p(x)=x⁴-2x³+2x²-3x+6 to (x-1)​

The error Justin made in his calculation is "He should have added the values in the numerator before dividing by 2".

The correct answer choice is option B

(x + y + 5) / 2

Where,

x and y are his parents’ current heights in inches,

Mom’s height = 54 inches

Dad’s height = 71 inches

Substitute into the expression

(71 + 54 + 5) / 2

= 130/2

= 65 inches

Justin's work:

( 71 + 54 + 5 ) / 2

= 71 + 27 + 5

= 103 inches

Therefore, Justin should have added the numerators before dividing by 2.

Read more on expressions:

https://brainly.com/question/1859113

#SPJ1

Answer:

b

Step-by-step explanation:

Answer:

Where is the number line?? ;-;

Step-by-step explanation:

Dude I cant answer if you dont show me the number lines

→ the lenght = 13 square units

→ the width = 2 square units

→ the area of the rectangle = 13×2 = 26 square units

→ the area of the triangle = 26 : 2 = 13 square units

Answer:

Step-by-step explanation:

you would copy and paste another triangle on top to form a rectangle. That would make the rectangle's length 13 units and its width 2 units. the area of a rectangle is found by A=length x width which in this case is 26 units^2. A single triangle's area is 1/2 the area of the rectangle making it 26/2 which is 13.

So the area of the triangle is 13 units^2.

Both the pairs of opposite sides in a parallelogram are parallel and congruent.

According to the question,

We've proved that one pair of sides in parallelogram must be congruent

Let ABCD is a parallelogram ,

We know that AB // CD

Here, AC is transversal for the parallel lines AB and CD

So, ∠BAC = ∠DCA    (Using interior angle property) --------(1)

Similarly , We also know that BC // AD

=> ∠BCA = ∠DAC -----------(2)

Now , In ΔABC and ΔADC,

Therefore , ΔABC ≅ ΔADC    (as per ASA congruence rule)

Therefore , AB = CD and BC=AD   (Corresponding sides of congruent triangles are equal)

Hence , Both the pairs of opposite sides in a parallelogram are parallel and congruent.

To know more about parallelogram here

https://brainly.com/question/1563728

#SPJ4

It is accurate to say that Jayla biked the same speed but in the opposite direction as Sarah and Justin if they all cover the same distance at a given time.

Speed is used to measure the rate at which an object moves. The speed is based in the distance covered and the time used.

An individual may bike the same speed but in different direction if the time and distance covered is the same. But when there is a disparity, it not safe to say they run or bike the same speed.

To know if the bike the same speed, both Jayla, Sarah and Justin speed should be computed.

Therefore, It is accurate to say that Jayla biked the same speed but in the opposite direction as Sarah and Justin if they all cover the same distance at a given time.

Learn more on speed below

https://brainly.com/question/4931057

#SPJ1

The probability that it will not be orange is 0.9

What is probability?

Probability is the branch of mathematics concerning numerical descriptions of how probably an event is to do, or how likely it's that a proposition is true.

given:

There are:

5 pink marbles

9 green marbles,

13 blue marbles, and

3 orange marbles.

There is a total of 30 marbles in the jar.

Step 1. Take 1 marble from the jar.

Step 2. Probability that it is orange, = P(orange) = ( 3/30 ) = ( 1/10 ) = 0.10 = 10%

Step 3. Probability that the chosen marble is not orange, = ( 1 - Probability that the chosen marble IS orange) = ( 1 - 0.1 ) = 0.9 = 90%.

hence , the probability that it will not be orange is 0.9

to know more about probability , visit:

https://brainly.com/question/24756209

#SPJ4

The explicit formula for f^-1 is (x-3)^(1/4) and this is obtained by switching the roles of x and y and solving for y in terms of x.

