Mathematics High School

## Answers

**Answer 1**

**Answer:**

x-intercept: 14y-intercept: 28/5

**Step-by-step explanation:**

You want the **x- and y-intercepts** of the equation ...

** 2x +5y = 28**

Intercepts

The x-intercept is found by solving for x when y = 0. Generically, this is ...

ax +by = c

ax + 0 = c

x = c/a . . . . . . . . constant divided by x-coefficient

Similarly, the y-intercept is the value of y when x = 0:

y = c/b . . . . . . . . constant divided by y-coefficient

Application

The x-intercept is ...

x = 28/2

** x = 14**

The y-intercept is ...

** y = 28/5**

__

*Additional comment*

As you can see, the intercepts are easily found when the equation of the line is written in standard form like this. Knowing these intercepts makes the function easy to graph: plot the intercept points, and draw a line through them.

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## Related Questions

What are the solutions to the equation 4x^2-52x+169=121

### Answers

**Answer: x = 12**

**x = 1**

**Step-by-step explanation:**

move terms the left side

three point charges of -2.0 µc, 4.0 µc, and 6.0 µc are placed along the x axis as shown below. how much work is required to move a 10 nc charge from infinity to point p (x = 0, y = 0.2 m)?

### Answers

the work required to **move** a 10 nC charge from **infinity** to point P is 4.80 x 10^-4 J.

To calculate the work required to move a charge from infinity to **point** P, we need to use the formula:

W = q * (ΔV)

where q is the charge being moved and ΔV is the **change** in electric potential energy.

To calculate the electric potential energy at point P, we need to first calculate the electric potential at point P due to each of the three charges. The electric **potential** at a point due to a point charge q is given by:

V = k * (q / r)

where k is Coulomb's constant, q is the charge, and r is the distance between the point charge and the point at which the potential is being calculated.

Using this formula, we can calculate the electric potential at point P due to each of the three charges:

V1 = k * (-2.0 µC) / (0.2 m) = -8.99 x 10^9 V

V2 = k * (4.0 µC) / (0.2 m) = 1.80 x 10^10 V

V3 = k * (6.0 µC) / (0.2 m) = 2.70 x 10^10 V

The total electric potential at point P is the sum of the individual potentials:

V = V1 + V2 + V3 = 4.80 x 10^10 V

The change in electric potential energy as the charge is moved from infinity to point P is:

ΔV = V - 0 = 4.80 x 10^10 V

Finally, we can calculate the work **required** to move the charge:

W = q * ΔV = (10 nC) * (4.80 x 10^10 V) = 4.80 x 10^-4 J

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the surface area of the figure shown is 192cm^2

### Answers

**Answer:384**

**Step-by-step explanation: all you have to do is multiply by 2 **

What is 24・3/4? Show your work.

### Answers

**Answer:**

**Step-by-step explanation:**

[tex]24.\frac{3}{4}\\ = 6.3 \\= 18[/tex]

i need help with this

### Answers

**Answer:**

The answer is B

**Step-by-step explanation:**

2n<-6

divide both sides by 2

2n/2<-6/2

n<-3

-3n+2<-4

C.L.T.

-3n<-4-2

-3n<-6

divide both sides by-3

-3n/-3<-6/-3

n<2

Give a polynomial with an odd degree and a negative leading coefficient, with an irrational zero.

### Answers

**Answer:**

**Step-by-step explanation:**

Definitions:

**Polynomial:** equation with terms

**Odd Degree:** the highest exponent must be odd

Ex. x³ or [tex]x^{7}[/tex]

**Negative Leading Coefficient: **the number in front of the highest

exponented term is negative

Ex. -5x³

**Irrational Zero:** Solution that has a decimal with no repeats and goes on

infinitely

Ex. √7 or pi

Now that we have our meanings let's put it together:

**y = -5x³ - 7 **

This would give and irrational 0 if we solved for x when y=0

find the inequalities

### Answers

**Answer: c**

**Step-by-step explanation:**

c

I’m in the middle of taking a refresher homework for calc 2 and need help with this question.

