if polynomial ax3 + 3x2 - 3 and 2x3 - 5x + a leaves the same remainder when each is devided by x - 4 find the valuse of a

Answer:

53 1/3 km/h

Step-by-step explanation:

average speed = (total distance)/(total time)

average speed = distance/time

time * average speed = distance

time = distance/(average speed)

250 km at 75 km/h

distance = 250 km

time = (250 km)/(75 km/h) = 3.33333... hours

350 km at 70 km/h

distance = 350 km

time = (350 km)/(70 km/h) = 5 hours

200 km at 30 km/h

distance = 200 km

time = (200 km)/(30 km/h) = 6.6666...  hour

total distance = 250 km + 350 km + 200 km = 800 km

total time = 3.33333... hours + 5 hours + 6.66666... hours = 15 hours

average speed = (total distance)/(total time)

average speed = (800 km)/(15 hours)

average speed = 53 1/3 km/h

The average speed of whole journey of the train is 45 km/hr

Average speed is the ratio of total distance travelled to total time taken. It is given by:

Average speed = total distance / total time

Given that a train travels 250 km with a average speed of 75 km/hr, hence:

75 = 250/time

time = 3.33 hours

It the travel 200 km with average speed of 30km/hr, hence:

30 = 200/time

time = 6.67 hours

The total distance = 200 km + 250 km = 450 km

The total time = 3.33 hr + 6.67 hr = 10 hours

Average speed = total distance/total time = 450 km/10 hours = 45 km/hr

The average speed of whole journey of the train is 45 km/hr

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The table represents a function because each input (x-value) corresponds to exactly one output (y-value)

If we had repeated x values, then that is a sign we don't have a function. So for instance, if we had the two points (1,5) and (1,6) then we don't have a function because the input x = 1 corresponds to outputs y = 5 and y = 6 simultaneously.

Note: the y values are allowed to repeat and we still have a function, but this function is not one-to-one because of the repeated value y = 2.

Answer:

No idea dude

Step-by-step explanation:

I just need points

Answer:

The functions are [tex]f(x) = 7\cdot x+10[/tex] and [tex]g(x) = \frac{1}{x^{2}}[/tex], respectively.

Step-by-step explanation:

Let suppose that [tex]g(x) = \frac{1}{x^{2}}[/tex], then [tex]f(g(x))[/tex] is:

[tex]f(g(x)) = 7\cdot \left(\frac{1}{x^{2}} \right) + 10[/tex]

[tex]f(g(x)) = 7\cdot g(x) + 10[/tex]

Thus,

[tex]f(x) = 7\cdot x + 10[/tex]

The functions are [tex]f(x) = 7\cdot x+10[/tex] and [tex]g(x) = \frac{1}{x^{2}}[/tex], respectively.

Answer:

B = 15.1°, C = 34.9°, c = 39.6

Step-by-step explanation:

law of sines

53/sin 130 = 18/sin B

sin B = .26;   B = 15.1°

C = 180 - 15.1 - 130 = 34.9°

c/sin 34.9 = 53/sin 130

c = 39.6

Answer:

Hope it helps U can still ask me if u have confusions

Answer:

  60+16√30 cm² ≈ 147.64 cm²

Step-by-step explanation:

You can figure the height of the object from ...

  V = Bh

  120 cm^3 = (30 cm^2)h

  4 cm = h . . . . . divide by 30 cm^2

However, this is insufficient to tell you the surface area.

__

If you assume that the base is square, then its side length is

  A = s^2

  s = √A = √(30 cm^2) = (√30) cm

The lateral surface area can then be found from the perimeter of the base and the height

  LA = Ph = (4√30 cm)(4 cm) = 16√30 cm^2

The total surface area will be the sum of this lateral area and the area of the two bases:

 total area = 16√30 cm^2 +2·30 cm^2

 total area = (60 +16√30) cm^2 ≈ 147.64 cm^2

__

For any other shape, the total area will be larger. It can be arbitrarily large, unless limits are put on the dimensions of the object.