To find the inverse function of f(x)=x^4+3, we need to switch the roles of x and y, and solve for y.
Let y = x^4+3
Subtract 3 from both sides to get:
y - 3 = x^4
Take the fourth root of both sides to isolate x:
(x^4)^(1/4) = (y-3)^(1/4)
Simplify:
x = (y-3)^(1/4)
So the inverse function of f(x) is:
f^-1 (x) = (x-3)^(1/4)
This is the explicit formula for the inverse function of f(x).
To know more about explicit formula visit:

https://brainly.com/question/18069156

#SPJ11

The derivative of the function f(x) = ln(14 - e^(-2x)) is f'(x) = [4xe^(-2x)] / [e^(2x) - 14].

The derivative of the function f(x) = ln(14 - e^(-2x)) is given by:

f'(x) = [1/(14 - e^(-2x))] * [-2e^(-2x)]

To simplify this expression, we can factor out a -2 from the numerator:

f'(x) = [-2/(14 - e^(-2x))] * [e^(-2x)]

Now, we can use the chain rule to differentiate the second factor:

f'(x) = [-2/(14 - e^(-2x))] * [-2x e^(-2x)]

Simplifying further, we get:

f'(x) = [4xe^(-2x)] / [e^(2x) - 14]

Therefore, the derivative of f(x) is f'(x) = [4xe^(-2x)] / [e^(2x) - 14].

For more questions like Function click the link below:

https://brainly.com/question/12431044

#SPJ11

The intensity of excercise increases the heart rate, that is, more intensity the excersice, greater the heart rate.

It means that there is a positive correlation between int

the probability of choosing exactly 5 red marbles when 12 marbles are chosen at random is approximately 0.028.

This is a hypergeometric probability problem .

The total number of ways to choose 12 marbles from 27 is:

${{27}\choose{12}} = \frac{27!}{12!15!} = 10,!626,!766$

The number of ways to choose 5 red marbles and 7 blue marbles is:

$ {{15}\choose{5}}\cdot{{12}\choose{7}} = \frac{15!}{5!10!}\cdot\frac{12!}{7!5!} = 300,!450$

So the probability of choosing exactly 5 red marbles is:

$P(\text{5 red}) = \frac{300,!450}{10,!626,!766} \approx 0.028$

what is probability?

Probability is the measure of the likelihood or chance of an event occurring. It is a quantitative measure that ranges from 0 to 1, where 0 indicates an impossible event and 1 indicates a certain event.

To learn more about probability visit:

brainly.com/question/30034780

#SPJ11

The length of the deep end is 12 feet of the swimming pool.

Given: Area of the swimming pool is 210 square feet

Width of the pool = 10 feet

The length of the shallow end is 9 feet and the length of the deep end is d.

To find the value of d.

Let's solve the problem.    

The area of the swimming pool is 210

The width is 10

The deep end length is d

The shallow end length is 9

The total length of the swimming pool = The length of the deep end + The length of the shallow end

=> d + 9

Therefore, the total length of the swimming pool is d + 9

The surface of the swimming pool is rectangular, so

The area of rectangle = width × length

Therefore,

area of swimming pool = width of the pool × length of the swimming pool

=> 210 = 10 × (9 + d)

or 10 × (9 + d) = 210

Dividing both sides by 10:

10 × (9 + d) / 10 = 210 / 10

9 + d = 21

Subtracting 9 on both sides:

9 + d - 9 = 21 - 9

d = 12

Therefore the length of the deep end is 12 feet

Hence the length of the deep end is 12 feet of the swimming pool.

Know more about "areas" here: https://brainly.com/question/27683633

#SPJ4

The length of the deep end of the swimming pool is 12 feet.

We are given that:

The Area of the swimming pool = 210 square feet

width of the swimming pool = 10 feet

Length of shallow end = 9 feet

Let the length of the deep end be d.

Total length of the swimming pool = length of deep end + length of shallow end =  d + 9

Area of swimming pool = width × length

Substituting the values, we get that:

210 = 10 × (9 + d)

9 + d = 21

d = 12

Therefore the length of the deep end of the swimming pool is 12 feet.

