If the original quantity is 10 and the new quantity is 3​, what is the percent​ decrease?

The equation of the tangent line to the curve when y = -1 is y = -4x - 1.

To find the equations of all tangent lines to the curve when y = -1, we can use the definition of a tangent line, which is a line that touches a curve at a single point and has the same slope as the curve at that point.

To find the slope of the curve at a given point, we can use the slope formula:

slope = (y₂ - y₁) / (x₂ - x₁)

In this case, we can set y₁ = -1 and y₂ = -1 + h, where h is a small positive number, and find the corresponding value of x₂ by substituting these values into the equation x - x²y - 2y² = 0. This will give us the slope of the curve at the point (x, -1).

Substituting these values into the equation, we get:

x - x²(-1) - 2(-1 + h)² = 0

Expanding the second term and rearranging, we get:

x - x² + 2(1 - 2h + h²) = 0

This simplifies to:

x - x² + 2 - 4h + 2h² = 0

This can be rewritten as:

x - x² + 2h² - 4h + 2 = 0

To find the slope of the curve at the point (x, -1), we can take the derivative of this equation with respect to x and evaluate it at x = x and h = 0:

slope = (2h² - 4h)'|h=0

= 0 - 4

= -4

Now that we have the slope of the curve at the point (x, -1), we can use the point-slope form of a linear equation to find the equation of the tangent line:

y - (-1) = -4(x - x)

y + 1 = -4x

y = -4x - 1

Therefore, when y = -1, the equation of the tangent line to the curve is y = -4x - 1.

To learn more about tangent lines click here:

https://brainly.com/question/23265136

#SPJ1

The rectangle's area is increasing at a pace of 128 in2 /s.

What in math is a rate?

A rate is a unique ratio where the two words are expressed in several units. For instance, the price is 69 for 12 ounces if a 12-ounce can of maize costs 69. This is not a proportion of two comparable units, like shirts. This ratio compares two dissimilar units: ounces and cents

Give L and W the length and breadth, respectively. The rectangle's surface area is

A = L ⋅ W.

To obtain, differentiate both sides of the aforementioned equation with regard to time t.

dA ⁄ dt = dL ⁄ dt ⋅ W + L ⋅ dW ⁄ dt

Given the circumstances,

dL ⁄ dt = 10 and dW ⁄ dt = 4

So at the moment when L = 12 and W = 2,

dA ⁄ dt = (10)(12) + 4(2 )

          = 128

The rectangle's area is increasing at a pace of 128 in2 /s.

Learn more about rate

brainly.com/question/119866

#SPJ1

The percentage of oxygen in the water is 0.0002%.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given that a 2000 ml sample of water was collected and found to have 0.004 mL of oxygen. Therefore, the percentage oxygen in water is equal to,

Percentage = Volume of oxygen in the water / Volume of water

                   = 0.004 mL / 2000 mL

                   = 0.004 mL / 2 mL

                   = 0.0002% of water

Therefore, the percentage of oxygen in the water is 0.0002%.

Learn more about Percentages here:

https://brainly.com/question/6972121

#SPJ1

Answer: y=-4x+6

Step-by-step explanation:

The exponential function best represents the growth of the investment.

What is exponential function?

An exponential function can be used to depict the investment's growth. The formula for an exponential function is y = a * b^x, where an is the starting point (in this case, 45,000), b is the growth factor (in this case,

1 + 0.018 = 1.018), and x is the number of time periods (in this case, the number of months).

For example, if we let x represent the number of months, the function would be:

y = 45,000 * 1.018^x

This function represents the growth of the investment as a function of the number of months. As the number of months increases, the value of the investment will grow exponentially according to the formula.

Hence, the exponential function best represents the growth of the investment.

To know more about exponential function, click on the link,

https://brainly.com/question/2456547

#SPJ1

The least number of seats she is setting up 40 seats are needed.

The least number is zero (0). Zero (0) is the smallest natural number and is the additive identity of the set of whole numbers. It is the only number that is neither positive nor negative and is, therefore, regarded as neither odd nor even. Zero (0) is essential in mathematics and is used to represent the absence of a quantity. It is also used to represent the additive identity of real numbers and complex numbers.

Given: Mandy can place 8 seats at each table or 10 seats at each table with no left over.

We have to find the least number of seats needed.

Find the prime factors of 8:

⇒ 8 = 2 x 2 x 2 = 8 = 2³

Find the prime factors of 10:

⇒ 10 = 2 x 5

Find the LCM of 8 and 10:

⇒ 8 = 2³

10 = 2 x 5

LCM = 2³ x 5

LCM = 40

Hence, a minimum of 40 seats are needed.

To learn more about least number

https://brainly.com/question/29466493

#SPJ1

Answer:

The range is found by the y axis. Find the length by comparing it to the graph.

