Solve each equation. State the restrictions. Check your solution.
1)
4
2x
=
5
x+6

Answer:

\( \frac{2}{3} \times 2 \\ = \frac{4}{3} \)

omitir

Step-by-step explanation:

_________________

The limit of the function as x approaches -2 is 20.To find the limit of the function (if it exists), we can substitute the given value into the function and simplify. Given function: f(x) = 4x² + 5x - 6x + 2

To find the limit as x approaches -2, we substitute -2 into the function:

f(-2) = 4(-2)² + 5(-2) - 6(-2) + 2
      = 4(4) - 10 + 12 + 2
      = 16 - 10 + 12 + 2
      = 20

Therefore, the limit of the function as x approaches -2 is 20.

To write a simpler function that agrees with the given function at all but one point, we can use a graphing utility. By plotting the given function and observing its behavior, we can create a simpler function that matches the original function except at one point.

However, without further information about the specific behavior of the given function, it is not possible to provide a more detailed explanation or a graph of the simpler function.

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Answer:

  t ≈ 0.0664731

Step-by-step explanation:

Use the inverse sine function.

  sin(12t) = 141/197

  12t = arcsin(141/197)

  t = arcsin(141/197)/12

  t ≈ 0.0664731 . . . . . . . radians

__

This is the principal value. There are other solutions at values of t that have integer multiples of π/6 added to this. There are also solutions where any of those values is subtracted from π.

_____

In general, angles in math are assumed to be in radians, unless specified otherwise. This angle corresponds to about 3.81°. (In geometry, the usual assumption is that angles are measured in degrees.)

Answer:

Taco Yum because 9.99/12 = .8325 which makes it 83 cents per taco at taco ringer and taco yum's are .79 cents

Step-by-step explanation:

Answer:

Taco Yum sells the cheapest tacos

Step-by-step explanation:

Taco Yum sells his tacos for $0.79

Taco Ringer sells his tacos for around $0.84 (by the math problem 9.99/12)so by $0.05 Taco Tum is cheaper

Given that the height of a object thrown within a gravitational field is given as a quadratic equation in time, t, the time at which the object is at a specified height can be found by the quadratic formula

The values of, t, for which the height of the rocket is 82 feet are;

t = 12.21 seconds or t = 0.42 seconds

Question: Parts of the question that appear missing but can be found online are (i) To find the values of the time, t, when the rocket's height is 82 feet and round answers to the nearest hundredth

The known parameters of the rocket are;

The initial upward velocity of the rocket, v = 202 ft./s

The given function representing the height, h, (in feet) after t seconds is presented as follows;

H = 202·t - 16·t²

The unknown;

The time for which the height of the rocket is 82 feet

Method;

Substitute H = 82 feet in the height function equation and solve for t as follows;

When H = 82, we get;

82 = 202·t - 16·t²

Therefore;

16·t² - 202·t + 82 = 0

Dividing the above equation by 2 gives;

(16·t² - 202·t + 82)/2 = 0/2

8·t² - 101·t + 41 = 0

By using the quadratic formula, we get;

\(\mathbf{t = \dfrac{101 \pm \sqrt{(-101)^2 - 4 \times 8 \times 41} }{2 \times 8} = \dfrac{101 \pm \sqrt{8889} }{16}}\)

Therefore, the values of t given by rounding off to the nearest hundredth are;

t = 12.21 or t = 0.42

The values of the time, t, at which the height of the rocket is 82 feet are t = 12.21 seconds or t = 0.42 seconds

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Answer:

1/6 hour, or 10 minutes

Step-by-step explanation:

This is a subtraction problem.

1/2 - 1/3 =

We need a common denominator for 2 and 3. We can use 6.

= 1/2 * 3/3 - 1/3 * 2/2

= 3/6 - 2/6

= 1/6

Answer: 1/6 hours, or 10 minutes

The distance of the base of the mast to the stay is 12 feet.

The mast and the stay form a right angled triangle. In order to determine the distance of the base from the stay , Pythagoras theorem would be used.

