Simplify x^2+3x+2/x+1

A. X+2
B. X-2
C. X^2+1
D. X^2-1

they use 12 oranges

4•4=16-4=12 which is 3 of the 4/4

The fraction 3/4 of 16 will be the number of oranges and it will be the 12 oranges.

In such a fraction, the value that appears above the horizontal line is referred to as the numerator.

In another word, the fraction is the division of the two numbers but the division is not wholly complete.

As per the given,

They make orange juice using 3/4 of the oranges.

3/4 of 16

(3/4)16 = 3 x 4 = 12 oranges

Hence "The fraction 3/4 of 16 will be the number of oranges and it will be the 12 oranges".

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Answer:

a) C

b) A

Step-by-step explanation:

The wingspan is the dependent variable while the bird height is the independent variable.

a) Since R2 is the dependent variable, it can be expressed by the independent variable. An R2 of 93% represents 93% of the variation in the wingspan which can be explained by using the birds height. This means that the appropriateness of the model should not be determined by R2 but by using a scatter plot.

b) The model predicts the value of wingspan using the value of bird height. We cannot say that the bird 10 inches tall has a wingspan if 17 inches instead, we say that the wingspan of the bird which is 10 inches tall is 17 inches.

It is therefore possible that the wing span is not exactly 17 inches

Final answer:

The R2 value does not indicate the appropriateness of the model, and regression models provide predictions, not actual values.

Explanation:

A. R2 is an indication of the nonlinearity of the model, not the appropriateness of the model. A regression line is the indicator of an appropriate model.

A bird 10 inches tall will have a wingspan of 17 inches.

A. Regression models give predictions, not actual values. The student should have said, "The model predicts that a bird 10 inches tall is expected to have a wingspan of 17 inches."

The maximum possible width of the fence is 7.5 feet.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Let's start by assigning variables to the length and width of the fence.

Let x be the width of the fence in feet, then the length of the fence is x + 10 feet

(since the length is at least 10 feet longer than the width).

Now,

The perimeter of the fence is the sum of the lengths of all its sides.

Since the fence has four sides of equal length,

The perimeter is 4 times the length of one side.

So,

The equation for the perimeter, P, in terms of x.

P = 4(x + x + 10)

  = 8x + 40

Now,

We know that Jake wants the perimeter to be no more than 100 feet,

So we can write an inequality:

8x + 40 ≤ 100

Solving for x:

8x ≤ 60

x ≤ 7.5

Therefore,

The maximum possible width of the fence is 7.5 feet.

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Final answer:

To find the maximum width for Jake's fence with the given constraints, set up inequalities with the perimeter and length requirements. Solving for the width, we find that the maximum possible width Jake can use is 20 feet.

Explanation:

Jake is constructing a fence around his property and wishes for the perimeter to not exceed 100 feet, while the length must be at least 10 feet longer than the width. Let's denote the width of the property as w and the length as l. According to the constraints:

The perimeter (2w + 2l) ≤ 100 feet

The length (l) ≥ w + 10 feet

Using these inequalities, we have:

2w + 2(w + 10) ≤ 100

2w + 2w + 20 ≤ 100

4w ≤ 80

w ≤ 20

The maximum possible width is therefore 20 feet.

Answer:

(a) The ONLY explicit rule for the nth term of the sequence is [tex]a_n = 7  \times (-1)^{n-1}\\[/tex].

Step-by-step explanation:

Here, the given sequence is 7, -7, 7, -7, ...

The first term = 7, Second term = -7, Third term =-7 and so on..

Now check the given sequence for each given formula, we get:

(1)  [tex]a_n = 7  \times (-1)^{n-1}\\[/tex]

Now, for n = 1 : [tex]a_1 = 7  \times (-1)^{1-1}\\[/tex]

                                       [tex]= 7 \times (-1)^0 =  7 \times 1 = 7 \implies a_1 = 7[/tex]

Similarly, for, n = 2:  [tex]a_2 = 7  \times (-1)^{2-1}\\[/tex]

                                       [tex]= 7 \times (-1)^1 =  7 \times (-1) = -7 \implies a_2 = -7[/tex]

Hence, the given formula satisfies the given sequence.

