A school has 4 steps to the front door. Each step is 7 inches tall. Design a ramp for the

school.

So, here we are to factor the polynomials :

[tex]\\ 1. \sf \qquad5a^2b^2 + 10ab +25a\\ \\[/tex]

[tex] \longrightarrow\sf \qquad5a(ab^2 + 2b +5)\\ \\[/tex]

[tex]\\ 2. \sf \qquad 8m^2n^2 - 24mn^3 +16mn\\ \\[/tex]

[tex] \longrightarrow\sf \qquad 8mn(mn - 3n^2 +2)\\ \\[/tex]

[tex]\\ 3. \sf \qquad 9xz^3 + 18yz^2 + 24z^2\\ \\[/tex]

[tex]\longrightarrow \sf \qquad 3z(3xz^2 + 6yz+ 8z)\\ \\[/tex]

[tex]\\ 4. \sf \qquad 16x^6y + 16x^2y^4 + 32x^3y^2\\ \\[/tex]

[tex] \longrightarrow \sf \qquad 16 {x}^{2} y(x^4 + y^3 + 2xy)\\ \\[/tex]

Some points to know :

Answer:

8/9

Step-by-step explanation:

4/9 ÷ 1/2 =  dividing by 1/2 is the same as multiplying by its reciprocal 2/1

4/9 × 2/1 = (4×2)/(9×1) multiply numerators (top numbers) and multiply denominators (bottom numbers)

Answer:

2/10

Step-by-step explanation:

Since the denominator is 10, we must find what the numerator is so that the fraction can be equal to 1/5. Since 10 is twice of 5, we multiply 2 by 2 as well. With that, we get a final answer of 2/10.

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{k}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{k}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{1}}}~~ = ~~\stackrel{\stackrel{m}{\downarrow }}{2} \\\\\\ \cfrac{k-3}{4}=2\implies k-3=8\implies k=11[/tex]

Answer:

First choose a common denominator, here i picked 11 then we think of 3 diffrent numbers so that their sum is 11 such as 2+4+5=11 so a possible equasion would be

Step-by-step explanation:

Answer:

0.3

Step-by-step explanation:

15/50=0.3

OR

(15*2)/(50*2)

30/100=0.3

we can use hmmm any value per se for the card, hmmm say let's use $2, if the baseball card was initially 2 bucks, and after 10 years it went up in value by 50%, well 50% of 2 is 1, so the new value is 3 bucks, then

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill &3\\ P=\textit{initial amount}\dotfill &2\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &10\\ \end{cases} \\\\\\ 3=2(1 + \frac{r}{100})^{10}\implies \cfrac{3}{2}=(1 + \frac{r}{100})^{10}\implies \cfrac{3}{2}=(\frac{100+r}{100})^{10} \\\\\\ \sqrt[10]{\cfrac{3}{2}}=\cfrac{100+r}{100}\implies 100\sqrt[10]{\cfrac{3}{2}}=100+r \\\\\\ 100\sqrt[10]{\cfrac{3}{2}}-100=r\implies 4\approx r[/tex]

Answer:c

Step-by-step explanation:

Answer:

18.32 gm

Step-by-step explanation:

= 35 ( 1-.0525)^12 = 18.32 gm remain

Answer:

11

Step-by-step explanation: Uh- if X=3 then it would be 2(3) +5. 2x3 is 6, and 6+5 is 11.

Answer:

11

Step-by-step explanation:

2(3) + 5

simplify

6 + 5 = 11

hope this helps

Answer:

The answer would be 64,000.

Step-by-step explanation:

To find the area of one concrete block you will multiple length x width x height. Using the measurements provided, one block will equal 40. You will then multiple this by 1,600 to equal 64,000.

Answer:

  90√2 feet

Step-by-step explanation:

The geometry of the problem can be modeled by a right triangle with sides 90 feet. The length of the hypotenuse is the distance from home plate to 2nd base. The Pythagorean theorem tells you that distance (c) is ...

  c² = a² +b²

  c² = (90 ft)² +(90 ft)² = 8100 ft² +8100 ft²

  c² = 16200 ft²

  c = √16200 ft = 90√2 ft

The distance between home plate and second base is 90√2 feet.

Answer:

A baseball field is in the shape of a square. The distance between each pair of bases along the edge of the square is 90 feet. What is the distance between home plate and second base?

(90) StartRoot 2 EndRoot feet

Step-by-step explanation:

Answer:23%

Step-by-step explanation: 800-616= 184

Discount is 184

percentage is 184/800 ×100/1 =23%

This experiment has 36 possible combinations, and we will see that:

First, we need to find the total number of outcomes.

We have two dice with 6 outcomes each, so the total number of outcomes of the experiment of tossing the two dice is:

C = 6*6 = 36

Such that the sample space is all the numbers between 2 and 12 (because our variable is the sum of the two values).

Now, to get the probability of winning we need to count the number of outcomes that add to 7 or 11, these are:

(Add to 7)

dice 1    dice 2            

   1            6                  

  2            5                  

   6           1

   5            2

    4           3

    3            4

(Add to 11)

dice 1    dice 2          

  5            6

  6             5

So there are 8 outcomes, then the probability of winning is:

P = 8/36  =0.22

The probability of losing is when the sum adds to 2, 3, or 12.