### Answers

**Answer:**

z = (5 + ln 36) / (1 + ln 36)

**Step-by-step explanation:**

36 e⁵⁻ᶻ − 6²ᶻ = 0

Add 6²ᶻ to both sides:

36 e⁵⁻ᶻ = 6²ᶻ

Change 36 to 6².

6² e⁵⁻ᶻ = 6²ᶻ

Divide both sides by 6².

e⁵⁻ᶻ = 6²ᶻ / 6²

Use exponent rule.

e⁵⁻ᶻ = 6²ᶻ⁻²

Take natural log of both sides.

ln e⁵⁻ᶻ = ln 6²ᶻ⁻²

Use log rule.

(5 − z) ln e = (2z − 2) ln 6

Simplify and solve.

5 − z = (2z − 2) ln 6

5 − z = (2 ln 6) z − 2 ln 6

5 + 2 ln 6 = (2 ln 6) z + z

5 + 2 ln 6 = (1 + 2 ln 6) z

z = (5 + 2 ln 6) / (1 + 2 ln 6)

You can use log rule to simplify further.

z = (5 + ln 36) / (1 + ln 36)

**Solution:**

[tex]z=\frac{ln(36)+5}{2ln(6)+1} \approx 1.8727[/tex]

**Step-By-Step:**

Refer to the attached image, please follow carefully.

equations that equal -27

### Answers

**Answer:**

-19-8=-27

**Step-by-step explanation:**

approximate the area under the function f(x)=4x on the interval [1,5] using 8 left-sided rectangles. give your answer as a fraction.

### Answers

the **approximate** area under the curve is 52 square **units**.

Using 8 left-sided **rectangles**, the width of each rectangle is Δx = (5-1)/8 = 0.5. The left endpoints of the 8 subintervals are x = 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5. The area of each rectangle is f(x)Δx = 4x(0.5) = 2x. Therefore, the total **area** is:

A ≈ 2(1) + 2(1.5) + 2(2) + 2(2.5) + 2(3) + 2(3.5) + 2(4) + 2(4.5)

= 2(1 + 1.5 + 2 + 2.5 + 3 + 3.5 + 4 + 4.5)

= 2(26)

= 52

what is rectangles?

Rectangles are geometric shapes with four sides and four right angles. The opposite sides of a rectangle are **parallel** and have the same length. The area of a rectangle is found by multiplying the length and width of the rectangle, while the perimeter is the sum of the lengths of all four sides. Rectangles are commonly used in mathematics and geometry to solve problems related to area, **perimeter**, and volume.

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use the formula for present value of money to calculate the amount you need to invest now in one lump sum in order to have $100,000 after 18 years with an apr of 10% compounded quarterly. round your answer to the nearest cent, if necessary.

### Answers

You would need to invest approximately $34,175.85 now in one lump sum in order to have $100,000 after 18 years with an **annual interest rate of **10% compounded quarterly.

Using the formula for **present** **value** of money, you would need to invest approximately $34,175.85 now in one** lump sum **in order to have $100,000 after 18 years with an annual interest rate of 10% compounded quarterly.

To calculate the** **present value** **of an investment, we can use the formula for the present value of money:

PV = FV / (1 + r/n)^(n*t)

Where:

PV = Present Value

FV = Future Value ($100,000 in this case)

r = Annual interest rate (10% or 0.10)

n = Number of compounding periods per year (4 for quarterly compounding)

t = Number of years (18 years in this case)

Plugging in the values into the formula, we get:

PV = 100,000 / (1 + 0.10/4)^(4*18)

Calculating the expression inside the parentheses first:

PV = 100,000 / (1 + 0.025)^(72)

Simplifying the exponent:

PV = 100,000 / (1.025)^(72)

Calculating the value inside the parentheses:

PV = 100,000 / 2.925169596

Calculating the final **present value**:

PV ≈ $34,175.85

Therefore, you would need to invest approximately $34,175.85 now in one lump sum in order to have $100,000 after 18 years with an annual interest rate of 10% compounded quarterly.