Learn more about area here:

brainly.com/question/27683633

#SPJ4

Answer:

I am confused what the question is asking

Step-by-step explanation:

Could you please comment down below and restate the question?

Answer: ok so.. exponential function's is kinda the same process as slopes and linear equations and functions ok so........

For slopes its rise over run but for this question its...... TO BE CONTINUED LOL (go to the explanation)

Step-by-step explanation:

So for the run on the x axis its 7 you can see it goes upward a little bit on the 7 but the 7 still counts :D

ok so we got 7 and as the line rises 9go to the picture added for more understanding) So as the line rises we can see from were i marked it in the picture that it touches the 2. So we got 2 as the rise and 7 as the run but remember this is not slopes lol so its kinda different.

THE ANSWER IS A

The rate of change of the area as a function of time is:

A'(t) = 6.28*(R₀ + 4ft/min*t)*(4ft/min)

Remember that for a circle of radius R, the area is:

A = 3.14*R^2

Now, if the radius increases at a rate of 4 ft/min, then we can rewrite R as:

R(t) = R₀ + 4ft/min*t

Where t is the time in minutes, and R₀ is the initial radius.

So the area function is:

A(t) = 3.14*(R₀ + 4ft/min*t)^2

The rate of change is given by the differentiation with respect to t, it is:

A'(t) = 2*3.14*(R₀ + 4ft/min*t)*(4ft/min)

A'(t) = 6.28*(R₀ + 4ft/min*t)*(4ft/min)

The rate at which the area increases, as a function of time, is given by:

A'(t) = 6.28*(R₀ + 4ft/min*t)*(4ft/min)

If you want to learn more about rates of change, you can read:

https://brainly.com/question/8728504

The distance of the student from the foot of the tower is 25.63m the nearest 1/2 is 25.5m.

Given that From the top of a tower 14m high

The angle of depression of a student is 32°

we can use trigonometry to find the distance from the foot of the tower to the student:

tan(32°) = opposite/adjacent = 14/distance

Rearranging this equation gives:

distance = 14/tan(32°)

= 25.63m

Therefore, the distance of the student from the foot of the tower is approximately 25.63m nearest 1/2, this is 25.5m.

To learn more on trigonometry click:

https://brainly.com/question/25122835

#SPJ1

Except than x = 1, all real numbers fall within the function's domain.

Since there are no limitations on what we can substitute for x, the domain of a function, f(x), is all real numbers because any real numbers would make f(x) a defined function. As a result, when this is not the case, the domain of a function, f(x), is not all real numbers.

The rational function r(x) = 2x/(x-1) is defined as follows.

So, we set the denominator to zero and solve for x in order to determine the domain of r(x):

x - 1 = 0

x = 1

Hence, x = 1 is the only value of x that causes the denominator to equal 0. R(x) therefore has a domain of all real numbers other than x = 1.

We can express the domain as follows in interval notation:

(-∞, 1) U (1, ∞)

Except than x = 1, all real numbers fall within the function's domain.

To know more about function visit:-

https://brainly.com/question/14830166

#SPJ1

Question:

Which of the following correctly describes the domain of the function shown below?

r(x) = 2x x-1

A. {x:x0}

B. {x: x = 1}

c. x all .real .numbers}

D. xx1}

Answer:

19 inches total

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

An equilateral triangle has 3 sides. The exterior angle = 360 / 3 = 120

A square has 4 sides. Each exterior angle = 360 / 4 = 90

A regular n gon has n sides. The exterior angles will be 360/n

Answer:

1590 minutes

Step-by-step explanation:

November 17 ends on 12:00, which is 8 hours after 4:00 pm. The time from the beginning of November 18 to noon is 12 hours, and the distance from noon to 6:30 is 6 hours and 30 minutes, so the total time in hours is 8+12+6 +1/2=26 1/2.

