[tex]3a - 2 - b - a[/tex]

[tex]\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+6}x\stackrel{\stackrel{c}{\downarrow }}{+9}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{\underline{one real solution}}~~\textit{\Large \checkmark}\\ positive&\textit{two real solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ 6^2-4(1)(9)\implies 36-36\implies 0[/tex]

[tex]\bf \cfrac{x^8}{x^{14}}\implies x^8x^{-14}\implies x^{8-14}\implies x^{-6}\implies \stackrel{\textit{using the power rule}}{-6x^{-7}\implies \cfrac{-6}{x^7}}[/tex]

Question 1:

We have the following expression:

[tex]4x ^ {-4}[/tex]

By definition of power properties we have to:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Then, rewriting the expression:

[tex]\frac {4} {x ^ 4}[/tex]

ANswer:

[tex]\frac {4} {x ^ 4}[/tex]

Question 2:

For this case we have the following expression:

[tex]\frac {x ^ 8} {x ^ {14}} =[/tex]

By definition of power properties of the same base we have:

[tex]x ^ n * x ^ m = x ^ {n + m}[/tex]

Then, we can rewrite the denominator of the expression as:

[tex]\frac {x ^ 8} {x ^ 8 * x ^ 6} =[/tex]

Simplifying terms of the numerator and denominator:

[tex]\frac {1} {x ^ 6}[/tex]

ANswer:

[tex]\frac {1} {x ^ 6}[/tex]

Answer:

[tex]f(x) = {2}^{x } \\ f(x) = 8 \\ \\ {2}^{x} = 8 \\ \\ {2}^{x } = {2}^{3} \\ \\ x = 3[/tex]

The value of x when f(x) = 8 is 3 in f(x) = 2^x

from the question, we have the following parameters that can be used in our computation:

f(x) = 2^x

To find the value of x when f(x) = 8, we need to solve the equation 2^x = 8.

We can rewrite 8 as 2^3

So, the equation becomes:

2^x = 2^3

Since the bases are the same, we can equate the exponents:

x = 3

Hence, the value of x when f(x) = 8 is 3.

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Answer:

178.98 square feet

Step-by-step explanation:

Alright so we need to find two areas here and find the difference to find the area of the path.

The two shapes involved is a smaller circle inside a bigger circle.

Let's look at the smaller circle, the gardening area.

You are given is has a radius of 8 ft.

The area of a circle is [tex]\pi \cdot r^2[/tex] where r is the radius.

So the area of the smaller circle is [tex]\pi \cdot 8^2[/tex].

Now time to look at the bigger area (which will have some overlapping area with the smaller one which will subtract out to find the area of path).

The diameter of the smaller circle was (8+8)=16 feet.

What is the diameter of the bigger one.  The path is 3 ft wide so we have to add a 3 before the diameter of the smaller circle to another 3 after that diameter to get the diameter of the bigger circle.  So the diameter of the bigger circle is (3+16+3)=22 feet.  The radius is half the diameter so the radius is 22/2=11.

The area of the bigger circle is [tex]\pi \cdot 11^2[/tex].

The area of the path=

the area of bigger circle     -      the area of smaller circle=

[tex]\pi \cdot 11^2-\pi \cdot 8^2[/tex]

Type this into your calculator with 3.14 instead of the [tex]\pi[/tex] button.

178.98 square feet

The answer is:

[tex]PathArea=178.98ft^{2}[/tex]

To calculate the are of the path alone, we need to add the width of the path to the radius of the garden in order to know is radius, then, calculate the total  area (using garden radius plus path width) and then, subtract it the area of the circular garden.

We know that the radius of the circular garden is equal to 8 feet, and the circular path has a width of 3 feet, so, the radius of the circular path will be:

[tex]CPath_{radius}=8feet+Path_{width}\\\\Path_{radius}=8feet+3feet=11[/tex]

Now, calculating the areas, we have:

Garden Area:

[tex]CircularGardenArea=\pi *radius^{2}\\\\CircularGardenRadius=\pi *8ft^{2}=3.14*64ft^{2}=200.96ft^{2}[/tex]

Total Area:

[tex]TotalArea=\pi *(8feet+3feet)^{2}=\pi *(11ft)^{2}=3.14*121ft^{2}=379.94ft^{2}[/tex]

Now, calculating the area of the path, we have:

[tex]TotalArea=CircularGardenArea+PathArea\\\\PathArea=TotalArea-CircularGardenArea\\\\PathArea=379.94ft^{2}-200.96ft^{2}=178.98ft^{2}[/tex]

Hence, we have that:

[tex]PathArea=178.98ft^{2}[/tex]

Have a nice day!

