[tex]\sqrt{4x+15} -3\sqrt{x} =0[/tex]

[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]

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:

  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:

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:

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.

The company inventory consists of 51 bags of Colombian and 33 bags of Brazilian beans. Each bag holds 80 pounds of beans, so in total the company has 4080 pounds of Colombian and 2640 pounds of Brazilian beans.

The company wants to use up its entire inventory, a total of 6720 pounds of beans.

Let [tex]r[/tex] and [tex]m[/tex] denote the amount (in pounds) of the robust and mild blends, respectively, that the company should end up producing.

To use the entire inventory, we must have

[tex]r+m=6720[/tex]

Each pound of the robust blend uses 12 ounces (3/4 = 0.75 pound) of Colombian beans, and each pound of the mild blend uses 6 ounces (3/8 = 0.375 pound) of Colombian beans, so that

[tex]0.75r+0.375m=4080[/tex]

while each pound of the robust blend uses 4 ounces (1/4 = 0.25 pound) of Brazilian beans, and each pound of the mild blend uses 10 ounces (5/8 = 0.625 pound) of Brazilian beans, so that

[tex]0.25r+0.625m=2640[/tex]

Multiply both equations by 8 to get rid of the rational coefficients:

[tex]\begin{cases}6r+3m=32640\\2r+5m=21120\end{cases}[/tex]

Subtract 3(second equation) from (first equation) to eliminate [tex]r[/tex]:

[tex](6r+3m)-3(2r+5m)=32640-3\cdot21120[/tex]

[tex]-12m=-30720\implies\boxed{m=2560}[/tex]

Then

[tex]r+2560=6720\implies\boxed{r=4160}[/tex]

So the company needs to produce 4160 pounds of the robust blend and 2560 pounds of the mild blend.

Check the picture below.

Answer:

the vertex is:

(2, -1)

Step-by-step explanation:

First solve the equation for the variable y

[tex]x^2-16y-4x-12=0[/tex]

Add 16y on both sides of the equation

[tex]16y=x^2-16y+16y-4x-12[/tex]

[tex]16y=x^2-4x-12[/tex]

Notice that now the equation has the general form of a parabola

[tex]ax^2 +bx +c[/tex]

In this case

[tex]a=1\\b=-4\\c=-12[/tex]

Add [tex](\frac{b}{2}) ^ 2[/tex] and subtract [tex](\frac{b}{2}) ^ 2[/tex] on the right side of the equation

[tex](\frac{b}{2}) ^ 2=(\frac{-4}{2}) ^ 2[/tex]

[tex](\frac{b}{2}) ^ 2=(-2) ^ 2[/tex]

[tex](\frac{b}{2}) ^ 2=4[/tex]

[tex]16y=(x^2-4x+4)-4-12[/tex]

Factor the expression that is inside the parentheses

[tex]16y=(x-2)^2-16[/tex]

Divide both sides of the equality between 16

[tex]\frac{16}{16}y=\frac{1}{16}(x-2)^2-\frac{16}{16}[/tex]

[tex]y=\frac{1}{16}(x-2)^2-1[/tex]

For an equation of the form

[tex]y=a(x-h)^2 +k[/tex]

the vertex is: (h, k)

In this case

[tex]h=2\\k =-1[/tex]

the vertex is:

(2, -1)

Answer:

  A.  Algebraic, common difference = −10

Step-by-step explanation:

The difference between the first two terms is -10, as it is between the next two terms. The ratio of the first two terms is -1; of the next pair: -15/-5 = 3. There is a common difference, but not a common ratio.

The sequence is algebraic with a common difference of -10.

Answer:

Correct answer is A.  Algebraic, common difference = −10

I can't understand the question

Rewrite/edit the question and I may be able to help you with the answer!

if henry goes to the library the world is a better place

Answer:

-x⁴ + 3x² is the standard form, and this is a quartic binomial.

Step-by-step explanation:

We look to see if there are any like terms first. x² and 2x² are like terms; they combine to make 3x². So this polynomial really only has two terms when simplified.

