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1 year ago

One number is 6 more than another. The difference between their squares is 204. What are the numbers?

Mathematics

2 answers:

Elenna [48]1 year ago

7 0

Answer: 20 and 14

Step-by-step explanation:

Using a little guess and check, we can figure out that the numbers are 6 apart and the difference between their squares is 204.

$20^2 = 400\\14^2=196$

$20^2-14^2 = 204$

A trick to doing this is to start with a number that is easily squared like 10 or 20 and see if the difference between their numbers is larger or smaller and change your numbers based on them.

Hope this helped :)

Crazy boy [7]1 year ago

4 0

Answer:

14 and 20

Step-by-step explanation:

Let x and y be two numbers where x < y.

We are given :

y - x = 6

y² - x² = 204

Then

y - x = 6

(y - x)(y + x) = 204

Then

y - x = 6

6 × (y + x) = 204

then

y - x = 6 (Equation 1)

y + x = 34 (Equation 2)

Then

(Equation 1) + (Equation 2) ⇒ 2y = 40 ⇒ y = 20

Now ,we substitute y by 20 in equation 1 :

y - x = 6

⇔ 20 - x = 6

⇔ 20 - 6 = x

⇔ x = 14

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Answer:

Step-by-step explanation:

Average rate of change is the same thing as the slope. This is a quadratic so the slope is not something that is constant like it is in a line. Here you have the x coordinates of 1 and 5; each one of these x coordinates has a y coordinate that goes with it. If we draw a line from one of these coordinates to another, that line will have a slope. That is the slope we are trying to find. Thus, we need the y coordinates that go with each of these x coordinates. To do that, plug x into the equation and do the math to find y:

Let's start with x = 1.

f(1) = $17-(1)^2$ so

f(1) = 16 and the coordinate is (1, 16).

f(5) = $17-(5)^2$ so

f(5) = -8 and the coordinate is (5, -8). Now we apply the slope formula:

$m=\frac{-8-16}{5-1}=\frac{-24}{4}=-6$ So the answer is -6.

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2 years ago

On a rectangle hyperbola, if one point is (2,3) and y varies inversely to x, find y when x is 6

s344n2d4d5 [400]

The graph of y against x in inverse proportion is a rectangular hyperbola but I don't see at all how this knowledge/observation is any help in solving the problem.

Inverse proportion means that as x doubles y will halve and the equation is xy = k where k is some number. A good example of inverse proportion is speed and time taken over some fixed distance. In this case x could represent the speed (mph) and y the time (h) and then k is the distance in miles.

Since we know y=3 when x=2 we have xy = 6. Now it's easy to see when x=6 y=1.

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3 years ago

Simplify 6m2n3 – 3m3n2 + 8m2n3 + 12m3n2

NISA [10]

Hello! Hope I can assist you.

Let us simplify some terms first!

$6m\cdot \:2n\cdot \:3 \ \textgreater \ 36mn$
$3m\cdot \:3n\cdot \:2 \ \textgreater \ 2\cdot \:3^2mn$
$8m\cdot \:2n\cdot \:3 \ \textgreater \ 48mn$
$12m\cdot \:3n\cdot \:2 \ \textgreater \ 72mn$

$36mn-2\cdot \:3^2mn+48mn+72mn$

From here, group like terms
$36mn-2\cdot \:3^2mn+48mn+72mn$

$\mathrm{Add\:similar\:elements:}\:36mn+48mn+72mn=156mn$
$156mn-2\cdot \:3^2mn$

$2\cdot \:3^2mn \ \textgreater \ 2\cdot \:9mn \ \textgreater \ 18mn$

$156mn-18mn$

$\mathrm{Add\:similar\:elements:}\:156mn-18mn=138mn$

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3 years ago

What is the equation of the line that passes through the point (8, 8) and has a slope of -22

Likurg_2 [28]

Answer:

Step-by-step explanation:

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3 years ago

An island is 1 mi due north of its closest point along a straight shoreline. A visitor is staying at a cabin on the shore that i

Elanso [62]

Answer:

The visitor should run approximately 14.96 mile to minimize the time it takes to reach the island

Step-by-step explanation:

From the question, we have;

The distance of the island from the shoreline = 1 mile

The distance the person is staying from the point on the shoreline = 15 mile

The rate at which the visitor runs = 6 mph

The rate at which the visitor swims = 2.5 mph

Let 'x' represent the distance the person runs, we have;

The distance to swim = $\sqrt{(15-x)^2+1^2}$

The total time, 't', is given as follows;

$t = \dfrac{x}{6} +\dfrac{\sqrt{(15-x)^2+1^2}}{2.5}$

The minimum value of 't' is found by differentiating with an online tool, as follows;

$\dfrac{dt}{dx} = \dfrac{d\left(\dfrac{x}{6} +\dfrac{\sqrt{(15-x)^2+1^2}}{2.5}\right)}{dx} = \dfrac{1}{6} -\dfrac{6 - 0.4\cdot x}{\sqrt{x^2-30\cdot x +226} }$

At the maximum/minimum point, we have;

$\dfrac{1}{6} -\dfrac{6 - 0.4\cdot x}{\sqrt{x^2-30\cdot x +226} } = 0$

Simplifying, with a graphing calculator, we get;

-4.72·x² + 142·x - 1,070 = 0

From which we also get x ≈ 15.04 and x ≈ 0.64956

x ≈ 15.04 mile

Therefore, given that 15.04 mi is 0.04 mi after the point, the distance he should run = 15 mi - 0.04 mi ≈ 14.96 mi

$t = \dfrac{14.96}{6} +\dfrac{\sqrt{(15-14.96)^2+1^2}}{2.5} \approx 2..89$

Therefore, the distance to run, x ≈ 14.96 mile

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2 years ago