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2 years ago

What is the distance between the points (3, 7) and (15, 16) on a coordinate plane?

1 answer:

7 0

Square root of (3-15)^2 +(7-16)^2
Square root of (-12)^2 + (-9)^2
Square root of 144+81
Square root of 225
The distance is 15

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PLEASE HELP AND EXPLAIN ALSO SHOW WORK

Goryan [66]

Answer:

x=10

Step-by-step explanation:

Make 2x the only variable on the left side of the equation. Do that by taking 3 and 5 to the left. Note: if you move/transpose any number the sign must change.

2x = 18+5-3

2x=20

Divide both sides of the equation by 2 to make x the only variable left.

x=10

6 0

2 years ago

A cone has a radius of 5 ft and a height of 15 ft. It is empty and is being filled with water at a constant rate of 15 15 ft 3 f

kvasek [131]

Answer:

$\frac{dr}{dt}=0.11062ft/sec$

Step-by-step explanation:

From the question we are told that:

Radius $r=5ft$

Height $H=15ft$

Rate $R=15ft/3sec =5ft/s$

Surface Radius $R_{surf}=2.2ft$

Generally the equation for Volume is mathematically given by

$V=\frac{1}{3}\pi*r^2h$

Since radius to height ratio gives

$\frac{r}{h}=\frac{5}{15}$

$\frac{r}{h}=\frac{1}{3}$

$h=3r$

Therefore

$V=\frac{1}{3}\pi*r^2(3r)$

$V=\pi r^3$

Generally the equation for Change of Volume is mathematically given by

$\frac{dv}{dt}=\pi \frac{d}{dt}(r^3)$

$\frac{dv}{dt}=\pi 3*r^2 \frac{dr}{dt}$

$\frac{dv}{dt}=\pi 3*(2.2)^2 \frac{dr}{dt}$

$\frac{dr}{dt}=\frac{5}{45.62}$

$\frac{dr}{dt}=0.11062ft/sec$

3 0

3 years ago

Joe has read 30 % of a book. He has 63 more pages to finish. How many pages are there in the book?

meriva

Answer:

90 pages

Step-by-step explanation:

30% complete

70% to go = 63 pages

t = total number of pages

0.7t = 63

∴ t = ⁶³/₀.₇

⁶³/₀.₇ = 90

4 0

2 years ago

Find the solution set of the inequality

Brilliant_brown [7]

Answer:

$\boxed{\textsf{ Hence the solution set is$ \bf{\bigg( \dfrac{33}{4},\infty \bigg) }$}}.$

Step-by-step explanation:

A inequality is given to us and we need to find the solution set. So the given inequality to us is ,

-4x + 35 >2

$\bf\implies -4x + 35 > 2 \\\\\bf\implies -4x > 2-35 \\\\\bf \implies -4x > -33 \\\\\bf \implies x >\dfrac{-33}{-4}\\\\\bf \implies x > \dfrac{33}{4} \\\\\bf\implies \boxed{\pink{\bf x \in \bigg(\dfrac{33}{4}, \infty \bigg) }}$

<h3>★ Hence the solution set is x € ( 33/4 , ∞ ).</h3>

3 0

2 years ago

How to do composition of functions

KengaRu [80]

<h2>If you rather have the link to get this info lmk!!</h2>

Example: f(x) = 2x+3 and g(x) = x2

"x" is just a placeholder. To avoid confusion let's just call it "input":

f(input) = 2(input)+3

g(input) = (input)2

Let's start:

(g º f)(x) = g(f(x))

First we apply f, then apply g to that result:

Function Composition - (g º f)(x) = (2x+3)2

What if we reverse the order of f and g?

(f º g)(x) = f(g(x))

First we apply g, then apply f to that result:

Function Composition - (f º g)(x) = 2x2+3

We get a different result! When we reverse the order the result is rarely the same. So be careful which function comes first.

<h2 />

5 0

3 years ago