Answer:

a) irrational

b) irrational

c) rational

d) rational

e) irrational

Note:

rational numbers are numbers that can be expressed in fractions.

irrational numbers are numbers that cannot be expressed in fractions i.e. they are never-ending-non-repeating decimals. examples √2, pi etc.

Answer:

(7,-4) ; 12

Step-by-step explanation:

Basically, three corners of a rectangle are already on the graph. If you put a dot at (7,-4), that is the last corner(vertex) that finishes the rectangle

Then to find base of the rectangle, you find the length of the longer side, (the distance between the x coordinates). So you would subtract -5 from 7 and get 12, and 12 is the length of your base.

Answer:

0.5% error

Step-by-step explanation:

We can use the percentage error formula, which is

[tex]\frac{|approx-exact|}{exact}\cdot100[/tex].

We know that the approximated value was 8.04, however it is actually 8cm, so we can substitute inside the equation.

[tex]\frac{|8.04 - 8|}{8}\cdot100 \\\\\frac{0.04}{8}\cdot100 \\\\0.005\cdot100 \\\\0.5[/tex]

Hope this helped!

Answer:

It would take 6 days for 500 students to be affected.

Step-by-step explanation:

Given that:

1. Seven kids returned with the virus.

2. The aggressive virus spreads at 130% each day.

We want to find how many days until 500 students are infected by the virus.

First day:

7 students have the virus, 130% of 7 student will contract the virus again.

130% of 7 = (130/100) × 7

= 1.3 × 7 = 9.1 ≈ 9

9 new students are affected

New total affected = 7 + 9 = 16 students.

Day 2:

Affected = 1.3 × 16 = 20.8 ≈ 20

New total affected = 20 + 16 = 36

Day3

Affected = 1.3 × 36 = 46.8 ≈ 46

New total affected = 36 + 46 = 82

Day4

Affected = 1.3 × 82 = 106.6 ≈ 106

New total affected = 106 + 82 = 188

Day5

Affected = 1.3 × 188 = 244.4 ≈ 244

New total affected = 244 + 188 = 432

Day6

Affected = 1.3 × 432 = 561.6 ≈ 561

New total affected = 561 + 432 = 993

Therefore, it would take 6 days for 500 students to be affected.

Answer:

3. Fifth degree polynomials are also known as quintic polynomials. Quintics have these characteristics: One to five roots. Zero to four extrema.

4. x = -5 or x = 0 or x = 5

Step-by-step explanation:

Solve for x:

6 x^5 - 150 x^3 = 0

The left hand side factors into a product with four terms:

6 x^3 (x - 5) (x + 5) = 0

Divide both sides by 6:

x^3 (x - 5) (x + 5) = 0

Split into three equations:

x - 5 = 0 or x^3 = 0 or x + 5 = 0

Add 5 to both sides:

x = 5 or x^3 = 0 or x + 5 = 0

Taking cube roots gives 0 times the third roots of unity:

x = 5 or x = 0 or x = 0 or x = 0 or x + 5 = 0

Subtract 5 from both sides:

x = 5 or x = 0 or x = 0 or x = 0 or x = -5

There are {2} duplicate solutions:

Answer: x = -5 or x = 0 or x = 5

Answer:

0.577

Step-by-step explanation:

inv. sin (0.5) = 30

tan (30) = 0.577

The value of Tan[tex](Sin^{-1}(1/2))[/tex] is 0.58.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

Tan[tex](Sin^{-1}(1/2))[/tex]

[ Sin 30° = 1/2 ]

= Tan([tex]sin^{-1}sin30)[/tex])

= Tan 30°

= 0.58

Thus,

0.58 is the value of Tan[tex](Sin^{-1}(1/2))[/tex] is 0.58.

