What is the range of the function y=3√x+8?
O-∞ O-8 O 0≤y<∞
O 2≤y<∞

The basic parabola is stretched in the y-direction by a factor of 2 (and hence made steeper) and translated.

To create a new parabola that resembles the fundamental parabola, we can translate the parabola vertically. The graph of the function y=x2+b simply resembles a regular parabola with the vertex moved b units down the y-axis. The vertex is so situated at (0,b). The parabola shifts upward if b is positive and downward if b is negative.

The parabola can also be translated horizontally. The graph of the function y=(x-a)^2 resembles a conventional parabola with the vertex moved one unit down the x-axis. then, the vertex is found at (a,0). Observe how we go to the right if an is positive and to the left if an is negative.

All parabolas can be obtained from the basic parabola by a combination of:

Thus, all parabolas are similar.

Hence the basic parabola is stretched in the y-direction by a factor of 2 (and hence made steeper) and translated.

Learn more about Parabola here:

https://brainly.com/question/4061870

#SPJ10

Answer:

y=55x

Step-by-step explanation:

(y1-y2)/(x1-x2)=(165-55)/(3-1)=55

55 is the slope

To find y-intercept:

y=55x+b

substitute 1 for x and 55 for y

55=55(1)+b

b=0

So y= 55x

the equation of the line passing through the points (3, 165) and (1, 55) is y = 55x. To write the equation of the line that passes through the points (3, 165) and (1, 55), you can use the point-slope form of a linear equation, which is: y - y₁ = m(x - x₁)

where (x₁, y₁) is one of the points on the line, m is the slope of the line.

First, calculate the slope (m) using the given points (3, 165) and (1, 55):

m = (y₂ - y₁) / (x₂ - x₁) = (55 - 165) / (1 - 3) = (-110) / (-2) = 55

Now that you have the slope (m = 55) and one of the points (let's use (3, 165)), you can plug them into the point-slope form:

y - 165 = 55(x - 3)

Now, you can simplify and rewrite this equation in slope-intercept form (y = mx + b):

y - 165 = 55x - 165

To isolate y, add 165 to both sides:

y = 55x

So, the equation of the line passing through the points (3, 165) and (1, 55) is y = 55x.

to know more about equation:

https://brainly.com/question/32543980

#SPJ3

Answer:

  [tex]\left(\dfrac{1}{2},-\dfrac{\sqrt{3}}{2}\right)[/tex]

Step-by-step explanation:

An angle is co-terminal with the same angle that has any multiple of 360° added to it.

__

The angle -420° is co-terminal with (-420° +720°) = 300°. The attached unit circle chart shows the coordinates of the terminal side of that angle.

These coordinates are ...

  (x, y) = (cos(300°), sin(300°))

  (x, y) = (1/2, -√3/2)

Answer: 40 km

Step-by-step explanation:

As corresponding sides of similar triangles are proportional, if we let the distance across Clarence lake be x,

[tex]\frac{x}{8}=\frac{15}{3}\\\\\frac{x}{8}=5\\\\x=\boxed{40 \text{ km}}[/tex]

Step-by-step explanation:

sorry sorry ^$£%£$¥#^÷£=₩€%¥=£=;÷¥÷¥9=

Answer:

f'(x) = 7x^4 (5 ln(x) + 1) + x^2

Explanation:

[tex]\sf Let \ f(x)=7x^5 ln(x) + \dfrac{1}{3} x^3[/tex]

Properties used while differentiating:

[tex]i) \quad \sf \dfrac{d}{dx} (ln(x)) = \dfrac{1}{x}[/tex]

[tex]ii) \quad \sf \dfrac{d}{dx} (x^n) = n(x)^{n-1}[/tex]

[tex]iii) \quad \sf \dfrac{d}{dx}(uv)=u \dfrac{dv}{dx}+v \dfrac{du}{dx}[/tex]

Begin solving:

f'(x) =

[tex]\Longrightarrow \sf \dfrac{d}{dx}\:\left(7x^5\:ln\left(x\right)\:+\:\dfrac{1}{3}\:\:x^3\right)[/tex]

[tex]\Longrightarrow \sf \dfrac{d}{dx}\:\left(7x^5\:ln\left(x\right)\right) + \dfrac{d}{dx}\left(\dfrac{1}{3}x^3\right)[/tex]

