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3 years ago

50 POINTS NEED HELP QUICK!!

Mathematics

2 answers:

sweet [91]3 years ago

7 0

The correct answer is B, <span>(25−2x)(20−2x)x.</span>

MatroZZZ [7]3 years ago

6 0

The appropriate choice is ...
(25−2x)(20−2x)x

_____
When x is cut from each side of the 25 dimension, the remaining dimension of the bottom of the box is 25-2x. Similarly, when x is cut from each side of the 20 dimension, the remaining dimension of the bottom of the box is 20-2x. The length of the side that is folded up is x, so that is how deep the box is.

The volume is the product of the dimensions of the bottom and the side:
(25−2x)(20−2x)x

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Isaac made 2 quarts and 1 cup of cupcake batter. If 6 ounces of batter make one cupcake, and Isaac is making 10 cupcakes, how mu

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There will be 12 ounces left

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2 years ago

Malia's retirement party costs $35, plus an additional $1 for each guest she invites. If there

Bas_tet [7]

Answer:

$85

Step-by-step explanation:

$35 + $1 x 50 guests = $85

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2 years ago

Solve b to the second power=77

zubka84 [21]

Answer:

$\large\boxed{b=\pm\sqrt{77}}$

Step-by-step explanation:

$b^2=77\iff b=\pm\sqrt{77}\\\\\text{because}\\\\(-\sqrt{77})^2=77\ \text{and} \ (\sqrt{77})^2=77$

3 0

3 years ago

4. a) A ping pong ball has a 75% rebound ratio. When you drop it from a height of k feet, it bounces and bounces endlessly. If t

Klio2033 [76]

First part of question:

Find the general term that represents the situation in terms of k.

The general term for geometric series is:

$a_{n}=a_{1}r^{n-1}$

$a_{1}$ = the first term of the series

$r$ = the geometric ratio

$a_{1}$ would represent the height at which the ball is first dropped. Therefore:

$a_{1} = k$

We also know that the ball has a rebound ratio of 75%, meaning that the ball only bounces 75% of its original height every time it bounces. This appears to be our geometric ratio. Therefore:

$r=\frac{3}{4}$

Our general term would be:

$a_{n}=a_{1}r^{n-1}$

$a_{n}=k(\frac{3}{4}) ^{n-1}$

Second part of question:

If the ball dropped from a height of 235ft, determine the highest height achieved by the ball after six bounces.

$k$ represents the initial height:

$k = 235\ ft$

$n$ represents the number of times the ball bounces:

$n = 6$

Plugging this back into our general term of the geometric series:

$a_{n}=k(\frac{3}{4}) ^{n-1}$

$a_{n}=235(\frac{3}{4}) ^{6-1}$

$a_{n}=235(\frac{3}{4}) ^{5}$

$a_{n}=55.8\ ft$

$a_{n}$ represents the highest height of the ball after 6 bounces.

Third part of question:

If the ball dropped from a height of 235ft, find the total distance traveled by the ball when it strikes the ground for the 12th time. 

This would be easier to solve if we have a general term for the <em>sum </em>of a geometric series, which is:

$S_{n}=\frac{a_{1}(1-r^{n})}{1-r}$

We already know these variables:

$a_{1}= k = 235\ ft$

$r=\frac{3}{4}$

$n = 12$

Therefore:

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{1-\frac{3}{4} }$

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{\frac{1}{4} }$

$S_{n}=(4)(235)(1-\frac{3}{4} ^{12})$

$S_{n}=910.22\ ft$

8 0

2 years ago

2x² - 5x+1 has roots alpha and beta. Find alpha⁴+beta⁴ without solving the equation.

shepuryov [24]

Answer:

Step-by-step explanation:

$\alpha+\beta=\dfrac{5}{2} \\\\\alpha*\beta=\dfrac{1}{2} \\\\\alpha^2+\beta^2=\dfrac{21}{4} \ (see\ previous\ post)\\\\(\alpha+\beta)^4=\dfrac{625}{16} \\\\=\alpha^4+\beta^4+4*\alpha^3*\beta+6*\alpha^2*\beta^2+4*\alpha*\beta^3\\\\=\alpha^4+\beta^4+4*(\alpha*\beta)(\alpha^2+\beta^2)+6*\alpha^2*\beta^2\\\\\alpha^4+\beta^4=(\alpha+\beta)^4-4*(\alpha*\beta)(\alpha^2+\beta^2)-6*\alpha^2*\beta^2\\\\= \dfrac{625}{16} -4*\dfrac{1}{2} *\dfrac{21}{4} -6*(\dfrac{1}{2})^2 \\\\$

$= \dfrac{625}{16}- \dfrac{168}{16}-\dfrac{24}{16}\\\\\\= \dfrac{433}{16}$

7 0

2 years ago