The event "not rolling 1, 3, 4, or 5" is the same event as "rolling 2 or 6".

Since the possible outcomes of a number cube have the same probability, the probability of rolling 2 or 6 is given by

[tex]\dfrac{\text{\# of good outcomes}}{\text{\# of possible outcomes}}=\dfrac{2}{6}=\dfrac{1}{3}[/tex]

Answer:

y-2=-4(x-1)

Step-by-step explanation:

point slope form is written as y-y1=m(x-x1). y1 and x1 are both the coordinates on the line. x1 is the x coordinate y1 is y coordinate. m is the slope.

Final answer:

The truth value of the conditional statement ¬q → ¬p, with p being true and q being false, is false.

Explanation:

The question is asking about the truth value of the conditional statement ¬q → ¬p, where p is true and q is false. In a conditional statement of the form 'if q then p', written symbolically as q → p, the statement is false only when q is true and p is false. Otherwise, the statement is true. In this case, ¬q means 'not q' and ¬p means 'not p'. Given that q is false, ¬q is true. Given that p is true, ¬p is false. Thus, the statement ¬q → ¬p is of the form 'true → false', which makes the entire conditional statement false.

Final answer:

The truth value for the conditional statement ¬q → ¬p when p is true and q is false is false. This is because the contrapositive of any conditional statement must have the same truth value as the statement itself, and the given condition does not maintain this logical equivalence.

Explanation:

The truth value for the following conditional statement ¬q → ¬p when p is true and q is false is what we are trying to determine. The proposition ¬q → ¬p is the contrapositive of the conditional p → q. According to logic, a conditional proposition and its contrapositive always have the same truth value. Since we are given that p is true and q is false (¬q is true), using the definitions of the logical operators, we find that the contrapositive of the original conditional should also be true if the original is true.

In this case, the contrapositive is ¬q → ¬p, which, when translated in terms of the given truth values, becomes true → false. This suggests that if ¬q is true, then ¬p is true as well; however, since we know p is true, the situation given (¬q is true, ¬p is false) is not possible because it would not uphold the truth of the original proposition. Thus, the provided sequence of truth values does not maintain the logical equivalence of the contrapositive, making it incorrect. Therefore, the truth value of ¬q → ¬p is false under the given conditions.

Answer:

ƒ(x) = (x - 1)(x - 2)(x - 3)  

Step-by-step explanation:

The graph shown is that of a cubic equation with zeros at x = 1, 2, and 3

The function in factored form must be

ƒ(x) = (x - 1)(x - 2)(x - 3).

When you solve for the zeros, the sign of the constant changes. For example

x - 1 = 0

   x = 1

Answer:

y = - x + 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (4, - 3)

m = [tex]\frac{-3-2}{4+1}[/tex] = [tex]\frac{-5}{5}[/tex] = -1, hence

y = - x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (- 1, 2), then

2 = 1 + c ⇒ c = 2 - 1 = 1

y = - x + 1 ← equation in slope- intercept form

The equation is y = –x + 1.

To find the slope-intercept form of a line passing through two points, calculate the slope using the given points and then use one point to find the y-intercept. The final equation for the line through the points (–1, 2) and (4, –3) is y = –x + 1.

To write an equation in slope-intercept form for the line passing through the points (–1, 2) and (4, –3), we first need to calculate the slope (m) using the formula
m = (y2 - y1) / (x2 - x1). Plugging in our points gives us m = (–3 – 2) / (4 – (–1)) = –5 / 5 = –1. Now that we have the slope, we can use one of the points to find the y-intercept (b). Using the point (–1, 2) and the slope-intercept formula y = mx + b, we plug in the values to get 2 = (–1)×(–1) + b, simplifying to 2 = 1 + b, which yields b = 1. Thus, the equation is y = –x + 1.

Answer: 32

Step-by-step explanation: You need to use PEMDAS. First, multiply the two numbers.

3(8) = 24

Then, add 8.

24 + 8 = 32

32 is your answer.