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Answer:

24

Step-by-step explanation:

What you have here is a permutation, seeing as each element can only be used once.

We have 4 letters initially, so we can choose any 1 as our first letter. We have 4 choices for our first letter

However, once we choose our first letter, we can't use it anymore, so, for our second letter, we can only choose from the remaining 3 letters.

Furthermore, once we choose our second letter, we can only choose our 3rd letter from the remaining two letters we didn't choose yet.

Finally, our last letter will always be the one we didn't choose the last 3 times. So there is only one choice here.

Going off of this, we have four choices for the 1st letter, three choices for the 2nd letter, two choices for the 3rd letter, and one choice for the 4th letter

The way to calculate how many permutations we have without repetition is using factorials

N!

Where N is the number of elements you have.

In this case, it would be 4!

4! is 4 * 3 * 2 * 1

Which equals 24

If you notice, each number in 4! is the number of options we have for each choice. 4, then 3, and so on

Answer:

first answer

Step-by-step explanation:

(8x³ - 22x² - 4) / (4x - 3)

when you do long division you get the first answer

Answer:

No, all of her work is correct.

Step-by-step explanation:

Answer:

No, all of her work is correct.

Step-by-step explanation:

All of her work is correct.

The first step is showing factorization of √50

The second step is simplifying the factorization

The third step is simplifying the entire radical.

When you take a square root of a square, they cancel out, so:

√5² = 5

We multiply it with our leftover √2 and we get:

5√2

Answer:

discuss this question is about packhouse a small plant can travel 400 kilometre aur 2000 kilometre find the speed with a plan with no wind and a speed on the answer you will be given to you divide 5 400 the four hundred and 51 you divide the answer to get dawat 310 you will find the extra answer

Answer:

[tex]\large \boxed{e^{i\pi}+1=0}[/tex]

Step-by-step explanation:

Hello, please consider the following.

For any x real number,

[tex]e^{ix}=cos(x)+i\cdot sin(x)\text{, right? So}\\\\e^{i\pi}=cos(\pi)+i\cdot sin(\pi)\\\\e^{i\pi}=-1+i\cdot 0=-1\\\\\text{ We add 1 to both sides of the equation.}\\\\\large \boxed{e^{i\pi}+1=0}\\[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

First, an irrational number is a number that has infinite digits after the decimal point, in such way that those digits do not form any pattern.

The irrational set is called a dense set, wich means that in between two elements of the set, we can find infinite other elements of the set.

For example, between 1 and 2, we have

1.12312412513513532....

1.123224124312432432....

and between those two numbers, we can find infinite irrational numbers, and so on.

Then between -12 and +49, we have infinite irrational numbers.

Answer:

[tex]\sqrt{2}[/tex] or 1.414

Step-by-step explanation:

1) Find the mean. 1+2+3+4+5 = 15. 15/5= 3

2) For each data point, find the square of its distance to the mean. (4, 1, 0, 1, 4)

3) Sum the values from Step 2. 10

4) Divide by the number of data points. 10/5= 2

5) Take the square root. [tex]\sqrt{2}[/tex]

Answer:

the answer square root of 2! just did the test and got it right :)

Step-by-step explanation:

Answer:

543.48 millimetre

Step-by-step explanation:

mass/density = volume

500 grams / 0.92 grams per millimetre = 543.48

Answer:

volume = 543.478 cm³

Step-by-step explanation:

Density = mass / volume

0.92g/ml = 500g / volume

volume (0.92g/ml) = 500g

volume = 500g / (0.92g/ml)

volume = 543.478 ml    (aprox. to the nearest mililiter)

1 ml = 1cm³

543.478ml = 543.478 cm³

Answer:

we would be facing the North West

Answer:

1. Apples, Cauliflower, Green beans

2. Apples, Cauliflower, Salmon

...

27. Grapes, Corn, Almonds

Step-by-step explanation:

There are 3x3x3 = 27 combinations possible. You can enumerate them systematically.

