An astronaut was exploring the moon of a distant planet, and found some glowing goo at the bottom of a very deep crater. She brought a 10-gram sample of the goo to her laboratory. She found that when the goo was exposed to light, the total amount of goo increased by 100% every hour.
How much goo will she have after 1 hour? After 2 hours? After 3 hours? After n hours?
When she put the goo in the dark, it shrank by 75% every hour. How many hours will it take for the goo that was exposed to light for n hours to return to the original size?

Answer:

[tex]y=x^2+2x-2[/tex]

Step-by-step explanation:

Vertex form is expressed as: [tex]y=a(x-h)^2+k[/tex], and is super useful when analyzing the vertex, which is given to be (h, k).

Standard form is expressed as: [tex]y=ax^2+bx+c[/tex], and is also useful in certain cases.

When converting standard to vertex we have to complete the square to rewrite the equation using a perfect square binomial, which is what really distinguishes the two. Now when we want to convert back into standard form, we simply need to get rid of this perfect square binomial, which we can do by expanding out the perfect square binomial into a trinomial.

So in other words, we want to multiply out the following: [tex](x+1)(x+1)[/tex], which becomes: [tex]x^2+2x+1[/tex] which you can solve by using polynomial multiplication, which is essentially just extending the logic of the distributive property. In general when given two polynomials to multiply, you look at one polynomial, and then multiply it by each term in the other polynomial, now repeat this for each term in the polynomial you were initially looking at. I'll provide a picture to better illustrate this. You can use FOIL if it helps you with multiplying binomials, but remembering how to generally use it, will help you when multiplying polynomials in general.

Now that we've multiplied out the expression, we can substitute it into the equation: [tex]y=x^2+2x+1-3[/tex], now just combine the constants: [tex]y=x^2+2x-2[/tex], and now you've converted it into standard form!

On solving the provided question, we can say that - the value of x and y by the linear equation will be x = 12 and y = -21

The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

here, we have

3x-2y = 3

-4x + 5y = -11

and on solving we got

x = 12 and y = -21

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Answer:

Below

Step-by-step explanation:

"Lynn is making a snack. The recipes call for 3/8 cup of water for oats and 1/4 cup"

(I changed the numbers to fractions ....)

she needs   3/8 + 1/4 cup ....add them together by finding a common denominator

1/4 = 2/8    

then   3/8 + 2/8 = (3+2)/8 = 5/8 cup

  if she has one cup of water she has enough....she only needs 5/8 cup

Orange marble selection has a 0.33 experimental probability.12 over 60 is the experimental probability of landing on a number smaller than 2

Probability theory, a subfield of mathematics, gauges the likelihood of an event or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a comprehensive set of equally likely outcomes that result in a certain occurrence compared to the total number of outcomes.

given

In each of the three studies, Sandy's experimental probability matched the theoretical probability to the letter.

The theoretical likelihood of landing on orange is one-fourth, but the actual likelihood is 20%.

Orange marble selection has a 0.33 experimental probability.

12 over 60 is the experimental probability of landing on a number smaller than 2.

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The rate of change of the end points of the line is 32/10

What is slope?

Slope is defined as the rate of change of y with respect to x.  Also it is defined as increase in y over increase in x or decrease in y over decrease in x

slope is denoted by the formula = Δy/Δx

Where Δy = change in y

Δx= change in x

The given points are (-9, -2) and (5, 119/5)

The slope of the end points   (119/5 + 21)/(5+9)

The slope is (119+105)/5

M= 44.8/14

The slope is 3.2 = 32/10

Therefore the rate of change is given as 32/10

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The equation connecting y and x is y = 63/x and the value of y when x =21 is 3

From the question, we have the following parameters that can be used in our computation:

Variation = inverse variation

y = 7, x = 9

An inverse variation is represented as

k = xy

Where k is the constant of proportion

Substitute the known values in the above equation, so, we have the following representation

k = 7 * 9

Evaluate

k = 63

So, we have the following representation

xy = 63

Make y the subject

y = 63/x

Substitute the known values in the above equation, so, we have the following representation

y = 63/21

Evaluate

y = 3

Hence, the solution is 3

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Maria’s vegetable garden measures 5⅔ feet by 6⅚ feet. 38.72 feet² is the area of the garden. This can be solved using the concept of the area of rectangle.

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. Because the opposing sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

Each and every square is a rectangle since it is a quadrilateral with right angles on all four sides. But not all rectangles are squares; for a shape to be a square, all of its sides must have the same length.

So a square is also a rectangle and a rhombus. There is no square shape in the rectangle or rhombus. The trapezium shape is a parallelogram.

Maria’s vegetable garden measures 5⅔ feet by 6⅚ feet.

So, it is a rectangular garden.

Now, area = 5⅔ feet × 6⅚ feet

or, area = 17/3 feet × 41/6 feet

or, area = 697 /18 feet²

or, area = 38.72 feet²

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Since the lengths EH and FG have the identical slope ratios as the parallel lines problem that is being given, assertion 4 is true, and so statement 4 is: EHFG.

