expand (2x -5)(x+5)

Step-by-step explanation:

9.

we get the extreme values of y (a function) by finding the zeroes of the first derivative (that gives us the x-positions) and then using these x values in the original function.

a quadratic function has only one extreme value (1 less than the degree of the polynomial). but 2 zeroes (exactly the degree of the polynomial) - don't mix these two things up.

as the leading coefficient is positive (1), we know that the parabola is opening upwards, and the extreme value will be the vertex and therefore the minimum.

y = (x + 4)² + 6

y = x² + 8x + 16 + 6 = x² + 8x + 22

y' = 2x + 8

2x + 8 = 0

2x = -8

x = -4

(-4 + 4)² + 6 = 0² + 6 = 6

the smallest possible value of y = 6 (at x = -4).

10.

the intercept form of a parabola equation is

y = a(x - p)(x - q)

p and q are the x-intercept values.

in our case we see p = -3, q = 3.

also, we see the vertex being (0, 9), which we need to get "a".

y = a(x - -3)(x - 3) = a(x + 3)(x - 3)

using the vertex coordinates to get a :

9 = a(0 + 3)(0 - 3) = -9a

a = 9/-9 = -1

so, the quadratic equation is

y = -(x + 3)(x - 3) = -(x² - 9) = -x² + 9

11.

I assume the thinking here is : the flight curve of every falling object is a parabola.

the vertex of this parabola is (0, 36), as x represents the time in seconds, and y represents the height in ft.

the vertex form of a parabola is

y = a(x - h)² + k

with (h, k) being the vertex.

y = a(x - 0)² + 36 = ax² + 36

a must be negative, as the fall parabola opens downwards.

for typical fall situations on Earth a = -g/2 ≈ -16 (g being the gravity constant of 32.17405... ft/s²).

so, we have

y = -16x² + 36

for what x is y = 0 ?

0 = -16x² + 36

16x² = 36

x² = 36/16 = 9/4

x = 3/2 = 1.5

the coin hits the water after 1.5 seconds.

The explicit formula for the arithmetic sequence an = 15 + 5(n - 1) in function form is; aₙ = 5n + 10

The explicit formula for an arithmetic sequence is usually expressed as;

an = a + (n - 1)d

It could also be that any term of the sequence can be computed, without even knowing the other terms of the sequence. In general, the explicit formula is the nth term of arithmetic sequence.

We are given that the arithmetic sequence is represented by;

aₙ = 15 + 5(n - 1)

To write in function form, we apply distributive property to the terms within the bracket (parentheses) to get:

aₙ = 15 + 5n - 5

Rearranging gives us;

aₙ = 15 - 5 + 5n

aₙ = 5n + 10

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Complete question is;

Which represents the explicit formula for the arithmetic sequence an=15+5(n−1) in function form?

A

f(n)=5n+15

B

f(n)=n+20

C

f(n)=5n+10

D

f(n)=n+10

========================================================

Explanation

Use the pythagorean theorem to find b

a^2+b^2 = c^2

b = sqrt(c^2 - a^2)

b = sqrt(20^2 - 16^2)

b = sqrt(400 - 256)

b = sqrt(144)

b = 12

The missing leg of this right triangle is 12 feet long. This isn't the final answer, but it does lead to the answer. Choice B is a trick answer, so be careful.

We have a right triangle with sides 12, 16 and 20. The perimeter is therefore 12+16+20 = 28+20 = 48 feet which is the amount of fencing needed. The answer is choice D.

Side note: Your teacher mentions the shortest side is 16 feet, but that's clearly not the case since it should be 12 feet instead. This seems like a typo.

Answer:

Step-by-step explanation:

The range is [-4, ∞)

Using a graphing calculator (desmos) we can obtain a graph of the following function.

Explanation:

In the graph, we can see that there is a point a -4 and nothing lower, making it our minimum y-value. However, we cannot see an ending for the function; therefore, it is indeterminable and thus, infinity. As for notation. we use the solid bracket because we know the definite point, though because infinity is not definite we just use a parentheses to enclose it.