[tex]\Longrightarrow \sf \dfrac{d}{dx}(7x^5)\:\ \times ln\left(x\right) + \dfrac{d}{dx}(ln(x)) \times \ 7x^5 + \left(3\:\times \dfrac{1}{3}x^{3-1}\right)[/tex]

[tex]\Longrightarrow \sf 5(7x^{5-1})\:\times\ ln(x) + \dfrac{1}{x} \:\times\ 7x^5 \ + x^2[/tex]

[tex]\Longrightarrow \sf 35x^{4} ln(x) + \ 7x^4 \ + x^2[/tex]

[tex]\Longrightarrow \sf 7x^4(5 ln(x) + 1) \ + x^2[/tex]

Answer:

2x(7x-3) + (x²+1)(7)

Step-by-step explanation: use product rule

Si administran 500 ml. La tasa de goteo requerida en gotas por minuto es de 21 gtt/min.

Usando esta fórmula

Tasa de goteo requerida=(ml administrado×gotas/mL)÷ (Número de horas×Número de minutos por hora)

Vamos a conectar la fórmula

Tasa de goteo requerida =(500 mL x 20 gtt/mL) ÷ (8 hrs. x 60 min)

Tasa de goteo requerida =10,000÷480

Tasa de goteo requerida = 20.8

Tasa de goteo requerida =21 gtt/min (Aproximadamente)

Por lo tanto, la tasa de goteo requerida en gotas por minuto es de 21 gtt/min.

Obtenga más información sobre la tasa de goteo requerida aquí: https://brainly.com/question/27370811

#SPJ1

Answer:

P(Event) = N(Favorable Outcomes) / N (Total Outcomes)

P(sum of 10 or 11) = 5/36

Step-by-step explanation:

Probability states how likely an event is about to happen. The probability of an event can exist only between 0 and 1 where 0 indicates that event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty.

The higher or lessen the probability of an event, the more likely it is that the event will occur or not respectively. For example – An unbiased coin is tossed once. So the total number of outcomes can be 2 only i.e. either “heads” or “tails”. The probability of both outcomes is equal i.e. 50% or 1/2.

So,

P(Event) = N(Favorable Outcomes) / N (Total Outcomes)

Sample Space:

All the possible outcomes of an event are called Sample spaces.

Examples-

• If two dice are rolled together then total outcomes will be 36 and

Sample space will be

[ (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)  

  (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

  (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

  (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)

  (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

  (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) ]

Probability of rolling a sum of 10 or 11 with two dice:

When two dice are rolled together then total outcomes are 36 and

Sample space is

[ (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)

  (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

  (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

  (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)  

 (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)  

 (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) ]

So, pairs with sum 10 or 11 are (4, 6) (5, 5) (6, 4) (5,6) (6,5) i.e. total 5 pairs

Total outcomes = 36

Favorable outcomes = 5

Probability of getting the sum of 10 or 11 = Favorable outcomes / Total outcomes

                                                               = 5 / 36

So, P(sum of 10 or 11) = 5/36

Read to see a similar question related to probability:

https://brainly.com/question/743546?referrer=searchResults

#SPJ10

It takes more to prove that quadrilaterals are similar because there are several quadrilaterals such as rectangle, square, etc.

It should be noted that a quadrilateral simply means a shape that has four sides and four angles.

In orde to prove that triangles are similar, we only need to prove corresponding angles congruency.

On the other hand, it takes more to prove that quadrilaterals are similar because there are several quadrilaterals such as rectangle, square, etc. This makes them more elaborate.

Learn more about triangles on:

brainly.com/question/17335144

#SPJ1

Answer:

237 grams

50 * 4

= 200

4 weight of 50 g

1 weight of 20g

1 weight of 10g

7 weight of 1g

Answer:

Step-by-step explanation:

Answer:

Using the concept of number line, we find that Libby owes more than Daniel.

Step-by-step explanation:

Given that the account balance of Daniel is -$1.25 and of Libby is -$2.00. Sandra has as much savings in her account as the amount Daniel owes the bank. So, her account balance is +$1.25.

The numbers to be plotted on the number line are -2.00, -1.25 and 1.25.

The number line is in the attachment.

These numbers are related as: -2 < -1.25 < 1.25.

From the number line, all the names that come left to the origin owe some amount to the bank while all the names that come right to the origin have some money as savings in their account.