Two non-vertical lines with the same slope that are located in the same plane are said to be parallel. Two parallel lines cannot cross each other. Right angles connections are those that intersect two non-vertical line in the same plane at a right angle.

Here,

The slope values in EH and FG are the same.

the exhibited proof, which is zero.

This implies that they follow one another in a straight line.

Since the sections EH and FG share the same gradient values as the parallel lines problem that is being given, assertion 4 is true, and so statement 4 is: EH||FG.

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The line that parallels y = 1/2 x + 8 and goes through the point (-2, 2) is represented by the equation y = 1/2 x + 3.

The entire time, the x-coordinate -2 is shown. A function is NOT what this is. A number is multiplied three times by itself to form a cube. The symbol for the cube of a number is x. 3.

To increase an integer to the third power is to cube it. A function is an equation with just one solution for every value of y in the equation. A function pairs each input of a particular type with exactly one output. Instead of y, it is typical to name functions f(x) or g(x). f(2) instructs us to calculate the value of our function when x is equal to 2.

A function, in general, is a relationship between two variables. In other words, the relationship x = y2 is not a function.

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Answer:

81

Step-by-step explanation:

9x9 = 81

Answer: D

Step-by-step explanation: x is a variable, and so is the number of tractors he sells. he is going to get paid $1000 for sure each month.

So 150x(the number of tractors) + 1000(his pay each month)

The answer of given parabola question is 6.125ft.

a curve produced by the intersection of a cone's surface with a plane perpendicular to a straight line; a curve produced by a moving point whose distance from a fixed point is equal to its distance from a fixed line.

x² = 4py

x=radius which can be found by dividing d=14ft by half

x = d/2 = 11/2 = 7ft

y=2ft is the depth

p is the vertex of the parabola

p = x²/4y

p = 7²/4×2

p=6.125ft

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After conquering indigenous civilizations in Mexico and South America, Spanish Colonial Rule became wealthy thanks to the gold and silver it discovered.

The objectives of Spanish Colonial Rule were to take gold and silver from the Americas, to boost the Spanish economy, and to increase Spain's might. Additionally, Spain sought to evangelize Native Americans.

Further Spanish conquistadors, who were mostly poor nobility from Spain's destitute west and south, were able to conquer the vast empires of the New World with the aid of sickness (which reduced native resistance), superior military equipment, and tactical strategies such as surprise attacks and strong.

However, it was challenging to convince immigrants to colonize there due to friction with the local Indian population and the absence of significant silver or gold discoveries.

Thus these are the most leading factors that prevent to become more successful for Spanish Colonial Rule.

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The measure for θ is 25.747121°.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

Hypotenuse = 14.5 meters

Opposite side = 6.3 meters

Now, using Trigonometry

sin θ = Opposite side / Hypotenuse

by putting the given values we get

sin θ = 6.3 / 14.5

sin θ = 63/145

sin θ = 0.4344

θ =25.747121°

Hence, the angle is 25.747121°.

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The number that goes beneath the radical is 7

The Pythagoras theorem is used to find side or angle of a right angled triangle.

If you are dealing with any right triangle with  given sides, using the Pythagorean Theorem, as shown below, makes things relatively simple.

Note that the Pythagorean Theorem: is  a²+b²=c²

a  and b are both the smaller sides of the triangle, while c is the hypotenuse (the longest side of the triangle).

This impies in this case, that  we have 4 equivalent right triangles with given sides  and  for the hypotenuse, so let's see what we need to solve for by writing down what we know in a form following the Pythagorean Theorem.

The Pythagoras Equation is a²+b²=c²

Where  a=3, b =? c=4

Isolate the unknown value without plugging in our known values yet. This step is unnecessary, but can help if you have trouble with making mistakes with your algebra.

a²+b²=c²

⇒b²=c²-a²

a=√(c²-a²)

Plug in our given values and solve for .

a=√(4²-3²)

a=√(16-9)

a=√7

Conclusively, the radical number that goes beneath 7

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Complete question :

The complete question is found on the attachment

The value of u is given by the equation u = 37°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the sum of total internal angles of a triangle be = 180°

Now , the triangle be ΔABC

The measure of ∠A = u + 4°

The measure of ∠B = u

The measure of ∠C = ( 180° - ( u + 41° ) ) ( angles on a straight line = 180° )

From the triangle theorem ,

u + 4° + u + ( 180° - ( u + 41° ) ) = 180°   be equation (1)

On simplifying the equation , we get

2u + 184° - u - 41° = 180°

u + 143° = 180°

Subtracting 143° on both sides of the equation , we get

u = 37°

Therefore , the value of u is 37°

Hence , the value of u in the triangle is 37°

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Answer:

105.72 meters

Step-by-step explanation:

We can set up a system of equations to represent the information given in the problem, and then use algebra to solve for the length of the blue rope. Let x be the length of the red rope.

According to the problem statement:

blue rope = 3 * red rope = 3x

green rope = 4 * blue rope = 4 * 3x = 12x

we know that:

red rope + blue rope + green rope = 563.84

x + 3x + 12x = 563.84

then we can solve for x:

16x = 563.84

x = 35.24

So the length of the red rope is 35.24 meters.

