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bonufazy [111]
1 year ago
7

After finishing the prep work, Gilberta and María start removing wallpaper at the same time. Gilberta removes the paper at a con

stant rate of
4.3

m
2
4.3m
2
4, point, 3, start text, m, end text, squared per hour, while María removes
3.4

m
2
3.4m
2
3, point, 4, start text, m, end text, squared of paper per hour. Gilberta's room starts with
35

m
2
35m
2
35, start text, m, end text, squared of paper, and María's room starts with
30.5

m
2
30.5m
2
30, point, 5, start text, m, end text, squared of paper.
Let
t
tt represent the time, in hours, since Gilberta and María start removing the wallpaper.
Complete the inequality to represent the times when Gilberta has more wallpaper left in her room than María has in hers.
t
tt

select inequality symbol


hours

Show Calculator
Mathematics
1 answer:
Alexxx [7]1 year ago
4 0

Using linear functions, the inequality that represents when Gilberta has more wallpaper left in her room than María has in hers is: t < 5.

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

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

For this problem, we consider:

  • The initial amount as the y-intercept.
  • The rate as the slope.

Hence the amounts Gilberta and Maria have left after t hours are given by:

  • G(t) = 35 - 4.3t.
  • M(t) = 30.5 - 3.4t.

Gilberta has more papers when:

G(t) > M(t).

Hence:

35 - 4.3t > 30.5 - 3.4t

-0.9t < -4.5

Multiplying by -1:

0.9t < 4.5

t < 4.5/0.9

t < 5.

Hence the inequality is:

t < 5.

More can be learned about linear functions at brainly.com/question/24808124

#SPJ1

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Solve the following equation. 2x - 1 ≤ x 5
wariber [46]

<span><span><span>2x</span>−1</span>≤<span>x5

</span></span>Let's find the critical points of the inequality.

<span><span><span>2x</span>−1</span>=<span>x^5

</span></span><span><span><span><span>2x</span>−1</span>−<span>x^5</span></span>=<span><span>x^5</span>−<span>x^5 </span></span></span>(Subtract x^5 from both sides)

<span><span><span><span>−<span>x^5</span></span>+<span>2x</span></span>−1</span>=0

</span><span><span><span>(<span><span>−x</span>+1</span>)</span><span>(<span><span><span><span><span>x^4</span>+<span>x^3</span></span>+<span>x^2</span></span>+x</span>−1</span>)</span></span>=0  </span>(Factor left side of equation)

<span><span><span><span>−x</span>+1</span>=<span><span><span><span><span><span>0<span> or </span></span><span>x^4</span></span>+<span>x^3</span></span>+<span>x^2</span></span>+x</span>−1</span></span>=0   </span>(Set factors equal to 0)

<span><span><span>x=<span><span>1<span> or </span></span>x</span></span>=<span><span>0.51879<span> or </span></span>x</span></span>=<span>−<span>1.290649</span></span></span>
5 0
3 years ago
[25 POINTS] A cylinder has a volume of 400π cm3. Find the dimensions that minimize its surface area.
miss Akunina [59]

Answer:

r = 5.848cm, h = 11.696cm

Step-by-step explanation:

Surface area: SA=2\pi rh+2\pi r^2

Volume: V=\pi r^2h

Therefore, the height of a cylinder given its volume would be h=\frac{V}{\pi r^2}, thus:

SA=2\pi r(\frac{V}{\pi r^2})+2\pi r^2\\\\SA=\frac{2V}{r}+2\pi r^2\\\\SA=\frac{2(400\pi)}{r}+2\pi r^2\\\\SA=\frac{800\pi}{r}+2\pi r^2

We now find the derivative of the surface area of the cylinder with respect to its radius and set it equal to 0, solving for the radius:

\frac{d(SA)}{dr}=-\frac{800\pi}{r^2}+4\pi r

0=-\frac{800}{r^2}+4\pi r

0=800\pi+4\pi r^3

-800\pi=4\pi r^3

-200=r^3

r\approx5.848

If 0If [tex]r>5.848, then the surface area of the cylinder increases

Therefore, the surface area is minimized when the radius is r=5.848cm, making the minimum height h=\frac{V}{\pi r^2}=\frac{400\pi}{\pi(5.848)^2}\approx11.696cm.

In conclusion, the 2nd option is correct.

3 0
2 years ago
Add 6.004 + 0.08 + 954 + 3.5 =
stiv31 [10]
The answer is 963.584.
3 0
2 years ago
Read 2 more answers
Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and sin ∠X = 5 over 5 and 59 hundredths.
Vikentia [17]

The relationship between Traingle XYZ and ACB is that they are similar triangles. tanX = tanA = 5 over 2 and 5 tenths, where

  • AC = 2 x  XY
  • CB = 2 x  YZ

<h3>What is the dilation about?</h3>

Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB, hence XYZ and ACB are similar triangles.

Angles Y and C are said to measure 90 degrees, and angles A and X are known to be congruent. Thus:

tanX = tanA = 5 over 2 and 5 tenths

AC = 2 x  XY

CB = 2 x  YZ

Another way to solve for it is by:

Note that Dilation of the triangle ΔXYZ was by a factor of "2".

Since m∠Y = m∠C = 90º   - given

ΔXYZ and ΔACB are said to be right triangles.

Since ∠X ≅ ∠A   - given

Then ∠X and ∠Z are  said to becomplementary angles

Since m∠Z = 90° - m∠X   -- given

Then ∠A and ∠B are said to be complementary angles

Since m∠B = 90° - m∠A  --- given

Then, ∠Z ≅ ∠B

Therefore ΔXYZ ∼ ΔACB are  similar triangles because it has its corresponding sides to be proportional and its corresponding angles to be congruent.

Note:

sin ∠X = 5/5.59

sin ∠X = YZ/XY

YZ = 5  seen in ΔXYZ

XZ = 5.59 seen in hypotenuse of ΔXYZ

Then one need to Calculate the length of one aspect of XY:

XY = √((5.59)2 - 52)

= 2.4996

Note CB/YZ = 2

CD = 2*YZ = 2 x 5

= 10

AC/XY = 2

AC = 2* XY

= 2 x 2.4996

= 4.999

Learn more about dilation from:

brainly.com/question/27517432

#SPJ1

7 0
2 years ago
Is 500 x 30 a good estimate for the number of tickets sold at the number of tickets sold at the theater in one month
salantis [7]

Answer:

It depends if business is steady. If they make about 500 a day that is a fair estimate. Make sure that the month you are talking about has 30 days.

3 0
2 years ago
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