A right rectangular prism has these dimensions: Length ? Fraction 1 and 1 over 2 units Width ? Fraction 1 over 2 unit Height ? Fraction 3 over 4 unit How many cubes of side length Fraction 1 over 4 unit are required to completely pack the prism without any gap or overlap? 36 45 51 60

Answer:

No it is not true because plugging in something like x = pi/4 radians (equivalent to 45 degrees) leads to the left side not being equal to 1. The left side will simplify to sqrt(2). So the equation is not true when x = pi/4 radians. There are infinitely other counter examples to use

Answer:

Step-by-step explanation:

The distance from Q to S is 2 - (-14), or 16.

We start at point Q.  Note how 3 and 5 add  up to 8, which allows us to write:

R = Q + (3/8)(16), or R = -14 + 6, or R = -8.

From R to S it is (5/8)(16), or 10 units.

The directed line segment is partitioned into segments of lengths 6 and 10, whose combined length is 16, as expected.

Answer:

14/5 or A

Step-by-step explanation:

I just took this assignment.

The four solutions to the function 4x - y = 4 are determined by selecting different x values and calculating the corresponding y values, resulting in the ordered pairs (0, -4), (1, 0), (2, 4), and (3, 8).

To find four solutions to the function 4x – y = 4, we need to choose four different values for x and compute the corresponding y values.

For example, let's choose x = 0, x = 1, x = 2, and x = 3. Substituting these values into the equation:

So the four solutions (order pairs) are (0, -4), (1, 0), (2, 4), and (3, 8).

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To find solutions for the given equation 4x - y = 4, pick x values and plug them into the equation to solve for y, resulting in ordered pairs like (0, -4) and (1, 0).

Given equation: 4x - y = 4

Choose x values and plug them into the equation to solve for y.

Write the solutions as ordered pairs (x, y).

Four solutions are (0, -4), (1, 0), (2, 4), and (3, 8).

The first equation can be further simplified so first do that by subtracting 15 to both sides

y - 3x + (15 - 15) = 10 - 15

y - 3x = -5

We know from the second equation that y is 6 - 4x so in the equation y - 3x = -5 plug in 6 - 4x for y

(6 - 4x) - 3x = -5

6 - 4x - 3x = -5

Combine like terms

6 - 7x = -5

(6 - 6) - 7x = -5 - 6

-7x = -11

Isolate x

-7x/-7 = -11/-7

x = 11/7

To solve for y plug in 11/7 in for x in the equation 6 - 4x = y

6 - 4(11/7) =y

6 - 44/7 = y

y = -2/7

so...

(11/7 , -2/7)

Hope this helped!

~Just a girl in love with Shawn Mendes

1.) Solving for X problem 1#

y-3x+15=10

-3x+15-15=10-15-y

-3x=-y-5

-3x/-3=-y-5/3

x=(-y-5)/3

2.) Solving for Y problem 1#

y-3x+15=10

y-3x+3x+15-15=10-15+3x

y=3x-5

1.) Solving for X problem 2#

6-4x=y

-4x+6-6=y-6

-4x/4=y-6/4

x=(y-6)/4

2.) Solving for Y problem 2#

6-4x=y

y=-4x+6

Answer:

Step-by-step explanation:

126 mi/h = (126 mi)/(1 h)·(5280 ft)/(1 mi)·(1 h)/(3600 s) = (126·5280/3600) ft/s

126 mi/h = 184.8 ft/s = 924/5 ft/s

__

In 2 seconds, the parachutist falls ...

  (184.8 ft/s)·(2 s) = 369.6 ft

Answer:

p(-5)=-11,987

p(3)=-227

Step-by-step explanation:

To find the value of the function p(-5) just substitute x=-5 into the function expression instead of x:

[tex]p(-5)=2\cdot (-5)^5-9\cdot (-5)^4-2\cdot (-5)^2+12\cdot (-5)-2=\\ \\=-6,250-5,625-50-60-2=-11,987[/tex]

To find the value of the function p(3) just substitute x=3 into the function expression instead of x:

[tex]p(3)=2\cdot 3^5-9\cdot 3^4-2\cdot 3^2+12\cdot 3-2=\\ \\=486-729-18+36-2=-227[/tex]

