sally picks seashells by the seashore.she lost 17 of them on her way home.with the remaining seashells,she planned to fill 5 jars with the same number of seashells in each.how many seashells did she originally pick?

The true statement about the two functions is:

"Both f(x) and g(x) increase on the interval of (–4 , ∞)."

Here we have the functions:

f(x) = log₂(4x)

g(x) = 4x - 3

That can be seen in the graph at the end. In the graph the green one is the logarithmic function.

As you can see there, both of these have similar ranges that go from (-∞, ∞) and both are increasing functions.

Then the correct statement is:

Both f(x) and g(x) increase on the interval of (–4 , ∞).

Where f(x) is actually increasing on all it's domain which is  (-∞, ∞), so the statement is true.

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Answer:

Both f(x) and g(x) have a common domain on the interval (0, ∞).

Step-by-step explanation:

The person explained it perfectly in this link shown below

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pls give me brainist for finding the answer

Also, the answer to the question

"What type of function is f(x) = 2x^3 – 4x^2 + 5?"

A) Exponential

B) Logarithmic

C) Polynomial

D) Radical

The answer is C) Polynomial

Explanation:

The exponential equation would look like this: f(x) = 2^x

with x for the exponent

The logarithmic equation would look like this: f(x) = log2 + 4

with log in the equation

The radical equation would look like this: f(x) = x^2 + 4x -1

                                                                              3x^2 -9x +2

With divide by something

Answer:

3602 people in 15 years

Step-by-step explanation:

2000 ( 1 + .04)^n         .04 is 4%    n = years

2000 ( 1.04)^15 = 3602 people

Answer:

[tex]C=20degrees[/tex]

Step-by-step explanation:

[tex]75 -55=20[/tex]

or [tex]20+55=75[/tex]

So the degrees of Angle C is [tex]20[/tex]

Answer:

x=

1

3

y+

17

3

Step-by-step explanation:

This is all i can get so far, if can improve opon this let me know

All four sides of a square are congruent and they all equal 90 degrees

Step-by-step explanation:

Simplify the expression by using the Distributive Property.

For this expression, we'll be distributing. In simpler terms, multiplying 3 into the values inside the parentheses.

Think of the expression as;

[tex]3(3a-6)=(3 \times3a)+(3 \times -6)[/tex]

Multiply;

[tex]3 \times 3a=9a[/tex] (Multiply the whole number.)

[tex]3 \times -6=-18[/tex]

Your simplified expression is [tex]9a-18.[/tex]

Answer:

The answer is 3.2

Step-by-step explanation:

Answer:

E and F.

Step-by-step explanation:

This can be written in quadratic formula.

x = -b +- √b² - 4ac/2a

The equation to solve is written as ax² + bx + c = 0.

a = 2, b = 7, c = 3

x = -7 +- √49 (7²) - 24 (4*2*3, or 4ac).

x = -7 +- √25

x = -7 +- 5

divide by 2a (4)

-7/4 = -1.75

5/4 = 1.25

now we do -1.75 +- 1.25

x = -1/2 (F.)

x = -3 (E.)
Sorry for the late response, I had made an error and had to fix it.

Answer:

answer down below

Step-by-step explanation:

Answer: G

Step-by-step explanation:

1 pound equals =16 ounces

12.5 * 16=200

so 200 ounces.

Answer:

The answer is 240 degrees

Step-by-step explanation:

A full circle is 360 degrees.

We know one angle is 120 degrees.

360-120=240 degrees

Answer:

7/10

Step-by-step explanation:

We can use the slope formula to find the slope

m = ( y2-y1)/(x2-x1)  where ( x1,y1) and (x2,y2) are two points on the line

m = ( 24-17)/(25-15)

   = 7/10

  = 7/10

Answer:

48

Step-by-step explanation:

Straight line=180 degrees

we already know one angle and thats 132

so we're trying to find the other angle demention so we do 180-132 and end up with 48

Hope that helps :)

Answer:

So the answer is (15.8)

[tex]cos^{-1}[cos(\omega)]\implies \omega \\\\[-0.35em] ~\dotfill\\\\ cos\left( -\frac{\pi }{6} \right)\implies \stackrel{symmetry~identity}{cos\left( \frac{\pi }{6} \right)} \\\\\\ cos^{-1}\left[ cos\left( -\frac{\pi }{6} \right) \right]\implies cos^{-1}\left[ cos\left( \frac{\pi }{6} \right) \right]\implies \cfrac{\pi }{6}[/tex]

why did we use the positive version of π/6?

well, the inverse cosine function has a range of [0 , π], and -π/6 is on the IV Quadrant, out of the range for it, however it has a twin due to symmetry on the I Quadrant, that is π/6, thus the reason.

The angle in the interval (0, pi) whose cosine value is √3 / 2 is π/6 radians.

Cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse of a right angled triangle.

We have to find the angle in the interval (0, π) such that the cosine of the angle is √3 / 2.

We know that, ratio of sides of 30-60-90 triangle is 1 : √3 : 2.