The standard form of a polynomial has all of its terms in decreasing order of degree.

  -x⁴ ⇒ degree 4

  3x² ⇒ degree 2

Therefore, standard form is

  -x⁴ + 3x²

The degree of this polynomial is the degree of the highest degree term, which is 4. A degree 4 polynomial is called a quartic polynomial.There are two terms, so we can further classify this as a binomial.

Therefore, the answer is quartic binomial

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:

y= -2/3x - 2 and y= -2/3x+2

Step-by-step explanation:

There are two standard forms given

1) 2x + 3y= -6

2) 2x + 3y = 6

Equation of a graphed line is written as y=mx+c

Step 1: Make y the subject on the left side. On the right side, make sure that x comes first.

1) 2x + 3y= -6

  3y = -6 - 2x

  y = -6-2x

          3

  y = -2x/3 - 2

2) 2x + 3y = 6

   3y = 6 - 2x

    y = 6-2x

          3

  y = -2x/3 + 2

!!

Answer:

the answer is aaaaaaaaaaaaaaaaa

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.

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.

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:

Choice C

Step-by-step explanation:

5 Thousand  + 15 hundred = 6500

Answer:

it c

Step-by-step explanation:

To round the sum of a sequence properly, consider the precision of the terms given. For example, an answer of 921.996 from a calculator should be rounded to 922.00, aligning with the hundredth place of the term 13.77 as the most precise figure. Apply appropriate rounding rules such as rounding up if the next digit is greater than 5.

When calculating the sum of a sequence and needing to round the answer to a specific decimal place, we must pay close attention to the significant figures and rounding rules.

For instance, if a calculator gives an answer of 921.996, we should round to the nearest hundredth.

This is because the last significant figure in the given sequence's general term (for example, 13.77) is in the hundredth place.

Following the rule of rounding, if the first digit to be dropped is greater than 5, we round up.

Therefore, the answer would be rounded to 922.00.

Let's consider other examples:

For the calculation resulting in 119.902, since we're limiting it to the tenths place, we round down to 119.9.

For 201.867, rounding to the hundredth place gives us 201.87.

When rounding 2,085.5688 to five significant figures, we get 2,085.6.

For a quick intuitive check, recall that one eighth of 1,000 is 125, a simple multiplication by a reciprocal number without doing long division.

In summary, always align your rounding method to the precision indicated by the sequence terms or the specific requirements of the question.

Answer:

The area of the kite is [tex]56\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The area of the kite is equal to

[tex]A=\frac{1}{2}(D1*D2)[/tex]

where

D1 and D2 are the diagonals of the kite

we have

[tex]D1=4+4=8\ cm[/tex]

[tex]D2=10+4=14\ cm[/tex]

Find the area

[tex]A=\frac{1}{2}(8*14)=56\ cm^{2}[/tex]

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:

  17.2 m

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you the relationship between the adjacent side of a right triangle and the opposite side is given by ...

  Tan = Opposite/Adjacent

Filling in the given information, we have ...

  tan(25°) = (8 m)/distance

  distance = (8 m)/tan(25°) ≈ 17.156 m

The man is about 17.2 meters from the tower.

Final answer:

The distance of the man from the tower can be found by dividing the height of the tower (8m) by the tangent of the 25-degree angle, using trigonometry.

Explanation:

The distance of the man from the tower is determined using trigonometry, where we have a right-angled triangle with the tower's height as the opposite side and the distance of the man from the tower as the adjacent side to the 25-degree angle.

To find the adjacent side (the distance from the man to the tower), we can use the trigonometric function tangent, which relates the opposite side to the adjacent side in a right-angled triangle.