(2)  [tex]a_n = 7  \times (-1)^{n}\\[/tex]

Now, for n = 1 : [tex]a_1 = 7  \times (-1)^{1}\\[/tex]

                                       [tex]= 7 \times (-1)^1 =  7 \times (-1) = -7 \implies a_1 = -7[/tex]

But, First term = 7

Hence, the given formula DO NOT satisfy the given sequence.

(3)  [tex]a_n = 7  \times (1)^{n-1}\\[/tex]

Now, for n = 1 : [tex]a_1 = 7  \times (1)^{1-1}\\[/tex]

                                       [tex]= 7 \times (1)^0 =  7 \times 1 = 7 \implies a_1 = 7[/tex]

Similarly, for, n = 2:  [tex]a_2 = 7  \times (1)^{2-1}\\[/tex]

                                       [tex]= 7 \times (1)^1 =  7 \times (1) = 7 \implies a_2 = 7[/tex]

But, Second term = -7

Hence, the given formula DO NOT satisfy the given sequence.

(4) [tex]a_n = 7  \times (1)^{n+1}\\[/tex]

Now, for n = 1 : [tex]a_1 = 7  \times (1)^{1+1}\\[/tex]

                                       [tex]= 7 \times (1)^2 =  7 \times 1 = 7 \implies a_1 = 7[/tex]

Similarly, for, n = 2:  [tex]a_2 = 7  \times (1)^{2+1}\\[/tex]

                                       [tex]= 7 \times (1)^3 =  7 \times (1) = 7 \implies a_2 = 7[/tex]

But, Second term = -7

Hence, the given formula DO NOT satisfy the given sequence.

So, the ONLY explicit rule for the nth term of the sequence is [tex]a_n = 7  \times (-1)^{n-1}\\[/tex].

Answer:

an=7•(-1)^n-1

Step-by-step explanation:

Answer:

0.0421

Step-by-step explanation:

Mean(μ) = 12.00 oz

Standard deviation (σ) = 0.11 oz

Z = (x - μ)/σ

Z = (12.19 - 12.00) / 0.11

Z= 0.19/0.11

Z = 1.727

From the normal distribution table, Z = 1.727 = 0.4579

Φ(Z) = 0.4579

Recall that if Z is positive

Pr(x>a) = 0.5 - Φ(Z)

Pr(x > 12.19) = 0.5 - 0.4579

= 0.0421

Answer:

the answer is 17.7

Step-by-step explanation:

Apply tanθ =  

opposite

adjacent

tanθ =  

7

22

θ = tan−1(

7

22

)

θ = 17.7°

The angle the ladder that will make with the wall is 17.7°.

What is tangent of an angle?

Tangent of the angle is the ratio between the opposite side and adjacent side of the angle in the right angle triangle.

So according to the asked question,

the distance between lader foot and the wall  is 7feet.

the height of the wall is 22feet.

So in triangle ΔABC ,

the height of the wall =AB=22feet

the distance between lader foot and the wall=BC=7feet

∠ABC=90°

the angle between the ladder and the wall= ∠BAC=θ

So in ΔABC,

tan ∠BAC=tan θ=BC/AB

⇒tan θ=7/22

⇒θ=tan⁻¹(7/22)

⇒θ=17.7⁰

Therefore the angle the ladder that will make with the wall is 17.7°.

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The inclination angle is 10°

Step-by-step explanation:

The given scenario forms a right angled triangle where the length of ramp is hypotenuse and the rise of ramp is the perpendicular

Given

H = 4.2m

P = 0.7m

We have to use the trigonometric ratios to find the angle. The ratio that has to be used should involve both perpendicular and hypotenuse

Let x be the angle

then

[tex]sin\ x = \frac{P}{H}\\sin\ x = \frac{0.7}{4.2}\\sin\ x = 0.1666\\x = sin^{-1} (1.666)\\x = 9.59 => 10[/tex]

Hence,

The inclination angle is 10°

Keywords: Trigonometric ratios, Right angled triangle

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The angle of inclination of the wheelchair ramp to the nearest degree is 9 degrees.

