find the slope of the points
a. (-4,-7) and (-2,16)
b. (3,-6) and (3,9)​

The half-life of this substance is approximately 17.32 days.

The continuous exponential decay model is given by the equation:

\(A(t) = A0e^{-kt}\)

where A0 is the initial mass,

t is the time elapsed in days, and

k is the decay rate parameter.

We want to find the half-life, which is the time it takes for A(t) to decrease to half of A0. In other words, we want to solve the equation:

A(t) = A0/2

\(A0e^{-kt} = A0/2\)

\(e^{-kt} = 1/2\)

Taking the natural logarithm of both sides:

-ln(2) = -kt

t = ln(2)/k

The decay rate parameter k is given as 4% per day, or 0.04 per day. Substituting this value into the formula for t, we get:

t = ln(2)/0.04 ≈ 17.32 days

Therefore, the half-life of this substance is approximately 17.32 days.

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Answer:

$50

Step-by-step explanation:

Answer:

21/2 or 10.5

Step-by-step explanation:

7 = 7/1

When dividing fractions we use KFC :

K - Keep the first fraction :

7/1

F - Flip the second fraction :

2/3 ⇒ 3/2

C - Change the sign :

÷ ⇒ ×

Now we have :

7/1 × 3/2 =

Now we multiply the first numerator with the second numerator and the first denominator with the second denominator :

7×3 = 21

1×2 = 2

So our final answer is 21/2 or 10.5

Hope this helped and have a good day

The vertical displacement is of 2 units down, the correct option is B.

Remember that for a function f(x), a vertical displacement of N units is written in general form as:

g(x) = f(x) + N

If N > 0, the translation is upwards.

if N < 0, the translation is downwards.

Here we assume that we start with the parent cosine function:

y = cos(x)

And the transformed function is:

y = -2 - cos(x - π)

So we have some transformations, but the vertical translation is of 2 units down. So the correct option is B.

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For figure {0}, the number of tiles will be equal to 2.

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a graph as shown in the image.

The line passes through point -

(3, 8) and (4, 10)

So, the slope of the line will be -

m = (10 - 8)/(4 - 3)

m = 2

y = 2x + c

For the point (3, 8), we can write -

8 = 6 + c

c = 2

For figure {0}, the number of tiles will be equal to 2.

Therefore, for figure {0}, the number of tiles will be equal to 2.

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The equation of the parabola that opens to the right, has a focus (-1, -3), and a focal diameter of 8 is y = (1/16)x²+ (10/16)x - (23/16)

To determine the equation of a parabola that opens to the right, has a focus at (-1, -3), and a focal diameter of 8

we can use the standard form of the equation for a parabola with a horizontal axis:

(x - h)² = 4p(y - k)

Where (h, k) is the vertex of the parabola and p is the distance from the vertex to the focus.

Since the parabola opens to the right, the vertex will be to the left of the focus.

Therefore, the vertex will be at (-1 - p, -3).

The focal diameter is given as 8, which means the distance between the vertex and the focus is p = 8/2 = 4.

Plugging these values into the equation, we have:

(x - (-1 - 4))² = 4 × 4 × (y - (-3))

Simplifying:

(x + 5)² = 16(y + 3)

x² + 10x + 25 = 16y + 48

Rearranging to isolate y:

16y = x² + 10x + 25 - 48

16y = x² + 10x - 23

Dividing by 16:

y = (1/16)x² + (10/16)x - (23/16)

Therefore, the equation of the parabola that opens to the right, has a focus (-1, -3), and a focal diameter of 8 is y = (1/16)x²+ (10/16)x - (23/16)

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Answer:

4 oranges, 5 apples, 6 pears in each bag

Step-by-step explanation:

theyre all divisible by 4

Answer:

x^2

Step-by-step explanation:

1^2=1

2^2=4

3^2=9

Answer:

p = 6 , q = 43

Step-by-step explanation:

x² + 12x - 7

using the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² + 12x

=x² + 2(6)x + 36 - 36 - 7

= (x + 6)² - 43 ← in the form (x + p)² - q

with p = 6 and q = 43

Answer:

total profit = $2,023,338,517  (nearest whole number)

Step-by-step explanation:

Use geometric sum formula:

\(S_n=\dfrac{a(1-r^n)}{1-r}\)

where \(a\) is the initial value and \(r\) is the common ratio

We have been told that the initial value is 171000, so \(a=171000\).

If the company's profit increases by 33% per year, this means each year's profit is 133% of the previous year's profit. 133% = 133/100 = 1.33

Therefore, \(r = 1.33\)

We need to calculate the total profit earned over 29 years, so \(n = 29\)

Inputting these values into the formula:

\(\implies S_{29}=\dfrac{171000(1-1.33^{29})}{1-1.33}=\$2,023,338,517 \ \textsf{(nearest whole number)}\)

The correct option is B. The students knew whether or not music was playing while they were taking the exam

Given,

The class was split into two groups.

The first group took the midterm exam while background music was playing, and the second group took the exam without any background music.

In a blind experiment, any information that might affect the subjects is kept secret until the experiment is over. The pupils in this instance are aware of their group membership.

In order to answer this question, an experiment is carried out to see how music affects learning. One group of students studies while background music is playing, while the other group does not.

However, because of the background music playing here, the pupils are aware of which group they belong to. The experiment's outcomes are impacted by this.

Therefore the correct option is B. The students knew whether or not music was playing while they were taking the exam.

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Each of the questions should be correctly classified as statistical or not statistical as follows:

In Mathematics, a statistical question can be defined as a type of question in which the resulting answer is in the form of an average, percentage, or a range such as "How many TV shows did each student in my class watch yesterday?"

A non-statistical question simply refers to a question that is not non-statistical and it can be defined as a type of question which has an exact or fixed answer such as "How many students in my class can swim?"

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Answer:

growth rate: 4

y-value: 19

equation: y=4x+19

Step-by-step explanation:

Growth Rate:
The growth rate of a linear function is constant. This means that the function will increase or decrease by the same amount for every unit increase in x.
This can be found by dividing the change in y-values by the change in x-values.

For the question:
The change in y-values is 11-7=4,

and the change in x-values is +1.

Therefore, the growth rate is 4.

\(\hrulefill\)

Initial Value: The initial value of a linear function is the value of the function when x is 0.

In this case, the initial value is 19.

This can be found by looking at the y-value of the point where x is 0.

In this case, the y-value is 19.

\(\hrulefill\)Equation: The equation of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Using the table you provided, we can find the slope by using two points on the line.

Let’s use (-3, 7) and (1, 23).

The slope is (y2-y1)/(x2-x1)=(23-7)(1-(-3)=16/4=4

Now,

Taking 1 point (-3,7) and slope 4.

we can find the equation by using formula:

y-y1=m(x-x1)

y-7=4(x+3)

y=4x+12+7

y=4x+19

Therefore, the equation of the given table is y=4x+19\(\hrulefill\)

Answer:

Growth rate:  4

Initial value:  19

Equation:  y = 4x + 19

Step-by-step explanation:

The slope of a linear function represents its growth rate.

Therefore, the growth rate of a linear function can be found using the slope formula.

Substitute two (x, y) points from the table into the slope formula, and solve for m.  Substituting points (0, 19) and (1, 23):

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{23-19}{1-0}=\dfrac{4}{1}=4\)

Therefore, the growth rate of the linear function is 4.

The initial value of a linear function refers to the y-intercept, which is the value of the y when x = 0.

From inspection of the given table, y = 19 when x = 0.

Therefore, the initial value of the linear function is 19.

To write a linear equation given the growth rate (slope) and initial value (y-intercept), we can use the slope-intercept formula, which is y = mx + b. The slope is represented by the variable m, and the y-intercept is represented by the variable b.

As the growth rate of the given linear function is 4, and the initial value is 19, substitute m = 4 and b = 19 into the slope-intercept formula to create the equation of the linear function represented by the given table:

\(\boxed{y=4x+19}\)

Answer:

Se pueden hacer 5040 permutaciones con la palabra COLUMNA.

Explanation:

La palabara COLUMNA posee 7 letras, por lo que debemos hacer permutación sin repetición.

La formula es:

P_^{n}: n!

Donde n son todos los elementos.

The approximate difference in the circumference of the orange and grapefruit would be = 15.07cm.

The circumference of a circular object is defined as the area around the circular object or its perimeter.

The formula for the circumference of a circle = 2πr

For the orange;

The radius (R) = 2.4 cm

π = 3.14 (constant)

circumference of orange = 2× 3.14 × 2.4

= 15.07cm

For the grapefruit;

the radius (R) = 4.8 cm

π = 3.14 (constant)

circumference of the grapefruit= 2× 3.14 × 4.8

= 30.14 cm

Therefore the difference in the circumference of both object = 30.14 - 15.07 = 15.07cm

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The total number of points scored is given by the equation A = 23 points

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total points scored be represented as A

Now , the equation will be

Substituting the values in the equation , we get

A = 3x + 2y + z   be equation (1)

where x = red team = 3 points

y = yellow team = 5 points

z = blue team = 2 points

So , A = 3 ( 3 ) + 2 ( 5 ) + 2

A = 9 + 10 + 2

A = 21 points

Hence , the equation is A = 21 points

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Answer:

The length of the rectangle would be 4.

Step-by-step explanation:

We can start by naming the width x.

Therefore, the length would 3x-2.

The perimeter of the rectangle would then be:

2(3x-2+x)

We can set up the given equation

2(3x-2+x)=12

Solve for x.

Divide both sides by 2.

3x-2+x=6

Combine like terms.

4x-2=6

Add 2 to both sides.

4x=8

Divide both sides by 4.

x=2

The width would then be 2.

We can plug that into the expression for length.

3x-2

3(2)-2

6-2

4

The length of the rectangle would be 4.

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

Answer:

6.67lbs

Step-by-step explanation:

let's write cookies as C.

we know dozen means 12 so we multiply 5 by 12 to know how many cookies that the bakery uses 2lbs of butter for.

That would be; 2lbs= 5×12 C

2lbs=60C.

now we can find how much butter is used for a single cookie(C) by dividing both sides by 60;

\(\frac{2}{60}\)lbs=C;

C= \(\frac{1}{30}\)lbs

since we know what C is, we can use that in finding how much butter will be needed for 200 cookies(C)

200C=200(\(\frac{1}{30}\)lbs)

200C= \(\frac{200}{30}\)lbs

200C= 6\(\frac{2}{3}\)lbs or 6.67lbs

If bakery uses 2 lbs of butter to make 5 dozen cookies. then 20/3  pounds of butter would be used to make 200 cookies

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

A bakery uses 2 lbs of butter to make 5 dozen cookies.

1lb=1 pound

We know that 1 dozen = 12

5 dozen =5 × 12 =60 cookies

We need to find pounds of butter would be used to make 200 cookies.

Let x be the number of pounds butter would be used to make 200 cookies

60/2=200/x

Apply cross multiplication

60x=400

Divide both side by 60

x=400/60=20/3

Hence 20/3 pounds of butter would be used to make 200 cookies

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Answer:

to what?

Step-by-step explanation:

Answer:

x+y=z

Step-by-step explanation:

Answer:

x+41=-11 I guess

Step-by-step explanation:

L and J share no common elements, so their intersection is the empty set (c).

The intersection of sets L and J is represented as L∩J = ∅. (Option D)

In mathematics, when dealing with sets, it's essential to understand how different sets interact with each other. In this case, we have two sets, L and J, each containing specific elements. We need to find the intersection of these two sets, which refers to the elements that are common to both sets.

The intersection of two sets, denoted as L∩J, refers to the collection of elements that appear in both sets L and J. In other words, it includes all the elements that are common to both sets.

Now, let's examine the elements of sets L and J:

L = {d, e, g}

J = {b, c, h}

To find the intersection, we look for the elements that appear in both L and J. As we observe, there are no common elements between the two sets. Set L contains elements {d, e, g}, and set J contains elements {b, c, h}, but there are no elements that are shared between these two sets. Therefore, the intersection of L and J, denoted as L∩J, is an empty set (symbolized by ∅).

L∩J = ∅

The above equation means that there are no elements that are common to both sets L and J. In other words, the intersection of L and J is an empty set, indicating that there are no shared elements between the two sets.

To summarize, when we compare sets L and J, we find that their intersection is an empty set, which means there are no elements that are present in both sets. Therefore, option C (L∩J = ∅) is the correct choice. Option A (L∩J = {b, c, d, e, g, h}), option B (L∪J = {b, c, d, e, g, h}), and option D (L∪J = ∅) are not correct in this case, as they represent the union of sets or an empty set, which do not accurately reflect the intersection of L and J.

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The money loaned at 9% annual interest was 1500 and the money loaned at 11% annual interest was 19000.

Let the amount of money loaned at 9% be x

the amount of money loaned at 11% be y

According to the question,

Total money loaned = 20,500

Thus the equation formed is,

x + y = 20,500 ------ (i)

Simple interest is calculated by

I = P * r * t

where I is the simple interest

r is the rate of interest

t is the time

Thus, the interest on x = 0.09x

the interest on y = 0.11y

Total interest gained = 2,225

Thus the equation formed is,

0.09x + 0.11y = 2225 -------(ii)

Multiply (i) by 0.09

0.09x + 0.09y = 1845

Subtract the above from (ii)

0.02y = 380

y = 19000

x = 1500

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Answer:

i think the answer is 60

Step-by-step explanation:i did the math