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Find the length of HB and measure of angle HGB.

NEED ASAP!!!

### Answers

The **measure **of length of HB = 4.1 in

The measure of **angle **HDB is 30 degrees

How to find the measure of angle HGB

**Each triangle** will have an apex angle of calculated using the formula below

= angle in a circle (point) divided by the number of sides

= 360 / 6

= 60

angle HGB = 60/2 = 30 degrees

side HB = 1/2 of the side length of the **hexagon**

side HB = 1/2 * 8.2 in

side HB = 4.1 in

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Select all of the following functions for which the extreme value theorem guarantees the existence of an absolute maximum and minimum Select all that apply: f(r) =xn2 over [-1, 1] g(x) = over (1.4) h(x) V3 _ X over (1,3) k(x) over [1,3] None of the above

### Answers

Among the given **functions**, f(x) = xⁿ² over [-1, 1] and k(x) over [1,3] satisfy these conditions and hence the** theorem **applies to them.

The extreme value** theorem** states that if a function f(x) is continuous on a closed and bounded interval [a, b], then it must have an absolute maximum and **minimum value** at some points within the interval. This means that the function takes on its largest and smallest values at least once in the interval, either at the endpoints or at some point in between.

Among the given functions, f(x) = xⁿ2 over [-1, 1] and k(x) over [1,3] are continuous on closed and bounded intervals, as they are defined over finite** intervals **and involve only polynomial functions, which are continuous over their domains. Therefore, the extreme value theorem guarantees that these functions have an absolute **maximum** and minimum value somewhere within their respective intervals.

On the other hand, the function g(x) = over (1.4) and h(x) = V3 _ X over (1,3) are not continuous on closed and bounded intervals, as they involve discontinuities or singularities within their domains. Thus, the extreme value **theorem** does not apply to these functions. Finally, the option "None of the above" is incorrect, as two of the given functions satisfy the conditions for the theorem to hold.

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Mario says he found the height of a cone that has a volume of 72 cubic millimeters and a diameter of 12 millimeters. 72π = 1 3 π(12²)h 1. 72π = 1 3 π(144)h 2. 72π = 48π(h) 3. 1.5 = h Analyze Mario’s work. Is he correct? If not, what was his mistake? a. Yes, he is correct. b. No, he did not correctly square 12 on the left side. c. No, he did not use the radius measure in the formula. d. No, he did not correctly undo the multiplication on the right side.

### Answers

**Answer:**

h = 6 is the correct answer.

**Step-by-step explanation:**

To find the height (h) of a cone with volume V and diameter d, we can use the formula:

V = (1/3)πr^2h, where r is the radius of the cone and d = 2r.

In this problem, we are given that the volume V = 72 cubic millimeters and the diameter d = 12 millimeters. Therefore, the radius r = d/2 = 6 millimeters.

Substituting these values into the formula, we get:

72π = (1/3)π(6^2)h

72π = 12πh

h = 6

So, the correct answer is h = 6, which means that Mario's work is incorrect.

Looking at Mario's work, he correctly wrote down the formula for the volume of a cone and substituted the given values, but he made a mistake in simplifying the equation.

On the left side of the equation, he correctly multiplied 72 by π, but he should have divided the result by 3 to get (1/3)π(144), instead of π(144).

On the right side of the equation, he correctly wrote down the product of (1/3)π(12^2) and h, but he simplified it incorrectly by multiplying 48π by h instead of 12π by h.

Therefore, the correct equation after simplification would be:

(1/3)π(144)h = 72π

Simplifying this equation further would give us h = 6, which is the correct answer.

(Reference to Chatgpts work)

**Answer:**

C) No, he did not use the radius measure in the formula.

**Proof: **

Find the number of terms and the degree of this polynomial

S^2 + 1

### Answers

The **polynomial** "[tex]S^2[/tex] + 1" has 2 terms and the degree of the polynomial is 2.

