The **function **h(x) = |x - 2| + 5 is increasing for x values greater than 2. Mathematically, we can express this interval as (2, ∞).

So, the correct option is A. (2, ∞)

To determine on which interval the function h(x) = |x - 2| + 5 is **increasing**, we need to examine the behavior of the function as x increases.

First, let's analyze the absolute value function |x - 2|. The **absolute value **of a number is always non-negative, so |x - 2| is greater than or equal to zero for all values of x. Therefore, it does not affect the overall increasing or decreasing behavior of the function h(x).

Now, let's consider the term |x - 2| + 5. As x increases, the value of |x - 2| remains **constant **(as long as x is greater than or equal to 2), but the value of the entire expression |x - 2| + 5 increases. This is because we are adding a positive constant (5) to |x - 2|.

Therefore, the function h(x) = |x - 2| + 5 is increasing for x values greater than 2. Mathematically, we can express this **interval **as (2, ∞).

So, the correct option is A. (2, ∞)

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Graph the equation shown below by transforming the given graph of the parent

function.

**Answer:**

**Step-by-step explanation:**

it is only moving 3 to the right, so shift the green dot to (3,0)

I used desmos . com for the graph

Two cars leave towns 850 kilometers apart at the same time and travel toward each other. One car's rate is 16 kilometers per hour less than the other's. If they meet in 5 hours, what is the rate of the slower car? Do not do any rounding.

**Answer:9.5**

**Step-by-step explanation:**

What is B^2+8b+7??

Can someone explain it step by step please?

**Step-by-step explanation:**

B^2+8b+7 is a quadratic expression. It can be factored as (b+7)(b+1).

To factor a quadratic expression, you can use the following steps:

1. Find two numbers that add up to the coefficient of the middle term (8) and multiply to the constant term (7).

2. Write the quadratic expression as a product of two binomials, with the two numbers you found in step 1 as the coefficients of the terms in each binomial.

In this case, the two numbers that add up to 8 and multiply to 7 are 7 and 1. So, we can factor B^2+8b+7 as follows:

(b+7)(b+1)

This means that B^2+8b+7 is equal to the product of (b+7) and (b+1).

Here is a step-by-step explanation of how to factor B^2+8b+7:

1. The coefficient of the middle term is 8.

2. The constant term is 7.

3. The two numbers that add up to 8 and multiply to 7 are 7 and 1.

4. Therefore, B^2+8b+7 can be factored as (b+7)(b+1).

B^2+8b+7 is a quadratic expression.

To solve it, you can use the quadratic formula, which is:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 1, b = 8, and c = 7.

So, substituting the values, we get:

x = (-8 ± √(8^2 - 4(1)(7))) / 2(1)

x = (-8 ± √(64 - 28)) / 2

x = (-8 ± √36) / 2

x = (-8 ± 6) / 2

x = -1 or -7

Therefore, B^2+8b+7 is equal to -1 or -7.

To solve it, you can use the quadratic formula, which is:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 1, b = 8, and c = 7.

So, substituting the values, we get:

x = (-8 ± √(8^2 - 4(1)(7))) / 2(1)

x = (-8 ± √(64 - 28)) / 2

x = (-8 ± √36) / 2

x = (-8 ± 6) / 2

x = -1 or -7

Therefore, B^2+8b+7 is equal to -1 or -7.

Which of the following answers to the question below is correct (multiple answers can be chosen)?

Question: Let s(t) be the position of a moving particle at time t. Choose ALL that represent the average speed of the particle over the time interval [0,4]?

1. s(4)/4

2. s(4)-s(0)/4

3. The slope of the secant line from (0, s(0)) to (4, s(4))

4. The slope of the tangent line at (0, s(0))

**Answer:**

The average speed of a particle over a time interval is defined as the total distance traveled divided by the time elapsed. In this case, the average speed of the particle over the time interval [0,4] is represented by * options 2 and 3*. Option 2 represents the change in position over the time interval [0,4] divided by the time elapsed. Option 3 represents the slope of the secant line connecting the points (0,s(0)) and (4,s(4)), which is equivalent to the average rate of change of position over the time interval [0,4].

the correct answers are, 2 and 3

pedro walks at a rate of 4 miles per hour and runs at a rate of 8 miles per hour. Each Week, his exercise program requires him to cover a total fist of 20 miles with some combination of walking and/or running.

