Find the equation of the perpendicular bisector of the given segment by following these steps. 1. Determine the slope of the given segment.

Answer:

You need to find the number of times x goes into 3x^2 which is 3x, so you write 3x as the beginning of the quotient to start the division.

Answer:

3x^2 / x.

Step-by-step explanation:

The first step is to divide 3x^2 by the first term of x - 2 ( that is x).

Answer:

430

Step-by-step explanation:

All you have to do is add up all the sides So 80+80+250+20=430 And there you have it!

Answer:

Mason wins after 18 total moves

Step-by-step explanation:

Mason's optimal strategy is to keep the total number of marbles at 11n+1, so he will take 10 marbles to start. For each move Jason makes, Mason will take a number of marbles that makes the sum from the two turns be 11.

After each of Mason's 9 turns, the number of remaining marbles will be ...

89, 78, 67, 56, 45, 34, 23, 12, 1

It doesn't matter how many marbles Jason takes. He will lose on his 9th turn.

Mason's best strategy is to stay the overall variety of marbles at 11n+1, thus he can take ten marbles to begin. for every move Jason makes, Mason can take variety of marbles that creates the add from the 2 turns be eleven.

After every of Mason's nine turns, the amount of remaining marbles are

89, 78, 67, 56, 45, 34, 23, 12, 1

It doesn't matter what number marbles Jason takes. He can lose on his ninth flip.

mason will win after 18 moves

Answer:

  59.0°

Step-by-step explanation:

Many triangle solvers are available for your phone, tablet, or browser. The attachments show the input and output of one of them.

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You can use the law of cosines to compute the result yourself.

  b^2 = a^2 + c^2 - 2ac·cos(B)

  cos(B) = (a^2 +c^2 -b^2)/(2ac) = (22^2 +18^2 -20^2)/(2·22·18) = 408/792

  B = arccos(408/792) ≈ 58.9924° ≈ 59.0°

Answer:

x = 5 and y = 35

OR

x = -4 and y = 8.

Step-by-step explanation:

Equate the right-hand side of the two equations:

x² + 2 x = y = 3 x + 20.

x² + 2 x - 3 x - 20 = 0.

x² - x - 20 = 0.

Quadratic discriminant

Δ = b² - 4 a · c

= (-1)² - 4 × 1 × (-20)

= 81.

There are two roots:

x₁ = (-b + [tex]\sqrt{\Delta}[/tex]) / (2 a)

= (- (-1) + [tex]\sqrt{81}[/tex]) / (2 × 1)

= (1 + 9) / 2

= 10 / 2

= 5

and

x₂ = (-b - [tex]\sqrt{\Delta}[/tex]) / (2 a)

= (1 - 9) / 2

= -4.

Find the value of y in both case.

y₁ = 3 × 5 + 20 = 35.

y₂ = 3 × (-4) + 20 = 8.

The solution to the system of equations is [tex]\( x = 5 \)[/tex] with [tex]\( y = 35 \)[/tex] and [tex]\( x = -4 \)[/tex] with [tex]\( y = 8 \)[/tex].

To solve these equations algebraically, we'll set them equal to each other since they both represent [tex]\( y \)[/tex].

Given equations:

[tex]\[ y = x^2 + 2x \][/tex]

[tex]\[ y = 3x + 20 \][/tex]

Setting them equal to each other:

[tex]\[ x^2 + 2x = 3x + 20 \][/tex]

Now, let's rearrange this equation to solve for \( x \):

[tex]\[ x^2 + 2x = 3x + 20 \[/tex]

[tex]x^2 + 2x - 3x - 20 = 0 \[/tex]

[tex]x^2 - x - 20 = 0[/tex]

This is a quadratic equation in the form [tex]\( ax^2 + bx + c = 0 \)[/tex]. We need to factorize or use the quadratic formula to solve for [tex]\( x \)[/tex]. Factoring might work here:

[tex]x^2 - x - 20 = 0[/tex]

[tex](x - 5)(x + 4) = 0[/tex]