Clearly, Daniel and Libby owe the bank.

But since Libby comes before Daniel, Libby owes more than Daniel.

For more explanation, refer the following link:

https://brainly.com/question/4727909

#SPJ10

Answer:

-4*(x+1)

Step-by-step explanation:

Simplify

⇒ 8x2 + 8x/-2x

2:  Pulling out like terms

4.1     Pull out like factors :

  8x2 + 8x  =   8x • (x + 1)

Canceling Out :

4.2    Canceling out x as it appears on both sides of the fraction line

Final result :

 -4 • (x + 1)

Answer:

-4(x+1)

Step-by-step explanation:

factor out -2x

-2x(-6x + 2x - 4) / -2x

the -2x in numerator and denominator cancel out

-6x + 2x - 4

-4x - 1

-4(x+1)

Applying the distance formula, the length of AB is: D. About 9.4 units.

Distance formula is given as: [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].

Given the following:

A(4, 2) = (x1, y1)

B(9, 10) = (x2, y2)

Apply the distance formula

AB = √[(9−4)² + (10−2)²]

AB = √[(5)² + (8)²]

AB = √89

AB ≈ 9.4 units

Learn more about the distance formula on:

https://brainly.com/question/661229

#SPJ1

Answer:

22-3d=x

Step-by-step explanation:

where d is the days that it melts and the amount of snow x is the snow that is left.

The value of x in the given quadrilateral is; x = 3

The diagonals of a parallelogram bisect each other.

Thus, from the image attached, we can say that;

WC = CY.

Thus;

2x + 5 = 3x + 2

Subtract 2x from each side to get;

5 = x + 2

Subtract 2 from each side to get;

5 - 2 = x + 2 - 2

x = 3

The complete question is;

In quadrilateral WXYZ, WC = 2x + 5 and CY = 3x + 2. What must x equal for quadrilateral WXYZ to be a parallelogram?

Read more about Quadrilateral angle at; https://brainly.com/question/4099416

#SPJ1

The opening price of the stock at the beginning of the day was $82.5 and the stock of Company A gained 6% today to $87.45.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

We have:

The stock of Company A gained 6% today to $87.45.

Let x be the opening price of the stock in the beginning of the day.

(x + 0.06x) = 87.45  

Because gained 6% today to $87.45

1.06x = 87.45

x = $82.5

Thus, the opening price of the stock at the beginning of the day was $82.5 and the stock of Company A gained 6% today to $87.45.

Learn more about the percentage here:

brainly.com/question/8011401

#SPJ1

Differentiate both sides with respect to [tex]t[/tex], treating both [tex]x[/tex] and [tex]y[/tex] as functions of [tex]t[/tex].

[tex]x^3 + y^3 = 9 \implies 3x^2 \dfrac{dx}{dt} + 3y^2 \dfrac{dy}{dt} = 0[/tex]

Then when [tex]x=1[/tex], [tex]y=2[/tex] and [tex]\frac{dx}{dt}=-3[/tex], we get

[tex]3\times1^2\times(-3) + 3\times2^2\dfrac{dy}{dt} = 0 \implies \dfrac{dy}{dt} = \dfrac9{12} = \boxed{\frac34}[/tex]

Answer: [tex]x=5\sqrt{3}[/tex]

Step-by-step explanation:

As the triangle is equilateral, we know that all sides have a length of 10. Thus, if we consider either of the right triangles, we know they have legs of lengths 5 and x (since an altitude of an equilateral triangle bisects the side it is drawn to), and a hypotenuse of 10.

Thus, by the Pythagorean theorem,

[tex]5^{2}+x^{2}=10^{2}\\\\25+x^{2}=100\\\\x^{2}=75\\\\\boxed{x=5\sqrt{3}}[/tex]

The number of pairs of parallel sides of the polygon have no parallel sides if n is odd and n/2 pair of parallel sides if n is even.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

A regular polygon has n sides.

Then the number of pairs of parallel sides of the polygon will be

IF n is odd, then none of the sides are parallel.

If n is even, then the number of pair of parallel sides will be n / 2.

More about the polygon link is given below.

https://brainly.com/question/17756657

#SPJ1

Answer:

117

Step-by-step explanation:

The total population is 117 million

Answer:

y = 2/3x + 4/3

Step-by-step explanation:

Voy a suponer que necesitas resolver para y.

2x + 3y = 4

3y = -2x + 4

y = -2/3x + 4/3

A set is a mathematical model for a collection of items. The set of W' is {5, 20, 30}.

A set is a mathematical model for a collection of items; it comprises elements or members, which may be any mathematical object: numbers, symbols, points in space, lines, other geometrical structures, variables, or even other sets.

The complete question is given below.

Q13.

T ∪ V = Data points that are in T or V or both.

T ∪ V = {5, 10, 20, 30}

Q14.

T ∩ W = Data points that are in T and W both.

T ∩ W = {10}

Q15.

W' = Data points that are not in W.

W' = {5, 20, 30}

Hence, the set of W' is {5, 20, 30}.

Learn more about Set:

https://brainly.com/question/8053622

#SPJ1

Answer: (I am copying and pasting my answer from the same question you did before in case you are waiting for an answer on this instead.)

1/2

Step-by-step explanation:

To find the x-int of any equation, you will need to replace the y with a 0 since when the x-int is when y is 0.

8x+2y = 4 ➨ 8x+2*0 = 4

Now I will do 2*0 which anything times 0 is equal to 0. And we are left with the equation of:

8x = 4

Now I will divide both sides by 8, which isolates our x.

x = 1/2

The x-int is 1/2.

Answer:

(0.5 , 0) or (1/2 , 0)

Step-by-step explanation:

Any x-intercept must be at (x,0), so we substitute y=0 into the equation.

8x + 2(0) = 4

8x = 4

x = 1/2 = 0.5

Therefore, the x-intercept is at (0.5 , 0) or (1/2 , 0)

Probability helps us to know the chances of an event occurring. The probability she will do her homework without complaining given that she ate her dinner without complaining is 2/5.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Let eating dinner without complaining be A, and doing homework without complaining be B.

Given the probability my daughter will eat her dinner without complaining is 5/7. So, we can write,

P(A) = 5/7

Also, The probability she will eat her dinner and do her homework all without complaining is 2/7. So, we can write,

P(A∩B) = 2/7

Now, the probability she will do her homework without complaining given that she ate her dinner without complaining is,

[tex]P(B|A)= \dfrac{P(A\cap B)}{P(A)}[/tex]

             [tex]= \dfrac{\dfrac{2}{7}}{\dfrac57}\\\\\\= \dfrac25[/tex]

Hence, the probability she will do her homework without complaining given that she ate her dinner without complaining is 2/5.

Learn more about Probability:

https://brainly.com/question/795909

#SPJ1

The polar coordinates of (-4, 150°) will be  [tex]\sqrt[2]{5629}\\[/tex]  and 5069.09939523°

The formula for this conversion will be:

r = [tex]\sqrt{x^2 + y^2}[/tex]

θ = [tex]tan ^-1 (\frac{y}{x} )[/tex]

[tex]r = \sqrt{(4^2) + (150^0)^2} \\\\θ = tan ^-1 (\frac{y}{x} )\\\\\\r = \sqrt[2]{5629} \\\\ = tan ^-1 (\frac{150}{4} )\\[/tex]

= [tex]\frac{75}{2}[/tex]

the inverse of:  [tex]\frac{75}{2}[/tex] is   θ = 5069.09939523°

Therefore:

[tex]r = \sqrt[2]{5629}\\[/tex]

θ = 5069.09939523°

So the polar coordinates of (-4, 150°) will be [tex]\sqrt[2]{5629}\\[/tex]  and 5069.09939523°

Learn more about polar coordinates from

https://brainly.com/question/14965899

#SPJ1

Answer:

4(49v²+25)

Step-by-step explanation:

[tex]196 {v}^{2} + 100[/tex]

[tex]4(49 {v}^{2} + 25)[/tex]

Answer:

25

Step-by-step explanation:

find the greatest common factor (GCF) of the 3 quantities using prime factorisation.

125 = 5 × 5 × 5

150 = 2 × 3 × 5 × 5

225 = 3 × 3 × 5 × 5

Next, identify those prime factors that the 3 numbers have in common and multiply them.

the common factors are 5 × 5 = 25

then

125 ÷ 25 = 5

150 ÷ 25 = 6

225 ÷ 25 = 9

the 25 students each get 5 apples, 6 oranges and 9 mangoes