A. write an equation that represents the different amounts of time pedro can walk, x, and run, y, each week.

B. graph the equation

C. what is the y- intercept? what does this tell you?

The equation showing the problem is: 4x + 8y = 20

The **graph** is attached and the **y intercept** is (0, 2.5)

Assuming that:

Time spentSince Pedro walks at a rate of 4 miles per hour, the distance he covers by walking would be

4x milesAlso Pedro runs at a rate of 8 miles per hour, the distance he covers by running would be

8y milesAccording to the given information, the total distance Pedro covers each week is 20 miles. Therefore, we can write the equation:

4x + 8y = 20

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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

**Answer:**

**Step-by-step explanation:**

32 60 68

100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

The** length **of the **arc** LM is 8.72 cm.

We have,

The** length** of an **arc** is the distance that runs through the curved line of the circle making up the arc.

The** length **of an arc is expressed as;

l = tetha/360 × 2πr

tetha = R

R = 100°

and, radius = 5 units

so, we get,

l = 100/360 × 2 × 3.14 × 5

l = 8.72 cm (1.dp)

therefore the **length **of th**e arc** LM is 8.72 cm

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Multiplying polynomials 4n2(n2 + 5n - 8)

**Answer:**

4n^4 + 20n^3 - 32n^2

**Step-by-step explanation:**

We have to distribute 4n2 to each term.

4n2 x n2. We can multiply the two n2 together resulting in 4n^4.

Now we do 4n2 x 5n. Here we multiply 4 x 5 which equals 20. Then, we multiply the n2 and n. Which results in n^3. Now we put them together; 20n^3.

Finally, we multiply 4n2 by -8. Since 8 doesn't have any variables, we just multiply the 4 and -8. Which equals to -32, now we just combine -32 and the variable; -32n2.

Now we combine these terms together. Our final answer is, 4n^4 + 20n^3 -32n^2.

^ represents an exponent.

Descrive in words the rule that is used to determine the term value from its position in the sequence

The **rule **used to determine the term value from its position in the **sequence **is often referred to as the "**nth term**" rule.

The **nth-term rule** involves identifying a pattern or relationship between the position (n) of a term in the sequence and the value of that term.

By analyzing the pattern, such as the **common difference **or **common ratio**, the nth-term rule allows us to express the value of any term in the sequence based on its position.

This rule provides a formula or **equation **that relates the position of a term to its corresponding value in the sequence.

Mathematically, the rule is:

T(n) = a + (n - 1) * d

where:

T(n) represents the value of the term at position n.a represents the first term in the sequence.n represents the position or index of the term in the sequence.d represents the common difference (for arithmetic sequences) or the common ratio (for geometric sequences) between consecutive terms.More on **sequence **and **series **can be found here: https://brainly.com/question/15583579

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What is the value of x?.

4

B

24

Q

R

15

40

C

X

1 2

The **value **of x would be,

⇒ x = 15

We have to given that;

A figure with QC is **parallel **to BR

Now, We can formulate that,

**Triangle **BDR and triangle CDQ are similar.

Hence, By using **proportionality **we get;

⇒ BD / DR = QD / CD

Substitute all the values we get;

⇒ (24 + 40) / (15 + x) = 40 / x

Solve for x,

⇒ 64 / (15 + x) = 40 / x

⇒ 64x = 40 (15 + x)

⇒ 8x = 5 (15 + x)

⇒ 8x = 45 + 5x

⇒ 8x - 5x = 45

⇒ 3x = 45

⇒ x = 15

Thus, The **value **of x would be,

⇒ x = 15

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Find the x-intercept and the y-intercept of the line below. Click on "None" if applicable.

6543/2

-24

1-3-

**Answer:**

x intercept at( -2)

y intercept at (4)

The x-intercept and the y-intercept are **-2 and 4 **respectively.

The **X-intercept** is the point where the line of an equation intersects the X-axis. While **y-intercept** is the point where the line of an equation intersects the Y-axis. Here, the X-axis is the horizontal axis, and the Y-axis is the vertical axis.