Setting each factor equal to zero:

[tex]\[ x - 5 = 0 \] or \( x + 4 = 0 \)[/tex]

Solving for [tex]\( x \)[/tex] in each case:

[tex]\[ x = 5 \] or \( x = -4 \)[/tex]

Now that we have found the potential values of [tex]\( x \)[/tex], let's find the corresponding [tex]\( y \)[/tex] values using either of the original equations. Let's use [tex]\( y = x^2 + 2x \)[/tex]:

For [tex]\( x = 5 \)[/tex]:

[tex]y = 5^2 + 2(5)[/tex]

[tex]y = 25 + 10[/tex]

[tex]y = 35[/tex]

For [tex]\( x = -4 \)[/tex]:

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

[tex]y = 16 - 8[/tex]

[tex]y = 8[/tex]

Therefore, the solution to the system of equations is [tex]\( x = 5 \)[/tex] with [tex]\( y = 35 \)[/tex] and [tex]\( x = -4 \)[/tex] with [tex]\( y = 8 \)[/tex].

Answer:

  cot(x) = 3

Step-by-step explanation:

The cotangent is the reciprocal of the tangent.

  cot(x) = 1/tan(x) = 1/(1/3) = 3

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It is helpful to memorize the relationships between the trig functions: SOH CAH TOA is a mnemonic that relates triangle sides to trig function values. The remaining relationships you need to know are ...

  secant = 1/cosine . . . . . . so cosine = 1/secant

  cosecant = 1/sine . . . . . so sine = 1/cosecant

  cotangent = 1/tangent . . . . . so tangent = 1/cotangent

It is also helpful to realize that ...

  tan = sin/cos

  sin² + cos² = 1 . . . the "Pythagorean" relationship between sine and cosine

  sec² = 1 + tan²

  csc² = 1 + cot²

Answer:

[tex]y=-\frac{3+\sqrt{5}}{2}[/tex] AND [tex]y=-\frac{3-\sqrt{5}}{2}[/tex]

Step-by-step explanation:

Given: [tex]y^2+3y=-1[/tex]

To solve for [tex]y[/tex], we need to get everything on one side of the equal sign and set it to zero. We can do this by adding 1 to both sides. We then get:

[tex]y^2+3y+1=0[/tex]

We can solve for [tex]y[/tex] by using the quadratic formula:

[tex]y=\frac{-b+\sqrt{(b)^2-4(a)(c)}}{2a}[/tex] AND [tex]y=\frac{-b-\sqrt{(b)^2-4(a)(c)}}{2a}[/tex]

Let's identify our values:

[tex]a: 1\\b: 3\\c: 1[/tex]

Plug in the values and simplify.

[tex]y=\frac{-3+\sqrt{(3)^2-4(1)(1)}}{2(1)}\\y=\frac{-3+\sqrt{5}}{2}\\-------------------------\\y=\frac{-3-\sqrt{(3)^2-4(1)(1)}}{2(1)}\\\\y=\frac{-3-\sqrt{5}}{2}\\[/tex]

Your final answers are:

[tex]y=-\frac{3+\sqrt{5}}{2}[/tex] AND [tex]y=-\frac{3-\sqrt{5}}{2}[/tex]

The quadratic function y=x^2+10x+25 intersects the x-axis at a single point (x = -5).

A quadratic function intersects the x-axis when the value of y is equal to 0. To find the number of times the function intersects the x-axis, we need to determine the number of solutions for y = 0. The given quadratic function is y = x^2 + 10x + 25. We can solve this equation by factoring or using the quadratic formula.

Factoring: Factoring the quadratic equation, we get (x + 5)(x + 5) = 0.

Since both factors are the same, the function intersects the x-axis at a single point (x = -5).

Quadratic formula: The quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a.

Plugging in the values from the given quadratic function, we get x = (-10 ± √(100 - 4(1)(25))) / 2(1).