Answer:

ship B is going in a straight line north ship A is going diagonal make a straight line where each ship is moving towards and where ever they intersect will be where the ship in distress is located

hope this helped

Check the picture below, that's just an example of a parabola opening upwards.

so the cost equation C(b), which is a quadratic with a positive leading term's coefficient, has the graph of a parabola like the one in the picture, so the cost goes down and down and down, reaches the vertex or namely the minimum, and then goes back up.

bearing in mind that the quantity will be on the x-axis and the cost amount is over the y-axis, what are the coordinates of the vertex of this parabola?  namely, at what cost for how many bats?

[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ C(b) = \stackrel{\stackrel{a}{\downarrow }}{0.06}b^2\stackrel{\stackrel{b}{\downarrow }}{-7.2}b\stackrel{\stackrel{c}{\downarrow }}{+390} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\bf \left( -\cfrac{-7.2}{2(0.06)}~~,~~390-\cfrac{(-7.2)^2}{4(0.06)} \right)\implies (60~~,~~390-216) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (\stackrel{\textit{number of bats}}{60}~~,~~\stackrel{\textit{total cost}}{174})~\hfill[/tex]

To find the number of bats that should be produced to minimize costs, we need to find the minimum point on the cost curve given by the function C(b) = 0.06b^2 - 7.2b + 390. Using the vertex formula, we find that the minimum occurs at b = 60.

To find the number of bats that should be produced to keep costs at a minimum, we need to determine the minimum point on the cost curve given by the function C(b) = 0.06b^2 - 7.2b + 390. The minimum point of a quadratic function can be found using the vertex formula: b = -b / (2a), where a is the coefficient of the quadratic term and b is the coefficient of the linear term. In this case, a = 0.06 and b = -7.2. Plugging these values into the formula, we get b = -(-7.2) / (2 * 0.06) = 60.

Therefore, the number of bats that should be produced to keep costs at a minimum is 60.

Answer:

946

Step-by-step explanation:

To find just the remainder when dividing a polynomial by x-3, you could just plug in 3 into that polynomial.

If you were dividing by x+3, the remainder would just be the polynomial evaluated at x=-3.

Anyways plugging in 3 gives

7(3)^4 + 12(3)^3 + 6(3)^2 - 5(3) + 16

Just put this into your nearest calculator .

It should output 946.

You could use synthetic division or even long.

Synthetic Division.

We put 3 on outside because we are dividing by x-3.

3. | 7. 12. 6. -5. 16

| 21. 99. 315. 930

________________________

7. 33. 105. 310. 946

The remainder is the last number in the last column.

The plugging in and the synthetic division will always work when dividing by a linear expression.

Answer:

77°

Step-by-step explanation:

[tex]\\ T = \frac{1}{2}  (RU - SU)\\ \\ 21 =\frac{1}{2}(119 - SU)\\ \\ 42 = 119 - SU\\ SU=77[/tex]

The measure of mSU from the given diagram is 77 degrees

The half of the difference of the intecepted arc is equal to the measure of the angle at the vertex

Applying this theorem to the given figure, we will havea;

1/2(119 - mSU) = 21

119 - mSU = 2(21)

119 - mSU = 42

Determine the measure of mSU

mSU = 119 -42

mSU = 77degrees

Hence the measure of mSU from the given diagram is 77 degrees

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Answer:

78 and 46

Step-by-step explanation:

Substitution (look it up it's hard to explain lol)

Answer:

Step-by-step explanation:

A line with undefined slope is a vertical line.

An equation of a vertical line: x = a  (a - real number).

Each point on a line x = a has coordinates (a, b)  (b - any real number).

We have the point (4, 0) → x = 4

The equation of the line with the following characteristics is: x = 4.

------------

Traditionally, the equation of a line is given by:

[tex]y = mx + b[/tex]

However, if the slope is undefined, there is a vertical line, given by equation:

[tex]x = c[/tex]

In this question, it goes through point (4,0), that is, [tex]c = 4[/tex], and the equation if:

[tex]x = 4[/tex].

A similar problem is given at https://brainly.com/question/15789516

Answer:

[tex]\huge \boxed{90}[/tex]

Step-by-step explanation:

First thing you do is subtract.

10-2=8

[tex]\displaystyle \frac{10!}{8!}[/tex]

Then you cancel the factorials.

[tex]\displaystyle \frac{10!}{8}=10\times9[/tex]

Multiply numbers from left to right to find the answer.