[tex]\[ \theta = \arctan\left(\frac{\text{rise}}{\text{run}}\right) \][/tex]

Given the rise of the ramp is 0.7 m and the run (length) is 4.2 m, we can plug these values into the formula:

[tex]\[ \theta = \arctan\left(\frac{0.7}{4.2}\right) \][/tex]

Now, we calculate the value of θ:

[tex]\[ \theta = \arctan\left(\frac{1}{6}\right) \][/tex]

Using a calculator, we find:

[tex]\[ \theta \approx \arctan(0.1667) \] \[ \theta \approx 9.4623 \text{ degrees} \][/tex]

Rounding to the nearest degree, we get:

[tex]\[ \theta \approx 9 \text{ degrees} \][/tex]

Therefore, the angle of inclination of the wheelchair ramp is approximately 9 degrees to the nearest degree.

Answer:

C

Step-by-step explanation:

Rearranging x - y ≤ 2

- y ≤ 2 - x ( multiply through by - 1 )

y ≥ - 2 + x ← change direction of inequality symbol

This region is above the yellow line

y ≥ 0 is above the x- axis

x ≥ 0 is to the right of the y- axis

Thus the solution is the indicated blue region

The inequalities from C satisfy the given graph

Answer:

No real roots

Step-by-step explanation:

The given quadratic equation is

[tex] {x}^{2} + 5x + 7 = 0[/tex]

Comparing this to the general quadratic equation:

[tex]a {x}^{2} + bx + c = 0[/tex]

We have a=1, b=5 and c=7

Recall that the discriminant is

[tex]D = {b}^{2} - 4ac[/tex]

We plug in the values to get:

[tex]D = {5}^{2} - 4(1)(7)[/tex]

[tex]D =25- 28 = - 3[/tex]

Since the discriminant is less than zero, the given equation has no real roots

To find the probability of both Alex and Bob winning at least 2 games during their 5 games chess play, principles of geometric probability and the Multiplication rule are used. The equation _(p^2)*(5 choose 2)*((p/3)^2)*(5 choose 2)*[(p+(p/3))] is formed considering Alex is 3 times more likely to win than Bob.

Calculating Probability of Games

In this scenario, Alex and Bob are playing 5 games with Alex being 3 times more likely to win than Bob. The primary question is to find the probability for both of them winning at least 2 games.

We would utilize the principles of geometric probability to solve this. Geometric probability treats each game as a Bernoulli trial, a game of win or lose. Moreover, we operate with the Multiplication rule in finding the probability of both events, Alex and Bob winning 2 games, happening.

Firstly, we define the probability of Alex winning as p, therefore, the probability of Bob winning is p/3. Bob and Alex must win 2 games each, leaving one game open to any outcome. Since the games are independent, the Multiplication rule applies. Therefore, the probability is calculated by multiplying probabilities for each win and possible combinations of five games taken two at a time. In other words, the equation will look like  _(p^2)*(5 choose 2)*((p/3)^2)*(5 choose 2)*[(p+(p/3))].

The resulting value will be the probability for both of them winning at least 2 games.

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Answer:

Step-by-step explanation:

Suppose you drive a car 392 miles on one tank of gas. The tank holds 14 gallons of gas. This means that

1 gallon of gas would be used to drive 392/14 = 28 miles

a) The number of miles traveled varies directly with the number of gallons of gas used.

Let x =number of gallons of gas you use.

Let y = the number of miles travelled.

