Need help. Thanks for helping me.

Answer:

The amount of salads sold that day were 93.

Step-by-step explanation:

Information to note:

Salad = $6.50

Drinks = $2.00

Total amount sold = 209

Total amount of money gained = $836.50

Set the system of equation. Let salad = s, and drinks = d

s + d = 209

6.50s + 2d = 836.50

Isolate the variable s in the first equation. Note the equal sign, what you do to one side, you do to the other. Subtract d from both sides:

s + d = 209

s + d (-d) = 209 (-d)

s = 209 - d

Plug in the new expression for s into the second equation:

s = 209 - d

6.50s + 2d = 836.50

6.50(209 - d) + 2d = 836.50

Simplify. Isolate the variable, d. First, distribute 6.50 to all terms within the parenthesis:

6.50(209 - d) = 1358.5 - 6.50d

1358.5 - 6.50d + 2d = 836.50

Simplify. Combine like terms:

1358.5 + (-6.50d + 2d) = 836.50

1358.5 - 4.50d = 836.50

Isolate the variable, d. Note the equal sign, what you do to one side, you do to the other.

Subtract 1358.5 from both sides:

1358.5 (-1358.5) - 4.50d = 836.50 (-1358.5)

-4.50d = 836.50 - 1358.50

-4.50d = -522

Isolate the variable, d. Divide -4.50 from both sides:

(-4.50d)/-4.50 = (-522)/-4.50

d = -522/-4.50

d = 116

The amount of drinks sold were 116.

Plug in 116 for d in one of the equations:

s + d = 209

s + (116) = 209

Isolate the variable, s. Subtract 116 from both sides:

s + 116 (-116) = 209 (-116)

s = 209 - 116

s = 93

The amount of salads sold that day were 93.

~

Answer:

Step-by-step explanation:

The total of the three exams must be at least 93*3 = 279

The total so far is

98 + 87 + x > 279

185 + x > 279                   Subtract 185 from both sides.

185-185+x > 279-185

x > 94

So I think you should pick 95

If you need a whole number result, you should pick 97

Answer:

1)A'(8,-10), B'(10,-8), C'(2,-4)

2)A''(8,-4), B''(10,-6), C''(2,-10)

Step-by-step explanation:

Given:

Points A(8,8) B(10,6) C(2,2)

reflection over y=-1

Perpendicular distance between points y-coordinates of points (A, B and C) and y=-1 are 9,7 and 3

after reflections, the perpendicular distance will be 18,14,6 and the points will be at

A'(8,-10), B'(10,-8), C'(2,-4)

Now

Points A(8,-10), B(10,-8), C(2,-4)

reflection over y=−7

Perpendicular distance between points y-coordinates of points (A, B and C) and y=-7 are 3,1 and 3

after reflections, the perpendicular distance will be 6,2,6 and the points will be at

A''(8,-4), B''(10,-6), C''(2,-10) !

Answer:

right, isosceles

Step-by-step explanation:

The lines on the two sides means that they are congruent.

Two sides being equal means that the triangle is isosceles.

The box in the corner means that the angle is equal to 90 degrees

A ninety degree angles means the triangle is a right triangle

Answer: Tammy's sample may not be vaild because she surveyed the students only from her class and it is likely that other classes might not like the subject maths. She might get the accurate results by surveying a larger number of people in the school instead of just her class.

Answer: Y = -7X-2

Step-by-step explanation:

if there are two co-ordinates (x1,y1) and (x2,y2).

If the line is passing through these co-ordinates

Then Slopw of the line  = (y2-y1)/(x2-x1)

We have one co-ordinate (-1,5) let it be (X1,Y1)

Let second co-ordinate be (X,Y)

Slope = -7 = (Y-5) / (X-(-1))

-7  = (Y-5)/(X+1)

Y-5 = -7 (x+1)

Y-5 = -7x-7

ADDING 5 ON BOTH SIDES OF THE EQUATION

Y-5+5 = -7X-7+5

Y = -7x-2

[tex]\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})~\hspace{10em} slope = m\implies -7 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-5=-7[x-(-1)]\implies y-5=-7(x+1) \\\\\\ y-5=-7x-7\implies y=-7x-2[/tex]

Answer:

The correct option is C

Step-by-step explanation:

The expressions are:

=(3x²+5x-8)+(5x²-13x-5)

Open the parenthesis

=3x²+5x-8+5x²-13x-5

Now solve the like terms:

=8x²-8x-13

Thus the correct option is C....