Hypotenuse = 2x

Adjacent side to 30° = √3 x

Cos (30°) = Adjacent side / Hypotenuse

               = √3 x / 2x

               = √3 / 2

30 degrees is equivalent to 30 × (π/180) = π/6 in radians

Hence π/6 is the angle in the interval (0, π) whose cosine value is √3 / 2.

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Answer:

260m

Step-by-step explanation:

the length and the width of a football field is 80m and 50 meters.

perimeter- (80+50)×2= 260m

hope it helps

Answer:

Question 1

F

T

T

The volume of figure A can be found by multiplying (5 · 7)(2).

Question 2

T

T

F

The total volume of the figure is 442 mm³

Question 3

T

F

T

The volume of the triangular prism is 108 in³

Step-by-step explanation:

Formula used

Volume of a prism = base area × height

Area of a rectangle = width × length

Area of a triangle = 1/2 × base × height

Volume of a cube = s³  (where s is the side length)

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

⇒ Volume of Figure A = (5 · 7)(2)

                                     = 70 cm³

⇒ Volume of Figure B = (13 · 7)(2)

                                     = 182 cm³

⇒ Total Volume = Volume of Figure A + Volume of Figure B

                           = 70 + 182

                           = 252 cm³

The first statement is false.

Rewritten statement:

The volume of figure A can be found by multiplying (5 · 7)(2).

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

⇒ Volume of rectangular prism = (15 · 15)(2)

                                                    = 450 mm³

⇒ Volume of central cube = 2³

                                            = (2 · 2 · 2)

                                            = 8 mm³

⇒ Total Volume = Volume of rectangular prism - Volume of cube

                           = 450 - 8

                           = 442 mm³

The third statement is false.

Rewritten statement:

The total volume of the figure is 442 mm³

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

⇒ Volume of rectangular prism = (12 · 3)(8)

                                                    = 288 in³

⇒ Volume of triangular prism = (1/2 · 12 · 6)(3)

                                                 = 108 in³

⇒ Total Volume = Volume of rectangular prism + Volume of triangular prism

                           = 288 + 108

                           = 396 in³

The second statement is false.

Rewritten statement:

The volume of the triangular prism is 108 in³

Answer:

36

Step-by-step explanation:

[tex] \frac{40}{32} = \frac{45}{?} \\ \frac{32 \times 45}{40 } = 36[/tex]

If quadrilateral H is a scaled copy of quadrilateral G then the value of i is 36.

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles.

Given that Quadrilateral H is a scaled copy of quadrilateral G.

Two quadrilaterals are similar if their corresponding angles are equal and also their corresponding sides must be proportional.

The sides are proportional.

40/32 = 45/i

We have to find the value of i

Apply cross multiplication

40i=45(32)

40i = 1440

Divide both sides by 40

i = 1440/40

i = 36

Hence, if quadrilateral H is a scaled copy of quadrilateral G then the value of i is 36.

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Answer:

1125 m

Step-by-step explanation:

Given equation:

[tex]h=-5t^2+150t[/tex]

where:

Method 1

Rewrite the equation in vertex form by completing the square:

[tex]h=-5t^2+150t[/tex]

[tex]\implies h=-5t^2+150t-1125+1125[/tex]

[tex]\implies h=-5(t^2-30t+225)+1125[/tex]

[tex]\implies h=-5(t-15)^2+1125[/tex]

The vertex (15, 1125) is the turning point of the parabola (minimum or maximum point).  As the leading coefficient of the given equation is negative, the parabola opens downward, and so vertex is the maximum point.  Therefore, the maximum height is the y-value of the vertex: 1125 metres.

Method 2

Differentiate the function:

[tex]\implies \dfrac{dh}{dt}=-10t+150[/tex]

Set it to zero and solve for t:

[tex]\implies -10t+150=0[/tex]

[tex]\implies 10t=150[/tex]

[tex]\implies t=15[/tex]

Input found value of t into the original function and solve for h:

[tex]\implies -5(15)^2+150(15)=1125[/tex]

Therefore, the maximum height is 1125 metres.

Convert to vertex form y=a(x-h)²+k

Vertex at (15,1125)

As a is negative parabola is opening downwards hence vertex is maximum

Answer:

[tex]30^{\circ}[/tex].

Step-by-step explanation:

Let [tex]\theta[/tex] denote the unknown angle of elevation. Let [tex]h[/tex] denote the height of the tower.

Refer to the diagram attached. In this diagram, [tex]{\sf A}[/tex] denotes the top of the tower while [tex]{\sf B}[/tex] denote the base of the tower; [tex]{\sf BC}[/tex] and [tex]{\sf BD}[/tex] denote the shadows of the tower when the angle of elevation of the sun is [tex]60^{\circ}[/tex] and [tex]\theta[/tex], respectively. The length of segment [tex]{\sf AB}[/tex] is [tex]h[/tex]; [tex]\angle {\sf ACB} = 60^{\circ}[/tex], [tex]\angle {\sf ADB} = \theta[/tex], and [tex]{\sf BD} = 3\, {\sf BC}[/tex]..