Step-by-step explanation:

The function is an exponential growth function growth decay percent rate of change of the function is 110 %.

Given :

What type of exponential function is f(x)=0. 75(2. 1)^x what is the function's percent rate of change.

we know that,

exponential growth function in the form of y = a ( 1 + r )^x

on comparing both functions we get ,

1 + r = 2.1

r = 2.1 - 1

r = 21 / 10 - 1

= 21 - 10 / 10

= 11 / 10

= 1.1

converting into percentage:

= 1.1 * 100 %

= 110 %

Learn more about the function here:

https://brainly.com/question/28303908

#SPJ4

The total distance Desiree travelled was 14km.

Always remember,

Average speed= Total distance travelled/ Total time taken

So, in this case, we have to find the distance,

Distance= Speed × Time

When she  ran 16km per hour for 30 minutes,

⇒ Distance= 16×30/60

⇒ Distance= 8km --------------------(1)

When she ran 8km per hour for 45 minutes,

⇒ Distance= 8×45/60

⇒ Distance= 6km --------------------(2)

Adding equations (1) and (2) we get,

⇒ Distance = 8+6=14km

Hence, the Total Distance travelled was 14km.

Learn more about the Time and Distance:

https://brainly.com/question/26046491

Reflection of point across x-axis

preimage (-3, 2)         Image (-3, -2)

Reflection of point across y-axis

preimage (-3, 2)         Image (3, 2)

Reflection is one of the movements in transformation that involve creation of mirror image

Transformation rule for reflection over x-axis at origin (0, 0)) is

(x, y) → (x, -y)

Transformation rule for reflection over line y-axis at origin (0, 0)) is

(x, y) → (-x, y)

The reflection to be done is (-3, 2)

Transformation for reflection over x-axis → (-3, -2)

Transformation for reflection over line y-axis  → (3, 2)

Learn more about reflection over a line here:

https://brainly.com/question/29444410

#SPJ1

Answer:

L1 = L2 = 16.5 cm and L3 = 7cm

Step-by-step explanation:

Triangle perimeter = L1 + L2 + L3 = 40 cm

L1 = L2 = L

L3 = 7

Then:

40 = 2L +7

33 = 2L

L = 33/2

L = 16.5 cm

The Wonderful Wizard of Oz, according to American historian Henry Littlefield, was a metaphor for the 1890s Populist movement, which was an uprising by disaffected manufacturing and agricultural workers to gain control from the financial elite. Littlefield made this claim in 1964.

Judy Garland's character Dorothy and her dog Toto are carried away in their home to the fantastical country of Oz as a cyclone tear across Kansas.

As they travel along the Yellow Brick Road to the Emerald City to visit the Wizard, they encounter characters like the brainless Scarecrow (Ray Bolger), the heartless Tin Man (Jack Haley), and the Cowardly Lion (Bert Lahr).

The Wizard of Oz set and filming process was toxic, from bosses demanding their injured and sickly players return to set despite still needing to heal to the director smacking a 16-year-old and forcing her to take drugs to control her hunger and keep thin.

Therefore, the Wonderful Wizard of Oz, according to American historian Henry Littlefield, was a metaphor for the 1890s Populist movement, which was an uprising by disaffected manufacturing and agricultural workers to gain control from the financial elite. Littlefield made this claim in 1964.

Know more about Wizard of Oz here:

https://brainly.com/question/24236729

#SPJ4

Answer:

The arithmetic sequence in the given series of numbers is 11. The common difference in an arithmetic sequence is the number that is added to each term to get the next term in the sequence. In this case, the common difference is 11, because when we add 11 to the first term, 12, we get 23, which is the second term in the sequence. Similarly, when we add 11 to the second term, 23, we get 34, which is the third term in the sequence, and so on. Therefore, the arithmetic sequence in the given series of numbers is 11

Answer:

137

Step-by-step explanation:

triangles always equal 180 degrees for internal angles

20+23-180

Step-by-step explanation:

you did not write this question well

Step-by-step explanation:

8x + 3y = 7 --------(1)

2x + y = 2 ----------(2)

y = 2 – 2x ---------(3)

just substitute for y in equation (1)

8x + 3(2–2x) = 7

8x + 6 – 6x = 7

8x – 6x + 6 = 7

2x = 7 – 6

2x = 1

x = ½

since x = ½ just substitute for x in equation(3)

y = 2 – 2x

y = 2 – 2(½)

y = 2 – 1

y = 1

so x = ½,y = 1

i hope this helped

Answer: I think its 3.5

Step-by-step explanation:

Answer:

Each Girl scored 3.71 points

Each boy scored 12 points

Blossoms age now will be 5 years.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let Blossom age be x

The information will be illustrated as:

3x + 5 = 2(x + 5)

3x + 5 = 2x + 10

3x - 2x = 10 - 5

x = 5.