The Pythagoras theorem: a² + b² = c²

where:

√37² - 35²

= √144 = 12 ft

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Answer:

X = 11/36

Step-by-step explanation:

First, find the common denominator of the fractions and convert them.

(4/9) x 4 = 16/36

(3/4) x 9 = 27/36

X + 16/36 = 27/36

Now you can solve for X

X = 11/36

The fraction cannot be simplified

The average rate of change (AROC) of a function f(x) on an interval [a, b] is equal to the slope of the secant line to the graph of f(x) that passes through (a, f(a)) and (b, f(b)), a.k.a. the difference quotient given by

\(f_{\mathrm{AROC}[a,b]} = \dfrac{f(b)-f(a)}{b-a}\)

So for f(x) = x² on [1, 5], the AROC of f is

\(f_{\mathrm{AROC}[1,5]} = \dfrac{5^2-1^2}{5-1} = \dfrac{24}4 = \boxed{6}\)

The value of the longest of the four side lengths is 13 meters.

Let us assume the smallest side of quadrilateral be x. The consecutive sides of quadrilateral will be (x + 1), (x + 2) and (x + 3). As per the known fact, the perimeter is the sum of all the sides of quadrilateral.

x + x + 1 + x + 2 + x + 3 = 42

Performing addition on Left Hand Side of the equation

4x + 6 = 42

Shifting 6 to Right Hand Side of the equation

4x = 42 - 6

Performing subtraction on Right Hand Side of the equation

4x = 36

Shifting 4 to denominator on Right Hand Side of the equation

x = 36 ÷ 4

Performing division Right Hand Side of the equation

x = 9 meters

Longest side of quadrilateral = x + 4

Longest side of quadrilateral = 9 + 4

Longest side of quadrilateral = 13 meters

Therefore, the longest side of quadrilateral is 13 meters.

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Answer:

from the graph we can see that

for 2 gallones - it can travell 70 miles

4 gallones - 140 miles

we will take the first case

2 gallones - 70 miles

17 gallones - ? miles

cross multiply

\( \frac{17 \times 70}{2} \)

= 595 miles

Answer:

\(x = 14\)

\(2x = 28\)

Step-by-step explanation:

Given

See attachment

Required

Find x and 2x

From the attached image, we have:

\(2x = 28\) --- vertical angles

Divide both sides by 2

\(x = 14\)

Answer:

31

Step-by-step explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)

a = 1, b = 1 and c = -930

\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)

\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31

5 feet and 3 inches, 1 foot=12 inches, 12×5=60+3=63×5=315. so your answer is 315

\(1.4 < \sqrt{2} < 1.5\hspace{5em}1.7 < \sqrt{3} < 1.8 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lllll} 1.7& < &\sqrt{3}& < &1.8\\\\ 1.7-\sqrt{2}& < &\sqrt{3}-\sqrt{2}& < &1.8-\sqrt{2}\\\\ 1.7-1.5& < &\sqrt{3}-\sqrt{2}& < &1.8-1.4\\\\ 0.2& < &\sqrt{3}-\sqrt{2}& < &0.4 \end{array}\)

we're subtracting the upper-bound of √2, so is the most we can subtract from 1.7, and we're subtracting the lower-bound of √2 from 1.8, that way the resultant is within range.

Answer:

Given:

Area of the sector (A) = 104π/9 square inches

Central angle (θ) = 65 degrees

The formula for the area of a sector of a circle is:

A = (θ/360) * π * r^2

We can rearrange this formula to solve for the radius (r):

r^2 = (A * 360) / (θ * π)

Plugging in the given values:

r^2 = (104π/9 * 360) / (65 * π)

r^2 = (104 * 40) / 9

r^2 = 4160 / 9

r^2 ≈ 462.22

Taking the square root of both sides:

r ≈ √462.22

r ≈ 21.49

Therefore, the radius of the circle is approximately 21.49 inches.

Answer: 8 inches

Step-by-step explanation:

Answer:

6000 lbs is greater then 5000!