Answer with Step-by-step explanation:

We are given a function:

[tex]p(x) = 2x^5-9x^4-2x^2+12x-2[/tex]

We have to find the value of p(-5) and p(3)

[tex]p(-5) = 2\times (-5)^5-9\times (-5)^4-2\times (-5)^2+12\times (-5)-2\\\\=-6250-5625-50-60-2\\\\=-11987[/tex]

[tex]p(3) = 2\times 3^5-9\times 3^4-2\times 3^2+12\times 3-2\\\\=486-729-18+36-2\\\\=-227[/tex]

Hence, p(-5)= -11987

and p(3)= -227

Answer:

A. EAB and EDC by AAA because congruent corresponding angles lead to similar triangles regardless of side length. This postulate works because the parallel lines cause angle a and angle d to be congruent as well as angle b being congruent to angle c, and vertical angle e is congruent.

Step-by-step explanation:

[tex]x^3-8=0[/tex]

[tex]x^3=8=8\mathrm{cis}\,0^\circ[/tex]

By DeMoivre's theorem, we have

[tex]x=8^{1/3}\mathrm{cis}\left(\dfrac{0^\circ+360^\circ k}3\right)[/tex]

with [tex]k=0,1,2[/tex]. Then we have three solutions,

[tex]x=2\mathrm{cis}\,0^\circ=2[/tex]

[tex]x=2\mathrm{cis}\,120^\circ[/tex]

[tex]x=2\mathrm{cis}\,240^\circ[/tex]

v + 4 + v = 8

The first thing I'd do is add up those two vs:

2v + 4 = 8

Answer: last choice, 2v + 4 = 8

Answer:

d. 2v  + 4 = 8

Step-by-step explanation: just took the test

Answer:

  375 ft

Step-by-step explanation:

The increase in height in the 1st second is 103 ft. In the 2nd second, it is 192-103 = 89 ft, a decrease of 14 ft. In the next three seconds, the increases in height can be expected to be ...

  89 -14 = 75 ft

  75 -14 = 61 ft

  61 -14 = 47 ft

for a total increase in height over those 3 seconds of ...

  75 + 61 + 47 = 183 ft

Then the height  after 5 seconds in the air is ...

  192 ft + 183 ft = 375 ft

_____

You can model the height function with the quadratic equation ...

  h(t) = at^2 +bt

We need to find the values of "a" and "b", which we can do by substituting the given data point values. The given data is ...

  h(1) = a + b = 103

  h(2) = 4a + 2b = 192

Subtracting twice the first equation from the second, we get

  (4a +2b) -2(a +b) = (192) -2(103)

  2a = -14 . . . . . simplify

  a = -7 . . . . . . . divide by 2

  b = 103 -a = 110 . . . . find b using the first equation

Then the quadratic model of height is ...

  h(t) = -7t^2 +110t

and the height at 5 seconds is ...

  h(5) = -7·25 +110·5 = 375 . . . feet

Answer:

  x = 9

Step-by-step explanation:

Adjacent angles A and D are supplementary:

  (30 +5x)° +(15 +10x)° = 180°

  15x +45 = 180 . . . . . collect terms, divide by °

  15x = 135 . . . . . . . . . subtract 45

  135/15 = x = 9 . . . . . divide by the coefficient of x

The value of x is 9.

Answer:

Probably because learning to do polynomials by hand boosts understanding of the topic and improves general algebraic solving ability,both of which are required in further topics like advanced calculus and algebra

Learning polynomial division by hand is crucial for understanding concepts, enhancing problem-solving skills, and fostering critical thinking in mathematics.

The importance of learning polynomial division by hand despite the availability of computer algebra systems lies in developing a deep understanding of the underlying concepts, fostering problem-solving skills, and enabling visualization of geometric interpretations.

By manually carrying out mathematical operations, students can better grasp the logic behind the processes, which aids in building a strong foundation for more complex mathematical tasks.

Furthermore, mastering hand calculations equips students with the ability to perform quick mental math, apply critical thinking skills, and comprehend the practical applications of the mathematical concepts.

Answer:

graph g(x)=1/4 x^2 - 2

Step-by-step explanation:

You are to replace x with (1/2x) in the expression x^2-2

So you have (1/2x)^2-2

1/4 x^2-2

Graph some points for g(x)=1/4 x^2-2

The vertex is (0,-2) and the parabola is open up.