Since the given graph shows the line intersecting the X-axis i.e. the horizontal axis at -2, the x-intercept of the line would be -2. Whereas, since the line intersects the Y-axis at 4, the y-intercept is 4. The points that show these intercepts are **(-2,0)** for the x-intercept and **(0,4)** for the y-intercept.

∴ The intercepts are -2,4 respectively.

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Phil spends no more than 12 hours per week knitting. It takes him 2 hours to knit a hat and

3 hours to knit a scarf. He uses 150 yards of yarn for each hat and 400 yards of yarn for each

scarf. Which combinations of complete hats and scarves can Phil knit if he has 900 yards of yarn?

Select all of the correct answers.

A. 1 hat, 1 scarf

B. 3 hats, 2 scarves

C. 6 hats, 0 scarves

D. 4 hats, 1 scarf

E. 0 hats, 4 scarves

F. 2 hats, 1 scarf

The correct options regarding the **inequality** are:

A. 1 hat, 1 scarf

D. 4 hats, 1 scarf

F. 2 hats, 1 scarf

How to explain the inequalityBased on the time **constraint**, Phil can spend a maximum of 12 hours knitting, so we can set up the following inequality:

2h + 3s ≤ 12,

Phil can knit at most 6 hats per week, because 6 hats * 2 hours/hat = 12 hours.

Phil can knit at most 4 scarves per week, because 4 **scarves** * 3 hours/scarf = 12 hours.

Phil can use at most 900 **yards** of yarn, because he has 900 yards of yarn.

Phil can knit 1 hat and 1 scarf, because 1 hat * 150 yards/hat + 1 scarf * 400 yards/scarf = 550 yards < 900 yards.

Phil can **knit** 4 hats and 1 scarf, because 4 hats * 150 yards/hat + 1 scarf * 400 yards/scarf = 900 yards.

Phil can knit 2 hats and 1 scarf, because 2 hats * 150 yards/hat + 1 scarf * 400 yards/scarf = 700 yards < 900 yards.

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50 Points! Multiple choice geometry question. Photo attached. Thank you!

**Answer:**

8 feet

**Step-by-step explanation:**

Let b be the length of the base. Then the height is b+6 ft.

The area of the parallelogram is given by:

Area = b(b + 6) = 160

Solving for b, we get,

[tex]b^2 + 6b - 160 = 0[/tex]

Factoring the expression, we get:

(b - 8)(b + 20) = 0

Therefore, b = 8 or b = -20.

Since the base cannot be negative, b = 8.

Therefore, the length of the base of the parallelogram is 8 feet.

a pyramid and a cone are both 10 centimeters tall and have the same volume what statement

**Answer:**** "The pyramid and the cone have the same volume despite their different shapes."**

**Step-by-step explanation: **If a pyramid and a cone are both 10 centimeters tall and have the same volume, then the statement that can be made is:

**"The pyramid and the cone have the same volume despite their different shapes."**

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Please help (easy economics question)!!!

The dollar value of total revenue at each price is $[tex]0[/tex], $[tex]10[/tex], $[tex]12[/tex], $[tex]12[/tex], $[tex]10[/tex], and $[tex]6[/tex]. Total **revenue **will be the greatest at a price of $[tex]4[/tex], with [tex]3[/tex] units sold.

To find the dollar value of total revenue at each price, we can multiply the price by the **corresponding quantity **in the demand schedule:

Price: $[tex]6[/tex]

Quantity: [tex]0[/tex]

Total Revenue: $[tex]6 \times 0[/tex] = $[tex]0[/tex]

Price: $[tex]5[/tex]

Quantity: [tex]2[/tex]

Total Revenue: $[tex]5 \times 2[/tex] = $[tex]10[/tex]

Price: $[tex]4[/tex]

Quantity: [tex]3[/tex]

Total Revenue: $[tex]4 \times 3[/tex] = $[tex]12[/tex]

Price: $[tex]3[/tex]

Quantity: [tex]4[/tex]

Total Revenue: $[tex]3 \times 4[/tex] = $[tex]12[/tex]

Price: $[tex]2[/tex]

Quantity: [tex]5[/tex]

Total Revenue: $[tex]2 \times 5[/tex] = $[tex]10[/tex]

Price: $[tex]1[/tex]

Quantity: [tex]6[/tex]

Total Revenue: $[tex]1 \times 6[/tex] = $[tex]6[/tex]

To determine at which **price **the total revenue will be the greatest, we observe that the highest total revenue occurs at the price with the highest quantity sold. In this case, the price with the highest quantity is $[tex]3[/tex], and the corresponding quantity sold is [tex]4[/tex] units.