Answer:  The standard deviation is 443.6  (rounded up to one decimal place)

Step-by-step explanation:

σ2 = (Σ(xi - μ)^2)/N

= ((3940 - 3682.5)^2 + ... + (4040 - 3682.5)^2)/8

= 1574150/8

= 196768.75

σ = [tex]\sqrt{196768.75}[/tex]  

= 443.58623738795

Frequency Table

Value Frequency

2990 1 (12.5%)

3200 2 (25%)

3810 1 (12.5%)

3940 1 (12.5%)

4040 1 (12.5%)

4140 2 (25%)

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Answer: y = -x-1

Step-by-step explanation:

The function (equation) that returns Amir's altitude, y, with respect to time, x,  y = -11·x + 440, when differentiated, to find the rate of change of the altitude, indicates that rate at which Amir descended is D. 11 meters per minute

Differentiation is the process or method by which the derivative of a function is found. The derivative indicates the instantaneous rate at which the value of the function changes with respect to the change in the argument of the function.

The equation of the function that gives his altitude relative to the sea level as a function of time is; y = -11·x + 440

The differentiation of the function for the height, y, in terms of the time, x, gives the speed which is the same as the at which Amir descended as follows;

[tex]Speed = \dfrac{dy}{dx} = \dfrac{d}{dx} \left(-11\cdot x+400\right) = -11[/tex]

The speed with which Amir descends is 11 meters per minute

The correct option is D. 11 meters per minute

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Answer:

5.7 gal / hour

5.7 gal / 60 min

5.7(16) c / 60 min

Answer:

2160°

Step-by-step explanation:

We have,

Number of Sides, n = 14

So,

Sum of all interior angle = pi ( n - 2 )

or, Sum of all interior angle = pi ( 14 - 2 )

or, Sum of all interior angle = 12 pi radians.

We know,

1 radian = ( 180 / pi ) (degree)

or, 12 radians = 2160 (degree)

Yes, monotone is a sequence.

We say that a sequence (xn) is increasing if xn ≤ xn+1 for all n and strictly increasing if xn < xn+1 for all n.

Similarly, we define decreasing and strictly decreasing sequences. Sequences which are either increasing or decreasing are called monotone.

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The pair of lines perpendicular to RS are EA and FG.

A flat surface on which a straight line joining any two points on it would wholly lie is known as a plane.

What is plane?

A plane is a point, a line, and three-dimensional space's equivalent in two dimensions.

Main Body:

Given

E,F and G are on plane X. R and S are in both planes X and Y. EA and FG are parallel. AE and FG are vertical lines and are present on plane X. RS is present at the intersection of the 2 planes.

Explanation:

The lines which together could be perpendicular to RS are EA and FG.

We have to first draw both the planes according to the given information in question.

X is a vertical plane so draw a plane vertical on the horizontal plane that is Y plane. Now plot A and F And G in X plane and R,S in such a way that they  are in both plane so they will be at the intersection of both the planes. Now draw lines from A and F to form lines EA and FG.

Hence we can observe that lines EA and FD are perpendicular on line RS.

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The statement (B) "the range is (-26, 1)" is TRUE.

So, we have:

The statement is:

Therefore, the statement (B) "the range is (-26, 1)" is TRUE.

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The probability of getting a number < 9 is 28/37.

What is probability?

The ratio of good outcomes to all possible outcomes of an event is known as the probability. It has a range from 0 to 1.

Probability(Event) = Favorable Outcomes / Total Outcomes

Main Body:

Total numbers on the spinner greater than 9  = 37 - 10 + 1 = 28

(we are subtracting 10 because we need number that is greater than 10.)

and adding 1 because both the ends of interval is counted.

total numbers on spinner =37

P( x>9) = 28/37.

Hence the probability of getting a number greater than 9 on spinning is 28/37.