The given polynomial is [tex]S^2[/tex]

[tex]S^2[/tex] + 1200. It has two terms: [tex]S^2[/tex] and 1200.

The degree of a polynomial is the **highest power** of the variable in any of its terms.

The given polynomial is "[tex]S^2[/tex] + 1".

It has two terms, particularly "[tex]S^2[/tex]" and "1".

The diploma of the polynomial is the very best energy of the variable "S" in the polynomial.

The absolute best strength of "S" is 2

Therefore, the **diploma** of the polynomial is 2.

So, the polynomial "[tex]S^2[/tex] + 1" has two phrases and the diploma of the polynomial is 2.

n this case, the highest power of S is 2, so the degree of the polynomial is 2.

The number of terms and the degree of a given polynomial.

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Please help find X for question 25. Please explain too.

### Answers

The **value** of x is 11.

Given that the measure of the **arc** VYX is 282° and the measure of the **angle** ∠UVX = (4x-5)°,

So,

Arc VX = 360° - arc VYX

Arc VX = 360° - 282°

Arc VX = 78°

We know that the,

If a **tangent** and a **chord intersect** at a point on a circle, then the measure of each angle formed is **one-half **the measure of its **intercepted** arc.

Therefore,

∠UVX = 1/2 Arc VX

4x-5 = 1/2 × 78

4x-5 = 39

4x = 44

x = 11

Hence the **value** of x is 11.

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The number of magazine subscriptions sold for a student fundraising event has been declining at an annual rate of 12%. If there are currently 983 magazine subscriptions, how long ago, to the nearest tenth of a year, were there 2,521 magazine subscriptions?

A 2.3 years

B) 3.2 years

C)7.4 years

D) 8.3 years

### Answers

**Answer:**

7.4 years

**Step-by-step explanation:**

declining at rate of 12% a year is same as saying the rate year upon year is 0.88%.

call n our number of years between 983 subs and 2521 subs.

if we go back n years, our current number of subs was 2521.

we need to find how far in the future will there be 983 subs.

use the formula for 'compound growth and decay.'

that is N = A (1 + increase) ^n

Where N is future amount, A is initial amount, increase is percentage increase/decrease, n is number of mins/hours/days/months/years.

we have 2521 (0.88)^n = 983.

divide both sides by 2521:

0.88^n = (983/2521)

take logarithms of both sides:

log 0.88^n = log (983/2521). simplify by bringing down the n:

n log 0.88 = log (983/2521)

divide both sides by log 0.88:

n = (log (983/2521)) / log 0.88

= 7.37

= 7.4 years (to nearest tenth of a year)

PLEASE ANSWER A.S.A.P

Priceless Portrait Studio signed a note with a face value of $48, 000 that requires 24 monthly payments of $2,900. The studio's owner would like to pay the debt in full after 21 months, when there are 3 payments remaining. Find the amount of unearned interest using the Rule of 78.

$490

$432

$561

$252

### Answers

**Answer:**

$432

**Step-by-step explanation:**

Tabitha explains to her classmate how to find the volume of a cylinder. Which shows a correct explanation

### Answers

One possible correct explanation of how to find the volume of a cylinder is:To find the volume of a** cylinder**, you need to multiply the area of the base by the height.

The base of a cylinder is a circle, so the area of the base is equal to pi times the radius **squared**. The height of the cylinder is the distance between the two circular bases. So, if you know the radius of the base and the height of the cylinder, you can use the** formula** [tex]V = pi × r² × h[/tex] to find the volume of the cylinder.

It's important to note that the units used for the radius, height, and volume should be consistent. For example, if the radius is given in meters and the height is given in **centimeters**, they need to be converted to the same unit before the formula is applied. And the resulting volume should have units cubed, such as cubic meters or cubic centimeters.

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￼please please help me

### Answers

In the given diagram, the **measure **of **angle** G, m ∠G, is 42°

Calculating the measure of an angle

From the question, we are to determine the **measure **of **angle **G in the given diagram.