The formula is:

tangent(25 degrees) = opposite / adjacent

Plugging in the value of the tower's height:

tangent(25 degrees) = 8m / distance

Solving for the distance:

distance = 8m / tangent(25 degrees)

[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]

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

The answer is:

The interval notation will be:  (-∞,-1.59) and (-4.41,∞+)

To solve the expression, we need to perform the following steps:

- Find the roots or zeroes of the expression:

Using the quadratic equation, we have:

[tex]\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}[/tex]

We are given the quadratic expression:

[tex]x^{2} +6x+7[/tex]

Where,

[tex]a=1\\b=6\\c=7[/tex]

Then, substituting and calculating we have:

[tex]\frac{-6+-\sqrt{6^{2}-4*1*7 } }{2*1}=\frac{-6+-\sqrt{36-28 } }{2}\\\\\frac{-6+-\sqrt{36-28}}{2}=\frac{-6+-\sqrt{8}}{2}\\\\x_{1}=\frac{-6+\sqrt{8}}{2}=\frac{-6+2.82}{2}=-1.59\\\\x_{2}=\frac{-6-\sqrt{8}}{2}=\frac{-6-2.82}{2}=-4.41[/tex]

- Inequality interpretation:

Now that we already know the roots of the quadratic expression, and we can see that the parabola open upwards (positive quadratic coefficient), we can conclude that the function is less than 0 between the numbers -4.41. and -1.59

The interval notation will be:and  (-∞,-1.59) and (-4.41,∞+)

Have a nice day!

Note: I have attached a picture for better understanding.

Answer:

The other guy is absolutely right, however

we can change his 4.41 to 3 + or - sqrt2

Step-by-step explanation:

So C

Answer:

x=10

Step-by-step explanation:

$52-$22=$30

$30/3=$10=x

The price of each shirt is x=10

Cost price is the complete sum of money that a manufacturer must spend to create a specific good or render a specific service.

Given

x to represent the shirt's price

$52-$22=$30

$30/3=$10=x

To know more about cost price refer to :

https://brainly.com/question/19104371

#SPJ2

Answer: Option 1) 2.33

Step-by-step explanation:

For the 98% confidence interval we have that the area between 0 and the z score is equal to:

98% corresponds to 0.98

then the area between 0 and z is half of that:

a = 0.98/2 = 0.490

Now you can search in a table, and you will find that the z-score for this is z = 2.326

So the correct answer is 1) 2.33

where the result is rounded up.

The value of z we should  use when making a 98% confidence interval for p is mathematically given as

x= 2.33

Option A

Generally, we solve for

1/2* 0.98 = 0.49

Using the Normal curve table we determine that the nearest value  0.4901 and its z value is 2.33

Option A

For more information on Arithmetic

https://brainly.com/question/22568180

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:

Option D. The number of butterflies Kyle started with

Step-by-step explanation:

In this problem we have

x -----> the time in years

f(x) ----> the number of Kyle's butterfly collection

Observing the table

For x=0

f(0)=5 -----> this is the initial value of butterflies Kyle started with

For x=2

f(2)=20 -----> the number of butterflies in two years

For x=4

f(4)=80 -----> the number of butterflies in four years

therefore

5 represent the number of butterflies Kyle started with

Answer:

option D

Step-by-step explanation:

Answer:

Right side towards positive x axis

Step-by-step explanation:

Let us see the basic rule to find the orientation of parabolas.

1.  If power if x is 2 and y is 1 , the parabola opens up or down.

2. If the power of y is 2 and that of x is 1 , the parabola opens right or left.

3. If the coefficient of [tex]x^{2}[/tex] in case 1 is negative it opens downward

4. If the coefficient of [tex]y^{2}[/tex]  in case 2 is negative , it opens left towards negative x axis.

Hence our equation is

[tex]x=y^2-9[/tex]

here is satisfies the case 2. hence it opens right or left . Also the coefficient of  

[tex]y^{2}[/tex] is positive so it opens up to the right side , that is towards positive x axis.

the correct answer is c.) right.

The student's question pertains to the orientation of a parabola described by the equation x = y² - 9. In order to determine the direction in which the parabola opens, we observe the equation. The parabola relates y² to x, indicating that for every value of y, we have a corresponding value of x. Since y² is the variable being squared and x is by itself, the parabola is a sideways parabola. Furthermore, because there is no negative sign in front of the y² term, the parabola opens to the right of the coordinate system. Therefore, the correct answer is c.) right.