On a coordinate plane, a parabola opens down with solid circles along the parabola at (negative 3, negative 5), (negative 2, 0), (negative 1, 3), (0, 4), (1, 3), (2, 0), (3, negative 5). Which statement is true regarding the intervals where the function is increasing and decreasing? The function is increasing from (–∞, 0). The function is increasing from (0, ∞). The function is decreasing from (–∞, 0). The function is decreasing from (–∞, ∞).

[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve for x ~

[tex]\qquad \sf  \dashrightarrow \: 5x = 3x + 12[/tex]

[ by vertical opposite angle pair ]

[tex]\qquad \sf  \dashrightarrow \: 5x - 3x = 12[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x = 12[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 12 \div 2[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 6[/tex]

Therefore, the correct choice is D. 6

The range of y = sin(x) is [-1,1]

The function is given as:

y = sin(x)

The above function is the parent function of a sine function.

A sine function has a minimum of -1 and a maximum of 1.

This is represented by the interval [-1,1]

Hence, the range of y = sin(x) is [-1,1]

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Answer:

6.5 seconds

Step-by-step explanation:

Ok so the equation you gave is -16T^2 + 676 in the comments which is what I'll be using for this problem. The problem is really just asking you to find the zeroes of the equation excluding any negative solutions since that doesn't really represent anything in this context since T is time.

So the first step is to set the equation equal to 0

[tex]0 = -16t^2 + 676[/tex].

Subtract 676 from both equations.

[tex]-676 = -16t^2[/tex]

Divide both sides by -16

[tex]42.25 = t^2[/tex]

Take the square root of both sides

[tex]\pm6.5 = t[/tex]

Ignore the negative and take only the positive solution, since in this context it doesn't make much sense. So after 6.5 seconds the height is 0, meaning it hits the ground after 6.5 seconds.

Answer:

4/7

Step-by-step explanation:

2/3 × 6

7

4/7

and bro that's really it

Substituting into point-slope form,

[tex]y+5=-\frac{5}{3}(x-15)\\\\y+5=-\frac{5}{3}x+25\\\\\boxed{y=-\frac{5}{3}x+20}[/tex]

The graph of all the inequalities are given below.

Inequality is defined as an equation that does not contain an equal sign.

This part of the question is for simplifying your work: Make a graph and shadow the interested regions of the inequalities in the given picture.

y ≥ x, the region is left to the line.

y < -(3/7)x – 7, the region is left to the line.

y ≤ (5/3)x – 8, the region is right to the line.

y ≥ 14 – (11/12)x, the region is right to the line.

y = -(3/2)x + 5, this is the equation of line.

All the graphs are shown below.

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The average speed of sneeze is about 100 miles per hour.

The average speed of sneeze is determined from the total distance traveled by the sneeze to the total time of motion of the sneeze.

Averagely a sneeze can travel as fast as 100 miles in an hour, which is equivalent to 44.7 m/s.

Thus, the average speed of sneeze is about 100 miles per hour.

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Answer: A. 6, 18, 54, 162

Step-by-step explanation:

Each term is 3 times the last, meaning the common ratio is 3.

Answer:

A = 60 ft²

Step-by-step explanation:

the area (A) of the shaded sector is calculated as

A = area of circle × fraction of circle

   = 90 × [tex]\frac{240}{360}[/tex]

   = 90 × [tex]\frac{2}{3}[/tex]

    = 30 × 2

    = 60 ft²

Answer:

58.83 ft^2

Step-by-step explanation:

Finding the radius:

A = πr^2

90 = πr^2

90/π = r^2

28.6 = r^2

5.3 = r

Using the area of a sector of a circle formula:

θ/360 x πr^2

240/360 x π(5.3)^2

= 58.83 ft^2

Using proportions, considering the relation between the height and the shadow, it is found that the cell phone tower is 50 feet.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

When the shadow is of 8 feet, the height is of 10 feet. What is the height when the shadow is of 40 feet? The rule of three is:

8 feet - 10 feet

40 feet - h feet

Applying cross multiplication:

8h = 10 x 40

Simplifying by 8:

h = 10 x 5 = 50 feet.