[tex]\displaystyle 10\times9=90[/tex]

[tex]\huge \textnormal{90}[/tex], which is our answer.

Hope this helps!

Final answer:

The value of 10!/(10-2)! simplifies to 90 after canceling out the common factorial terms, hence the correct answer is option C (90).

Explanation:

The expression 10!/(10-2)! represents a calculation involving factorials. The factorial of a number n is denoted n! and means the product of all positive integers from 1 up to n.

So, to simplify this expression, we can expand both factorials:

10! means 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1,
and (10-2)! or 8! means 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1.

When we divide 10! by 8!, the terms 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 (which is 8!) cancel out, leaving us with:

10 x 9 = 90.

Therefore, 10!/(10-2)! simplifies to 90, which is option C.

Answer:

12:1

Step-by-step explanation:

12:1Answer:

Step-by-step explanation:

Answer:

log3c-log3(9) i.e. [tex]log_{3}c-log_{3}9[/tex]

Step-by-step explanation:

As per logarithmic relation

[tex]log_{base}\frac{A}{B}=log_{base}A-log_{base}B[/tex]

Now, in the given question base value is 3. Therefore

[tex]log_{3}\frac{c}{9}=log_{3}c-log_{3}9[/tex]

Hence the correct answer is third option.

The expression is equivalent to log₃ (c/9) is log₃ (c) - log₃ (9).

The power to which a number must be increased in order to obtain additional values is referred to as a logarithm. The easiest approach to express enormous numbers is this manner. Numerous significant characteristics of a logarithm demonstrate that addition and subtraction logarithms can also be written as multiplication and division of logarithms.

We have,

log₃ (c/9)

We know the from the property of logarithm

logₐ (c/d) = logₐ (c) - logₐ(d)

and, logₐ (cd)= logₐ(c) x logₐ (d)

So, log₃ (c/9)

= log₃ (c) - log₃ (9)

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Answer:

There are 86,400 / 3,600 = 24 frames/second

Step-by-step explanation:

Since there are 60 minutes in an hour and 60 seconds in a minute, in an hour you have 60 x 60 = 3,600 seconds.

You have 86,400 frames of animation in 1 hour.

Divide 86,400 by 3,600 to get the number of frames per second.

There are 86,400 / 3,600 = 24 frames/second

To solve, make a simple equation.

86400/3600=x

In order to get x, divide 86400 by 3600 and which x will be 24.

You can either divide the long way or the short way.

Algorithm, mental.

Get rid of the two 0s.

Then you'll get 864/36. .... 24... x=24

So 24 is the answer.

Hope this helps:)

Answer:

x = 150

D

Step-by-step explanation:

1 / tan(90 - x) = -√3/3                   Cross multiply

3 = -√3 * tan(90 - x)                     Divide by -√3

3/-√3 = tan(90 - x)                       Rationalize the denominator

3 * √3 /  (- √3 * √3  ) =tan(90-x)

3 * √3 / - 3 = tan(90 - x)               Divide

- √3           = tan(90 - x)               Take the inverse tan of -√3

tan-1(-√3) = 90 - x

-60 = 90 - x                                  Add x to both sides.

x - 60 = 90                                   Add 60 to both sides

x = 150

Answer:

-1280

Step-by-step explanation:

There are 2 ways you could do this. You could just do the question until you come to the end of f(4). That is likely the simplest way to do it.

f(1) = 160

f(2) = - 2 * f(1)

f(2) = -2*160

f(2) = -320

f(3) = -2 * f(2)

f(3) = -2 * - 320

f(3) = 640

f(4) = - 2 * f(3)

f(4) = - 2 * 640

f(4) = - 1280

I don't know that you could do this explicitly with any real confidence.

[tex]f(1)=160\\f(n+1)=-2f(n)\\\\f(2)=-2\cdot 160=-320\\f(3)=-2\cdot(-320)=640\\f(4)=-2\cdot 640=-1280[/tex]

Let's solve for x.

−b3+3b2+8−x−5b2−9=5b3+852+17

Step 1: Add b^3 to both sides.

−b3−2b2−x−1+b3=5b3+869+b3

−2b2−x−1=6b3+869

Step 2: Add 2b^2 to both sides.

−2b2−x−1+2b2=6b3+869+2b2

−x−1=6b3+2b2+869

Step 3: Add 1 to both sides.

−x−1+1=6b3+2b2+869+1

−x=6b3+2b2+870

Step 4: Divide both sides by -1.