I would graph 2 more points besides the vertex

x   |  g(x)                     ordered pairs to graph

-----------                         (-1,-1.75) and (0,-2) and (1,-1.75)

-1        -1.75

0         -2

1         -1.75

Comment has been deleted

Answer:

the second option and x=20

Answer:

the second one and then x=20

Step-by-step explanation:

What he said. It's correct.

Answer:

  7 days

Step-by-step explanation:

At 25% per day, it will take approximately 3 days to double the population, so approximately 6 days for the population to quadruple. Checking that number, we find it is not quite enough for the experiment, so another day is required.

"Guess and check" as a method of solution works especially well if you have an automated checker to evaluate your guess. A graphing calculator or spreadsheet can work well for this.

_____

We guess 3 days as the doubling time using the "rule of 72" that says the product of percentage and doubling time is about 72. That is, 72/25 ≈ 3. (This is only a very rough approximation of doubling time, best for rates near 8%.)

Answer:

the answer is 20P4 = 4845

Step-by-step explanation:

Answer:

There are 20 ways to pick the first book, 19 ways for the second

Step-by-step explanation:

If order of the 4 books does not matter then

₂₀C₄ = 20! / (20-4)!4! = 20!/(16!*4!) = 4845 ways

Answer:

A. 10mn³

Step-by-step explanation:

To divide numbers in power form but to the same base, we simply subtract the powers and then divide the coefficients of the the bases.

-50m³n⁵ /-5m²n²

=10m⁽³⁻²⁾ n⁽⁵⁻²⁾

=10mn³

A negative number divided by a negative number = a positive number.

Answer:

b

Step-by-step explanation:

hope this helps

Answer:

width 8 centimeters

length 24 centimeters

Step-by-step explanation:

L=3W : equation a       .

W=64/xW : equation b .

x=2L+2W                       .

 =2(3W)+2W                  .

x=8W                              .

Answer:

Length = 24 cm

and, Width = 8 cm

Step-by-step explanation:

It is given that,

Length = 3 × (width)

⇒ L = 3W        → (1)

Also, since perimeter = 64 cm

And perimeter of rectangular garden = 2(L + W) = 64

From equation (1)

2(3W + W) = 64

2 × 4W = 64

⇒ 8W = 64

⇒ W = 8 cm

Putting value in equation (1)

L = 3 × 8 = 24 cm

thus, Length = 24 cm

and, Width = 8 cm

Answer: The slope of the line is: [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

The slope can be calculated with this formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

You need to choose two points of the line. You can pick the point (6,2) and the point (-6,-6)

You can identify that:

[tex]y_2=-6\\y_1=2\\x_2=-6\\x_1=6[/tex]

Now, you must substitute these values into the formula:

[tex]m=\frac{-6-2}{-6-6}[/tex]

With this procedure you get that the the slope of the line on the graph is:

[tex]m=\frac{-8}{-12}[/tex]

[tex]m=\frac{2}{3}[/tex]

Step-by-step explanation:

log(7·x + 7) = 1

7·x + 7 = 10^1

7·x = 10 - 7

x = 3/7 = 0.4285714285

Answer:

0.429

Step-by-step explanation:

Answer:

Step-by-step explanation:

Observational probability

Answer:

0.5

Step-by-step explanation:

A roulette wheel is half red and half black.  Each spin is independent: past spins don't change the probability of future spins.  So even if you got 8 reds in a row, the probability of the next spin being red is still 50/50.

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A=4000\left(1+\frac{0.055}{1}\right)^{1\cdot 4}\implies A=4000(1.055)^4\implies A\approx 4955.2986[/tex]

Answer:

$ 4955.30 ( approx )

Step-by-step explanation:

The formula for compound interest is,

[tex] A(t)=P(1+i)^t[/tex]

Where, P is the principal amount,

i is the rate per period,

t is the number of periods,

Here, P = $ 4000,

i = 5.5% = 0.055

t = 4 years,

By substituting the values,

The amount in the account after 4 years would be,

[tex]A=4000(1+0.055)^4=4000(1.055)^4=4955.2986025\approx \$4955.30[/tex]

Answer: 720 mph or 12 miles a minute

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

(I actually have the problem in front of me, and I think you switched the minute and hour hands on the clock)

Adel

left at 5:30 and arrived at 8:30. That’s 3 hours, which is 180 minutes. 180/180 = 1 mile per minute

60 minutes in an hour

60*1 = 60 mph

4, 5, and 7 are mutually coprime, so you can use the Chinese remainder theorem right away.