Answer:

x=17

Step-by-step explanation:

3(2x+4)=7(x-1)+2

Simplify

6x+12=7x-7+2

6x+12=7x-5

   -12       -12

6x=7x-17

Must isolate x on 1 side

-7x      -7x

-x=-17

/-1   /-1

x=17

Hope this helps

Answer:

The t-shirt shop sold 21 long sleeve shirts and 17 short sleeve shirts.

Step-by-step explanation:

To solve this problem, we should create a system of equations.  Let's let short sleeve t-shirts be represented by the variable s and long sleeve t-shirts be represented by the variable l.  

We know that the shop sold 38 total shirts, or in other words, the amount of long sleeve and short sleeve shirts combined is 38.  If we write this as an equation, we get: s + l = 38.

We can make another equation with the prices of the shirts.  If we take each type of shirt and multiply each price by the number sold and add them together, we should get the shop's total profits.  Represented as an equation, this is: 10s + 15l = 485.

Now that we have two equations, we should try to solve the system.  In this case, it is easiest to use substitution, so we are going to rewrite the first equation in terms of one variable.

s + l = 38

s = 38 - l

If we substitute this equivalent value for the variable s into the second equation, we get:

10s + 15l = 485

10(38 - l) + 15l = 485

Now we have an equation that only has one variable, so we can simplify both sides and then isolate the variable.

380 - 10l + 15l = 485

380 + 5l = 485

5l = 105

l = 21

Now, we can substitute this value for l back into the first equation to solve for the variable s.

s + l = 38

s + 21 = 38

s = 17

Therefore, the t-shirt shop sold 21 long sleeve shirts and 17 short sleeve shirts.

Hope this helps!

Answer:

(x-5)(x-5)

Step-by-step explanation:

Ok... This ones actually pretty simple.

So all you have to do is find 2 numbers that add up to -10, and multiply to 25. You will quickly realize that the only 2 numbers that do that are -5 and -5. Then, all you have to do is write the now factored equation. (x-5)(x-5)

There are 2 ways to check your work. The first is to FOIL (first, inside, outside, last). This should get you back to your original equation

The second way to do it is to plug it into a graphing program. If you graph your factored equation and your original equation, they should be the same!

I hope this helps!

If you have any other questions just feel free to ask me.

For this case we must factor the following expression:

[tex]x ^ 2-10x + 25[/tex]

For this, we must find two numbers that when multiplied give 25 and when added to -10.

These numbers are -5 and -5:

[tex]-5-5 = -10\\-5 * -5 = 25[/tex]

Then, the factorization is given by:

[tex](x-5) (x-5)\\(x-5) ^ 2 [/tex]

Answer:

[tex](x-5) ^ 2 [/tex]

Answer:

16. 5/3

Step-by-step explanation:

let the no of tranquilizer be x

therefore

5/4 + x =18

x= 18-5/4

= 16 5/3

For this case, the first thing to do is define a variable.

We have then:

Then we write the equation that models the problem:

[tex]\frac {2} {3} x = 18[/tex]

From here, we clear the value of x.

We have then:

[tex]x = \frac {3} {2} (18)\\x = 3 * 9\\x = 27[/tex]

Answer:

 the total number of children in the class is:

[tex]x = 27[/tex]

To calculate the total number of children in the fourth-grade class, divide the number of girls by 2 to find one-third of the class, then multiply by 3. The total class size is 27 children.

To find the total number of children in the fourth-grade class, we start by understanding that two-thirds of the children are girls. If there are 18 girls, which is two-thirds of the class, we need to calculate the full class size which constitutes three-thirds (or the whole).

Step 1: Represent two-thirds of the class as 2/3.
Step 2: Equate two-thirds of the class to the number of girls: 2/3 of the class = 18 girls.
Step 3: Find one-third of the class by dividing the number of girls by 2: 18 girls \/ 2 = 9 children.
Step 4: Calculate the full class size (which is three-thirds) by multiplying one-third of the class by 3: 9 children x 3 = 27 children.

Therefore, the total number of children in the fourth-grade class is 27.