−x

−1

=

6b3+2b2+870

−1

x=−6b3−2b2−870

Answer:

x=−6b3−2b2−870

Answer:

the answer is the first option -6b^3

Step-by-step explanation:

yup

Answer:

the measure of angle 4 should be 45

Step-by-step explanation:

since angle 2 and 4 are congruent, 2x+15 = x + 30

so x = 15

15 + 30 = 45

Answer:

[tex]Pr=\dfrac{45}{208}\approx 0.216.[/tex]

Step-by-step explanation:

You are given the information about students:

In total, there are 45 + 60 + 82 + 21 = 208 students.

Use the definition of the probability:

[tex]Pr=\dfrac{\text{Number of favorable outcomes}}{\text{Number of all possible outcomes}}[/tex]

Number of favorable outcomes = 45

Nomber of all possible outcomes = 208,

hence,

[tex]Pr=\dfrac{45}{208}\approx 0.216.[/tex]

Answer:

Step-by-step explanation:

Start by removing the brackets.

Left Brackets

30(1/2 x - 2)

30*1/2 x - 30*2

15x - 60

Right Bracket

40(3/4 y - 4)

40*3/4 y - 4*40

10*3 y - 160

30y - 160

Now put these 2 results together.

15x - 60 + 30y - 160     Combine the like terms.

15x + 30y - 220            That's one answer Others are possible.

5(3x + 6y - 44)

Answer:

74

Step-by-step explanation:

Answer:

The zero's are -1, -2/5, 8

Step-by-step explanation:

f(x) = (x + 1)(x − 8)(5x + 2)

We can use the zero product property

0 = (x + 1)(x − 8)(5x + 2)

0 = x+1   0 = x-8   0 =5x+2

x=-1     x=8      -2 =5x

x=-1     x=8      -2/5 =x

The zero's are -1, -2/5, 8

Answer:

The graph in the attached figure

Step-by-step explanation:

we have that

[tex]f(x)=x-4[/tex] ------> For [tex]x < 2[/tex]

[tex]f(x)=-2x+2[/tex] ------> For [tex]x\geq2[/tex]

To graph this piece wise- defined function

In the interval (-∞,2) ----> graph the line [tex]f(x)=x-4[/tex]

In the interval [2,∞) ----> graph the line [tex]f(x)=-2x+2[/tex]

The function is continue -----> the domain is all real numbers

using a graphing tool

see the attached figure

[tex]\bf \stackrel{\mathbb{P~E~M~D~A~S}}{7+3^2+(12-8)\div 2\times 4}\implies 7+3^2+(\stackrel{\downarrow }{4})\div 2\times 4\implies 7+\stackrel{\downarrow }{9}+(4)\div 2\times 4 \\\\\\ 7+9+\stackrel{\downarrow }{2}\times 4\implies 7+9+\stackrel{\downarrow }{8}\implies \stackrel{\downarrow }{16}+8\implies 24[/tex]

Answer:

The graph in the attached figure

Step-by-step explanation:

Let

x -----> time of the first process in minutes

y -----> time of the second process in minutes

we know that

The time of the first process multiplied by 4 (because is repeated 4 times) plus the time of the second process multiplied by 1 (because is repeated only once) must be less than or equal to 3 minutes

so

The inequality that represent this situation is

[tex]4x+y\leq 3[/tex]

The solution of the inequality is the shaded area below the solid line

The equation of the solid line is [tex]4x+y=3[/tex]

The y-intercept of the solid line is the point (0,3)

The x-intercept of the solid line is the point (0.75,0)

The slope of the solid line is negative m=-4

using a graphing tool

The solution is the shaded area

The graph in the attached figure

Remember that the time cannot be a negative number

Answer:

The inequality represents the situation is:

[tex]4x+y\leq 3[/tex]

And the graph is attached in the solution.

Step-by-step explanation:

Given information:

Time of first process in minutes[tex]=x[/tex]

Time of second process in minutes [tex]=y[/tex]

As we know that ,

according to the given information in the question we can write:

the inequality represents the situation is:

[tex]4x+y\leq 3[/tex]

Here, the y-intercept of the solid line is the point (0,3)

And the x-intercept of the solid line is the point (0.75,0)

And the slope is negative [tex]m=-4[/tex]

Now the graph of the above inequality can be formed as attached in the solution:

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