Therefore, Blossoms age now will be 5 years.

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

Step-by-step explanation:

y = 160°

take the derivative of both sides

y'= d÷dx(160°)

the derivative of a constant is always 0

y' = 0

Answer:

12? lol

Step-by-step explanation:

<3

If UV≅PM then UV≅PM → Definition of congruence, EF≅EF → Reflexive property of congruence, If AB≅LM and LM≅ST then AB≅ST  → Transitive property of congruence.

A statement that is accepted as true without evidence, also referred to as an axiom. Lemmas and theorems are deduced from postulates, which serve as their fundamental building block. For instance, Euclid's postulates, a set of five postulates, provide the foundation of all of Euclidean geometry.

A) If and only if two segments have equal amounts of each, they are congruent.

If UV≅PM then UV≅PM → Definition of congruence

B) An angle, line segment, or shape is always congruent to itself, according to the reflexive characteristic of congruence in geometry.

EF≅EF → Reflexive property of congruence

C) According to the transitive characteristic of congruence, "all sides are congruent to each other if two sides are congruent to the third side."

If AB≅LM and LM≅ST then AB≅ST  → Transitive property of congruence

D) Actually fairly straightforward, equality has the symmetric condition. According to this criterion, if a = b, then b must also be a. In other words, even if two equations' sides are switched, the equation still makes sense.

If AB=XY then XY =AB  → Symmetric property of equality

E) The additive property of equality in an equation asserts that the sides stay equal whether we add or subtract the same amount from both sides of the equation. For entire numbers as well, this property is valid.

If 2x-3=13 then 2x=16 → Addition property of equality

Add 3 on both the sides of equation we get

2x-3+3=13+3

⇒ 2x=16

Therefore, the statement If 2x-3=13 then 2x=16 follows addition property of equality.

Learn more about the postulates here:

https://brainly.com/question/11084273.

#SPJ1

Answer: 14/16 & 28/32

Step-by-step explanation: For 14/16, is simply multiplied 7/8 by 2 for the numerator and denominator, so 7 x 2 = 14, and 8 x 2=16. And, I did the same thing for 28/32. Just multiply both sides by 4. I hope this helped!

The true equation would be = DE/DF = AB/AC

What does an equivalent ratio look like?

When we compare two ratios, they are said to be equivalent. To determine whether two or more ratios are equivalent, they can be compared to one another. For instance, the ratios 1:2 and 2:4 are equivalent.

Are all proportions an equivalent ratio?

Proportional quantities are represented by a collection of corresponding ratios. We can claim, for instance, that 2:3 and 4:6 are proportionate.

Is proportion a constant?

"X is to Y as A Is to B" is how a proportion is expressed. Cross products are the xb and ay products. A proportion's cross products are consistently equal.

Learn more about equivalent proportion

https://brainly.com/question/19994681

#SPJ1

Using Pythagoras theorem, 11.31 is  the length of one leg of a right triangle .

What is the Pythagorean theorem in plain English?

The Pythagorean Theorem states that the squares on the hypotenuse of a right triangle, which is the side that faces the right angle, are equal when added together.

                           This is written as a2 + b2 = c2 in the familiar algebraic notation.

Theorem: a^2 + b^2 = c^2. a and b are the legs, and c is the hypotenuse.                  

                       14^2 + b^2 = 18^2

                        196 + b² = 324

                            b² = 324 - 196

                              b = √128

                             b = 11.31

Learn more about Pythagoras theorem

brainly.com/question/343682

#SPJ1

False, an industry standard is to randomly select 10% of the completed surveys for purposes of making a call-back to validate that the interview was conducted.

What are industries standards?

A collection of standards within an industry referring to how activities are typically carried out in their respective domains of production.

                  In other words, it refers to the standards that are commonly accepted by an industry's participants.

Why is this industry norm?

Industry standards are primarily intended to make products compatible with one another and to ensure that consumers can mix and match products from various brands without risk.

                             Best Industry Standards refers to benchmarks that, taking into account elements like the nature and size of the parties, are in the upper quartile in the relevant industry for the delivery of comparable services that are essentially similar to the Services or the relevant part of them.

Learn more about  industry standard

brainly.com/question/1538175

#SPJ4

Answer:

The answer is 246

Step-by-step explanation:

So,

S₁₂ = 12/2 [2(4) + (12 - 1)3]

S₁₂ = 6 [8 + (11)3]

S₁₂ = 6 × (8 + 33)

S₁₂ = 6 × 41

S₁₂ = 246

Thus, The S₁₂ of given A.P is 246