Therefore, at a price of $[tex]3[/tex], the total revenue will be the **greatest**, with [tex]4[/tex] units sold.

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Change 0.12 to a ratio.

Answer:

3:25

Step-by-step explanation:

The photo shows how it's solved.

**Answer: 3:25**

**Step-by-step explanation:**

Step 1) Convert the decimal number to a fraction by making 0.12 the numerator and 1 the denominator

0.12 = 0.12/1

Step 2) Multiply the numerator and denominator by 100 to eliminate the decimal point.

0.12 x 100

------------ = 12/100

1 x 100

Step 3) Simplify the fraction in the previous step by dividing the numerator and the denominator by the greatest common factor (GCF) of 12 and 100. (The GCF of 12 and 100 is 4.)

12 ÷ 4

--------- = 3/25

100 ÷ 4

Step 4) Convert the fraction in the previous step to a ratio by replacing the divider line with a colon like this:

3

25 = 3:25

100 Points! Geometry question. Photo attached. Use the Pythagorean Theorem to find x. Please show as much work as possible. Thank you!

The **value** of x is,

⇒ x = 21.65

We have to given that,

A **right triangle** is shown in image.

Since, The **Pythagoras theorem **states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Hence, We get;

⇒ 25² = 12.5² + x²

⇒ 625 = 156.25 + x²

⇒ x² = 625 - 156.25

⇒ x² = 468.75

⇒ x = 21.65

Thus, The value of x is,

⇒ x = 21.65

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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

Angle C of the triangle **measures **68°.

**Side** AC = 22.90

**Side** BC = 14.26

**Given** triangle,

∠A = 37°

∠B = 75°

AB = 22

**Now**,

Sum of all the** interior **angles of triangle is 180.

**So**,

∠A + ∠B +∠C = 180°

37° + 75° + ∠C = 180°

∠C = 68°

Now,

**According** to sine rule,

**Ratio** of side length to the sine of the opposite angle is equal.

Thus,

a/SinA = b/SinB = c/SinC

**Let**,

BC = a

AC = b

AB = c

So,

a/Sin37 = b/Sin75 = c/Sin68

a/0.601 = b/0.965 = 22/0.927

**Solving**,

BC = a = 14.26

AC = b = 22.90

Thus with the properties of** triangle** side length and angles can be calculated.

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geometry worksheet find the measure of the arc or angle indicated

The value of the **measure **of the **arc **or **angle **indicated are,

⇒ m ∠DCE = 54°

⇒ m ∠MON = 53°

Now, We can simplify as,

4) As shown in figure,

m arc DE = 360° - (121° + 131°)

m arc DE = 360° - 252°

m arc DE = 108°

So, We get;

⇒ m ∠DCE = m DE / 2

⇒ m ∠DCE = 108 / 2

⇒ m ∠DCE = 54°

4) As **shown **in figure,

m arc MN = 360° - (109° + 145°)

m arc MN = 360° - 254°

m arc MN = 106°

So, We get;

⇒ m ∠MON = m MN / 2

⇒ m ∠MON = 106 / 2

⇒ m ∠MON = 53°

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For Exercises 24-29, find each value.

24. Sin x

25 cos x

26 tan x

27. Sin y

28. Cos y

29. Tan y

All the **values **of **expressions **are,

24. Sin x = 1/√17

25 cos x = 4/√17

26 tan x = 1/4

27. Sin y = 4/√17

28. Cos y = 1/√17

29. Tan y = 4

We have to given that,

A **right triangle **is shown in figure.