Answer:

There are 27 combinations possible.

Hope this helps!

Answer:

The simplest form of the given expression is 8.

Step-by-step explanation:

(-11/2x + 3) - 2(-11/4x - 5/2)

Distribute 2 to (-11/4x - 5/2)

(-11/2x + 3) - (-11/2x - 5)

Now, combine like terms. The terms with the x value will cancel each other out because a negative plus a positive of the same number will equal zero. For example, -2 + 2 = 0.

So, the expression in the simplest form is going to be 8. The x values have cancelled each other out so all there is left is the constant number which is 8.

Answer:  f(x) will have vertical asymptotes at x=-2 and x=2 and horizontal asymptote at y=3.

Step-by-step explanation:

Given function: [tex]f(x)=\dfrac{3x^2}{x^2-4}[/tex]

The vertical asymptote occurs for those values of x which make function indeterminate or denominator 0.

i.e. [tex]x^2-4=0\Rightarrow\ x^2=4\Rightarrow\ x=\pm2[/tex]

Hence, f(x) will have vertical asymptotes at x=-2 and x=2.

To find the horizontal asymptote , we can see that the degree of numerator and denominator is same i.e. 2.

So, the graph will horizontal asymptote at [tex]y=\dfrac{\text{Coefficient of }x^2\text{ in numerator}}{\text{Coefficient of }x^2\text{ in denominator}}[/tex]

i.e. [tex]y=\dfrac{3}{1}=3[/tex]

Hence, f(x) will have horizontal asymptote at y=3.

Answer:

0.375

Step-by-step explanation:

0.125 x 3 = 0.375

Answer:

0.375

Step-by-step explanation:

3 x 125

8 x 125

=

375

1000

=

0.375

Other sample problem:

5 = 5×125 = 625 = 0.625

8         8×125         1000

Hope this helps, have a good day :)

Answer:

C.) 4(750c-700t) ; D.) 2800t - 3000c

Step-by-step explanation:

Time taken :

Tatenda = t sec/m^2

Ciara = c sec/m^2

Tatenda = 700m^2 per week

Ciara = 750m^2 per week

Which expressions can we use to describe how many more seconds Tatenda spends than Ciara spends mowing lawns during 4

Total Time taken over four weeks :

Tatenda = 4(t * 700) = 4(700c)

Ciara = 4(c * 750) = 4(750c )

Number of seconds Tatenda spends more than Ciara : meaning Tatenda spends more seconds than

Tatenda - Ciara

4(700t) - 4(750c) = 4(700t - 750c)

4(700t - 750c)

Or

4(700t - 750c) = 2800t - 3000c

2800t - 3000c

Answer:

[tex]4x^2-21x-2[/tex]

Step-by-step explanation:

Given that:

Difference of two trinomials is [tex]x^2 - 10x + 2[/tex]

One of the two trinomials is  [tex]3x^2 - 11x - 4[/tex]

To find:

The other trinomial = ?

Four options are:

[tex]2x2 - x - 2 \\2x2 + x + 6 \\4x2 + 21x + 6\\ 4x2 - 21x - 2[/tex]

Solution:

Let the two trinomials be A and B.

Given A - B = [tex]x^2 - 10x + 2[/tex]

B = [tex]3x^2 - 11x - 4[/tex]

We have to find the other trinomial A.

A - B = [tex]x^2 - 10x + 2[/tex]

A - ([tex]3x^2 - 11x - 4[/tex]) = [tex]x^2 - 10x + 2[/tex]

[tex]\Rightarrow[/tex] A = [tex]x^2 - 10x + 2[/tex] + ([tex]3x^2 - 11x - 4[/tex])

[tex]\Rightarrow[/tex] A = [tex]4x^2-21x-2[/tex]

So, the correct answer is [tex]4x^2-21x-2[/tex].