Since y varies directly with x, we will introduce a constant of proportionality, k. Therefore,

y = kx

If 28 miles will require 1 gallon of gas, it means

28 = 1×k

k = 28

So y = 28x

b) we want to determine how far you can drive with 3.7 gallons of gas.

x = 3.7

y = 28x = 28×3.7

y = 103.6 miles

Answer: (D) 3.21

Step-by-step explanation:

Let [tex]t_A=[/tex] Time taken by one outlet to fill the pool.

[tex]t_B=[/tex]Time taken by second outlet to fill the pool.

Given : The time taken by one outlet to fill the entire pool : [tex]t_A=[/tex] 9 hours

The time taken by second outlet to fill the entire pool : [tex]t_B=[/tex] 5 hours

Now , if both outlets are used at the same time, approximately what is the number of hours required to fill the pool (T) , then the time required to fill the pool will be :_

[tex]\dfrac{1}{T}=\dfrac{1}{t_A}+\dfrac{1}{t_B}\\\\\Rightarrow =\dfrac{1}{T}=\dfrac{1}{9}+\dfrac{1}{5}\\\\\Rightarrow\ \dfrac{1}{T}=\dfrac{9+5}{(9)(5)}=\dfrac{14}{45}\\\\\Rightarrow\ T=\dfrac{45}{14}=3.21428571429\approx3.21[/tex]

Hence, the approximate time taken by both outlets to fill the pool together = 3.21 hours.

Thus , the correct option is  (D) 3.21

The question is about rate, time and work. Using the given rates of the outlets, we determine the combined rate. We then use the time = work/rate formula to calculate the time it would take for both outlets to fill the pool, which comes out to approximately 3.21 hours.

This question is a typical problem in rate time and work, which is a common topic in mathematics especially algebra. The problem talks about two outlets with different rates filling a pool.

Let's consider the rate of the first outlet as 1/9 pool/hour and the second outlet as 1/5 pool/hour. If both outlets are working at the same time, their rates would add up. Hence, the combined rate would be 1/9 + 1/5 = 14/45 pool/hour.

To find how long it would take for both outlets to fill the pool, we use the equation time = work/rate. Plugging in our values, we get time = 1 pool / 14/45 pool/hour. Therefore, the time is amounts to approximately 3.21 hours.

Therefore, "the correct answer is (D) 3.21".

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Answer:

Step-by-step explanation:

g(-2)=2(-2)^3+3(-2)^2-3(-2)+4=-16+12+6+4=6

g(-1)=2(-1)^3+3(-1)^2-3(-1)+4=-2+3+3+4=8

it does  not change sign ,so there is no real zero between -2 and -1.

Answer:

B) The sample size was 100

Step-by-step explanation:

Number of sample size in January = 100

Number of sample size in March   = 100

Number of sample size in June     = 100

Number of sample size in  September = 100

The average sample size for the study = (100 +100+100+100)/4  

                                                                =  400/4

                                                                = 100

So the average sample size for the study is 100 women between 18 to 21 years.

Answer:

15.5 yards

They will be picked up at an elevation of 15.5 yards

Step-by-step explanation:

Here we are going to make the ski slope of the mountain as the hypotenuse of a right-angled triangle where the top of the slope and bottom of the slope are two ends of the hypotenuse.

We first have to find the height of the top of the mountain with respect to the bottom.

Here we have been given heights with respect to sea level above and below.

Clearly, sum of the distances above and below sea level will be total elevation with respect to the bottom.

h1 - Height of summit above sea level

h2 - Height of bottom below sea level

Hb - Elevation of top w.r.t bottom

Hb = h1 + h2

Hb = [tex]17\frac{3}{4}+13\frac{1}{4}[/tex]

Hb = 31 yards

Now, the ski lift is picking them up in the middle of the slope (hypotenuse of the triangle).

By midpoint theorem line segment parallel to base joins the midpoints of the other 2 sides.

Thus the elevation will clearly be half of total elevation.

Height at which they are picked up is Hb/2

Therefore,

They will be picked up at an elevation of 15.5 yards

Answer:

Option C.

Step-by-step explanation:

Let x represent the number of loaves of pumpkin bread and y represent the number of loaves of zucchini bread Susan bakes.