Now, We can simplify all the values,

24. Sin x = Opposite / Hypotenuse

sin x = 2 / 2√17

sin x = 1/√17

25) cos x = Base / **Hypotenuse**

cos x = 8 / 2√17

cos x = 4/√17

26) tan x = **Opposite **/ Base

tan x = 2 / 8

tan x = 1/4

27. Sin y = Opposite / Hypotenuse

sin y = 8 / 2√17

sin y = 4/√17

28. Cos y = Base / Hypotenuse

cos y = 2 / 2√17

cos y = 1/√17

29. Tan y = Opposite / Base

tan y = 8 / 2

tan y = 4

Thus, All the **values **of **expressions **are,

24. Sin x = 1/√17

25. cos x = 4/√17

26. tan x = 1/4

27. Sin y = 4/√17

28. Cos y = 1/√17

29. Tan y = 4

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Ochenta y nueve en número romano ??

**Answer:**

LXXXIX

**Step-by-step explanation:**

ochenta y nueve es 89.

89 en numero romano es LXXXIX.

50 Points! Multiple choice algebra question. Photo attached. Thank you!

**Answer:**

**B. 108 ft³**

**Step-by-step explanation:**

solution given:

**We have Volume of solid = Area of base * length**

over here

base : 9ft

height : 6 ft

length : 4ft

Now

Area of base : Area of traingle:½*base*height=½*9*6=27 ft²

Now

Volume : Area of base*length

Volume: 27ft²*4ft

Therefore **Volume of the solid=108 ft³**

Given the number pattern:

20; 18: 14; 8;

a) Determine the nth term of this number pattern.

b) Determine the value of T12 in this number pattern.

c) Which term in this number pattern will have a value of - 36?

A quadratic number pattern has a second term equal to 1, a third term equal to -6 and a fifth term equal to - 14.

a) Calculate the second difference of this quadratic number pattern.

b) Hence, or otherwise, calculate the first term of this number pattern.

**Answer:**

[tex]\textsf{a)} \quad T_n=-n^2+n+20[/tex]

[tex]\textsf{b)} \quad T_{12}=-112[/tex]

[tex]\textsf{c)} \quad \sf 8th\;term[/tex]

a) Second difference is 2.

b) First term is 10.

**Step-by-step explanation:**

The given** number pattern** is:

To determine the type of **sequence**, begin by calculating the** first differences** between consecutive terms:

[tex]20 \underset{-2}{\longrightarrow} 18 \underset{-4}{\longrightarrow} 14 \underset{-6}{\longrightarrow}8[/tex]

As the first differences are *not *the same, we need to calculate the **second differences** (the differences between the first differences):

[tex]-2 \underset{-2}{\longrightarrow} -4 \underset{-2}{\longrightarrow} -6[/tex]

As the **second differences** are the *same*, the **sequence **is **quadratic **and will contain an **n² term**.

The coefficient of the n² term is half of the second difference.

As the second difference is -2, the **coefficient **of the **n² term** is **-1**.

Now we need to **compare -n²** with the given **sequence **(where n is the position of the term in the sequence).

[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5}n&1&2&3&4\\\cline{1-5}-n^2&-1&-4&-9&-16\\\cline{1-5}\sf operation&+21&+22&+23&+24\\\cline{1-5}\sf sequence&20&18&14&8\\\cline{1-5}\end{array}[/tex]

We can see that the **algebraic operation** that takes -n² to the terms of the sequence is to **add (n + 20)**.

[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5}n&1&2&3&4\\\cline{1-5}-n^2&-1&-4&-9&-16\\\cline{1-5}+n&0&-2&-6&-12\\\cline{1-5}+20&20&18&14&8\\\cline{1-5}\sf sequence&20&18&14&8\\\cline{1-5}\end{array}[/tex]

Therefore, the **expression **to find the the **nth term** of the given **quadratic sequence** is:

[tex]\boxed{T_n=-n^2+n+20}[/tex]

To find the value of T₁₂, **substitute n = 12** into the nth term equation:

[tex]\begin{aligned}T_{12}&=-(12)^2+(12)+20\\&=-144+12+20\\&=-132+20\\&=-112\end{aligned}[/tex]

Therefore, the** 12th term **of the number pattern is **-112**.