Step-by-step explanation:

Answer:

Yes the samples can be drawn from a population with the same mean and standard deviation 10 hours

Step-by-step explanation:

We are given;

Sample mean for male employees; x1¯ = 63

Sample mean for female employees; x2¯ = 66

Sample size = 50

Standard deviation; σ = 10

First,let's define the hypotheses of the question;

Null hypothesis; H0: μ1 = μ2

Alternative hypothesis; Ha: μ1 ≠ μ2

Now, let's find the test statistic from the formula;

z = (x1¯ - x2¯)/(σ√(2/n))

Thus;

z = (63 - 66)/(10√(2/50))

z = -3/2 = - 1.5

Now, we are not given the significance value but usually when it is not given, we can adopt α = 0.05.

Thus, from online p-value from z-score calculator using; z = -1.5; α = 0.05; two tailed test; we have;

p-value = 0.13364

The p-value is greater than the significance value and thus we will fial to reject the null hypothesis and conclude that these samples can be drawn from a population with the same mean and standard deviation

a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation, we can rewrite it in the form:

\(x' = Ax\)

where x is a vector and A is a square matrix.

b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.

If all eigenvalues have negative real parts, the system is stable.

If at least one eigenvalue has a zero real part, the system is neutrally stable.

If at least one eigenvalue has a positive real part, the system is unstable.

c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation

\(det(A - \lambda I) = 0\),

where λ is the eigenvalue and I is the identity matrix.

By solving this equation, we obtain the eigenvalues.

Substituting each eigenvalue into the equation

\((A - \lambda I)v = 0\),

where v is the eigenvector, we can solve for the eigenvectors.

d) Once we have computed the eigenvalues and eigenvectors of matrix A, we can construct the diagonalization relationship as follows:

\(A = PDP^{(-1)}\)

where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix whose diagonal elements are the eigenvalues of A.

To show that this relationship is valid, we can compute \(PDP^{(-1)}\) and verify that it equals A.

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Answer:

56 minutes

Step-by-step explanation:

We can use proportions to solve.

6 miles            8 miles

------------     = ------------------

42 minutes        x minutes

Using cross products.

6x = 42 *8

Divide each side by 6

x = 42/6 * 8

x = 7*8

x = 56

Answer:

D.

Step-by-step explanation:

To find how much tons each tank can hold, we can use this equation:

So, each tank can hold 28 tons.

To solve for the number of tanks needed to ship 420 tons of gasoline, we can use this equation:

To check, we can use this equation:

Therefore, to ship 420 tons of gasoline with each tank containing 28 tons, the company will need 15 tanks.

Answer:

\(r=-3\)

Step-by-step explanation:

The line that passes through the two points (6, -23) and (11, r) has a slope of 4.

We want to determine the missing value of r.

We can use the slope formula:

\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)

Let (6, -23) be (x₁, y₁) and let (11, r) be (x₂, y₂). The final answer should be 4. Therefore:

\(\displaystyle \frac{r-(-23)}{11-6}=4\)

Simplify and evaluate:

\(\displaystyle \frac{r+23}{5}=4\)

Multiply both sides by 5:

\(r+23=20\)

Therefore:

\(r=-3\)

Answer:6 pens are blue

Step-by-step explanation:because 14-8=6 pens would be left and would be blue

Answer:

Slope (m): 1/2

Step-by-step explanation:

The rise is 1. As you can see on (-6,0), it goes up one and goes to the right 2 times. ( rise/run). This pattern continues as you can see on your graph.

Answer:

Step-by-step explanation:

21/4= 5.25

or round to 5 whole slices per pizza

1+2+3+4+5+6+7+8+9×2+14

Answer:

correct answer is a = (v - u)/t

Answer:

correct answer is a = (v - u)/t

Step-by-step explanation:

Answer:

18 student gave there speech yesterday

36 students gave there speech today

Step-by-step explanation:

54 total

54 * 1/3 = 18 student gave there speech yesterday

54*2/3 = 36 students gave there speech today

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