Because we know that one hour is 60 minutes, 26 hours is going to be 60*26, which is equal to 60*20+60*6=1560.

1/2 * 60 = 30. 1560+30=1590, so the value of minutes is 1590 minutes.

Answer:

(x + 1)(x + 2) is divisible by 3.

Step-by-step explanation:

Assume that x is not divisible by 3. This means that x can be expressed as x = 3k + r, where k is an integer and r is the remainder when x is divided by 3. Since x is not divisible by 3, the remainder r must be either 1 or 2.

Case 1: r = 1

If r = 1, then x = 3k + 1. Now let's consider (x + 1)(x + 2):

(x + 1)(x + 2) = (3k + 1 + 1)(3k + 1 + 2)

= (3k + 2)(3k + 3)

= 3(3k^2 + 5k + 2)

We can see that (x + 1)(x + 2) is divisible by 3.

Case 2: r = 2

If r = 2, then x = 3k + 2. Now let's consider (x + 1)(x + 2):

(x + 1)(x + 2) = (3k + 2 + 1)(3k + 2 + 2)

= (3k + 3)(3k + 4)

= 3(3k^2 + 7k + 4)

We can see that (x + 1)(x + 2) is divisible by 3.

Hence, the statement is proven.

Read more about integers,

brainly.com/question/12540626

brainly.com/question/26376738

The derivative of \(\(g(u) = \sqrt[3]{8u+2}\) is \(g'(u) = \frac{8}{3} \cdot (8u+2)^{-\frac{2}{3}}\).\)

To find the derivative of the function \(g(u) = \sqrt[3]{8u+2}\), we can use the chain rule.

The chain rule states that if we have a composite function \(f(g(u))\), then its derivative is given by \(\((f(g(u)))' = f'(g(u)) \cdot g'(u)\).\)

In this case, let's find the derivative \(\(g'(u)\) of the function \(g(u)\)\).

Given that \(g(u) = \sqrt[3]{8u+2}\), we can rewrite it as \(g(u) = (8u+2)^{\frac{1}{3}}\).

To find \(g'(u)\), we can differentiate the expression \(\((8u+2)^{\frac{1}{3}}\)\) using the power rule for differentiation.

The power rule states that if we have a function \(f(u) = u^n\), then its derivative is given by \(\(f'(u) = n \cdot u^{n-1}\).\)

Applying the power rule to our function \(\(g(u)\)\), we have:

\(\(g'(u) = \frac{1}{3} \cdot (8u+2)^{\frac{1}{3} - 1} \cdot (8)\).\)

Simplifying this expression, we get:

\(\(g'(u) = \frac{8}{3} \cdot (8u+2)^{-\frac{2}{3}}\).\)

Learn more about derivative here :-

https://brainly.com/question/29144258

#SPJ11

The height of the monument is 570 feet. Since the shadow of the monument and the shadow of the tourist are cast at the same time, their angles of elevation are the same.

To solve this problem, we need to use the concept of similar triangles. We can set up a proportion: (height of Monument) / (length of Monument's shadow) = (height of tourist) / (length of tourist's shadow)

Let x be the height of the Monument. Then we have:

x / 285 = 5 / 2.5

Cross-multiplying, we get:

2.5x = 5 * 285

Simplifying, we get:

x = 570

Therefore, the Monument is 570 feet tall.

To find the height of the monument, we can use the concept of similar triangles. Since the shadow of the monument and the shadow of the tourist are cast at the same time, their angles of elevation are the same.

Set up a proportion using the height and shadow length of the tourist and the monument:

(height of monument) / (shadow of monument) = (height of tourist) / (shadow of tourist)

Let x represent the height of the monument. Then:

x / 285 = 5 / 2.5

Now, solve for x:

x = (5 / 2.5) * 285
x = 2 * 285
x = 570 feet

The height of the monument is 570 feet.