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Answer:

∴ a = -4.61 or 2.61 (to 3sf)

Step-by-step explanation:

      (a + 3)(a - 1) = 3(2 + 1)

  a² + 3a - a - 3 = 3(3)

       a² + 2a - 3 = 9

  a² + 2a - 3 - 9 = 0

      a² + 2a - 12 = 0

[(a + 1)² - 1²] - 12 = 0

       (a + 1)² - 13 = 0

              (a + 1)² = 13

∴ a = -4.61 or 2.61 (to 3sf)

The solutions of the expressions -(-1), -|-1|, -|1|, |1|, and |-1| are 1, -1, -1, 1, and 1.

We are given five expressions. An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. The first expression is -(-1). The simplified solution of the first expression is 1. The second expression is -|-1|. The simplified solution of the first expression is -1. The third expression is -|1|. The simplified solution of the first expression is -1. The fourth expression is |1|. The simplified solution of the first expression is 1. The fifth expression is |-1|. The simplified solution of the first expression is 1.

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x is 6.215 km and the total time taken for the whole journey is 3.61 hours.

Boat's speed in still water = u = 4 km/h

Speed of stream = v

Distance between A and B = 5 km

Upstream speed = u - v

                            = 4 - v

Time taken = [tex]T_{1}[/tex] = [tex]\frac{5}{4-v}[/tex]

Downstream speed = x = u + v

                                       = 4 + v

Time taken = [tex]T_{2}[/tex] = [tex]\frac{5}{4+v}[/tex]

According to question,

      [tex]T_{1}= T_{2}+2[/tex]

    [tex]\frac{5}{4-v}=\frac{5}{4+v}+2[/tex]

    [tex]\frac{5}{4-v}=\frac{5+2(4+v)}{4+v}[/tex]

    [tex]\frac{5}{4-v}=\frac{5+8+2v}{4+v}[/tex]

5(4+v) = (13+2v)(4-v)

20+2v = -2[tex]v^{2}[/tex]-5v+52

[tex]2v^{2}+10v-32 = 0[/tex]

[tex]v^{2}+5v-16 = 0[/tex]

v = 2.215 or -7.215

Speed can't be negative.

Therefore, v = 2.215

Upstream speed = 4 - 2.215

                            = 1.785 km/h

Downstream speed = 4 + 2.215

                                 = 6.215 km/h

[tex]T_{2}[/tex] = 5/6.215

    = 0.805 h

[tex]T_{1}[/tex] = 2 + 0.805

   = 2.805 h

Total time = 2.805 + 0.805

                 = 3.61 h

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Answer: 13 Hours

Step-by-step explanation:

1. 270/9 = 30 dollars per hour

2. 390/30 = 13 hours

Answer: y=2/3x-8

Step-by-step explanation:

Insert the given information into the y=Mx+b equation

A pound of banana has its cost to be (c) $0.59

From the question, we have the following parameters that can be used in our solution:

Amount spent on bananas = $3.54 degrees

Number of pounds = 6 pounds

From the above parameter, we can calculate the cost of one pound using the unit rate formula

The unit rate is calculated as

Unit rate = Amount spent on bananas/Number of pounds

Substitute the known values in the above equation

So, we have the following equation

Unit rate = 3.54/6

Evaluate the quotient

Unit rate = 0.59

Hence, the cost of one pound is $0.59

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The original Length is, 6500 m.

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The equivalent Algebraic Expression is represented by  [ (1.5)³/(1.3)⁴ ]⁻⁶  .

An Algebraic Expression is defined as an expression that is made up of constants and variable and joined by mathematical operators .

In the question ,

a expression is expressed in words , we have to write an equivalent expression for it .

the statement 1.5 cubed is (1.5)³

1.5 cubed over 1.3 is = (1.5)³/1.3

1.5 cubed over 1.3 raised to the fourth power = (1.5)³/(1.3)⁴

and all raised to the power of negative six = [ (1.5)³/(1.3)⁴ ]⁻⁶

Therefore , The equivalent Algebraic Expression is represented by  [ (1.5)³/(1.3)⁴ ]⁻⁶  .

