A line contains the point (4, 5) and has a slope of -2.
Which point is also on the line?
(5,7)
(6,2)
(5,3)
(4.1)

Answer: TRS is congruent to CSE

Step-by-step explanation:

You can find congruent angles by locating the ones with the same number of lines. You want to start with the angles in the order of TRS.

Angle T has 1 line, so is congruent to C, which also has 1 line.

Angle R has 2 lines, so is congruent to S, which also has 2 lines.

Angle S has 3 lines, so is congruent to E, which also has 3 lines.

You want to keep these in the same order, so TRS, in the order of 1-2-3 lines, is congruent to CSE, also in the order of 1-2-3 lines (aka congruency markings).

(i) The exponential growth model to predict the number of rabbits after 'x' years is [tex]A = 2e^{6.21460809842x}[/tex].

(ii) The number of rabbits at the end of 3 years will be 250000000.

A continuous exponential growth function is of the form [tex]A = Pe^{rt}[/tex], where A is the final amount, which was initially P, growing continuously at the rate of r, after a time of t years.

In the question, we are asked to construct an exponential model to predict the number of rabbits after 'x' years.

We assume the exponential growth model to be a continuous model, of the form [tex]A = Pe^{rt}[/tex], where A is the final amount of rabbits, which was initially P, growing continuously at the rate of r, after a time of t years.

The initial quantity of rabbits, P = 2.

Time, t = x years.

Substituting the values, we get:

[tex]A = 2e^{rx}[/tex] ... (i)

We have been told that after 1 year, the number of rabbits was 1000.

Thus, substituting A = 1000, and x = 1, we get:

[tex]1000 = 2e^{r*1}\\\Rightarrow 1000 = 2e^r\\\Rightarrow e^r = 1000/2 = 500[/tex]

Taking log on both sides, we get:

[tex]log_ee^r = log_e500\\\Rightarrow rlog_ee = log_e500\\\Rightarrow r = 6.21460809842[/tex]

Thus, the rate of growth, r = 6.21460809842.

Substituting r = 6.21460809842 in (i), we get:

[tex]A = 2e^{6.21460809842x}[/tex], which is the required model.

To find the number of rabbits at the end of 3 years, we put x = 3, in the above equation to get:

[tex]A = 2e^{6.21460809842*3}\\\Rightarrow A = 2e^{18.6438242953}\\\Rightarrow A = 2*125000000\\\Rightarrow A =250000000[/tex]

Thus, there would be 250000000 rabbits at the end of 3 years.

Learn more about the exponential growth model at

https://brainly.com/question/13223520

#SPJ1

Answer:

Step-by-step explanation:

add both the equations then you will get

3x^3-x^2+2

but in the standard form there should be an x^1 term or x term since there is no term like that we write it as 0x

so the equation will be

3x^3-x^2+0x+2

Answer:

[tex]g(x)=-7x+6[/tex]

Step-by-step explanation:

Translations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

Parent function:

[tex]f(x)=-7x+7[/tex]

Translation of 2 units left:

[tex]\implies f(x+2)=-7(x+2)+7[/tex]

Translation of 13 units up:

[tex]\implies f(x+2)+13=-7(x+2)+7+13[/tex]

Simplifying:

[tex]\implies g(x)=-7(x+2)+7+13[/tex]

[tex]\implies g(x)=-7x-14+7+13[/tex]

[tex]\implies g(x)=-7x+6[/tex]

Learn more about graph transformations here:

https://brainly.com/question/28041916

https://brainly.com/question/27930491

The critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881

The scatter plot of the election is added as an attachment

From the scatter plot, we have the following highlights

Start by calculating the degrees of freedom (df) using

df =n - 2

Substitute the known values in the above equation

df = 8 - 2

Evaluate the difference

df = 6

Using the critical value table;

At a degree of freedom of 6 and significance level of 0.01, the critical value is

z = 0.834

From the list of given options, 0.834 is between  -0.881 and 0.881

Hence, the critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881

Read more about null hypothesis at

https://brainly.com/question/14016208

#SPJ1

Using proportions and the markup concept, it is found that the cost to store is of $12.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The markup price of 80% means that the selling price is of 180% = 1.8 of the cost to store of x. The selling price is of $21.60, hence:

1.8x = 21.60

x = 21.60/1.8

x = $12.

The cost to store is of $12.

