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:

dL/dt  = - 2,019 m/h

Step-by-step explanation:

L²  =  x²  +  y²   (1)    Where  x, and  y are the legs of the right triangle and L the hypotenuse

If the base of the triangle, let´s call x is increasing at the rate of 2 m/h

then  dx/dt =  2 m/h. And the height is decreasing at the rate of 3 m/h or dy/dt = - 3 m/h

If we take differentials on both sides of the equation (1)

2*L*dL/dt = 2*x*dx/dt  + 2*y*dy/dt

L*dL/dt  = x*dx/dt + y*dy/dt         (2)

When  the base is 9  and the height is 22 according to equation (1) the hypotenuse is:

L = √ (9)² + (22)²       ⇒    L = √565       ⇒  L  = 23,77

Therefore we got all the information to get dL/dt .

L*dL/dt  = x*dx/dt + y*dy/dt

23,77 * dL/dt  = 9*2 + 22* ( - 3)

dL/dt  =  ( 18 - 66 ) / 23,77

dL/dt  = - 2,019 m/h

Using implicit differentiation and the Pythagorean Theorem, it is found that the hypotenuse is changing at a rate of -2.02 meters per hour.

The Pythagorean Theorem states that the square of the hypotenuse h is the sum of the squares of the base x and of the height h, hence:

[tex]h^2 = x^2 + y^2[/tex]

In this problem, [tex]x = 9, y = 22[/tex], hence, the hypotenuse is:

[tex]h^2 = 9^2 + 22^2[/tex]

[tex]h = \sqrt{9^2 + 22^2}[/tex]

[tex]h = 23.77[/tex]

Applying implicit differentiation, the rate of change is given by:

[tex]2h\frac{dh}{dt} = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]

Simplifying by 2:

[tex]h\frac{dh}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]

The rates of change given are: [tex]\frac{dx}{dt} = 2, \frac{dy}{dt} = -3[/tex].

We want to find [tex]\frac{dh}{dt}[/tex], hence:

[tex]h\frac{dh}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]

[tex]23.77\frac{dh}{dt} = 9(2) + 22(-3)[/tex]

[tex]\frac{dh}{dt} = \frac{18 - 66}{23.77}[/tex]

[tex]\frac{dh}{dt} = -2.02[/tex]

The hypotenuse is changing at a rate of -2.02 meters per hour.

A similar problem is given at https://brainly.com/question/19954153

Answer and Step-by-step explanation: The described right triangle is in the attachment.

As it is shown, AC is the hypotenuse and BC and AB are the sides, so use Pytagorean Theorem to find the unknown measure:

AC² = AB² + BC²

[tex]AB^{2} = AC^{2}-BC^{2}[/tex]

[tex]AB =\sqrt{AC^{2}-BC^{2}}[/tex]

[tex]AB =\sqrt{7^{2}-4.5^{2}}[/tex]

[tex]AB =\sqrt{28.75}[/tex]

AB = 5.4

Then, right triangle ABC measures:

AB = 5.4cm

BC = 4.5cm

AC = 7cm

Answer:

13/3

Step-by-step explanation:

Write as a fraction first,

0.65/0.15

convert decimal to fractions,

13/20/3/20 = 13/3

Answer:

12 to the power of -2 is 0.00694444444

Step-by-step explanation:

When ever doing a number to the power of a negative number, the result will always be a fraction of a number.

Or

Fraction:

1/12^2

which is

1 / 144

Percentage:

0.00694444444 * 100 = 0.694444444%  

Hope this helps, have a good day :)

(brainliest would be appreciated?)

The simplest form of the given expression [tex]12^{-2}[/tex] is 1/144.

The given expression is,

[tex]12^{-2}[/tex]

Here we can see that 12 has inverse power of 2.

Simplify it using basic rules of exponents.

To do so, we need to understand that a negative exponent indicates that the base should be inverted.

In other words, [tex]12^{-2}[/tex] is the same as 1/12²

To simplify this further,  

Evaluate 12², which is,

12² = 12 x 12

     =  144

Therefore, 1/12² can be expressed as 1/144.

Hence,

In the simplest form, we can write [tex]12^{-2}[/tex] as 1/144.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ6

Answer:

78 nickels and 22 dimes

Step-by-step explanation:

Nickels = n, Dimes = d

Number of coins = 100

Total sum in the piggy bank = $6.60

Consider the first equation in the second:

Answer: nickels 78 and dimes 22

Answer:

78 nikes and dimes 22

solving these linear equations simultaneously, x = 22y = 8z= 11hence the answer is B. 11

Step-by-step explanation:

Answer:

Hey there!

5. f(4) is 3. f(3) is 2. Thus, f[f(4)]=2

6. g(2) is 3. g(3) is 1. g[g(2)]=1

Hope this helps :)

Answer:

$5,000 per week

Step-by-step explanation:

Ruri is a 30 year old female.

there are about 4 weeks per month

there are about 52 weeks per year

52*5000 = 260,000

She would get 260,000 per year and lets see how much she would have at 40.