The given question is incomplete , the complete question is

Write an equivalent expression for 1.5 cubed over 1.3 raised to the fourth power all raised to the power of negative six ?

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Answer:

39mm=6m52/39= 1 1/31 1/3 times 6 meters4/3 times 6/1 = 24/324/3=8The actual length of the living room is 8 meters

The value of x that makes m || n is x = 20

acc to our question-

Solving this for ''x'' :.

The value of x that makes the opposite inner angles congruents (making 3x° congruent to 2x+20°) is x = 20.

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Answer:

Step-by-step explanation:

c

Answer:

D

Step-by-step explanation:

hope it helped:)

Answer:

1

Step-by-step explanation:

4+1=5

5-4=1

Answer:

you have 1 friend

Step-by-step explanation:

you have 4 then you add another

that's 5

then you lose 4

5-4 is 1

Answer:

P=34in

Step-by-step explanation:

just want to help <33333

Answer:34

Step-by-step explanation:34

a. The equation that has one solution will be;

⇒ x + 3 = 4x

b. The equation that has no solution will be;

⇒ x + 3 = x

c. The equation that has infinitely many solution will be;

⇒ x + 3 = 3 (x/3 + 1)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ x + 3

Now,

Use the expression x + 3, we can find as;

Let us defined an expression as;

⇒ x + 3 = 4x

Solve for x as;

⇒ x + 3 = 4x

⇒ x + 3 - 4x = 0

⇒ - 3x = - 3

⇒ x = 1

Hence, The equation has one solution.

Let us defined an expression as;

⇒ x + 3 = x

Solve as;

⇒ x + 3 = x

Subtract x both side, we get;

⇒ x + 3 - x = x - x

⇒  3 ≠ 0

Thus, The equation has no solution.

Let us defined an expression as;

⇒ x + 3 = 3 (x/3 + 1)

Solve as;

⇒ x + 3 = 3 (x/3 + 1)

⇒ x + 3 = 3x/3 + 3

⇒ x + 3 = x + 3

Subtract x we get;

⇒  3 = 3

Thus, The equation has infinitely many solution.

Therefore,

a. The equation that has one solution will be;

⇒ x + 3 = 4x

b. The equation that has no solution will be;

⇒ x + 3 = x

c. The equation that has infinitely many solution will be;

⇒ x + 3 = 3 (x/3 + 1)

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Answer:

1/ x+3 = 4x

2/ x=x

3/ x+3 = 3

Step-by-step explanation:

Hope you find it helpful!

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percent change in enrollment from last year students  is

Work out the difference (reduction) between the two numbers you are comparing before calculating the percentage drop. Then, increase the result by 100 after dividing the decrease by the initial number. The outcome expresses the change as a percentage, or the change in percentage.

Last year students =320

This year students =352

We need to find the percent increase in enrollment.

The increase in no of students = 320 -352

= 32

Percentage = (increase/initial no of students) × 100

% =32/352*100

9%

Hence, the percent increase is 9%.

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Answer:

1  7/24

Step-by-step explanation:

2/3+ 5/8=  (2 × 8)(3 × 8)+ (5 × 3)(8 × 3) = 16/24+ 15/24=  16 + 15/24=  31/24 =  1 7/24

Answer:1 7/24

Step-by-step explanation:

The length of BC rounded to 3 decimal places is 4.307 meters.

It states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the base and perpendicular. Mathematically -

h² = p² + b²

We have the following length and angle as shown in the figure -

[x] = AB = 8.1

θ = ∠BAC = 28°

Using the tangent rule we can write -

tanθ = BC/AB

BC = AB tanθ

BC = 8.1 x tan(28°)

BC = 4.307

Therefore, the length of BC rounded to 3 decimal places is 4.307 meters.

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