Answer:

9

Step-by-step explanation:

We can set up a systems of equations to find the value of the third side.

Let's assume that [tex]x[/tex] is the length of both sides 1 and 2. Let's also assume that [tex]y[/tex] is the length of the third side.

We know that [tex]x + x + y = 23[/tex], and looking at the first clue we can make the equation [tex]y = 2x-5[/tex].

We can substitute y into the equation [tex]x + x + y = 23[/tex].

[tex]x + x + (2x-5) = 23\\\\2x + 2x-5 = 23\\4x-5 = 23\\4x = 28\\x = 7[/tex]

So the length of the side that is the same as the second is 7.

Now we can plug this into the equation [tex]y = 2x-5[/tex] to find [tex]y[/tex].

[tex]y = 2(7) - 5\\\\y = 14-5\\\\y = 9[/tex]

Hope this helped!

Answer:

9 cm

Step-by-step explanation:

Let's say that the length of the 2 equal sides is x.

That means:

Side 1 = x

Side 2 = x

We know that the third side is 5 less than twice the length of the 2 equal sides, or 2x-5

Side 3 = 2x-5

The perimeter is all sides together.

Side 1 + Side 2 + Side 3

We know the length of each side, so let's put that in instead.

x + x + 2x-5

Let's simplify this expression:

x + x + 2x - 5

2x + 2x - 5

4x - 5

We know the perimeter, 4x-5, is 23 cm.

4x - 5 = 23

4x = 28

x = 7

The third side is 2x-5. If x is 7...

2*7 - 5 = 14-5 = 9

Answer: 9 cm

Answer:

B) 3

Step-by-step explanation:

Traveling at a rate of 70 miles per hour, a car travels 26 miles per gallon of gasoline.

In 300 miles journey the gallon of gasoline consumed will be

300/26= 11.54 gallons

Traveling at a rate of 45 miles per hour, the same car travels 36 miles per gallon of gasoline.

In 300 miles journey the gallon of gasoline consumed will be

300/36= 8.33 gallons

The amount of gasoline saved= 11.54-8.33

The amount of gasoline saved= 3.21

approximately 3 gallons of gasoline

Answer:

Step-by-step explanation:

1) Diagonal bisect the angles of Rhombus

∠CAB = ∠CAD

∠CAB = 71

2) ∠DAB = ∠CAB + ∠CAD

 ∠DAB = 71 + 71 = 142

In Rhombus, adjacent angles are supplementary

∠DAB + ∠ABC = 180

142 + ∠ABC = 180

           ∠ABC = 180 - 142

         ∠ABC = 38

3)  In rhombus, opposite angles are congruent

∠ADC = ∠ABC

∠ABC = 38

In rhombus, diagonal bisect angles

∠BDC = (1/2)*∠ADC

∠BDC= 38/2

∠BDC = 19

4) Diagonals bisect each other at 90

∠DEC = 90

5) Diagonals bisect each other

BE = DE

BE + DE = DB

7x -2 +7x -2 =24   {add like terms}

        14x - 4 =24

              14x = 24+4

              14x = 28

                 x = 28/14

                 x = 2 m

6) AB = 13m

BE = 7x - 2 = 7*2 -2 = 14 -2 = 12 m

In right angle ΔAEB,  {use Pythagorean theorem}

AE² + BE² = AB²

AE² + 12² = 13²

AE² + 144 = 169

         AE² = 169 - 144

         AE² = 25

         AE = √25

        AE = 5 m

Diagonals bisect each other

AE = EC

AC = 2*5

AC = 10 m

7)Side = 13 m

Perimeter = 4*side

                  = 4*13

 Perimeter = 52 m

8) d1 = AC = 10 m

   d2 = DB = 24 m

Area = [tex]\frac{d_{1}*d_{2}}{2}[/tex]

         [tex]=\frac{10*24}{2}\\[/tex]

          = 10 *12

          = 120 m²