Answer:

[tex]\large\boxed{\dfrac{1}{(m-4)(m-3)}=\dfrac{1}{m^2-7m+12}}[/tex]

Step-by-step explanation:

[tex]\dfrac{\frac{m+3}{m^2-16}}{\frac{m^2-9}{m+4}}=\dfrac{m+3}{m^2-16}\cdot\dfrac{m+4}{m^2-9}=(*)\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\m^2-16=m^2=4^2=(m-4)(m+4)\\m^2-9=m^2-3^2=(m-3)(m+3)\\\\(*)=\dfrac{m+3}{(m-4)(m+4)}\cdot\dfrac{m+4}{(m-3)(m+3)}\\\\\text{cancel}\ (m+3)\ \text{and}\ (m+4)\\\\=\dfrac{1}{m-4}\cdot\dfrac{1}{m-3}=\dfrac{1}{(m-4)(m-3)}\\\\\text{use\ FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=\dfrac{1}{(m)(m)+(m)(-3)+(-4)(m)+(-4)(-3)}\\\\=\dfrac{1}{m^2-3m-4m+12}=\dfrac{1}{m^2-7m+12}[/tex]

No. Since we cannot factor,

[tex]c^5-49[/tex].

Hope this helps.

r3t40

The correct answer is: b. no [tex]c^5 - 49[/tex] is not a difference of squares

Difference of squares refers to an expression of the form [tex]a^2 - b^2[/tex], which can be factored into [tex](a - b)(a + b)[/tex].

In this case, [tex]c^5 - 49[/tex] cannot be expressed in the form of [tex]a^2 - b^2[/tex] because [tex]c^5[/tex] is not a perfect square (a number raised to the power of 2) since it is c raised to the power of 5. To be a difference of squares, both terms must be perfect squares.

49 on the other is a perfect square of 7 but because of [tex]c^5[/tex] the expression [tex]c^5 - 49[/tex] cannot be converted to the form of [tex]a^2 - b^2[/tex] and is thus not considered a difference of squares.

Thus, The correct answer is: b. no  [tex]c^5 - 49[/tex] is not a difference of squares

Answer:

[tex]4\ hours[/tex]

Step-by-step explanation:

we know that

1 hour=60 minutes

we know that

To find out how many hours and minutes it will take Michelle to listen to the 5 CDs, add the times for each CD.

so

[tex]2(51)+3(46)=240\ minutes[/tex]

Convert to hours

[tex]240=240/60=4\ hours[/tex]

Answer:

B

Step-by-step explanation:

if we add (or subtract) the same amount from both sides, it does not affect the inequality and we can solve it

Answer:

b on edge 2020

Step-by-step explanation:

For this case we have:

a)

[tex]\frac {1} {10}[/tex]to convert as a percentage we have:

[tex]\frac {1} {10}[/tex] * 100% = 10%

b)

[tex]\frac {1} {4}[/tex], if we multiply the numerator and denominator by 25 we have:

[tex]\frac {25} {100}[/tex]

c)

Now we must write a fraction that represents 50%.

We have[tex]\frac {1} {2}[/tex]. If we multiply the numerator and denominator by 50 we have:

[tex]\frac {50} {100}[/tex]

Answer:

10%

[tex]\frac {25} {100}\\\frac {1} {2}[/tex]

Answer:

[tex]a=10\%\\\\b=\frac{25}{100}\\\\c=\frac{1}{2}[/tex]

Step-by-step explanation:

To find "a" you can multiply [tex]\frac{10}{100}[/tex] by 100, then this is:

[tex]a=\frac{10}{100}*100\\\\a=10\%[/tex]

To find "b", you can multiply the numerator and the denominator of the fraction [tex]\frac{1}{4}[/tex] by 25, getting:

[tex]b=\frac{1*25}{4*25}\\\\b=\frac{25}{100}[/tex]

To find "c", you can reduce the fraction [tex]\frac{50}{100}[/tex]. Then you get that this is:

[tex]c=\frac{50}{100}\\\\c=\frac{25}{50}\\\\c=\frac{5}{10}\\\\c=\frac{1}{2}[/tex]

Lucy earned a total of $225.50 for the week by combining her regular and holiday earnings.

Lucy's earnings for the week:

Answer:

x=-3

Step-by-step explanation:

f(x) = -2(x + 3)^2 – 5

This quadratic is in the form

f(x) = a(x - h)^2 + k

f(x) = -2(x -  -3)^2 + - 5

Where (h,k) is the vertex

(-3,-5)

We know the axis of symmetry is along the vertex

x=h is the axis of symmetry

x=-3

The axis of symmetry of the function f(x) = -2 (x + 3)² - 5 is x = -3.