From one of the **circle theorems**, we know that angles in the same segment are equal.

In the diagram, angle G and angle J are in the same segment.

Thus,

We can write that

m ∠G = m ∠J

9x + 33° = x + 41°

Solve for x

9x + 33° = x + 41°

9x - x = 41° - 33°

8x = 8°

x = 1°

But,

m ∠G = 9x + 33°

Substitute the value of x

m ∠G = 9(1) + 33°

m ∠G = 9° + 33°

m ∠G = 42°

Hence, **measure **of **angle **G, m ∠G = 42°

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Apply the Law of Exponents to write an equivalent expression of -4x³y2 - 3x5y6

### Answers

The **equivalent** form of 4x³y³ - 3x⁵y⁶ is ,

⇒ [tex]x^{3} y^{3}( 4 - 3x^{2}y^{3})[/tex]

The given **expression** is.,

4x³y³ - 3x⁵y⁶

Here we have to write the equivalent form of the given expression by using **exponent** law,

Since we know that,

Exponent is defined as the method of expressing large **numbers** in terms of powers.

That means, exponent refers to how many times a number multiplied by itself. For example, 6 is **multiplied** by itself 4 times,

i.e. 6 × 6 × 6 × 6.

This can be written as 64. Here, 4 is the exponent and 6 is the **base**. This can be read as 6 is raised to power 4.

Therefore,

Applying exponent law of product,

[tex]x^{a} x^{b} = x^{a+b}[/tex]

So we can write the given **expression** as

⇒ [tex]4x^{3} y^{3} - 3x^{5} y^{6}[/tex]

⇒ [tex]4x^{3} y^{3} - 3x^{3+2} y^{3+3}[/tex]

⇒ [tex]4x^{3} y^{3} - 3x^{3} x^{2} y^{3}y^{3}[/tex]

⇒ [tex]x^{3} y^{3}( 4 - 3x^{2}y^{3})[/tex]

Hence the expression,

[tex]x^{3} y^{3}( 4 - 3x^{2}y^{3})[/tex] is **equivalent** to the given expression.

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pls help me with this

Use long division to divide 1,911 ÷ 6

Responses

322 R1

317 R9

318 R3

321 R5

### Answers

The correct response is: 317 R9

To divide 1,911 by 6 using** long division**, follow these steps:

Start by dividing the **leftmost digit **of the dividend (1) by the divisor (6). The result is 0. Write this as the first digit of the quotient above the division symbol.

6 | 1,911

Multiply the divisor (6) by the first digit of the quotient (0). Write the result (0) below the first digit of the dividend.

6 | 1,911

Subtract the result (0) from the **first digit** of the dividend (1). Write the difference (1) below the line.

6 | 1,911

1

4. Bring down the next digit of the dividend (9) next to the difference.

6 | 1,911

19

5. **Divide** the new number (19) by the divisor (6). The result is 3. Write this as the next digit of the quotient above the line.

03

6 | 1,911

19

6. **Multiply** the divisor (6) by the new digit of the quotient (3). Write the result (18) below the new portion of the dividend.

03

6 | 1,911

18

7. **Subtract **the result (18) from the new portion of the dividend (19). Write the difference (1) below the line.

03

6 | 1,911

18

1

8. Since there are no more digits in the dividend, the division is complete. The quotient is 319, and the remainder is 1.

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To divide 1,911 by 6 using long division, you follow these steps:

Step 1: Start by dividing the first digit of the dividend (1) by the divisor (6). Since 1 is less than 6, you move to the next digit, which is 19.

Step 2: Divide 19 by 6. The quotient is 3, and the remainder is 1.

Step 3: Bring down the next digit from the dividend, which is 1, and place it next to the remainder (1). You now have 11.

Step 4: Divide 11 by 6. The quotient is 1, and the remainder is 5.

Step 5: Bring down the next digit from the dividend, which is 1, and place it next to the remainder (5). You now have 51.