Visit here to learn more about  angles : https://brainly.com/question/28451077
#SPJ11

Given equation of lines :

Since the lines are parallel

From the propertoes of parallel lines, the slope of parallel lines are always equal,

where in the general equation of line

On comapring the the first equation of line with general equation of line

we get m=-2/3

so, slope of first line is -2/3

similarly on comparing second equation of line with the general equation of line,

we get m=3/a

so, slope of second line is 3/a

since slope of both the lines are equal because they are paralle,

So, the value of a is -9/2

Answer : C. -9/2

Answer:

tan ∠L = 65/72

Step-by-step explanation:

The tangent ratio is:

tan of angle x = opposite/adjacent

Looking from the perspective of angle L, find the opposite side.

This side is MN, measuring 65 units.

opposite = 65

Now let's find the adjacent side.

This side is LN, measuring 72 units.

adjacent = 72

Therefore, the tangent ratio of angle L is 65/72.

Answer:

65/72

Step-by-step explanation:

Answer:

a5 = -199

Step-by-step explanation:

The formula to find the nth term in an arithmetic sequence is:

\(a_{n}=a_{1}+(n-1)d\), where a1 is the first term, n is the term position (e.g. 5th, 13th), and d is the common difference.

To find a5, we at least need to find a1.  We can plug in a13 (-111) for an and 13 for n:

\(-111=a_{1}+(13-1)11\\ -111=a_{1}+12*11\\ -111=a_{1}+132\\ -243=a_{1}\)

Since we now know a1, we can find find a5 (remembering to plug in 5 for n):

\(a_{5}=-243+(5-1)11\\ a_{5}=-243+4*11\\ a_{5}=-243+44\\ a_{5}=-199\)

This problem is an example of the use of synthetic division. This can be used to divide polynomials when the divisor has the form (x-a), with a constant.

The steps in this algorithm are:

• 1. write the divisor as ,a,;

In this problem, a = -1.

• 2. write the dividend as the coefficients starting with the leading coefficient, in descending order of the terms' degrees;

In this problem, since the dividend is 3x³-2x²+3x-5, we should write:

3 -2 3 -5

• 3. bring down to the third row the leading coefficient;

In this problem, it's 3. So far, we obtained:

-1 | 3 -2 3 -5

3

• 4. multiply the leading coefficient by a and write the result in the second row;

In this problem, we have 3 * (-1) = -3. Thus, we obtain:

-1 | 3 -2 3 -5

-3

3

• 5. add the numbers on the second row:

-1 | 3 -2 3 -5

-3

3 -5

• 6. repeat steps 4 and 5 for the next coefficients:

-5 * (-1) = 5

3 + 5 = 8

8 * (-1) = -8

-5 - 8 = -13

-1 | 3 -2 3 -5

-3 5 -8

3 -5 8 -13

• 7. the obtained numbers on the third row are the coefficients of the quotient (with one degree less than the dividend), and the last number on the right is the remainder.

In this problem, we have:

Therefore, the statement is True.

When a data line on a graph slopes down as it goes to the right, it is depicting that the relationship between the variables on the graph is inverse.

An inverse relationship is a kind of correlation between two variables, in which one variable decreases while the other increases, or vice versa. An inverse relationship happens when one variable increases while the other decreases, or when one variable decreases while the other increases.

On a graph, when a data line slopes down as it goes to the right, this is an indication that the relationship between the variables on the graph is inverse. As the values of x increase, the values of y decrease. Therefore, we can conclude that there is an inverse relationship between x and y.

To learn more about inverse relationship refer :

https://brainly.com/question/4147411

#SPJ11

Answer: 45 cm

Step-by-step explanation:

Assuming the rectangles r put together as per the attached picture.

length = 6+3 = 9 cm

Width = 3+3 = 6cm

Perimeter = 2(l+w)

P = 3(9+6)

P = 3 * 15

P = 45 cm