              Pumpkin bread           zucchini bread                Total

Eggs               2                                     3                           15        

Flour(cups)     3                                     4                           16

Selling price    $5                                  $4

Susan wants to maximize the money raised at the bake sale.

Objective function :

[tex]P=5x+4y[/tex]

Subject to constraints:

[tex]2x+3y\leq 15[/tex]

[tex]3x+4y\leq 16[/tex]

[tex]x,y \geq 0[/tex]

Since the objective function is P = 5x + 4y, therefore the correct option is C.

Answer:

c

Step-by-step explanation:

i got it correct on edgenunity

Answer:

Step-by-step explanation:

The relation between speed, time, and distance is ...

  speed = distance/time

Against the wind, the speed is ...

  (3310 mi)/(5 h) = 662 mi/h

With the wind, the speed is ...

  (3810 mi)/(5 h) = 762 mi/h

The jet stream adds to the speed in one direction, and subtracts in the other direction, so the difference in travel speeds is twice the speed of the jet stream:

  (762 mi/h -662 mi/h)/2 = jet stream speed = 50 mi/h

__

The speed of the plane is the average of the two speeds, or the sum of jet stream speed and the lower speed, or the difference of the higher speed and the jet stream speed. Any of these calculations will give the plane's speed in still air:

  (762+662)/2 = 662 +50 = 762 -50 = 712 . . . mi/h

Answer:

x = 7.8

Step-by-step explanation:

If AE is parallel to BD, then you can use the theorem called ratio of sides of parallel line.

AC/AB = EC/ED

x+11/x = 12/5

x=7.8

Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. The length of the unknown sides will be equal to 7.857 units.

Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. It is denoted by the symbol "~".

For the two similar triangles, ΔAEC and ΔBDC, the ratio of the sides will be,

11/7 = (11+x)/(5+7)

11/7 = (11+x)/12

(11×12)/7 = 11+x

18.857 - 11 = x

x = 7.857

Hence, the length of the unknown sides will be equal to 7.857 units.

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Answer:

The answer to your question is Stacy multiplies the second equation by 4.

Step-by-step explanation:

                                             24x - 39y = 165    (I)

                                             - 6x + 13y = -51     (II)

Multiply the second equation by 4

                                             24x -    39 y = 165

                                           -24x  +   52y  = -204  

Simplify

                                              0    +  13y = 39

                                                           y = 39/ 13

                                                           y = 3

Find "x" value                       24x - 39(3) = 165

                                             24x - 117 = 165

                                             24x = 165 + 117

                                             24x = 282

                                                 x = 282 / 24

                                                 x = 47/4

Answer:

y-intercept: when x = 0

For Line A:

y = 0 + 7 = 7

For line B:

when x = 0, the value is -5

7 > -5, so y-intercept of line A is greater than line B's.

Answer:

test statistic (Z) is 2.5767 and p-value of the test is .009975

Step-by-step explanation:

[tex]H_{0}[/tex]: percentage of students who smoke did not change

[tex]H_{a}[/tex]: percentage of students who smoke has changed

z-statistic for the sample proportion can be calculated as follows:

z=[tex]\frac{p(s)-p}{\sqrt{\frac{p*(1-p)}{N} } }[/tex] where

Then, z=[tex]\frac{0.25-0.18}{\sqrt{\frac{0.18*0.82}{200} } }[/tex] ≈ 2.5767

What is being surveyed is if the percentage of students who smoke has changed over the last five years, therefore we need to seek two tailed p-value, which is .009975.

This p value is significant at 99% confidence level. Since .009975 <α/2=0.005, there is significant evidence that the percentage of students who smoke has changed over the last five years

Answer:

[tex]p(x)= -\frac{1}{10}x + 685[/tex]

Step-by-step explanation:

Since, Function of demand is the linear function of quantity.

Let x represents the quantity and p represents the price of each unit.