260,000*10

at 40 she would have 2,600,000

2,600,000*10

at 50 she would have 26,000,000

at 50 she already has earned more money that the $20 million.

She should go with the $5000 per week if she would like more money.

Answer:

$18

Step-by-step explanation:

$18.02 rounds to $18

Answer:

  $17

Step-by-step explanation:

Rounded, the listed numbers are ...

  12 + 5 -1 +3 -2 = 17

The estimate of total cost is $17.

Answer:

3000 words

Step-by-step explanation:

450 words in 3 minutes is 150 words in 1 minute. 20 minutes = 1 times 20.          

1 minute = 150 words so 150 words times 20 minutes = 3000 words.

Answer:

Hey there!

The temperature started at -8 degrees.

The total rise of the temperature was 6(4) or 24 degrees.

-8+24=16

The temperature after 6 hours was 16 degrees.

Let me know if this helps :)

The temperature after 6 hour is 16°. Therefore, option B is the correct answer.

Temperature is a degree of hotness or coldness the can be measured using a thermometer. It's also a measure of how fast the atoms and molecules of a substance are moving. Temperature is measured in degrees on the Fahrenheit, Celsius, and Kelvin scales.

Given that, One January day, the low temperature in Fargo, ND was -8 degrees.

Over a period of six hours, the temperature rose 4 degrees per hour.

So, total temperature rose in 6 hours is 24 degrees

Temperature after 6 hour is -8+24

= 16°

The temperature after 6 hour is 16°. Therefore, option B is the correct answer.

Learn more about the temperature here:

https://brainly.com/question/11464844.

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Answer:

3 1/6 cups of flour.

Step-by-step explanation

Answer:

66.9 degrees

Step-by-step explanation:

The Law of Sines states that a/sinA = c/sinC. Plugging in the values for c, a, and M < A, we get:

71/sin40 = 102/sinC

Cross multiplying, we get:

102(sin40deg) = 71(sinC)

Now, we simplify the left side and get:

65.56 = 71(sinC)

Next, we divide 65.56 by 71 to get:

0.92 = sinC

Taking the inverse sign we get:

C = 66.9 degrees

Answer:

13x3= 39

Step-by-step explanation:

10x3=30

3x3=9

30+9=39

Hope it helps!

Answer:

x = 50

Step-by-step explanation:

Since the angle is right = 90°, then

40 + x = 90 ( subtract 40 from both sides )

x = 50

Answer:

[tex]\boxed{\sf x = 50\ degrees}[/tex]

Step-by-step explanation:

x = 90 - 40    [Complementary angles add up to 90 degrees]

x = 50 degrees

Answer:

The answer is D. A reflection, a rotation and a translation will prove that shape 2 is congruent to shape 1.

Answer:

No

Step-by-step explanation:

Linear equations must have no squares, roots, cubes, or any powers. If the graph has an asymptote or any restrictions, it is not a linear function.

A linear function will only appear in either point-slope form or slope-intercept form. These forms will not have square roots or powers in them.

-x + 3y² = 18

We know here that this is not a linear function. But we can try to write it in slope-intercept form:

3y² = x + 18

y² = x/3 + 6

y = √(x/3 + 6)

We can see from here that our graph is a square root function and has a restricted domain (no negative numbers).

Alternatively, we can graph the equation to see if it is a constant line (linear equation) or not. When we do so, we see that it is definitely not a linear function:

Step-by-step explanation:

when you are cooking you need to measure fractions of ingredients

Answer:

9, 13, 17, 21

Step-by-step explanation:

If x=2,

y=1+4(2)

y=9

This goes on, like a pattern. If x increases by 1, y inreases by 4. So, if y=3, x=13. If x=4, y=17, and so on.

Answer:

1.417

Step-by-step explanation:

102/72=1.417

Answer:

9.71 m

Step-by-step explanation:

Surface area of cube is given by 6a^2 where a is the edge length.

Given

Surface area  =565.7 m²

let a be the edge length of required cube

then

6a^2 = 565.7 m²

=> a^2 = 565.7 /6 m² = 94.28

=> a = [tex]\sqrt{94.28}[/tex] = 9.71

Thus, first option  9.71 m is correct choice.

Answer:

Step-by-step explanation:

C=153.86153...

100000C=15386153.86153...

subtract

99999C=15386000

C=15386000/99999

2 π r=15386000/99999

r=7693000/99999π≈24.5

Answer:

(3.5,4)

x coordinate =

[tex] \frac{5 + 2}{2} [/tex]

= 3.5

y coordinate =

[tex] \frac{ - 1 + 9}{2} [/tex]

= 4

midpoint = (3.5,4)

Answer:

(  3.5,4)

Step-by-step explanation:

To find the midpoint

Add the x coordinates together and divide by 2

(5+2)/2 = 7/2 = 3.5

Add the y coordinates together and divide by 2

(9+-1)/2 = 8/2 = 4

( 3.5,4)

Answer:

p(x), q(x), and their product are all polynomials.

p(x) · q(x) = 6x² + 10x - 63

Step-by-step explanation:

First of all P(x) and q(x) are polynomials because polynomials refer to any sum, difference, or product of a collection of algebraic terms. The word polynomials is general. P(x) and q(x) are polynomials but more specifically they are binomials since they only have two terms. Their product is a polynomial as well, but more specifically its a trinomial because it has three terms.

process of multiplying

Using the distributive property (or foil method) when multiplying p(x) and q(x) you would first get the expression 6x² - 18x + 28x - 63. From here you would combine "like terms". This would give you your final answer of

6x² + 10x - 63. Sorry, I couldn't help you with the D question but I hope this helps ;)

Answer:

False

Step-by-step explanation:

[tex]( {9}^{9} ) \times ( {9}^{ - 20} ) \\ = {9}^{9 + ( - 20)} \\ = {9}^{ - 11} [/tex]

Answer:

I'm pretty sure its false

Answer:

A. 183 meters

Step-by-step explanation:

Building A and building B are 500 meters apart. There is no road between them, so to drive from building A to building B, it is necessary to first drive to building C and then to building B. About how much farther is it to drive than to walk directly from building A to building B? Round to the nearest whole number. A) 183 meters B) 250 meters C) 366 meters D) 683 meters

Find distance BC

Cos (60°)=BC / AB (Adjacent divided by the hypotenuse)

Cos (60°)=1/2

BC=a

AB=500

Cos (60°)=BC / AB

1/2=a/500

1/2 * 500=a

250=a

a=250m

Find distance AC

Sin(60°)=AC/AB (opposite side divided by hypotenuse)

Sin(60°)=√3/2

AC=b

AB=500

Sin(60°)=AC/AB

√3/2=b/500

√3/2 * 500=b

250√3=b

b=433m

Distance AC and BC=AC+BC

433m+250m=683m

Subtract the distance AB from AC+BC

= 683m - 500m

=183m

Answer is A. 183 meters

Answer:

A. 183 meters

Step-by-step explanation:

sin(60) = x/500

= 433

tan(60) = 433/x

= 250

This is the driving distance. 433+250= 683. Directly walking (using hypotenuse distance) is 500.

683-500=183!

Answer:

Yes it will occur

Step-by-step explanation:

The lobby measures 45 feet by 45 feet

Area of the lobby = 45 * 45

=2025 ft^2

So, the lobby has 2025 tiles

subtract 1 black tile in the center

2025 tiles - 1 black tile =2024 tiles

The number of blue tiles and black tiles is 2024 tiles

He wants the outer edge to be the same color as the center tile so, divide by 2

2024/2 = 1012 tiles

The number of tiles in the outer edge is 1012 tiles and the number of tiles in the center is 1012 tiles

Answer:

The answer to the nearest hundredth is 0.07 liters per minute

Step-by-step explanation:

In this question, we are told to express the given metric in liters per minute.

The key to answering this question, is to

have the given measurements in the metric in which we want to have the answer.

Hence, we do this by converting milliliters to liters and seconds to minute.

Let’s start with milliliters;

Mathematically;

1000 milliliters = 1 liters

10 milliliters = x liters

x * 1000 = 10 * 1

x = 10/1000

x = 1/100

x = 0.01 liters

For the seconds;

We need to convert the seconds to minutes;

Mathematically;

60 seconds = 1 minute

8.5 seconds = y minutes

60 * y = 8.5 * 1

y = 8.5/60

y = 0.14167 minutes

Now, our rate of flow is liters per minute, that means we have to divide the volume by the time;

Hence, we have ;

0.01/0.14167 = 0.070588235294

Which to the nearest hundredth is 0.07

Answer:

$36,400

Step-by-step explanation:

Mr Jamison deposited $100 in January

February=3*100=$300

March=3{3(100)=3^2(100)=9*100=$900

April=3^3(100)=27*100=$2,700

May=3^4(100)=81*100=$8,100

June=3^5(100)=243*100=$24,300

Total amount=$100 + $300 + $900 + $2700 + $8100 + $24300

=$36,400

The total amount deposited by Mr Jamison on June 15 is $36,400

Answer:

The minimum score necessary to be in the top 10% of the distribution is 628.

Step-by-step explanation:

Given that a normal distribution has a mean of μ = 500 and a standard deviation = σ= 100

The Significance level  for this test = 10 % = 0.1

For one tailed test ∝= 0.1 the value of Z∝= ±1.28

Since it a normal distribution the test statistic used is

Z= X= u / σ/√n   ( taking n= 1)

1.28 = X- 500/100/√1

128 + 500 = X

or X = 628

The minimum score necessary to be in the top 10% of the distribution is 628.

To add fractions with different denominators you must find the highest common factor (the highest number they both go into).

For 1 - The highest common factor is 8, 2x4 = 8, 4x2 = 8

now, whatever you do to the bottom, you must do to the top.

So:

3 x 2 = 6 and 5 x 4 = 20

Therefore, your answer would be 6/8 + 20/8

You do that for the rest of them as well, do you get it?

Answer:

    3.  4/15 + 4/5 = 4/15 + 12/15 = (4+12)/15 = 16/15

    5.  2/3  + 7/10 = 20/30 + 21/30  = (20+21)/30 = 41/30