Simplifying further, we get x = (-10 ± √(100 - 100)) / 2, which reduces to x = -5. This indicates that the quadratic function intersects the x-axis at a single point (x = -5).

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Since f(x) = -3x + 2, the slope of f(x) is greater than the slope of g(x).

Hence, the answer is (D).

The slope of f(x) is greater than the slope of g(x) because the slope of f(x) is 1 option (D) is correct.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

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

We have:

g(x) = -2x - 6

f(x) is shown in the graph

The slope of g(x), m = -2

From the graph:

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

M = (1-2)/(-1) =  1

Thus, the slope of f(x) is greater than the slope of g(x) because the slope of f(x) is 1 option (D) is correct.

Learn more about the slope here:

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Answer:

s= 15x+3x and s=18x

Step-by-step explanation:

Answer:

The total cost for the special would be $15.45

Step-by-step explanation:

One equation would be 15 x 1.03 = 15.45

Second equation would be (15 x .03) + 15 = $15.45

Answer:

  73

Step-by-step explanation:

Put the values of the variables where the variables are, then do the arithmetic.

  (2·5)^2 -3·3^2 = 10^2 -3·9 = 100 -27 = 73

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Or, you can let a calculator or spreadsheet evaluate the function for you.

Answer:

The correct answer is 2.

Step-by-step explanation:

To find this, first identify the ordered pairs at those two points. They would be (3, -2) and (6, 4). Then use the slope formula with those two points to find the rate of change.

m(slope) = (y2 - y1)/(x2 - x1)

m = (4 - - 2)/(6 - 3)

m = 6/3

m = 2

Answer:

2

Step-by-step explanation:

Rate of change on the given interval a to b is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

a=3 and b=6

f(a) and f(b) are the y values on the graph at x=3  and x=6

f(3)= -3  and f(6) is 4

Now plug in the values in the formula

[tex]rate of change =\frac{4-(-2)}{6-3} =\frac{6}{3} =2[/tex]

answer is 2

If [tex]b[/tex] is Ben's age and [tex]i[/tex] is Ishaan's age, then

Rewrite the second equation as

[tex]b-6=6(i-6)\implies b-6=6i-36\implies b+30=6i[/tex]

Substitute [tex]b=4i[/tex] into this equation to solve for [tex]i[/tex]:

[tex]b+30=6i\implies4i+30=6i\implies30=2i\implies i=15[/tex]

Then

[tex]b=4i\implies b=4\cdot15=60[/tex]

So Ben is 60 years old now.

A random supporter roots the home team with probability 0.9, and the away team with probability 0.1.

Choosing 6 out of 8 supporters who root for the home team has probability

[tex]\displaystyle\binom{8}{6}\cdot 0.9^6\cdot 0.1^2 = 28\cdot0.531441\cdot 0.01=0.14[/tex]

Answer:

3.5 pounds of nuts; 6.5 pounds of M&Ms

Step-by-step explanation:

Let m represent the number of pounds of M&Ms to use. Then 10-m is the number of pounds of nuts, and the cost of the mix is ...

6·m + 3·(10-m) = 4.95·10 . . . . . cost = cost per pound times pounds

3m +30 = 49.5 . . . . . . simplify

3m = 19.5 . . . . . . . . . . . subtract 30

m = 6.5 . . . . . . . . . . . . . divide by 3

Then 10-m = 10-6.5 = 3.5.

The manager should use 3.5 pounds of nuts and 6.5 pounds of M&Ms in the mix.

Answer:

Step-by-step explanation:

When you have a non-trivial number of sets of equations to solve, it can be useful to let a machine solve them for you. Here, suitable equations for chair cost (c) and table cost (t) can be written as ...

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I find a graphing calculator easy to use for solving such equations.

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A spreadsheet programmed with Cramer's Rule can do it, too. The second attachment shows the spreadsheet formulas used to solve the standard-form linear equations of the kind that can be written for this problem. The third attachment shows the solution(s).