The outcomes that add to that:

(Add to 2)

dice 1    dice 2    

1               1

(Add to 3)

dice 1    dice 2    

 1              2

 2              1

(Add to 12)

dice 1    dice 2    

  6            6

There are 4 outcomes that add to these values, so the probability of losing is:

P = 4/36 = 0.11

If you want to learn more about probability, you can read:

https://brainly.com/question/251701

Answer:

40x 12 year olds
50x 13 year olds
10x  14 year olds

Step-by-step explanation:

40% of 100 is 40
50% of 100 is 50
100%-90%=10%, 10% of 100 = 10

Students of 12 years are 40%, students of 13 years are 50% and students of 14 years are 10%.

A percentage is a figure or ratio that can be stated as a fraction of 100. If we need to calculate the percentage of a number, we must divide it by its full value and then multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." It is represented by the symbol "%".

Given, total students in band  = 100

40% are of  12 years

40% of 100 = 0.4 x 100  = 40

12 years student = 40 = 40%

1/2 of 13 years

1/2 of 100 = 1/2 x 100 = 50 =50%

13 years of student = 50

and rest are 14 years

100 - 50 - 40 = 10

14 years student = 10 = 10%

Hence 40% students are 12 years, 50% are of 13 years and 10% of students are of 14 years.

Learn more about percent;

https://brainly.com/question/28840349

#SPJ2

Answer:

Sue is incorrect

Step-by-step explanation:

Using proportions, it is found that Yes, there could be 5 kids, with 3 boys and 2 girls.

A proportion is a fraction of a total amount.

In this problem, supposing a total of 5 kids:

Hence, Yes, there could be 5 kids, with 3 boys and 2 girls.

More can be learned about proportions at https://brainly.com/question/24372153

Answer:

33.51 units³

Step-by-step explanation:

Volume of a sphere is given by the formula :

V = [tex]\frac{4}{3} \pi r^{3}[/tex]

Because we have the radius we can plug it into the equation to give us :

V  = (4/3)×π×(2)³

V = 4/3×8π

V ≈ 33.51

Units will be units³ since no measurement is given but it to the power of 3 since it is volume.

Answer:

A) repelled by each other, I did this on usa testprep

Step-by-step explanation:

Answer:

b atracted to each other

Step-by-step explanation:

got it right on usatestprep

Answer:

those are corrisponding angles which means they equal each other making <H and <G both 57 degrees

Answer:

B

Step-by-step explanation:

Answer:

y = 5x

Step-by-step explanation:

Hey there!

To start with the hypotenuse of a triangle is the longest side of it

and to get an equation of a line you would use

y = mx + b

where m is the slope

and b is the y-intercept

to get the slope you would do rise over run

rise/run

take 2 points and see how much it rises and runs to the next point

you would then get 5

then we figure out the y-intercept where the line intercepts the y-axis

in this case 0

In conclusion the answer is y = 5x + 0

we can also remove the 0 because it is unnecessary

y = 5x

Answer:

Step-by-step explanation:

1. The sequence is not arithmetic.

2. d=-30

Answer:

B

Step-by-step explanation:

i got it right on edge

Answer:

It is B

Step-by-step explanation:

Answer:

The current of the circuit at t = 0 is equal to 0.

If we take the limit as t approaches infinity, the current is equal to ε/R or V/R.

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:

[tex]\displaystyle (cu)' = cu'[/tex]

Derivative Property [Addition/Subtraction]:

[tex]\displaystyle (u + v)' = u' + v'[/tex]

Derivative Rule [Basic Power Rule]:

Slope Fields

Integration

Integration Rule [Reverse Power Rule]:

[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:

[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:

[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Method: U-Substitution

Electricity

Ohm's Law: V = IR

Circuits

Step-by-step explanation:

*Note:

In the given equation, our variable of differentiation is x. I will rewrite this as current I for physics notation purposes.

Step 1: Define

Identify given.

[tex]\displaystyle L \frac{dI}{dt} + RI = V[/tex]

[Assuming switch S is closed] Recall that an inductor is used in a circuit to resist change. After a long period of time, when it hits steady-state equilibrium, we expect to see the inductor act like a wire.

Step 2: Find Current Expression Pt. 1

Step 3: Find Current Expression Pt. 2

Identify variables for u-substitution.

Step 4: Find Current Expression Pt. 3

Recall that our initial condition is when t = 0, denoted as u₀, and we go to whatever position u we are trying to find. Also recall that time t always ranges from t = 0 (time can't be negative) and to whatever t we are trying to find.

Recall that our initial condition u₀ (derived from Ohm's Law) contains only the voltage across resistor R, where voltage is supplied by the given battery. This is because the current is stopped once it reaches the inductor in the circuit since it resists change.

Step 5: Solve

If we are trying to find the strength of the electrical current I at t = 0, we simply substitute t = 0 into our current function:

[tex]\displaystyle\begin{aligned}I(t) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}t} \\I(0) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}(0)} \\& = \boxed{\bold{0}}\end{aligned}[/tex]

If we are taking the limit as t approaches infinity of the current function I(t), we are simply just trying to find the current after a long period of time, which then would just be steady-state equilibrium:

[tex]\displaystyle\begin{aligned}I(t) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}t} \\\lim_{t \to \infty} I(t) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}(\infty)} \\& = \boxed{\bold{\frac{\mathcal E}{R}}}\end{aligned}[/tex]

∴ we have found the current I at t = 0 and the current I after a long period of time and proved that an inductor resists current running through it in the beginning and acts like a wire when in electrical equilibrium.

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Topic: AP Physics C - EMAG

Unit: Induction