Step 6: Divide 51 by 6. The quotient is 8, and the remainder is 3.

Step 7: There are no more digits in the dividend, so you have finished dividing. The final quotient is the series of quotients you obtained in each step, which are 3, 1, and 8. The remainder is the last remainder you obtained, which is 3.

Therefore, when you divide 1,911 by 6 using long division, the correct answer is 318 with a remainder of 3.

Out of the given options, the correct answer is 318 R3.

if the diagonals of a quadrilateral bisect each other and one angle of a quadrilateral is a right angle, then the quadrilateral is a rectangle. prove that

### Answers

We can** prove** that if the** **diagonals of a quadrilateral bisect each other and one angle of a quadrilateral is a **right angle**, then the **quadrilateral** is a **rectangle**.

How to prove that the quadrilateral is a rectangle?

Let ABCD = a **quadrilateral** such that its diagonals AC and BD bisect each other at point O.

Let ∠A = a **right angle**.

Required: Prove that ABCD is a **rectangle**.

First, quadrilateral ABCD is a** parallelogram**. Since the diagonals bisect each other, we have:

OA = OC (diagonals bisect each other)

OB = OD (diagonals bisect each other)

Therefore, **triangle** AOB is congruent to triangle COD by SAS (Side-Angle-Side) congruence:

AB = CD (corresponding sides of congruent triangles)

Next, triangle BOC is congruent to triangle DOA, as:

BC = AD (corresponding sides of congruent triangles)

So, we have proved that opposite sides of quadrilateral ABCD are congruent, which implies that ABCD is a parallelogram.

Next, we show quadrilateral ABCD has right angles at both B and D. Since ∠A is a right angle, we have:

∠BOC = 180° - ∠A (linear pair)

∠BOC = 180° - 90° (since ∠A is a right angle)

∠BOC = 90°

Again, we show that ∠AOD = 90°. So, we have shown that quadrilateral ABCD has right angles at both B and D.

Finally, we can prove that quadrilateral ABCD is a rectangle.

Since ABCD is a parallelogram with opposite angles B and D, both right angles, then ABCD is a rectangle.

Therefore, if the diagonals of a quadrilateral bisect each other and one angle of the quadrilateral is a right angle, then the quadrilateral is a **rectangle**.

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the rogers family and the jackson family each used their sprinklers last summer. the water output rate for the rogers family's sprinkler was per hour. the water output rate for the jackson family's sprinkler was per hour. the families used their sprinklers for a combined total of hours, resulting in a total water output of . how long was each sprinkler used?

### Answers

The **Rogers family** used their sprinkler for hours and the Jackson family used their **sprinkler **for hours.

To solve this problem, we can use a system of **equations**. Let's let x be the number of hours the Rogers family used their sprinkler, and y be the **number **of hours the **Jackson **family used their sprinkler. Then we have two equations: x + y = total number of hours used (given as a known value) output rate of Rogers family's sprinkler * x + output rate of Jackson family's sprinkler * y = total water output (also given as a known value) We can then substitute the given **values **into the equations and solve for x and y. Once we have x and y, we know how long each sprinkler was used.

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the population of the city is 125,00.what is the range of the number of residents in the city who regularly eat organic food

### Answers

**Answer:**

Without more information, I cannot determine the range of number of residents who regularly eat organic food. Please add more information.

**Step-by-step explanation:**

Geometry: Help with assignment

### Answers

The **solution** of A ∪B for their **set** of data that can be derived using a **Venn** diagram is A ∪B = {0, 1, 2, 3, 4, 5}, which makes option C correct.

What is Venn diagram

**Venn** diagrams are commonly used in mathematics, statistics, and logic to illustrate relationships between **sets** of data. It consists of circles that overlap to show the similarities and differences between the sets like in the case of students data.

A ∪B is read as A union B, which implies the **set** of all datas in set A and set B without repeating any data.