Answer:

t = 58x or t + 7x = 65x

The expression that represents a senior citizen's total cost for the plumber in 2 different ways can be written as: Method 1: Total Cost = $65 - $7 per hour. Method 2: Total Cost = $65 - ($7 per hour x Number of hours)

The expression that represents a senior citizen's total cost for the plumber in 2 different ways can be written as:

Method 1 calculates the total cost by applying the discount of $7 per hour directly to the base rate of $65. Method 2 calculates the total cost by multiplying the discount per hour ($7) by the number of hours and subtracting it from the base rate of $65.

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Answer:

Step-by-step explanation:

After you've worked a couple of "optimum cylinder" problems, you find that the cylinder with the least surface area for a given volume has a height that is equal to its diameter. So, the volume equation becomes ...

  V = πr²·h = 2πr³ = 39 in³

Then the radius is ...

  r = ∛(39/(2π)) in ≈ 1.83779 in ≈ 1.84 in

  h = 2r = 3.67557 in ≈ 3.68 in

_____

The total surface area of a cylinder is ...

  S = 2πr² + 2πrh

For a given volume, V, this becomes ...

  S = 2π(r² +r·(V/(πr²))) = 2πr² +2V/r

The derivative of this with respect to r is ...

  S' = 4πr -2V/r²

Setting this to zero and multiplying by r²/2 gives ...

  0 = 2πr³ -V

  r = ∛(V/(2π)) . . . . . . . . looks a lot like the expression above for r

__

If we substitute the equation for V into the equation just above this last one, we have ...

  0 = 2πr³ - πr²·h

Dividing by πr² gives ...

  0 = 2r - h

  h = 2r . . . . . generic solution for cylinder optimization problems

Out of 170 students in 12th grade, 27+23 = 50 students have more than 1 college in mind.

So 50/170, or 29% is your answer.

Answer:

29%

Step-by-step explanation:

The answer is D. 45%

The answer would be 45%

To solve this pretend that 370 is 100

Then put (x) as the value you are looking for

So 100%=370

(x)%=166.5

Then set it up like this:

100%. 370

=

x%. 166.5

Then divide or do cross multiplication and you find out that x is 45%

Hope this helps! :3

Answer:

255π (cm³).

Step-by-step explanation:

1. the initial formula for the required volume is V=V1-V2, where V1=π(r1)²h, V2=π(r2)²h;

h=20m=2000cm, r1=0.5*d1, r2=0.5*d2;

d1=1cm., d2=0.7 cm.

2. the final formula of the required volume is

[tex]V=\frac{ \pi*h}{4} (d_1^2-d_2^2);[/tex]

3. if to substitute the values of d1, d2 and h, then

[tex]V=\frac{ \pi*2000}{4} (1-0.49)=500 \pi*0.51=255 \pi \ (cm^3).[/tex]

Answer:

Step-by-step explanation:

If we take 1 candy bar and split it between 8 people, each person will get 1/8 of a candy bar. 1/8 for each of those 12 candy bars will give each person 12 × 1/8 = 12/8, or 3/2 = 1 1/2 bars.

You are trying to share 12 candy bars between 8 friends.

Therefore,

12 candy bars ÷ 8 friends = 1.5 bars per person

12 ÷ 8 = 1.5 candy bars

Answer:

  a.  -25

  b.  -52

  c.  54

  d.  8/7 = 1 1/7

Step-by-step explanation:

Evaluate each of the functions for each of the variable values and compute the composite as defined.

a. (f+g)(3) = f(3) + g(3) = 3^2 -5·3 + 8 -3^3 = -25

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b. (g -f)(4) = g(4) -f(4) = 8 -4^3 -(4^2 -5·4) = 8 -64 -16 +20 = -52

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c. (f*g)(-1) = f(-1) · g(-1) = ((-1)^2 -5(-1)) · (8 -(-1)^3) = 6·9 = 54

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d. (g/f)(-2) = (8 -(-2)^3)/((-2)^2 -5(-2)) = (8+8)/(4+10) = 16/14 = 8/7

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Comment on approach to the problem

When there are a number of evaluations of the same function with different values of the variable, it can be convenient to let a calculator or spreadsheet do those for you.