∵ Manufacture has been selling 1450 television sets a week at $540 each,

i.e. [tex](x_1, p_1) = (1450, 540)[/tex]

Also, for each $13 rebate offered to a buyer, the number of sets sold will increase by 130 per week.

i.e. [tex](x_2, p_2) = (1580, 527)[/tex]

Thus, the linear equation of the price,

[tex]p-p_1 = \frac{p_2-p_1}{x_2-x_1}(x-x_1)[/tex]

[tex]p-540 = \frac{527 - 540}{1580-1450}(x-1450)[/tex]

[tex]p-540 = -\frac{13}{130}(x-1450)[/tex]

[tex]p-540 = -\frac{1}{10}(x-1450)[/tex]

[tex]p = -\frac{1}{10}x + 145 + 540[/tex]

[tex]\implies p = -\frac{1}{10}x + 685[/tex]

Hence, the function representing price as a function of the demand is,

[tex]p(x)= -\frac{1}{10}x + 685[/tex]

For this case we have the following arithmetic sequence:

[tex]a_ {n} = 15 + 5 (n-1)[/tex]

To write in function form, we apply distributive property to the terms within parentheses:

[tex]f (n) = 15 + 5n-5[/tex]

Different signs are subtracted and the major sign is placed.

We simplify:

[tex]f (n) = 5n + 10[/tex]

Answer:

[tex]f (n) = 5n + 10[/tex]

Option C

The explicit formula for the arithmetic sequence an=15+5(n−1) in function form is f(n)=5n+10.

The explicit formula for the arithmetic sequence an=15+5(n−1) in function form is f(n)=5n+10 (Option C).

The arithmetic sequence is represented as an=15+5(n−1). This equation can be further simplified to an=15+5n-5, which eventually gives us an=5n+10. So the explicit formula for this arithmetic sequence in function form is option C, which is f(n)=5n+10. This function f(n), directly gives us the nth term of the arithmetic sequence.

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Answer:

Cube.

Step-by-step explanation:

We are asked to find the solid figure, which has congruent squares on all six sides.

We know that a solid, whose length, width, and height are equal in measure is known as cube.

Upon looking at our attached file, we can see that length, width, and height for the solid are equal to x units, which makes its each face a square.

We know that a cube is a three dimensional figure, which contains six equal squares of all six sides.

Therefore, cube has congruent squares on all six sides.

Answer:

Step-by-step explanation:

Total number of students: 33 +47 +37 = 117 students

Students in 9th class = 37

So probabilty of selecting a 9th class student from a class of 117 students is:

=>(Total student in 9th class)/(Total student in the sample)

=>37/117 =>Ans

To find the probability of selecting a ninth-grade student from a school population, divide the number of ninth-grade students by the total population.

To find the probability that a randomly selected student is in the ninth-grade, we need to calculate the fraction of ninth-grade students out of the total population of students. Here's how:

The probability that the randomly selected student is in the ninth-grade is approximately 0.316, or 31.6%.

Answer:

$9.50

Step-by-step explanation:

Solution is in the attachment . You can see it.

Answer:

a) 80 ibs

b) 40 ibs

Step-by-step explanation:

Let X be the pound of the high quality bean at $6.50

(120-x) will be the pound of the cheaper bean at $2.50

6.5x + 2.5(120 - x) = 5.17(120)

6.5x + 300 - 2.5x = 620.4

Collect like terms

6.5x - 2.5x = 620.4 - 300

4x = 320.4

x = 320.4/4

x= 80.1

x = 80 ibs(to the nearest pounds)

For the cheaper bean we have 120 -x

= 120 - 80

= 40 ibs

Sarah would blend 80 ibs of quality bean and 40 ibs of cheaper bean

Sarah should blend 80 pounds of high quality beans and 40 pounds of cheaper beans to achieve her target blend of 120 pounds at $5.17 per pound.