Line of symmetry of a figure or a shape is the line which divides the figure or shape in to equal and symmetrical parts.

This line is also called as axis of symmetry.

It is sometimes also called as mirror line since the line divides in to parts which looks like mirror images.

The given equation,

f(x) = -2 (x + 3)² - 5

f(x) = -2x² - 12x - 18 - 5

f(x) = -2x² - 12x - 23

For a quadratic function of the form, f(x) = ax² + bx + c, the axis of symmetry is,

x = -b/2a

Here,

x = 12 / (2 × -2) = -12/4 = -3

Hence the axis of symmetry is x = -3.

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Answer:

Part 1) [tex]324\pi\ units^{2}[/tex] ------> [tex]7,776\pi\ units^{3}[/tex]

Part 2) [tex]36\pi\ units^{2}[/tex] ------> [tex]288\pi\ units^{3}[/tex]

Part 3) [tex]81\pi\ units^{2}[/tex] ------> [tex]972\pi\ units^{3}[/tex]

Part 4) [tex]144\pi\ units^{2}[/tex] ------> [tex]2,304\pi\ units^{3}[/tex]

Step-by-step explanation:

we know that

The largest cross sectional area of that sphere is equal to the area of a circle with the same radius of the sphere

Part 1) we have

[tex]A=324\pi\ units^{2}[/tex]

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

so

[tex]324\pi=\pi r^{2}[/tex]

Solve for r

[tex]r^{2}=324[/tex]

[tex]r=18\ units[/tex]

Find the volume of the sphere

The volume of the sphere is

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

For [tex]r=18\ units[/tex]

substitute

[tex]V=\frac{4}{3}\pi (18)^{3}[/tex]

[tex]V=7,776\pi\ units^{3}[/tex]

Part 2) we have

[tex]A=36\pi\ units^{2}[/tex]

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

so

[tex]36\pi=\pi r^{2}[/tex]

Solve for r

[tex]r^{2}=36[/tex]

[tex]r=6\ units[/tex]

Find the volume of the sphere

The volume of the sphere is

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

For [tex]r=6\ units[/tex]

substitute

[tex]V=\frac{4}{3}\pi (6)^{3}[/tex]

[tex]V=288\pi\ units^{3}[/tex]

Part 3) we have

[tex]A=81\pi\ units^{2}[/tex]

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

so

[tex]81\pi=\pi r^{2}[/tex]

Solve for r

[tex]r^{2}=81[/tex]

[tex]r=9\ units[/tex]

Find the volume of the sphere

The volume of the sphere is

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

For [tex]r=9\ units[/tex]

substitute

[tex]V=\frac{4}{3}\pi (9)^{3}[/tex]

[tex]V=972\pi\ units^{3}[/tex]

Part 4) we have

[tex]A=144\pi\ units^{2}[/tex]

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

so

[tex]144\pi=\pi r^{2}[/tex]

Solve for r

[tex]r^{2}=144[/tex]

[tex]r=12\ units[/tex]

Find the volume of the sphere

The volume of the sphere is

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

For [tex]r=12\ units[/tex]

substitute

[tex]V=\frac{4}{3}\pi (12)^{3}[/tex]

[tex]V=2,304\pi\ units^{3}[/tex]

Answer:68

Step-by-step explanation:

In an isosceles triangle with angle BCA equal to 44 degrees, the measure of angle CXA is also 44 degrees because the sum of the two bisected base angles is 44 degrees.

In an Isosceles Triangle, the base angles are always equal. Therefore, if m∠BCA (angle BAC) is 44 degrees, then m∠ABC is also 44 degrees.

Because BFAD and CE are bisectors, they split ∠ABC and ∠ACB into two equal angles. So, ∠ABF (or ∠ABX) and ∠ACD (or ∠ACX) are each 22 degrees.

m∠CXA is the sum of ∠ABX and ∠ACX. Therefore, m∠CXA is 22 degrees + 22 degrees = 44 degrees.