Answer:

The base = 4 units and the height = 3 units

Step-by-step explanation:

* Lets remember the rule of the distance between 2 points

- The two points are (x1 , y1) and (x2 , y2)

∴ The distance = √[(x2 - x1)²+(y2 - y1)²]

* The vertices of the triangles are (-3 , 4) , (1 , 4) , (1 , 1)

- If two points have the same y-coordinate

∴ The line joining the to point is horizontal

∴ Its length = x2 - x1

- Because √[(x2 - x1)²+(y2 - y1)²] and y2 = y1

∴ d = √(x2 - x1)² ⇒ cancel power 2 with the radical sign

∴ d = x2 - x1

* Similar you can find the vertical distance

- If two points have the same x-coordinate

∴ The line joining the to point is vertical

- Its length = y2 - y1

∵ The points (-3 , 4) , (1 , 4) have same y-coordinate

∴ This side of the triangle is horizontal

∴ Its length = 1 - -3 = 4

∵ The points (1 , 4) , (1 , 1) have same x-coordinate

∴ This side of the triangle is vertical line

∴ Its length = 4 - 1 = 3

* The two sides of the triangle are ⊥

∴ One of them is the base of the triangle and the other is the height

* The base = 4 units and the height = 3 units

The second one is d I’m pretty sure

Answer:

#23, A

#24, D

Hope this helped!!

~A̷l̷i̷s̷h̷e̷a̷♡

Answer:

A. lim [x ⇒ -∞] g(x) = -5 . . . . . . written in text form, not typeset

Step-by-step explanation:

A horizontal asymptote is a line that the function approaches but never reaches. It represents the limiting value that the function can have. (The function can come as close to that value as you like for some value of x, but can never actually reach that value.)

Here, you're told the asymptote for negative x values is -5. That means g(x) gets closer and closer to -5 for values of x that are more and more negative. That is, as x approaches infinity, g(x) approaches -5. We say -5 is the limit of g(x) as x approaches negative infinity.

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The attached graph shows a function that has characteristics like those of g(x).

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This question is about vocabulary: what is the meaning of "asymptote" and "limit", and how do you read a description of a limit written using math language.

A kite is a quadrilateral.

So the correct answer is A.

Hope this helps,

Davinia.

Final answer:

A kite is a quadrilateral, which is a shape with four sides, but with unique properties that differentiate it from parallelograms, rectangles, and trapezoids.

Explanation:

A kite in geometry is a quadrilateral. A quadrilateral is a kind of shape with four sides, which might not be as commonly discussed in early education as shapes like squares and triangles. A kite is defined by two pairs of adjacent sides that are equal in length, with one pair longer than the other. Unlike a parallelogram, the sides of a kite do not always have to be parallel to each other. In addition, a kite does not necessarily have right angles as a rectangle does, nor does it have only one pair of parallel sides as a trapezoid does. Therefore, when characterizing a kite, the correct answer is A. quadrilateral.

Answer:

  4.  maximum: 22; minimum: 1

  5.  maximum: 24; minimum: -6.25

  6.  maximum: 49.7; minimum: 39.625

Step-by-step explanation:

I find a graphing calculator to be "appropriate technology" for answering questions of this sort. For the first and last questions, the extremes are the values of the function at the ends of the intervals specified.

For the second question, the parabola opens upward and the vertex is in the given interval, so the vertex is the minimum. The maximum is found at the end of the interval that is farthest from the vertex.

Answer:

First account (simple interest)

Step-by-step explanation:

The amount of interest earned by the first account is ...

I = Prt = $2000·0.04·7 = $2000·0.28 = $560

The amount in the second account at the end of 7 year is ...

FV = P·(1+r)^t = $2000·1.02^7 = $2297.37

so you have earned $297.37 in interest on the second account.

$560 is more than $297, so the First Account (simple interest) earns more money.