Given that **set** A = {0, 1, 2, 3, 4} and B = {1, 3, 5}

All **data** of set A and B are: 0, 1, 2, 3, 4, 5

so;

A ∪B = {0, 1, 2, 3, 4, 5}

Therefore, the **solution** of A ∪B that can be derived using a **Venn** diagram is A ∪B = {0, 1, 2, 3, 4, 5}

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Please help me with a word problem and thank u

### Answers

The **algebraic expression **for the total number of pages that Rachel will need to write is given as follows:

3(b + s).

How to write the algebraic expression?

The **variables **used to write the algebraic expression are given as follows:

Variable b: number of pages in a book report.Variable s: number of pages in a science report.

Rachel writes 3 book reports and 3 science report, hence the **pages **are given as follows:

3b pages of book reports.3s pages of science reports.

Hence the **algebraic expression **for the total number of pages that Rachel will need to write is given as follows:

3b + 3s = 3(b + s).

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The exponential growth of the deer population in the country can be calculated using the model T 70,000(1+07) where 70,000 is the initial deer population and.07 is the rate of growth. T is the total population after n years have passed. (a) Predict the total population after 4 yr The total population after 4 yr is about (Round to the nearest thousand as needed.) (b) If the initial population was 30,000 and the growth rate was .11, approximately how many deer would be present after 5 yr? After 5 yr approximately deer would be present. (Round to the nearest thousand as needed.)

### Answers

(A) The total **population** of deer after 4 years is approximately 153,000.

(B) 64,000 deer would be present after 5 **years**.

(a) The total **population **of deer after 4 years can be predicted using the given model as T = 70,000(1+0.7)^4. Solving this **equation**, we get T ≈ 153,33. Therefore, the total population of deer after 4 years is approximately 153,000.

(b) If the initial **population** of deer is 30,000 and the growth rate is 0.11, then the total population of deer after 5 years can be calculated as T = 30,000(1+0.11)^5. Solving this equation, we get T ≈ 63,531. Therefore, approximately 64,000 deer would be present after 5 years.

**Exponential growth** is a mathematical concept that describes how a quantity increases exponentially over time. In this case, the deer population is growing exponentially with a given rate of growth. The equation T = 70,000(1+0.7)^4 is used to calculate the total population of deer after 4 years. Similarly, the equation T = 30,000(1+0.11)^5 is used to calculate the total population of deer after 5 years, given the initial population and **growth rate.** The solutions to these equations are approximations rounded to the nearest thousand, and they provide estimates of the expected deer population in the future.

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(2x^2y + xy - 5xy^2 ) - (4x^2 - 2xy + 3y^2)

### Answers

Answer-2x^2y + xy - 5xy^2 - 4x^2 + 2xy - 3y^2

Simplify by combining like terms:

2x^2y - 4x^2 - 5xy^2 + xy + 2xy - 3y^2

2x^2y - 4x^2 - 5xy^2 + 3xy - 3y^2

Nora and Lila are reading the same novel for book club. Nora is on page 128 and plans to read 8 pages per day until the next club meeting. Lila is on page 100 and plans to read 12 pages per day until the next club meeting.

After how many days of reading will Nora and Lila be on the same page of the book? What page will they be on?

Nora and Lila will be on the same page after

days of reading. On that day, they will both be on page

.

### Answers

**Answer:**

Lola needs a twix..............

**Answer/explanation:**

**Nora is on page 128 and reads 8 pages per day, which means:**

**Day 1: 128 + 8 = 136****Day 2: 136 + 8 = 144****Day 3: 144 + 8 = 152****Day 4: 152 + 8 = 160****Day 5: 160 + 8 = 168**

**Lila is on page 100 and reads 12 pages per day, which means:**

**Day 1: 100 + 12 = 112****Day 2: 112 + 12 = 124****Day 3: 124 + 12 = 136****Day 4: 136 + 12 = 148****Day 5: 148 + 12 = 160**

**Therefore, Nora and Lila will be on the same page of the book on Day 5, and they will be on page 160.**

**So, after 5 days, Nora will be on page 168, and Lila will be on page 160.**

**hope this works**