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Answer:

The angular speed is 3,227 rad/min

Step-by-step explanation:

Remember that

1 mile=63,360 inches

step 1

Find the circumference of the wheels

The circumference is equal to

[tex]C=\pi D[/tex]

we have

[tex]D=36\ in[/tex]

substitute

[tex]C=\pi (36)[/tex]

[tex]C=36\pi\ in[/tex]

step 2

we know that

The speed of the wheel is 55 mi/h

Convert to mi/min

55 mi/h=55/60 mi/min

Convert to in/min

(55/60) mi/min=55*63,360/60 in/min= 58,080 in/min

we know that

The circumference of the wheel subtends a central angle of 2π radians

so

using proportion

Find out how much radians are 58,080 inches

[tex]\frac{36\pi }{2\pi }=\frac{58,080}{x} \\\\x=2*58,080/36\\\\x=3,226.67 \ rad[/tex]

therefore

The angular speed is 3,227 rad/min

Final answer:

To calculate the angular speed in radians per minute for a truck with 36-inch diameter wheels traveling at 55 mi/h, convert the diameter to radius in meters, convert the speed to meters per minute, and then use the relationship v = r theta.

Explanation:

To find the angular speed of the wheels in radians per minute, we can use the relationship between linear speed and angular speed, which is given by v = r  * theta, where v is the linear speed, r is the radius of the wheel, and theta is the angular speed.

First, convert the diameter to radius: radius = diameter / 2 = 36 in / 2 = 18 in. Then, convert inches to meters as 1 inch is 0.0254 meters. So, radius in meters = 18 in * 0.0254 m/in = 0.4572 m.

Next, convert the speed from miles per hour to meters per minute:

Convert miles to meters: 1 mile = 1609.34 meters,

Speed in meters per minute: 55 mi/h  * 1609.34 m/mi * 1h/60min = 1,486.86 m/min.

Now we can find the angular speed:  theta = v / r = 1,486.86 m/min / 0.4572 m = 3,252.3 rad/min.

Answer:

30

Step-by-step explanation:

Find lowest common multiple of 5 and 6

Multiples of 5                             Multiples of 6

5 × 1 = 5                                       6 × 1 = 6                                      

5 × 2 = 10                                    6  × 2 = 12

5 × 3 = 15                                     6 × 3 = 18

5 × 4 = 20                                    6 × 4 = 24

5 × 5 = 25                                    6 × 5 = 30

5 × 6 = 30

5 × 7 = 35

5 × 2 = 10

5 × 3 = 15

5 × 4 = 20

5 × 5 = 25

5 × 6 = 30

5 × 7 = 35

30 is the lowest number which comes in both lists

It's 30... if your looking at a simple answer, it's 30.

Answer:

Should be 1st number, 3rd number, 2nd number

Step-by-step explanation:

Mixed fraction has a 3 in it, which means its over 100%. 6/20 is 30%, and the other one is negative.

Answer:

3 32/40, 6/20, - 2/10

Step-by-step explanation:

3 32/40,  -2/10  , 6/20

We want greatest to least

Positive numbers are greater than negative numbers, so the negative number is the smallest

Since there is only one number with a whole number attached and none of the numbers are improper fractions (numerator larger than denominator) it would be the largest

3 32/40, 6/20, - 2/10

Answer:

√11/√11

Step-by-step explanation:

in order to rationalize the denominator we must multiply it with the a radical that simplifies the radical in denominator

in given case radical in denominator is√11, in order to simplify it we need to multiply numerator and denominator by √11.

2√10/3√11 x √11/√11

=2√110/3(11)

=2√110/33!

For this case we must rationalize the denominator of the following expression:

[tex]\frac {2 \sqrt {10}} {3 \sqrt {11}} =[/tex]

To rationalize the denominator, that is, remove the root of the denominator, we must multiply by:

[tex]\frac {\sqrt {11}} {\sqrt {11}}[/tex]

So, we have:

[tex]\frac {2 \sqrt {10}} {3 \sqrt {11}} * \frac {\sqrt {11}} {\sqrt {11}} =\\\frac {2 \sqrt {10} * \sqrt {11}} {3 (\sqrt {11}) ^ 2} =\\\frac {2 \sqrt {110}} {3 * 11} =\\\frac {2 \sqrt {110}} {33}[/tex]

Answer:

Option B

Answer:

The inequality that models the situation is [tex]2.25x+4.75y \leq 80[/tex]

Step-by-step explanation:

Let

x ----> represent the number of small candles

y ----> represent the number of large candles

we know that

The inequality that represent this situation is equal to

[tex]2.25x+4.75y \leq 80[/tex]

using a graphing tool

The solution is the shaded triangular area, because the number of candles cannot be a negative number

see the attached figure

Answer:

[tex]A.\\\\x+y\leq200\\\\4x+3y\leq750[/tex]

Step-by-step explanation:

x - number of adults

y - number of campers

The room for 200 people: x + y ≤ 200

Each adult costs $4, and each camper costs $3: 4x and 3y

A maximum budget of $750: 4x + 3y ≤ 750

The correct option for the given scenario is option A, which includes two inequalities: one for the capacity constraint (x + y ≤ 200) and one for the budget constraint (4x + 3y ≤ 750), where x is the number of adults and y is the number of campers.

The correct system of inequalities to represent the scenario where x is the number of adults and y is the number of campers, with a room capacity for 200 people and a maximum budget of $750, is:

This corresponds to option A, where the first inequality represents the capacity constraint and the second inequality represents the budget constraint.

Answer:

See below in bold.

Step-by-step explanation:

52, 19, 44, 49, 37, 46, 52, 36, 54, 13, 14, 17, 34, 16, 51

The mean =  35.6

The absolute differences from the mean =

16.4, 16.6, 8.4, 13.4, 1.4, 10.4, 16.4, 0.4, 18.4, 22.6, 21.6, 18.6, 1.6, 19.6, 15.4

The squares of these differences =  

268.96, 275.56, 70.56, 179.56, 1.96, 108.16, 268.96, 0.16, 338.56, 510.76, 466.56, 345.96, 2.56, 384.16, 237.16.

The Sum of these squares = 3459.6

Sample Variance  3459.6 / 14 = 247.11 and

Population  Variance = 3459.6 / 15  = 230.64

Sample standard deviation =  √247.11 = 15.72

Population Standard deviation = √230.64 =  15.19.

Sample standard deviation =  √247.11 = 15.72

Population Standard deviation = √230.64 =  15.19.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

Given

52, 19, 44, 49, 37, 46, 52, 36, 54, 13, 14, 17, 34, 16, 51

The mean =  35.6

The absolute differences from the mean =

16.4, 16.6, 8.4, 13.4, 1.4, 10.4, 16.4, 0.4, 18.4, 22.6, 21.6, 18.6, 1.6, 19.6, 15.4

The squares of these differences =  

268.96, 275.56, 70.56, 179.56, 1.96, 108.16, 268.96, 0.16, 338.56, 510.76, 466.56, 345.96, 2.56, 384.16, 237.16.

The Sum of these squares = 3459.6

Sample Variance  3459.6 / 14 = 247.11 and

Population  Variance = 3459.6 / 15  = 230.64

Sample standard deviation =  √247.11 = 15.72

Population Standard deviation = √230.64 =  15.19.

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Answer:

[tex]P_n=10+90n[/tex]

Step-by-step explanation:

So it said it was linear and gave us two points on that line: (0,10) and (5,460).

y=mx+b is slope-intercept form where b is the y-intercept or the initial amount of beetles and m is the slope (or rate of change in population to number weeks) of the line.  Our variables (x,y) are really (n,P) here.

The slope of the line can be computed using [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1) \text{ and } (x_2,y_2) \text{ are points on the line }[/tex].

You can also just line up the points vertically and subtract, then put 2nd difference over first difference.

Like this:

(5  ,  460)

-(0  ,    10)

--------------

5       450

So the slope is 450/5=90.

The y-intercept is where the line crosses the y-axis.  A graph crosses the y-axis when it's x value is 0.  Luckily, they give us the y-intercept which is (0,10) so b=10.  Your problem gave us this as well and was just asking for the slope of the line.

Anyways the equation is

y=90x+10

or

y=10+90x

or since we are using P and n:

[tex]P_n=10+90n[/tex]

The explicit formula for the beetle population after n weeks is Pn = 10 + 90n.

To find an explicit formula for the beetle population after n weeks, we need to determine the rate of growth. From the given information, we know that the population increased by 460-10=450 beetles in 5 weeks. Therefore, the rate of growth is 450/5=90 beetles per week.

To find the explicit formula, we can use the formula for a linear growth model: Pn = Po + r*n, where Pn is the population after n weeks, Po is the initial population, r is the rate of growth, and n is the number of weeks.

Substituting the given values, we have: Pn = 10 + 90n.

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