Note that in right triangle [tex]\triangle {\sf ABC}[/tex], segment [tex]{\sf AB}[/tex] (the tower) is opposite to [tex]\angle {\sf ACB}[/tex]. At the same time, segment [tex]{\sf BC}[/tex] (shadow of the tower when the angle of elevation of the sun is [tex]60^{\circ}[/tex]) is adjacent to [tex]\angle {\sf ACB}[/tex].

Thus, the ratio between the length of these two segments could be described with the tangent of [tex]m\angle {\sf ACB} = 60^{\circ}[/tex]:

[tex]\begin{aligned}\tan(\angle {\sf ACB}) &= \frac{\text{opposite}}{\text{adjacent}} = \frac{{\sf AB}}{{\sf BC}}\end{aligned}[/tex].

[tex]\begin{aligned}\frac{{\sf AB}}{{\sf BC}} = \tan(60^{\circ}) = \sqrt{3}\end{aligned}[/tex].

The length of segment [tex]{\sf AB}[/tex] is [tex]h[/tex]. Rearrange this equation to find the length of segment [tex]{\sf BC}[/tex]:

[tex]\begin{aligned} {\sf BC} &= \frac{{\sf AB}}{\tan(\angle ACB)} \\ &= \frac{h}{\tan(60^{\circ})}\\ &= \frac{h}{\sqrt{3}} \\ &\end{aligned}[/tex].

Therefore:

[tex]\begin{aligned}{\sf BD} &= 3\, {\sf BC} \\ &= \frac{3\, h}{\sqrt{3}} \\ &= (\sqrt{3})\, h\end{aligned}[/tex].

Similarly, in right triangle [tex]{\sf ABD}[/tex], segment [tex]{\sf AB}[/tex] (the tower) is opposite to [tex]\angle {\sf ADB}[/tex]. Segment [tex]{\sf BD}[/tex] (shadow of the tower, with [tex]\theta[/tex] as the angle of elevation of the sun) is adjacent to [tex]\angle {\sf ADB}[/tex].

[tex]\begin{aligned}\tan(\angle {\sf ADB}) &= \frac{\text{opposite}}{\text{adjacent}} = \frac{{\sf AD}}{{\sf BD}}\end{aligned}[/tex].

[tex]\begin{aligned}\frac{{\sf AB}}{{\sf BD}} = \tan(\theta) \end{aligned}[/tex].

Since [tex]{\sf AB} = h[/tex] while [tex]{\sf BD} = (\sqrt{3})\, h[/tex]:

[tex]\begin{aligned}\tan(\theta) &= \frac{{\sf AB}}{{\sf BD}} \\ &= \frac{h}{(\sqrt{3})\, h} \\ &= \frac{1}{\sqrt{3}}\end{aligned}[/tex].

Therefore:

[tex]\begin{aligned}\theta &= \arctan\left(\frac{1}{\sqrt{3}}\right) \\ &= 30^{\circ}\end{aligned}[/tex].

In other words, the angle of elevation of the sun at the time of the longer shadow would be [tex]30^{\circ}[/tex].

This transformation of the polygon ABCD to A'B'C'D' is a by a factor of 2

The coordinates are given as:

Calculate the distance AB and A'B' using:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

This gives

[tex]AB = \sqrt{(3-1)^2 + (0-0)^2} = 2[/tex]

[tex]A'B' = \sqrt{(6-2)^2 + (0-0)^2} = 4[/tex]

Divide A'B' by AB to determine the scale factor (k)

k = 4/2

k = 2

Hence, this transformation is a by a factor of 2

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Answer:

0.06

Step-by-step explanation:

Answer:

.06

Step-by-step explanation:

If 1 is 100%, then .06 is 6%.

Hope this helps!

Answer: $26

Step-by-step explanation:

   If $19.50 is 3/4, we need to find 4/4.

3/4 -> 0.75

4/4 -> 1

    We will set up a proportion and solve.

[tex]\frac{19.5}{0.75} =\frac{x}{1}[/tex]

19.5 = 0.75x

26 = x

         The professional ball is $26.

Answer:

$26

Step-by-step explanation:

19.50 = 3/4

so

to find 1/4, we do 19.50 / 3 = 6.5

6.5 = 1/4

so the price of a professional ball would be 4/4 (1 whole)

6.5 x 4 = 26

Hope this makes sense.

- profparis

Answer:

Step-by-step explanation:

21   22    23   23   23   24   24   24   27   29

(23 + 24)/2= 47/2= 23.5 is the median temperature

Answer:

2.3

Step-by-step explanation:

4²+b²=4.6²

16+b²=21.16

-16 -16

b²= 5.16

b=√5.16

b= 2.3

Answer:

2.27 in   ~2.3 in to the nearest tenth

Step-by-step explanation:

It is a right triangle ....so yo can use pythagorean theorem

4^2 + b^2 = 4.6^2

b = 2.27

Answer:

x = 60

Step-by-step explanation:

Let x = ?

120 + 95 +85 +x =360

x +300 =360

x = 360-300

x = 60