We construct a number [tex]x[/tex] such that taking it mod 4, 5, and 7 leaves the desired remainders:

[tex]x=3\cdot5\cdot7+4\cdot2\cdot7+4\cdot5\cdot6[/tex]

[tex]x\equiv3\cdot5\cdot7\equiv105\equiv1\pmod4[/tex]

so we multiply the first term by 3.

[tex]x\equiv4\cdot2\cdot7\equiv51\equiv1\pmod5[/tex]

so we multiply the second term by 2.

[tex]x\equiv4\cdot5\cdot6\equiv120\equiv1\pmod7[/tex]

so we multiply the last term by 7.

Now,

[tex]x=3^2\cdot5\cdot7+4\cdot2^2\cdot7+4\cdot5\cdot6^2=1147[/tex]

By the CRT, the system of congruences has a general solution

[tex]n\equiv1147\pmod{4\cdot5\cdot7}\implies\boxed{n\equiv27\pmod{140}}[/tex]

or all integers [tex]27+140k[/tex], [tex]k\in\mathbb Z[/tex], the least (and positive) of which is 27.

Answer:

e. none of the above

Step-by-step explanation:

I had this question as well and if you look closely, the question describes the function in terms of rabbits, when the actual question describes fish. I believe that because the question is asking for fish when only information on rabbits has been given, the only logical answer would be e. none of the above...

Final answer:

The correct formula representing the total number of rabbits after x weeks, with a starting population of 150 and a decrease of 15% per week, is F(x) = 150 (0.85)ˣ. The correct option is d.

Explanation:

The rabbit population in a small zoo starts with 150 rabbits and decreases at a rate of 15% each week. To represent the total number of rabbits, F(x), after x number of weeks, we need to find the correct formula. A decrease of 15% per week is the same as the population being at 85% of the previous week's population (100% - 15% = 85%). So, the correct formula would be the initial population multiplied by the weekly percentage to the power of the number of weeks. Therefore, the correct formula is F(x) = 150 (0.85)ˣ, which corresponds to option d.

Answer:

35 combinations

Step-by-step explanation:

You have to use the formula for finding combinations in probability.  It looks like this:

₇C₃ = [tex]\frac{7!}{3!(7-3)!}[/tex]

so that gives you

₇C₃ = [tex]\frac{7*6*5*4!}{3*2*1*4!}[/tex]

The 4 factorials cancel each other out, and when you do the math, you get 210/6.  That divides evenly into 35.  So there are 35 combinations.

Answer:

There are 10 possible ways the student can schedule the three classes

Step-by-step explanation:

The college student is choosing 3 classes to take during the first, second, and third semester from 5 electives.

Therefore, the student is choosing 3 items from a total of 5 and the order is not of key concern here. This is thus a combination problem;

5C3 = 10

read as 5 choose 3

The above mathematical operation can be performed using any modern calculator.

Answer:

  (x, y) = (2, -3/4)

Step-by-step explanation:

The point of the "elimination" technique is to combine the equations in a way that eliminates one of the variables. Sometimes this involves multiplying one or both of the equations by constants before you add those results together. In any event, the first step is to look at the coefficients of the variable terms to see if there is a simple combination of them that will result in zero.

The y terms have coefficients that are opposites of each other (4, -4), so you can simply add the two equations to eliminate y as a variable.

  (2x +4y) +(x -4y) = (1) +(5)

  3x = 6 . . . . . simplify

  x = 2 . . . . . . divide by 3

Now, you find y by substituting this value into one of the equations. I would choose the equation with the positive y-coefficient:

  2(2) +4y = 1

  4y = -3 . . . . . . subtract 4

  y = -3/4

Then the solution is ...

  (x, y) = (2, -3/4)

_____

A graphing calculator confirms this solution.