To find the **position of the term** that has a value of -36, **substitute Tₙ = -36** into the **nth term equation** and **solve for n**:

[tex]\begin{aligned}T_n&=-36\\-n^2+n+20&=-36\\-n^2+n+56&=0\\n^2-n-56&=0\\n^2-8n+7n-56&=0\\n(n-8)+7(n-8)&=0\\(n+7)(n-8)&=0\\\\\implies n&=-7\\\implies n&=8\end{aligned}[/tex]

As the position of the term cannot be negative, the **term **that has a **value of -36** is the **8th term**.

[tex]\hrulefill[/tex]

Given **terms **of a **quadratic number pattern**:

We know the** first differences** are **negative**, since the difference between the second and third terms is -7. Label the unknown differences as -a, -b and -c:

[tex]T_1 \underset{-a}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-b}{\longrightarrow}T_4 \underset{-c}{\longrightarrow} -14[/tex]

From this we can create **three equations**:

[tex]T_1-a=1[/tex]

[tex]-6-b=T_4[/tex]

[tex]T_4-c=-14[/tex]

The **second differences** are the *same *in a **quadratic sequence**. Let the second difference be x. (As we don't know the sign of the second difference, keep it as positive for now).

[tex]-a \underset{+x}{\longrightarrow} -7\underset{+x}{\longrightarrow} -b \underset{+x}{\longrightarrow}-c[/tex]

From this we can create **three equations**:

[tex]-a+x=-7[/tex]

[tex]-7+x=-b[/tex]

[tex]-b+x=-c[/tex]

Substitute the equation for -b into the equation for -c to create an **equation for -c **in terms of x:

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

[tex]-c=2x-7[/tex]

Substitute the equations for -b and -c (in terms of x) into the second two equations created from the first differences to create** two equations for T₄ **in terms of x:

[tex]\begin{aligned}-6-b&=T_4\\-6-7+x&=T_4\\T_4&=x-13\end{aligned}[/tex]

[tex]\begin{aligned}T_4-c&=-14\\T_4+2x-7&=-14\\T_4&=-2x-7\\\end{aligned}[/tex]

**Solve for x** by equating the two equations for T₄:

[tex]\begin{aligned}T_4&=T_4\\x-13&=-2x-7\\3x&=6\\x&=2\end{aligned}[/tex]

Therefore, the **second difference** is **2**.

Substitute the found** value of x** into the equations for -a, -b and -c to find the **first differences**:

[tex]-a+2=-7 \implies -a=-9[/tex]

[tex]-7+2=-b \implies -b=-5[/tex]

[tex]-5+2=-c \implies -c=-3[/tex]

Therefore, the** first differences** are:

[tex]T_1 \underset{-9}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-5}{\longrightarrow}T_4 \underset{-3}{\longrightarrow} -14[/tex]

Finally, calculate the** first term**:

[tex]\begin{aligned}T_1-9&=1\\T_1&=1+9\\T_1&=10\end{aligned}[/tex]

Therefore, the **first term** in the number pattern is **10**.

[tex]10 \underset{-9}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-5}{\longrightarrow}-11 \underset{-3}{\longrightarrow} -14[/tex]

Note: The **equation** for the **nth term** is:

[tex]\boxed{T_n=n^2-12n+21}[/tex]

Taylor recorded Weekly grocery expense for the past 16 weeks and determine the mean weekly expense was $83.20 later she discovers that one week expense of $90 was incorrectly recorded at $38. What is the mean

The **mean **weekly expense, after correcting the incorrectly recorded week, is** $81.25.**

Given that Taylor recorded the past 16 weeks' expenses, excluding the incorrect **recording **of $90 as $38, we have 15 correct expense values.

**Sum of correct expenses** = $83.20 * 15 = $1248

Now we need to include the corrected expense of $90 instead of $38.

**New sum of expenses** = $1248 - $38 (incorrectly recorded) + $90 (corrected) = $1300

Finally, we calculate the **mean **by dividing the new sum by the total number of weeks, which is 16.

**Mean weekly expense **= $1300 / 16 = $81.25

Therefore, the **mean **weekly expense, after correcting the incorrect recording, is $81.25.