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Answer:

1. 8

2. 3

Step-by-step explanation:

[tex]f(g(3)) \\= f(2(3)-3))\\=f(3)\\=3^2-1\\= 9-1\\=8\\\\g(f(-2))\\= g((-2)^2-1)\\=g(4-1)\\=g(3)\\=2*3-3\\=3[/tex]

[tex]\text{First I would recommend replacing the question mark with x}\\\text{We have two ratios, }\\\text{and we need to solve that hard-looking equation}\\\text{in terms of x}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{We can multiply x times 36:: 36x}\\\text{We can multiply 4 times 27:: 108}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{Now it's easier to solve for x:: 36x=108; x=3}\\\text{ (we divided by 36 on both sides of the = sign)}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{The missing number is 3}[/tex]

Answer:

angle 1 is 105degrees and angle 2 is 75degrees

Step-by-step explanation:

The angle below angle 2, presumably angle 6, is also 75 degrees since line c and line d are parallel. If angle 2 is 75 degrees then we know that angle 1 is 105 degrees since both angles equal a straight line and a straight line has 180 degrees.

Answer:

  B.  2x = y; 2x +1.5y = 20

Step-by-step explanation:

The two given relations can be written as two equations, one for the numbers of fish, and one for their cost.

__

The number of goldfish (y) is twice the number of tetras (x), so one equation can be ...

  2x = y

The tetras (x) are $2 each, and the goldfish (y) are $1.50 each. Their total cost is the sum of products of the number of fish and the cost of each. That total is given as $20, so the other equation could be ...

  2x +1.5y = 20

Then the appropriate system of equations is ...

_____

Additional comment

The solution can be found by substituting for 2x to get ...

  y +1.5y = 20 . . . . . . substitute for 2x

  y = 20/2.5 = 8 . . . . divide by the coefficient of y

  x = y/2 = 4 . . . . . . . find the number of tetras

Rick bought 4 tetras and 8 goldfish.

__

The wording "twice as many goldfish as tetras" easily causes confusion. It is helpful to reword it as "goldfish were twice the number of tetras."

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:2x - 3 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: (f - g)(x)[/tex]

[tex]\qquad \tt \rightarrow \: f(x) - g(x)[/tex]

Simple procedure :

[tex]\qquad \tt \rightarrow \: 3x - 1 - (x + 2)[/tex]

[tex]\qquad \tt \rightarrow \: 3x - 1 - x - 2[/tex]

[tex]\qquad \tt \rightarrow \: 3x - x - 1 - 2[/tex]

[tex]\qquad \tt \rightarrow \: 2x - 3[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

n = [tex]\frac{1}{36}[/tex]

Step-by-step explanation:

n × 18 = [tex]\frac{1}{2}[/tex]

To find the value of n we have to divide both sides by 18.

Let us solve it now.

18n = [tex]\frac{1}{2}[/tex]

[tex]\frac{18n}{18}[/tex] = [tex]\frac{1}{2}[/tex] ÷ 18

n =  [tex]\frac{1}{2}[/tex] ÷ 18

n = [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{18}{1}[/tex]

n =  [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{18}[/tex]

n = [tex]\frac{1}{36}[/tex]

(a) If [tex]\alpha[/tex] and [tex]\beta[/tex] are roots of [tex]f(x)[/tex], then we can factorize [tex]f[/tex] as

[tex]f(x) = x^2 + (k - 6) x + 9 = (x - \alpha) (x - \beta)[/tex]

Expand the right side and match up coefficients:

[tex]x^2 + (k-6) x + 9 = x^2 - (\alpha + \beta) x + \alpha \beta \implies \begin{cases} \alpha + \beta = -(k-6) \\ \alpha \beta = 9 \end{cases}[/tex]

Now, recall that [tex](x+y)^2 = x^2 + 2xy + y^2[/tex]. It follows that

[tex]\boxed{\alpha^2 + \beta^2} = (\alpha + \beta)^2 - 2\alpha\beta = (-(k-6))^2 - 2\times9 = \boxed{k^2 - 12k + 18}[/tex]

and

[tex]\boxed{\alpha^2\beta^2} = 9^2 = \boxed{81}[/tex]

(b) If [tex]9(\alpha^2+\beta^2) = 2\alpha^2\beta^2[/tex], then

[tex]9 (k^2 - 12k + 18) = 2\times81 \implies 9k^2 - 108k = 0 \implies 9k (k - 12) = 0[/tex]

Since [tex]k\neq0[/tex], it follows that [tex]\boxed{k=12}[/tex].

(c) The simplest quadratic expression with roots [tex]\frac1{\alpha^2}[/tex] and [tex]\frac1{\beta^2}[/tex] is

[tex]\left(x - \dfrac1{\alpha^2}\right) \left(x - \dfrac1{\beta^2}\right)[/tex]

which expands to

[tex]x^2 - \left(\dfrac1{\alpha^2} + \dfrac1{\beta^2}\right) x + \dfrac1{\alpha^2\beta^2}[/tex]

Reusing the identity from (a-i) and the result from part (b), we have

[tex]\left(\dfrac1\alpha + \dfrac1\beta\right)^2 = \dfrac1{\alpha^2} + \dfrac2{\alpha\beta} + \dfrac1{\beta^2} \\\\ \implies \dfrac1{\alpha^2} + \dfrac1{\beta^2} = \left(\dfrac{\alpha + \beta}{\alpha\beta}\right)^2 - \dfrac2{\alpha\beta} = \left(\dfrac{-(k-6)}9\right)^2 - \dfrac29 = \dfrac29[/tex]

We also know from part (a-ii) that [tex]\alpha^2\beta^2=81[/tex].