The length of the blue rope is 3x = 3 * 35.24 = 105.72 meters.

Answer: The question is asking for the number of households that have between 3.67 and 4.35 people, which corresponds to the number of households whose number of people per household falls within one standard deviation of the mean.

A normal distribution is symmetric, so approximately 68% of the data falls within one standard deviation of the mean. So, we can estimate that approximately 68% of the 1,500 households have between 3.67 and 4.35 people.

The calculation is:

1,500 households x 68% = 1,020 households

So, approximately 1,020 households have between 3.67 and 4.35 people.

This is a rough estimate and the actual number may be slightly different, but it can be considered as a good approximation. From the given options, The answer closest to 1,020 is 945 households.

Step-by-step explanation:

The required exponential function is given as y = aˣ where the value of a should be positive always.

The function which is in format f(x) =aˣ where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

here,
Since from the above definition exponential function is given as y = aˣ,
This shows the exponential increase and decrease, by means of exponential increase and decrease, a sudden in increase and sudden decrease of function as the value of a varies, see in the graph after the answer. And the value of an always remains positive.

Thus, the required exponential function is given as y = aˣ where the value of a should be positive always.

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now, this is implicit differentiation, so it comes with the assumption that "y" is a function in "x terms", as opposed to a plain vanilla variable, whilst "x" is just that, so

[tex]\cfrac{d}{dx}[x^2+y^4=20]\implies 2x+\stackrel{chain~rule}{4y^3\cdot \cfrac{dy}{dx}}=0\hspace{5em}\cfrac{d}{dx}\left[ 2x+4y^3\cdot \cfrac{dy}{dx}=0 \right] \\\\\\ 2+\stackrel{product~rule}{\left( 12y^2\cdot \cfrac{dy}{dx}+4y^3\cdot \cfrac{d^2y}{dx^2} \right)}=0\implies 2+12y^2\cdot \cfrac{dy}{dx}+4y^3\cdot \cfrac{d^2y}{dx^2}=0 \\\\\\ 2+12y^2\cdot \cfrac{dy}{dx}=-4y^3\cdot \cfrac{d^2y}{dx^2}\implies {\Large \begin{array}{llll} \cfrac{2+12y^2\cdot \frac{dy}{dx}}{-4y^3}=\cfrac{d^2y}{dx^2} \end{array}}[/tex]

Answer

A(-10, 9), A'(-4, 9)

B(-4, 2), B'(-10, 2)

C(-7, 9), C'(-7, -4)

Example 3:

A(-3, 5), A'(3, 5)

B(-3, 0), B'(3, 0)

C(-3, 5), C'(-3, -10)

3 x 3 x 3 x 3 x 3 x 3 x 2 x 3 x 3 x 434 = 5,694,948

Step-by-step explanation:

a) x+20+x+90=180 [sum of 3 angel of triangle]

2x + 110 = 180

2x = 180- 110

2x = 70

x = 70÷2

x = 35

b) 2y + y + y = 180

4y = 180

y = 180÷4

y= 45

c) 4z-30 + 2z = 180

6z = 180 + 30

6z = 210

z = 35

Answer:

t = 0.5 seconds

Step-by-step explanation:

Given formula:

[tex]h=-16t^2+s[/tex]

where:

Dan drops the treat 5 feet above the ground.

Therefore, when t = 0, h = 5 ft.  

To find the value of s, substitute these values into the given formula:

[tex]\implies -16(0)^2+s=5[/tex]

[tex]\implies s=5[/tex]

Therefore:

[tex]h=-16t^2+5[/tex]

To calculate how long the treat falls before Lola catches it, substitute h = 1.5 into the formula:

[tex]\implies -16t^2+5=1.5[/tex]

[tex]\implies -16t^2=-3.5[/tex]

[tex]\implies t^2=0.21875[/tex]

[tex]\implies t=\sqrt{0.21875}[/tex]

[tex]\implies t=\pm0.467707173...[/tex]

[tex]\implies t=\pm0.5\; \; \sf (nearest\;tenth)[/tex]

As time is positive, t = 0.5 seconds (nearest tenth) only.

Therefore, it took 0.5 seconds for Lola to catch the treat after it fell.

Answer: Angles 2 and 4 = 38, Angle 1 = 142

Step-by-step explanation:

Given that angle 3 is equal to 142, the angle between 2 and 3 has to add up to 180. 142 + 38 = 180. The same applies for angle 4 and 3. So, angle 1 + angle 2 has to add up to 180. We already know angle 2, so now we just have to subtract that from 180 to find angle 1.

[tex] \sf \: 5(4x -1.5x) + 12 = 4x - 124 \\ \sf \: 5 \times 2.5x + 12 = 4x - 124 \\ \sf \: 12.5x + 12 = 4x - 124 \\ \sf \: 12.5x - 4x = - 124 - 12 \\ \sf \: 8.5x = - 136 \\ \sf \: x = - 16[/tex]

Answer:

ASA

Step-by-step explanation:

The hash marks are telling which sides are congruent and the angle mark is telling us that those angles are congruent.

Answer:

It is a known fact that there are rectangular prisms with the same volume but different dimensions.