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For what value of x is the rational expression below undefined?

x-3

3+x

A. 3

OB. -1

O C. 0

OD. -3

**Answer:**

x= -3

**Step-by-step explanation:**

x-3

-----------

x+3

This **expression is undefined** when the denominator is zero.

x+3 =0

x= -3

The centre of a circle is the point with coordinates (-1, 2)

The point A with coordinates (5, 9) lies on the circle.

Find an equation of the tangent to the circle at A.

Give your answer in the form ax + by + c = 0 where a, b and c are integers.

The **equation **of the **tangent **to the **circle **at point A is 6x + 7y - 93 = 0

The **equation **of a **circle** in standard form is (x-h)² + (y-k)² = r²,

(h,k) is the center of the circle

r is the radius.

The **radius **formula ⇒ **√((x₂ - x₁)² + (y₂ - y₁)²).**

Here,

x₁ = -1, y₁ = 2 (center of the circle),

x₂ = 5, y₂ = 9 (point A on the circle).

∴

r = √((5 - (-1))² + (9 - 2)²) = √(36 + 49) = √85.

Now, we have the equation of the circle: (x - (-1))² + (y - 2)² = 85, or (x + 1)² + (y - 2)² = 85.

The slope of the radius from the center of the circle to point A ⇒ (y₂ - y₁) / (x₂ - x₁)

= (9 - 2) / (5 - (-1)) = 7/6.

**tangent line** is the negative reciprocal of the slope of the radius, ∴ -6/7.

The equation of a line in **point-slop**e form is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.

The slope of the tangent line (m) is -6/7 and it passes through point A(5,9). Substituting these values in, it becomes

y - 9 = -6/7 (x - 5).

Multiplying every term by 7 to clear out the fraction and to have the equation in the ax + by + c = 0 form, we get:

7y - 63 = -6x + 30,

or

6x + 7y - 93 = 0.

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A truck travels from warehouse A at (–4,8) to warehouse B at (–4,–1). If each unit represents 20 miles per hour, how long will it take the truck to travel this distance?

It will take the truck 9 **hours **to travel from warehouse A to warehouse B.

To determine the time it takes for the truck to **travel **from warehouse A at (-4, 8) to warehouse B at (-4, -1), we need to calculate the distance between these two points and then convert it to time using the given unit of 20 miles per hour.

First, let's find the vertical **distance **between the two points. The y-coordinate of warehouse A is 8, and the y-coordinate of warehouse B is -1. So the vertical distance is 8 - (-1) = 9 units.

Next, we **convert** the vertical distance to miles. Since each unit represents 20 miles per hour, we multiply the vertical distance by 20: 9 units × 20 miles/unit = 180 miles.

Now, we can calculate the time it takes to travel this distance. We divide the distance by the **speed **of the truck, which is 20 miles per hour: 180 miles / 20 miles per hour = 9 hours.

Therefore, it will take the truck 9 hours to travel from **warehouse **A to warehouse B.

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(02.02 MC)

If trapezoid ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A′′′ lie?

Trapezoid formed by ordered pairs A at negative 4, 1, B at negative 3, 2, C at negative 1, 2, D at 0, 1.

(1, −1)

(−4, 1)

(1, 1)

(−4, −1)

The **location **of point A''' after the three **transformations** would be (-4, 1).

To determine the location of point A''', we need to apply the three **transformations** (reflection over the y-axis, reflection over the x-axis, and rotation of 180°) to point A.

When a point is reflected over the y-axis, the x-coordinate is negated while the y-coordinate remains the **same**.

So, the reflection of point A (-4, 1) over the y-axis would be (4, 1).

When a point is **reflected** over the x-axis, the y-coordinate is negated while the x-coordinate remains the same. So, the reflection of point (4, 1) over the x-axis would be (4, -1).

When a point is rotated 180°, the x-coordinate and y-coordinate are both negated. So, the rotation of point (4, -1) by 180° would be (-4, 1).

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Multiply the following binomials (2x - 3y)(8x - y)

**Answer:**

16x + [tex]3y^{2}[/tex] - 26xy

**Step-by-step explanation:**PEMDAS

(2x - 3y)(8x - y)

= 16x - 2xy - 24xy + [tex]3y^{2}[/tex]

= 16x + [tex]3y^{2}[/tex] - 26xy

which table does not show y as a function of x?

**Answer:**

I am confident the answer is H.

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