So, the simplest quadratic that fits the description is

[tex]x^2 - \dfrac29 x + \dfrac1{81}[/tex]

To get one with integer coefficients, we multiply the whole expression by 81 to get [tex]\boxed{81x^2 - 18x + 1}[/tex].

Using translation concepts, the equation for the transformed logarithm is given by:

[tex]f(x) = \log{(x + 3)} - 3.48[/tex]

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The logarithm function is given by:

[tex]f(x) = \log{x}[/tex].

We have that:

Hence:

[tex]f(x) = \log{x + 3} + b[/tex]

To find the shift up/down, we consider that f(0) = -3, hence:

[tex]-3 = \log{0 + 3} + b[/tex]

[tex]b = -3 - \log{3}[/tex]

b = -3.48.

Hence the function is given by:

[tex]f(x) = \log{x + 3} - 3.48[/tex]

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Answer:

B. y = (x+1)(x+5)

Step-by-step explanation:

If the x-intercepts are (-1,0) and (-5,0), then the solutions (also called zeros and x-intercepts) are

x = -1 and x = -5

This is a "working backwards" kind of problem. If you were solving the equation, right before the final step, x=-1 would have been:

x + 1 = 0

Right before x=-5

would have been,

x + 5 = 0.

These two: x+1 and x+5 are called the linear factors. You multiply them back together to find the equation.

y = (x+1)(x+5)

Step-by-step explanation:

Let X be the mail arrival time to a department that follows uniform distribution over 0 to 60 minutes.

The probability function of X is:

f

(

x

)

=

1

60

,

0

<

x

<

60

Now, the probability that the mail arrival time is more than 40 minutes on a given day is calculated below:

P

(

X

>

40

)

=

∫

60

40

1

60

d

x

=

[

x

60

]

60

40

1) [tex]V=lwh=5(x)(8)=\boxed{40x}[/tex]

2) [tex]V=\pi r^{2}h=(\pi)(3^{2})(8)=\boxed{72}\pi[/tex]

3) [tex]40x=72\pi\\\\x=\frac{72\pi}{40} \approx \boxed{5.7}[/tex]

Answer:

The volume of the pyramid with a base area of s² and the heights iss

The formula for calculating the volume of a square based pyramid is expressed as:

Volume = 1/3* Base area* Height

Since it is a square-based pyramid, the base area is calculated as:

Base Area = s ^ 2

If the height of the pyramid is equal to of the length of a side on the base, hence h = s

Substituting the base area and the height into the formula for the volume, this will give;

V = BH / 3

V = (s ^ 2 * s)/3

V = (s ^ 3)/3

V = 1/3 * s ^ 3

Hence the volume of the pyramid with a base area of s ^ 2 and the height s is 1/3 * s ^ 3

Answer:

4

Step-by-step explanation:

[tex] \frac{9 - 1}{3 - 1} = 4[/tex]

The average rate of change on the interval [3, 9] will be 4.

The average rate of change between two points is given by the slope formula:

 m = average rate of change = (y2 -y1)/(x2 -x1)

The sequence an = 1(3)n − 1 is graphed below:

 m = (9 -1)/(3 -1) = 8/2

 m = 4

The average rate of change on the interval [3, 9] will be 4.

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Answer:

  (a)  5440.42 g

Step-by-step explanation:

The amount remaining (Q) is given in terms of the initial amount (Q₀) by the exponential decay formula ...

  Q = Q₀(1/2)^(t/330) . . . . . where t is in days

__

The amount after 540 days is ...

  1750 g = Q₀(1/2)^(540/330) = 0.321666Q₀

  Q₀ = (1750 g)/(0.321666) ≈ 5440.42 g

The initial quantity was about 5440.42 grams.

[tex]A \cup B[/tex] represents the set that contains all the elements that are in at least one of the sets, so [tex]A \cup B=\{1, 2, 5, 6, 7, 8, 9, 10, 12, 16, 18, 19, 20, 21, 22, 23, 25\}[/tex].

We want the complement of this set (in other words, the set with all the elements in the universal set but not in the given set).

This set is {3, 4, 11, 13, 14, 15, 17, 24}

Answer:

There is no line plot

Step-by-step explanation: