asap pls

Simplify the expression and write the answer with
only positive exponent
(2p²)-³q4
(6q)-¹p-7​​

The drag point point is shown on the graph.

What is drag point?

When a single point or the center of a circle is specified numerically, the point can be moved, and the mouse can be used to edit graphs (ex. translation of a parabola).

Consider, the given equation

[tex]g(x) = -\frac{5}{3} x-1[/tex]

We have to find the value of g(x) at x = 3.

So, plug x = 3 in the above equation.

[tex]g(3) = -\frac{5}{3}(3)-1\\ g(3)=-5-1\\g(3) = -6[/tex]

Therefore, the point is (3, -6).

We have to drag the point (3, -6) on the graph.

The drag point graph is attached below.

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Using implicit differentiation at the given point gives;

a) dy/dx = 4

b) dy/dx = -³/₈

In implicit differentiation, what we are doing is that we are differentiating each side of an equation with two variables (usually x and y) by treating one of the variables to act as a function of the other. This implies the use of chain rule

13) x² + y³ = 5

Using implicit differentiation gives;

2x + y²(dy/dx) = 0

dy/dx = -2x/(y²)

At (-2, 1), we have;

dy/dx = -2(-2)/(1²)

dy/dx = 4

14) x³ = -4y² + 3

Using implicit differentiation gives;

3x² = -8y(dy/dx) + 0

dy/dx = -³/₈x²/y

At (-1, 1), we have;

dy/dx = -³/₈(-1)²/1

dy/dx = -³/₈

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Answer: up and down line at -2

Step-by-step explanation: Desmos

The function y = (e⁻⁽ˣ⁺²⁾) / x + 2  increases along intervals of (-∞, 3) and decreases along (-3, -2), (-2, ∞) and the function y = 2x - 1 / (x - 1)² has no inflection points but  concave downwards along (-∞, 1) ∪ (1 ,∞)

An extremum (or extreme value) of a function is a point at which a maximum or minimum value of the function is obtained in some interval. A local extremum (or relative extremum) of a function is the point at which a maximum or minimum value of the function in some open interval containing the point is obtained.

The function given;

y = (e⁻⁽ˣ⁺²⁾) / x + 2

The extrema and intervals of increase or decrease of this function are

(-1, 1.63) and it increases along (-∞, 3) and decreases along (-3, -2), (-2, ∞)

2. The inflection points and intervals of concavity and convexity of the function

y = 2x - 1 / (x - 1)² are

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Answer:

18 days

Step-by-step explanation:

this question is actually pretty simple, so all you have to do is take the total km which is 2880 divide it by 240 which is 12 then add 6 to it which makes 18 days

The total surface area of the cylinder is 157 square feet.

Given the radius of the cylinder = 4 inches

height of the cylinder = 9 inches

Total surface area is calculated by the formula:

A = 2πr² + 2πh

A = 2 × 3.14 × 4² + 2 × 3.14 × 9

or, A = 157 square feet.

Therefore the total surface area of the cylinder is 157 square feet.

The surface area of a solid item is a measurement of the total volume that the surface of the thing occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more complicated than the definition of arc length for one-dimensional curves.

The definition of surface area for polyhedral (i.e., particles with flat polygonal faces), where the surface area is equal to the sum of the areas of its faces. When smooth surfaces, like spheres, are represented as parametric surfaces, their surface area can be calculated.

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12% of total animals are ring-tailed lemurs.

A percentage is a fraction of an amount expressed as a particular number of hundredths of that amount.

Given that, 30% of the animals in a wildlife park are lemurs, 40% are ring-tailed lemurs.

Let total animals be 100.

30% of 100 = 30

40% of 30 = 12

12/100*100 = 12%

Hence, 12% of total animals are ring-tailed lemurs.

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Using the proportionality theorem, to find the values of x and y, we have:

a. x = 1.25; y = 1.75

b. x = 15; y = 4

c. x = 3; y = 2

According to the proportionality theorem, the side lengths of similar triangles have the same ratio, or are proportional to each other.

Using the proportionality theorem, we can find the following missing values of x and y.

a. (5 + x)/5 = 10/8 [proportionality theorem]

Cross multiply

8(5 + x) = (5)(10)

40 + 8x = 50

8x = 50 - 40

8x = 10

x = 10/8

x = 1.25

5/x = 7/y

Plug in the value of x

5/1.25 = 7/y

5y = 8.75

y = 1.75

b. x/5 = 18/6 [proportionality theorem]

6x = 90

x = 90/6

x = 15

12/y = 18/6

Cross multiply

18y = 72

y = 72/18

y = 4

c. x/6 = 1.5/3 [proportionality theorem]

3x = 9

x = 9/3

x = 3

y/4 = 1.5/3

Cross multiply

3y = 6

y = 6/3

y = 2

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Answer:

a. x = 1.25; y = 1.75

b. x = 15; y = 4

c. x = 3; y = 2

Step-by-step explanation:

Answer:

$610,498.30

Step-by-step explanation:

P = C (1 + r/n)^nt

4% = 0.04

P = 500 000(1+0.04/12)^(12*5)

P = 500 000 (1.003333)^60

P = 500 000 (1.220997)

P = $610 498.296971

Answer:

1a (or) a

Step-by-step explanation:

Given expression,

→ a(5 - 4)

Let's simplify the expression,

→ a(5 - 4)

→ a(1)

→ a × 1

→ 1a (or) a

Therefore, the answer is 1a.

The amount of force used to pull the cart from 60 N to 90 N, the new acceleration of the cart is, 1.5 m/s²

The definition of force is the pushing or pulling of anything. Push and pull are the result of two things interacting with one another. Stretch and crush are two more phrases that can be used to describe force.

Formula of force,

F = ma

Given that,

A man pulled a cart filled with stones that had a total mass of 60 kg

He increased the amount of force used to pull the cart from 60 N to 90 N

New acceleration of cart = ?

F  = ma

Old acceleration,

60  = 60a

a   =  1 m/s²

New acceleration,

90 = 60a

a   = 90/60

a   =  3/2

a   =  1.5 m/s²

Hence, the new acceleration is 1.5 m/s²

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The required equation of the line is given as y = -4/3x - 2/3.

Given that,
The equation of the line that is perpendicular to the line below and passes through the point (4,-6).

A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.

Here,
The slope of the given line = 3/4
So the slope of the perpendicular line = -4/3
Now,
The perpendicular line passes from (4, -6)
The standard form of the equation,
y - y₁ = m [ x - x₁]
Substitute the value in the above expression,
y + 6 = -4/3[x - 4]
y = -4/3x + 16/3 - 6
y = -4/3x - 2/3

Thus, The required equation of the line is given as y = -4/3x - 2/3.

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Answer:

8 days = 192 hours

Step-by-step explanation:

Formula we use,

→ 1 day = 24 hours

Conversion of 8 days into hours,

→ n days × 24 hours

→ 8 × 24

→ 192 hours

Hence, there are 192 hours.

The number of tiles that would be required to cover a floor that is 288 square feet is 512.

According to the question,

We have the following information:

Area of the tile = 9*9 square inches

Area of the tile = 81 square inches

Area of the floor = 288 square feet

So, we will convert the area of the floor from square feet to square inches.

We know that 1 feet = 12 inches.

So, we have the following expression:

Area of the floor = (288*12*12) square inches

Area of the floor = 41,472 square inches

Number of tiles required to cover the floor = area of the floor/area of the tile

Number of tiles required to cover the floor = 41,472/81

Number of tiles required to cover the floor = 512

Hence, the number of tiles that would be required to cover a floor that is 288 square feet is 512.

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Answer:

You insert 5 back into the equation

Step-by-step explanation:

17 +2.6b=30

17 +2.6(5)=30

17 +13=30

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$2411\\ P=\textit{original amount deposited}\dotfill & \$2000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]2411=2000e^{\frac{r}{100}\cdot 4}\implies \cfrac{2411}{2000}= e^{\frac{r}{25}}\implies \log_e\left( \cfrac{2411}{2000} \right)=\log_e\left( e^{\frac{r}{25}} \right) \\\\\\ \log_e\left( \cfrac{2411}{2000} \right)=\cfrac{r}{25}\implies 25\cdot \ln\left( \cfrac{2411}{2000} \right)=r\implies \stackrel{\%}{4.67}\approx r[/tex]

The value of  the height of the water at  midday  is 14 feet.

Height, altitude, and elevation all refer to the vertical distance between something's top and bottom or its base and something above it. Height is used to describe everything that may be measured vertically, high or low.

Similarly, we will determine the height at other times during the day, at midday . we have the value $t=3$, so using the formula, we have

[tex]H(3)=10+4 \sin \left(\frac{\pi}{6} \cdot 3\right)=10+4 \cdot \sin \frac{\pi}{2}[/tex]

Taking into account that

[tex]\sin \frac{\pi}{2}=1[/tex]

we get the following:

H=10+4 [tex]\cdot \sin \frac{\pi}{2}=10+4 \cdot 1=14[/tex]

Thus, the value of  the height of the water at  midday . is 14 feet.

The value of the height of the water at midday is 14 feet.

Height, altitude, and elevation all refer to the vertical distance between something's top and bottom or its base and something above it. Height is used to describe everything that may be measured vertically, high or low.

Similarly, we will determine the height at other times during the day, at midday. we have the value[tex]$\$ \mathrm{t}=3 \$$[/tex], so using the formula, we have [tex]$H(3)=10+4 \sin \left(\frac{\pi}{6} \cdot 3\right)=10+4 \cdot \sin \frac{\pi}{2}$[/tex]Taking into account that

[tex]$\sin \frac{\pi}{2}=1$[/tex]

we get the following:

[tex]$\mathrm{H}=10+4 \cdot \sin \frac{\pi}{2}=10+4 \cdot 1=14$[/tex]

Thus, the value of the height of the water at midday . is 14 feet.

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To have the same price, 40 stickers will have to be ordered and the equation is 16 = 0.40p.

What is the equivalent equation?

Equivalent equations are algebraic equations with identical solutions or roots. Adding or subtracting the same number or expression from both sides of an equation yields an equivalent equation. An equivalent equation is created by multiplying or dividing both sides of an equation by the same non-zero number.

We have,

for company A :

Design Fee = $30

Costvper sticker = $0.80

for company B :

Design Fee = $14

Cost per sticker = $1.20

Let the number of stickers = p

Total cost of company A = 30 + 0.80p

Total cost of company B = 14 + 1.20p

For the cost to be the same :

Company A = Company B

30 + 0.80p = 14 + 1.20p

Collect like terms :

30 - 14 = 1.20p - 0.80p

16 = 0.40p

p = 16/0.40

p = 40 stickers

Therefore, to have the same price, 40 stickers will have to be ordered and the equation would be 16 = 0.40p.

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Answer:

4) Melody is 9 and her sister is 24

5) The numbers are 3 and 9

6) 14 feet per second

Step-by-step explanation:

Questions 4

There is a lot going on here.  This is probably hard to follow.  If it is, it is me and not you.

Let m = Melody and s = sister

m - 4 = 1/4(s-4)                     m + 6 = 1/2(s + 6)  Clear the fractions

4m - 16 = s -4                        2m -s = -6

Multiple the second equation by -1 and add together

4m - s = 12

-2m + s = 6

2m = 18  Divide both sides by 2

m = 9  Substitute this in to find the sister's age

2m + 12 = s + 6

2(9) +12 + s + 6

18 + 12 = s + 6

30 = s + 6  Subtract 6 from both sides

24 = s

Questions 5

x + y = 12              x = 5y - 6

Plug in 5y - 6 in the first equation for x

5y - 6 + y = 12  Combine like terms

6y - 6 = 12  Add 6 to both sides

6y = 18  Divide both sides by 6

y = 3

x + y = 12

3 + y = 12  Subtract 3 from both sides

y = 9

I am little confused by this because it says, "The value of the number..."  What number are they referring to?

Question 6

To find the rate taking into consideration the walkway rate:

[tex]\frac{48}{3}[/tex] - w  Which is equivalent to 16 - w

[tex]\frac{24}{2}[/tex] + w  Which is equivalent to 12 + w

Set these expression equal to each other and find the rate of the walkway

16 - w = 12 + w  Add w to both sides

16 = 12 + 2w  Subtract 12 from both sides

4 = 2w  Divide both sides by 2

2 = w

The rate of the walkway is 2 feet per second.  Subtract that from 16 or add is to the 12 to get 14 steps per second.

For the given expression, the variable is p, coefficient is 17 and the exponent is 5.

Expression:

Expression refer the algebraic expression that consists of variables, numbers and math operators.

Given,

Here we have the expression 17p⁵

Now, we have to find the exponent, coefficient and variable.

As per the definition of exponent, the term exponent refers the power value of the expression.

So, the exponent is 5.

And the definition of coefficient is an integer that is written along with a variable or it is multiplied by the variable.

So, the coefficient is 17.

And the variable of this expression is p.

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Answer:

Step-by-step explanation:

1 gallon = $29.95

Nikki needs 12.25 gallons, so,

12.25 gallons= 12.25 × 29.95 =  $ 366.8875 = $ 366.89

Answer:

ab + ac

Step-by-step explanation:

Given expression,

→ a(b + c)

Simplifying the expression,

→ a(b + c)

→ (a × b) + (a × c)

→ ab + ac

Hence, answer is ab + ac.

Answer:

25 x 26 = 650

0.25 x 0.26 = 0.065

Step-by-step explanation:

I'm assuming your equation was:

        [tex]y-2=\dfrac{1}{5}(x-3)[/tex]

Both Jules' line and Lauren's line have a slope of -5 or [tex]-\dfrac{5}{1}[/tex] and those two lines are parallel since they have the same slope.

Perpendicular lines have slopes that are opposite reciprocal values.  

The opposite reciprocal of [tex]-\dfrac{5}{1}[/tex] is a positive [tex]\dfrac{1}{5}[/tex], which is why these two lines are perpendicular to the line at the top of my answer.

Required equation of line in slope intercept form

y = 4x - 7

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan \theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Slope of the line = 4

y - intercept of the line = -7

The line passes through (0. -7)

Equation of the required line

y - (-7) = 4(x - 0)

y + 7 = 4x

y = 4x - 7

Option D is correct

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Step-by-step explanation:

if x→+∞, then y→-∞ [increasing];

if x→-∞, then y→+∞ [decreasing].

Answer:

Y=4 is a function

Step-by-step explanation:

And to me function is relation

Hope i got this right and have a great day :)

Answer: Yes

Step-by-step explanation:

Yes, y = 4, which is often written as f(x) = 4, is a function that means “take any input, and no matter what it is, produce an output of 4”.

The perfect square trinomial and binomial of the expression [tex]q^{2}[/tex] + [tex]\frac{5}{6}q[/tex] are  [tex]q^{2}[/tex] + [tex]\frac{5}{6}q[/tex] + [tex]\frac{25}{144}[/tex] and [tex](q + \frac{5}{12}) ^{2}[/tex]

Perfect squares are numbers or expressions that are the product of a number or expression multiplied to itself. 7 times 7 is 49, so 49 is a perfect square. x squared times x squared equals x to the fourth, so x to the fourth is a perfect square.

[tex]q^{2}[/tex] + [tex]\frac{5}{6}q[/tex] expression can be made into a perfect square by adding the square of half the coefficient of q

coefficient of q = [tex]\frac{5}{6}[/tex]

Half of [tex]\frac{5}{6}[/tex] = [tex]\frac{5}{12}[/tex]

square [tex]\frac{5}{12}[/tex] we have [tex](\frac{5}{12}) ^{2}[/tex] which becomes [tex]\frac{25}{144}[/tex]

so the perfect square trinomial = [tex]q^{2}[/tex] + [tex]\frac{5}{6}q[/tex] +  [tex]\frac{25}{144}[/tex]

the binomial is  [tex](q + \frac{5}{12}) ^{2}[/tex]

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