More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1

simple interest= principal x time x rate/100

The dimensions (length and width) of the poster are 6 inches and 2 inches

Represent the length with x and the width with y

From the question, we have the following parameters

x = 5 + 0.5y

Area, A = 12

The area of a rectangle is represented as:

A = xy

Substitute the known values in the above equation

(5 + 0.5y) * y = 12

Expand the bracket

5y + 0.5y^2 = 12

Multiply through by 2

10y + y^2 = 24

Rewrite as:

y^2 + 10y - 24 = 0

Expand

y^2 + 12y - 2y - 24 = 0

Factorize the expression

(y - 2)(y + 12) = 0

Solve for y

y = 2 or y = -12

The dimension cannot be negative.

So, we have

y = 2

Substitute y = 2 in x = 5 + 0.5y

x = 5 + 0.5 * 2

Evaluate

x = 6

Hence, the dimensions (length and width) of the poster are 6 inches and 2 inches

Read more about area at:

https://brainly.com/question/24487155

#SPJ1

Part I: The correct formula is D. ((x₁ + x₂)/2, (y₁ + y₂)/2)

Part II: The midpoint of the segment with endpoints (-2, -1) and (0, 9) is (-1, 4)

From the question, we are to determine the formula for calculating the midpoint of a segment

The midpoint of a segment can be determined by using the formula,

Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)

The correct formula is D. ((x₁ + x₂)/2, (y₁ + y₂)/2)

II. To determine the midpoint of the segment with endpoints (-2, -1) and (0, 9)

x₁ = -2

y₁ = -1

x₂ = 0

y₂ = 9

Putting the parameters into the formula,

Midpoint of the segment = ((-2 + 0)/2, (-1 + 9)/2)

Midpoint of the segment = (-2/2, 8/2)

Midpoint of the segment = (-1, 4)

Hence, the midpoint of the segment with endpoints (-2, -1) and (0, 9) is (-1, 4)

Learn more on Midpoint of a segment here: https://brainly.com/question/896396

#SPJ1

Answer:

thanks for your support of the personal information on the direction of economics class

Answer:

take 14/0.4the multiply by ten both the denominator and .numerator then simplify by two your final answer will be 35

Answer:

X-intercepts:

[tex] (\frac{3}{7} ,0)[/tex]

Y-intercepts:(0,3)

Step-by-step explanation:

Hello!

given expression

[tex]y = - 7x + 3[/tex]

x-intercept is the point on the graph where y=0

solve

[tex] - 7x + 3 = 0 \\ - 7x = - 3 \\ x = \frac{3}{7} [/tex]

Thus, x-intercept

[tex]( \frac{3}{7} ,0)[/tex]

y-intercept is the point on the graph where x=0

solve

[tex]y = - 7(0) + 3 \\ y = 0 + 3 \\ y = 3[/tex]

Thus, y-intercept (0,3)

Hope it helps!

The perfect square trinomial is x² - 2x + 1.

Hence, the value needed to complete the square of the expression ( x² - 2x + --- ) is 1.

The quadratic expression in its standard form is;

ax² + bx + c

Given the expression in the question;

x² - 2x + ------

Compared with the standard for a quadratic expression

Let the missing value be represented by "c"

x² - 2x + c

Now, to find the value of c, we divide the coefficient of x by 2 and then square the result.

Note that, coefficient of x is b

c = ( b/2 )²

We substitute

c = ( -2/2 )²

c = ( -1 )²

c = 1

The perfect square trinomial is x² - 2x + 1.

Hence, the value needed to complete the square of the expression ( x² - 2x + --- ) is 1.

Learn more about quadratic expressions here: https://brainly.com/question/12356597

#SPJ1

Hi

if he has 24 point he scored 24/ 6 = 4 times

As he score points every 11 ennemies,

He had : 4*11= 44 ennemies.

The expression can be used to find the area, in square units, of the Shaded triangle in the Square is  1/2 ( 4 · 4 ) .

The area of a square can be calculated as the square of the sides of a given figure.

The area of a square = side x side

where s = side length.

If a diagonal is drawn to create 2 halves, then area of each half is 8.

So, The area of a square = 1/2 ( 4 · 4 ) = 16.

If a square has a side length of 4, then the area of the square is 16.

The expression can be used to find the area, in square units, of the Shaded triangle in the Square is  1/2 ( 4 · 4 ) .

Learn more about the area;

https://brainly.com/question/1658516

#SPJ1

Answer:

[tex]3x^2[/tex]

Step-by-step explanation:

First main thing to know is the product and quotient rule of exponents.

Product Rule:

  [tex]x^a*x^b = x^{a+b}[/tex]

  And if this doesn't make sense, you can think of the exponent like this:

  [tex]x^a*x^b = (x*x*x*x...\text{ a amount of times}) * (x * x * x \text{ b amount of times})[/tex]

  and since multiplication is commutative, we can just combine all these x's, and since the total amount on the left is "a", and the right is "b", the total combined x's should be a+b, which can be expressed as:
   [tex]x*x*x... \text{ a+b amount of times}[/tex]

   which can be expressed as an exponent (x^(a+b))

Quotient Rule:

   [tex]\frac{x^a}{x^b} = x^{a-b}[/tex]

  You can use similar reasoning for this, since if you write it out you get

   [tex]\frac{x*x*x...\text{ a amount of times}}{x*x*x\text{ b amount of times}}[/tex]

  and since you have an x in the numerator and the denominator, you can simply cancel the x's out. In doing this you want to remove the denominator, so you cancel out "b" x's. So there will be (a-b) x's left in the numerator, and a 1 in the denominator, so it's just x^(a-b)

Ok so now let's apply these to solve your question

[tex]\frac{(15x^{-4})*x^{15}}{(5x^4)*x^5}\\[/tex]

So let's combine the exponents in the numerator and denominator using the product rule

[tex]\frac{15x^{11}}{5x^9}\\[/tex]

Now we can divide the 15 by 5, and divide the x^11 by the x^9 using the quotient rule

[tex]3x^2[/tex]

Explanation:

We're applying the dot product.

u dot v = 3*(-4) + (-8)*8

u dot v = -12 - 64

u dot v = -76

The idea is that we multiply the x coordinates together, and the y coordinates together separately. Afterward you add the products. The result of any dot product is a scalar value, aka a single number.

The dot product is useful in many applications. One of which is to determine if two vectors are orthogonal.

The value of the expression when g = -2 is -1

Given the expression;

(5+2g)exp5

(5+2g)^5

For g = -2

Let's substitute the value of g in the expression

= ( 5 + 2 ( -2) ) ^5

Expand the bracket

= ( 5 - 4) ^ 5

Find the difference

= (-1) ^5

= -1

Thus, the value of the expression when g = -2 is -1

Learn more about algebraic expressions here:

https://brainly.com/question/4344214

#SPJ1

8.9 pounds of coffee A, 27.3 pounds of coffee B and 17.8 pounds of coffee C are need to make a blend that sells for $12.61 per pound.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent coffee A, y represent coffee B and z represent coffee C, hence:

x + y + z = 54   (1)

Also:

2x = z        (2)

And:

15.21x + 13.21y + 10.39z = 12.61(54)   (3)

x = 8.9, y = 27.3 and z = 17.8

8.9 pounds of coffee A, 27.3 pounds of coffee B and 17.8 pounds of coffee C are need to make a blend that sells for $12.61 per pound.]

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The table in the list of tables that represent an actual function is the first table i.e.

x y

-3 10

4 4

-5 -3

4 4

The table of values is given as:

Table 1

x y

-3 10

4 4

-5 -3

4 4

Table 2

x y

2 8

6 9

6 3

5 7

Table 3

x y

1 2

1 4

1 6

1 8

Table 4

x y

5 2

-3 2

2 2

1 7

For a table to represent a function, each of the x value on the table must correspond to exactly one y value

i.e.

x1 = y1

x2 = y2

And so on

Using the above highlights, the table that represents a function is table 1

Hence, the table in the list of tables that represent an actual function is the first table i.e.

x y

-3 10

4 4

-5 -3

4 4

Read more about tables and functions at:

https://brainly.com/question/15602982

#SPJ1

Answer:

0.85

Step-by-step explanation:

1 - 15% = 1 - 0.15 = 0.85

[tex] y = (0.85)^\frac{t}{12} [/tex]

Answer: 0.85

Using the z-distribution, the margin of error for the 95% confidence interval used to estimate the population proportion is 0.0683 = 6.83%.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

For this problem, the parameters are given as follows:

[tex]n = 198, \pi = \frac{80}{198} = 0.404[/tex]

Hence the margin of error is:

[tex]M = 1.96\sqrt{\frac{0.404(0.596)}{198}} = 0.0683[/tex]

The margin of error for the 95% confidence interval used to estimate the population proportion is 0.0683 = 6.83%.

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1

Answer:

30calories

Step-by-step explanation:

Answer:

30 calories per ounce

Step-by-step explanation:

The answer given by rachelwang2022 is correct.

I am just adding to the explanation

Since there are 150 calories in a 5-ounce container, you can determine the number of calories per ounce by simply dividing 150 by 5.

150/5 = 30 calories per ounce

The Gauss-Jordan elimination method different from the Gaussian elimination method in that unlike the Gauss-Jordan approach, which reduces the matrix to a diagonal matrix, the Gauss elimination method reduces the matrix to an upper-triangular matrix.

Gauss-Jordan Elimination is a technique that may be used to discover the inverse of any invertible matrix as well as to resolve systems of linear equations.

It is based on the following three basic row operations that one may apply to a matrix: Two of the rows should be switched around. Multiply a nonzero scalar by one of the rows.

Learn more about Gauss-Jordan elimination method:

https://brainly.com/question/12090959

#SPJ1

The perimeter becomes double when each side is twice as long as the original.

According to the statement

we have given that the perimeter of a rectangle is 24 inches. and we have to find that the what effect does this enlargement have on the perimeter.

So, For this purpose, we know that the

A rectangle is a parallelogram all of whose angles are right angles especially : one with adjacent sides of unequal length.

The formula to find the perimeter of rectangle is 2(L + B)

And we the length is goes to increased by double then the perimeter will also goes to double.

Because perimeter is directly proportional to the length and breadth of rectangle.

So, The perimeter becomes double when each side is twice as long as the original.

Learn more about rectangle here

https://brainly.com/question/19819849

#SPJ1

See attachment for the graph of the hyperbola 12x^2 - 3y^2 - 108 = 0

The equation of the hyperbola is given as:

12x^2 - 3y^2 - 108 = 0

Start by calculating the transverse axis

So, we have:

Transverse axis

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

Where

a = 3 and b = 6

The transverse axis is calculated as:

y = ±b/a(x - h) + k

So, we have:

y = ±6/3(x - 0) + 0

Evaluate the difference and sum

y = ±6/3x

Evaluate the quotient

y = ±2x

This means that the transverse axes are y = 2x and y =-2x

The vertices

In the above section, we have:

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

The co-vertices

In the above section, we have:

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

And

a = 3 and b = 6

The co-vertices are

(h - a, k) and (h + a, k)

So, we have:

(0 - 3, 0) and (0 + 3, 0)

Evaluate

(-3,0) and (3, 0)

See attachment for the graph of the hyperbola

Read more about hyperbola at:

https://brainly.com/question/26250569

#SPJ1

The simplified value  of expression -36/(27/3*2) is -8.

Given an expression -36/(27/3*2).

We are required to find the simplified value of given expression. To simplify the expression we need to use addition,subtraction,multiplication, division, brackets, etc. We can say that we have to use BODMAS in order to find the simplified value of expression.

Expression is combination of numbers, symbols, coefficients, determinants, indeterminants, fraction,algebraic operations,etc.  usually not found in equal to form.

The given expression :

=-36/(27/3*2)     (Multiplying 3 and 2 first)

=-36/(27/6)

=(-36*2)/9   (Invert the fraction given in denominator)

=-72/9          (Multiplying -36 to 2)

=-8

Hence the simplified value of expression -36/(27/3*2) is -8.

Learn more about expression at https://brainly.com/question/723406

#SPJ1

Answer:

d = [tex]\sqrt{65}[/tex]

Step-by-step explanation:

The distance between two points is found by

d = [tex]\sqrt{( x2-x1)^2 + ( y2-y1)^2}[/tex] where (x1,y1) and (x2,y2) are the two points

d = [tex]\sqrt{(-2 - -1)^2+(-6 - -14)^2 }[/tex]

d =[tex]\sqrt{( -2+1)^2 + (-6+14)^2}\\[/tex]

d = [tex]\sqrt{(-1)^2 +( 8)^2 }[/tex]

d = [tex]\sqrt{1+64}[/tex]

d = [tex]\sqrt{65}[/tex]