(1 - \frac{r}{100})^{t}$ ........... (1)

Comparing this equation with the original equation given as

$f(x) = 2(0.95)^{x}$ ............ (2) we get,

$(1 - \frac{r}{100}) = 0.95$

⇒ $\frac{r}{100} = 0.05$

⇒ r = 5%.

Therefore, the decay rate is 5%. (Answer)

7 0

3 years ago

Is the following relation a function. <br><br> A) yes<br> B) no

dmitriy555 [2]

Answer:

yes

Step-by-step explanation:

A relation is a function in which for each input there is only one output.

In a relation, y is a function of x.

Now we look at the mapping

For input 6, -1 is the output

for input -1, 2 is the output

for input 4, 3 is the output

for input 0, 3 is the output

For each input , there is an output. Input is not repeating. Input is occurring only once.

So this relation is a function.

4 0

2 years ago

Given: ∆ABC, m∠C = 90° CB = 8, m∠B = 38º Find the area of a circumscribed circle. Find the area of the inscribed circle.

vitfil [10]

Answer:

Circumscribed circle: Around 80.95

Inscribed circle: Around 3.298

Step-by-step explanation:

Since C is a right angle, when the circle is circumscribed it will be an inscribed angle with a corresponding arc length of 2*90=180 degrees. This means that AB is the diameter of the circle. Since the cosine of an angle in a right triangle is equivalent to the length of the adjacent side divided by the length of the hypotenuse:

$\cos 38= \dfrac{8}{AB} \\\\\\AB=\dfrac{8}{\cos 38}\approx 10.152$

To find the area of the circumscribed circle:

$r=\dfrac{AB}{2}\approx 5.076 \\\\\\A=\pi r^2\approx 80.95$

To find the area of the inscribed circle, you need the length of AC, which you can find with the Pythagorean Theorem:

$AC=\sqrt{10.152^2-8^2}\approx 6.25$

The area of the triangle is:

$A=\dfrac{bh}{2}=\dfrac{8\cdot 6.25}{2}=25$

The semiperimeter of the triangle is:

$\dfrac{10.152+6.25+8}{2}\approx 24.4$

The radius of the circle is therefore $\dfrac{25}{24.4}\approx 1.025$

The area of the inscribed circle then is $\pi\cdot (1.025)^2\approx 3.298$ .

Hope this helps!

6 0

3 years ago

Please help i’ve been here for hours so can someone please tell me what to put here

andreev551 [17]

Answer:

If you divide the amount $60.20 (60.20) by 5 (amount of hours), you can find out the amount of money Andrew gets paid in dollars per hour. The quotient is 12.04, $12.04. Therefore, Andrew is payed $12.04 per hour.

Step-by-step explanation:

HOPE THIS HELPS

HAVE A GOOD DAY

STAY SAFE BYEE

❤

6 0

3 years ago

Read 2 more answers

Using the slope formula, find the slope of the line through the given points 8,5 and 6,1