Sarah Meeham needs to blend high quality and cheaper coffee beans to create a blend selling for $5.17 per pound, using a total of 120 pounds. Let x be the pounds of high-quality beans and 120 - x be the pounds of cheaper beans. Setting up the equation for the total cost of the blend, we have:

6.50x + 2.50(120 - x) = 5.17 \\times 120

Solving for x, we get:

6.50x + 300 - 2.50x = 620.4

4x = 320.4

x = 80.1

To the nearest pound, Sarah should blend 80 pounds of high quality beans and 120 - 80 = 40 pounds of cheaper beans.

Answer: The inner diameter of the ring is 16 mm.

Step-by-step explanation:

As we know that ,

Circumference of a circle = [tex]\pi d[/tex] , where d = diameter of the circle .

We are given that ,

The circumference of the outside of a ring is 66 mm and it has an outer diameter of 21 mm .

Now , if circumference of the inside the ring is 50 mm, then we have

[tex]50 = \pi d[/tex] , where d= diameter of the inner circle .

Then , [tex]d=\dfrac{50}{\pi}=\dfrac{50}{\dfrac{22}{7}}=\dfrac{50\times7}{22}\approx15.909090909\approx16\text{ mm}[/tex]

Hence , the inner diameter of the ring is 16 mm.

The diameter of the inner ring is 15.92mm

The formula for calculating the circumference of a circle is expressed as:

C = πd

d is the diameter

Given the following parameters

C = 50mm

The diameter of the inner ring is given as:

d = C/π

d = 50/3.14
d = 15.92mm

Hence the diameter of the inner ring is 15.92mm

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Answer:

3. [tex]\displaystyle 1\frac{1}{3} = x[/tex]

2C. [tex]\displaystyle III.[/tex]

2B. [tex]\displaystyle I.[/tex]

2A. [tex]\displaystyle II.[/tex]

1. [tex]\displaystyle Set-Builder\:Notation: [x|7, 0 ≠ x] \\ Interval\:Notation: (-∞, 0) ∪ (0, 7) ∪ (7, ∞)[/tex]

Step-by-step explanation:

3. See above.

2C. The keyword is ratio, which signifies division, so you would choose "III.".

2B. The keyword is percent, which signifies multiplication of a ratio by 100, so you would choose "I.".

2A. The keyword is total, which signifies addition, so you would choose "II.".

1. Base this off of the denominator. Knowing that the denominator CANNOT be zero, you will get this:

[tex]\displaystyle x^2 - 7x \\ x[x - 7] = 0; 7, 0 = x \\ \\ Set-Builder\:Notation: [x|7, 0 ≠ x] \\ Interval\:Notation: (-∞, 0) ∪ (0, 7) ∪ (7, ∞)[/tex]

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We found the domain restrictions of a rational expression by checking the values that make the denominator zero. A formula was suggested to calculate Sara's future percentage score. To solve the third equation, a common denominator was found and used to simplify the expression.

1. The domain restrictions for the rational expression 14x-2x/x^2-7x are all real numbers except for the numbers which make the denominator zero. Solving the equation x^2-7x=0, we get x=0 or x=7. Therefore, the domain restrictions are x≠0 and x≠7.

2. There is no picture provided but generally, to calculate the future percentage score given the current percentage score, total points possible, and future total points, you would use the formula (current score/current total points) * 100% + (future score/future total points) * 100%.

3. To solve for x in the equation 3 / (x+2) - 1 / x = 1 / (5x), we first need to find a common denominator. In this case, it would be 5x^2 + 10x. Multiplying each term by the common denominator and simplifying would then give the value of x.

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m=16t can be used to determine the distance in miles Han has gone after t hours.

Step-by-step explanation:

Speed of Han = 16 miles per hour

Let,

m be the distance covered by Han in miles;

t be the number of hours Han has been biking,

According to formula,

Distance = Speed*Time

[tex]m=16*t\\m=16t[/tex]

m=16t can be used to determine the distance in miles Han has gone after t hours.

Keywords: distance, speed

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Answer:

y = mx + b ( y = 16t + 0

Step-by-step explanation: